Asymmetric Nanopore Membranes

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Title:
Asymmetric Nanopore Membranes Single Molecule Detection and Unique Transport Properties
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english
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Bishop,Gregory W
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Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemistry
Committee Chair:
Martin, Charles R
Committee Members:
Castellano, Ronald K
Cao, Yun Wei
Smith, Benjamin W
Orazem, Mark E

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Subjects / Keywords:
asymmetric -- electroosmotic -- membrane -- mica -- nanopore -- polymer -- rectification -- sensing -- transport
Chemistry -- Dissertations, Academic -- UF
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Chemistry thesis, Ph.D.
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Abstract:
Biological systems rely on the transport properties of transmembrane channels. Such pores can display selective transport by allowing the passage of certain ions or molecules while rejecting others. Recent advances in nanoscale fabrication have allowed the production of synthetic analogs of such channels. Synthetic nanopores (pores with a limiting dimension of 1-100 nm) can be produced in a variety of materials by several different methods. In the Martin group, we have been exploring the track-etch method to produce asymmetric nanopores in thin films of polymeric or crystalline materials. Asymmetric nanopores are of particular interest due to their ability to serve as ion-current rectifiers. This means that when a membrane that contains such a pore or collection of pores is used to separate identical portions of electrolyte solution, the magnitude of the ionic current will depend not only on the magnitude of the applied potential (as expected) but also the polarity. Ion-current rectification is characterized by an asymmetric current-potential response. Here, the interesting transport properties of asymmetric nanopores (ion-current rectification and the related phenomenon of electroosmotic flow rectification) are explored. The effects of pore shape and pore density on these phenomena are investigated. Membranes that contain a single nanopore can serve as platforms for the single-molecule sensing technique known as resistive pulse sensing. The resistive-pulse sensing method is based on the Coulter principle. Thus, the selectivity of the technique is based largely upon size, making the analysis of mixtures by this method difficult in many cases. Here, the surface of a single nanopore membrane is modified with a molecular recognition agent in an attempt to obtain a more selective resistive-pulse sensor for a specific analyte.
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Statement of Responsibility:
by Gregory W Bishop.
Thesis:
Thesis (Ph.D.)--University of Florida, 2011.
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Adviser: Martin, Charles R.

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1 ASYMMETRIC NANOPORE MEMBRANES: SINGLE MOLECULE DETECTION AND UNIQUE TRANSPORT PROPERTIES By GREGORY WILLIAM BISHOP A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORID A IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011

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2 2011 Gregory William Bishop

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3 To my parents William and Martha and my wife-to-be, Rachel

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4 ACKNOWLEDGMENTS I would like to begin by thanking my resear ch advisor, Dr. Charles R. Martin, for his support, guidance, and patience and for present ing me with interesting problems to explore during my time here at t he University of Florida. I al so must thank Dr. Martin for sharing the wisdom of past generations. “Root pi g or die” and “hit ‘em where they ain’t” have served as inspirational mottos for perse verance in the face of adversity and the importance of independent thinking and scientific cr eativity. Dr. Martin has taught me to strive to “do an experiment that’s never been done before” because “something good will happen.” I have been privileged to have been able to meet and collaborate with so many wonderful people during my time in the Martin group. I would like to thank Drs. Lindsay T. Sexton and Warren K. Mino, Jr. for helping me get st arted in the Martin group research laboratory. I woul d like to thank Drs. Hitomi Mu kaibo, Pu Jin, Dooho Park, Jillian Perry, and Lloyd Horne, Jr. for their helpful suggestions and discussions. I am appreciative of the friendship and assistanc e offered by all past and present Martin group members (especially Funda Mira, William Hardy, and Li Zhao). I would be remiss if I failed to specifically mention the tremendous research efforts of undergraduate group member Marcos Lopez, Jr. His motivation to l earn, ability to think critically, and capacity for creative problem-solving have been instrument al over the course of the past year’s collaboration. I am thankful for the tremendous support offered by the D epartment of Chemistry. Serving as a teaching assistant under the s upervision of Drs. Benjamin W. Smith, James C. Horvath, and John A. Mitche ll was a memorable experience and great learning opportunity. I appr eciate the assistance and gui dance of Graduate Coordinator

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5 Dr. Benjamin W. Smith and Graduate Affairs Program Assistant Lori Clark; Analytical Division Head Dr. Richard A. Yost and Analytical Division Program A ssistant Antoinette Knight; and Martin Group Senior Secretary Cynthia L. Marsh. I am also grateful for the Interdisciplinary Center for Biotechnology Res earch (ICBR) at the Un iversity of Florida (particularly Karen Kelley and Kim Backer-Kell ey) for providing training and support in scanning electron microscopy. I would also like to express my gratit ude to my undergraduate research advisor Dr. Dennis G. Peters. While enro lled at Indiana University, I dec ided to join Dr. Peters’ electroanalytical chemistry research group. His support, guidance, and patience were critical to my development as a research scientist. He is truly a great teacher and promoter of chemistry and ac ademic research. The challe nges and accomplishments I encountered during that undergr aduate opportunity helped fortify my decision to attend graduate school and conduct research in the Martin group. I owe many thanks to my family and friends for their incredible patience and boundless encouragement. Everythi ng that I have accomplished is a direct result of the values and dedication instilled in me by my parents, William and Ma rtha. I am also thankful for the support of my brother, Kevi n, and sisters, Erica and Alison. Daniel Shelby of the Omenetto group has proven to be an invaluable friend as well as a great resource for scientific discussion. I am fo rever indebted in gratitude to my wife-to-be Rachel Shelby. She has been most patient wit h me, even to the point of waiting in the parking lot for me as I fini sh cleaning up after the day’s experiments. She has motivated me to succeed with her encouragem ent, dedication, and patience.

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6 TABLE OF CONTENTS page ACKNOWLEDG MENTS..................................................................................................4 LIST OF TABLES............................................................................................................9 LIST OF FI GURES ........................................................................................................10 ABSTRACT ...................................................................................................................14 CHAPTER 1 INTRODUC TION....................................................................................................16 Importance of Nanopor es.......................................................................................16 Resistive-Pulse Sensing with Nanopore Me mbranes.............................................16 The Coulter Pr incipl e........................................................................................16 Extension of the Coulter Principle to Nanoparticles and Small Molecules........18 Resistive-pulse sensing with biologic al channels in lipid bilayers..............18 Resistive-pulse sensing with synthetic nanopor es.....................................19 Fabrication of Sy nthetic N anopores ........................................................................20 The Track-Etch Method....................................................................................20 Origins of the Tra ck-Etch Me thod.....................................................................21 Damage Tracks and Chem ical Etch ing............................................................21 Production of SinglePore Memb ranes .............................................................23 Etching to Produce Asy mmetric N anopores .....................................................23 Characterization of Conical N anopores..................................................................26 Microscopy Te chniques....................................................................................26 Measuring Pore Size by K nudsen Flow of Gases............................................28 Measuring Pore Size by Membrane Re sistance...............................................28 Transport Properties of Conical N anopores ............................................................32 Ion-Current Rect ificatio n...................................................................................32 Electroosmoti c Flow .........................................................................................36 Surface Charge Density...................................................................................37 Summary ................................................................................................................44 2 RESISTIVE-PULSE SENSING OF A PROTEIN ANALYTE USING A CHEMICALLY MODIFIED CONICAL NA NOPORE................................................53 Motivati on...............................................................................................................53 Experiment al...........................................................................................................54 Material s...........................................................................................................54 Nanopore Prepar ation......................................................................................54 Nanopore Charac terizati on...............................................................................55 Modification of N anopores with Folate.............................................................56 Resistive-Pulse Sens ing Measur ements..........................................................57

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7 Results and Discussion...........................................................................................58 Single-Nanopore Membrane Characteri zation.................................................58 Ion-Current Rectification and Pore Modi ficati on...............................................58 Resistive-Pulse Sensing of Folate-Binding Protein..........................................61 Summary ................................................................................................................62 3 COMPARISON BETWEEN THE ION-CURRENT RECTIFICATION CAPABILITIES OF ASYMMETRIC NANOPORES IN MICA AND POLY(ETHYLENE TEREPHTH ALATE) MEMB RANES.........................................69 Motivati on...............................................................................................................69 Experiment al...........................................................................................................70 Material s...........................................................................................................70 Fabrication of Nanopores by the Track-Etch Method.......................................71 Imaging Na nopores ..........................................................................................72 Current–Voltage Curv e Measurem ents............................................................74 Zeta Potential Measurem ents...........................................................................74 Oxidation of Single-Po re PET Me mbranes .......................................................76 Modification of Single-Pore Mica Membranes with an Amine Silane................76 Results and Discussion...........................................................................................77 Pore Characte rizati on.......................................................................................77 Ion-Current Rectif ication St udies ......................................................................78 Zeta Potentials of Multi-Pore PET and Mica Membranes Measured by EOF...82 Ion-Current Rectification of Oxid ized Single-Pore PET Memb ranes................89 Ion-Current Rectification of Amine-M odified Single-Pore Mica Membranes.....91 Summary ................................................................................................................92 4 EFFECT OF TRANSMEMBRANE CURR ENT ON ELECTROOSMOTIC FLOW RECTIFICATION IN PYRAMIDAL-P ORE MICA MEMB RANES...........................104 Motivati on.............................................................................................................104 Experiment al.........................................................................................................105 Material s.........................................................................................................105 Etching Pyramidal Nanopor es........................................................................105 Membrane Characte rization ...........................................................................106 Measurement of Tip Size ................................................................................108 Ion-Current Rect ificatio n.................................................................................109 EOF measurem ents.......................................................................................110 Results and Di scussion.........................................................................................110 Membrane Characte rization ...........................................................................110 Ion-Current Rectific ation Proper ties...............................................................111 Physical Pore Overlap in Multi-Pore Me mbranes ...........................................115 Overlap of Diffusion Layers in Multi-Pore Membranes ...................................117 EOF Rectification Properti es..........................................................................122 Summary ..............................................................................................................125

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8 5 SELECTIVE TRANSPORT OF CHARGED SPECIES THROUGH ASYMMETRIC MICA NANOPO RE MEMBRA NES..............................................130 Motivati on.............................................................................................................130 Experiment al.........................................................................................................130 Material s.........................................................................................................130 Nanopore Membrane Pr eparation and Charac terizati on................................131 Transport Exper iments...................................................................................131 Ion-Current Rect ificatio n.................................................................................133 Results and Di scussion.........................................................................................134 Transport of a Positively Charged Por phyrin..................................................134 Transport of a Negatively Charged Por phyrin................................................137 Summary ..............................................................................................................138 6 CONCLUSION S...................................................................................................144 Resistive-Pulse Sensing.......................................................................................144 Ion-Current Rect ificatio n.......................................................................................144 Electroosmotic Flow Rectificat ion.........................................................................145 Selective Tr ansport...............................................................................................146 LIST OF REFE RENCES.............................................................................................147 BIOGRAPHICAL SKETCH ..........................................................................................159

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9 LIST OF TABLES Table page 2-1 Rectification ratios after each modi fication step for a PET membrane that contains a single a symmetric nanopore. ............................................................66 3-1 Zeta potentials and surface charge densities for mica and PET membranes calculated from electroo smotic flow data..........................................................100 3-2 Corrected zeta potentials and surfac e charge densities for mica and PET membranes calculated from el ectroosmotic fl ow data. .....................................100 4-1 Effect of applied transmembrane current on the electroosmotic flow of phenol and electroosmotic flow rectification ratio for a 106 cm-2 pyramidal-pore mica membrane. .......................................................................................................129 4-2 Effect of applied transmembrane current on the electroosmotic flow of phenol and electroosmotic flow rectification ratio for a 107 cm-2 pyramidal-pore mica membrane. .......................................................................................................129

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10 LIST OF FIGURES Figure page 1-1 General approach used in Coulte r counter devices and resistive-pulse sensor s...............................................................................................................45 1-2 Illustration of the protein -hemolysin ( -HL) embedded in a lipid bilayer membr ane.......................................................................................................... 46 1-3 Electric field strength distri bution in an asy mmetric nanopore. ...........................46 1-4 General overview of the track-etch met hod........................................................47 1-5 Depiction of the formati on of latent damage tra cks.............................................47 1-6 Chemical structures and hydrolysis reaction products of polymers commonly used in the tracketch me thod............................................................................48 1-7 Scanning electron microgr aph of pores produced in PE T by the track-etch method. ..............................................................................................................48 1-8 Chemical structure of muscovite mica................................................................48 1-9 Geometry for a pore produced in muscovi te mica by the track-etch method......49 1-10 Depiction of the chemical etchi ng process of a hea vy-ion-induced damage track in a th in film................................................................................................49 1-11 General approach for the production of asymmetric nanopores by the tracketch meth od........................................................................................................50 1-12 Representation of equipotentials and curr ent flow lines in a conically shaped resistor ................................................................................................................50 1-13 Description of the elec trical double-layer that forms at charged surfaces in soluti on...............................................................................................................51 1-14 Schematic explanatio n of the ion-current re ctification phenomenon. ..................51 1-15 Ion distribution and electroosmoti c flow in a char ged capill ary...........................52 2-1 Chemical structur e of folic acid...........................................................................64 2-2 Reaction scheme for amine m odification of pore walls .......................................64 2-3 Reaction scheme for modification of pore walls wi th folate................................64

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11 2-4 Base opening of an asymmetric nanopor e produced in PET by the track-etch method. ..............................................................................................................64 2-5 I–V curves used to estima te pore tip size...........................................................65 2-6 I–V curves used to verify pore modifi cation. .......................................................65 2-7 I–V curves used to verify pore modifi cation obtained with different pH buffered electrolyt e soluti ons..............................................................................66 2-8 Current-time traces for resistive-pulse sensing of folate-binding protein using a folate-modified single asymmetric nanopore. ..................................................67 2-9 Effect of applied transmembrane pot ential on current-time traces for resistive-pulse sensing of folate-binding protein.................................................67 2-10 Scatter plot and histogram for curr ent pulses obtained during resistive-pulse sensing of folate-b inding prot ein. ........................................................................68 2-11 Long-lived current pulse events due to resistive-pulse sensing of folatebinding pr otein....................................................................................................68 3-1 SEM images of asymmetric nanopores etched in PET.......................................94 3-2 SEM images of asymmetric nanopores etched in mica......................................94 3-3 I–V responses and rectification ratios for single-pore mica and PET membranes obtained in 1 M K Cl, 10 mM PBS (p H 7.4).....................................95 3-4 I–V responses and rectification ratios for single-pore mica and PET membranes obtained in 0.1 M KCl, 10 mM PBS (pH 7.4).................................96 3-5 I–V responses and rectification ratios for multi-pore mica and PET membranes used in the ze ta potential studies...................................................97 3-6 Absorbance of the solution on the pe rmeate side of the symmetric-pore (~106 cm-2) membranes used in the zeta potential studies ..........................................98 3-7 Translocation of phenol th rough the symmetric-pore (~106 cm-2) membranes used in the zeta pot ential studi es.......................................................................99 3-8 Effect of applied current on elec troosmotic flow velocity through the symmetric-pore (~106 cm-2) membranes used in the zeta potential studies.....100 3-9 SEM images of the symmetric-pore (~106 cm-2) membranes used in the zeta potential studi es................................................................................................101 3-10 I–V responses for a PET membrane that contains a single asymmetric nanopore before and afte r oxidati on.................................................................101

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12 3-11 Ion-current rectificati on ratios for a PET membrane that contains a single asymmetric nanopore before and after oxidat ion..............................................101 3-12 I–V responses for three PET membranes that contain similar single asymmetric nanopores before and after oxid ation............................................102 3-13 Ion-current rectificati on ratios for three PET membranes that contain similar single asymmetric nanopores befo re and after ox idation.................................103 3-14 I–V responses for a mica membrane that contains a single asymmetric nanopore before and after surface m odification with an amine. .......................103 4-1 Images of asymmetric nanopor es etched in mica.............................................126 4-2 SEM images of large pores used to determine membrane pore density..........126 4-3 Current–voltage responses obtain ed in the presence and absence of pyramidal-pore mica membranes that di splay ion-current re ctification.............127 4-4 Rectification ratio shown as a f unction of transmembrane potential for pyramidal-pore mica membranes (in 10 mM phosphate buffer, pH 7.4)...........127 4-5 Absorbance of the solution on the pe rmeate side of the pyramidal-pore (106 cm-2) mica memb rane.......................................................................................128 4-6 Translocation of phenol by EO F through a pyramidal-pore (106 cm-2) mica membrane using different transme mbrane current values. ..............................128 5-1 Chemical structures of the ioni c porphyrins used in selective transport studies. .............................................................................................................139 5-2 Absorbance spectra for the porphyr ins used in the selective transport studies. .............................................................................................................139 5-3 Absorbance of the permeate soluti on monitored during the transport of MTMAP. ...........................................................................................................140 5-4 Amount of MTMAP detect ed in the permeate solution during the course of transport studi es...............................................................................................140 5-5 Depiction of the inci rcle of a r hombus. ..............................................................141 5-6 Translocation of phenol by EO F through a pyramidal-pore (107 cm-2) mica membrane using different transme mbrane current values. ..............................141 5-7 I–V curves and rectification ratios fo r a mica membrane with asymmetric pores (107 cm-2) before and after exposu re to MT MAP....................................142

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13 5-8 Absorbance of the permeate soluti on monitored during the transport of PCTS. ...............................................................................................................143 5-9 I–V curves and rectification ratios fo r a mica membrane with asymmetric pores (107 cm-2) before and after exposu re to PC TS........................................143

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14 Abstract of Dissertation Pr esented to the Graduate School of the University of Florida in Partial Fulf illment of the Requirements for t he Degree of Doctor of Philosophy ASYMMETRIC NANOPORE MEMBRANES: SINGLE MOLECULE DETECTION AND UNIQUE TRANSPORT PROPERTIES By Gregory William Bishop August 2011 Chair: Charles R. Martin Major: Chemistry Biological systems rely on the transport properties of tran smembrane channels. Such pores can display selective transport by allowing the passage of certain ions or molecules while rejecting others. Recent advances in nanoscale fabrication have allowed the production of synthetic analogs of such channels. Synthetic nanopores (pores with a limiting dimension of 1-100 n m) can be produced in a variety of materials by several different methods. In the Ma rtin group, we have been exploring the tracketch method to produce asymmetric nanopores in thin films of polymeric or crystalline materials. Asymmetric nanopores are of particular intere st due to their ability to serve as ioncurrent rectifiers. This means that when a membrane that contains such a pore or collection of pores is used to separate ident ical portions of electrolyte solution, the magnitude of the ionic curr ent will depend not only on the magnitude of the applied potential (as expected) but also the polarity. Ion-current rectificatio n is characterized by an asymmetric current–potential response. Here the interesting transport properties of asymmetric nanopores (ion-current rect ification and the re lated phenomenon of

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15 electroosmotic flow rectification) are ex plored. The effects of pore shape and pore density on these phenomena are investigated. Membranes that contain a single nanopore c an serve as platforms for the singlemolecule sensing technique known as resist ive pulse sensing. The resistive-pulse sensing method is based on the Coulter principle. Thus, the selectiv ity of the technique is based largely upon size, making the analysis of mixtures by this method difficult in many cases. Here, the surface of a single nanopore membrane is modified with a molecular recognition agent in an attempt to obtain a more selective resistive-pulse sensor for a specific analyte.

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16 CHAPTER 1 INTRODUCTION Importance of Nanopores Nanopores (pores or channels with at l east one characteristic dimension between 1 and 100 nm1-3) have garnered much attention due to their presence in biological systems,4 interesting transport properties,1-3 implementation as sensing platforms,5-8 and ability to serve as starting materials fo r the fabrication of other nanostructures.9 As demonstrated by potassium ion channe ls and the water channel aquaporin,4 nature has long known that highly selective transport into and out of cells can be achieved by tailoring the size and surface charge of the pore through which materials are transported across the lipid bilayer. Howeve r, experiments with biological pores are often limited by the fragili ty of the lipid bilayer.5-8 With the advent and development of nanoscale fabrication tools and techniques, synthetic nanopores with properties similar to those of bi ological channels10-12 can be produced in more robust thin films or membranes and characterized with high confidence. Resistive-Pulse Sensing with Nanopore Membranes The Coulter Principle Although several techniques that utilize nanopores in sensor design have been developed,5-8, 13-23 many sensing paradigms that employ nanopore membranes are based on the resistive-pulse sensing method5-8 (also known as the stochastic sensing method13). The resistive-pulse sensing met hod itself is derived from the Coulter principle. In the 1950s, W. H. Coulter showed that a small electrolyte-filled channel in a membrane can be used to size and count particles or cells.6 Coulter counter devices

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17 rely on a membrane with a small (micrometer-sized7) channel (or pore) that separates two electrolyte solutions (Figure 1-1). Elec trodes placed in each solution on each side of the membrane are used to drive an ionic current through the channel.6 As particles or cells that are similar in si ze to the channel traver se the small orifice (Figure 1-1B), electrolyte solution in t he channel is displaced. This transient displacement of electrolyte leads to a temporary increas e in channel resistance and, consequently, a decrease in current (Figure 1-1C). These momentary decreases in current are called pulses or ev ents. Information about partic le (or cell) size, mobility, and concentration is encoded in the current pulse magnitude, duration, and frequency. Due to its simplicity and impressive sensitivit y, the Coulter counter is still widely used in medical laboratories to determi ne biological cell concentrations.6 Resistive-pulse sensing devices operate by the same principle as the Coulter counter. However, the sensing element possesses smaller dimensions such that proteins,14-17 nucleic acids,18-23 or small molecules24, 25 can be detected. It is important to note that, while current pulses are typica lly analogous to those observed with Coulter counter devices (i.e., current decreases as analyte is present in the pore), current pulses that correspond to a decrease in resistance (i.e., an increase in current)18, 21, 26 have also been observed in resistive-pulse sensing devices. In these limited cases, current increases as analyte is present in the pore. This observation is the opposite of that which is expected by the Coulter principle. Reports of this type are few; howeve r, researchers that have observed this behavior attribute the unexpected decrease in resistance to the surface charge of the analyte.18, 21, 26 Highly charged analyte species may carry additional ions with them into the pore. Thus,

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18 though a certain volume of electrolyte is di splaced by an analyte molecule within the pore, the additional ions ushered in by t he highly charged analyte may offset or even overcome the ion loss due to electrolyte disp lacement. The presence of additional ions results in a net increase in ion concent ration and a corresponding increase in current (decrease in resistance). Extension of the Coulter Principle to Nanoparticles and Small Molecules Recent advances in nanoscale fabricati on as well as the characterization and isolation of biological pores have extended the Coulter principle to smaller particles and even molecules.5-8 DeBlois and Bean were the first to expand the utility of the Coulter principle to particles less than 400 nm in diameter.5 Using a 500 nm diameter pore in a polycarbonate (PC) membrane, DeBlois and Bean were abl e to obtain signal from polystyrene spheres as sma ll as 60 nm in diameter.27 This resistive-pulse sensing method was later used to detect and size viruses.28-30 Resistive-pulse sensing wi th biological channels in lipid bilayers With a sensing platform that cons isted of the biological channel -hemolysin ( HL) embedded in a lipid bilayer membrane (Figur e 1-2), Kasianowicz et al. were able to use the resistive-pulse method to det ect single-stranded RNA and DNA molecules.19 Due to the small size of the -HL opening (~2 nm in di ameter), double-stranded polynucleotides were unable to traverse t he membrane. These findings led to great interest in the use of biological pores (especially -HL) as resistive-pulse sensors.5-8, 13, 31-33 In addition to sensing the aforem entioned RNA and DNA polynucleotides, -HL can tolerate drastic alterati ons to its amino acid sequence5 and thus can be engineered to detect proteins,16 polypeptides,23 small organic molecules,25 and metal ions.34

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19 However, due to the lipid bilayer’s lack of durability,5-8, 31 resistive-pulse sensing with biological pores is confined to the laborat ory, and experiments can typically only be conducted for a few hours befor e the bilayer ruptures.31 Lipid bilayers are susceptible to vibrati ons as well as changes in pH, temperature, applied potential.8 In resistive-pulse sensing experi ments, the lipid bilayer is usually suspended across an aperture (typically 30 to 100 m in diameter35) in a polymer film or another material.31 Although researchers continue to investigate the importance of the supporting material as well as the size of the supporting aperture in a ttempts to increase bilayer stability,31, 35-37 there has been increasing interest in using more robust synthetic nanopores as resistive-pulse sensing platforms. Resistive-pulse sen sing with synthetic nanopores Synthetic nanopores are desirable in resist ive-pulse sensing because they can be produced in durable polymer and inorganic material s. In contrast to biological pores that have fixed sizes, the size of synt hetic nanopores can be controlled to a certain degree depending on the technology that is employed during the f abrication process.6-8, 38 Certain fabrication technologies also permit some control over the shape of the nanopore.17, 39-42 Recently, it has been suggested that coni cally shaped (or asymmetric) pores may offer advantages over cylindrical (or symme tric) pores as resistive-pulse sensors.8, 43, 44 Conical nanopores exhibit different aperture si zes at each end of the pore. The larger opening is called the base and the smaller opening is called the tip. Compared to a cylindrical pore of the sa me limiting diameter, a conical pore possesses a lower resistance and hence supports a lar ger current for a given voltage.8, 43, 44

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20 Conical nanopores have also been found to be less susceptible to permanent blocking or clogging than thei r cylindrical counterparts.8 Furthermore, when a transmembrane potential is applie d across a conical nanopore, t he electric field will be focused near the smaller (tip) opening, lead ing to a highly sensitive detection zone (Figure 1-3).45 Only analyte present in this part of the pore will give appreciable signal during resistive-pulse sensing experiments.43 Resistive-pulse sensing systems based on conical nanopores have been used to detect a variety of analytes, including nucleic acids,43, 46 proteins,17 and small molecules.24 Fabrication of Synthetic Nanopores The Track-Etch Method Several fabrication methods have been developed for the production of nanopores.6-8, 38, 47-49 Two of the most promis ing and widely used technologies7 are electron-beam48 or ion-beam47 lithography and the track-etch method.8 Lithographybased methods employ a beam of electrons or ions to drill a hole in an inorganic (e.g., silicon dioxide) thin film.7 With these techniques, pores wit h diameters as small as 1 nm can be prepared.7, 48 The track-etch method require s a beam of heavily ionizing, nuclear particles that is passed through a thin membrane of di electric material (Figure 1-4).50 Bombardment with these high-energy particles creates damage tracks in the membrane. With help of a properly chosen chemical reagent, t hese damage tracks can be preferentially and rapidly etched. The Martin group8, 17, 24, 42, 46, 51, 52 and others11, 12, 39, 43, 53-68 have utilized the track-etch method to produce pores as small as 2 nm in polymeric65, 69 and crystalline68 thin films.

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21 Origins of the Track-Etch Method In 1958, Young reported that fission fragments from a U3O8 film create damage in lithium fluoride crystals.70 This damage could be observed microscopically after the lithium fluoride was subjected to an etching solution that contained hydrofluoric acid, acetic acid, and ferric fluoride. Etching resu lted micrometer-sized etch pits, the number of which corresponded well to the fission fragment dose.70 In a separate investigation in 1959, Silk and Barnes found t hat tracks from fission fragments passed through thin sheets of a silicate material (known as mica) could be observed with an electron microscope.71 Throughout the 1960s, researchers at the Gener al Electric Research Laboratory in Schenectady, New York studied the formation and etching of damage tracks in various materials.72-78 They found that such damage tra cks could be produced in virtually all insulating solids, including polymers.72, 75-77 Moreover, after formation, these tracks will remain in the material indefinitely under normal conditions.76 Damage Tracks and Chemical Etching Due to the extensive research effo rts during the 1960s, damage tracks are believed to be created by an ion explosion74, 76 (also known as coulomb explosion79) mechanism that occurs as highly charged ions pass through the material (Figure 1-5). As a positively charged ion travels through a cr ystalline material, it will collect electrons from the crystal lattice, leavi ng behind positive ions. A disr uption in the crystal lattice results as these newly formed positive i ons rapidly repel one another (Figure 1-5A).76 A similar process is expected to occur in organi c polymers. A charged particle that travels through the polymer will ionize and excite molecules resulting in broken chains and new highly chemically reactive chain ends (Figure 1-5B).76

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22 Damage tracks can be chemically etched into highly uniform pores73 with the selection of an appropriate etching solution. For example, damage tracks in PC (Figure 1-6) and some other polymers like poly(ethy lene terephthalate) (PET ) (Figure 1-6) can be produced by a simple hydrolysis reaction using a hydroxide solution.12, 72, 76, 80 The resulting pores possess circular openings (Figur e 1-7) that are characterized by their diameters.17, 42 Damage tracks in the crystalli ne material muscovite mica81, 82 (chemical formula KAl2(AlSi3)O10(OH)2) (Figure 1-8) can be etched into po res with a hydrofluoric acid (HF) solution.75, 77, 78, 83, 84 Muscovite mica pores etched in this manner exhibit rhomboidal apertures with a major angle of ~120o (Figure 1-9).83, 85 Due to the geometric properties of the openings, the pores can be described in te rms of the length of the long axis or in terms of equivalent diameter, deq.86, 87 The equivalent diameter is the diameter of a circular opening with an area that is com parable to the area of the rhomboidal mica pore. s l eqa a d 2 (1-1) where al is the length of the l ong axis of the rhombus and as is the length of the short axis of the rhombus. In contrast, damage tracks in muscovite mica that are etched with boiling hydroxide solutions yield hexagonal pores.85 Tracks in phlogopite mica (chemical formula K(Mg3FeII)3(Si3Al)O10(OH,F)2) can be etched by HF into triangular or hexagonal pores depending on the energy used to produce the damage.88-90 Nanoporous membranes generated by the track-etch me thod from mica and polymer films are

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23 typically microns (~10 m) thick. Recently, the tra ck-etch method has been used to produce nanopores in thinner silicon nitr ide films (~300 nm thick) as well.68 The commercial importance of the tracketch method first became evident in 1964 when Fleischer et al. used the technique in polymers to produce a novel filter for biological materials.73 Filter membranes of this type, known as Nuclepore filters, have found many applications and are st ill routinely used today. In fact, it was the Nuclepore filter that inspired the original resi stive-pulse sensor of DeBlois and Bean.27 Production of Single-Pore Membranes DeBlois and Bean were able to obtain a PC membrane that contained a single pore by first limiting the exposure of t he membrane to high energy fission fragments such that only a few tracks in a small area would result.27, 91 These researchers then etched the tracks and sealed off all but one of the resulting pores, which were located using a microscope. Researchers at Gesellschaft fr Schw erionenforschung (GSI) in Darmstadt, Germany have improved upon the method of DeBlois and Bean by employing the Universal Linear Accelerator (UNILAC).79, 91, 92 With the UNILAC, a fine ion beam of very low intensity is passed through the memb rane. Once a particle has successfully traversed the material, it is registered by an electronic particle counter, and the ion beam is turned off to avoid double irradiation.79 This gating method can ensure that no more than one ion passes through the membrane.91 The resulting track can then be etched as desired to produce a single pore. Etching to Produce Asymmetric Nanopores In general, pore shape is determined by the etching rate along the damage track, vT, as well as the etching rate of the bulk material, vB (Figure 1-10).50 Typically, vT is

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24 much faster than vB such that the pores that result by immersing ion-tracked films into an etching solution are cylindrical. Howe ver, the ratio betw een these two quantities (known as the track-etch ratio79, 93) is dependent on the material and etching conditions. For example, the vT and vB have been reported as ~10 m hr-1 and ~2 nm min-1 (~0.12 m hr-1), respectively, for damage tracks in PET etched with 9 M NaOH at 25 oC.39 For damage tracks in mica etched with 20% HF at 25 oC, vB has been consistently reported as ~0.6 s-1 (~3.6 nm min-1 or ~0.216 m hr-1).77, 94 Sun et al. have reported vT and vB for mica membranes etched with 20% HF at 20 oC to be 1136–1250 /sec (~6.8–7.5 m min-1 or ~408–450 m hr-1) and 0.35 /sec (2.1 nm min-1 or 0.126 m hr-1), respectively.84 The track-etch ratio, vT/vB, for a mica membrane is typically >> 104.79 However, Quinn et al. have noted that vB may differ by a factor of two even when the HF solution is prepared from concentrated acid that originated from the same manufacturing source.94 Quinn et al. attributed these findi ngs to the possible presence of some inhibiting impurity such as fluorosilic ic acid in the etching solution.94 Similarly, Fischer and Spohr have also stated that large variations in vB (on the order of 300% or more) exist from batch to batch fo r track-etched mica membranes.79 Bean and DeSorbo realized that pore geometry can be better controlled by managing the etching conditions on each side of the membrane.39 In their method, one side of the membrane is expos ed to the etching solution whil e the other side is exposed to a solution that does not etch the track. This solution also neutralizes the etching solution and is often referred to as the stopping medium.39

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25 Apel et al. revisited this asymmetric etching method in 2001 to produce membranes that each contained a singl e conical nanopore in poly(ethylene terephthalate) (PET).39 A sodium hydroxide solution was selected as the etching solution, while a solution that contained form ic acid and potassium chloride (KCl) served as the stopping medium (Fi gure 1-11). These researcher s also applied a potential across the membrane during the etching process. This wa s done for two reasons. First, application of a potential during the etching process enables one to monitor the progress of t he pore development.39 Bean et al. first incorporated this idea in their studies of etching mica membranes that contained multiple damage tracks.83 In those earlier studies, the membrane resistance wa s measured during the course of the etching process. Breakthrough, the comple tion of pore formation, was observed by a sudden decrease in the membrane resistanc e (or equivalently, an increase in transmembrane current as shown in Figure 1-11B). Moreover, membrane resistance was related to the pore size during the etchi ng process to demonstrate control over pore size. Second, in the experiments of Apel et al. the applied transmembrane potential also helped shape the pore by making it more difficu lt for hydroxide to approach and etch the smaller tip opening.39 In addition to using a transmembrane potential,39, 40 researchers have also added organic solvent s to help control pore shape.95, 96 Furthermore, plasma etching of track-etched membranes to m anipulate pore shape has also been detailed.44 It can be difficult to reproducibly prepar e conical nanopores with a desired tip diameter ( dtip) using the track-etch method. Wh ile pores with a desired base diameter ( dbase) can be etched ( ~10 %), dtip may vary greatly.42 For example, Wharton et al.

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26 etched conical nanopores in PET under the anisotropic conditions described above with 9 M sodium hydroxide (NaOH) on one side of the membrane and a stopping solution of 1 M formic acid with 1 M KCl on the other.42 They found that dbase was 520 45 nm after 2 hours of etching, while dtip ranged from 1 to 7 nm.42 Wharton et al. demonstrated that dtip could be better controlled by subjecting the etched PET membranes to a second etching step.42 During the second step, identical portions of 1 M NaOH (etching solution) were placed on each side of the membrane that contained the conical nanopores. Again a pot ential was applied, and the current was monitored to observe the pore widening proc ess. This second etching step was carried out for a short time such that the change in dbase was very small or even negligible.42 By modifying the etching method with this sec ond step, Wharton et al. showed that pores with dtip of ~20 nm or great er could be etched reproducibly ( ~10 %).42 Wharton et al. also suggested that smaller tip diameters can be reproducib ly prepared by optimizing the conditions of the first and second etching steps.42 Characterization of Conical Nanopores Microscopy Techniques Aperture size measurements are cr itical for the proper use of nanopore membranes as sensing and separations platforms. Fortunately, technological advances in the field of microscopy have made obtaining measurements of objects on the nanoscale possible. Typically, field em ission scanning electron microscopy (FESEM),17, 42, 97 transmission electron microscopy (TEM),68, 98 and/or atomic force microscopy (AFM)84 are used to obtain images of the openings. Locating a single pore developed in a me mbrane that contained a single damage track can prove to be a difficult task. Ther efore, the aperture size of a single-pore

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27 membrane is often determined by etching a membrane that contains multiple damage tracks under the same conditions used to etch the single-pore membrane.17, 42 The resulting multi-pore membrane is then im aged with an appropriate microscope. The size of the aperture in the single-pore me mbrane is assumed to be equivalent to the microscopically measured pore size for the multi-pore membrane. The three-dimensional structure of nanopores c an also be observed by microscopy techniques. This is typicall y accomplished by the template synthesis method,9 during which the pores ar e filled with another materi al such as a metal or carbon. For example, gold can be deposited inside track-etched PC40, 99 and PET17 pores with an electrole ss plating method. Freshly etched PC99 and PET12, 17, 80 membranes exhibit carboxylate groups on their pore walls (Figure 1-6). During the electroless plating method, the pore walls are first sensitized by exposing the membrane to a solution that contains tin(II) ions.99 Tin(II) coats the pore walls by forming an electrostatic complex with the surface carboxylate groups. Subsequent exposure of the membrane to a solution that contains silver-ammonia complex ions results in the oxidation of tin(II) to tin (IV) and the reduction of the silver-ammonia comp lex ions to elemental silver.99 This process yields a layer of silver nanoparticles on the pore wa lls. Immersion of t he membrane in a gold plating bath leads to the displacement of silver nanoparticles with gold nanoparticles as gold ions are reduced by formaldehyde that is present in the solution.99 Depending on the membrane ma terial, electroplating100, 101 or chemical vapor deposition87 may also be used to fill the pores wit h certain metals or carbon. The membrane can then be dissolved to liberate the pore replicas. These three-dimensional

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28 models of the pore struct ure can subsequently be imaged using an appropriate microscopy technique. Measuring Pore Size by Knudsen Flow of Gases For multi-pore membranes produced by the track-etch method, pore size can be determined by measuring the rate of trans port (Knudsen flow) of various gases through the membrane with a method first reported by Petzny and Quinn.102 When the pore diameter is smaller than the mean free path (or the average distance a moving particle travels before it collides with another moving particle) of the permeating gas molecules, kinetic theory can be used to calculate the pore size from the measurement of permeation rates.102 The flux is directly proportional to the pore size and gas pressure and inversely proportional to the molecula r weight of the permeating gas. Measuring Pore Size by Membrane Resistance As previously mentioned, Bean et al. were th e first to report that pore size could be estimated during the course of the etch ing process by measuring the membrane resistance.83 Anderson and Quinn later compared a similar method for calculating pore size based on the measurement of membrane conductance (which is inversely related to resistance) to the Knudsen flow method.103 Anderson and Quinn used multi-pore (105 cm-2) mica membranes (7 m thick) in their studies. They found t hat when pores even as small as 10 nm in equivalent diameter (Equation 1-1) were filled with a 0.1 M KCl solution, the measured conductivity of the solution showed only slight devia tions (less than 5 %) from the bulk conductivity.103 Thus, pore size can be determined by measuring the conductance of an electrolyte-filled nanopor ous membrane. This method is commonly employed especially in the case of memb ranes that contain conical nanop ores due to its simplicity.

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29 Since it can be difficult to determine bot h the larger (base) opening and smaller (tip) opening of a conical nanopore by any si ngle measurement, conical pores are often characterized by first measuring the base si ze for a multi-pore membrane (etched under the same conditions as the single-por e membrane under investigation) by an appropriate microscopy technique. The tip size of a single conical pore is then estimated by measuring the membrane conductance, G (in siemens, S), and using the following relationship:39, 42, 104 L d d Gbase tip4 (1-2) where is the specific conductivity of the electrolyte (in S m-1), dtip is the diameter of the smaller tip opening, dbase is the diameter of the larger (base) opening, and L is the length of the pore (also the thickness of the membrane). G is often measured by placing the single-nanopore membrane between two identical portions of an electrolyte solution. An appropriate nonpolarizable electrode is placed in each electrolyte solution chamber. Using a potentiostat, the potential of one of the electrodes is varied while the other is held constant, and th e resulting current through the pore is measured. T he slope of this current–potential ( I – V ) response is equivalent to the conductance. Equation 1-2 is derived under the assumptions that the pore possesses uniform conductivity and can be divided into differential slabs of conductance.105 These assumptions require that the planar faces of the conducting slabs be equipotentials (Figure 1-12). In reality, th is is a poor visualization of the channel as it means that current would not be parallel to the insulating sides of the conductor; instead, current would be able to flow in through the sides (Figure 1-12A). Equipotentials must be

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30 curved so that they are perpendicular to the insulating sides of the conductor (Figure 112B).105 The simplifications used to derive E quation 1-2 can lead to an overestimation of pore conductance since current flow is more constrained in reality.105 Though Equation 1-2 can lead to an overes timation of pore size, under certain conditions, Equation 1-2 will gi ve an acceptable estimation for dtip. Romano and Price used a numerical method to solve Laplace’s equation for a conical resistor with dtip/ L = and dbase/ L = 1.105 From the computed solution, t hey were able to calculate the resistance of the cone. T hey found that the conductance estimated by Equation 1-2 was 9% higher than the conductance calc ulated by solving Laplace’s equation. Romano and Price conceded, ho wever, that Equation 1-2 yields an acceptable conductance value if the cone possesses only a slight taper.105 The finite element simulation program CO MSOL Multiphysics 3.4 (Comsol, Inc., Burlington, MA) can be used to solve Laplace’ s equation for a conical resistor in the manner of Romano a nd Price. One can find t he conductance for a pore with dbase = 487 nm, dtip = 17 nm, and L = 12 m (typical for a conical pore produced in PET by the track-etch method17). For a pore with this geomet ry, Equation 1-2 will lead to an overestimation of conductance that is only ~0.02% higher than the conductance calculated by the computati onal method. Furthermore, t he estimated conductance is only ~2% higher than the calcul ated conductance for a pore with dbase = 5 m, dtip = 10 nm, and L = 12 m. Thus, it is important to no te that the above geometric mean approximation of the membrane conductance (Equation 1-2) is valid when the taper of the conical pore is small105 (i.e., the difference ( dtip– dbase) << L or, equivalently, the cone angle, is small) as is the case for the por es presented in the following studies.

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31 The specific conductivity in Equation 1-2 is often taken to be the measured bulk conductivity of the electrolyt e. This assumption is only valid for high electrolyte concentrations (~0.1 M KCl or higher). Since pore walls can be charged due to the presence of certain chemical functi onal groups (such as carboxylates17, 24, 39, 66 or silanols51), an electrical double-layer106 (Figure 1-13) forms in el ectrolyte-filled pores. The double-layer is often charac terized by the Debye length, -1 (in m):106, 107 I e N 2 T kA o r 2 1 (1-3) where NA is the Avogadro constant; k is the Boltzmann constant; e is the elementary charge; T is temperature; o and r are the permittivity of free space and relative permittivity, respectively; and I is the ionic strength (equivale nt to the concentration for a 1:1 electrolyte). Equation 13 shows that the double-layer thickness is inversely related to the square root of electrolyte concentration. The double-layer contains an excess of counter-ions to oppose the surface charge. Therefore, under certain conditions due to wall charge, co-ions may be excluded (Donnan exclusion) from a small pore.2 These effects can result in ion enrichment or depletion within the nanopore such that electrolyte conductivity within the pore can differ significantly from bulk conductivity.108 Ho et al. found that the conductivity of the electrolyte within single nanopores (1 to 3 nm in diameter) in 10 nm thick silicon ni tride membranes was much larger than the measured bulk conductivity for dilute (10 mM) electrolyte concentrations.109 However, the conductivity of the elec trolyte within the same singl e nanopores was comparable to or less than the measured bulk conductivity for high (1 M) electrolyte concentrations.

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32 These experimental observations were a ttributed to the electrical double-layer since nanopores in silicon nitride posse ss a surface charge density of -0.02 C m-2.109 The Debye length was larger than the pore radi us for dilute electrolyte concentrations (~3 nm for 10 mM). Therefore, elec trolyte concentration (and consequently conductivity) within the pore was governed la rgely by the surface charge on the pore walls. For high electrolyte concentrations the Debye length was smaller than the pore radius (~0.3 nm for 1 M). Recall that ear lier Anderson and Quinn concluded that the measured conductivity for 0.1 M KCl in 10 nm diameter pores differed by less than 5% from the bulk conductivity.103 Thus, Equation 1-2 can be used to determine dtip for conical nanopores with the sele ction of an electrolyte solution of high concentration.17, 42 Transport Properties of Conical Nanopores Ion-Current Rectification Apel et al. found that single conical nanop ore membranes produced in PET by the aforementioned track-etch method gave highly non-linear current–potential ( I – V ) responses when dilute electrolyte solutions (10 mM) were used.39 When identical portions of a dilute electrolyte solution ar e placed on each side of a single conical nanopore membrane, and current through the pore is measured as a function of applied transmembrane potential (as described above) a higher current is observed for a certain electrode polarity and a lower current for the opposite polarity (Figure 1-14). This phenomenon is known as ion-current rect ification and was previously reported to occur in quartz nanopipet electrodes by Wei et al.110 The extent of ion-current re ctification is commonly characterized by computing the rectification ratio, ric, which is usually defined as the abs olute value of t he quotient of the current at a certain potential divided by t he current at the potential of equal magnitude

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33 but opposite polarity (i.e., | I (V )/ I (+ V) |). Ion-current rectific ation is dependent on many parameters, including pore size, pore shape, surface charge, and electrolyte composition. Woermann suggested t hat this phenomenon could be qualitatively explained111-113 through Schmid’s model of a membrane with narrow pores.114 Most researchers have directly invoked this model or proposed similar theories to explain ioncurrent rectification.52, 62, 69, 111-113, 115-117 Ion-current rectification occurs in an asymmetric pore that possesses surface charge due to the difference in transference between cations (positively charged ions) and anions (negatively charged ions) through t he pore. For exam ple, consider a membrane that contains a single conical nanopore which exhibits negative surface charge on its pore walls (as is the case for track-etched pores in PET and PC membranes due to surface carboxylate gr oups). The membrane is placed between identical portions of a dilute electrolyte solution and transme mbrane potential is applied. If the electrode in the solution facing the tip serves as the anode and the electrode in the solution on the base side serves as the cathode (Figure 1-14A), anions will be driven from the base side of the membrane to the tip side and cations will be driven in the opposite direction (from the ti p side of the membrane to t he base side). Recall that an electrical double-layer will extend from t he pore walls into the solution due to the surface charge. This doublelayer contains excess cations to counteract the negative wall charge. Therefore, if the electrolyte is dilute enough such that the double-layer occupies a substantial amount of the tip aperture (i.e., -1 is comparable to the tip radius),62, 110, 118 anions find it difficult to traverse the small tip opening of pore due to unfavorable interactions with the negative charges on the pore walls.111-113

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34 Though the applied potential forces anions in to the pore through the larger base opening, the repulsion between the negatively charged pore walls and anions prevents the anions from exiting the pore through the tip opening. Therefore, anions accumulate inside the pore. To offset the resulting in crease in negative charge within the pore, the cation concentration inside the pore also increas es. Thus, with this electrode polarity, an increase in electrolyte concentration is expected within the pore. Consequently, a relatively high conductance state is reac hed and a large ionic current is observed (Figure 1-14A).111-113, 116 If the electrode in the solution facing the tip serves as the cathode and the electrode in the solution on the base side serves as the anode for the same membrane with negative surface charge des cribed above (Figure 1-14B), anions will be driven from the tip side of the membrane to the base si de. Cations will be driven in the opposite direction (from the base side of the membrane to the tip side). For the same reasons stated above, anions will find it di fficult to traverse the tip region of the pore. For the electrode configuration considered here, this statement means that few anions will enter the pore from the tip side. Mo reover, anions inside the pore will readily vacate it as they move toward the electrode through the larger base opening. These actions result in a decrease in the number of anions within the por e. Due to the presence of fewer anions inside the pore, fewer cations are required to maintain electroneutrality. Ultimately, the electrolyte concentration within the pore is relati vely low for this electrode configuration. As a result, a relatively low conductance st ate is reached, and a small ionic current is observed (Figure 1-14B).111-113, 116

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35 Now consider a membrane t hat contains a single coni cal nanopore with positively charged pore walls. If we consider the sa me treatment for the single conical pore membrane described above, the el ectrical double-layer in this case will contain excess anions and the pore will be less hospitable for ca tions. If the electrode in the solution facing the tip serves as the anode, and the el ectrode in the solution on the base side serves as the cathode (Figure 1-14C), cati ons will be driven from the tip side of the membrane to the base side; and anions will be driven in the opposite direction (from the base side of the membrane to the tip side). However, cations wi ll find it difficult to enter the pore through the small tip opening due to r epulsion from the positively charged pore walls. Cations initially inside the pore will be driven out through the base side due to the applied transmembrane potential. A low cation concentration inside the pore will result, and, consequently, fewer anions wil l be required inside the pore. The low conductance state that has been described yields a small current (Figure 1-14C). For the same pore with positive surface c harge, if the electrode in the solution facing the tip serves as the cathode, and t he electrode in the solution on the base side serves as the anode for the same membrane described above (Figure 1-14D), cations will be driven from the base side of the membrane to th e tip side; and anions will be driven in the opposite direction (from the ti p side of the membrane to the base side). Though the transmembrane potential forces cati ons into the pore from the base side, few cations are able to exit through the sm all tip opening due to electrostatic repulsion (from the positively charged pore walls). The resulting increase in cation concentration inside the pore requires the presence of more anions in the pore. The high conductance state that has been described yields a large current (Figure 1-14D).

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36 In general, the high conductance (“on”) st ate occurs when ions move from a portion of the pore where they enjoy relatively high transference to a portion of the pore where they experience lower transference (Fi gures 1-14A and 1-14D). This scenario is expected to result in accumulation of ions within the pore. The low conductance (“off”) state occurs when ions travel from a portion of the pore where they experience relatively low transference to a portion of the pore where they enjoy higher transference (Figures 1-14B and 1-14C). These circumstances are expected to result in depletion of ions within the pore. There has been great interest in using mat hematical models to explain ion-current rectification.110, 115-117, 119-123 These calculations primarily rely on Poisson–Nernst– Planck (PNP) theory115-117, 119-123 and often employ the finite element method116, 123 to solve the system of differential equations. However, since the degree of ion-current rectification is influenced by many fact ors including pore size, pore shape, surface charge, and electrolyte composit ion, it can be difficult to determine which aspects make the most important contributions to the phenomenon. Some researchers have still found this unique property of ioncurrent rectification useful in providing qualitative proof for the success of reactions designed to modify the pore surface charge.54, 67, 124 Also, sensors for small organic molecules,125 metal ions,126 and proteins55 have been developed by methods in which the ion-current rectification properties of asymmetric nanopore systems are monitored. Electroosmotic Flow If an ionic current is passed through an adequately small channel or porous medium that contains sufficient surface charge, all species tend to move in the direction of the counter-ions (Figure 1-15). Th is electrokinetic phenomenon is called

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37 electroosmotic flow (EOF) and occurs becaus e there are more counter-ions than coions present in the channel or porous m edium due the surface c harge. EOF is an important factor in the separation tec hnique known as capillary electrophoresis.127 Similarly, the phenomenon has also been employ ed in microfluidic devices to pump fluids.128 When the channel opening approaches the Deby e length (Equation 1-3), electrical double-layer overlap results.3 This can affect EOF by altering the flow profile from pluglike (as is the case in microchannels) to parabolic.2 Thus, in many cases EOF rates in nanochannels are reduced compared to those observed in microchannels.1 However, EOF in nanochannels can still be an important factor in transport. Researchers have investigated the consequences of EOF in resistive-pulse sensing129 and ion-current rectification51, 107 studies. Recently, the Martin gr oup has reported that electroosmotic flow in asymmetric nanopore membranes is also rectified.51 Electroosmotic flow rectification is closely related to ioncurrent rectification and (like ion-current rectification) is expected to result from the dependence of the electrolyte composition within the pores on the electrode configuration.51 Surface Charge Density Along with pore geometry, the surface charge of the me mbrane material plays an important role in transport properties. T he studies presented in the following chapters focus mostly on asymmetric nanopores in PET and mica membranes. Many researchers have used experimental methods and theoretical calculations to determine the surface charge densities of mica and PET. However, va lues reported in literature for such quantities vary widely.59, 80, 81, 86, 118-120, 130-135

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38 Values for the surface charge density of PET membranes have been reported to be as low as -0.0133 e nm-2 and as high as -47.5 e nm-2,131 where e is the elementary charge (-1.6 x 10-19 C). Berezkin et al. determined t he surface charge by measuring the streaming potential through seve ral track-etched filter memb ranes (with pores diameters ranging from 20 to 200 nm) in a 10 mM KCl electrolyte solution.131 With this method, the surface charge density was found to generally increase in magnitude with increasing pore diameter and ra nged from -0.0133 e nm-2 to -0.0539 e nm-2.131 In the same report by Berezkin et al., results obtained from streaming potential measurements were compared to those obt ained by electron paramagnetic resonance (EPR) spectroscopy of the same memb ranes to which copper ions had been bound.131 By EPR measurements, the su rface charge density of a me mbrane with 20 nm pores was found to be -47.5 e nm-2. Surface charge densities fo r the larger pore membranes used in the studies were lower and ranged from -0.121 e nm-2 to -12.5 e nm-2.131 Berezkin et al. reasoned that a highly charged gel -like layer that is virtually impermeable to solvent, and, therefore undetectable by streaming potential measurements, must exist on the pore surface.131 This gel layer was invoked to explain the large differences between the surface charge densities dete rmined by the two methods (streaming potential and EPR). Following the work of Berezkin et al., Dja rdin et al. determined the surface charge density of track-etched PET membranes again by measuring the streaming potential in a 10 mM KCl electrolyte solution.132 A surface charge density of -0.056 e nm-2 was reported for membranes that contained por es larger than 70 nm in radius.132 For pores with radii between ~17 and 70 nm, a slightly higher surface charge density of -0.078 e

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39 nm-2 was calculated.132 The difference was attributed to the supposition that pore walls for openings larger than 70 nm in radius must consist of bulk material while the walls of smaller pores may still exhibit some of the material that comprised the original heavyion-induced damage track. More recently, Xue et al. carried out measurements of pore conductance and streaming current to calculate the su rface charge density of track-etched PET membranes with pores that ranged from 60 to 150 nm in radius.135 From streaming current measurements, Xue et al. calculated surface charge densities between -0.0625 e nm-2 and -0.125 e nm-2 and found no systematic dependence on pore size.135 A higher surface charge density of -0.56 e nm-2 was calculated from pore conductance measurements.135 This value is in agreement with the value of -0.5 e nm-2 (also based on pore conductance measurement s) that was reported by Apel and Pretzsch.130 However, Apel and Pretzsch offered no experimental details; they stated only that charge density was calculated from “preliminary conductivity measurements of potassium chloride at different concentrations” in membranes that contained pores of 15 and 30 nm in diameter.130 Xue et al., like Berezkin et al., accredited the lower surface charge density values obtained by the streami ng current method to the inability of this technique to probe a gel-like surface layer.135 Xue et al. characterized this gel-like layer as a collection of negatively charged polymer chain-ends that are “hydrodynamically immobile.”135 The surface charge density of PET nanopores has also been estimated by Poisson–Nernst–Planck (PNP) modeling of experimental I–V curves obtained for membranes that contain single asymmetric (conical) nanopores.115, 117, 120, 123 The PNP

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40 model treats ions as point charge s and ignores electroosmotic effects.115, 117, 120, 123 Surface charge density is typically the only adj ustable parameter in the model. Cervera et al. used this approach to model experimental ion-current rectification data that had been reported by Siwy et al.52 for a single conical gold -plated (prepared by an electroless plating method) nanopore (tip di ameter 10 nm and base diameter 600 nm) in a PET membrane.120 Cervera et al. obtained the best agreement between their model and the experimental data for a surface charge density of -1 e nm-2. In the case of this gold-plated conical nanopore, surface charge is determined by adsorbed chloride ions (the electrolyte was 0.1 M KCl).120 Though the preceding PNP-derived surfac e charge density was determined for a pore with gold-coated walls, the surface charge density for PET has, seemingly coincidentally, been widely accepted118, 122, 123, 136, 137 as -1 e nm-2. This value for surface charge density has been fa vored in recent literature,118, 122, 123, 136, 137 though its origins are somewhat nebulous. Cervera et al. reported this value after modeling experimental data (for two separate single-pore PET membranes with tip diameters of 44 and 6 nm and base diameters of 336 and 440 nm respectively) with the previously described PNP-based theory.115 The authors of this study stated that -1 e nm-2 “is within the range of experimental values re ported for cylindrical and PET nanopores,”115 citing earlier work by Siwy et al.138 However, the cited work by Siwy et al. only offers that “etching produces approximat ely 1 carboxylate group per 1 nm2”138 while referencing work by Wolf et al.139 A surface charge density calculation or even a definitive statement about the magnitude of the surface c harge density does not appear in the work by Wolf et al.139

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41 The same PNP-based arguments used above have resulted in vastly different surface charge density values for PET nanopores In a separate study from those listed above, Cervera et al. used the same method to model the I–V response of a conical nanopore in PET with a tip diameter of 8 nm and a base diameter of 220 nm.119 The authors reported the surface charge density to be -0.3 e nm-2 for this PET pore.119 Furthermore, studies rooted in the PNP theory have suggested that rect ification is highly sensitive to pore geometry117, 123 and surface charge distribution.123, 140 Ramrez et al. have shown that PNP theor y predicts that a conical nanopore with a surface charge density of -0.1 e nm-2 will exhibit nearly the same rectification ratio as the same conical nanopore with a surface ch arge density that is 10 times higher (-1 e nm-2) when 0.1 M KCl is used as the electrolyte.117 The work by Ramrez et al. also suggests that pores with more bullet-like profil es yield higher rectification ratios than those that are conical.117 PNP simulations also suggest that surface charge distribution is important to ioncurrent rectification. This has been ve rified by experimental work with bipolar nanofluidic diodes.67, 141, 142 Vlassiouk and Siwy prepared si ngle conical nanopores that possess positive surface charge in one por tion of the channel and negative surface charge in another.67 This was accomplished by diffusion-controlled surface modification143 with an amine molecule.67 Using this strategy, Vlassiouk and Siwy were able to increase the rectification ratio of a conical nanopore (with a tip diameter 2.5 nm and a base diameter of 500 nm). Fewer reports of the surface charge dens ity for mica have been encountered. Koh and Anderson reported a surfac e charge density of -0.00625 e nm-2 to -0.0521 e nm-2

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42 for measurements of electroosmotic flow th rough a membrane that contained symmetric track-etched pores (equivalent diameter of 24 nm) in mica.86 The electrolyte concentration was varied from 0.1 to 200 mM in their experiments, but the pH was constant at 7. Higher char ge density magnitudes were calc ulated for higher electrolyte concentrations. Westermann-Clark and Anderson late r used streaming pot ential and pore conductivity measurements to calculate the su rface charge density of pores in mica membranes.134 Larger pores (> 200 nm in equival ent diameter) were evaluated by streaming potential, while smal ler pores (~20 nm in equival ent diameter) were assessed with pore conductivity measurements. Surf ace charge density values calculated from streaming potential measur ements ranged from -0.018 e nm-2 to -0.05 e nm-2.134 Conductivity measurements suggested that the surface charge density was -0.031 e nm-2 to -0.106 e nm-2.134 Frhlich and Woermann determined the surface charge density for mica membranes that contained symmetric pores (equivalent diameter of ~100 nm) from measurements of membrane potential ( due to a transmembrane concentration difference), electrical conducti vity, and streaming potential.59 Each method resulted in a calculated surface charge density of -0.00625 e nm-2.59 Streaming potential measurements for the plane of cleavage (basal plane, which is perpendicular to pore axis) of mica gave surface charge densit y values that were 3–6 times higher. Based on the crystal structur e of mica, the charge densit y of the basal plane has been estimated to be -2.1 e nm-2.81 However, this corresponds to an unrealistic situation in which all potassium ions are removed from the plane of cleavage (Figure 1-

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43 8).81 The surface charge of the basal pla ne arises from isomorphic substitution,81 whereas the pore wall charge is expected to originate fr om surface silanol groups.134 In aqueous solutions, the surface charge density of the basal plane is normally orders of magnitude lower (appr oximately -0.014 e nm-2 according to the force measurements between smooth curved mica surfaces completed by Pashley144) due to the presence of cations.81 Though it is clear that the surface charge densities of mica and PET nanopores are highly dependent on experimental conditi ons, a few general observations about the surface charge densities of mica and PET nanopores have been made. First, as previously stated, surface charge density values report ed for PET range from -0.0133 e nm-2 to -47.5 e nm-2.131, 132, 135 For mica, the reported surface charge density values reside between -0.00625 e nm-2 and -0.106 e nm-2.58, 86, 134 Surface charge densities reported by el ectrokinetic measurements (streaming current, streaming potential, and electroos mosis) are usually lower than those calculated from measurement s of pore conductivity or PNP-based models. Surface charge density values reported for PET memb ranes using electrokinetic measurements range from -0.0133 e nm-2 to -0.125 e nm-2.131, 132, 135 Electrokinetic measurements on mica membranes have yielded surface char ge density values in the range of -0.00625 e nm-2 to -0.0521 e nm-2.59, 86, 134 Pore conductivity measur ements performed on PET memb ranes led to surface charge density values of approximately -0.5 e nm-2,130, 135 while similar experiments conducted on mica membranes resulted in surface charge density values that ranged from -0.031 e nm-2 to -0.106 e nm-2.59, 134 The widely accepted surface charge density

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44 for PET membranes118, 122, 123, 136, 137 (-1 e nm-2) is larger than most experimentally determined values and was determined by PNP-based modeling of experimental data.115, 117, 120, 123 Several recent publications117, 119, 123, 140 have shown that PNP theory predicts that ion-current re ctification is highly dependent on pore geometry and surface charge distribution. These findings seem to undermine the certitude of the accepted value for PET surface charge density (-1 e nm-2). PNP theory has not yet been used to model experimental I–V data for asymmetric mica nanopores. Summary Nanopore membranes have become a focal point for many research efforts due to their limited size and interesting transport properties. Researchers have shown that such membranes can be used for size-based molecule separations,145-149 as sensing platforms,5-8, 16, 55, 125, 150-157 and as templates to produce other nanomaterials.9, 100, 101 Since the transport properties of n anopore membranes depend on pore geometry and surface charge density, the proper characteri zation of such parameters is critically important in membrane optim ization and applications. In the following chapters, the properties and applications of nanopore membranes are explored. The particular focus of this work has been centered on asymmetric nanopores in PET and mica membranes. A PET membrane that contained a single asymmetric nanopore has been chemically modifi ed with a molecular recognition agent to sense a particular analyte. Ion-current rectification was monitored to verify successful surface modification. The ion-current rectification capabilities of asymmetric nanopores in mica and PET membranes have also been compared. Additionally, electroosmotic flow rectification and sizeand charge-based selective transport in mica membranes have been explored.

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45 Figure 1-1. General approach used in Coul ter counter devices and resistive-pulse sensors. A) Analyte is present on one side of the membrane in an electrolyte solution, and a background current is measured while a transmembrane potential is applied. B) Analyte has entered the s ensing element (pore or channel) and displaced a portion of the elec trolyte solution within, resulting in a decrease in the measured current. C) Analyte has exited the pore. The measured current returns to the backg round level. The current pulse is identified by the duration ( t) and magnitude ( i). (Figure is not drawn to scale.) [Figure adapted from Reference 6.]

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46 Figure 1-2. Illustra tion of the protein -hemolysin ( -HL) embedded in a lipid bilayer membrane. [Figure adapted from References 5 and 6.] Figure 1-3. Electric fiel d strength distribution in an asymmetric nanopore. The boundary on the far left represents the centra l axis of the pore and is taken to be the axis of symmetry. The pore is 10 m in length with a tip opening diameter of 30 nm and a base opening diam eter of 520 nm. Electric field strength was simulated according to det ails in References 17 and 45. As shown by the inset, the highest electric field is located near the tip region.

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47 Figure 1-4. General overview of the track-et ch method. A) A thin film or membrane is exposed to a beam of swift, heavy ions B) An ion has passed through the membrane leaving behind a latent damage track in the material. C) The damage track has been chemically etc hed to produce a single nanopore. (Figure not to scale.) Figure 1-5. Depiction of the formation of latent damage tracks. A) A swift, heavy ion has passed through a crystalline material, leaving behind newly formed ions. The crystal lattice is disrupted as thes e newly formed ions rapidly repel one another B) A swift, heavy ion has passed through a polymer film. The process has ionized and excited molecu les, resulting in broken chains and the formation of new chain ends. [Figure adapted from Reference 76.]

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48 Figure 1-6. Chemical st ructures and hydrolysis reac tion products of polymers commonly used in the track-etch met hod. Damage tracks in polycarbonate (PC) and poly(ethylene terephthalate) (PET) can be etched by simple hydrolysis reactions. The resulting nanopores exhibit surface carboxylate groups. Figure 1-7. Scanning electron micrograph of pores produced in PET by the track-etch method. Figure 1-8. Chemical structur e of muscovite mica. A) Lay er composition of muscovite mica. [Adapted from Reference 82.] B) De tailed lattice structure of muscovite mica. [Adapted fr om Reference 81.]

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49 Figure 1-9. Geometry for a pore produced in muscovite mica by the track-etch method. A) Scanning electron micrograph of a typical pore produced in muscovite mica by the track-etch method. B) Pr ojected atomic arra ngement in the (001) plane of muscovite mica. Pore wa lls (red lines) correspond to oxygenterminated planes of the crystal lattice [Adapted from Reference 84.] Figure 1-10. Depiction of the chemical etching proce ss of a heavy-ion-induced damage track in a thin film. Pore shape is defined by the track-etch ( vT) and bulk-etch ( vB) rates. Pore geometry can be described in terms of the cone half-angle /2. [Figure adapted from Reference 76.]

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50 Figure 1-11. General approac h for the production of asymmetric nanopores by the track-etch method. A) A membrane containing a single damage track is placed between two different solutions. A transmembrane potential is applied and a negligible current is initially meas ured. B) An asymmetric pore has resulted from the etching process. T he larger (base) opening is located on the side of the membrane that was in c ontact with the etching solution. The smaller (tip) opening is located on the side of the membrane that was in contact with the stopping solution. Br eakthrough of the etching solution is observed by the sudden increase in current. (Figure is not to scale.) [Figure adapted from Reference 39.] Figure 1-12. Representation of equipotentials and current flow lines in a conically shaped resistor. A) Equipotentials (l eft) and current flow lines (right) predicted under the typica l geometric mean derivati on used to estimate the resistance (or conductance) of a conical resistor. Current is assumed to be able to flow from the insulating sides. B) A more realistic representation of equipotentials (left) and curr ent flow lines (right) in a conically shaped resistor. Current flow is more constrained than t hat which is predicted by the geometric mean derivation used to estimate the resistance. [Figure adapted from Reference 105.]

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51 Figure 1-13. Description of the electrical dou ble-layer that forms at charged surfaces in solution. A) Structure of the electrical double-lay er. (Note that solvent molecules are not shown for simplicity.) [Adapted from Reference 106.] B) Basic description of the potential drop in the electrical double-layer according to the Gouy–Chapman–Stern model. [Adapted from Reference 106.] Figure 1-14. Schematic explanat ion of the ion-current rect ification phenomen on. A) Ion transport through a negatively charged a symmetric pore due to a given transmembrane potential. Arrows indicate relative ion transference values. Expected current is shown on the left. B) Ion transport through a negatively charged asymmetric pore due to a tr ansmembrane potential of the opposite polarity shown in part A. Expected cu rrent is shown on the right. C) Ion tranport through a positively charged asymmetric pore due to a given transmembrane potential. Expected current is shown on the left. D) Ion transport through a positively ch arged asymmetric pore due to a transmembrane potential of the opposite pol arity shown in par t C. Expected current is shown on the right. (Figure is not to scale.)

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52 Figure 1-15. Ion dist ribution and electroosmotic flow in a charged capillary. Here, the negatively charged surface ensures that more cations will be present in the channel. Thus, electroosmotic flow is in the direction of cation motion (toward the cathode). [Figure adapt ed from Reference 127.]

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53 CHAPTER 2 RESISTIVE-PULSE SENSING OF A PROTEIN ANALYTE USING A CHEMICALLY MODIFIED CONICAL NANOPORE Motivation The electrochemical single-molecule sensing technique known as resistive-pulse sensing has been the subject of much recent interest.5-8, 14-25, 31-33 In this method, a membrane that contains a single synthetic or biological nanopore is used to separate two portions of an electrolyte solution.5-8 A potential difference is applied across the membrane, and the current is m easured. When analyte is present in one of the solution portions, and the potential is applied in such a way to drive the analyte from one side of the membrane to the other, anal yte will transiently perturb t he measured current as it traverses the small channel. The magnitude and duration of these perturbations are related to the size, shape, and charge of the analyte.5-8 Resistive-pulse sensing is an elegantly simple technique based on the Coulter principle. However, applicat ion of the method to complex mixtures, especially ones that contain species of size simila r to the analye, can be difficult.8 More selective resistivepulse sensors based on the protein channel -hemolysin have been developed for a variety of analytes with the aid of genet ic engineering and chemical modification.5, 8, 13, 16, 31, 34 However, the utility of such pores is limited by the lipid bilayer’s lack of durability.5-8, 31 Here, more robust single synthetic nanopores in PET are modified with a molecular recognition agent (folate) in an attempt improve the selectivity of the resistive-pulse sensing method as it is applied to a particular analyte (folate-binding protein).

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54 Experimental Materials Poly(ethylene terephthalate) (PET) films, each containing a single damage track generated by a heavy ion, were obtained from GSI (Darmstadt, Germany). N -(3dimethylaminopropyl)N’ -ethylcarbodiimide hydrochlor ide (EDC, commercial grade), ethylenediamine ( 99%), N -hydroxysuccinimide (NHS, 98%), folic acid (~98%), folatebinding protein from bovine m ilk (~30% protein), and MES ( 99%) were all obtained from Sigma-Aldrich (St. Louis, MO) and used as received. All other chemicals were obtained and used without further pur ification from Fisher Scientific (Fairlawn, NJ). All solutions were prepared in 18 M water, obtained by passing distilled water through a Barnstead (Dubuque, IA) E-pure water purification system. Nanopore Preparation A 12 m-thick PET membrane containi ng a single damage track was mounted between two compartm ents and etched as previously described.39 A solution of 9 M sodium hydroxide (etching solution) wa s added to one compartment, while a solution containing 1 M potassium chloride and 1 M fo rmic acid (stopping solution) was added to the other. One platinum wire electrode was placed in each solution-containing compartment, and a potential of 1 V was app lied across the membrane using a Keithley model 6487 picoammeter/voltage source (Cle veland, OH). The potential was applied such that the electrode in contact with t he etching solution served as the anode. After two hours the etching process was stopped by draining each solution-containing compartment, rinsing each compartment with stopping solution, and allowing the membrane to stay in contact with the st opping solution for fifteen minutes.

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55 Often, a second etching step was also completed to tailor the tip size.42 For this second step, a 1 M NaOH solution was placed on each side of the membrane and again a potential of 1 V was applied across the me mbrane. With knowledge of the etching solution conductivity (16.0 S m-1 as measured by a YSI 3200 conductivity meter, Yellow Springs, OH), the pore tip can be etched to a preferred size by monitoring the current (Equation 1-2).42 The current was monitored and t he etching process was allowed to occur until the desired current wa s reached. The effect of th is second etching step on the pore base side is commonly ignored. Since the base is much larger than the tip, the change in the base size is often neglible.42 Nanopore Characterization According to a previous report,42 etching PET membranes using the previously described conditions yields pores with base o penings of 520 ( 45) nm as measured by scanning electron microscopy. In these studi es, this was confirmed with the aid of a Hitachi S-4000 field-emission scanning electron microscope (Tokyo, Japan). Membranes that contained a higher pore density (~106 cm-2) were etched in the same fashion that was used to prepare the si ngle-pore membranes. These multi-pore membranes were divided into small pi eces and adhered to SEM specimen mounts using double-sided carbon tape such t hat the base opening could be imaged. Since the tip size can be difficult to di rectly measure by imaging techniques, the diameter of this smaller opening was esti mated by a previously described method based on measuring pore c onductance (Equation 1-2).39, 42 This method requires measurement of t he current–potential ( I–V ) response. I-V curves were taken by placing a desired electrolyte solution on each side of t he membrane. Bulk conductivity of the electrolyte was determined with a YSI 3200 conducti vity meter. A silver/silver chloride

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56 (Ag/AgCl) electrode (Bioanalytic al Systems, West Lafayette IN) was also placed in each solution-containi ng compartment. A Keithley picoammeter/voltage source was used to obtain I-V curves. The potential was scanned from -2.0 V to +2.0 V in increments of 0.05 V every 2 seconds. For these and all other I-V experiments, the potent ial of the electrode in contact with the solution on the base (larger openi ng of the conical nanopore) si de was varied while the potential of the electrode in contact with t he solution on the tip (smaller opening of the conical nanopore) side serv ed as the reference. Modification of Nanopores with Folate Functionalizing the freshly et ched pore surface with folate is a two step process because folate must be attached through the glutamate end of the molecule (Figure 21). This is because the pteridine ring (Figur e 2-1) has been determined to be crucial to the binding interaction with folate-binding protein (FBP).158 The track-etching process used to produce nanopores in PET results in the formation of surface carboxylate groups. These surface carboxylates served as points of attachment for folate. First amidation of the surface carboxyl ate groups using EDC and ethylenediamine was performed (Figure 2-2). Following published reports,54, 67 the membrane was immersed in a pH 5.5 buffer solution of 10 mM MES with 0.1 M potassium chloride, 0.1 M EDC, and 0.2 M NHS. The reaction, whic h results in an amine-reactive NHS ester intermediate (Figure 2-2),54 was allowed to continue for four hours. After this time the membrane was rinsed with buffer and t hen exposed to a solution of 0.2 M ethylenediamine (in buffer) for four hours. This procedure is expected to result in the presence of amine groups on the pore walls. Using previous research reports as a

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57 guide,54, 67 this supposition was verified by meas uring ion-current re ctification using I-V curves obtained in the previ ously described manner. Folate has been successfully attached to su rfaces that contai n free amine groups (via the carboxylate groups of the molecule’s glutamate moiety) for various applications without detriment to its bi nding interaction with FBP.159-165 In order to a ttach folate to the amine-modified pore walls in this study a pH 5.5 buffer solution of 10 mM MES with 0.1 M potassium chloride, 5 mM folic ac id, 5 mM NHS, and 5 mM EDC was prepared. The membrane was submerged in this solu tion, and the surface amine groups were allowed to react with the activated carboxyl ate groups of folate for six or more hours (Figure 2-3). After this time, the membrane was agai n rinsed with buffer, and I-V curves were taken to monitor the rectification of ion current through the pore and help confirm the desired pore modification. Resistive-Pulse Sens ing Measurements Once the folate-functionalized pore was prepared, the membrane was again placed between two compartments, each cont aining pH 5.5 buffer solution of 10 mM MES with 0.1 M potassium chloride. This solution was selected because the isoelectric point of folate-binding protein (FBP) occurs between pH 7 and 8.166 Moreover, FBP has been found to bind folate in solutions of pH as low as 5.166-168 A silver/silver chloride electrode wa s placed in each solution-containing compartment and connected to the Axopatch 200B patch-clamp amplifier (Molecular Devices Corp., Union City, CA, USA). T he solution pH ensured that FBP would be positively charged. Thus, the potential was applied such that t he cathode was located in the solution on the base side of the memb rane to help encourage FBP to move from the tip side of the membrane through the pore to the base side. Electrode configuration

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58 was such that the reference electrode was hous ed in the solution facing the tip side of the membrane. The desired transmembrane potential was applied, and the resulting current through the nanopore was measured at a sa mpling frequency of 20 kHz using the Axopatch. Data were recorded and analyzed with pClamp 10.1 software (Molecular Devices Corp.). A threshol d of three times the standard deviation of the background current was used to define current pulses. The current pulse duration was defined as the time that the current remained beyond this threshold. The current pulse magnitude was measured as the difference between the peak current and the background. Results and Discussion Single-Nanopore Membrane Characterization Figure 2-4 shows a scanning electron micr ograph of a typical base opening for the asymmetric nanopores prepared in these studie s. As previously stated, the base openings for pores etched under the conditions used here possess diameters of 520 ( 45) nm. Using a supporting electrolyte solution of 1 M KCl with 10 mM PBS (pH 7.4, bulk conductivity 10.8 S m-1), tip diameters of single-po re membranes were estimated from pore conductance meas urements and ranged from ~20 nm to ~60 nm for the membranes used in these studies. I–V responses used to determine tip sizes for two asymmetric nanopores employed in these st udies are depicted in Figure 2-5. Ion-Current Rectificati on and Pore Modification Ion-current rectification is related to the charge state of the pore walls. The twostep modification strategy employed here (Figur es 2-2 and 2-3) is expected to result in changes to the surface charge. Therefore, successful pore m odification was verified by monitoring changes in ion-cu rrent rectification through I–V responses. I–V curves were

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59 obtained in electrolyte solutions of low enough concentration (0.1 M KCl) such that ioncurrent rectification could be observed. Notice that the pH of the electrolyte so lution is also important to ion-current rectification since pore wall charge is dependent on the charge state of surface carboxylate and/or amine groups after each m odification step. After etching, the carboxylate groups present on the pore wall ex hibit negative charge in solutions with pH > ~3.8, 39, 64 In solutions with pH < ~10,169, 170 pore walls modified with ethylenediamine (Figure 2-2) should possess positive charge. Finally, folate-modified pore walls (Figure 2-3) may possess both positive and negative surface charge. The p Ka values of the and -carboxylates of the folate molecule (Fi gure 2-1) are 3.5 and 4.8, respectively.171, 172 Protonation of the pteridine ring (Figure 2-1) occurs in solutions of low pH (< ~7.7).172 Ideally, all carboxylate groups will be f unctionalized with ethlyenediamine during the first step (Figure 2-2) such that the i on-current rectification behavior will completely reverse (as surface charge changes from negative to positive) in a properly chosen buffer. The second step of the modificati on (Figure 2-3) should reintroduce some surface carboxylates and decrease the re ctification (result in a more linear I–V response). Figure 2-6 shows the I–V response (in 0.1 M KCl with 10 mM MES buffer pH 5.5) of a single asymmetric nanopore after each step of pore modification. In this case, successful surface modification is at least qualitatively evident due to the drastically different I–V responses obtained after eac h modification step. However, it must be noted, that, in so me instances, successful modification could not be verified through the use of a single electr olyte solution as in Figure 2-6. This is

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60 most likely due to the possibility of incomplete conversion during the modification steps. In these instances, I–V responses were obtained in additional electrolyte solutions (0.1 M KCl) buffered at different pH values (10 mM phosphate buffer with pH 7.4 or 2.0). Figure 2-7 shows the I–V responses for a pore that did not initially appear to be completely modified by ethylenediamine. Res ponse of this pore in pH 5.5 (Figure 2-7B) did not change as drastically upon modificati on as the pore observed in Figure 2-6. However, successful attachment of ethylenedi amine is verified by the data obtained with the pH 2.0 electrolyte solu tion (Figure 2-7C). Modification with folate was deemed successful due to the differences exhibited that resulted in the I–V curves obtained in each electrolyte solution (Figure 2-7). This data can also be visualized in terms of the ion-current rectific ation ratio. This quantity is simply defined as t he absolute value of the curr ent obtained at a potential of a given magnitude divided by the current obt ained at the same magnitude but opposite polarity (i.e., | I(-V)/I(+V) |).67 Here, the ion-current rectification ratio is determined by the currents obtained at -2 V and +2V. Ioncurrent rectification ratios for the I–V data in Figure 2-7 are compiled in Table 2-1. As expected, the rectification ratio is ~1 after etching for the PET pore in the pH 2.0 electrolyte solution (Tabl e 2-1). This is because su rface carboxylate groups are expected to be protonated at this low pH, thereby neutralizing the pore wall surface charge. After attachment of ethylenediamine, the rectific ation ratio drops below one in the pH 2.0, indicating a positively charged su rface. The increase in rectification ratio from 2.67 ( 0.04) to 5.1 ( 0.5) observed for the pH 7.4 electrolyte after modification with ethylenediamine is certainl y worth mention. This incr ease actually strengthens the

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61 case that the pore wall was partially modified with folate since comparable results were obtained by Vlassiouk and Siwy during their studies in preparing bipolar nanofluidic diodes from similarly prepared asymmetric nanopores in PET.67 Folate modification leads to changes in the rectification ratios obtained in each electrolyte solution as can be seen in Table 2-1. Resistive-Pulse Sensing of Folate-Binding Protein After folate modifi cation was confirmed, the single nanopores were used as resistive-pulse sensing platforms for folate -binding protein (FBP). First, the background current response (only supporting electrolyte pr esent) was obtained (Fi gure 2-8A). After the background current was found to be suffici ently stable (usually this required less than ten minutes, but backgroun d currents were observed for longer periods of time in separate experiments to conf irm stability), FBP was added to the solution on the tip side of the membrane (final FBP concent ration was ~4 ppm or ~130 nM). Approximately one hour after the addition of FBP, pertur bations in the measured current began to appear (Figure 2-8B). Sinc e negative potentials were applied in these studies (cathode in the solution on the bas e side of the membrane), all currents in Figure 2-8 are negative. Thus, the current pulses observed in Figure 2-8 correspond to a decrease in current magnitude (increase in por e resistance) that is consistent with the Coulter principle. The frequen cy of the current pulses increas ed over time as is evident from the current-time trace obtained approximately two hours after the addition of FBP (Figure 2-8C). The effect of applied transmembrane pot ential on the current -time trace is depicted in Figure 2-9. Notice that decreasing the magnit ude of the applied transmembrane potential (parts A-C of Figur e 2-9) results in the appearance of more

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62 long-lived current pulses. No current pulse s were observed when the polarity of the applied transmembrane potential wa s changed such that the electode in the solution on the tip side of the membrane (same side as F BP) served as the cathode (Figure 2-9D). This observation supports the supposition that current pulses originate from the translocation of FBP. A scatter plot of the current pulse (e vent) data obtained duri ng resistive-pulse sensing experiments is displayed in Figure 210 (parts A-C). Data for over 7800 events (> 470 events obtained with -700 mV; > 2100 events obtained with -800 mV; > 3500 events obtained with -900 mV; and >1700 event s obtained with -1000 mV) are plotted in Figure 2-10. Resistive-pulse sensing ex periments led to a wide range in both event magnitude and duration. Longerlived events were more common at lower potentials; however, these pulses occurred with very low frequency (Figure 2-10D). Interestingly, long-lived events could be disrupted by applic ation of voltage pulses of alternating polarity (Figure 2-11B). Summary Folate-modified single asymmetric nanopores were prepared in track-etched PET membranes to serve as resistive-pulse s ensing platforms. Surf ace modification was verified by changes in the ion-current rect ification properties of the asymmetric nanopores. Folate-binding protein (FBP) was successfully identified with the resistivepulse sensing technique as indicated by the observation of potential-dependent pulses upon exposure of the folate -modified nanopores to FBP. Long-lived events were more frequent with lower applied potentials. Ho wever, the current pulse duration and magnitude values displayed a wide range, making it difficult to argue for the selectivity and practicality of this strategy for FBP.

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63 The wide range displayed in both event magnitude and duration may be attributed to multiple simultaneous binding events, or binding may have been somewhat disrupted by the presence of the electric field. Though these are simply speculative hypotheses, it is worth noting that FBP has been report ed to undergo a conformational change upon binding to folate.173 Perhaps the structural flexibility of the protein is reflected here in the wide range of current pulse characteristics.

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64 Figure 2-1. Chemical st ructure of folic acid. Figure 2-2. Reaction scheme for amine m odification of pore walls. [Figure adapted from Reference 55.] Figure 2-3. Reaction scheme for modifi cation of pore walls with folate. Figure 2-4. Base opening of an asymme tric nanopore produced in PET by the tracketch method.

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65 Figure 2-5. I–V curves used to estimate pore tip size. I–V responses are shown for two PET membranes that each contained a single asymmetric nanopore. The supporting electrolyte was 1 M KCl with 10 mM PBS (pH 7.4). The base diameter of each pore was 520 ( 45) nm. With the application of Equation 12, pore tip diameters are estimated to be 21 ( 2) nm (solid line) and 28 ( 2) nm (dotted line). Figure 2-6. I–V curves used to verify pore modification. I–V responses are shown for a PET membrane that contains a single asymmetric nanopore. The supporting electrolyte was 0.1 M KCl with 10 mM MES (pH 5.5). The base diameter and tip diameter were 520 ( 45) nm and 28 ( 2) nm, respectively. Curves correspond to data obtained after etching (solid line), after modification with ethylenediamine (dashed line), and after modification with folate (dotted line).

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66 Figure 2-7. I–V curves used to verify pore modifi cation obtained with different pH buffered electrolyte solutions. I–V responses are shown for a PET membrane that contains a single asymmetric nanopor e. The supporting electrolyte was 0.1 M KCl with A) 10 mM phosphate (pH 7. 4); B) 10 mM MES (pH 5.5); C) 10 mM phosphate (pH 2.0). The base diameter and tip diameter were 520 ( 45) nm and 21 ( 2) nm, respectively. Curves correspond to data obtained after etching (solid line), after modification with ethylenediamine (dashed line), and after modification with folate (dotted line). Table 2-1. Rectification ratios after eac h modification step for a PET membrane that contains a single asymmetric nanopore. Electrolyte pH After etching A fter ethylenediamin e After folate 2.0 1.15 ( 0.04) 0.28 ( 0.07) 0.34 ( 0.03) 5.5 2.2 ( 0.2) 2.22 ( 0.02) 0.94 ( 0.01) 7.4 2.67 ( 0.04) 5.1 ( 0.5) 1.5 ( 0.2)

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67 Figure 2-8. Current-time traces for resist ive-pulse sensing of folate-binding protein using a folate-modified single asymmetric nanopore. All traces were obtained with a transmembrane potential of 1000 mV (cathode in solution on base side of the membrane). The supporting electrolyte solution was 0.1 M KCl with 10 mM MES (pH 5.5). A) Backgr ound current. B) One hour after the addition of FBP. C) Two hour s after the addition of FBP. Figure 2-9. Effect of applied transme mbrane potential on curr ent-time traces for resistive-pulse sensing of folate-bindi ng protein. The supporting electrolyte solution was 0.1 M KCl with 10 mM M ES (pH 5.5). In each case, the electrode in the solution on the tip side of the membrane served as the reference. The position of zero current is indicat ed for each trace. A) -900 mV. B) -800 mV. C) -700 mV. D) +1000 mV.

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68 Figure 2-10. Scatter plot and histogram fo r current pulses obtained during resistivepulse sensing of folate-binding protein. A-C) Scatter plot of current pulse magnitude and duration shown for different time scale s. Data obtained for transmembrane potentials of -700 mV (s olid navy squares), -800 mV (open blue triangles), -900 mV (open purple circles), and -1000 mV (black Xs) are displayed. D) Histogram of event duration data. Figure 2-11. Long-lived current pulse events due to resistive-pulse sensing of folatebinding protein. Each trace was init ially recorded at -700 mV (reference electrode is housed in the solution on t he tip side of the membrane). The position of zero current is indicated in each trace. A) Current rapidly decreases in magnitude due to blockage of pore. B) Long-lived current pulse is disrupted by the application of voltage pulses (-1000 or +1000 mV).

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69 CHAPTER 3 COMPARISON BETWEEN THE ION-CURRENT RECTIFICATION CAPABILITIES OF ASYMMETRIC NANOPORES IN MICA AN D POLY(ETHYLENE TEREPHTHALATE) MEMBRANES Motivation Nanopores with asymmetric geometry39, 52-54, 60-62, 64, 69, 97, 109, 111-113, 115-120, 122, 123, 125, 126, 137, 138, 140, 174-176 and/or surface charge67, 123, 177-182 have been shown to rectify ion current. This phenomenon is observed thr ough the asymmetric current–potential response that results when a membrane that c ontains such a pore or collection of pores is used to separate two identical portions of an electrolyte solution. When a potential is applied across the membrane, an ionic current will flow through the pore or pores. The amount of current that results will not only depend on the magnitude of the transmembrane potential (as expected) but al so on the polarity of the potential. Ion-current rectification has been the subject of many th eoretical and experimental studies.39, 52-54, 60-62, 64, 67, 69, 97, 109, 111-113, 115-120, 122, 123, 125, 126, 137, 138, 140, 174-182 The phenomenon is dependent on pore geometry, surface charge, and electrolyte composition. Sensors for small organic molecules,125 metal ions,126 and proteins55 have been developed from nanopores by m onitoring changes in ion-cu rrent rectification. Most ion-current rectificat ion studies and applications have been performed with asymmetric pores in polymer membranes55, 64, 66, 67, 125, 136, 141 or quartz110, 126, 183 (or glass116) nanopipettes. These pores typically possess circular cross-sectional openings. Recently, we reported that asymmetr ic pores can be produced in muscovite mica.51 This is accomplished through application of the track-etch method in the same manner that is used to generate asymmetric nanopores in polymers.39 Track-etched

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70 mica nanopores possess rhomboida l cross-sectional openings.83, 85 Thus, the asymmetric mica nanopores that result from the track-etch method are pyramidal in shape.51 Here we compare the ion-current rectification properties of pyramidal nanopores in mica to conical nanopores in poly(ethylene terephthalate) (PET). Experimental Materials Muscovite mica (KAl2(AlSi3)O10(OH)2) membranes (10 m thick and 3 cm in diameter) were obtained from Spruce Pine Co (Spruce Pine, NC). Using the linear accelerator (UNILAC) at GSI (Darmstadt, Ge rmany), these membranes were irradiated with heavy ions (11.4 MeV/nucleon) to i nduce damage tracks (1 per membrane for single-pore membrane studies or 106–108 cm-2 for multi-pore membrane studies). Iontracked PET membranes (12 m thick and 3 cm in diamete r) were also obtained from GSI. Hydrofluoric acid (HF) used to etch the damage tracks in mica was obtained from Acros Organics USA (Morris Plains, NJ). Fo r chemical vapor deposition of carbon, an ethylene/helium mixture (30% ethylene) wa s obtained from Praxair (Danbury, CT). Argon gas was supplied by Airgas South (Kennes aw, GA). Commercial gold electroless plating solution, Oromerse Pa rt B, was obtained from Technic, Inc. (Cranston, RI). Phenol, 3-aminopropyltriet hoxysilane, and 1,1,1,3,3,3hexafluoro-2-propanol were obtained from Sigma-Aldrich (St. Louis, MO). All other chemicals were reagent grade and were used as received from Fisher Scientif ic (Fairlawn, NJ). All solutions were prepared using water that was purified by passing house-distilled water through a Barnstead (Dubuque, IA) E-pure water purification system.

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71 Fabrication of Nanopores by the Track-Etch Method A previously described chemical etching method39, 42, 51 was used to develop the heavy-ion induced damage tracks into asymme tric nanopores. Briefly, PET membranes were placed between the two halves of an etching cell39 as described previously. One side of the membrane was exposed to a NaOH solution while the other side was in contact with a solution that contained 1 M formic acid and 1 M KCl. Platinum wire electrodes were placed in each solution, and a Keithley 6487 picoammeter/voltage source (Cleveland, OH) was used to apply a transmembrane potential of 1 V (with the anode in the NaOH solution) and m easure the resulting current.42 NaOH preferentially etches the damage trac ks in PET. The formic acid solution (stopping solution) present on the other si de of the membrane neut ralizes the etching solution once it traverses the membrane. Etching was terminated by removing and replacing each solution with stopping soluti on. The membrane was then thoroughly rinsed by replacing the stopping so lution with purified water. Mica nanopores were etched in a similar fa shion except a 20 % (v/v) HF solution served as the etching solution and 10 M NaOH as the stopping solution.51 Also a transmembrane potential of 10 V (instead of 1 V) was applied during mica etching.51 Application of a potential dur ing the etching process hel ps shape the nascent nanopore and also allows one to monitor the etching progress.39 The breakthrough of etching solution to the side of the membrane wit h stopping solution is observed by a sudden increase in measured current. For ion-current rectification comparisons and determination of pore zeta potentials, membranes that contained symmetric nanopores were also prepared. This was accomplished by simply exposing each face of the membrane to identical portions of an

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72 appropriate etching solution. Etching was terminated after a certain exposure time by removing the etching solution and placing an appropriate stopping solution on each side of the membrane. These membranes were also rinsed thoroughly by replacing the stopping solution with purified water. Imaging Nanopores In order to compare the ion-current rectification capabilities of mica and PET nanopores, single nanopores with similar geometric characteristics were prepared in each material. Pore geometries were dete rmined by obtaining SEM images of the base openings and pore replicas for multi-pore PET and mica membranes. Ion-current rectification studies were completed with single-pore PET and mica membranes that were etched under the same conditions used to prepare the multi-pore membranes. A Hitachi S-4000 field-emission scanning electron microscope (Tokyo, Japan) was used to observe the base and tip openings of the nanopores. Etched membranes were divided into small pieces and adhered to SEM specimen mounts with the aid of doublesided carbon tape such that the base (lar ge opening) and tip (small opening) sides could be imaged. Pore shape was determined by preparing replicas of the etched tracks through application of the template synthesis9 method. Carbon was deposi ted in the mica pores by a previously described c hemical-vapor deposition method.87 An etched membrane, supported on a quartz stand, was placed into a quartz tube (diameter = 4.5 cm, length = 48 cm). The quartz tube was inserted in to a high-temperature tube furnace (Thermolyne 21100, Aldrich) and heated to 670 C under argon flow. The mica membrane was oriented such that t he base openings faced the gas flow.

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73 When the temperature stab ilized, chemical vapor deposition of carbon was initiated. The argon gas was replaced with a 30% ethylene/helium mixt ure at a flow rate of 20.0 sccm (standard cm3 min-1). After 6 hours of chemical vapor deposition of carbon, the flow was changed back to argon. The fu rnace heater was turned off, and the tube was allowed to cool to r oom temperature. The memb rane was then dissolved in 50% HF to liberate the rhomboi dal graphitic carbon nanotubes.51, 87 The resulting mixture was filtered onto a polycar bonate membrane with 0.08 m pores and was imaged from this surface. Replicas of PET nanopores were pr epared through a previously described electroless gold plating technique.99 After plating for 8 hours, the PET membrane was dissolved in 1,1,1,3,3,3-hexaf luoro-2-propanol to liberate t he gold replicas of the pores.96 The resulting mixture was filter ed onto a porous anodic alumina membrane with 0.1 m pores. Images were obtained from this surface. The pore density of the ~106 pores cm-2 membranes used for EOF studies was measured by etching damage tracks into relati vely large pores (> 300 nm) such that a number of these pores could be observed under low magnification (3000X or less). After etching, the membranes were carefu lly removed from the etching solution and rinsed several times with purified water. Prior to imaging, all samples were s puttered with Au/Pd us ing a Denton Vacuum Desk II cold sputter instrument (Moorestown, NJ). The sputtering current was ~45 mA, the Ar pressure was 75 mTorr, and the sputtering time was 30 seconds.

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74 Current–Voltage Curve Measurements Each face of the membrane (still mounted in the etching cell) was exposed to identical portions of an electrolyte solution (pH 7.4). A silver/silver chloride electrode (Bioanalytical Systems, West Lafayette, IN) was pl aced into each solution portion, and a current–voltage ( I–V ) curve was obtained by scanning the pot ential from -2 .0 V to +2.0 V in increments of 0.05 V (or -10.0 V to +10.0 V in increments of 0.25 V) every 2 seconds with a Keithley 6487 picoammeter/voltage source. The electrodes were configured such that the electr ode in contact with the soluti on adjacent to the tip served as the reference. Tip size was estimated by measuring the membrane conductance (Equation 1-2) from the I–V response. 1 M potassium ch loride with 10 mM phosphate buffer was selected as the electrolyte to minimize the effects of the electrical double-layer on the membrane conductance. With this hi gher electrolyte concentration, the I–V curve is linear with a slope that is relat ed to the membrane conductance, G (Equation 1-2). The resistance for a membrane that contains a single pore is much higher than the cell resistance (which is determined by measur ing the conductance without the membrane present). Therefore, the m easured conductance (slope of the I–V curve) is directly related to the membrane conductance for single-pore membranes. Zeta Potential Measurements Ion-current rectification is determined (at least in part) by surface charge density. Surface charge is closely related to zeta () potential.132, 184 This quantity is defined as the potential at the boundary (shear plane) between the charged surface and the electrolyte solution.185 The location of this boundary is somewhat arbitrarily defined.185

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75 However, it is identified as the plane at whic h the mobile portion of the diffuse layer can “slip” or flow past the charged surface.185 The potentials of the nanopore walls we re calculated by measuring the electroosmotic flow (EOF) velocity of a neutral probe molecule51, 186-190 across membranes that contained ~106 symmetric pores cm-2. In this study, phenol served as the EOF probe. A nanopore-containing membr ane (still mounted in the etching cell) was exposed to the electrolyte solution on one side (permeate side) and electrolyte solution to which 10 mM phenol had been ad ded on the opposite side (feed side). Due to the design of the etching cell,42 a 0.79 cm2 portion of each membrane face was directly in contact with the solution. A platinum wire electrode was plac ed in each solution, and a constant transmembrane current was supplied usin g a Solartron SI1287 electrochemcial interface (Hampshire, England). Si nce the pore walls of both the mica59, 134, 191 and PET membranes possess negative surface charge, the direction of EOF was from the anode toward the cathode. Thus, the galvanosta t was configured such that the working electrode (anode) was housed in the feed side and the reference/counter electrode (cathode) was located on the permeate side. As per previous work,51, 186, 187, 189 the EOF rate was dete rmined from the rate of phenol transport, which was interpreted by m easuring the absorbance of the solution on the permeate side. The permeate solution was continuously pumped through a flowthrough quartz cell using an Agilent peristalt ic pump 1FS (Waldbronn, Germany). The UV absorbance of phenol in the permeate solution was measured by an Agilent 8453 UV-visible spectroscopy system. The conc entration of phenol in the permeate solution

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76 was calculated using a calibration curv e prepared from m easurements of the absorbance maximum at a wavelength of 270 nm. Oxidation of Single-Pore PET Membranes Since ion-current rectificati on is related to surface charge, an attempt was made to increase the number of surface carboxyl ate groups (and, consequently, the surface charge density) in single-pore PET membranes. The etching process results in the formation of both surface carboxylate and surf ace alcohol groups (Fi gure 1-6). Alcohol groups can be oxidized to carboxylat e groups upon exposure to a permanganate solution.80 Following the work of Marchand-Brynaert et al.,80 track-etched membranes were exposed to a 5% (w/w) soluti on of potassium permanganate (KMnO4) in 2 M sulfuric acid (H2SO4) at room te mperature (21oC) for 24 hours. Exposu re to permanganate took place while the membrane was still mounted in t he etching cell, placed in a Petri dish, or mounted in a glass U-cell. During the c ourse of the reaction, a brown manganese dioxide (MnO2) layer forms on the surface of the PET membrane. Upon completion, the layer was removed by rinsing and gently sw abbing the membrane with 6 M hydrochloric acid (HCl). The membrane was then rinsed with purified water and remounted in the etching cell (or in a glass U-cell) so that I–V curves could be recorded. Modification of Single-Pore Mica Me mbranes with an Amine Silane Researchers have demonstrated that the direction of ioncurrent rectification in polymer nanopore membranes54, 67 and quartz nanopipettes183 can be reversed by reversing the polarity of the surface charge. Positive surface charge can be achieved by functionalizing the surface with an amine.54, 67 Since mica pore walls possess

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77 surface silanol groups,58, 134 track-etched mica membra nes were modified with 3aminopropyltriethoxysilane.58 A mixture of 5% (v/v) 3aminopropyltriethoxysilane and 5% (v/v) 50 mM acetate buffer (pH 5.2) in ethanol192 was added to each side of t he track-etched single-pore mica membrane. Platinum wire electrodes we re placed in each solution, and a Keithley 6487 picoammeter/voltage source was used to apply a transmembrane potential of 0.5 V (with the anode in the soluti on on the base side of the membrane). The current was monitored to ensure that t he pore would not become block ed. After ten minutes, the silane solutions were removed and repl aced with ethanol once followed by purified water three times to rinse the membrane. T he resulting reaction should result in the presence of amine-terminat ed groups on the pore walls.58, 192 I–V curves were then recorded to determine the effect of surface m odification on the ion-current rectification capabilities of the si ngle-pore membrane. Results and Discussion Pore Characterization SEM images of asymmetric pores produced in PET are compiled in Figure 3-1. The diameter of the base opening (Figure 31A) for the asymmetric PET nanopores was found to be 420 ( 49) nm based on the measurement of 8 pores A gold replica of an asymmetric PET nanopore is depicted in Figure 3-1B. The length of the gold replicas was measured to be 12.2 ( 0.7) m (based on the measurement of four replicas), which coincides we ll with the membrane thickness (~12 m). The cone angle was determined to be 1–2o, which is in agreement wit h the cone angle reported for

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78 asymmetric pores prepared in PE T by the track-etch method.39 Tip diameter was found to be ~30 nm (Figure 3-1C). The length of the long axis for the bas e opening (Figure 3-2A) of the mica nanopores was found to be 330 ( 12) nm (w hich corresponds to an equivalent diameter of ~200 nm) based on the measurement of 25 pores. Figure 3-2B shows a carbon replica of an asymmetr ic mica nanopore. Based on the measurement of four such replicas, the pore length was found to be 9.0 ( 0.7) m, which is in agreement with the membrane thickness (~10 m). Like the asymmetric PET pores, the cone angle for the asymmetric mica pores was determined to be 1–2o. Again, similar to the asymmetric PET pores, tip size for the asym metric mica pores was found to be ~30 nm (Figure 3-2C). Ion-Current Rectification Studies I–V responses of the membranes in an electr olyte of relatively high concentration (1 M KCl with 10 mM phosphate buffer at pH 7.4) are presented in Figure 3-3A. In addition to the PET and mica membranes that contain single nanopores of similar geometry, results for a mica membrane t hat contains a single symmetric nanopore and a PET membrane that contains a larger asymmetric nanopore are also included for comparison. Figure 3-3A shows that the asymmetric mica nanopore clearly rectifies ion-current in the electrolyte solution of high concentration. Moreover, the current that passes through the asymmetric mica nanopore is higher than that which passes through the analogous asymmetric PET nanopore (of simila r geometry). Due to the fact that the PET membranes used in these studies are somewhat thicker than the mica membranes (12 m compared to 10 m), the mica nanopore is expe cted to exhibit a lower

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79 resistance. However, this resistance diffe rence cannot completely explain the large difference between the current displayed by the mica and PET na nopores in Figure 33A. With a transmembrane potential difference of +2 V, the asymmetric mica nanopore passes ~7 times more current than the PET nanopore of similar geometry. For a transmembrane potential difference of -2 V, the difference in current is even more profound; the mica nanopore passes ~24 times mo re current than the PET nanopore. For this reason, results from a larger a symmetric PET nanopore were also included in Figure 3-3A for comparison. The lar ger asymmetric PET nanopore was etched according to a previous report42 and was determined to possess a base opening of 520 ( 45) nm and a tip opening of 38 ( 3) nm With positive potentials, this larger asymmetric PET nanopore passes a current that is similar to those presented by the asymmetric mica nanopore (Figure 3-3A). Ion-current rectification is often described in terms of the rectification ratio,54, 67 which is simply the absolute value of the current at a potential of a given magnitude divided by the current at the potential of the same magnit ude but opposite polarity (i.e., | I(-V)/I(+V) |). The dependence of rectification ra tio on applied transmembrane potential for the single-nanopore membranes used in this study is depicted in Figure 3-3B. Of course, a rectification ratio of one is observed (as expected) at all pot entials for the mica membrane that contains a single symmetric nanopore (Figure 3-3B). The membranes that contain single asymmetric PET nanopores also yield rectification ratios near one throughout the selected potential range. This too is expected as I–V curves obtained in 1 M KCl are typically deemed to be linear enough such that the slope can be used to

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80 determine tip size (Equation 1-2).39, 42 Only the asymmetric mica nanopore membrane exhibits rectification ratios much different than one (Figure 3-3B). I–V responses for the single-nanopore me mbranes in 0.1 M KCl with 10 mM phosphate buffer (pH 7.4) are presented in Figur e 3-4A. Again, the asymmetric mica nanopore passes higher current s than does the asymmetric PET nanopore of similar geometry. At positive trans membrane potentials, the lar ger asymmetric PET pore passes currents that are similar to those exhibited by the asymmetric mica nanopore (Figure 3-4A). However, at negative potentia ls the currents passed by the asymmetric mica nanopore are again much higher than any of the other pores used in these studies. Ion-current rectification ratios for the single-nanopore membranes in 0.1 M KCl with 10 mM phosphate buffer (pH 7. 4) are shown as a function of potential in Figure 34B. As expected, the membrane that c ontains the single symmetric mica nanopore again produced a rectification ratio of approxim ately one for all potentials used in this study. Both asymmetric PET nanopores rectif y ion current to some degree. However, the larger asymmetric PET nanopore rect ifies ion current less than the smaller asymmetric PET nanopore. The ion-current rectification rati o for the larger asymmetric PET nanopore is 3.3 ( 0.2) at 2 V, while the ion-current rect ification ratio for the smaller asymmetric PET nanopore is 7.3 ( 0.1) at 2 V (Figure 3-4B). The asymmetric mica nanopore is a better ion-current rectifier than the asymmetric PET nanopores and exhibits a rectification ratio of 23 ( 1) at 2 V (Figure 3-4B). The asymmetric mica nanopore was compar ed to an asymmetric PET nanopore of similar geometry in an attempt to attribute any differences in ion-current rectification to

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81 differences in the cross-sectional openi ng shapes. However, since ion-current rectification is related to pore geometry, surf ace charge, and electrolyte composition, it is difficult to determine exactly why t he asymmetric mica nanopore displays better rectification capabilities. Surface charge density for mica nanopores is governed by silanol groups on the pore walls, whereas su rface charge density for PET nanopores is attributed to carboxylate gr oups. Many researchers hav e used experimental methods and theoretical calculations to determine the surface charge densities of mica and PET. However, the values reported in literature for such quantities vary widely (Chapter 1).59, 80, 81, 86, 118-120, 130-135 For example, the surface charge densit y values reported for PET membranes using electrokinetic measurements (str eaming current, str eaming potential, and electroosmosis) range from -0.0133 e nm-2 to -0.125 e nm-2.131, 132, 135 Electrokinetic measurements on mica membranes have yiel ded surface charge density values in the range of -0.00625 e nm-2 to -0.0521 e nm-2.59, 86, 134 In contrast, pore conductivity measurements performed on PET membranes led to surface charge density values of approximately -0.5 e nm-2,130, 135 while similar measurements carried out on mica membranes resulted in surface charge dens ity values that ranged from -0.031 e nm-2 to -0.106 e nm-2.59, 134 The widely accepted118, 122, 123, 136, 137 surface charge density for PET membranes (-1 e nm-2) is higher than most experimentally determined values and was determined by PNP-based modeling of experimental data.115, 117, 120, 123 Several recent publications have shown that PNP theory pr edicts that ion-current rect ification is highly dependent on pore geometry and surface charge distribution.117, 119, 123, 140 These findings seem to

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82 undermine the certitude of the accepted PET surface charge density value (-1 e nm-2). PNP theory has not yet been us ed to model experimental I–V data for asymmetric mica nanopores. Zeta Potentials of Multi-Pore PET and Mica Membranes Measured by EOF In an attempt to obtain a more direct comparison between the surface charge densities of mica and PET nanopores, EOF experiments were used to determine the zeta () potentials of the pore wall s for the two materials. In accordance with previous studies,51, 186, 187, 189 electroosmotic flow velocities ( veof) were measured by monitoring the current-assisted transport of a neutral molecule (pheno l) through the membranes. Analogous experiments were completed in the absence of applied current to determine the rate of diffusion ( Ndiff). Ni (the rate of transport with applied current i ) and Ndiff were used to calculate the enhancement factor, E :51, 189, 193 diff iN N E / (3-1) which was required to determine the Peclet number, Pe :51, 189, 193 ) 1 (Pee Pe E (3-2) The relationship between Pe and veof is51, 189, 193 L D Pe veof (3-3) where D is the diffusion coefficient for phenol and L is the pore length (or, equivalently, the membrane thickness). Finally, the potential of the por e walls can be determined from the following equation:189 / J vapp eof (3-4)

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83 where , and are the permittivity, resistivity, and viscosity of the solution, respectively. For potential measurements, PET and mica membranes that contained comparable symmetric pores and pore densities (~106 cm-2) were prepared. Similarity between the PET and mica membranes wa s confirmed by comparing their I–V responses (Figure 3-5). Typical phenol tr ansport data generated with the PET and mica membranes are depicted in Figure 3-6. The diffusion transport rates of phenol thro ugh each membrane were very similar– 0.21 ( 0.02) nmol min-1 with the mica membrane and 0.23 ( 0.02) nmol min-1 with the PET membrane. However, the mica nano pore membrane displayed much higher EOF transport rates than those ex hibited by the PET nanopore membrane (Figure 3-7). Electroosmotic flow velocities (Figure 38) were calculated from Equation 3-3 and phenol transport data (Figure 37). It is again important to note that the PET membranes were slightly thicke r than the mica membranes (~12 m compared to ~10 m). However, the difference in thickness cannot completely account for the difference in EOF velocity (Figure 3-8). Since veof is proportional to potential (Equation 3-4), these data seem to support the conclusion that the nanopores in mica possess higher a surface charge density than those in PET. To calculate potential from Equation 3-4, the so lution resistivity must be known. In this case, solution resistivity () was determined from the I–V responses of the membranes (Figure 3-5B). Under the a ssumption that the pores behave as parallel resistors, can be determined by invoking the equation for membrane conductance, G (Equation 1-2).

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84 L d A n G 42 (3-5) where n is the pore density (cm-2) and A is the area of the membrane (cm2) that contains pores and is exposed to solution (0.79 cm2 in these studies). Therefore, the product nA gives the total number of pores thr ough which current ma y be transported. L again refers to the membrane thickness, and d is the pore diamet er (or equivalent diameter for mica pores – Equation 1-1). Due to the lower resistance of multipore membranes compared to single-pore membranes (that contain pores of comparable diameter), it is often necessary to compensate for the contribution of the cell resistance (resist ance of the cell without the membrane present) to the meas ured resistance (inverse of conductance). Here, this was done by obtaining I–V curves of the electrolyte so lutions in the absence of any membrane. Thus, G was determined by the experimentally measured quantities Gtotal (slope of the I–V curve obtained with the membrane in place) and Gcell (slope of the I–V curve obtained in the absence of any membrane). total cell cell totalG G G G G (3-6) By noting that Japp is the applied current, Iapp, divided by the total pore area (the total number of pores multipli ed by the area of a single pore) Equations 3-4 to 3-6 can be combined and rearranged to obtain the following relationship for potential: app total cell eof cell totalI G G L v G G (3-7) Gcell was found to be 205.7 ( 0.8) S for the 10 mM phosphate bu ffer solution that was used for EOF experiments. Gtotal obtained for the mica membrane was 46 ( 2) S in

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85 this same solution (Figure 3-5B), while Gtotal for the PET membr ane was 53 ( 0.8) S under the same conditions (Figure 3-5B). Values for potential obtained with each applied current are collected in Table 31. The mica membrane exhibits a higher potential than the PET membrane. Using the slope of veof versus Iapp (Figure 3-8) in Equation 3-7, the potential is -33 ( 6) mV for the mica membrane and -6 ( 1) mV for the PET membrane. Surface charge density s can be estimated from potential with the Gouy– Chapman equation:106, 131, 132, 184 T k e e c NB A s2 sinh 41 (3-8) where NA and c are the Avogadro constant and bulk concentration of the electrolyte, respectively; e is the elementary charge; -1 is the Debye length (Equation 1-3); kB and T are the Boltzmann constant and temperature, respectively. Surface charge density values for the mica and PET membranes ar e collected in Table 3-1. Using the potentials determined by the slopes of the veof versus Iapp plots (Figure 3-8), the surface charge density values for the mica and PET me mbranes used in this study are -0.05 ( 0.01) e nm-2 and -0.009 ( 0.001) e nm-2, respectively. The membranes used in this study possessed similar pore densities (~106 cm-2), exhibited similar I–V responses, and yielded similar di ffusion transport ra tes. Thus, these results suggest that the pore walls of mica nanopores are more highly charged than those of comparable PET nanopores. However, the above analysis ignores pore shape and surface conductance effects.

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86 Berezkin et al. employed an analogous strategy (to that which is described above) to calculate the surface charge densities of PET membranes with pores as small as 20 nm in diameter.131 However, many authors have c oncluded that the above analysis is sufficient only when the ratio of pore radi us to Debye length (also known as the dimensionless electrokinetic radius) d/2 is >> 1.184, 194-201 This is because the electrical double-layer, which extends from the charged pore walls (Figure 1-13), overlaps inside the pores (to some extent) if the electr okinetic radius is ~1 or less. To determine the electrokinetric radii for the mica and PET membranes used in this study, pore sizes were determined by membrane conductance measurements (Equations 3-5 and 3-6). For the mica membrane, the por e density was found to be 1.0 ( 0.1) x 106 pores cm-2 by SEM measurements. The pore density of the PET membrane was slightly lar ger at 2.8 ( 0.3) x 106 pores cm-2. With this information, pore size can be estimated from the I–V curve obtained in 1 M KCl, pH 7.4 (Figure 3-5A) for each membrane (Equations 3-5 and 3-6). By this analysis, t he estimated diameter of a pore in the PET membrane is 24 ( 3) nm and the estimated equivalent diameter of a pore in the mica membrane is 55 ( 7) nm (meaning that the length of the long axis of the rhomboidal opening is 91 ( 12) nm). Th ough it was difficult to image pores of such small dimensions, SEM images seem to corre spond with the estimated sizes (Figure 39). From these pore size meas urements, the dimensionles s electrokinetic radii (d/2) are ~9 and ~4 for the mica and PET membranes, respectively. Many researchers have suggested corrections to account for double-la yer overlap in electrokinetic transport through small capillaries.184, 194-201 Employing a theory developed by Rice and

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87 Whitehead,198 Djardin et al. repor ted that the measured potential is related to the true potential (true) by132 2 / 2 / 2 / 2 / 1 1 12 0 2 1 2 2 2d F d I d I d Ftrue true (3-9) where 2 / 2 / 2 / 2 1 2 /0 1d I d d I d F (3-10) I1 and I0 are the zero-order and first-order modifi ed Bessel functions of the first kind, respectively; and is the resistivity of the electrolyte. The bulk resistivity of the 10 mM PBS electrolyte was measured to be 6.8 m with a conductivity meter (YSI, Yellow Spri ngs, OH). For the analyses here, however, was calculated from I–V data (Figure 3-5B) and Equations 3-5 and 3-6. The calculated for the electrolyte in each membrane was lower than the measured bulk resistivity. These values are 3.2 ( 0.5) m and 1.2 ( 0.2) m for the mica and PET membranes, respectively. According to Djardin et al. 4 4 2 14 3 2 1u u u u u F (3-11) and 4 8 34 3 2 1 2 0 2 1u u u u u I u I u F (3-12)

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88 Truncation of the above series to the fourth order leads to approximations that deviate from the actual values by ~2 % or less for an electroki netic radius less than ~3 (and even lower deviations for a larger electrokinetic radius value).132 Values for true are determined by inco rporating the measured potentials (Table 3-1) into Equations 3-9 to 312. These values are assembl ed in Table 3-2. Using the potentials that were calc ulated from the slopes of veof versus Iapp plots (Figure 3-8), true values are -44 ( 7) mV and -11 ( 2) mV for the mica and PET membrane, respectively. Corresponding surface charge density values (Equation 3-8) are -0.07 ( 0.01) e nm-2 for the mica membra ne and -0.016 ( 0.003) e nm-2 for the PET membrane. Again, the physical soundness of these values is difficult to ascertain due to the fact that pore shape effects are ignored in this analysis. The surface charge density values reported for mica and PET membrane s here are certainly within the limits reported in literature, where surface charge density values differ by at least an order of magnitude for each material (Chapter 1). It is also conceded that these analyses are inherently deficient due to t he relatively complex electrol yte used for these EOF studies (10 mM PBS). Most membrane transport theories simplif y the Poisson–Boltzmann equation by assuming a symmetric (1:1) electrolyte.184, 197, 198 The Gouy–Chapman equation (Equation 3-8) is only truly valid for 1:1 electrolytes. Furthermore, the Rice and Whitehead theory198 employed here (and previously132 by Djardin et al.) is based on the Debye–Hckel approximatio n of Poisson–Boltzmann equat ion. This approximation is deficient for high values of pore wall potential (> 25 mV).194, 197, 202

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89 Ion-Current Rectificat ion of Oxidized Single-Pore PET Membranes It is difficult to determine whether diffe rences in surface charge density or pore shape play a more important role in the diffe rences between the ioncurrent rectification capabilities of asymmetric mica and PET nanopore membranes. T herefore, an attempt was made to increase the surface charge density of single-pore PET membranes so that the effect of surfac e charge on ion-current rectif ication could be directly investigated. Marchand-Brynaert et al. repor ted that the carboxyl ate density of tracketched PET membranes could be increased from ~30 pmol cm-2 (which corresponds to a charge density of -0.18 e nm-2) to ~50 pmol cm-2 (-0.30 e nm-2) upon permanganate oxidation.80 Permanganate oxidizes alcohol chain ends that result from etching (Figure 1-6) to carboxylate groups. Figure 3-10 shows the I–V response for an asymmetric PET nanopore (dbase ~520 nm and dtip ~34 nm) before and after oxidation. The nanopore clearly exhibits better ion-current rectification after oxidation. Ion-current rectif ication ratios obtained in the lower concentration electrolyte (0.1 M KCl with 10 mM PBS) before and after oxidation are plotted in Figure 3-11. Before oxidati on the nanopore displays a rectification ratio of 2.31 ( 0.01) at 2 V (Figure 311). After oxidation the ion-cu rrent rectification ratio at 2 V is 5.1 ( 0.2), more than two times higher than t he pre-oxidation value. While the increase in ion-cu rrent rectification observed in Figures 3-10 and 3-11 is attributed to an increase in charge densit y due to oxidation of alcohol groups to carboxylates, it must be noted that this desired result was not always observed in single-pore membranes. Figure 3-12 shows the I–V responses for three other singlepore PET membranes obtained before and after oxidation. Two pores used to obtain the data in Figure 3-12 possessed bas e (~520 nm) and tip (~32 nm and ~36 nm)

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90 diameters (parts A-D of Figur e 3-12) that were similar to those of the pore used in Figures 3-10 and 3-11. Like the pore in Fi gure 3-10, these two pores show little change before and after oxidation in 1 M KCl with 10 mM PBS (Figure 3-12A and 3-12C). However, in 0.1 M KCl with 10 mM PBS, both pores show more of an increase in the “off” state current (current obtained at positive potentials ) than was observed with the pore in Figures 3-10B and 3-11. Consequently, oxi dation only slightly increases the ioncurrent rectification capabilities of t hese two pores (Figure 3-13A and 3-13B). Figures 3-12E and 3-12F depict data obtai ned for a larger asymmetric PET nanopore (dbase ~520 nm and dtip ~57 nm). In contrast to the data obtained for the pores described above, the data obt ained for this larger pore a fter oxidation show that a larger current was passed in the 1 M KCl wi th 10 mM PBS electrolyte (Figure 3-12E). However, lower currents were observed afte r oxidation for the 0.1 M KCl with 10 mM PBS electrolyte (Figure 3-12F). Figure 3-13C shows that oxidation increased the ioncurrent rectification capabilit ies of this larger pore. The reasons for the range of behaviors that were observed after oxidation are not immediately clear. However, simulati on studies have shown that ion-current rectification is sensitive to surface charge inhomogeneity.123, 203 Moreover, oxidation of the alcohol groups on PET with permanganate leads to the formation of manganese dioxide (due to the r eduction of permanganate).80 Oxidized membranes became coated with this thin brown metal oxide film. Though the manganese dioxide layer could be easily removed from the each face of t he membrane by exposure to a dilute hydrochloric acid solution, successful re moval of manganese dioxi de from the pore wall is difficult to validate. Mo reover, the complexity of the oxidation reaction (due to the

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91 inherent formation of manganes e dioxide) may have contri buted to irreproducibility issues. Regardless, oxidized PET membrane s that contained single asymmetric pores were still unable to match the ion-current rectification capabi lities of the single asymmetric mica nanopore membrane (Figures 3-3 and 3-4). Ion-Current Rectification of Amine -Modified Single-Pore Mica Membranes Modification of the mica pore walls with an amine-silane imparts a more positive surface charge (Figure 3-14). As depicted in Figure 3-14A, the modification of the single-pore mica membrane with an amine-silane led to a loss of rectification when the pH of the electrolyte solution was 7.4. In th is electrolyte solution, the rectification ratio at 2 V, |I(-2 V)/I(+2 V)|, was 22 ( 2) before modifica tion and 11.5 ( 0.4) after modification (Figure 14A). If the surface charge was co mpletely converted from negative to positive after modification, one woul d expect the rectification ratio at 2 V to be 0.045 (or 1/22).141 Though not all surface silanol groups appeared to become successfully modified with the amine from Figure 3-14A, the I–V response of the single-pore mica membrane in pH 2.0 (Figure 3-14B) shows that pos itive charge was definitely present on the membrane after amine modification. In this electrolyte, the rectification ratio at 2 V was 0.84 ( 0.05) before modification and 0.084 ( 0.04) after modification (Figure 3-14B). At pH 2.0, the surface char ge is somewhat positive even before modification with the amine (as indicated by the rectificati on ratio < 1 described above). The apparent positive surface charge of mica pores in so lutions of pH < 4.5 has been previously noted134 and has been ascribed to the amphiprot ic character of silanol groups (i.e., silanol groups may be protonated to yield SiOH2 +).191

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92 Summary In order to take advantage of the ion-current rectificati on capabilities of single-pore membranes to develop sensors, it is desir able to produce such membranes that are able to rectify ion current to a high degree. This permits changes in rectification to occur over a large scale, thus provid ing an adequate response range that would be required for a sensor.141 For example, if a pore exhibi ts a rectification ratio of 5, complete conversion of surface charge sign woul d result in a rectification ratio of 1/5 – a 25 fold difference.141 This is preferred over the 4 fold difference that one would obtain (for the same complete charge conversion scenar io) with a pore that initially exhibits a rectification ratio of 2. As shown in these studies, mica memb ranes that contain single asymmetric nanopores seem to exhibit better ion-current rectification capabilities than analogous asymmetric nanopores prepared in PET memb ranes. Additionally, the crystalline structure of mica may offer advantages over the polymer PET. For example, some authors have contended that PET nanopores often exhibit current fluctuations due to dangling polymer chain ends on the pore walls.66 It must also be noted, however, that nanopores produced in polyimide (Kapton) films by the track-etch method do not seem to suffer from such current fluctuations (presumably because the surface carboxylates that result upon etching polyi mide are stabilized by the more rigid aromatic ring structure of the Kapton polymer chains66). Recently, Vlassiouk and Siwy have show n that the ion-curr ent rectification capabilities of single asymmetric nanopores in PET can be enhanced by selective modification of portions of the pore walls.67 Diffusion-controlled modification143 of a portion of the pore wall with an amine group results in t he formation of a bipolar

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93 nanofluidic diode. Bipolar nanofluidic diodes67, 141 exhibit ion-current rectification properties similar to those of the single asymmetric mica nanopore presented in these studies. An analogous surface modifi cation strategy based on silanization58, 59 may be developed to improve the alr eady impressive ion-current rectification capabilities of asymmetric mica nanopores.

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94 Figure 3-1. SEM images of asymmetric nanopores etched in PET. A) Image of a base opening. B) Image of a gold replica of an asymmetric pore in PET. C) Image of tip openings. Figure 3-2. SEM images of asymmetric nanopores etched in mica. A) Image of base openings. B) Image of a carbon replica of an asymmetric pore in mica. C) Image of a tip opening.

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95 Figure 3-3. I–V responses and rectification ratios for single-pore mica and PET membranes obtained in 1 M KCl, 10 mM PBS (pH 7.4). A) Average I–V responses for asymmetric nanopores of similar geometry in mica (solid blue line) and PET (solid orange line). I–V responses for membranes that contain a larger asymmetric PET nanopore (dashed orange line) and a symmetric mica nanopore (dashed blue line) are al so shown for comparison. B) Dependence of rectification ratio on tr ansmembrane potential for asymmetric nanopores of similar geometry in mica (solid blue diamonds) and PET (solid orange squares). Rectification ratios for membranes that contain a larger asymmetric PET nanopore (open orange squares) and a symmetric mica nanopore (open blue diamonds) are show n for comparison. Error bars represent one standard deviation. M easurements were performed in triplicate.

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96 Figure 3-4. I–V responses and rectification ratios for single-pore mica and PET membranes obtained in 0.1 M KCl, 10 mM PBS (pH 7.4). A) Average I–V responses for asymmetric nanopores of similar geometry in mica (solid blue line) and PET (solid orange line). I–V responses for membranes that contain a larger asymmetric PET nanopore (dashed orange line) and a symmetric mica nanopore (dashed blue line) are al so shown for comparison. B) Dependence of rectification ratio on tr ansmembrane potential for asymmetric nanopores of similar geometry in mica (solid blue diamonds) and PET (solid orange squares). Rectification ratios for membranes that contain a larger asymmetric PET nanopore (open orange squares) and a symmetric mica nanopore (open blue diamonds) are show n for comparison. Error bars represent one standard deviation. M easurements were performed in triplicate.

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97 Figure 3-5. I–V responses and rectification ratios for multi-pore mica and PET membranes used in the zeta potential studies. A) Average I–V responses obtained in 1 M KCl with 10 mM PBS (pH 7.4) for mica (solid blue line) and PET (solid orange line) membranes t hat contain symmetric nanopores (~106 cm-2). B) Average I–V responses obtained in 10 mM PBS (pH 7.4) for mica (solid blue line) and PET (solid orange line) membranes that contain symmetric nanopores (~106 cm-2).

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98 Figure 3-6. Absorbance of the solution on the permeate side of the symmetric-pore (~106 cm-2) membranes used in the zeta potential studies. A) Absorbance corresponding to phenol transport by EO F through the mica membrane. B) Absorbance corresponding to phenol tr ansport by EOF through the PET membrane. A transmembrane current of 100 A was applied in each case.

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99 Figure 3-7. Translocation of phen ol through the symmetric-pore (~106 cm-2) membranes used in the zeta potential studies. A) Phenol transport through the mica membrane. B) Phenol trans port through the PET membrane. Data are labeled with the corresponding tr ansmembrane current used to assist transport.

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100 Figure 3-8. Effect of applied current on electroosmotic flow velocity through the symmetric-pore (~106 cm-2) membranes used in the zeta potential studies. Data for the mica (solid blue di amonds) and PET (solid orange squares) membranes are shown together. Error bars represent one standard deviation. At least three measurements of electrosmotic flow velocity were obtained with each current. Table 3-1. Zeta potentials and surface c harge densities for mica and PET membranes calculated from electroosmotic flow data. Current (A) mica (mV) mica (e nm-2) PET (mV)PET (e nm-2) 25 -37 ( 6) -0.06 ( 0.01 ) -10 ( 1) -0.014 ( 0.001) 50 -38 ( 6) -0.06 ( 0.01) -9.1 ( 0.9)-0.013 ( 0.001) 75 -39 ( 6) -0.06 ( 0.01) -8 ( 1) -0.011 ( 0.001) 100 -39 ( 6) -0.06 ( 0.01) -7.4 ( 0.9)-0.011 ( 0.001) 200 -35 ( 5) -0.054 ( 0.009)-6.0 ( 0.7)-0.009 ( 0.001) 300 -31 ( 5) -0.047 ( 0.009)-5.5 ( 0.7)-0.008 ( 0.001) Table 3-2. Corrected zeta potentials and surface charge densities for mica and PET membranes calculated from electroosmotic flow data. Current (A) mica (mV) mica (e nm-2) PET (mV)PET (e nm-2) 25 -49 ( 8) -0.08 ( 0.02)-18 ( 3)-0.026 ( 0.005) 50 -51 ( 8) -0.09 ( 0.02)-16 ( 3)-0.023 ( 0.005) 75 -52 ( 8) -0.09 ( 0.02)-15 ( 3)-0.022 ( 0.004) 100 -52 ( 8) -0.09 ( 0.02)-13 ( 2)-0.019 ( 0.003) 200 -46 ( 7) -0.08 ( 0.01)-11 ( 2)-0.016 ( 0.003) 300 -41 ( 6) -0.07 ( 0.01)-10 ( 2)-0.014 ( 0.003)

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101 Figure 3-9. SEM images of the symmetric-pore (~106 cm-2) membranes used in the zeta potential studies. A) Image of a small symmetric mica nanopore. B) Image of a small symmetric PET nanopore. Figure 3-10. I–V responses for a PET membrane that contains a single asymmetric nanopore before and after oxidation. A) Average I–V responses obtained in 1 M KCl with 10 mM PBS (pH 7.4) before ( dotted line) and after (solid line) oxidation. B) Average I–V responses obtained in 0.1 M KCl with 10 mM PBS (pH 7.4) before (dotted line) and a fter oxidation (solid line). Figure 3-11. Ion-current rect ification ratios for a PET me mbrane that contains a single asymmetric nanopore before and after oxidati on. Electrolyte solution is 0.1 M KCl with 10 mM PBS (see Figure 3-10B). Open data points (triangles) correspond to data obtained before oxidation. Filled data points (squares) correspond to data obtained after oxi dation. Error bars represent one standard deviation. Measurements were performed in triplicate.

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102 Figure 3-12. I–V responses for three PET membranes that contain similar single asymmetric nanopores before and after oxid ation. Dotted lines correspond to responses obtained before oxidation. Solid lines correspond to data obtained after oxidation. The base diameter for each nanopore was ~520 nm. The tip diameter for the nanopore used in A) and B) was ~32 nm; in C) and D) was ~36 nm; and in E) and F) was ~57 nm. A), C), E) Average I–V responses obtained in 1 M KCl with 10 mM PBS (pH 7.4). B), D), F) Average I–V responses obtained in 0.1 M KCl wi th 10 mM PBS (pH 7.4).

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103 Figure 3-13. Ion-current rect ification ratios for three PET membranes that contain similar single asymmetric nanopores befor e and after oxidation. Electrolyte solution is 0.1 M KCl with 10 mM PBS (F igure 3-12B,D,F). Open data points (triangles) correspond to data obtained before oxidation. Filled data points (squares) correspond to data obtained after oxidation. The base diameter for each nanopore was ~520 nm. The tip di ameter for the nanopore used in A) was ~32 nm; B) was ~36 nm; and C) was ~57 nm. Error bars represent one standard deviation. Measurements were performed in triplicate. Figure 3-14. I–V responses for a mica membrane t hat contains a single asymmetric nanopore A) before and B) a fter surface modification with an amine. Dotted lines correspond to responses obtained before amine modification. Solid lines correspond to data obtained after amine modification. Electrolyte solutions consisted of 0.1 M KCl with 10 mM phosphate buffer with pH A) 7.4 and B) 2.0.

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104 CHAPTER 4 EFFECT OF TRANSMEMBRANE CURR ENT ON ELECTROOSMOTIC FLOW RECTIFICATION IN PYRAMID AL-PORE MICA MEMBRANES Motivation Recently, the interesting transport proper ties of conical nanopores have garnered much attention. Due to the difference in cross-sectional area between each opening end of a conical nanopore, such pores may s how a preference for the direction in which a transmembrane current flows. In other words, the curr ent flowing through a pore may be higher (or lower) depending not only on the magnitude of the transmembrane potential (as expected) but also the polarit y. This phenomenon, known as ion-current rectification,110 is characterized by an asymmetric current–potential response and has been the subject of several theoretical69, 111-113, 115-117, 120-123, 137, 140, 203, 204 and experimental52-56, 60-62, 64, 65, 69, 115, 125, 138, 179, 205 studies with conical nanopores. Electroosmotic flow (EOF) is an electr okinetic phenomenon that results when an ionic current passes through a channel or porous medium that contains excess surface charge.127, 185 Building on previous work,51 we show here the effect of applied transmembrane current on EOF through mica me mbranes that have asymmetric pores. Although nanopores in mica membranes po ssess rhomboidal (instead of circular) openings, we have previously described a method51 to produce mica pores that vary in cross-sectional area along their central axes The resulting pyramidal nanopores are analogous to conical nanopores in that they too exhibit ioncurrent rectifying capabilities (Chapter 3). Moreover, we have shown t hat EOF through membranes containing such pores is also rectified. Here, we inve stigate the effects of applied transmembrane current and membrane pore density on EOF re ctification. These studies have been

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105 completed by monitoring the (transmembrane-cu rrent-assisted) transpor t rate of a small neutral molecule (phenol) across pyramidal-pore mica membranes. Experimental Materials Muscovite mica (KAl2(AlSi3)O10(OH)2) membranes (10 m thick and 3 cm in diameter) were obtained from Spruce Pine Co (Spruce Pine, NC). Using the linear accelerator (UNILAC) at GSI (Darmstadt, Germany), these membra nes were irradiated with heavy ions (11.4 MeV/nucle on) to induce damage tracks (~106–107 cm-2). Hydrofluoric acid (HF) used to etch the damage tracks was obt ained from Acros Organics (Morris Plains, NJ). For c hemical vapor deposition of carbon, an ethylene/helium mixture (30% ethylene) wa s obtained from Praxair (Danbury, CT). Argon gas was supplied by Airgas South (Kennesaw, GA). Phenol was obtained from Sigma-Aldrich (St. Louis, MO). All other chemicals were reagent grade and used as received from Fisher Scientific (Fairlawn, NJ). All solutions were prepared using water that was purified by passi ng house-distilled water through a Barnstead (Dubuque, IA) Epure water purification system. Etching Pyramidal Nanopores A previously described chemical etching method51 was used to develop the heavyion induced damage tracks into pyramidal nanopores. The etching method is analogous to those that have been used to pr epare conical nanopores in polymer films by the track-etch method.39, 42, 66 Briefly, the mica me mbrane was placed between the two halves of an etching cell39 as described previously.51 One side of the membrane was exposed to a 20% (v/v) HF solution while the other side was in contact with 10 M NaOH. Due to the desi gn of the etching cell,42 the area of mica membrane exposed to

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106 each solution was 0.79 cm2. Platinum wire electrodes were placed in each solution, and a Keithley 6487 picoammeter/voltage sour ce (Cleveland, OH) was used to apply a transmembrane potential of 10 V (with the anode in the HF solution) and measure the resulting current. HF preferentially etches mica along the damage track to create a pore that ultimately breaks through to the NaOH so lution on the opposite side. Breakthrough of the HF to the NaOH was detected by a sudden increase in the ionic current flowing through the membrane. For the 10 m-thick membranes used in these studies, breakthrough time was typically ~50 seconds. At room temperature (21 oC in these studies) NaOH does not etch mica at an appreciable rate, and it neutralizes the HF transported through the nascent pore from the etch solution. As a result, each por e has a small opening (tip) at one face and a large opening (base) at the opposite face. Because mica pores have a rhomboidal cross section,83, 85 these asymmetric pores are pyramidally shaped. A total etch time of 40 min was used, after which the etching and stopping solutions were removed, and the cell and mi ca membrane were rinsed with 1 M NaOH to quench etching. The membranes were then rinsed with water and, for the electrochemical experiments, used immediately without removing from the etching cell. Membrane Characterization Base openings were imaged using a mult imode atomic force microscope (AFM) with a Nanoscope IIIa controller (Digital Inst ruments, Santa Barbar a, CA). Adhesive tabs (Ted Pella, Redding, CA) were used to fasten pieces of etched membranes to AFM specimen discs (Ted Pella). The AFM was operated in tapping mode with high aspect

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107 ratio silicon-SPM-sensor tips (AR10-NCH-10 Nanosensors, Neuchatal, Switzerland). Images were recorded at a scan rate of 0.6 Hz. A Hitachi S-4000 field-emission scanning electron microscope (Tokyo, Japan) was also used to image the rhomboidal base and tip openings and to determine the pore density. Etched membranes were fractur ed into small pieces and adhered to SEM specimen mounts (Ted Pella) using double-sided carbon tape (Ted Pella). Pore shape was investigated by using a template synthesis method9 to prepare replicas of the pores. This entailed c hemical-vapor deposition (CVD) of carbon along the pore walls to make rhomboidal ca rbon nanotubes that mirror the pore shape.87 An etched membrane, supported on a quartz st and, was placed into a quartz tube (diameter = 4.5 cm, length = 48 cm). The quartz tube was inserted into a hightemperature tube furnace (Thermolyne 21 100, Aldrich) and heated to 670 C under argon flow. The mica membrane was oriented such that the base openings faced the gas flow. When the temperature stabiliz ed, carbon CVD was initiated. The argon gas was replaced with a 30% ethylene/ helium mixture at a flow rate of 20.0 sccm (standard cm3 min-1). After 6 hours of carbon CVD, the flow was changed back to argon. The furnace heater was turned off, and the tube was allowed to cool to room temperature. The membrane was then dissolved in 50% HF to liberate the rhomboi dal graphitic carbon nanotubes.51, 87 The resulting mixture was filt ered onto a polycarbonate membrane with 0.08 m pores and was imaged from this surface. Pore density was measured by etching mica with 50% HF on both sides of the membrane to obtain pores with a rhomboidal cross section, but with the same

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108 dimensions down the ent ire length of the pore; i.e., symmetrical pores. Etch times of 15 to 60 minutes were used to obtain lar ge pore openings (long axis > 300 nm). These large openings allow for low magnification images (5000X or less) that show many openings in each image. The pores in 5 or more such images were counted (> 35 pores per image) and the average pore density was calculated. Prior to SEM imaging, all samples were sputtered with Au/Pd using a Denton Vacuum Desk II cold sputter instrument (Moo restown, NJ). The sputtering current was ~45 mA, the Ar pressure was 75 mTorr, and the sputtering time was 30 seconds. Measurement of Tip Size A solution that was 1 M in KCl and 10 mM in pH = 7.4 phosphate buffer was placed on both sides of the mica membr ane. A Ag/AgCl reference electrode (Bioanalytical Systems, West Lafayette, IN) was placed into each solution, and a current-voltage (I–V) curve (associated with ion tr ansport through the pyramidal nanopores) was obtained using a Keithley 6487 picoammeter/voltage source.17, 42, 51 The I–V curve was obtained by stepping the potent ial in 0.05 V increm ents from -2.0 V to +2.0 V; each step was 2 sec, and current was sampled at the end of each step. Similar to I–V curves for nanopores with conical shape,39 the I–V curves for the pyramidal nanopores studied here are linear when high ionic strength (~1 M) solutions are used. The slope of the I–V curve is related to the ionic conductance, G (in Siemens), of the memb rane (Equation 1-2).39 Since the membrane resistance (inverse of conductance) for multi-pore membranes only accounts for a portion of the total measured resistance, the slope must be corr ected for the contri bution of the cell resistance by measuring the conductance without the membrane present (Equation 3-

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109 6).83, 84 If base size and pore density are k nown, tip size can be determined by the following relationship: 3 2, ,L a a A n Gtip l base l (4-1) where is the electrolyte bulk conductivity (0.107 S cm-1 as measured with a YSI 3200 conductivity meter, Yellow Springs, OH); L is the pore length (membrane thickness); n is the pore density; and A is the area of mica membrane used (0.79 cm2). Because mica pores have a rhomboidal cr oss section, they have a long and short axis. Since the major angle of the mica rhombus is ~120o,83, 84 the lengths of the two axes are related geometrically. Thus, onl y the long axes appear in Equation 4-1; al,base and al,tip are the long-axis lengths for the base and tip openings, respectively. Because al,base can be determined independent ly using scanning electr on microscopy, Equation 4-1 provides the tip size, al,tip, from the measured G value. This method is commonly used to determine the tip size of coni cal nanopores in polymeric membranes,8, 39, 42 and similar methods have been applied to mica memb ranes that contain multiple symmetric pores.83, 103, 206 Ion-Current Rectification I–V curves for these experiments were obtained with 10 mM phosphate buffer solutions (pH 7.4) on both sides of the membrane. At such low ionic strengths, asymmetric nanopores can show non-linear I–V curves – ion-current rectification.39, 51, 118 I–V curves were obtained by stepping the potential every 2 seconds in 0.25 V increments from -10.0 V to +10.0 V.

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110 EOF measurements In the EOF experiments, one face of the membrane was in contact with a “feed” solution that was 10 mM in phenol and 10 mM in the pH = 7.4 buffer. The other face was in contact with only the buffer, the per meate solution. The direction of EOF was always from feed to permeate, and as per prior work, the ra te of transport of phenol into the permeate solution provides the electroosmotic velocity.51, 186, 187, 189 A platinum wire electrode was placed in each solution, and a constant transmembrane current was supplied usin g a Solartron SI1287 electrochemcial interface (Hampshire, England). Since t he pore walls of the mica membrane carry negative surface charge,59, 134, 191 the direction of EOF was from anode to cathode.51 Thus, the galvanostat was configured such t hat the working electrode (anode) was in the feed solution and the reference/counter electrode (cathode) was in the permeate. The area of mica membrane exposed to the buffer solutions was 0.79 cm2. The rate of phenol transport was obtained by measuring the absorbance of the permeate solution as a function of time. This was accomplished by continuously pumping the permeate through a flow-thr ough quartz UV cell using an Agilent (Waldbronn, Germany) 1FS peristaltic pump. The UV absorbance of the phenol was measured at 270 nm using an Agilent 8453 UV-visible spectroscopy system. A calibration curve was used to convert t he measured absorbance values to the phenol concentration in the permeate. Results and Discussion Membrane Characterization Pore size and pore density for the membra nes used in the EOF experiments were determined by SEM and AFM. Figures 41A and 4-1B depict the base side of a

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111 pyramidal-pore mica membrane. T he long axis of the base opening ( al,base) was found to be 330 ( 12) nm (measurement of 25 po res). The long axis of the tip opening ( al,tip) was estimated to be ~30 nm from SEM im ages (Figure 4-1C) and 39 ( 3) nm by measuring the conductance of the membrane (Equation 4-1). A carbon replica of a mica nanopore is shown in Figure 4-1D. As can be seen (Figure 4-1), the etching process resu lts in asymmetric nanopores (cone angle 1–2o). The pore density was measured by counting a number of relatively large pores (> 300 nm) under low magnification (Figur e 4-2). Membranes with por e densities of 1.0 ( 0.1) x 106 cm-2 (Figure 4-2A) and 9 ( 1) x 106 cm-2 (Figure 4-2B) were used for EOF studies. These membranes are identifie d by their nominal pore densities (106 cm-2 and 107 cm-2, respectively) for simplicity. Ion-Current Rectification Properties As can be seen by the asymmetric I–V curves in Figure 4-3, the etched pyramidalpore mica membranes clearly rectif y ion current. The shape of the I–V response is determined by the pore structure, surface ch arge, and electrolyte composition. Since etching results in surface silanol gr oups that are deprot onated at pH > 4.5,134 the pyramidal-pore mica membranes in Figure 4-3 exhibit negative surface charge. As previously stated, the refer ence electrode was in contact with the solution on the tip side of the membrane during the I–V measurements. Therefore, a relatively large current (“on” state) is observed for negative transme mbrane potentials, and a relatively small current (“off” state) is observed for positive transmembrane potentials (Chapter 1). Ion-current rectification is expected to result from t he difference in electrolyte concentration (and hence resistivity) within the pores depending on the polarity of the applied potential (Chapter 1).69, 111-113, 115-117, 120-123, 137, 140, 203, 204 The dynamic

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112 restructuring of the electrolyte solution with in pores due to applied potential has recently been confirmed experimentally by Guerrette and Zhang.174 These authors have shown that ion-current rectification is scan-ra te dependent, reasoning that the concentration of the electrolyte solution within the pores must be given time to increase or decrease in order to achieve maximum rectific ation. The scan rate used for I–V curves in these studies is slow enough to allow the dynamic restructuring of the electrolyte solution within the pores and achieve maximum rectification.174 The degree of ion-current re ctification is typically characterized by the absolute value of the ratio of currents obtained at voltages of a given magnitude but opposite polarities (i.e., | I(-V)/I(+V) |).207 As shown in Figure 4-4, the ion-current rectification ratio is highest at large transmembrane potent ials. For the lower pore density (106 cm-2) membrane, the ion-current rectification ratio reaches 5.7 ( 0.4) at 10 V. The higher pore density (107 cm-2) membrane yields a lower ion-current rectification ratio of 2.2 ( 0.1) at 10 V. Since the lower pore density membrane co mprises a greater percentage of the total resistance than does the higher pore density membrane,208 a better comparison of rectification capabilities may be made th rough measurements of membrane resistance (or conductance; Equation 4-1). The resist ance of the cell was measured by taking an I–V curve without any membrane in place (do tted line in Figure 4-3) This resistance was found to be 4860 ( 19) (inverse of the slope of the dotted line in Figure 4-3). The total resistance measured for the 106 pores cm-2 membrane in the “on” state was 6500 ( 130) (inverse of the slope for negative potentials of the solid line in Figure 4-3). Thus, the membrane resist ance accounts for 25 ( 2)% of the total

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113 resistance for the “on” stat e polarity. The total re sistance measured for the 106 pores cm-2 membrane in the “off” state was 39000 ( 2000) (inverse of the slope for positive potentials of the solid line in Figure 4-3). Therefore, the membr ane resistance accounts for 88 ( 7)% of the total resistance for the “off” state polarity. Thus, the ratio of membrane resistance (or conductance) measured fo r the “off” and “on” st ates is 21 ( 2) for the 106 pores cm-2 membrane. In contrast, the total resistance measured for the 107 pores cm-2 membrane in the “on” state was only 5390 ( 25) (inverse of the slope fo r negative potentials of the dashed line in Figure 4-3). Thus, the me mbrane resistance only accounts for 9.8 ( 0.6)% of the total resistance for the “on” st ate polarity. The total resistance measured for the 107 pores cm-2 membrane in the “off ” state was 12500 ( 698) (inverse of the slope for positive potentials of the solid line in Figure 4-3). Therefore, in this case, the membrane resistance accounts for 61 ( 7)% of the total resistance for the “off” state polarity. Consequently, the ratio of membrane resistance (or conductance) measured for the “off” and “on” states is 14 ( 2) for the 107 pores cm-2 membrane. Ion-current rectification is determined by the ratio of cu rrents in the “on” and “off” states. Since current is related to resistanc e, it is clear from the above analysis that the “on” state current is most ly determined by the cell resi stance (resistance of the cell without the membrane in plac e) and not the membrane resi stance for membranes with high pore densities. This must lead to t he loss of ion-current rectification for high porosity membranes. However, even if the difference between pore density is accounted for by comparing the m easured membrane resistances, the 106 pores cm-2

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114 membrane still exhibits superior rectificat ion capabilities (according to the membrane resistance ratios described above) than the 107 pores cm-2 membrane. Notice from Equation 4-1 t hat the membrane resistance (inverse of conductance) for the 106 pores cm-2 membrane is expected to be 10 times higher than that of the 107 pores cm-2 membrane (assuming the electrolyte c onductivity within the pores is the same for each membrane) due to the dependence of resistance on the number of pores. However, the memb rane resistance of the 106 pores cm-2 membrane is only 4.5 ( 0.5) times higher than that of the 107 pores cm-2 membrane in the “off” state and only 3.1 ( 0.3) times higher in the “on” state. The resistance of the 107 pores cm-2 membrane may be higher than expected due to a more extens ive degree of pore overlap. When nanopore membranes (with char ged pore walls) are exposed to an electrolyte of low bulk concentration (as is the case for t he 10 mM phosphate buffer used in these studies), the electrolyte within the pores has been found to possess a higher conductivity (lower re sistivity) than the bulk value.109 One may reasonably assume that pore overlap may lead to a decreas e in conductivity (increase in resistivity) for the electroyte within overlapping pores compared to pores that do not overlap. Thus, the higher than expected resistance of the 107 pores cm-2 membrane (see above) can be explained due to the ex pectation that more extens ive pore overlap occurs in higher pore density membranes. Ion-current rectification must decrease as pore density increases due to the increasing degree of pore overla p at high porosities. Since the initial formation of damage tracks is a random process, pores are randomly located on the membrane after

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115 etching. Thus, as the pore density and por e size increase, t he probability of pore overlap increases. This problem has been described mathematically by several researchers.94, 209, 210 Physical Pore Overlap in Multi-Pore Membranes Quinn et al. used the binomial distributi on to deduce that the number of apertures formed by q overlapping single pores, m ( q ), in a membrane that initially contained n damage tracks can be estimated by94 3 2 1 13 32 8 4 1 4 4 1 4 ) ( f f f q f n f q f n q mq n q (4-2) where f is the pore area fraction that would re sult if all pores remained separate and distinct. This is simply the product of the area of a single por e and the pore density. From Equation 4-2, it follows that the fracti on of single pores is 3 23 32 8 4 1 4 1 ) 1 ( f f f n f n mn (4-3) and the fraction of apertures that overlap with one or more neighboring single pores is 3 23 32 8 4 4 1 1 ) 1 ( 1 f f f n f n mn (4-4) Thus, for a mica membrane with a pore density of 106 cm-2 and al,base 330 nm ( f 0.00031), the percentage of openings that overlap with one or more neighboring single pores is ~0.13%. Since the total area of the membrane that contained nanopores in these studies was 0.79 cm2, this small percentage corres ponds to ~1000 pores of the total 7.85 x 105 pores present in the membrane. For the higher pore density membrane (~107 cm-2) that was used ( f 0.0028), the percentage of openi ngs that overlap with one

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116 or more neighboring single pores is ~1.1% or ~79,500 pores out of the total 7.07 x 106 pores present in the membrane. This analysis is not exact since the probability of overlap is dependent on the number of overl apping apertures.94 For example, the area over which it is possible for three pores to overlap is sli ghtly larger than the area over which it is possible for two pores to overlap. However, few combinations of openings that overlap with two or more neighboring single pores are expected94 for the relatively small pore size and porosities used in these studies. Therefore, the results obtained from Equation 4-4 can be considered a good estimate of physical pore overlap. John et al. later used a Poisson distributi on to estimate that the probability of finding q randomly distributed holes in a given area (i.e., that q holes will overlap) is described by the following function:209 44q e f q pf q (4-5) where f is again the pore area fraction that woul d result if all pores remained separate and distinct. From Equation 4-5, one finds t hat the fraction of apertures that overlap with one or more neighboring pores is 1 1 21 1a a aa p a p a p a a p a (4-6) In Equation 4-3 above, a is used to denote the total number of apertures such that the product of a and p ( a ) yields the expected number of pores with a given overlap value. This ensures that the overlappi ng apertures are treat ed as separate pores instead of one large pore for counting purpose s. With Equation 46, the percentage of

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117 pores that overlap with one or more neighboring single pores is again ~0.13% for the 106 cm-2 pore density membrane and ~1.1% fo r the higher pore density membrane (~107 cm-2) used in these studies. Like Quinn et al.,94 John et al. state that Equat ion 4-5 gives only approximate probabilities for q > 2. Since the area of possible over lap for three or more single pores is slightly larger than 4 f ,209 Equation 4-6 underestimates the expected percentage of apertures that overlap with two or mo re neighboring pores. However, this underestimation is very slight209 as the probability of three or more pores overlapping is very small for membranes with low porosities and small pores. The above discussion only accounts for pores that are physically close enough to have merged during etching. Though more por es overlap in the membrane with the higher pore density, the fraction is still too small to completely explain the large difference in ion-current re ctification between the 106 pores cm-2 and 107 pores cm-2 membranes used in these studies. Theref ore, neighboring pores separated by some short distance must have the ability to feel the effects of one another. This observation is similar to previous results obtained for nanoelectrode ensembles (NEEs) prepared in track-etched membranes by the template-synthesis method.211 Overlap of Diffusion Layers in Multi-Pore Membranes As Hulteen et al. showed in their invest igation of gold NEEs, electrode density is critically important in deter mining the nature of the electr ochemical response due to the extent of diffusion layer overlap.211 These researchers prepared several NEEs with varying electrode densities using porous polymer membranes as templates and conducted basic electrochemical experiments. The electrochemical responses of each NEE were compared to that of a macrosc opic electrode with an ar ea equivalent to the

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118 area of the membranes used in the experiments. For a me mbrane with a large porosity and thus a high electrode density (~4 x 108 cm-2), the electrochemical response of the NEE was similar to that of the macro scopic electrode (i.e., the NEE behaved like one macroscopic electrode rather t han a collection of individual nanoelectrodes). This is because the large electrode density leads to the to tal overlap of the diffusion layers that result at each individu al electrode element. For membranes with low electrode densities (~105 cm-2), the diffusion layers of neighboring electrode elements were complete ly isolated from one another. This was confirmed by the pure-radial appearance of the electrochem ical response (similar in appearance to the response of a single nanoelectrode). Memb ranes with intermediate porosities gave intermediate responses However, membranes with 2 x 107 nanoelectrodes cm-2 gave electrochemical responses that were closer in appearance to the total overlap case, whereas membranes with 2 x 106 nanoelectrodes cm-2 gave responses that were closer in app earance to the pure-radial case. This previous study seemed to suggest t hat most pores in lower pore density membranes (106 cm-2 or lower) are isolated enough fr om one another such that they retain the properties of single pores. Ho wever, most pores in higher pore density membranes (107 cm-2 or higher) are close enough to one another such that their properties resemble those of larger por es. These assertions are echoed in the dependence of the ion-curr ent rectification on the pore density in these studies (Figures 4-3 and 4-4). Aside from pore density, t he membranes used in these studies may also be characterized in terms of the average (center-to-center) distance between pores212 ( d =

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119 0.5 n-1/2, where n is pore density). For the membr anes used in these studies, this distance is 5.0 ( 0.3) m for the 106 pores cm-2 membrane and 1.67 ( 0.09) m the 107 pores cm-2 membrane. Again during their inve stigations of the electrochemical properties of NEEs, Hulteen et al. found t hat the diffusion layers of individual nanoelectrodes were completely isolated from one another when t he average (centerto-center) distance betw een the electrodes was 18 m.211 The diffusion layers completely overlapped when the aver age distance between electrodes was 0.25 m. For NEEs with an average distan ce between electrodes of 1.1 m, diffusion layers largely overlapped. In contrast, a larger average distance between electrodes of 3.5 m led to mostly isolated diffusion layers.211 Thus, it is again reasonable that neighboring pores in the 107 pores cm-2 membrane experience the e ffects of one another to a greater extent than nei ghboring pores in the 106 pores cm-2 membrane, thereby explaining the diminished rectification c apabilities of the higher pore density membrane (Figures 4-3 and 4-4). It is important to note that several researchers have suggested that the diffusion layer thickness in a NEE is equivalent to 6 times the radius of the average nanoelectrode.213, 214 Thus, the individual elements in NEEs must be separated by a distance of at least 12 times their radius in order to avoid diffusion layer overlap.213, 214 Due to the small sizes of t he pores (especially on the tip side) used in these studies, one may suspect that diffusion layer overlap may not be an important factor in the difference between the rectification c apabilities of the high and low pore density membranes. However, even researchers th at have made this distinction about the diffusion layer thickness have noted that it is inconsistent with experimental data.213, 214

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120 For example, Baker and Crooks213 as well as Koehne et al.214 reported that nanoelectrodes separated by an average distance of ~1.3 m exhibited diffusion layer overlap even when the diffusion layer thickness was supposedly as low as 0.3 m. The authors of both studies attri buted this discrepancy to the random placement of the nanoelectrodes in the NEEs, which leads to di ffusion layer overlap for some neighboring nanoelectrodes.213, 214 The same random placement is shared by the pores in the membranes used in these studies. As others have reported, however, t he apparent inconsistency between average electrode separation distance and diffusion layer overlap may be ascribed to the somewhat arbitrary assignment of the diffusion layer thickness.215, 216 The selected value of 6 times the radius of the nanoelectrode for the diffusion layer thickness is rooted in theoretical work by Saito, who showed that, for a circular electrode, the concentration of an electroactive species atta ins 90% of its bulk value at a distance of ~6 times the radius of the electrode.217 Using 99% of the bulk concentration as a guideline, Lowe et al. commented that 2 to 4 m of spacing is required between individual carbon nanopippettes (radius 10 to 20 nm) for independent diffusion regimes to be established.218 Furthermore, Davies and Compton have suggested that while Saito’s theoretical concentration prof ile is accurate for electrodes 10 m in radius or larger, the theory significantly underestimate s the diffusion layer thickness for smaller electrodes.215, 216 Davies and Compton estimated the diffusion layer thickness to be 6.2 to 35 m (for scan rates of 0.005 to 2 V s-1) for nanoelectrodes that are 100 nm radius and 2.5 to 10 m (for scan rates of 0.005 to 2 V s-1) for nanoelectrodes that are 10 nm radius.215

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121 Though the above analysis requires analog ies to be drawn between nanoelectrode ensembles and the multi-pore membranes used in these studies, it is apparent that neighboring pores in higher pore density membr anes are more likely to feel the effects of one another than neighboring pores in lo wer pore density membranes. Since the conductivity of the electrolyt e inside the pore is different from the bulk conductivity,109 it is expected that the ion concentration inside the pore is different than the bulk concentration. Therefore, a concentration gradi ent, similar to that which is present for electroactive species in NEE experiment s, must exist for ions in the nanopore membranes in these studies. Concentra tion profiles for NEEs and multi-pore membranes may not be exactly the same due to differences in boundary conditions. However, diffusion layer overlap must also be experienced to some extent by the nanopore membranes used in these studies. The lower pore density (106 pores cm-2) membrane may rectif y ion current more than the higher pore density (107 pores cm-2) membrane because neighboring pores in the higher pore density membrane must not be isolated enough from one another. Since the degree of physical pore overlap is small in each membrane, the overlap of diffusion layers must contribute to the loss of rectification at higher porosity. The overlap of diffusion layers most likely resu lts in neighboring pores exhibiting properties that are more like larger por es and less like a collection of asymmetric nanopores. This would explain the obs ervation that the 107 pores cm-2 membrane was less effective at ion-current rectif ication than the 106 pores cm-2 membrane.

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122 EOF Rectification Properties Previously, we found that pyramidal -pore mica membranes exhibit EOF rectification capabilities.51 This was rationalized by the dependence of the electroosmotic flow velocity, veof, on solution resistivity, ,189 / J vapp eof (4-7) where and are the permittivity and viscosity of the solution, respectively; Japp is the constant applied current density; and is the zeta potential of the pore wall. As previously described,51 Equation 4-7 suggests that the high of the “off” state will produce a high veof, and the low of the “on” stat e will produce a low veof. It must be noted here that Equation 4-7 is an oversimplification of veof in the asymmetric-pore membranes used in these st udies. This is because the electric field within the pores is assumed to be cons tant in the derivat ion of Equation 4-7.51, 189 While this assumption is clearly not valid for the asymmetric pores studied here,17, 45, 111-113, 115, 120 Equation 4-7 has been previous ly appied to asymmetric pores with the reasoning that its application can provi de a highly averaged account of veof through the pores.51 As in previous studies,51, 189 the rate of phenol transport for the linear steady-state response was used to calculate veof values for tip-to-base and base-to-tip translocation experiments. For a given applied current, i, the rate of phenol transport, Ni, was calculated. The rate of phenol diffusion, Ndiff, was also determined by completing analogous experiments in the absence of applied current. Ni and Ndiff were used to calculate the enhancement factor, E,51, 189, 193 diff iN N E/ (4-8) which was used to determine the Peclet number, Pe.193

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123 ) 1 (Pee Pe E (4-9) Pe and veof are related via L D Pe veof (4-10) where D is the diffusion coefficient for phenol and L is the membrane thickness. Figure 4-5 shows data obtained for a typi cal phenol translocation experiment. The absorbance of the permeate side (tip side in Fi gure 4-5) was monitored over time while a current was applied to dr ive the phenol through the me mbrane from the feed side (base side in Figure 4-5). The effects of translocation directi on and transmembrane current on the phenol transport rates are depicted in Figure 4-6. When phenol was init ially placed in the solution facing the side of the membrane with the larger base openings and driven by EOF (using the “off” state elec trode polarity) toward the sm aller tip side (base-to-tip translocation), the phenol trans port rate was relatively hi gh. When phenol was initially present in the solution facing the side of the membrane with the smaller tip openings and driven by EOF (“on” stat e polarity) toward the la rger base side (tip-to-base translocation), the phenol trans port was relatively low. Recall that these results can be explai ned by Equation 4-7 si nce the “on” state electrode polarity applied during tip-to-base tr anslocation results in a lower electrolyte resistivity within the pores; and, the “off” state electrode polarity applied during the baseto-tip translocation results in a higher elec trolyte resistivity within the pores. Since veof is directly related resistivity (Equation 47), it is understandabl e that base-to-tip translocation experiments result in higher phenol transport ra tes than those obtained

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124 during tip-to-base experiments (Figure 4-6) Also as expected from Equation 4-7, phenol transport rate increases with increas ing current (Figure 4-6 and Tables 4-1 and 4-2). This trend was found to be true for bot h tip-to-base and base-to-tip translocation experiments for both membranes (106 cm-2 and 107 cm-2 pore densities) used in these studies (Tables 4-1 and 4-2). The calculated values for veof are compiled in Tables 4-1 and 4-2. The extent of EOF rectification, reof, defined as the veof for the “off” state polarity (base-to-tip translocation) divided by the veof for the “on” stat e polarity (tip-to-base translocation),51 are also shown in Tables 4-1 and 4-2. As depicted in Tables 4-1 and 4-2, reof increases with increasing current. It is interesting that reof appears to approach a maximum va lue. For the lower pore density membrane (106 cm-2), reof reaches of maximum of 12. The EOF rectification capabilities of t he higher pore density membrane (107 cm-2) are expected to be limited by the same pore density effects (e.g., diffusi on layer overlap) that limit the ion-current rectification (Figure 4-4). For the higher pore density membrane (107 cm-2), the maximum reof is 6. As Equation 4-7 shows, veof is also related to zeta potential and solution viscosity. These factors probably also change within th e pores as current is driven through the membrane. For example, zeta potential is related to surface charge, and Anderson et al. have shown that the surface char ge on mica nanopore walls is dependent on electrolyte concentration.86, 134 Thus, reof may be limited by the effects of the pore wall zeta potential and electrolyte visco sity at large applied currents.

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125 Summary The effects of pore density and appl ied current on t he ion-current and electroosmotic flow rectification capabilitie s of pyramidal-pore mica membranes were investigated. The extent of reof has been found to increase with increasing applied transmembrane current. However, a maximum reof is attained with large applied currents. This limit may be due to factors related to the el ectrolyte composition within the pores such as zeta potential and visco sity. The membrane with the higher pore density (107 cm-2) used in these experiments was less effective at both ion-current rectification and electroosmotic flow rectification. This is most likely due to the effects of neighboring pores on one another. For example, overlappi ng diffusion layers of neighboring pores may lead to tr ansport properties that more closely resemble those of a membrane with large pores rather than a collection of asymmetric nanopores.

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126 Figure 4-1. Images of asymmetric nanopores etched in mica. A) AFM image of a base opening. B) SEM image of base openings C) SEM image of a tip opening. D) SEM image of a carbon replica of an asymmetric mica nanopore. Figure 4-2. SEM images of large pores used to determi ne membrane pore density. A) Pores in a membrane with a nominal pore density of 106 pores cm-2. B) Pores in a membrane with a nominal pore density of 107 pores cm-2.

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127 Figure 4-3. Current–voltage responses obtained in the pres ence and absence of pyramidal-pore mica membranes that disp lay ion-current rectification. All data were obtained with 10 mM phos phate buffer (pH 7. 4). Data for membranes with nominal pore densities of 106 cm-2 (solid line) and 107 cm-2 (dashed line) are present ed with data obtained wi th no membrane present (dotted line). Figure 4-4. Rectification ratio shown as a function of transmembrane potential for pyramidal-pore (106 cm-2 blue diamonds and 107 cm-2 orange squares) mica membranes (in 10 mM phosphate buffer, pH 7.4). Measurements were performed in triplicate. Error bars represent one standard deviation.

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128 Figure 4-5. Absorbance of the solution on the permeate side of the pyramidal-pore (106 cm-2) mica membrane. Phenol was driven from the solution on the base side of the membrane to the solution on t he tip side of the membrane with the application of 100 A. Figure 4-6. Translocation of phenol by EOF through a pyramidal-pore (106 cm-2) mica membrane using different transmembr ane current values. Open data points correspond to tip-to-base translocation while filled data points correspond to base-to-tip translocation. Base -to-tip data are labeled with the transmembrane current that wa s used for each experiment.

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129 Table 4-1. Effect of applied transmembr ane current on the electr oosmotic flow of phenol, veof, and electroosmotic flow rectification ratio, reof for a 106 cm-2 pyramidal-pore mica membrane. veof (mm/s) Current (A) Tip-to-Base Base-to-Tip reof 25 0.11 ( 0.01) 0.49 ( 0.06) 4.5 ( 0.8) 50 0.19 ( 0.02) 1.1 ( 0.1) 5.8 ( 0.9) 75 0.22 ( 0.02) 2.0 ( 0.2) 9 ( 1) 100 0.24 ( 0.02) 2.8 ( 0.2) 12 ( 1) 125 0.29 ( 0.03) 3.5 ( 0.4) 12 ( 2) Table 4-2. Effect of applied transmembr ane current on the electr oosmotic flow of phenol, veof, and electroosmotic flow rectification ratio, reof for a 107 cm-2 pyramidal-pore mica membrane. veof (mm/s) Current (A) Tip-to-Base Base-to-Tip reof 50 0.04 ( 0.01) 0.07 ( 0.03) 1.8 ( 0.9) 100 0.11 ( 0.02) 0.14 ( 0.04) 1.3 ( 0.4) 250 0.16 ( 0.02) 0.44 ( 0.08) 2.8 ( 0.7) 500 0.24 ( 0.03) 1.1 ( 0.2) 4.7 ( 0.9) 750 0.32 ( 0.04) 1.9 ( 0.4) 6 ( 1) 1000 0.36 ( 0.05) 2.3 ( 0.3) 6 ( 1)

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130 CHAPTER 5 SELECTIVE TRANSPORT OF CHARGED SPECIES THROUGH ASYMMETRIC MICA NANOPORE MEMBRANES Motivation The Martin group has shown that membr anes with a collection of monodisperse nanopores can be used to separate molecu les based on differences in charge and size.145-149 Such membranes were prepared by elec troless gold plating of polymer filter membranes to decrease the nanopore internal diameter (ID) to ~1 nm for small molecule separations and ~20–30 nm for protein separations.145-149 Further control over selectivity and transport properties was demonstr ated by application of a potential to the gold layer146 or by chemisorption of a specific thiol molecule.147, 149 Recently, Nguyen et al. have repeated the experiments of the Martin group using track-etched poly(ethylene te rephthalate) (PET) membranes with cylindrical nanopores of ID < ~20 nm to separate sma ll organic and protein analytes.219 Here, the sizeand charge-based transport selectiv ity of a mica membrane t hat contains asymmetric nanopores is investigated. Experimental Materials Muscovite mica (KAl2(AlSi3)O10(OH)2) membranes (10 m thick and 3 cm in diameter) were obtained from Spruce Pine Co (Spruce Pine, NC). Using the linear accelerator (UNILAC) at GSI (Darmstadt, Germany), these membra nes were irradiated with heavy ions (11.4 MeV/nucle on) to induce damage tracks (~107 cm-2). Hydrofluoric acid (HF) used to etch the damage tra cks was obtained from Acros Organics (Morris Plains, NJ). The porphyrins used for transpor t studies, phthalocyanine tetrasulfonic acid (PCTS) and meso-tetra(4-N,N,N-trimethylanilinium) porphine (MTMAP), were obtained

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131 from Frontier Scientific ( Logan, UT). All other chemic als were reagent grade and used as received from Fisher Scientific (Fairl awn, NJ). All solutions were prepared using water that was purified by passing hous e-distilled water thr ough a Barnstead (Dubuque, IA) E-pure water purification system. Nanopore Membrane Preparat ion and Characterization The membrane used in this study was prepared and characterized in the same way as those that were used for the prev iously described EOF studies (Chapter 4). Since the etching conditions were the sa me as the membranes used in the EOF studies, al,base was 330 ( 12) nm (Chapter 4). As described previously (Chapter 4), the pore density was 9 ( 1) x 106 cm-2. Using the aforement ioned membrane conductance based method (Equation 4-1),39, 83, 84 al,tip for the membrane was estimated to be 12 ( 2) nm. Transport Experiments Transport experiments were performed in a manner analogous to the EOF experiments conducted for phenol transport (C hapter 4). In the porphyrin transport experiments here, one face of the membrane was in contact with a “feed” solution that was 250 M PCTS or 120 M MTMAP and 10 mM in the pH = 7.4 buffer. The other face was in contact with only the buffer, the permeat e solution. A platinum wire electrode was plac ed in each solution, and a constant transmembrane current of 400 A was supplied using a Solartron SI1287 electrochemcial interface (Hampshire, Engl and). MTMAP is positively charged in the buffer due to the presence of quaternary ami nes (Figure 5-1A), whereas PCTS is negatively charged in solution due to the depr otonation of sulfonic acid groups (Figure

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132 5-1B). This means that MTMAP will move toward the cathode and PCTS toward the anode when a transmembrane current is suppl ied. Therefore, the galvanostat was configured such that the wo rking electrode (anode) was in the feed solution and the reference/counter electrode (cathode) was in the permeate for the MTMAP transport experiments. PCTS transport experiments we re conducted with the opposite electrode configuration, i.e., cathode in the feed solution and anode in the permeate. Since the pore walls of the mica membrane carry negative surface charge,59, 134, 191 the direction of EOF was from anode to cathode.51 To determine if EOF was strong enough to carry the negatively charged PCTS through the membrane, additional PCTS transport experiments were conducted with the anode in the f eed solution and the cathode in the permeate. T he area of mica membrane expo sed to the buffer solutions was 0.79 cm2 in each transport experiment. The amount of MTMAP or PCTS trans port was obtained by measuring the absorbance of the permeate solution as a function of time. This was accomplished by continuously pumping the permeate through a flow-through quartz UV cell with an Agilent 1FS peristaltic pum p (Waldbronn, Germany). The absorbance was measured at 412 nm for MTMAP and 327 nm for PCTS (Figur e 5-2) using an Agilent 8453 UV-visible spectroscopy system. Calibration curves were used to convert the measured absorbance values to the phenol c oncentration in the permeate. The limitations of the s pectroscopy system were det ermined by measuring the absorbance spectrum of the buf fer solution 25 times over a span of three months. The average and standard deviation of this bl ank was determined at 327 nm and 412 nm. The lowest distinguishable analytical signal (the sum of the mean blank signal and 3

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133 times the standard deviation of the blank220) was found to be 0.00043 AU (arbitrary units) at both 327 and 412 nm. This is the si gnal for the limit of detection (or LOD: the minimum amount of analyte that can be detected at a known confidence level220), which is calculated as 3 times the standard deviati on of the blank divided by the slope of the calibration curve.220 The lowest signal at whic h quantitative meas urements can be made (the sum of the mean bl ank signal and 10 times t he standard deviation of the blank220) was found to be 0.0015 AU at both 327 and 41 2 nm. This is the signal for the limit of quantitation (or LO Q: the lowest amount of analyte at which quantitative measurments can be made220), which is calculated as 10 times the standard deviation of the blank divided by the slope of the calibration curve.220 Ion-Current Rectification To qualitatively investigate the possibi lity of MTMAP or PCTS adsorption, I–V curves were measured before and after the membrane was exposed to MTMAP or PCTS. MTMAP or PCTS was placed in cont act with the base side of the membrane for 35 minutes and allowed to transport thr ough the pores by diffusion. Though the absorbance signal was less than the signal for t he limit of quantitati on (0.0015 AU), the MTMAP or PCTS and permeat e solutions were removed and the solution chambers were rinsed with water. Buffer soluti on (10 mM phosphate buffer, pH 7.4) was then placed on each side of the membrane and I–V curves were taken by stepping the potential every 2 seconds in 0. 25 V increments from -10.0 V to +10.0 V using a Keithley 6487 picoammeter/voltage source (Cleveland OH). The membrane was then rinsed with 1 M HCl followed by 1 M NaOH and purif ied water to remove MTMAP or PCTS. I– V curves were also taken after this washing step.

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134 Results and Discussion Transport of a Positively Charged Porphyrin The positively charged porphyrin (MTMAP) was more readily transported from tipto-base than base-to-tip (Figure 5-3). T he amount of MTMAP trans ported from tip-tobase was ~15 times higher than the amount trans ported from base-to-tip (Figure 5-4). This observation stands in stark contra st to the transport data obtained for phenol (Chapter 4), which showed that the neutral mo lecule was more read ily transported from base-to-tip than tip-to-base. The different preferences in transport direction may be attributed to the differences in the si ze and/or charge of the two species. MTMAP is larger than phenol; thus, it may be possibl e that MTMAP can more effectively block the pores when transported fr om the base side of the membrane to the tip side, thereby limiting further transfer of MTMAP across the membrane. This effect was previously reported by Shaw et al. who used diffusion simulations and experiments involving the transport of macroscopic gl ass beads (1 mm) through a metal membrane with asymmetric apertures.221 Shaw et al. showed that, if the analyte is similar in size to the smaller end of the aperture, the openings will tend to become bl ocked when the analyte is transported from the side with the larger openings to the side with t he smaller openings (base-to-tip transport). This is because much analyte will be able to enter the apertures through the larger openings, but a limited amount of analyt e will be able to exit through the smaller opening.221 Blockage of the apertures limits transpor t by preventing further diffusion of analyte. When diffusion occurs from t he side of the membrane with the smaller openings to the side with the larger openi ngs (tip-to-base transport), permanent

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135 aperture blockage is less likely.221 Thus, higher transport ra tes are observed when the direction of translocation is from ti p-to-base rather t han base-to-tip. In order to validate the s upposition that analyte size may play a role in the differences between the transport of MTMA P and phenol, the pore and molecule sizes must be compared. In these studies, al,base was 330 ( 12) nm and al,tip was 12 ( 2) nm. The rhomboidal openings of the mica pores for t hese studies may be better characterized by invoking the inscribed circle (i ncircle) of the aperture (Figure 5-5). The incircle of a polygon is tangent to each of it s sides and is characterized by its radius (inradius or rincircle in Figure 5-5) and center (incenter).222 Simple geometric arguments (i.e., the inc enter lies at the intersection of the long and short axes of the rhombus and the incirc le is tangent to each side of the rhombus) can be used to show that the inradius is given by 2 2 , ,2base l tip l base l tip l incirclea a a a r (5-1) Since the major angle of the mica rhombus is ~120o,83, 84 the lengths of the two axes are related geometrically (al,base al,tip 3). Therefore, rincircle is al,base/4. Thus, rincircle,base and rincircle,tip for the pores in the memb rane used in these studies were 83 ( 3) nm and 3.0 ( 0.5) nm, respectively. If the analyte species tr ansported through the pores are assumed to be spherical in shape, the larges t analyte that would be able to traverse the base opening is 165 ( 6) nm in diameter, whereas the la rgest analyte that would be able to traverse the tip opening is 6 ( 1) nm in diameter. (Note that this analysis does not take into account any consideration of the electrical double-la yer that must exist

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136 inside the pore due to the charged walls. The Debye length is ~3 nm for the 10 mM buffer used in these studies.) The size of the porphyrins used in these studies was ~2 nm.24 Since MTMAP is similar in size to the small tip opening, it is plausible that MTMAP may block the tip when traversing the pore from base-to-tip, thereby limiting transport in this direction (Figures 5-3 and 5-4). Though the tip openings of the pores in the membrane used in these studies were found to be smaller than those used in the phenol transport studies (Chapter 4), it is likely that phenol is sma ll enough to avoid blocking the pores (and, consequently, not experience low base-to-tip transport). The length of a carbon–carbon bond in benzene is ~140 pm (0.14 nm),223 and the size of phenol has been estimated to be ~0.5 nm.224 Thus, it is reasonable that phenol is not able to block the tip when traversing the pore from base-to-tip. The supposition that phenol is too small to effectively block the tip was confirmed experimentally by repeating EOF transport of phenol experiments (C hapter 4) with the same membrane used here for the porphyrin studies (Figure 5-6) Just like the membranes used in previous phenol transpo rt studies (Chapter 4), this membrane showed higher transport of phenol from baseto-tip and lower phenol transport from tipto-base (Figure 5-6). As was previously explained (C hapter 4), more phenol is expected to be transported fr om base-to-tip than from tip-to-base due to the dependence of electrolyte resisivity (withi n the pores) on the pol arity of the applied potential. However, Shaw et al. also f ound that when an analyte is sufficiently smaller than the limiting opening of an asymmetric aperture, the diffusion rate will be higher when the analyte is transported from the la rger opening to the smaller opening (base-to-

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137 tip).221 This is because, by entering the aperture from the la rge opening and moving toward the small opening, t he analyte’s trajectory becomes focused toward the small opening end.221 Another reason that may explain the difference between the directional preferences in transport for MTMAP and phenol may lie in the difference in the charge of the two species. MTMAP is positiv ely charged, while phenol is neutral in the electrolyte solution. I–V curves measured before and after the membrane was exposed to MTMAP (Figure 5-7) suggest that some adsorption of MTMAP does occur during the course of the transport experiments. The increase in rectification ratio afte r exposure to MTMAP (Figure 5-7B) is possibly indicative of the formation of a bi polar diode (i.e., part of pore wall is positively charged and part is negatively charged).67, 141 Rinsing the membrane with 1 M HCl followed by 1 M NaOH and purified wate r removed adsorbed MTMAP and returned the rectification properties of t he mica membrane to those obs erved for the freshly etched state (Figure 5-7). The adsorption and intercalation of porphyrins in mica225 and montmorillonite226, 227 (another phyllosilicate group of minerals) have been previously reported. Transport of a Negatively Charged Porphyrin Absorbance measurements indi cated that very little of the negatively charged porphyrin (PCTS) was transported through t he membrane during the course of the experiments (Figure 5-8). In fact, the absorbance signa l was generally less than the lowest signal required for quantitative measurements (0.0015 AU) in the time scale of the transport experiments (Figur e 5-8). Thus, ~400 pmol (t he LOQ) or less PCTS was transported for both base-to-tip and tip-to-base experiments. In contrast, the lowest

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138 amount of MTMAP transport ed was ~630 pmol (~19 times higher than the LOQ for MTMAP), which was observed for bas e-to-tip transport (Figure 5-4). When transport experiments for PCTS were conducted with the opposite electrode polarity (i.e., with the anode located in t he feed side and cathode in the permeate side to test if PCTS could be transported by EOF), even lower absorbance signals (indistinguishable from backg round) were measured. I–V curves measured before and after exposure to PCTS were virtually the same (Figure 5-9A). Thus, adsorption of PCTS on the mica pore walls was not i ndicated by ion-curr ent rectification measurements (Figure 5-9B). Summary The mica membrane with asymmetric pores used in this study did appear to selectively transport the positively c harged porphyrin over the negatively charged porphyrin. This selectivity may be attribut ed to the small size of the tip openings and the negative surface char ge on the pore walls generat ed by deprotonated silanol groups. Interestingly, more MTMAP was tr ansported from tip-to-base than base-to-tip, which is directly opposite to the transport preference observed for the smaller neutral molecule phenol (Chapter 4 and Figure 5-6). The large si ze and/or charge of MTMAP may lead to blockage of the pores during ba se-to-tip transport, thus decreasing the transport rate in this direction.

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139 Figure 5-1. Chemical struct ures of the ionic porphyrins used in selective transport studies. A) MTMAP. B) PCTS. Figure 5-2. Absorbance spectra for the por phyrins used in the selective transport studies. The dotted line was obtained for a solution of 10 M PCTS, and the solid line was obtained for a solution of 1 M MTMAP. Both solutions were prepared using 10 mM phosphate buffer (pH 7.4).

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140 Figure 5-3. Absorbance of the permeate solution monito red during the transport of MTMAP. A) Base-to-tip transport. B) Tip-to-base transport. Figure 5-4. Amount of MTM AP detected in the permeate so lution during the course of transport studies. Data for base-to-tip (solid diamonds) and tip-to-base (open diamonds) are shown.

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141 Figure 5-5. Depiction of the incircle of a rhombus. Figure 5-6. Translocation of phenol by EOF through a pyramidal-pore (107 cm-2) mica membrane using different transmembr ane current values. Open data points correspond to tip-to-base translocation while filled data points correspond to base-to-tip translocation. Base -to-tip data are labeled with the transmembrane current that was used fo r each experiment. (Note that the data for base-to-tip transport with 50 A (solid gray circles) overlap with the data for tip-to-base transport with 100 A (open blue diamonds).)

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142 Figure 5-7. I–V curves and rectification ratios fo r a mica membrane with asymmetric pores (107 cm-2) before and after exposu re to MTMAP. A) I–V curves obtained in 10 mM phosphate bu ffer (pH 7.4) after etch ing (solid line); one month after etching (dotted line); after first exposure to MTMAP (open triangles); after washing with 1 M HCl followed by 1 M NaOH and water to remove adsorbed MTMAP from first exposure (gray +s); after second exposure to MTMAP (open squares); and after washing with 1 M HCl followed by 1 M NaOH and water to remove adsorbed MTMAP from second exposure (gray Xs). B) Rectificat ion ratios at 10 V for each I–V response in part A.

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143 Figure 5-8. Absorbance of the permeate solution monito red during the transport of PCTS. A) Base-to-tip transpor t. B) Tip-to-base transport. Figure 5-9. I–V curves and rectification ratios fo r a mica membrane with asymmetric pores (107 cm-2) before and after exposu re to PCTS. A) I–V curves obtained in 10 mM phosphate buffer (pH 7.4) after etching (solid line); one month after etching (dotted line); after exposure to PCTS (open triangles); after washing with 1 M HCl followed by 1 M NaOH and water to remove adsorbed PCTS from exposure (gray +s). B) Rect ification ratios at 10 V for each I–V response in part A.

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144 CHAPTER 6 CONCLUSIONS Resistive-Pulse Sensing Single asymmetric nanopores were pr oduced in PET membranes to serve as platforms for the single-molecule sensing tec hnique known as resistive-pulse sensing. These nanopores were modified with a mole cular recognition agent (folate) in an attempt to improve the selectivity of the sensing method for a particular analyte (folatebinding protein). Surface modification was qualitatively verified by observing changes in the pore wall surface charge through differences in ion-current rectification manifested in the I–V responses. Though a wide range was enc ountered in both curr ent pulse duration and magnitude, the data led to some interesti ng observations. Long-lived events were more persistent with lower applied transmembrane potentials. Also, by applying potential pulses of alternating polarity, long-lived events could be disr upted. These results seem to suggest that the applied pot ential and resulting electric field can affect the binding interaction between FBP and folate. It is also interesting that FBP has been reported to undergo a conformation change upon binding to folate.173 This may help explain the wide range of current pulse c haracteristics that were observed here in this study. Ion-Current Rectification Single asymmetric nanopores were pr oduced in PET and mica membranes to explore the differences in the ion-current rectification capabilit ies between pores in these materials. Mica nanopores prepared by the track-etch method exhibit rhomboidal cross-sectional openings, while PET nan opores possess circular openings. An asymmetric mica nanopore proved to be more im pressive at ion-cu rrent rectification

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145 than an analogous asymmetric PET nanopore. This observation may be attributed to differences in cross-sectional opening, pore surface charge, other transport or geometric factors, or a combinatio n of all of these aspects. Widely varying reports have been encountered in literature for the surface charge density values of nanopores in the two ma terials. Zeta potential measurements performed here seem to suggest that mica nanopores possess a higher surface charge than PET nanopores. However, this analysis ignores the cross-se ctional shape of the pores. Moreover, electrokinetic transpor t in nanopores is often complicated by the structure and effects of the electrical double-layer. Surface charge (and, thus, the ion-curr ent rectification c apability) of single asymmetric PET nanopores was increased by oxidation with perm anganate. However, success was variable. Even with surf ace charge enhancement, the ion-current rectification capabilities of PET nanopores did not approach those of the asymmetric mica nanopore. The effects of surface charge alterations on the ion-current rectification properties of a single asymmetric nanopore in mica were also explored. Successful modification of mica pore walls with an amine-silane was verified by changes in the measured I–V response. Electroosmotic Flow Rectification Electroosmotic flow rectification was obser ved to occur in mica membranes that contained asymmetric nanopores. The ext ent of this phenomeno n was determined by monitoring the current-assisted transport of a neutral reporter mole cule (phenol) through multi-pore membranes. Electroosmotic flow re ctification, like ion-cu rrent rectification, seems to occur because electrolyte compositi on inside the asymmetric pores is highly dependent on the polarity of the applied potential. E ffects of applied current and

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146 membrane pore density on the phenomenon were explored. The higher pore density membrane here displayed a lower capacity for electroosmotic flow and ion-current rectification. This observation could be eluc idated by the supposition that overlap of the diffusion layers of neighboring pores occurs to a larger extent in the higher pore density membrane. Selective Transport The sizeand charge-based selective transpor t properties of mica membranes that contained asymmetric nanopores were investi gated. The mica membrane transported a positively charged porphyrin at a higher rate than a negatively charged porphyrin, presumably because of the small size of the tip opening and the negative surface charge presented by silanol grou ps on the pore walls. Intere stingly, the transport rate was higher for the positively charged porphy rin when this analyte was transported from the solution on the tip side of the membrane to the solu tion on the base side of the membrane (tip-to-base transport) This observation was in direct opposition to the preferred transport direction of the smaller neut ral phenol molecule (i.e., the base-to-tip phenol transport rate was higher than the tip-to-base transport rate). The larger size and possible electrostatic interaction with the pore wall for the positively charged porphyrin may have led to pore blockage dur ing base-to-tip transport, thus explaining the lower transport rate.

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159 BIOGRAPHICAL SKETCH Gregory William Bishop was born in Law renceburg, Indiana and grew up in the neaby small southeastern Indiana town of Mil an. He graduated as the valedictorian of his class at Milan High School in 2002. During his undergraduat e career at Indiana University, he joined the research laboratory of Dr. Dennis G. Peters. This experience in electroanalytical chemistry led Greg to develop a deep interest and appreciation for scientific research. In 2006, he comple ted his undergraduate studies with high distinction and received a Bachelor of Sci ence degree in biochemistr y and a Bachelor of Science degree in mathematics. In the fa ll of that year, he enr olled in the graduate program of the department of chemistry at the University of Florida. Here he joined the research laboratory of Dr. Charles R. Martin to study fundamental properties and applications of nanopores. He completed his research in the summer of 2011 and obtained a Doctor of Philos ophy degree in chemistry.