<%BANNER%>

Investigation of Direct Methanol Fuel Cell Voltage Response for Methanol Concentration Sensing

Permanent Link: http://ufdc.ufl.edu/UFE0044418/00001

Material Information

Title: Investigation of Direct Methanol Fuel Cell Voltage Response for Methanol Concentration Sensing
Physical Description: 1 online resource (93 p.)
Language: english
Creator: Harrington, William J
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: dmfc
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A Direct Methanol Fuel Cell (DMFC) was tested undervarious transient load conditions in order to determine the sensitivity ofresponse to methanol concentration. In addition to varying load profiles, theDMFC was tested at several temperature and methanol concentration operatingconditions. The results demonstrated a strong correlation of open circuitvoltage transient response to methanol concentration with high repeatabilityand resolution in the methanol concentration range of 0.60 - 1.60 M. The findings and phenomena that were observed in theexperiments were further studied using a simple, 1-D, transient methanoldiffusion model. The model represents the transient methanol crossover withinthe membrane electrode assembly of the DMFC. The transient methanol crossovervalues that were calculated using the model were used to approximate thetransient oxygen consumption for an open cathode system. The results generatedby the computer model exhibited similar timescales compared to what wasobserved during the DMFC testing. This supports the theory of a cathodedominant response due to the change in methanol crossover with various methanolfeed concentrations. Finally, the measurements that were gathered during DMFCtesting were applied in a brassboard system. A table was generated allowing aDMFC open circuit transient voltage response to be correlated to a methanolconcentration. Due to the operation profile that a DMFC must undergo, the opencircuit transient voltage response could only be captured duringrest/rejuvenation cycles which typically occur every 10-20 minutes. Therefore,a secondary model had to be created in order to track the methanolconcentration between rest/rejuvenation cycles by predicting the consumption(Faradaic, crossover) and addition (methanol injection) of methanol in thesystem. Utilizing the transient open circuit voltage response with the methanolconcentration estimator allowed for over 20 hours of continuous operation in abrassboard without the use of a secondary methanol sensor.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by William J Harrington.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Lear, William E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044418:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044418/00001

Material Information

Title: Investigation of Direct Methanol Fuel Cell Voltage Response for Methanol Concentration Sensing
Physical Description: 1 online resource (93 p.)
Language: english
Creator: Harrington, William J
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: dmfc
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A Direct Methanol Fuel Cell (DMFC) was tested undervarious transient load conditions in order to determine the sensitivity ofresponse to methanol concentration. In addition to varying load profiles, theDMFC was tested at several temperature and methanol concentration operatingconditions. The results demonstrated a strong correlation of open circuitvoltage transient response to methanol concentration with high repeatabilityand resolution in the methanol concentration range of 0.60 - 1.60 M. The findings and phenomena that were observed in theexperiments were further studied using a simple, 1-D, transient methanoldiffusion model. The model represents the transient methanol crossover withinthe membrane electrode assembly of the DMFC. The transient methanol crossovervalues that were calculated using the model were used to approximate thetransient oxygen consumption for an open cathode system. The results generatedby the computer model exhibited similar timescales compared to what wasobserved during the DMFC testing. This supports the theory of a cathodedominant response due to the change in methanol crossover with various methanolfeed concentrations. Finally, the measurements that were gathered during DMFCtesting were applied in a brassboard system. A table was generated allowing aDMFC open circuit transient voltage response to be correlated to a methanolconcentration. Due to the operation profile that a DMFC must undergo, the opencircuit transient voltage response could only be captured duringrest/rejuvenation cycles which typically occur every 10-20 minutes. Therefore,a secondary model had to be created in order to track the methanolconcentration between rest/rejuvenation cycles by predicting the consumption(Faradaic, crossover) and addition (methanol injection) of methanol in thesystem. Utilizing the transient open circuit voltage response with the methanolconcentration estimator allowed for over 20 hours of continuous operation in abrassboard without the use of a secondary methanol sensor.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by William J Harrington.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Lear, William E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044418:00001


This item has the following downloads:


Full Text

PAGE 1

1 INVESTIGATION OF DIR ECT METHANOL FUEL CE LL VOLTAGE RESPONSE FOR METHANOL CONCENTRATI ON SENSING BY WILLIAM JASON HARRIN GTON A THESIS PRESENTED T O THE GRADUATE SCHOO L OF THE UNIVERSITY OF FLORIDA IN PARTIAL F ULFILLMENT OF THE REQUIREMENTS FO R THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2012

PAGE 2

2 2012 William Jason Harrington

PAGE 3

3 To my wife Ashley, my parents Bill & Xinia and brother Jesse, t hanks for your enduring love and support

PAGE 4

4 ACKNOWLEDGMENTS I thank the members of my committee Dr. William E. Lear, Dr. James H. Fletcher and Dr. David W. Mikolaitis for their support and guidance on this thesis. I must also thank Dr. Joseph L. Campbell, Dr. Philip Cox and Dr. Oscar D. Crisalle for their wisdom and advice. Finally, I would like to thank all of my fellow colleagues in the University of North Florida Fuel Cell Laboratory and University of Florida Energy Park for their encouragement and comradery

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .............. 4 LIST OF TABLES ................................ ................................ ................................ .......................... 7 LIST OF FIGURES ................................ ................................ ................................ ........................ 8 ABSTRACT ................................ ................................ ................................ ................................ .. 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ ................. 13 2 LITERATURE REVIEW ................................ ................................ ................................ ...... 17 Rechargeable Battery Technology Status ................................ ................................ .............. 17 Lithium ion Battery Advantages ................................ ................................ .................... 17 Lithium ion Battery Disadvantag es ................................ ................................ ................ 17 Direct Methanol Fuel Cells ................................ ................................ ................................ .... 18 Effects of Methanol Concentration ................................ ................................ ................ 19 Methanol Sensing Technologies ................................ ................................ ............................ 21 Physical Property Type Methanol Sensing ................................ ................................ ..... 21 Capacitance based sensors ................................ ................................ ...................... 21 Speed of sound based sensors ................................ ................................ ................. 22 Refractive index based sensors ................................ ................................ ............... 22 Infrared spectrum ba sed sensors ................................ ................................ ............. 23 Heat capacity based sensors ................................ ................................ .................... 23 Viscosity based sensors ................................ ................................ ........................... 24 Dynamic viscosity based sensors ................................ ................................ ............ 24 Electrochemical Type Methanol Sensing ................................ ................................ ....... 25 3 EXPERIMENTATION AND DATA ANALYSIS ................................ ............................... 29 Test Station Description ................................ ................................ ................................ ........ 29 Fuel Cell Hardware ................................ ................................ ................................ ................ 31 Experimentation ................................ ................................ ................................ ..................... 32 Active Load Method ................................ ................................ ................................ .............. 33 Experimentation ................................ ................................ ................................ ............. 35 Results ................................ ................................ ................................ ............................ 36 Passive Load Method ................................ ................................ ................................ ............. 39 Experimentation ................................ ................................ ................................ ............. 39 Results ................................ ................................ ................................ ............................ 43

PAGE 6

6 4 VERIFICATION MODEL ................................ ................................ ................................ .... 52 Methanol Concentration Distribution ................................ ................................ .................... 52 Steady State Concentration Distribution ................................ ................................ ........ 5 2 Transient Concentration Distribution ................................ ................................ ............. 54 Transient Oxygen Concentration Distribution ................................ ................................ ....... 56 Modeling Summary ................................ ................................ ................................ ............... 57 5 SYSTEM INTEGRATION ................................ ................................ ................................ ... 58 Methanol Concentration Tracking ................................ ................................ ......................... 58 Methanol Consumption Model ................................ ................................ ....................... 58 Faradaic oxidation ................................ ................................ ................................ ... 59 Methanol crossover ................................ ................................ ................................ 60 Methanol Injection Model ................................ ................................ .............................. 61 Methanol Concentration Determination ................................ ................................ ......... 63 Brassboard Operatio n ................................ ................................ ................................ ............ 63 6 CONCLUSIONS ................................ ................................ ................................ ................... 65 APPENDIX A DIFFUSION MODEL DEVE LOPMENT ................................ ................................ ............. 68 Ini tial Conditions ................................ ................................ ................................ ................... 70 Anode Diffusion Layer (0 z z AD ) ................................ ................................ ..................... 71 Anode Catalyst Layer (z AD z z AC ) ................................ ................................ ................... 72 Membrane Layer (z AC z z M ) ................................ ................................ ............................ 73 Cathode Catalyst Layer (z M z z CC ) ................................ ................................ .................. 75 Homogenous Equations ................................ ................................ ................................ ......... 77 Steady State Equations ................................ ................................ ................................ .......... 80 B DIFFUSION MODEL MATL AB CODE ................................ ................................ ............. 84 LIST OF REFERENCES ................................ ................................ ................................ .............. 90 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ........ 93

PAGE 7

7 LIST OF TABLES Table page 3 1 OCV rise time at 0.60 M and 0.80 M. ................................ ................................ .............. 45 4 1 Summary of methanol crossover results from model for various feed methanol concentrations with a current density of 150 mA/cm. ................................ ..................... 54 A 1 Matrix form of boundary equations for homogeneous equations. ................................ .... 80 A 2 Modified matrix of homogenous set of boundary equations. ................................ ........... 80 A 3 System of equations for homogeneous set of bound ary conditions. ................................ 80 A 4 Boundary conditions for steady state, non homogeneous boundary conditions. .............. 83

PAGE 8

8 LIST OF FIGURES Figure p age 2 1 The effect of methanol concentrat ion on a typical DMFC at 75C ................................ 19 2 2 The effect of methanol concentration on a typical DM FC at low current densities ........ 20 2 3 Transient behavior of DMFC with re spect to methanol concentration ............................. 27 3 1 Screenshot of LabVIEW inte rface on University of North Florida Test Stations ............ 29 3 2 University of North Florida standard fuel cell test station. ................................ ............... 30 3 3 UNF Fuel Cell Test Station instantaneous methanol control attachment. ........................ 30 3 4 P& ID for University of North Florida standard test station and methanol control attachment. ................................ ................................ ................................ ........................ 31 3 5 Compressed eight cell fuel cell stack. ................................ ................................ ............... 32 3 6 DMFC methanol concentration sensitivity with static loading. ................................ ........ 33 3 7 DMFC current density response with load change from 0.40 V to 0.35 V. ..................... 34 3 8 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.20 M and 50 C. ................................ ................................ ................................ .......................... 35 3 9 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.60 M and 50C. ................................ ................................ ................................ .......................... 36 3 10 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 1.60 M and 50C. ................................ ................................ ................................ .......................... 36 3 11 Unfiltered fuel cell transient response when electrically loaded from 0.40 V to 0.35 V at 50C. ................................ ................................ ................................ ......................... 37 3 12 Unfiltered fuel cell transient response when electrically loaded from 0.35 V to 0.40 V at 50C. ................................ ................................ ................................ ......................... 37 3 13 Filtered and normalized fuel c ell transient response when electrically loaded from 0.40 V to 0.35 V at 50C. ................................ ................................ ................................ 38 3 14 Filtered and normalized fuel cell transient response when electrically loaded from 0.35 V to 0.40 V at 50 C. ................................ ................................ ................................ 38 3 15 Current Density Transient Response Power Curve Fit Coefficients for 0.35 V and 0.40 V at 50C. ................................ ................................ ................................ ................. 39

PAGE 9

9 3 16 Representative f uel cell voltage response from loaded to unloaded operating point. ...... 40 3 17 Fuel cell air starve cycle with 0.60, 0.80 and 1.60 molar concentration at 50 C. ........... 41 3 18 Typical load cycle for DMFC OCV decay slope testing. ................................ ................. 42 3 19 OCV decay slope at 120 mA/cm at various methanol concentrations with error bars indicating first standard deviation. ................................ ................................ .................... 44 3 20 OCV decay slope at various current densities with 50C stack temperature. ................... 45 3 21 OCV Decay slope wit h constant current density and variable concentration and temperature. ................................ ................................ ................................ ...................... 47 3 22 Max OCV rise time at constant current density with varying temperature and methanol concentration. ................................ ................................ ................................ .... 48 3 23 OCV Rise Slope held at constant current density (40 mA/cm) with variable concentration and stack temperature with error bars indicating single standard deviation. ................................ ................................ ................................ ........................... 49 3 24 OCV Rise Slope held at constant current density (120 mA/cm) with variable concentration and stack temperature with error bars indicating single standard deviation. ................................ ................................ ................................ ........................... 50 4 1 R esults from model for MEA methanol concentration distribution for 0.80 M feed concentration at a current density of 150 mA/cm. ................................ ........................... 53 4 2 Results from model for MEA methanol concent ration distribution for various feed concentrations at a current density of 150 mA/cm. ................................ ......................... 53 4 3 Results from model for MEA transient concentration distribution from a current density of 120 mA/c m to 0 mA/cm at a feed concentration of 0.80 M. ......................... 54 4 4 Results from model for MEA transient concentration distribution from a current density of 120 mA/cm to 0 mA/cm at a feed concentration of 1.60 M. ......................... 55 4 5 Model results for transient methanol concentration response at cathode catalyst layer from a current density of 120 mA/cm to 0 mA/cm. ................................ ....................... 55 4 6 Model results for the mean transient oxygen content in the cathode. ............................... 57 5 1 UNF 20 W DP4 brassboard fuel cell system. ................................ ................................ ... 58 5 2 Simplified methanol consumption and injection model for DP4. ................................ ..... 59 5 3 Representative methanol crossover current density for DP4 stack at various stack temperatures, meth anol concentrations and current densities. ................................ .......... 60

PAGE 10

10 5 4 Performance Curve for Single Base Pump ................................ ................................ ..... 62 5 5 Comparison of Base Pump Performa nce versus various inlet pressures. ....................... 62 5 6 UNF DP4 brassboard operation using sensor less methanol sensing techniques. ............ 64 6 1 Idea l methanol concentration distribution at various load conditions. ............................. 68

PAGE 11

11 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master o f Science INVESTIGATION OF DIR ECT METHANOL FUEL CE LL VOLTAGE RESPONSE FOR METHANOL CONCENTRATI ON SENSING B y William Jason Harrington August 2012 Chair: William E. Lear, Jr. Major: Mechanical Engineering A Direct Methanol Fuel Cell (DMFC) was tested under various transient load conditions in order to determine the sensitivity of response to methanol concentration. In addition to varying load profiles, the DMFC was tested at several temperature and methanol concentration operating conditions. The results de monstrated a strong correlation of open circuit voltage transient response to methanol concentration with high repeatability and resolution in the methanol concentration range of 0.60 1.60 M. The findings and phenomena that were observed in the experime nts were further studied using a simple, 1 D, transient methanol diffusion model. The model represents the transient methanol crossover within the membrane electrode assembly of the DMFC. The transient methanol crossover values that were calculated using t he model were used to approximate the transient oxygen consumption for an open cathode system. The results generated by the computer model exhibited similar timescales compared to what was observed during the DMFC testing. This supports the theory of a cat hode dominant response due to the change in methanol crossover with various methanol feed concentrations.

PAGE 12

12 Finally, the measurements that were gathered during DMFC testing were applied in a brassboard system. A table was generated allowing a DMFC open circu it transient voltage response to be correlated to a methanol concentration. Due to the operation profile that a DMFC must undergo, the open circuit transient voltage response could only be captured during rest/rejuvenation cycles which typically occur ever y 10 20 minutes. Therefore, a secondary model had to be created in order to track the methanol concentration between rest/rejuvenation cycles by predicting the consumption (Faradaic, crossover) and addition (methanol injection) of methanol in the system. U tilizing the transient open circuit voltage response with the methanol concentration estimator allowed for over 20 hours of continuous operation in a brassboard without the use of a secondary methanol sensor.

PAGE 13

13 CHAPTER 1 INTRODUCTION The advances in multimedia (int ernet, social networking, multi megapixel photos, high definition video, high fidelity music, television programming, etc.) and wireless communications (Wi Fi, Bluetooth, WWAN, 4G, LTE, 3G, etc.) have transformed the way people communicate today. While th e computing power in portable electronics such as laptops and cell phones continues to double every two years [ 1 ], the energy density of the most common power source found in these devices (lithium ion batteries) only doubles every thirteen years [ 2 ].Consu mers demand access to content and services at all times through devices with la rger screens and faster processors while achieving a lighter weight and a thinner profiles. The use of such devices with existing battery technology has negatively impacted thei r run time. In addition to the deficiency of the energy density found in lithium ion batteries, power density has also become a technological limitation. As lithium ion batteries are pushed to higher power densities, the combination of added heat generatio n and the limitations in manufacturing have resulted in an increase of lithium ion battery related fires [ 3 ]. One of the most promising solutions that is being considered as a potential replacement for battery technology is the direct methanol fuel cell (D MFC) which offers advantages in both energy and power density. Fuel cells are electrochemical devices that convert chemical energy into electrical energy. The fuel cell is similar to a battery, as both operate through an electrochemical reaction; however f uel cells have the advantage of storing the fuel and oxidant externally. This enables the fuel cell to operate indefinitely provided that sufficient reactants are present. Because the energy conversion process that takes place in a fuel cell is not based o n the process that limits most typical heat engines (Carnot cycle), the fuel cell is able to achieve high efficiencies at low temperatures.

PAGE 14

14 The majority of PEM fuel cells accept hydrogen at the anode and oxygen at the cathode to electrochemically produce p ower. A DMFC ultimately uses hydrogen at the anode, however a methanol water solution is electrochemically converted to hydrogen without the use of intermediate steps or equipment. The use of methanol as a fuel has many advantages over hydrogen including e ase of storage, high availability and low cost. The DMFC has the distinct advantage of higher energy density over a typical hydrogen oxygen based fuel cell with low power applications (< 100 W). The high energy density of methanol fuel and the ease of stor age and handling enable the DMFC to perform for longer periods of time given the same system volume. This characteristic makes DMFC technology a prime candidate for portable electronic applications. 1 1 1 2 1 3 The anode ( 1 1 ) and cathode ( 1 2 ) half reactions can be combined to form an overall reaction ( 1 3 ) for the DMFC. Although there are many intermedi ate reactions that take place before the overall reaction is completed, the half reactions are the most simplified way to describe the processes that take s place within the fuel cell. At the anode, methanol and water are electrochemically converted to hydr ogen protons, electrons and carbon dioxide. In the cathode reaction, oxygen and the hydrogen protons generated at the anode react to form water. One of the most important operating parameters for a DMFC is the methanol concentration at the anode. Operation of a DMFC using very low concentrations (less than 0.4 Molarity) of methanol can result in reduced limiting current density, peak power and damage due to fuel starvation [ 4 ]. Due

PAGE 15

15 to the existing limitations of DMFC membrane technology, DMFCs should not op erate using equi molar ratios of pure methanol and water as implied by Equation 1 1 When high concentrations of methanol (greater than 1.0 Molarity) are exposed to the anode, excessive permeation of methanol acros s the membrane occurs; this phenomenon has been termed cathode and poor fuel utilization [ 5 ]. The methanol diffuses from the anode to the cathode across the membr ane, eventually reaching the platinum catalyst of the cathode, where it reacts with oxygen from the air, creating waste heat. In order to minimize methanol crossover and maintain reasonable DMFC output power levels, a DMFC will typically operate with an aq ueous so lution of methanol (0.6 1.0 Molarity). Due to the simplicity of operation at higher methanol concentrations, manufacturers are working to mitigate issues encountered with methanol crossover by improving membrane technology [ 6 ]. The essential task o f producing a membrane that has a higher ion exchange capacity while allowing less methanol to diffuse is difficult. PolyFuel Inc. developed a hydrocarbon 117. PolyFuel claims th at its family of membranes offers a 33 to 50 percent improvement in the level of methanol crossover, water flux, and power density when compared to Nafion [ 7 ]. Although advancements in membrane technology are critical to improving DMFC power and energy den sity, the methanol concentration will continue to be an essential factor for DMFC performance. In order to achieve optimum performance, the DMFC must operate in a tight methanol concentration band. A number of technologies exist to measure the concentrati on of methanol, however, few are able to meet the requirements (size, costs, weight, reliability, accuracy, etc.)

PAGE 16

16 and electrochemical sensing methods. Physical type sensors correlate methanol concentration to a physical property such as density or heat cap acity. Some of these sensors are fairly robust; however they usually do not package well for miniature applications and often require auxiliary devices (pumps, heaters, complex sensing systems) which increase parasitic power loads on the DMFC. Most electro chemical type sensors work using the same principles found in DMFCs where a signal can be interpreted based on electrochemical response. The most accessible electrochemical sensor to integrate into a DMFC system is the fuel cell stack itself. With the adde d benefit of reduced cost, weight and space, the stack is an ideal replacement for a methanol sensor. It is the goal of this thesis to correlate the transient voltage response of a DMFC to methanol concentration in order to eliminate the requirement for a discrete methanol concentration sensor in a DMFC system. Integration of a sensor less (operation without a methanol sensor) methanol sensing technique will significantly reduce system cost, weight and complexity accelerating the movement of DMFC technology

PAGE 17

17 CHAPTER 2 LITERATURE REVIEW Rechargeable Battery Technology Status Battery technology is the most prevalent form of portable power. Due to its convenience and low operating cost, rechargeable batteries account for 85% of fiscal battery sales [ 9 ]. According to McAllister and Farrell, the annual electrical demand for the average household in the state of California is 125 kWhr for rechargeable devices, which accounts for 2.3% of the total electrical load [ 8 ]. Typically only 15% of the energy that is used to recharge batteries is stored, while the remainder is wasted as heat [ 8 ]. The sales published by the Battery Association of Japan show that lithium ion battery technology is the most prevalent rechargeable battery chemistry used today, accounting for 47% of the fiscal sales of all rechargeable batteries [ 9 ]. Lithium ion Battery Advantages Lithium ion batteries have many advantages over other battery technologies. Lithium is the lightest metal in the periodic table, therefore lithium ion batteries are lighter than most other average open circuit potential of 3.7 Volts, result ing in one of the highest energy density battery chemistries [ 10 ]. As published by Powers, lithium ion battery technology also exceeds other battery chemistries in maximum charge cycles and off state discharge rates [ 10 ]. Lithium ion Battery Disadvantages However, lithium ion battery technology has its drawbacks. Scrosati and Vetter both observed accelerated degradation in the off state when storing lithium ion batteries at elevated temperatures [ 11 12 ]. Shim publ ished data for lithium ion battery testing at 60C, where the degradation was 15 times more than at 25C (10% annually at 25C) [ 13 ]. Researchers have determined that the root cause of high temperature degradation for lithium ion batteries occurs

PAGE 18

18 within th e morphology and composition of the solid electrolyte interface, which changes at elevated temperatures [ 12 ]. In addition to degradation, elevated temperatures can adversely affect the stability and safety of lithium ion batteries. To date, the Federal Aviation Administration has documented over 28 lithium ion related fires/explosions on commercial airline flights [ 14 ]. Due to the high level of energy that can be stored in lithium ion batteries, injury and/or de ath can occur due to failure. The major drawback for lithium ion batteries is the rate at which they technologically advance. Historically, lithium ion technology advances at a rate of approximately 5% annually while the microprocessors that most of these batteries power advance in processing speed at a rate of 40% annually [ 1 2 ]. This poses a major problem for the advancement of portable electronics in general. A recent development in the energy density of batteries in portable electronics has primarily been achieved by replacing off the shelf battery cells with custom fit, non user removable battery packs. Apple computers was one of the first major manufacturers to incorporate this strategy resul ting in a 30% increase in battery capacity [ 15 ]. Research institutes such as Stanford University have reported advances (nanowire technology) in lithium ion technology, however the timeline for implementation of these breakthroughs is 5 10 years away [ 16 ]. W consumer will see a slowdown in the progression of portable technology that is available today. Direct Methanol Fuel Cells Direct methanol fuel cells have the potential to replace lithium ion battery technology as a power source in portable electronics. Direct methanol fuel cells (DMFCs) work on similar principles to batteries. Both devices electrochemically convert fuel and oxidant into electricity; however the fuel cel l has the inherent advantage of storing its reactants externally. Instead of

PAGE 19

19 waiting for a battery to recharge, the fuel cell simply requires a new fuel cartridge of methanol to continue producing power. The possibility of carrying multiple batteries is an option to extend portable electronic runtimes; however the energy density of the liquid methanol that DMFCs use exceeds all common battery technologies. It is this property that enables DMFCs to excel over battery technology during extended durations (>10 hours). Direct methanol fuel cells are an enabling technology which can give portable electronics manufacturers the flexibility to expand the capabilities of portable devices without the risk of reducing portable operation duration. Effects of Methanol Co ncentration One of the major technological barriers that DMFCs must overcome are its sensitivity to methanol concentration. The Nernst equation for the concentration polarization at the anode suggests that the concentration losses can be minimized by incre asing the limiting current density. The limiting current density for the anode is directly related to the amount of methanol (methanol concentration) that is present [ 17 ]. However as shown in Figure 2 1 data prese nted by Song suggests that the performance of a direct methanol fuel cell does not always increase with increasing methanol concentration. Figure 2 1 The effect of methanol concentration on a typical DMFC at 75C [ 18 ].

PAGE 20

20 The effect of methanol concentration on DMFC performance indicates increased performance with increasing methanol concentration until reaching a feed solution concentration of 2.0 M. At high current densities (greater than 100 mA/cm), the eff ect of methanol crossover is less severe. Only until reaching 2.0 M do the benefits of reducing anode concentration losses outweigh the voltage losses due to methanol crossover [ 18 ]. Primarily driven by concen tration and pressure gradients, as the concentration of methanol at the anode increases, more methanol crosses the membrane depolarizing the cathode potential. Du, Zhao, and Yang report that the resulting decline in cathode electrode performance is related cathode catalyst from methanol oxidation intermediates such as CO [ 19 ]. The effect of the feed methanol concentration on DMFC performance is most evident at low current densities. As shown in Figure 2 2 Song presented data where a strong relationship of fuel cell performance at low current densities with respect to feed methanol concentration was established. With a low feed methanol concentration (0.25 M), the methanol crossover is reduced allowing for the fuel cell to operate with a 12.5% increase in performance relative to a high methanol concentration (4.0 M). Figure 2 2 The effect of methanol concentration on a DMFC at low cu rrent densities [ 18 ].

PAGE 21

21 Methanol Sensing Technologies There is strong evidence in the published literature that shows direct methanol fuel cell performance is heavily dependent on the feed methanol concentration at the anode [ 4 ], [ 18 ], [ 23 ], [ 20 ]. Therefore it is critical that the anode methanol concentration be kept at a level that is optimized for DMFC power output and efficiency. In order to monitor the methanol concentration in the DMFC, a methanol sensor can be used in the anode loop. A number of different methanol sensing technologies exist each with its own advantages and disadvantages. Mo st of the methanol sensors that are available today can be separated into physical property type sensors or electrochemical type sensors. Physical Property Type Methanol Sensing Capacitance based sensors Doerner proposed a capacitance based methanol sensor utilizing impedance spectrum analyzer electronics [ 21 ]. The sensor uses two planar sensing electrodes to measure the dielectric constant (capacitance) of a test solution in order to determine the methanol concentration. The sensor exhibited high signal to noise levels at low frequencies (>300 kHz) and a strong relationship with respect to temperature. Capacitance type sensors have been used in the past to determine the concentration of methanol in gasoline methanol fuel mixtures with reasonable results due to the high disparity of dielectric constants for gasoline (2.0 [ 22 ]) and methanol (32.6 [ 22 ]). The distinction between the dielectric constants for water (80.4 [ 22 ] ) and methanol (32.6 [ 22 ]) is much less. The resolution for measuring the dielectric constant of methanol solutions less than 5.0 Molar is small. In addition to errors that may arise from measurement resolution the corrosion of electrodes, CO 2 bubbles generated by the DMFC in the anode stream, or metallic ions can severely impact capacitance measurements [ 23 ].

PAGE 22

22 Speed of sound based sensors A speed of sound based methanol sensor was proposed in patent 6,748,793 by Rabinovich and Tulimieri utilizing an ultrasonic sensor. According to the patent literature, the sound propagation time is measured for a given distance in order to determine the speed of sound of the mixture. Primarily based on the density and bulk modul us of elasticity of the test medium, the speed of sound for methanol and water is 1580 m/s and 1150 m/s, respectively [ 23 ]. Like the capacitance type sensors, the disparity in sound velocities for methanol and water is not great enough to provide high resolution measurements, particularly at elevated temperatures. Temperature has a strong effect on the speed of sound of methanol water solutions, therefore Rabinovich and Tulimieri proposed a second measurement ch amber for a calibration sample (deionized water). This would allow the sensor to offset the temperature effects by compensating with the output of the calibration sample. In addition to the low resolution provided by speed of sound type sensors, this type of sensor is not easily miniaturized and can also suffer from measurement error due to anode CO 2 generation. Refractive index based sensors Longtin and Fan developed a refractive index based co ncentration sensor that uses a one mW 632.8 nm laser in conjunc tion with a semiconductor position sensor [ 24 ]. They were able to achieve a highly accurate, small and inexpensive concentration sensor. However some measurement error was observed attributed to vibration, air disturbances and laser fluctuations. In additio n, although the refractive index concept offers the most simple of designs, the change in refractive index at low concentrations provides the least resolution among the discussed concentration sensing methods. The refractive index for water is 1.333 [ 25 ] and the refractive index for pure methanol is 1.329 [ 25 ].

PAGE 23

23 Infrared spectrum based sensors DuPont currently holds a patent for an infrared spectrum based methanol sensor [ 26 ]. The sensor works using similar princip als found in the refractive index sensor. An IR source transmits a non visible light through a test medium where a photodetector analyzes the transmitted light and a microprocessor converts the signal to a methanol concentration. A strong relationship betw een absorption and methanol concentration can be determined from IR wavelengths in the range of 9.8 to 9.9 m. The infrared spectrum provides excellent resolution for low methanol concentrations (less than 1.5 M), however measurement accuracy is still effe cted by CO 2 bubbles [ 23 ]. Heat capacity based sensors Siargo has developed a prototype heat capacity type methanol sensor utilizing their flow measurement technology. The sensor requires a heat source, a consta nt flow rate and two temperature sensors. The methanol solution temperature is measured using one of the temperature sensors as heat is applied to the solution. The temperature of the solution downstream of the heater is measured to determine the correspon ding heat capacity. The isobaric specific heat capacity for methanol and water is 78.81 J/molK [ 27 ] and 75.40 J/molK [ 27 ], respectively. For aqueous methanol solutions, the heat capacity vs. methanol concentra tion curve is non linear. The heat capacity sharply increases until the molar concentration reaches 7.0 molarity, where it steadily starts to decrease with increasing methanol concentration. For a solution flow rate of 100 mL/min, the difference in tempera ture rise for a solution changing from 0.5 Molarity to 1.0 Molarity is 2.0 C [ 23 ]. Although this temperature difference is easily measured, the accuracy of heat capacitance type devices can be heavily influenc ed by movement. At constant flow velocities, a convection coefficient can be determined for the sensor. If the sensing device were to be abruptly shaken, the resulting convection coefficient

PAGE 24

24 would change resulting in a varied temperature rise across the he ater. In addition to the inaccuracies created by abrupt movements, the parasitic power from the heater and additional pumping requirements must also be taken into consideration when dealing with portable power applications. Viscosity based sensors Siemens currently holds a US patent for a methanol sensor that measures the viscosity of a methanol solution in order to determine its concentration [ 28 ]. The methanol solution is pumped through a constriction and the pressure drop across the constriction is measur ed in order to determine its viscosity using the Hagen Poiseuille equation. At 20C, water is characterized with a viscosity that is 1.5 times more than for methanol [ 29 ]. Interestingly, the viscosity of an aqueous methanol solution increases with concentra tion until reaching a concentration of 12.0 molarity [ 23 ]. The large change in viscosity for low methanol concentrations provides excellent resolution for correlating methanol concentration. Measuring the press ure drop across a flow restriction provides one of the simplest methods for determining fluid viscosity. Determination of methanol concentration using viscosity has its drawbacks. The CO 2 bubbles that are introduced into the solution line by the fuel cell can create large errors in viscosity determination. In addition, viscosity is a strong function of temperature. The viscosity of water is nearly half at 50C compared to its value at 20C [ 29 ]. Therefore an ac curate means of temperature measurement would also be required. Dynamic viscosity based sensors Integrated Sensing Systems (ISSYS) produces a methanol sensor that utilizes a micro machined resonating tube to measure kinematic viscosity [ 30 ]. Kinematic visco sity is composed of density and the dynamic viscosity. As the density of the test solution changes, the effective mass of the resonating tube shifts, therefore affecting the resonant frequency. Additionally, the

PAGE 25

25 damping effect on the resonator can be used to determine the dynamic viscosity. Kinematic viscosity sensors work well with low flow applications such as fuel cells. However, these sensors do not miniaturize well due to the requirement of a bulky counterbalance. In addition, previous experience has s hown that density type sensors severely suffer from impact shock and measurement drift over time. Electrochemical Type Methanol Sensing An electrochemical based methanol sensor was developed at the Jet Propulsion Laboratory based on the electro oxidation o f methanol to carbon dioxide on a platinum ruthenium catalyst [ 31 ]. The proposed methanol sensor operates on the same principles found in DMFCs. The anode potential is set at a constant voltage and the oxidation current is measured. At lower methanol concen trations, the oxidation current is limited by the transport of methanol to the electrode surface. Electrochemical based methanol sensors offer strong measurement resolution and are less sensitive to CO 2 compared to other methanol sensing technologies. In a ddition, electrochemical based methanol sensors can easily be constructed and miniaturized due to their simplicity and similarities to fuel cells. However, electrochemical based sensors suffer from nearly all issues encountered by DMFCs in cluding contamina tion, degradation, catalyst deterioration and slow response time [ 23 ]. Other electrochemical based methanol sensors have been developed including one from the Institute of Nuclear Energy Research in Taoyuan Cou nty, Taiwan. The sensing method utilizes the fuel cell stack by measuring an operating characteristic such as voltage, current or power and applies a control strategy for the methanol injection pump accordingly. Based on the performance of the stack, a cer tain amount of methanol is required in order for the methanol concentration in the system to remain constant. If a slightly higher amount of methanol is precisely metered into the system than what the system consumes, the methanol concentration

PAGE 26

26 will increa se. Response of the fuel cell stack can be analyzed in order to determine whether the system methanol concentration increased closer or further away from the optimal operating point. One inherent advantage to this control strategy is that the methanol conc entration can be optimized for a stack that has suffered from performance degradation [ 32 ]. However, operating close to the optimal methanol concentration poses a risk for fuel starvation due to the proximity of the optimal methanol concentration operating point to the fuel starvation point. One of the largest manufacturers of commercial DMFC systems is Smart Fuel Cells Energy Inc. They have developed many systems utilizing sensorless technology. Although the exact method for methanol concentration determina tion is undetermined, it is believed that a lookup table is used in order to determine the methanol concentration within the system based on key system parameters (fuel cell voltage, current, temperature, etc.). One of the major drawbacks to using a lookup table in a DMFC is the measurement error that is introduced when the fuel cell stack experiences a non standard degradation mechanism. In addition, repeated start up and shut downs can pose a major problem for methanol concentration determination due to t he lack of operation time resulting in minimal feedback of methanol concentration. This can lead to damage of the stack due to excessive methanol concentration or fuel starvation [ 33 ]. Differences in electrochemical response with respect to methanol conce ntration can also be seen in the transient behavior of direct methanol fuel cells. Essentially, the transient behavior of the fuel cell is characterized by the transport properties of methanol through the anode diffusion layer and membrane. The relationshi p of methanol crossover relative to feed methanol concentration is nearly linear [ 34 ]. When the fuel cell is operated under constant load, a certain quantity of methanol diffuses through the diffusion layer to the anode catalyst. The concentration

PAGE 27

27 g radient across the anode is different at varying load levels. When the load is abruptly changed, it takes time for the concentration gradient to reach equilibrium. Figure 2 3 Transient behavior of DMFC with respec t to methanol concentration. [ 35 ] As shown in Figure 2 3 the load on the DMFC oscillates from a loaded condition to open circuit. When the load on the fuel cell is removed, less methanol is required for the reactio n to take place. At this very moment, when the load is changed, the local concentration at the cathode catalyst is relatively low. The decreased load also allows for an increase in the amount of methanol that is available at the anode catalyst. The combina tion of low methanol concentration at the cathode (decreased methanol crossover) and high methanol concentration at the anode (decreased anode concentration overpotential) is ideal. As a result, the transient voltage performance when switching from a loade d to non loaded condition sharply increases until the diffusion of methanol is able to equilibrate. As shown in Figure 2 3 the dynamic behavior for each methanol concentration varies. Analysis of the effect of met hanol concentration on the

PAGE 28

28 transient electrochemical performance will be used in order to determine the feed solution methanol concentration in a direct methanol fuel cell.

PAGE 29

29 CHAPTER 3 EXPERIMENTATION AND DATA ANALYSIS Test Station Description In order to analyze t he transient behavior of a direct methanol fuel cell relative to methanol concentration, a test station had to be developed that would provide accurate, repeatable data for analysis. The University of North Florida acquired a number of disassembled, incomp lete, Fuel Cell Technologies, Inc. test stations. These test stations were refurbished utilizing the existing electric load b anks, temperature controllers and enclosures. All other components (data acquisition, cathode mass flow controller, signal conditio ning, anode solution heater and pump, computer, etc.) were procured and selected based on the engineering requirements. Figure 3 1 Screenshot of LabVIEW interface on University of North Florida Test Stati ons As shown in the screenshot in Figure 3 1 a new LabVIEW interface was written in order to control all of the applicable test station components. As shown in Figure 3 2 the University of North Florida standard test station is fully equipped including: Fuel cell load control Fuel cell voltage and current measurements Anode solution flow control Anode solution temperature control and measurement

PAGE 30

30 Fuel cell temperature control and measureme nt Fuel cell cathode flow rate control and measurement Customized LabVIEW interface Script enabled test operation Figure 3 2 University of North Florida standard fuel cell test station. In addition to the standard fuel cell test station, an attachment was developed in order to precisely control the methanol feed concentration delivered to the fuel cell. As shown in Figure 3 3 a PDS 100 dual head precision piston pu mp was mounted to an aluminum substructure with a USB enabled data acquisition controller. Figure 3 3 UNF Fuel Cell Test Station instantaneous methanol control attachment.

PAGE 31

31 The use of the methanol control attachment with the standard test station ( P& ID shown in Figure 3 4 ) enabled repeatable, accurate data collection with the flexibility of instantaneous methanol concentration control. Figure 3 4 P&ID for University of North Florida standard test station and methanol control attachment. Fuel Cell Hardware The eight cell stack shown in Figure 3 5 with an active area of 15.5 cm per cell was used to analyze the variation in transient performance relative to the feed methanol concentration. The MEA is composed of an in house hydrocarbon based membrane with a catalyst loading of 3.7 mg/cm on the anode and two mg/cm on the cathode. The composition of the catalyst on the anode is a 50/50 atomic ratio mixture of platinum/ruthenium, while the catalyst on the cathode is a solitary platinum catalyst. A flow channel plate is placed between each MEA in order to deliver various concentrations of methanol to the anode and oxygen (air) to the cathode. The anode and cathode

PAGE 32

32 each have a unique flow pattern that has been optimized for reactant delivery. The anode side of the flow channel plate is characterized with a serpentine flow channel, while the cathode has an open straight channel design. The simplicity of the open cathode allows for easy heat removal, however the cathode is typically subjected to operation at ambient conditions (pressure, temperature, humidity). In order to ac quire repeatable, consistent data, a PID temperature controller was used with a solution heater to preheat the anode solution entering the stack so that a uniform stack temperature could be achieved. For all of the testing that was conducted the minimum s to ichiometric flow rates for the anode and cathode were ten and three respectively. Figure 3 5 Compressed eight cell fuel cell stack. Experimentation Based on the data that is presented in Figure 3 6 the DMFC performance has a strong correlation relative to the feed methanol concentration. However, the optimal methanol concentration for these data is approximately 0.70 M. Without a reference of which side of the optimal concentr ation that the fuel cell is operating at, it is very difficult to determine the methanol co ncentration based on a static load measur ement. Therefore, the transient response of the DMFC was evaluated for sensitivity to methanol concentration.

PAGE 33

33 Figure 3 6 DMFC methanol concentration sensitivity with static loading. Active Load Method During the literat ure review, Argyropoulos, Scott and Taama [ 35 ] revealed a variation in the cell voltage response with respect to methanol concentration when a DMFC was brought from a loaded to an unloaded (OCV) condition It is less than desirable to interrupt fuel cell power production every time the methanol concentration needs to be determined. Wi th the intention of eliminating the unloaded condition to determine methanol concentration, an active load approach was tested initially In order to determine if a measurable correlation between methanol concentration and the transient behavior of the fue l cell exists, the fuel cell was operated with various transient electrical loads. Initially, the load was oscillated in constant voltage mode at different frequencies and magnitudes. By comparison, the published literature conducted their testing in const ant current mode. In order to prevent cell reversal, constant 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Current Density (mA/cm) Solution Concentration (Moles/Liter) Current Density vs. Solution Concentration (C v =0.35 V) 55.0 50.0 45.0

PAGE 34

34 voltage load steps were used. An exemplar transient load profile shown in Figure 3 7 identifies the critical points and terminology for data analysis. Figure 3 7 DMFC current density response with load change from 0.40 V to 0.35 V. As shown in Figure 3 7 the fuel cell was electrically loaded from a constant volt age of 0.40 V to 0.35 V. The transient fuel cell current that correspond s to the voltage load steps was analyzed. Immediately after the electrical load is changed, the fuel cell current experiences a rapid transient. Due to the actuation speed of the elect rical load bank, the initial peak, iden tified as the peak c utoff in Figure 3 7 is more than likely an artifact of the electrical load bank overshooting its target voltage. Therefore, any of the transient data prior to this peak w as disregarded for data analysis. In addition to the peak cutoff point, the maxima and minima for each voltage step is labeled.

PAGE 35

35 Experimentation A n algorithm was developed in LabVIEW to determine the cutoff point, maximum and minimum current for each electr ical load change. The data that exists between these two points was used to perform the analysis for methanol concentration sensitivity. During operation, the DMFC is typically operated at a voltage between 0.35 and 0.40 V in order to maximize output power and efficiency. Therefore, the load changes for experimentation were oscillated between 0.35 and 0.40 V. Furthermore, 10 seconds (5 seconds for each load step) were used for the load oscillation period in order to obtain frequent concentration measurement s The DMFC was tested at various methanol concentrations ranging from 0.20 M 1.60 M in 0.20 M increments T he DMFC was tested f or ten minutes for each methanol concentration setpoint. As shown in Figure 3 8 for low methanol co ncentrations (0.20 M) a very erratic behavior exists. Figure 3 9 with an operation methanol concentration of 0.60 M indicates a substantial change in the transient current density response relative to the 0.20 M sample. Finally Figure 3 10 represent s the upper level of methanol concentration setpoints with a more subtle change with respect to the 0.60 M test case. Figure 3 8 Transient current for a DM FC with load oscillations from 0.35 V to 0.40 V at 0.20 M and 50C

PAGE 36

36 Figure 3 9 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.60 M and 50C Figure 3 10 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 1.60 M and 50C Results The data presented in Figure 3 11 and Figure 3 12 represent one instanc e of the unfiltered (peak cutoff not removed) fuel cell current with load changes to 0.35 V and 0.40 V respectively. Figure 3 13 and Figure 3 14 are the same data that was presented in Figure 3 11 and Figure 3 12 however the data has been filtered and normal ized in order to facilitate data analysis. Based on an initial qualitative analysis, are large disparity forms between methanol concentration less th an

PAGE 37

37 0.50 M and greater than 0.50 M. For the 0.35 V case, the test that were conducted with the lower concentrations (<0.50 M) decreased, while the testing that was conducted with the higher methanol concentrations increased. For the 0.40 V testing, the oppo site relationship was established. With both the 0.35 V and 0.40 V case s the difference between the transient response with methanol concentrations greater than 0.80 M was minimal. Figure 3 11 Unfiltered f uel cell transient response when electri cally loaded from 0.40 V to 0.35 V at 50C Figure 3 12 Unfiltered f uel cell transient response when electri cally loaded from 0.35 V to 0.40 V at 50C 60 80 100 120 140 160 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Current Density (mA/cm) Elapsed Time (s) Fuel Cell Current Transient Response at 0.35 V 0.2 M 0.4 M 0.6 M 0.8 M 1.0 M 1.2 M 1.4 M 1.6 M 0 50 100 150 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Current Density (mA/cm) Elapsed Time (s) Fuel Cell Current Transient Response at 0.40 V 0.2 M 0.4 M 0.6 M 0.8 M 1.0 M 1.2 M 1.4 M 1.6 M

PAGE 38

38 Figure 3 13 Filtered and normalized fuel cell transient response when electrically loaded from 0.40 V to 0.35 V at 50C Figure 3 14 Filtered and normalized fuel cell transient response when electrically loaded from 0.35 V to 0.40 V at 50C For each oscillation a power curve fit was established of the form listed in Equation 3 1 The exponential b coefficient is representative of the slope o f the curve. The power curve fit coefficient s for each methanol concentration cycle was average and is shown in Figure 3 15 The active load measurement provides an acceptable resolution with concentrations ranging from 0.2 to 0.8 M, however this limited range for use in a DMFC is unsatisfactory for robust operation 100.0 102.5 105.0 107.5 110.0 112.5 115.0 117.5 120.0 122.5 125.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Current Density Responses at 0.35 V 0.20 M 0.40 M 0.60 M 0.80 M 1.00 M 1.20 M 1.40 M 1.60 M 110.0 120.0 130.0 140.0 150.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Current Density Responses at 0.40 V 0.20 M 0.40 M 0.60 M 0.80 M 1.00 M 1.20 M 1.40 M 1.60 M

PAGE 39

3 9 3 1 Figure 3 15 Current Density Tra nsient Response Power Curve Fit Coefficients for 0.35 V and 0.40 V at 50C Passive Load Method Based on t he rev iewed literature [ 35 ] and the results from the active method it was determined that the load profile that could provide the greatest resolution for methanol concentration determination is when the stack is operated from a loa ded (120 150 mA/cm) to an unloaded (OCV) operating point. This load profile is a realistic option for DMFC system integration. In order to minimize on state degradation due to cathode catalyst oxidation, a DMFC is subjected to a periodic rest cycle during operation. This cycle involves removing the load from the fuel cell stack, allowing the stack voltage to reach OCV and then reapplying the load with no oxygen flow to the cathode so that the cathode potential is reduced. Experimentation In order to gai n a better understanding of the voltage response, the stack was operated at various methanol concentrations. The initial experiments revealed three distinct paths for determining a correlation between the transient voltage response and methanol concentrati on. In -1.0E-02 -7.5E-03 -5.0E-03 -2.5E-03 0.0E+00 2.5E-03 5.0E-03 7.5E-03 1.0E-02 1.3E-02 1.5E-02 -3.E-02 -1.E-02 1.E-02 3.E-02 5.E-02 7.E-02 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 0.35 V Power Curve Fit Coefficient 0.40 V Power Curve Fit Coefficient Current Density Transient Response Power Curve Fit Coefficients 0.40 V Power Curve Fit Coefficient 0.35 V Power Curve Fit Coefficient

PAGE 40

40 Figure 3 16 a representative voltage response is shown with the Max OCV, Max OCV rise time and OCV decay slope identified. Figure 3 16 Representative fuel cell voltage response from loaded to unloaded operating point. As shown in Figure 3 17 a clear discrepancy is visible for methanol concentrations from 0.60 M to 1.60 M. Based on a qualitative analysis, the rise ti me provided the least amount of resolution for determining methanol concentration. The time to reach max open circuit voltage varied from three to 10 seconds. However, at higher methanol concentrations (C Feed > 1.0 M), the difference between rise times was less significant providing less measurement resolution. The Max OCV provides greater resolution than the MAX OCV rise time especially when comparing concentrations from 0.80 M to 1.60 M. Unfortunately, the degradation that occurs within the stack during operation has an intermediate effect on the open circuit voltage.

PAGE 41

41 Therefore, it was determined that Max OCV is not ideal for long term methanol concentration determination. Finally, the OCV decay slope was chosen as a primary candidate for data analysis. T his method for methanol determination provides a distinct variation for the various methanol concentrations providing great resolution. Figure 3 17 Fuel cell air starve cycle with 0.60, 0.80 and 1.60 molar concentration at 50 C. The fuel cell stack was operated at eight different methanol concentrations in order to determine a relationship with respect to OCV decay slope. For each concentration that was tested, the stack was operated at three different tem peratures and four different current densities. The fuel cell stack was operated for ten cycles on an accelerated rest cycle for each configuration 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 Cell Voltage (V) Elapsed Time (s) DMFC OCV Response with No Air Flow 0.60 M 0.80 M 1.00 M 1.20 M 1.40 M 1.60 M

PAGE 42

42 of methanol concentration, temperature and current density. The abbreviated rest cycle is shown in Figure 3 18 which consists of four distinct sub cycles. Figure 3 18 Typical load cycle for DMFC OCV decay slope testing. The cycle begins with a constant current density step (sub cycle 1) for two minutes. The next step following sub cycle one is the OCV response step (sub cycle 2) with the oxygen flow rate set to zero. The duration of this cycle varied based on the methanol concentration from 15 90 seconds. The data tha t was gathered during this sub cycle was used for all of the data analysis. During sub V) for thirty seconds in order to reduce the poten tial on the cathode. Sub cycle four is where the oxygen flow rate is turned back on and the voltage climbs back to open circuit voltage. The OCV response in sub cycle four has a different shape compared to the OCV response in sub cycle 2.

PAGE 43

43 The presence of continuously f lowing oxygen during sub cycle four allows for the OCV to continue climbing while the absence of oxygen fl ow during sub cycle two reduces the cell voltage. Finally the cycle returns back to the beginning at sub cycle 1. The iteration of this cycle occurred over one thousand times in ord er to collect data for the various operating conditions (temperature, current density, feed methanol concentration). Results The variation in OCV response is believed to be driven primarily by the consumption of oxygen at the cathode. Based on the concentr ation of methanol at the cathode catalyst layer, the oxygen will be consumed proportionally and subsequently the cell voltage will decay However, if oxygen continues to flow to the cathode, similar to the second OCV sub cycle, the oxygen will never be ent irely consumed resulting in a less dramatic signal for methanol concentration determination. Therefore, the first OCV sub cycle where the flow of oxygen is brought to zero was used for the OCV decay slope analysis. A strategy was developed in LabVIEW in order to determine the OCV decay slope. For each OCV response sub cycle, a linear regression was performed shortly after the peak OCV was achieved Equation 3 2 on the y referred to as the OCV decay slope. 3 2 In Figure 3 19 the OCV decay slope for methanol concentrations from 0.60 M to 2.0 M are shown at a nominal load and operating temperature. The OCV decay slopes have been made

PAGE 44

44 positive for enhanced viewing on the logarithmic scale. The error bars display the first standard deviation based on the ten cycles that were performed for each setpoint. Figure 3 19 OCV decay slope at 120 mA/cm at various methanol concentrations with error bars indicating first standard deviation for the measurements that were conducted for each cycle The OCV decay slope increases at nearly an order of magnitude with every 0. 20 M change in methanol concentration. Although less severe than what was observed for the active load measurements, a s the concentration approaches 1.60 M, the growth in the OCV decay slope tapers off; the amount of methanol found at the cathode catalyst layer reaches a saturation point, due primarily to the diffusion properties of methanol through the MEA. 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Absolute Value of OCV Decay Slope (V/s) Solution Concentration (M) OCV Decay Slope at 120 mA/cm at 50 C

PAGE 45

45 Figure 3 20 OCV decay slope at various current densities with 50C stack temperature. Figure 3 20 indicates a weak function of OCV decay slope with respect to current density. With the exception of the discrepancies at 0.80 M, the curves for all current densities follow a similar trend. One of the key difference s between the 40 and 80 mA/cm current densities compared to the 120 and 140 mA/cm current densities at 0.80 M are the max OCV rise times. As shown in Table 3 1 the OCV rise time for 120 and 140 mA/cm is an orde r of magnitude different when compare d to the OCV rise time at 40, 80 mA/cm and all of the data points collected at 0.60 M. Table 3 1 OCV rise time at 0.60 M and 0.80 M. Current Density (mA/cm) OCV Ris e Time (s) 0.60 M 0.80 M 40 83.7 35.2 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 OCV Decay Slope (V/s) Solution Concentration (M) OCV Decay Slope at Various Current Densities at 50 C 40 mA/cm 80 mA/cm 120 mA/cm 140 mA/cm

PAGE 46

46 Current Density (mA/cm) OCV Ris e Time (s) 0.60 M 0.80 M 80 78.0 12.4 120 73.4 8.0 140 75.1 7.2 One potential explanation for the divergence in data points is localized flooding at the cathode. With increasing methanol concentration, the amount of methanol crossov er (internal heating) also increases, therefore increasing the amount of cooling air required by the stack to maintain constant temperature. In addition, with increasing current density, the cooling requirements for the stack are also increased. At lower c athode flow rates, the stack is more prone to flooding [ 36 ], resulting in blocked reaction sites at the cathode. Any reduction of reaction sites would reduce the effective reactivity with oxygen and therefore the consumption rate of oxygen at the cathode. A t the prescribed concentrations and current densities, it is believed that the DMFC is operating on a knife edge with the two competing effects of cathode flooding and oxygen consumption. The curves presented in Figure 3 21 display a similar trend to what has been observed in Figure 3 19 and Figure 3 20 with the OCV decay slope increasing with methanol concentration. The stack curr ent density was held constant at 120 mA/cm while varying the stack temperature and concentration. A noticeable change in OCV decay slope is visible for varying temperature. With increasing temperature, the OCV decay slope (diffusion) also increases. This agrees well temperature [ 37 ]. Similar to what was described for Figure 3 19 at higher methanol concentrations, the diffusion o f methanol through the MEA appeared to reach a maximum at 1.80 M irrespective of temperature. The use of OCV decay slope provides a repeatable, accurate measurement for the determination of methanol concentration in a DMFC. In addition, this measurement te chnique

PAGE 47

47 can easily be integrated into any existing DMFC system with little system reconfiguration. In order to reduce on state degradation, a rest (air starve) is conducted multiple times per hour to remove any buildup of oxides on the cathode catalyst lay er [ 38 ]. This would be an ideal time to determine methanol concentration because generally the stack voltage is allowed to go to OCV before entering the air starved load condition. However, at reduced temperatures and methanol concentrations, the OCV decay slope can require as much as 100 seconds to be determined. In order to implement such a methanol sensing technique, the OCV rise time should not be greater than 15 seconds for most operating conditions. This time is typical for DMFC OCV rest cycles. As sho wn in Figure 3 22 the max OCV rise time falls in an acceptable range for methanol concentrations 1.0 M and greater. In order to operate with rest cycles less than 15 seconds, a nother technique must be used in orde r to determine the methanol concentration at lower temperatures or methanol concentrations. Figure 3 21 OCV Decay slope with constant current density and variable concentration and temperature. 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 OCV Decay Slope (V/s) Solution Concentration (M) OCV Decay Slope at 120 mA/cm 45 C 50 C 55 C

PAGE 48

48 Figure 3 22 Max OCV rise time at constant current density with varying temperature and methanol concentration. For all previous measurements, the OCV decay slope was the method used to determine methanol concentrat ion. However, due to the unacceptable rise time for Max OCV at low temperatures and methanol concentrations, the rise slope OCV was evaluated as an alternative to measuring OCV decay slope. For the experiment, the maximum OCV rise time was defined at 15 se conds. If the max OCV was not reached within 15 seconds, the OCV rise slope was determined for the last three seconds of OCV. For each temperature, methanol concentration and current density configuration, the OCV rise slope was evaluated ten times. As sho wn in Figure 3 23 the OCV rise slope at 40 mA/cm is characterized with a linear relationship relative to methanol concentration. However, as indicated by the error bars, the first standard deviation for the sampl e is considerably higher than the measured OCV decay slopes. In addition, the point with a solution concentration of 1.0 M and a stack temperature of 45C 0 10 20 30 40 50 60 70 80 90 100 110 120 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Max OCV Rise Time (s) Solution Concentration (M) Max OCV Rise Time at 80 mA/cm 45C 50C 55C

PAGE 49

49 exceeds an order of magnitude of the linear trend that is established by the existing points. As prev iously discussed, these anomalies could very well be caused by the fuel cell stack operating on a knife edge. At this condition, the stack could potentially be experiencing flooding, which would affect OCV response. Figure 3 23 OCV Rise Slope held at constant current density (40 mA/cm) with variable concentration and stack temperature with error bars indicating single standard deviation. The OCV rise slope at a current density of 40 mA/cm provides much uncertainty in methanol concentration determination. At a current density of 120 mA/cm, the uncertainty in methanol concentration determination increased with a weaker correlation between methanol concentration and OCV rise slope. The combination of weak correlation, with respect to methanol concentration and high uncertainty, make the OCV rise slope an unsatisfactory method for determining methanol concentration. 0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 3.0E-03 0.5 0.6 0.7 0.8 0.9 1.0 1.1 OCV Rise Slope (V/s) Solution Concentration (M) OCV Rise Slope at 40 mA/cm 45C 40C 35C

PAGE 50

50 Figure 3 24 OCV Rise Slope held at consta nt current density (120 mA/cm) with variable concentration and stack temperature with error bars indicating single standard deviation. The failure of the OCV decay slope to provide reliable measurements for methanol concentration determination leaves only a few methods for improving OCV decay slope response time. One possibility is to operate the fuel cell stack at an elevated temperature just before rest. Operation at an elevated temperature (55 60C) can significantly shorten the max OCV rise time to dur ations that would be acceptable for methanol concentration determination in a DMFC system. Another method for improving the max OCV rise time is to operate at an elevated methanol concentration. At an elevated methanol concentration (C Feed > 1.0 M), the ra tio of methanol to oxygen at the cathode catalyst layer would exist at a considerably higher level than for 0.60 M or 0.8 M. As previous data suggests, the OCV rise time would be significantly less. However, with an increase in methanol concentration, the stack would operate at a less efficient point resulting in less net power and poor fuel utilization. 0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03 0.5 0.6 0.7 0.8 0.9 1.0 1.1 OCV Rise Slope (V/s) Solution Concentration (M) OCV Rise Slope at 120 mA/cm 45C 40C 35C

PAGE 51

51 The last method for improving the max OCV rise time at reduced concentrations and temperatures would involve the modification of the MEA. The supporting theory for long duration max OCV rise times is the lack of oxygen consumption at the cathode catalyst due to poor diffusion and flooding. A single MEA on the stack could be optimized for oxygen transport methanol crossover and reduced flooding effects. Th is would promote the consumption of oxygen at the cathode catalyst layer with reduced max OCV rise times.

PAGE 52

52 CHAPTER 4 VERIFICATION MODEL A basic 1 D transient model was created i n order to gain a better understanding of the diffusion phenomena and transients measur ed with the fuel cell test station. The direct methanol fuel cell has many side reactions and transport dependencies that take place within the MEA, therefore many of the complex secondary factors (membrane swelling, two phase flow, electro osmotic drag catalyst loading, etc.) that contribute to DMFC performance have been neglected in order to simplify the model. The formulation of the model and all supporting boundary conditions and assumptions are outlined in Appendix A. The formulas that have been comp iled to solve the 1 D non homogeneous transient model were entered into MATLAB. This model enabled the prediction of methanol and oxygen concentration transient behavior through the MEA. The MATLAB code for the model can be found in Appendix B Methanol Co ncentration Distribution Steady State Concentration Distribution The model was initially assessed in a steady state configuration. As shown in Figure 4 1 the model was tested at a fuel cell current density of 150 mA/cm with a feed concentration of 0.80 M. The model reveals a non linear methanol concentration gradient across the anode catalyst layer. The non linear portion is a result of the methanol that is consumed for electrical power production by the fuel cell at 150 mA/cm. At the cathode catalyst layer, the methanol concentration approaches zero. The methanol crossover can be calculated based on the methanol concentration gradient across the cathode catalyst layer or membrane layer. In Figure 4 2 the model was executed for various feed concentration at 150 mA/cm. For a feed concentration of 0.40 or lower, the methanol concentration at the anode catalyst layer is

PAGE 53

53 below 0, which would result in a fuel starvation condit ion due to insufficient methanol. If the effects of relatively low stoichiometric ratios were taken into account, a fuel starvation condition would be realized at the end of the cell due to reduced feed methanol concentration relative to the beginning of t he cell. The variation of methanol concentration at the entrance of the cathode catalyst layer is an indication of the variation in meth anol crossover for various concentrations. The methanol crossover for each methanol concentration is summarized in Table 4 1 Figure 4 1 Results from model for MEA methanol concentration distribution for 0.80 M feed concentration at a current density of 150 mA/cm. Figure 4 2 Results from model for MEA methanol concentration distribution for various feed concentrations at a current density of 150 mA/cm. Anode Diffusion Layer Anode Catalyst Layer Membrane Layer Cathode Catalys t Layer

PAGE 54

54 Table 4 1 Summary of methanol c rossover results from model for various feed methanol concentrations with a current density of 150 mA/cm. Feed Concentration (M) Crossover Current Density (mA/cm) 0.6 8.2 0.8 20.1 1.0 32.0 1.2 43.9 1.4 55.8 1.6 67.7 Transient Concentration Distr ibution The next set of test conditions that were executed using the model evaluated the transient response of the methanol concentration distribution. The model was used to determine the methanol concentration response with a load profile where the load i s instantly removed. As shown in Figure 4 3 the methanol concentration distribution requires approximately 75 seconds to reach equilibrium. At the cathode catalyst layer, the non linear concentration gradient is e vident when the load is still engaged at t = 0 s. Once the load is removed (t > 0), the methanol concentration quickly increases and a linear concentration gradient is visible. Figure 4 3 Results from mod el for MEA transient concentration distribution from a current density of 120 mA/cm to 0 mA/cm at a feed concentration of 0.80 M. The transient methanol concentration distribution for relatively high feed methanol concentrations is shown in Figure 4 4 For a feed methanol concentration of 1.60 M, the

PAGE 55

55 methanol consumption for electrical power production is less significant. Therefore, the methanol concentration at the cathode catalyst is similar to that for the unl oaded points and is relatively high. Figure 4 4 Results from model for MEA transient concentration distribution from a current density of 120 mA/cm to 0 mA/cm at a feed concentration of 1.60 M. The resp onse of the methanol concentration at the cathode catalyst layers are shown in Figure 4 5 For each feed concentration, the response is similar in shape however the magnitude of the concentration is more than doubl e for a feed concentration of 1.6 compared to 0.80 M. Figure 4 5 Model results for transient methanol concentration response at cathode catalyst layer from a current density of 120 mA/cm to 0 mA/cm. 0 0.02 0.04 0.06 0.08 0.1 0.12 0 10 20 30 40 50 60 70 80 Methanol Concentration (M) Elapsed Time (s) Transient Methanol Concentration Response at the Cathode Catalyst Layer from 120 mA/cm to 0 mA/cm 0.80 M 1.60 M

PAGE 56

56 Tran sient Oxygen Concentration Distribution Due to the relatively slow response of the methanol concentration distribution, the effect of the transient methanol concentration distribution alone is not a viable means for methanol concentration determination. Ho wever, if the flow of cathode air is removed from the fuel cell, the oxygen on the cathode would quickly be consumed due to the methanol crossover. Using the methanol crossover model that has been developed, a basic oxygen consumption model was established in order to determine if the transient response of the cathode would provide a more rapid response. Based on the methanol concentration response and the diffusion coefficient at the cathode catalyst layer, the transient diffusion of methanol (methanol cro ssover) can be calculated. Assuming that for each mole of methanol that is consumed at the cathode catalyst layer, 1.5 moles of oxygen is consumed; the mean oxygen content at the cathode can be calculated. Even though an active air source is not present, t he oxygen that is consumed at the cathode can be replenished by means of natural convection or diffusion, due to the open cathode design of the modeled fuel cell. A basic linear model was used to accommodate for the oxygen that is replenished based on open cathode passive fuel cells. In addition to the replenished oxygen, the amount of oxygen stored in the cathode flow channels was also taken into account. As shown in Figure 4 6 the oxygen that is consumed at the c athode catalyst layer due to methanol crossover occurs relatively fast. With increasing methanol concentration, the consumption rate of oxygen on the cathode increases, resulting in shorter durations of high oxygen content. However, the timescales for oxyg en consumption for an open cathode are long compared to a closed cathode where replenished oxygen would not be available. In order to emphasize the transient oxygen concentration response for all methanol concentrations, a logarithmic time scale was used o n the x axis.

PAGE 57

57 Figure 4 6 Model results for the mean transient oxygen content in the cathode. The cathode potential on a DMFC is strongly dependent on the concentration of oxygen at the cathode [ 36 ]. The higher the partial pressure of oxygen at the cathode, the higher the cathode potential. Therefore with a transient response in the concentration of oxygen at the cathode, the voltage of the DMFC will also exper ience a dramatic transient. Modeling Summary Data provided by the model suggests that the dynamic behavior of the methanol concentration distribution is not rapid enough for practical use in a DMFC as a sensor less measurement technique. Therefore, the ai r flow was removed from the cathode in the model in order to accelerate the effects of methanol on the DMFC performance. The data from the transient 1 D model agrees with the data that was collected experimentally and highlights the importance of the remov al of an active oxygen supply at the cathode. Furthermore, the model showed that the feed methanol concentration has a greater influence on the anode methanol concentration distribution than the operating current density. 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 0.1 1 10 100 Oxygen Concentration Elapsed Time (s) Transient Mean Cathode Oxygen Concentration 1.6 M 1.4 M 1.2 M 1.0 M 0.8 M 0.6 M 0.4 M

PAGE 58

58 CHAPTER 5 SYSTEM INTEGRATION The Universit y of North Florida has the capability to operate an unpackaged DMFC system in a brassboard configuration. The brassboard platform shown in Figure 5 1 enables maximum flexibility for in situ testing of components an d system control strategies. The OCV decay slope method was implemented into the brassboard system in order to determine methanol concentration during operation. The DP4 (demonstration prototype 4) brassboard was designed to operate on ten minute rest cycl es. Assuming the methanol concentration can be determined during each rest cycle, the methanol concentration must be determined during non rest operation. Figure 5 1 UNF 20 W DP4 brassboard fuel cell syst em. Methanol Concentration Tracking Methanol Consumption Model As highlighted in Figure 5 2 t he methanol consumed by the stack to produce electrical current and the methanol consumed at the cathode catalyst due to methanol crosso ver are the two major contributors to methanol consumption in the DP4 system. The minor sources of methanol consumption include leakage through the CO 2 gas liquid separator and the solution storage tank.

PAGE 59

59 However, these sources of methanol consumption are n egligible relative to the rates of methanol consumption due to crossover and power production. A N O D E M E M B R A N E C A T H O D E Figure 5 2 Simplified methanol consumption and injection model for DP4. Faradaic oxidation The calculation of methanol consumption due to electrical current is a straightforward calculation based on the anode half reaction. Equation 5 1 states that for every six moles of conversion from amperes to moles of electrons can be made. Using these two factors, the final conversion from amperes to methanol consumption equals 1.73E 6 Moles of CH3OH/(sAmperecell). 5 1 M E T H A N O L C R O S S O V E R CH 3 OH

PAGE 60

60 M ethanol crossover The methanol consumption due to methanol crossover was calculated based on the amount of CO 2 that was measured on the cathode exhaust us ing a CO 2 analyzer. Carbon dioxide is a product of the methanol that crosses over to the cathode catalyst and the oxygen that is delivered to the cathode for the fuel cell reaction. For every mole of methanol that is oxidized at the cathode catalyst, one m ole of CO 2 is released into the cathode stream. The methanol consumption is converted to an equivalent crossover current density in order to simplify comparison to the stack current density. Figure 5 3 R epresentative methanol crossover current density for DP4 stack at various stack temperatures, methanol concentrations and current densities. 15.0 25.0 35.0 45.0 55.0 65.0 75.0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 Stack Current Density (mA/cm) Crossover Current Density (mA/cm) Methanol Crossover at Various Stack Temperature, Concentration and Current Densities 0.8 M at 45 C 1.0 M at 45 C 1.5 M at 45 C 0.8 M at 50 C 1.0 M at 50 C 1.5 M at 50 C 0.8 M at 55 C 1.0 M at 55 C 1.5 M at 55 C

PAGE 61

61 Methanol crossover is primarily a function of current density, temperature and methanol concentration. Therefore, t hese parameters were varied in order to determine the methanol crossover for the fuel cell stack. The crossover current measurements in Figure 5 3 exhibit a strong linear function with respect to stack current density. As the stac k current density approaches 0 mA/cm (OCV), the availability of methanol at the cathode catalyst reaches a maximum resulting in a maximum of crossover current density. With increased temperature, the diffusion coefficient for methanol across the MEA also increases resulting in higher methanol levels at the cathode catalyst layer. The last variable that was tested in order to determine the amount of methanol crossover rates in the MEA was the sensitivity to methanol concentration. With increasing methanol c oncentrations at the anode, the available methanol at the cathode catalyst would only increase, resulting in a higher methanol crossover rate. The values from Figure 5 3 were compiled in a 2 D matrix where they cou ld be used in a lookup table. Methanol Injection Model In order to accurately track the methanol concentration within the brassboard, the amount of methanol that is injected into the anode stream must be accounted for in addition to the methanol that is co nsumed. Methanol is injected into the brassboard using a single piezoelectric pump controlled by pulse width modulation (PWM). The pump was characterized at several duty cycles using a mass balance. As shown in Figure 5 4 the pump has a strong linear relationship with respect to PWM duty cycle. During preliminary testing, the accuracy of the methanol injection pump appeared to vary based on the fuel reservoir level. The fuel reservoir where the methanol is stored i s a 500 mL container. The difference in pressure head for when the fuel reservoir is full compared to when it is empty can be as much as six inches of methanol. In order to more accurately predict the amount of methanol injected into the system, the pump was characterized at two additional fuel

PAGE 62

62 levels. As shown in Figure 5 5 the pump is strongly affected by the pressure head that is applied to the inlet. Figure 5 4 Performance Curve for Single Base Pump Figure 5 5 Comparison of Base Pump Performance versus various inlet pressures. 0.0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30 35 40 45 50 Methanol Injection Pump Flow Rate (mL/min) Pump Duty Cycle (%) Base Pump Performance 0.0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30 35 40 45 50 Methanol Injection Pump Flow Rate (mL/min) Pump Duty Cycle (%) Base Pump Performance vs. Inlet Pressures No Inlet Head 4" of Negative Inlet Head

PAGE 63

63 Methanol Concentration Determination The empirical data that was collected for met hanol crossover and the methanol injection pump were used in conjunction with the methanol consumption model based on electrical current in order to determine a net mass balance of methanol for the system. To determine the methanol concentration within the system, an accurate model must be used to determine both the quantity of methanol and water in the system. The anode solution reservoir tank for the system features a tank level sensor that utilizes twelve points of conduction in order to determine the am ount of solution in the reservoir tank. In addition to the reservoir tank, anode solution is stored in the fuel cell stack, gas liquid separator, methanol sensor and the silicone lines that are used to connect each of the components. The fuel cell stack ge nerates CO 2 gas in the anode stream during power production, therefore the displacement of gas in the components must be taken into consideration in order to accurately account for the solution volume in the system. Based on the liquid inventory the previous methanol concentration ( the methanol consumption due to electrical current ( and methanol crossover ( the methanol injected by the feed pump ( the molar mass of methanol and the amount of time between the concentration measurements, the new calculated methanol concentration can be calculated. 5 2 Brassboard Operation The results shown in Figure 5 6 are operation data from the brassboard using the sensor less OCV decay slope methanol sensing technique. The system was able to maintain a constant metha nol concentration without metha nol excursions greater than 0.15 M for greater than

PAGE 64

64 eighteen hours. This data suggests that sensor less methanol sensing techniques are a feasible method for continuous, reliable DMFC operation. Figure 5 6 UNF DP4 brassboard operation using sensor less methanol sensing techniques. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 2 4 6 8 10 12 14 16 18 20 Methanol Concentration (M) Elapsed Time ( Hrs ) Actual Concentration (M) Sensorless Concentration (M)

PAGE 65

65 CHAPTER 6 CONCLUSIONS A new method for determining methanol concentration in a direct methanol fuel cell (DMFC) system was evaluated at the University of N orth Florida Fuel Cell Laboratory. In this study, a multilevel approach was used to move from concept to implementation. Initially, a literature review revealed the sensitivity of DMFC transient open circuit voltage (OCV) response with respect to methanol concentration. Initial testing was performed to evaluate various parameters of the DMFC transient OCV and their sensitivity to feed methanol concentration. Preliminary testing revealed that the OCV decay slope offered the greatest resolution for methanol concentrations from 0.60 M to 1.60 M. All future testing used OCV decay slope as a metric for methanol concentration determination. The OCV decay slope was mapped for eight different concentrations, four d ifferent current densities and three different oper ating temperatures, resulting in 96 unique operating points. For each operating point, the DMFC was cy cled 10 times in approximately three minute cycles. The testing revealed a high resolution and repeatability in the OCV decay slope for methanol concentra tions ranging from 0.60 M to 2.00 M. For each change in methanol concentration of 0.20 M, the OCV decay slope changed by nearly one order of magnitude, while the first standard deviation of the sample set remained relatively low, with less than 5% measurem ent error. The sensitivity of OCV decay slope with respect to current density was quite low with the exception of the points at reduced current densities and methanol concentrations. It is believed that the irregularity in the OCV decay response is a resul t of localized flooding in the cathode. At lower current densities and feed methanol concentrations, the amount of cathode cooling air that is required to maintain the same operating temperature is less, therefore increasing the likelihood of localized flo oding at the cathode.

PAGE 66

66 The sensitivity of OCV decay slope with respect to operating temperature was much higher when compared to the sensitivity to current density. With increasing temperature, the OCV decay slope also increased due to the higher level of d iffusion. The use of OCV decay slope provides a repeatable, accurate measurement for the determination of methanol concentration in a DMFC. However, the acquisition time for OCV decay slope can be as much as 90 seconds for low methanol concentrations (C Fee d < 0.80 M) at reduced operating temperatures (T < 50C). The OCV rise slope was used as an alternative measurement technique to reduce the acquisition time for operation at low methanol concentrations with reduced stack temperatures. Unfortunately, there was a very weak correlation between methanol concentration and OCV rise slope with very poor repeatability. Other techniques were recommended, however they were not tested. They included changing the DMFC operating profile to higher methanol concentrations and/or temperature during sensor less methanol detection, or optimization of the MEA cathode for OCV decay measurements. A simplified 1 D transient model was developed to approximate the transient methanol concentration distribution and verify the finding s that were observed in previous experiments The initial model revealed a sluggish response time for the methanol concentration distribution in the MEA. In order to better capture the phenomena that were occurring with respect to methanol concentration, t he computer model was modified to account for an open cathode with the active air supply removed. The lack of an active air supply accelerated the depletion of oxygen on the cathode due to methanol crossover resulting in timescales that were compliant with the DMFC open circuit voltage response time s measured These results agreed well with the measured data.

PAGE 67

67 The final level of testing was implementation of the sensor less OCV decay technique into a 20 W DMFC brassboard system. Integration of OCV decay meas urements into a DMFC system is trivial. During operation, the DMFC must undergo a periodic rest to remove the oxides that have accumulated on the cathode catalyst. This is achieved by removing the active air supply from the cathode and pulling the voltage down on the DMFC. The OCV decay measurement is profile. The only drawback to this measurement strategy is the frequency that the DMFC enters a rest period. Typic ally the time period between rest cycles is 10 20 minutes, therefore the methanol concentration must be tracked between rests. Methanol is consumed by the fuel cell stack through electrical power production and methanol crossover. The methanol that is con sumed for electrical power production can be calculated based on the DMFC anode half reaction while the methanol that is consumed through methanol crossover was measured at various methanol concentrations, temperatures and current densities in order to dev elop an empirical model to predict methanol concentration. In addition to the methanol that is consumed, a model was also developed to predict the amount of methanol that is injected into the system via the methanol injection pump. One last model was creat ed to monitor the amount of solution within the system. By determining the net methanol intake for the DMFC system and the level of anode solution, the methanol concentration can be tracked with reasonable accuracy. The combination of the transient OCV dec ay measurement technique and the methanol consumption model enabled the 20 W DMFC brassboard to successfully operate without a methanol sensor for over 18 hours with methanol concentration excursions less than 0.15 M. Integration of this sensor less methan ol sensing technique will significantly reduce system cost, weight and complexity accelerating the movement of DMFC technology.

PAGE 68

68 APPENDIX A DIFFUSION MODEL DEVE LOPMENT Figure A 1 Ideal methanol concentration distrib ution at various load conditions. The MEA is typically composed of five distinct layers. The anode electrode is characterized with a diffusion and catalyst layer. At the diffusion layer, the methanol water solution diffuses in the direction of the membran e, while the CO 2 gas generated by the anode reaction exits in the opposite direction. The catalyst layer at the anode is where the majority of the methanol is consumed [ 20 ]. However, some methanol continues to migrate across t he membrane to the cathode catalyst layer. In an oxygen and catalyst rich environment, the methanol is quickly consumed at the cathode catalyst layer [ 39 ]. Due to the assumption of complete methanol oxidation at the cathode catalyst layer, the effects of th e cathode diffusion layer were neglected. In addition, due to the limitations of the simplified 1 D model, the effects due to stoichiometric ratios between methanol consumption rates and methanol feed rate are neglected. The following assumptions were used to create the unsteady diffusion model: 1. Uniform material and reactant properties. 2. Negligible diffusion contact resistance. z axis Methanol concentration

PAGE 69

69 3. Consumption of methanol at the anode catalyst layer based purely on electrochemical conversion. 4. Complete consumption of methanol at the cathode catalyst layer regardless of concentration. 5. Concentration at the beginning (z = 0) of the anode diffusion layer is equal to the feed methanol concentration. 6. Methanol concentration at the interface between the anode diffusion and catalyst layers (z = z AD ) is equal. 7. Diffusion of methanol at the interface between the anode diffusion and anode catalyst layers (z = z AD ) is equal. 8. Methanol concentration at the interface between the anode catalyst and membrane layers (z = z AC ) is equal. 9. Diffusion of me thanol at the interface between the anode catalyst and membrane layers (z = z AC ) is equal. 10. Methanol concentration at the interface between the membrane and cathode catalyst layers (z = z M ) is equal. 11. Diffusion of methanol at the interface between the membra ne and cathode catalyst layers (z = z M ) is equal. 12. Methanol concentration at the end of the cathode catalyst layer (z = z CC ) is zero. 13. Negligible effects from cathode diffusion layer. usion. The concentration flux (J) is equal to the diffusion coefficient (D) times the concentration gradient, A 1 means for solving unsteady diffusion problems. A 2 At the anode and cathode catalyst layers, methanol is consumed through an oxidation reaction. At the anode catalyst layer, the methanol is electrochemically consumed based on the amount of electrica l current that is generated by the fuel cell. At the cathode catalyst layer, the crossover methanol from the anode and the oxygen from the cathode are readily consumed in the catalyst enriched environment.

PAGE 70

70 A 3 homogeneous, linear, partial differential equation. In orde r to simultaneously solve for the methanol concentration distribution across all four layers, the method of separation of variables and the orthogonal expansion technique were used. For each layer, the differential equations were divided into a homogeneous and non homogeneous set of equations as shown in Equation A 4 Equations A 7 through A 53 summarize the mass balance, boundary and initi al condition equations. A 4 The model that is presented is an attempt to simulate the methanol concentration distribution for varying fuel cell load levels. The simplified, ideal, 1 D model is used primarily for data verification and phenomena understanding. The model assumes that the fuel cell has been instantaneously loaded from an initial condition with a current density i o to a final load condition with a current density of i f Initial Cond itions Initial Condition 1 The methanol concentration in all of the MEA layers at t=0 is equal to the steady state methanol concentration at the initial current density (i o ), solution feed concentration and temperature. The steady state equation is only a function of space, methanol feed concentration, temperature and current density. Therefore the homogenous equation inherits the entire portion of the initial condition.

PAGE 71

71 A 5 A 6 Anode Diffusion Layer (0 z z AD ) The anode diffusion layer is where the feed methanol solution enters. No reaction is present, therefore at steady state, a linear concentration gradient occurs across the diffusion layer. For the anode diffusion layer, the formation of the homogeneous and non homogeneous equations are summarized in equations A 7 through A 10 Mass Balance Equations A 7 A 8 A 9 A 10 The equations that apply to t he boundary condition at the interface at the beginning of the anode diffusion layer are shown in equations A 11 through A 14 Boundary Conditions Boundary condition 1 The me thanol concentration at the anode diffusion layer inlet is equal to the feed methanol concentration. The boundary condition for the homogeneous set of equations is equal to zero. A 11

PAGE 72

72 A 12 A 13 A 14 Anode Catalyst Layer (z AD z z A C ) The anode catalyst layer is where the majority of the methanol in the fuel cell is consumed. The amount of m ethanol that is consumed at the anode catalyst layer (r AC ) is based entirely on the amount of electrical current that the fuel cell is producing. The mass balance equation for this region is defined in equations A 15 through A 18 A non linear distribution can be expected at the anode catalyst layer at steady state due to the methanol that is consumed at the anode catalyst layer. Mass Balance Equations A 15 A 16 A 17 A 18 Steady State Boundary Equations The boundary condition for the interface between the anode diffusion layer and the anode catalyst layer are defined in Equations A 19 through A 26

PAGE 73

73 Boundary condition 2 The methanol concentration at the anode diffusion layer exit is equal to the methanol concentration at the inlet of the anode catalyst layer. A 19 A 20 A 21 A 22 Boundary condition 3 The methanol concentration flux at the exit of the anode diffusion layer is equal to the methanol flux at the inlet anode catalyst layer. A 23 A 24 A 25 A 26 Membrane Layer (z AC z z M ) The membrane layer is what separates the anode and cathode reactions. However, crossover methanol migrates across this la yer and subsequent layers. It is assumed that the

PAGE 74

74 consumption of methanol at the membrane is zero, therefore a linear methanol concentration gradient can be expected after steady state is reached. Mass Balance Equations A 27 A 28 A 29 A 30 Boundary Equations The boundary condition for the interface between the anode catal yst layer and the membrane layer are defined in Equations A 31 through A 38 Boundary condition 4 The methanol concentration at the exit of the anode catalyst layer is eq ual to the methanol concentration at the inlet of the membrane. A 31 A 32 A 33 A 34

PAGE 75

75 Boundary conditi on 5 The methanol concentration flux at the exit of the anode catalyst layer is equal to the methanol flux at the inlet of the membrane. A 35 A 36 A 37 A 38 Cathode Catalyst Layer (z M z z CC ) The cathode catalyst layer is not the final layer found in a typical MEA, however it has been assumed that due to the presence of the cathode cataly st, the methanol is entirely oxidized with the oxygen from the cathode. The consumption of the methanol in the cathode catalyst layer is defined by r cc where the rate of methanol consumption is heavily dependent upon the local concentration at the cathode catalyst layer. The resulting steady state distribution of methanol concentration is non linear. Mass Balance Equations A 39

PAGE 76

76 A 40 A 41 A 42 Boundary Equations The boundary conditions six and seven are defined at the interface between the membrane and cathode catalyst layers, while boundary equation eight defines the condition at the exit of the cathode catalyst layer. Boundary condition 6 The concentration at the exit of the membrane layer is equal to the inlet at the cathode catalyst layer. A 43 A 44 A 45 A 46 Boundary condition 7 The concentratio n flux at the exit of the membrane is equal to the inlet at the cathode catalyst layer. A 47

PAGE 77

77 A 48 A 49 A 50 Bo undary condition 8 The concentration of methanol at the exit of the cathode catalyst layer is equal to zero. A 51 A 52 A 53 Homogenous Equations The boundary conditions and the differential equations for the st eady state and homogeneous portions have been defined. The homogenous equations were solved using the orthogonal expansion technique. The general solution for each layer is defined in Equations A 54 through A 57 n is the eigen function and the coefficients A and B for each equation represent constants. A 54

PAGE 78

78 A 55 A 56 A 57 In order to solve for the eight un knowns, eight equations were defined using the boundary equations. The eight boundary conditions are defined in general solution form in Equations A 58 through A 65 Bounda ry condition 1 A 58 Boundary condition 2 A 59 Boundary condition 3 A 60

PAGE 79

79 Boundary condition 4 A 61 Boundary condition 5 A 62 Boundary condition 6 A 63 Boundary condition 7 A 64 Boundary condition 8 A 65 Boundary condition equations one through eight are defined in matrix form under Table A 1. In order to avoid a trivial solution, the matrix from Table A 1 was modified assuming A AD is equal to unity resulting in Table A 2

PAGE 80

80 Table A 1 Matrix form of boundary equations for homogeneous equations. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Table A 2 Modified matrix of homogenous set of boundary equations. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The resulting system of equations is shown in Table A 3 The unique solution for each sy stem of equations was solved for the first thirty eigenvalues. Table A 3 System of equations for homogeneous set of boundary conditions. 0 0 0 0 0 0 0 0 0 0 X = 0 0 0 0 0 0 0 0 0 0 Steady State Equations Previously, the homogeneous equations were solved using the orthogonal expansion technique. The other half of the overall solution is characterized wi th non homogeneous boundary conditions. These steady state equations were solved using the differential relationships defined by Equations A 7 through A 53 The equations labeled A 66 through A 69

PAGE 81

81 are characterized with eight unknowns. Therefore eight equations were defined using the boundary conditions. A 66 A 67 A 68 A 69 The boundary equations for the steady state, non homogeneous conditions are listed as Equations A 70 through A 84 Boundary condition 1 A 70 Boundary condition 2 A 71 A 72 Boundary condition 3 A 73 A 74 Boundary condition 4 A 75

PAGE 82

82 A 76 Boundary condition 5 A 77 A 78 B oundary condition 6 A 79 A 80 Boundary condition 7 A 81 A 8 2 Boundary condition 8 A 83 A 84 In order to facilitate calculations using MATLAB software, the boundary equations were formatted into a matrix as shown in Table A 4.

PAGE 83

83 Tab le A 4 Boundary conditions for steady state, non homogeneous boundary conditions. 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 x = 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

PAGE 84

84 APPENDIX B DIFFUSION M ODEL MATLAB CODE clear T=50; %Cell Temperature (C) C_FEED = 0.4; %Feed methanol concentration (Moles/Liter) i_o = 120; %I nit i al Current Density (mA/cm) i_f = 0; %Final Current Density (mA/cm) T=T+273.15; %Convert from C to K. C_FEED=C_FEED/1000; %Convert from Moles/Liter to Moles/cm Beta_n_precision= 10; %Number of decimal places to apply to eigenvalues (14 is the ma x). n_max = 30; %Max number of n iterations for the summation of orthogonal functions. t_max = 75; %The number of seconds to evaluate the function for. (s) t_d = 6; %The number of divisions for the time space specified by t_max. z_d =200; %The number of z divisions for the thickness of the MEA. D_AD = 1.1175e 005; %Anode Diffusion Layer Di ff u s ion Coefficient (cm/s) t_AD = 0.015; %Anode Diffusion Layer Thickness (cm) D_AC = 2.8*10^ 5*exp(2436*(1/353 1/T)); %Anode Catalyst Layer Diffusion Coefficient (cm /s) t_AC = 0.0023; %Anode Catalyst Layer Thickness (cm) r_AC_o = i_o/1000/96485/6/t_AC; %Anode Catalyst Layer Reaction Coefficient before load change. [Moles of methanol/(cm*s), where i is the current density in mA/cm] r_AC_f = i_f/1000/96485/6/t_AC; %A node Catalyst Layer Reaction Coefficient after load change. [Moles of methanol/(cm*s), where i is the current density in mA/cm] D_M = (4.9*10^ 6*exp(2436*(1/333 1/T))); %Membrane Layer Di ff u s ion Coefficient (cm/s) "Determination of methanol diffusi on and electro osmotic drag coefficients in proton exchange membranes for DMFC" t_M = 0.018; %Membrane Layer Thickness (cm) [Alex's Model] D_CC = 2.8*10^ 5*exp(2436*(1/353 1/T)); %Cathode Catalyst Layer Diffusion Coefficient (cm/s) t_CC = 0.0023; %Cath ode Catalyst Layer Thickness (cm) [Alex's Model] r_CC = 70/1000/96485/6/t_CC; %Cathode Catalyst Layer Reaction Coefficient z_AD = t_AD; %D istance in the z direction to end of the anode diffu sion layer starting from the anode side. (cm) z_AC = t_AD+t_AC; %Distance in the z direction to to end of the anode catalyst layer starting from the the anode side. (cm) z_M = t_AD+t_AC+t_M; %Distance in the z direction to to end of the membrane layer starting from the the anode side. (cm) z_CC = t_AD+t_AC+t_M+t_CC; % Distance in the z direction to to end of the cathode catalyst layer starting from the the anode side. (cm)

PAGE 85

85 A_S = [0, 1, 0, 0, 0, 0, 0, 0; %Boundary Condition at Beginning of Anode Diffusion Layer (Concentration) z_AD, 1, z_AD, 1, 0, 0, 0, 0; %Bound ary Condition between Anode Diffusion and Catalyst Layers (Concentration) D_AD, 0, D_AC, 0, 0, 0, 0, 0; %Boundary Condition between Anode Diffusion and Catalyst Layers (Diffusion of Methanol) 0, 0, z_AC, 1, z_AC, 1, 0, 0; %Boundary Condition bet ween Anode Catalyst Layer and Membrane Layer (Concentration) 0, 0, D_AC, 0, D_M, 0, 0, 0; %Boundary Condition between Anode Catalyst Layer and Membrane Layer (Diffusion of Methanol) 0, 0, 0, 0, z_M, 1, exp(sqrt(r_CC/D_CC)*z_M), exp( sqrt(r_CC/D_ CC)*z_M); %Boundary Condition between Membrane Layer and Cathode Catalyst Layer (Concentration) 0, 0, 0, 0, D_M, 0, D_CC*sqrt(r_CC/D_CC)*exp(sqrt(r_CC/D_CC)*z_M), D_CC*sqrt(r_CC/D_CC)*exp( sqrt(r_CC/D_CC)*z_M); %Boundary Condition between Membrane Lay er and Cathode Catalyst Layer (Diffusion of Methanol) 0, 0, 0, 0, 0, 0, exp(sqrt(r_CC/D_CC)*z_CC), exp( sqrt(r_CC/D_CC)*z_CC)]; %Boundary Condition at exit of cathode catalyst layer. (Concentration) %Non_Homogeneous Conditions for Steady State ODEs at the initial condition B_o_S = [C_FEED; %Boundary Condition at Beginning of Anode Diffusion Layer (Concentration) r_AC_o*z_AD^2/2/D_AC; %Boundary Condition between Anode Diffusion and Catalyst Layers (Concentration) r_AC_o*z_AD; %Boundary Condit ion between Anode Diffusion and Catalyst Layers (Diffusion of Methanol) r_AC_o*z_AC^2/2/D_AC; %Boundary Condition between Anode Catalyst Layer and Membrane Layer (Concentration) r_AC_o*z_AC; %Boundary Condition between Anode Catalyst Layer and Me mbrane Layer (Diffusion of Methanol) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer (Concentration) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer (Diffusion of Methanol) 0]; %Boundary Condit ion at exit of cathode catalyst layer. (Concentration) %Non_Homogeneous Conditions for Steady State ODEs at the final condition B_f_S = [C_FEED; %Boundary Condition at Beginning of Anode Diffusion Layer (Concentration) r_AC_f*z_AD^2/2/D_AC; %Boundar y Condition between Anode Diffusion and Catalyst Layers (Concentration) r_AC_f*z_AD; %Boundary Condition between Anode Diffusion and Catalyst Layers (Diffusion of Methanol) r_AC_f*z_AC^2/2/D_AC; %Boundary Condition between Anode Catalyst Layer and Membrane Layer (Concentration) r_AC_f*z_AC; %Boundary Condition between Anode Catalyst Layer and Membrane Layer (Diffusion of Methanol) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer (Concentration) 0; %Boundary Cond ition between Membrane Layer and Cathode Catalyst Layer (Diffusion of Methanol) 0]; %Boundary Condition at exit of cathode catalyst layer. (Concentration)

PAGE 86

86 k_o = A_S \ B_o_S; %Steady State Coefficients for concentration gradient before load change. k_f = A_S \ B_f_S; %Steady State Coefficients for concentration gradient after load change. syms z C_AD_S = sym((k_f(1)*z+k_f(2))); %Steady state concentration gradient at anode diffusion layer after load change. C_AC_S = sym((r_AC_f/2/D_AC*z^2+k_f(3)*z+k_f (4))); %Steady state concentration gradient at anode catalyst layer after load change. C_M_S = sym((k_f(5)*z+k_f(6))); %Steady state concentration gradient at membrane layer after load change. C_CC_S = sym(k_f(7)*exp(sqrt(r_CC/D_CC)*z)+k_f(8)*exp( sqrt(r_C C/D_CC)*z)); F_AD = sym((k_o(1)*z+k_o(2))) C_AD_S; % Initial condition for Anode Diffusion Layer. F_AC = sym((r_AC_o/2/D_AC*z^2+k_o(3)*z+k_o(4))) C_AC_S; % Initial condition for Anode Catalyst Layer. F_M = sym((k_o(5)*z+k_o(6))) C_M_S; % Initial condition f or Membrane Layer. F_CC = sym(k_o(7)*exp(sqrt(r_CC/D_CC)*z)+k_o(8)*exp( sqrt(r_CC/D_CC)*z)) C_CC_S; %Inital condition for Cathode Catalyst Layer. syms Beta_n A_AD A_AC B_AC A_M B_M A_CC B_CC A_H = [sin(Beta_n*z_AD/D_AC^0.5), cos(Beta_n*z_AD/D_AC^0.5), 0, 0, 0, 0; Beta_n*D_AC^0.5*cos(Beta_n*z_AD/D_AC^0.5), Beta_n*D_AC^0.5*sin(Beta_n*z_AD/D_AC^0.5), 0, 0, 0, 0; sin(Beta_n*z_AC/D_AC^0.5), cos(Beta_n*z_AC/D_AC^0.5), sin(Beta_n*z_AC/D_M^0.5), cos(Beta_n*z_AC/D_M^0.5), 0, 0; Beta_n*D_AC^0.5*cos (Beta_n*z_AC/D_AC^0.5), Beta_n*D_AC^0.5*sin(Beta_n*z_AC/D_AC^0.5), Beta_n*D_M^0.5*cos(Beta_n*z_AC/D_M^0.5), Beta_n*D_M^0.5*sin(Beta_n*z_AC/D_M^0.5), 0, 0; 0, 0, sin(Beta_n*z_M/D_M^0.5), cos(Beta_n*z_M/D_M^0.5), sin(Beta_n*z_M/D_CC^0.5), cos(Beta_n* z_M/D_CC^0.5); 0, 0, Beta_n*D_M^0.5*cos(Beta_n*z_M/D_M^0.5), Beta_n*D_M^0.5*sin(Beta_n*z_M/D_M^0.5), Beta_n*D_CC^0.5*cos(Beta_n*z_M/D_CC^0.5), Beta_n*D_CC^0.5*sin(Beta_n*z_M/D_CC^0.5)]; B_H = [sin(Beta_n*z_AD/D_AD^0.5); Beta_n*D_AD^0.5*cos(Beta _n*z_AD/D_AD^0.5); 0; 0; 0; 0]; Psi_AD_n = sym(A_AD*sin(Beta_n*z/D_AD^0.5)); Psi_AC_n = sym(A_AC*sin(Beta_n*z/D_AC^0.5)+B_AC*cos(Beta_n*z/D_AC^0.5)); Psi_M_n = sym(A_M*sin(Beta_n*z/D_M^0.5)+B_M*cos(Beta_n*z/D_M^.5)); Psi_CC_n = sym(A_CC*s in(Beta_n*z/D_CC^0.5)+B_CC*cos(Beta_n*z/D_CC^0.5)); k_H = simple(A_H \ B_H);

PAGE 87

87 syms Beta_n_t %Homogenous Equations for Unsteady PDEs in matrix form to solve for Eigenvalues. A_H_E = [sin(Beta_n_t*z_AD/D_AD^0.5), sin(Beta_n_t*z_AD/D_AC^0.5), cos(Beta_n_ t*z_AD/D_AC^.5), 0, 0, 0, 0; Beta_n_t*D_AD^0.5*cos(Beta_n_t*z_AD/D_AD^0.5), Beta_n_t*D_AC^0.5*cos(Beta_n_t*z_AD/D_AC^0.5), Beta_n_t*D_AC^0.5*sin(Beta_n_t*z_AD/D_AC^0.5), 0, 0, 0, 0; 0, sin(Beta_n_t*z_AC/D_AC^0.5), cos(Beta_n_t*z_AC/D_AC^0.5), sin (Beta_n_t*z_AC/D_M^0.5), cos(Beta_n_t*z_AC/D_M^0.5), 0, 0; 0, Beta_n_t*D_AC^0.5*cos(Beta_n_t*z_AC/D_AC^0.5), Beta_n_t*D_AC^0.5*sin(Beta_n_t*z_AC/D_AC^0.5), Beta_n_t*D_M^0.5*cos(Beta_n_t*z_AC/D_M^0.5), Beta_n_t*D_M^0.5*sin(Beta_n_t*z_AC/D_M^0.5), 0, 0; 0, 0, 0, sin(Beta_n_t*z_M/D_M^0.5), cos(Beta_n_t*z_M/D_M^0.5), sin(Beta_n_t*z_M/D_CC^0.5), cos(Beta_n_t*z_M/D_CC^0.5); 0, 0, 0, Beta_n_t*D_M^0.5*cos(Beta_n_t*z_M/D_M^0.5), Beta_n_t*D_M^0.5*sin(Beta_n_t*z_M/D_M^0.5), Beta_n_t*D_CC^0.5*cos(Bet a_n_t*z_M/D_CC^0.5), Beta_n_t*D_CC^0.5*sin(Beta_n_t*z_M/D_CC^0.5); 0, 0, 0, 0, 0, sin(Beta_n_t*z_CC/D_CC^0.5), cos(Beta_n_t*z_CC/D_CC^0.5)]; P = simple(det(A_H_E)); %Solve for Eigenvalues Beta_n_t = 1/10^Beta_n_precision; for n = 1:1:n_max n_ max n+1 delta = 1; while delta >= 1/10^Beta_n_precision Test_b = subs(P) >= 0; Beta_n_t = Beta_n_t + delta; Test_a = subs(P) >= 0; if Test_a ~= Test_b Beta_n_t = Beta_n_t delta; delta = de lta/10; end end Beta_n_array(n) = Beta_n_t delta/2*10; Beta_n_t = Beta_n_t + delta*10; end t_array = linspace(0,t_max,t_d); z_array = linspace(0,z_CC,z_d); for n=1:1:n_max Beta_n = Beta_n_array(n); n_max n A_AD = 1;

PAGE 88

88 A_AC = subs(k_H(1)); B_AC = subs(k_H(2)); A_M = subs(k_H(3)); B_M = subs(k_H(4)); A_CC = subs(k_H(5)); B_CC = subs(k_H(6)); N_n = subs(int(Psi_AD_n^2,0,z_AD))+subs(int(Psi_AC_n^2,z_AD,z_AC))+subs(int(Psi_M_n ^2,z_AC,z_M))+subs( int(Psi_CC_n^2,z_M,z_CC)); tail = subs(int(Psi_AD_n*F_AD,0,z_AD))+subs(int(Psi_AC_n*F_AC,z_AD,z_AC))+subs(int(P si_M_n*F_M,z_AC,z_M))+subs(int(Psi_CC_n*F_CC,z_M,z_CC)); for j=1:1:t_d t=t_array(j) nose = subs(1/N_n*exp( Beta_n^2*t)) ; for i=1:1:z_d z=z_array(i); if j == 1 if z <= z_AD C_S(i) = subs(C_AD_S); elseif z <= z_AC & z_AD < z C_S(i) = subs(C_AC_S); e lseif z <= z_M & z_AC < z C_S(i) = subs(C_M_S); elseif z <= z_CC & z_M < z C_S(i) = subs(C_CC_S); end end if z <= z_AD C_H_n(i,j,n) = subs(n ose*Psi_AD_n*tail); elseif z <= z_AC & z_AD < z C_H_n(i,j,n) = subs(nose*Psi_AC_n*tail); elseif z <= z_M & z_AC < z C_H_n(i,j,n) = subs(nose*Psi_M_n*tail); elseif z <= z_CC & z_M < z C_H_n(i,j,n) = subs(nose*Psi_CC_n*tail); end if n == n_max C_H(i,j) = sum(C_H_n(i,j,:)); C(i,j) = C_H(i,j) + C_S(i); end end

PAGE 89

89 end end plot(z_array,C*1000, 'l inewidth' ,2) axis([0 z_CC 0 1.8]) set(gca, 'FontSize' ,16) xlabel( 'MEA Position (cm)' 'FontSize' ,16, 'FontWeight' 'Bold' ) ylabel( 'Methanol Concentration (M)' 'FontSize' ,16, 'FontWeight' 'Bold' ) Chart_Title = sprintf( 'MEA Methanol Concentration Distribution f rom %d mA/cm to %d mA/cm at %0.2f M' ,i_o, i_f,C_FEED*1000); title(Chart_Title, 'FontSize' ,24, 'FontWeight' 'Bold' ) leg1=sprintf( '%0.1f s (%d mA/cm)' ,0*t_max/(t_d 1),i_o); leg2=sprintf( '%0.1f s (%d mA/cm)' ,1*t_max/(t_d 1),i_f); leg3=sprintf( '%0.1f s (%d m A/cm)' ,2*t_max/(t_d 1),i_f); leg4=sprintf( '%0.1f s (%d mA/cm)' ,3*t_max/(t_d 1),i_f); leg5=sprintf( '%0.1f s (%d mA/cm)' ,4*t_max/(t_d 1),i_f); leg6=sprintf( '%0.1f s (%d mA/cm)' ,5*t_max/(t_d 1),i_f); legh=legend(leg1,leg2,leg3,leg4,leg5,leg6); set(legh, Position' [.733,.663,.145,.22]) line([z_AC z_AC],[0 1.8], 'linestyle' -' 'color' 'black' ) line([z_AD z_AD],[0 1.8], 'linestyle' -' 'color' 'black' ) line([z_M z_M],[0 1.8], 'linestyle' -' 'color' 'black' ) format short g Total_CH3OH=(C_FEED C(80,1))/z_ array(80)*D_AD*96485*6*1000 XO_CH3OH=(C(188,1) C(200,1))/(z_array(200) z_array(188))*D_CC*96485*6*1000 CH3OH_Ratio=XO_CH3OH/((C(188,2) C(200,2))/(z_array(200) z_array(188))*D_CC*96485*6*1000) format long poo=[C_FEED; i_o; D_AD; D_AC; r_AC_o; D_M; D_CC; r_C C; Total_CH3OH; XO_CH3OH; CH3OH_Ratio] format short

PAGE 90

90 LIST OF REFERENCES [ 1 ] Moore's La w: Made real by Intel innovation: 2009; Available at: http://www.intel.com/technology/mooreslaw/ Accessed 07/21, 2009. [ 2 ] M. Broussely, G. Archdale, J.Power Sources, 136 (2004) 386 3 94. [ 3 ] http://www.faa.gov/about/office_org/headquarters_offices/ash/ash_programs/hazmat/aircarri er_info/media/Battery_incident_chart.pdf [ 4 ] J.G. Liu, T.S. Zhao, R. Chen, C.W. Wong, Electrochemistry Communications, 7 (2005) 288 294. [ 5 ] A. Heinzel, V.M. Barragn, J.Power Sources, 84 (1999) 70 74. [ 6 ] M. Walker, K. M. Baumgrtner, M. Kaiser, J. Kerres, A. Ullrich, E. Ruchle, J Appl Polym Sci, 74 (1999) 67 73. [ 7 ] ATP Project Brief 00 00 7744: Available at: http://jazz.nist.gov/atpcf/prjbriefs/prjbrief.cfm?ProjectNumber=00 00 7744 Accessed 07/23, 2009. [ 8 ] J.A. McAllister, A.E. Farrell, Energy, 32 (2007) 1177 1184. [ 9 ] BAJ Website | Total battery produ ction statistics: 2011; Available at: http://www.baj.or.jp/e/statistics/01.html. Accessed 08/11, 2011. [ 10 ] R.A. Powers, Proceedings of the IEEE, 83 (1995) 687 693. [ 11 ] B. Scrosati, Electrochim.Acta, 45 (2000) 2461 2466. [ 12 ] J. Vetter, P. Novk, M.R. Wagne r, C. Veit, K. Mller, J.O. Besenhard, M. Winter, M. Wohlfahrt Mehrens, C. Vogler, A. Hammouche, J.Power Sources, 147 (2005) 269 281. [ 13 ] J. Shim, R. Kostecki, T. Richardson, X. Song, K.A. Striebel, J.Power Sources, 112 (2002) 222 230. [ 14 ] J. McLaughlin, (2008). [ 15 ] Ackerman D. New Apple MacBooks demystified. 06/08/09; Available at: http://news.cnet.com/8301 17938_105 10260001 1.html?tag=rb_content;contentMain. Accessed 08/19, 2011. [ 16 ] Stanford University. New Nanowire Battery Holds 10 Times The Charge O f Existing Ones. 2007; Available at: http://www.sciencedaily.com/releases/2007/12/071219103105.htm. Accessed 08/19, 2011.

PAGE 91

91 [ 17 ] K. Scott, W.M. Taama, S. Kramer, P. Argyropoulos, K. Sundmacher, Electrochim.Acta, 45 (1999) 945 957. [ 18 ] S. Song, W. Zhou, W. Li, G. Sun, Q. Xin, S. Kontou, P. Tsiakaras, Ionics, 10 (2004) 458 462. [ 19 ] C.Y. Du, T.S. Zhao, W.W. Yang, Electrochim.Acta, 52 (2007) 5266 5271. [ 20 ] B. Gurau, E.S. Smotkin, J.Power Sources, 112 (2002) 339 352. [ 21 ] S. Doerner, T. Schultz, T. Schneider, K. Sun dmacher, P. Hauptmann, Sensors, 2004. Proceedings of IEEE, (2004) 639 641 vol.2. [ 22 ] Dielectric Constants of Materials: 2008; Available at: http://clippercontrols.com/info/dielectric_constants.html#D. Accessed 07/24, 2009. [ 23 ] H. Zhao, J. Shen, J. Zhang, H Wang, D.P. Wilkinson, C.E. Gu, J.Power Sources, 159 (2006) 626 636. [ 24 ] J. P. Longtin, C. H. Fan, Microscale T hermophysical E ngineering, 2 (1998) 261 272. [ 25 ] CRC h andbook of c hemistry and p hysics, CRC Press; 1978 pp. 8 70 [ 26 ] A. Rabinovich, E. Diatzikis, J. Mullen, D. Tuli mieri, US patent 6,815,682 (2003). [ 27 ] G.C. Benson, P.J. D'Arcy, Journal of Chemical & Engineering Data, 27 (1982) 439 442. [ 28 ] M. Baldauf, W. Preidel, US Patent 6,536,262 [ 29 ] F.M. White, Fluid m echanics, 6th ed., McGraw Hill Higher Education, Boston MA ; 2008 pp. 864. [ 30 ] D. Sparks, R. Smith, V. Cruz, N. Tran, A. Chimbayo, D. Riley, N. Najafi, Sensors and Actuators A: Physical, 149 (2009) 38 41. [ 31 ] S.R. Narayanan, T.I. Valdez, W. Chun, Electrochem.Solid State Lett., 3 (2000) 117 120. [ 32 ] C.L. Chang, C.Y. Che n, C.C. Sung, D.H. Liou, J.Power Sources, 164 (2007) 606 613. [ 33 ] J. Cristiani, N. Sifer, E. Bostic, P. Fomin, D. Reckar, Annual Meeting of the American Institute of Chemical Engineers, (2005). [ 34 ] E. Antolini, R.R. Passos, E.A. Ticianelli, J.Appl.Electroc hem., 32 (2002) 383 388. [ 35 ] P. Argyropoulos, K. Scott, W.M. Taama, Electrochim.Acta, 45 (2000) 1983 1998. [ 36 ] Q. Ye, T.S. Zhao, H. Yang, J. Prabhuram, Electrochem.Solid State Lett., 8 (2005) A52 A54.

PAGE 92

92 [ 37 ] A. Casalegno, P. Grassini, R. Marchesi, Appl.Therm .Eng., 27 (2007) 748 754. [ 38 ] C. Eickes, P. Piela, J. Davey, P. Zelenay, J.Electrochem.Soc., 153 (2006) A171 A178. [ 39 ] F. Liu, C. Wang, J.Electrochem.Soc., 154 (2007) B514 B522.

PAGE 93

93 BIOGRAPHICAL SKETCH he moved with his family to Ormond Beach, Florida. In the spring o f 2006, Jason graduated with his Bachelor of Science in mechanical engineering from the University of North Florida There, he developed an interest in clean and renewable energy while working under Dr. James Fletcher as a laboratory assistant. In 2010, he began working as a systems engineer for direct methanol fuel cell s with the University of North Florida. Jason graduated with his Master of Science in mechanical engineering in the summer of 2012.