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OPTIMIZING TIME RESOLVED PHOSPHORIMETRY BY CHARLES GLENN BARNES A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1980 ACKNOWLEDGEMENTS I wish to first express my belief in the guidance of Jesus Christ in my life, and in my career. In addition, I would like to take this opportunity to express my gratitude to those people who have assisted me in this endeavor. To my research director, Dr. James D. Winefordner, go my appreciation and thanks for his patience and support, and for his willingness to make himself readily accessible to students. To Dr. John Legg of Mississippi College go my sincere thanks for his friendship and guidance, and for the example that he sets for myself and other students. I would like to express my loving gratitude to my wife, Joyce, who continued to love me even through the ultimate test of a marriage the writing of a dissertation; and to my parents and family who have con tributed their love and financial support for these 25 years. Many thanks to my friends at the Baptist Student Center for making me a part of your fellowship. Thanks are due to Art Grant and the Machine Shop gang for their artistry, and to the JDW group for their knowledge and the willingness to share it. TABLE OF CONTENTS Page ACKNOWLEDGEMENTS  ii LIST OF TABLES  iv LIST OF FIGURES  v ABSTRACT vii CHAPTER I. INTRODUCTION 1 1 Historical  1 Time Resolved Phosphorimetry  5 II. THEORETICAL CONSIDERATIONS  28 Kinetic Analysis of Molecular Processes  28 Intensity Expressions  30 Response Profiles  61 Summary  100 III. EXPERIMENTAL 102 Instrumentation 102 Reagents 112 Instrumental Procedure  113 Sampling Procedure 114 IV. RESULTS AND DISCUSSION 118 Validation of Theoretical Analysis  118 Time Resolution of Phosphor Mixtures  141 V. CONCLUSIONS 155 APPENDIX  157 LIST OF REFERENCES 164 BIOGRAPHICAL SKETCH 167 iii LIST OF TABLES TABLE Page 1. FINAL WORKING EQUATIONS FOR THE EXPONENTIAL METHOD OF TIME RESOLUTION FOR A BINARY MIXTURE  24 2. FINAL WORKING EQUATIONS FOR THE EXPONENTIAL METHOD OF TIME RESOLUTION FOR A TERNARY MIXTURE  25 3. DEFINITION OF PARAMETERS  38 4. KEY TO GATE WIDTH FOR FIGURES 57 51 5. PARAMETERS FOR RESPONSE PROFILES  63 6. EXPERIMENTAL EQUIPMENT AND MANUFACTURERS  105 7. PRELIMINARY LIFETIME MEASUREMENTS 119 8. PARAMETERS FOR EXPERIMENTAL VALIDATION  121 9. COMPARISON OF THEORETICAL AND EXPERIMENTAL INTENSITY RATIOS FOR THIORIDAZINE HC1  125 10. COMPARISON OF THEORETICAL AND EXPERIMENTAL INTENSITY RATIOS FOR VANILLIN  126 11. COMPARISON OF THEORETICAL AND EXPERIMENTAL INTENSITY RATIOS FOR NUPERCAINE HCl  127 12. AVERAGE RESULTS OF INTENSITY MEASUREMENTS FOR THREE PHOSPHORS  128 13. ANALYSIS OF BINARY MIXTURE I 147 14. ANALYSIS OF BINARY MIXTURE II  149 15. ANALYSIS OF TFRP.APY MIXTURE I 152 Al. KINETIC EVENTS IN A RIGID GLASS SYSTEM CONTAINING ONE SOLUTE 158 LIST OF FIGURES Figure 1. Schematic diagram and molecular electronic and vibrational energy levels 2. Schematic representation of the operation of a pulsed source gated phosphorimeter 3. Schematic representation of the excitation process with a pulsed source  4. A typical relative response profile 5. Optimum delay versus 6. Optimum delay versus 7. Optimum delay versus 8. Response profile Response Response Response Response Response Response Response Response Response Response profile profile profile profile profile profile profile profile profile profile 19. Response profile (tg (tg (tg (tg (tg (tg (tg (tg (tg (t g (tg (tg (t lifetime (f = 1 Hz)  lifetime (f = lifetime (f = 5x 3 , 5x10 s, = 5x10 3S, = 5x103, = 5xl03s, = 5x10 s, = 5xl4, = 5x10 s, = 5x10 5, 4 = 5x10 5s, = 5xlO4s, 5 = 5x10 s, 5 = 5x10 s, 5 = 5x10 S, 5 = 5x10 s, 10 Hz) 50 Hz) f = 1 Hz) f = 10 Hz)  f = 50 Hz)  f = 100 Hz) f = 1 Hz) f = 10 Hz) f = 50 Hz) f = 100 Hz) f = 1 Hz) f = 10 Hz) f 50 Hz) f = 100 Hz) 55  57  65 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. Page 20. Schematic representation of phosphorescence growth during the excitation pulse for two phosphors with different lifetimes  92 21. Schematic representation of the effect of gate width on observed phosphorescence signal 95 22. Schematic representation of the effect of frequency on pulsetopulse phosphorescence intensity growth  98 23. Block diagram of the experimental system  104 24. Growth profile for thioridazine HC1 at 1 Hz 132 25. Growth profile for thioridazine HC1 at 10 Hz 134 26. Growth profile for thioridazine HC1 at 100 Hz 136 27. Growth profile for nupercaine HC1 at 10 Hz  138 28. Growth profile for nupercaine HC1 at 100 Hz  140 Al. Kinetic processes occurring during growth and decay of phosphorescence  160 Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTIMIZING TIME RESOLVED PHOSPHORIMETRY By Charles Glenn Barnes December, 1980 Chairman: James Dudley Winefordner Major Department: Chemistry Time resolved phosphorimetry (TRP) is an analytical method with primary application to analysis of multi component mixtures of spectrally similar species. The resolution of such a mixture is attained by utilizing differences in the phosphorescence decay lifetimes (T) of the mixture components. Earlier work has relied heavily upon multichannel detection systems which scan the entire emission decay curve as a function of time. However, a phosphorimeter incorporating a pulsed excita tion source with a single channel gated detection system (boxcar average or integrator) has several characteris tics that make it attractive for TRP. These include relatively low cost and flexibility in selection of the operating parameters of gate width (t ), delay time (td), pulse repetition rate (f), and integration time constant. This flexibility should allow resolution of mixtures over a large range of phosphorescence lifetimes. vii In this work, the potential for applying such a system to TRP is examined. Theoretical expressions are derived which demonstrate the relationships of observed phosphorescence intensity on the phosphorescence lifetime and on the characteristic parameters of the experimental system. Plots of relative response versus lifetime under various sets of parameters are presented and are used to predict and interpret the effect of excitation peak width, t td f and T on the observed signal level. At a fixed set of parameters, there is a lifetime to which the system has optimum response, T max" An expression is presented which allows positioning this maximum at any selected lifetime. A pulsedlaser source boxcar average phosphorimeter is described. Experimental results are presented to demonstrate the validity of the theoretical expressions. The expressions are used to optimize the experimental system for TRP analysis of binary and ternary mixtures of spectrally similar species. Results indicate that this type of analysis requires a mixture with two or three components, the lifetimes of which differ by a factor of two or more. The major errors are due to photodecomposition of the samples and excessive source flicker noise. viii CHAPTER I INTRODUCTION Historical Phosphorimetry was first proposed as a method of chemical analysis by Lewis and Kasha (1). They reviewed the little that was known about phosphorescence at that time, and based upon their own research, wrote "for every substance, there is a unique phosphorescent state" (p.2102). Further, they ascribed phosphorescence to the triplet state of the unsaturated molecule. The next significant work on phosphorimetry was that of Keirs, Britt and Wentworth thirteen years later (2), which first demonstrated the enormous potential of phosphorimetry for chemical analysis. The authors discussed the experimental and theoretical aspects of phosphorimetry and demonstrated that binary mixtures of phosphors could be spectrally resolved by judicious selection of excitation and emission wavelengths. For mixtures of phosphors whose excitation and emission spectra were similar, they used a technique called "phos phoroscopic resolution," which resolved the components by utilizing differences in their phosphorescence decay rates. The technique was applicable to phosphors having lifetimes in the millisecond region. O'Haver and Winefordner in 1966 discussed the in fluence of mechanical phosphoroscope design on the detected phosphorescence intensity (3). Expressions were derived which related the measured and instantaneous phosphorescence intensity to the decay time of the phos phorescent species and to the characteristic parameters of the phosphoroscope used in the measurement system. Numerical results were given for two different phos phoroscopes. The expressions were later extended (4) to apply to pulsed sources and gated detection systems, specifically, to a pulsed flash tube and a pulsed photo multiplier tube, using an averagereading DC meter for output. They were able to predict the "sampletointer ferent ratio enhancement" under differing sets of experi mental conditions, based upon the relative lifetimes of the analyte and interferent. St. John and Winefordner (5) published the results of a study on "Time Resolved Phosphorimetry," in which binary mixtures of phosphors were resolved based upon differences in lifetime. The method employed a CW source and a DC readout system coupled with a logarithmic con verter to display logphosphorescence intensity versus time, following the cessation of excitation via a manual guillotine shutter. Hollifield and Winefordner (6) designed a unique singledisk phosphorimeter to measure intensity at small intervals along the emission decay curve and used it to time resolve several binary mixtures. The overall error was found to be largest when the lifetimes of the components were similar, or when one component was present in great excess. Winefordner suggested the potential advantages of utilizing a pulsed source fast (gated) readout system for time resolved phosphorimetry (7). Fisher and Winefordner (8) built such a system and applied it to the analysis of binary and ternary mixtures of phosphors. The system was designed primarily for rapidly decaying nir* phosphors and utilized a pulsed flash tube for excitation and a multichannel signal average coupled to a logarithmic converter for output. Expressions were derived which related measured phosphorescence signal to the concentration of each analyte phosphorr) in a multicomponent mixture of spectrally similar organic molecules. Three specific methods of data reduction were described and employed for estimating concentrations from phosphorescence signals measured at different times after the termination of excitation. O'Donnell et al. (9) modified the Fisher phosphorimeter by using a higher powered xenon flashlamp and a rotating sample cell, and quantitated mixtures of halogenated biphenyls. Harbaugh, O'Donnell, and Winefordner measured phosphor imetric lifetimes and qualitatively and quantitatively identified drug mixtures with this system (10,11). Wilson and Miller (12) described a versatile computercontrolled laser phosphorimeter. The phos phorescence spectra were recorded on magnetic tape as a family of signal averaged decay curves. The system would average one hundred decay curves at 1 nm intervals over a 150200 nm range. The technique of component resolved spectrometry was discussed in detail and illustrated by resolution of the phosphorescence spectra of a binary mixture. The data reduction involved a non linear least squares fit in ndimensional space (12,13). O'Donnell and Winefordner (14) reviewed advances in instrumentation and methodology for phosphorimetry, and discussed the potential of the pulsed source gated detec tion system over standard systems. Goeringer and Pardue (15) designed a silicon intensifiedtarget vidicon (SIT) camera for phosphorescence studies and described applica tions to room temperature phosphorimetry of salts of organic acids. The spectral decay data were processed by a variety of regression methods, which were based in part upon the work of Ridder and Margerum (16), Mieling and Pardue (17), and Willis et al. (18) on simultaneous kinetic analysis. In addition, the authors applied the internal standard method to phosphorimetry for the first time and reduced overall imprecision by two to five times. Boutilier and Winefordner (19) described a lasersource time resolved phosphorimeter and applied it to investigating the external 5 heavy atom effect on the phosphorescence lifetimes, relative intensities, and limits of detection of drugs. Time Resolved Phosphorimetry Phosphorescence is the longlived luminescence observed following excitation of some types of molecules with an external light source. The physical basis for phosphorescence can be seen in Figure 1, which is a schematic diagram of the processes taking place during excitation/emission of molecular luminescence (2,20). Absorption of a photon (A) excites the molecule to some vibrational level of an excited singlet state (10 15s). (Absorption to a triplet state is extremely unlikely, because the transition is spinforbidden.) Usually, the first excited singlet, Si, is the state that is optically pumped, but not always. Within the electronic state thus populated, vibrational relaxation (VR) (plus solvent relaxation), efficiently deactivates the molecule to the lowest vibrational level of that electronic state (10 13s). Further deactivation to a lower electronic level occurs by internal conversion (IC), which is a nonradiative relax ation to a lower electronic state of the same multiplicity 12 (10 12s). Once the molecule is in the S1 state, further deactivation can occur by further internal conversion to the ground state. However, because the energy gap between S and S1 is usually larger than that between the higher electronic states, the process is less efficient, and a Figure 1. Schematic diagram of molecular electronic and vibrational energy levels. I  ^ j 1 t II II A A I SC ISC P/ ISC P TRIPLET MANIFOLD SINGLET MANIFOLD spinallowed radiative transition, fluorescence (F), can compete effectively for depopulation of the S1 state. There is, however, another pathway for deexcitation of the S1 state. Due to spinorbital coupling, the less energetic T1 state can be populated from the S1 state. This nonradiative process, occurring between states of differing multiplicity,is intersystem crossing (ISC). The efficiency of ISC varies greatly from molecule to molecule, and is extremely dependent upon the molecular environment. The T1 state can be depopulated by further ISC to the ground state singlet, or by a spinforbidden radiative transition, T1* S0. This spinforbidden radiative tran sition between states of different multiplicity is phos phorescence (P). The probability of a spinforbidden 3 6 transition is 10 to 10 smaller than that of the corresponding spinallowed transition. Therefore, the mean lifetime of the T1 state is usually 10 3s to several seconds in duration, while the mean lifetime of the S 8 state is approximately 10 8s. Observation of molecular luminescence requires that the radiative processes compete effectively with the non radiative processes for depopulation of the excited states. Therefore, molecules possessing rigid molecular skeletons and large separations between the ground state and lowest excited states most often exhibit fluorescence/phosphores cence (20). Note that the two luminescence processes compete indirectly for depopulation of the T1 state. Aromatic molecules, possessing rigidring structures, form the largest class of compounds to exhibit lumines cence. Due to the long lifetime of the triplet state, many other processes compete with phosphorescence for depopulation of the triplet. These include collisional deactivation by solvent molecules; quenching by para magnetic species, especially oxygen; and photochemical processes. For this reason, phosphorescence is normally observed with the phosphorescent species phosphorr) frozen rigidly into a solvent matrix at or below liquid nitrogen temperatures (77 K). This minimizes collisional processes (20). The instrument used to measure phosphorescence is known as a phosphorimeter. The sample is irradiated with a suitable source, and the phosphorescence is usually ob served at 90 to the excitation axis. Because phospho rescence has a longer lifetime (i.e., persists for a longer time following termination of excitation) than scatter and fluorescence, phosphorescence can be measured without interference from either process by using an experimental system that excites the sample for some period of time, stops the excitation, and waits for fluorescence and scatter to disappear before making the intensity measurement (14). Normally, a mechanical shutter system (phosphoroscope) is employed, but pulsed systems have been applied to advantage (811,21). In order for phosphorescence to be used for quanti tative chemical analysis, there must be a welldefined relationship between analyte concentration and observed phosphorescence intensity. An approximate relationship is given by Equation (1), which assumes a dilute solution of the analyte, monochromatic radiation, and no prefilter or postfilter effects: P = P 2.3 abc Y (1) p 0 p In Equation (1), P is defined to be the radiant phospho P rescence power (W) emitted under a given set of experimental conditions, Y is the power efficiency (ratio of radiant P power emitted to radiant flux absorbed), a is the molar i I absorptivity (L mole cm ), b is the absorption path length (cm), and c is the molar concentration of the absorber (mole L ). The approximation (2.3 abc) < 0.05 is required for this linear relationship to be valid, and is normally met at the low concentration levels encountered in analytical phosphorimetry. This expression is strictly valid only when the excitation and emission have reached steady state (21,22,23). Conventional phosphorimetry, as an analytical method, exhibits excellent sensitivity, low limits of detection, and large linear dynamic ranges for many phosphors. Selectivity is inherent in the nature of phosphorimetry; both the excitation and emission wavelengths can be varied to selectively excite/monitor the phosphorescence due to one particular species. The principal Value of phosphorimetry was pointed out by O'Donnell and Winefordner in 1975 in a review article on phosphorimetry in clinical analysis. They stated: the greatest use of phosphorimetry in the clinical laboratory will not be for the analysis of very large numbers of samples for one species via automatic instrumentation, but rather will be for the analysis of those species impossible to measure by conven tional methods. . (14, p. 285) This statement summarizes quite well the contribution of phosphorimetry towards analytical chemistry as a whole. Although phosphorimetric analysis does have a high degree of inherent selectivity, cases obviously arise in which interfering phosphors cannot be adequately minimized by spectral resolution. Molecular emission bands are quite broad, and so spectral overlap occurs frequently. Increased selectivity is required to solve this problem, and the additional selectivity is achieved in the time domain. The observed phosphorescence intensity following an excitation pulse decays away slowly. In most cases, the shape of the "emission decay curve" is an exponential function, with the intensity at any time, t, given by I = I0 exp (t/T) (2) where I is the observed phosphorescence intensity at time t, I0 is the initial (t = 0) intensity, and T is the phos phorescence decay lifetime(s). In this work, T or "lifetime" will refer exclusively to the experimentally observed phosphorescence decay lifetime. Any other type of lifetime will be distinguished from T by a subscript or superscript. The experimental lifetime is a function of both the specific molecule phosphorr) and the specific environment and temperature. Fortunately, it does not vary greatly with temperature in the vicinity of 77 K. Neither does T show substantial variation with concentra tion over a limited concentration range, although changes in the solvent system, or even in the sampling/freezing process, can cause T to vary. However, for one specific set of experimental conditions, T is characteristic of the particular molecule under study, and is independent of analyte concentration in dilute solutions (7,21,24). Phosphors tend to fall into two relatively distinct categories with regard to lifetime. Molecules involving an nf* transition carbonylss, thiocarbonyls, and some azo compounds) tend to have lifetimes on the order of milliseconds. Those involving 7'T* transitions typically exhibit lifetimes ranging from tenths of a second to tens of seconds (25). The entire range of phosphorescence lifetimes is thus approximately 10 4s to 10 s. The probability of two different phosphors in a sample mixture possessing identical excitation maxima, emission maxima, and lifetimes is small, although this does occur. Resolu tion of spectrally similar phosphors based upon differences in phosphorescence lifetime is known as time resolved phosphorimetry (TRP). TRP is of value when instrumental or spectroscopic methods for resolution fail, or are not available; and if prior chemical treatment of the sample would not effect the desired separation, would result in lengthy analysis, or would introduce contamination (21). Conventional mechanical shutter phosphorimeters do not have the versatility required for application to TRP. Instead, a pulsed source gated detection system (which has advantages even for conventional phosphorimetry) is required. A pulsed source TRP system employing a conventional single channel ("boxcar" average or integrator) measurement system is shown schematically in Figure 2 (4). The source is pulsed on for a period of time of t the excitation pulse width (s). Phosphorescence is excited from the sample and decays exponentially follow ing termination of the excitation pulse. After a suitable delay time, td(s), the signal from the detector is sampled for a fixed period of time, known as the aperature dura tion or gate width, t (s). The excitation/measurement g cycle occurs at a repetition rate or frequency of f (Hz). The output signal level is proportional to the area under the emission decay curve bounded by the gate width. The exact nature of the relationship between signal level and area depends upon the specific measurement system employed. The theoretical advantages of the pulsed system over the conventional have been pointed out previously (7,8,14). Figure 2. Schematic representation of the operation of a pulsed source gated phosphorimeter. < AIISN2HINI I T These include increased precision resulting from increased signaltonoise ratios (SNR), due to minimization of non sourceinduced noise,and similar signal levels; lower detection limits resulting from increased SNR; and the ability to monitor phosphors having short lifetimes without interference from the slowly decaying trailing edge of a mechanically chopped excitation pulse. The most important advantage for application to TRP, however, is the versa tility of the system, due to the relatively independent variability of the gate width, delay time, and repetition rate. It must be noted that in practical applications, the predicted increase in SNR has never been fully realized (26,27). The recent trend in TRP instrumentation has been towards multichannel detection systems, such as the multi channel signal average and the computercontrolled phosphorimeter, which monitor the entire emission decay curve following each excitation pulse (810,12,15). Sophisticated data handling techniques are also becoming common (1518). However, there seems to be an enormous potential for applying less complex single channel in strumentation to TRP. This potential has never been ade quately explored. The single channel or boxcar system can be used to monitor the entire emission decay curve by scanning the gate in time, but this is a timeconsuming process. The strength of this type of system lies in measuring intensities at a few carefully selected times on the decay curve. Reasons for utilizing the pulsed source single channel gated detection system for TRP are as follows: (i) Boxcar averager/integrators are "relatively" inexpensive and readily available; (ii) The versatility of this type of instrument is enormous, due to the aforementioned independent adjust ability of operating parameters; (iii) Boxcar instruments are available to work on almost any time scale, from seconds to less than nano seconds; this, coupled with the versatility, make possible a TRP analysis over a large range of sample lifetimes; some earlier systems were limited to either very rapidly decaying species (8) or very slowly decaying species (5), but not to both; and (iv) The data manipulation can be as simple or as sophisticated as desired, while multichannel systems require manipulation of very large quantities of data, if the full potential of such an instrument is to be realized. This work is concerned with the application of a pulsedlaser source boxcar average phosphorimeter to TRP. The advantages of the laser as a pulsed excitation source are well known, and include high peak powers, short pulse widths, variable repetition rate, and nearly monochromatic output. It is important to realize that in most cases it is not possible to eliminate directly by time resolution the intensity contributions of all phosphors other than the one of interest; that is, one can not make a single intensity measurement and relate this to analyte concentration. What is usually necessary is to make intensity measurements at several times along the emission decay curve of the mixture, and then to extract mathematically (via simultaneous equations) the intensity contributions of the individual components. These deconvoluted intensities can then be related to the concentrations of the individual mixture components. Fisher and Winefordner (8) described three methods for this type of data reduction, two of which are suitable for TRP using a single channel detection system. Both require that the individual phosphors comprising the sample mixture behave independently of one another, which must be true for all multicomponent phosphorimetric analyses. In the multipleanalyticalcurve method (MAC), it is assumed that the analytical calibration curve (in linear coordinates) for a given phosphor has a slope which is dependent upon the delay time at which the intensity is measured (with f, t and t constant). By setting P g up simultaneous equations stating that the total intensity at any one delay time is equal to the sum of the inten sities of the individual components, expressions can be obtained which relate the concentrations of the individual phosphors to the intensity measurements obtained for the mixture. This method does not require knowledge of the lifetimes of the phosphors, but it is very time consuming, because it requires a calibration curve for each component at each delay time (n delay times required for an ncompo nent mixture). The exponential method (EM) is the technique chosen for this work. It does require measurement of the life times of the individual components of the mixture, but these can be determined by scanning the single channel system. As mentioned earlier, this scanning process is relatively slow, but is required only for the initial determinations, and not for the actual intensity measurements on the mixture. The advantage of this method is that only one calibration curve is required per component, and thus the exponential method should be less time consuming overall than the MAC method, even when preliminary lifetime measurements are considered. The working equations for EM are derived in the following manner (21). Let a hypothetical binary mixture consist of components A and B with lifetimes T and T , and let the intensities be measured at delay times t and td Equation (2) can be rewritten specifically for the "2 intensity contribution of A at delay time td "1 IA = I exp (td /TA) (3) A A0 1 A where I is the initial intensity (at arbitrary or actual A0 td= 0) of A. The equivalent expression for component B is IB = I exp (t /TA) (4) 1 B 0 d1B Similar expressions can be written for the intensity con tributions of A and B at delay time td Because the total intensity, IT at any time is the sum of the inten sities of A and B at that time, I = I exp (t /TA)+I exp (tA ) (5) T1 A0 d1 A B0 d1 B and I = I exp (td /TA)+ IB exp (t d/T ) (6) 2 0 "2 0 "2 B These two equations can be solved simultaneously for IA A0 and TB and these values, when substituted into Equations B0 3 and 4, yield I and I Actually, once I and I are A! B! ,I1 I1 A0 IB0 known, the intensities of A and B at any delay time, td, N can be found by multiplying by exp (td /T). The intensities N so obtained can be used to determine the concentration of A and B from calibration curves prepared for pure solutions of A and B at delay time td. Fisher and Winefordner (8) and N Fisher (21) derived the working equations for the two com ponent mixture. These are presented in Table 1, in a form that will allow calculation of the intensity of that com ponent at any delay time. The symbolism I refers to the XN intensity contribution of component X at delay time N. Note that the quantity in brackets is equal to the intensity of component X at td = 0 (I x), and that this is multiplied by an exponential term to yield the intensity at various t 's. This same approach can be applied to a three component ternaryy) mixture. In this case, there are three components, A, B, and C, with lifetimes TA, TB, and TC and three delay times, t, t and td. Fisher calculated one of d1 d2 d3 the expressions; the others were derived in this work. The three working equations are given in Table 2. It should be noted that, due to the complexity of the simultaneous equations, Cramer's Rule was required for their solution (28). Although the expressions appear formidable, if the exponential terms are calculated in advance, and inserted with the experimentally determined mixture intensities IT IT2 and I3 the mathematics is easily handled on a pocket calculator. An interesting question arises here. Only one cali bration curve per component is required for the exponential method. However, the intensity contribution of any component can be calculated at any delay time. Under what conditions, then, should the single calibration curve be prepared? Certainly, the largest intensity would occur at td = 0 (although there are some practical limitations on using td = 0), and one would expect that preparing all calibration curves at the shortest delay time would yield optimum results. This minor point will be examined (experimentally) to some extent. In order to insure that the results of such a multi component analysis have validity, there are several require ments that must be met. These were stated very clearly by Ridder and Margerum (16): multiple component analysis performed by the direct measurement of the physical properties of the com ponents . must meet several general require ments. First, the number of measurements obtained at different values of the independent variable (i.e., wavelength, time, etc.) must be at least equal to the number of components to be determined (however, additional data may improve precision). Second, the relative contributions of the components at each measurement must not be redundant (i.e., there must be at least as many non degenerate equations as there are components). Third, the absolute and relative contributions of each component to the measurement must be large enough to achieve the sensitivity desired. . (p. 2098) In TRP, the first requirement is met by taking measurements at as many different delay times as there are components to be quantitated. The second and third conditions for TRP may be explained as follows. Intensity measurements are made at different points in time, with the aim of correlating these mathematically to the ex perimental decays of the individual components. Obviously, each measurement must have significance (i.e., a good SNR). In addition, the delay times must be chosen in such a way as to insure a significant difference in total signal at the various points, because it is indirectly the difference in signal levels that contains the desired information. For experimental work, this requires that the difference in signal levels between the different times must be larger than the uncertainty of any of the measure ments. Thus, it is necessary that the relative intensities of the mixture components differ significantly at the various delay times, and also that the total intensity varies significantly. Knowing in advance that the second and third conditions will be met is much more difficult, because it requires some prior knowledge of the relative intensities of the components, as well as the total intensities, at several sets of experimental conditions. Because the actual number of measurements required for a TRP analysis is large, and sampling in phosphorimetry is normally time consuming, it is obvious that trial and error selection of experimental conditions is not a viable choice, although this has been done (8). Therefore, a large part of this work has explored how the choice of experimental conditions affects the relative intensity contributions from the individual components of a mixture, and how the conditions can be optimized for a particular separation. The overall goal of this work is to examine the potential of a pulsedlaser source boxcar average detection system for time resolved phosphorimetry. This is accomplished in part by deriving expressions relating observed phosphorescence intensity to the operating characteristics of the experimental system and to the lifetimes of sample components. This allows prediction of the relative effects of the various adjustable param eters, and gives insight into how the general require ments for multicomponent analysis can best be met for a given analysis. Experimental results are presented to verify the conclusions drawn from the theoretical work, which are then used to optimize the experimental system for TRP analysis of twocomponent and threecomponent mixtures of spectrally similar molecules. TABLE 1 FINAL WORKING EQUATIONS FOR THE EXPONENTIAL METHOD OF TIME RESOLUTION FOR A BINARY MIXTURE SITexp(td /TA) I T exp(td/TA) ixp(td /TA)exp(td /TB)exp(td /TB)exp(td /TA) 1 2 1 A exp(t d /T) Nexp(td/B exp(t /AB) 'N 'AN BBN TABLE 2 FINAL WORKING EQUATIONS FOR THE EXPONENTIAL METHOD OF TIME RESOLUTION FOR A TERNARY MIXTURE + (Y)IT +(Z) IT T3 Sexp(td /TA ) (Y)exp(t /T A)+(Z)exp(t d/TA) A^ A where X = exp(td /TB)exp(td /1 C)exp(td2/CC)exp(td/B) Y = exp(td /TC) exp(td /TB)exp(t /TB )exp(t d/tc) Z = exp(t d/T B)exp(td /Tc)exp(td /Tc)exp(t /B) continued IAN TABLE 2continued IBN where (X)I T + (Y)I T + (Z)I (X)exp(td /TB)+(Y)exp(t dAB)+(Z)exp(td /B) 1d23/ exp(t /TB ) (d B X = exp(t d/Tc )exp(td /TA )exp(t d/TA)exp(td /TC) Y = exp(t /TA)exp( /T)e(xp(t /TC )exp(t /TA) Z = exp(t /TC )exp(t d/TA )exp(t /TA )exp(td /T) continued (10) TABLE 2continued (X)IT + (Y)IT2 +(Z)I T (X)exp(T1 )+(Y)exp(t /)+(Z)exp(t3 / (X) exp (tdl/Tc) +(Y) exp (td2/TC)+(Z) exp (td3/Tc)j exp(t /TC ) N X = exp(td /TA)exp(td /TB)exp(td /TB)exp(td /TA) 2j 3 2~ 3J Y = exp(td/TB)exp(td/TA)exp(td/TA)exp(td3/TB) Z = exp(t /TA )exp(t d/TB)exp(td /TB)exp(td /TA) AL d2 1 2 I = CNwhere where (11) CHAPTER II THEORETICAL CONSIDERATIONS In this chapter, the theoretical aspects of TRP will be dealt with. First, the kinetic events occurring during excitation and initiation of phosphorescence emission will be discussed. The results of this analysis, coupled with the knowledge of how the gated detection system responds to the emitted luminescence, yields an expression which relates measured signal level to the parameters of excitation pulse width, repetition rate, delay time, gate width, and phosphorescence lifetime, T, of the analyte. This expression is used as a basis for predicting the effects of the individual parameters, and how these parameters may be optimized for a particular phosphorimetric analysis. Kinetic Analysis of Molecular Processes(29) This section is a summary of the conclusions reached by McGlynn, Srinivasan, and Maria (29) in a superb paper on the kinetic processes occurring during phosphorescence. The details of the mathematical model and the derivations employed are presented in the Appendix. Tables and figures are reprinted by permission of the publisher. The system studied is a phosphor species frozen into a glassy matrix. This matrix gives good optical characteristics, and minimizes solutesolute interactions. In this matrix, decay is usually first order (exponential), and the concept of mean phosphorescence lifetime is valid. As stated earlier in this work, T refers to the experimen tally observed phosphorescence decay lifetime. The analysis in the Appendix approximates T as a function of fundamental rate constants for the processes involved in excitation/deexcitation of the triplet state. There is, however, another lifetime associated with a phosphor, this being the phosphorescence growth lifetime, designated R T (R for rise). The growth lifetime describes the rate of phosphorescence intensity increase when a phosphor sample is irradiated. What is predicted theoretically, and observed experimentally, is that the observed phos phor intensity grows exponentially while the excitation continues, eventually reaching a steady state value. This steady state intensity level is designated 10 and is the maximum intensity observable for that sample and experi mental system. The actual relationship describing the growth of phosphorescence when the sample is subjected to constant intensity irradiation is I = [lexp(t/T ) ]I0 (12) where I is the intensity at time t. In addition to RD Equation 12, the difference between T and T is of great Interest. It has been found that in many cases, T and T interest. It has been found that in many cases, T and T are not identical, but that T < T. The magnitude of the difference between the two is expected to increase when T is large, when the quantum efficiency for intersystem crossing is large, and when the excitation intensity is large. In the limit of very small excitation intensity, R the difference between T and T approaches zero. Experi mental comparisons of the growth and decay of a number of phosphors were cited, and the results included values R for naphthalene, with T = 16.6 s and T = 19.9 s; for triphenylene, with T = 10.4 s and T = 13.4 s; and for R phenanthrene, with T = 3.3 s, and T = 3.9 s. The difference between T and T varies from 8% to 25% for these phosphors. Intensity Expressions O'Haver and Winefordner (3,4) derived an expression which related the observed phosphorescence intensity to the temporal characteristics of the luminescence and to the operating parameters of the measurement system. The system discussed was an averaging DC meter. The re sulting expression containrB observed luminescence intensity dependence upon T, t p, f, td, and t Plots of relative g intensity versus lifetime (other parameters constant) showed distinctive features, the most significant of which was that under various combinations of experimental pa rameters, there was a point of maximum intensity, correspond ing to a particular phosphorescence lifetime. The lifetime corresponding to the point of maximum instrumental response is designated T max. By using simplifying assumptions, it was possible to derive an expression that enabled one to choose the experimental conditions to shift that point of maximum response to a given phosphor lifetime. Possible applications were given, such as calculating theoretical analyte/interferent intensity ratios based on their life times. No experimental evidence for validation of the underlying model was given. In addition, the expression allowing calculation of optimum experimental conditions was based on an assumption which invalidates the expres sion for some very useful practical cases. In this chapter, a similar expression will be de rived. There will be several major differences,however. The measurement system employed for this derivation is the gated (boxcar) average. In the initial derivation, a distinction is made between phosphorescence growth life time, T and phosphorescence decay lifetime, T. Later, the expression for optimization will be derived in such a way as to be valid over a much wider range of conditions. Most importantly, major emphasis will be placed upon trying to explain on a physical basis the trends pre dicted from this theoretical analysis. The underlying factor throughout this chapter is the search for results of practical applicability. The concept of exponential growth of phosphorescence during irradiation is critical to the following derivations. Although the previous section states the reality of this growth process, it is somehow difficult at first inspection to rationalize the premise of a long life time for phosphorescence growth. It seems to contradict what is known about the rapid population of the triplet state by intersystem crossing following the absorption of photons. The fallacy is, of course, that although the ex citation process for one molecule is very fast, what is observed experimentally is the luminescence emitted from a very large number of excited molecules. One could simplistically visualize an excitation pulse beginning at time t = 0 and continuing indefinitely. Let the ex citation be temporally subdivided into a very large number of small segments of excitation intensity. By assuming only that the excitation process is very rapid, the following rationalization emerges. During the first excitation segment, a number of molecules,n, undergo absorption and subsequent population of the triplet state. Species in the triplet state will undergo deactivation via the characteristic exponential phosphorescence decay, exp(t/T). During each subsequent excitation segment, a population of n molecules are excited and phosphorescence. Although the excitation process for any subset of n molecules is very rapid, what is actually observed is the sum of phosphorescence intensity decays from a very large number of subsets of excited molecules. It can be seen that the overall phosphorescence intensity will continue to increase until the intensity contributed by the very first subset of excited molecules disappears. After this occurs, i.e., all of the molecules excited during the first excitation segment have returned to the ground state, the observed phosphorescence intensity will reach a steady state, because equal numbers of molecules are excited and deactivated at each instant. This steady state intensity is the I0 described earlier and will not be exceeded, regardless of how much longer the sample is irradiated. I represents the phosphorescence intensity level resulting from continuous (CW) excitation. Almost five phosphorescence decay lifetimes are required for phosphorescence intensity to decay to 1% of its initial value. Thus, it could take only milliseconds of excitation for a shortlived phosphor to reach 10, but a longlived phosphor might require ten seconds or longer. If the excitation is terminated (as with a pulsed source) before a sufficient time period has elapsed, the observed phosphorescence intensity will be some fraction of I . This same reasoning can be used to describe the ex citation process in a pulsed system. Figure 3 illustrates a train of excitation pulses of width t occurring at the P rate of f pulses per second. During each excitation pulse Rthe phosphorescence grows proportionately to T and the the phosphorescence grows proportionately to r and the Figure 3. Schematic representation of the excitation process with a pulsed source. TI IME intensity at the end of the first pulse is given by I0[lexp(t p/TR)]. When this pulse ends, the phos phorescence intensity decays. This takes place in dependently on each successive excitation pulse, with each pulse contributing the same amount of additional phosphorescence intensity. The observed intensity is the sum of the intensities resulting from all the preceding pulses. Therefore, one would expect that if a train of excitation pulses is incident upon a non excited"phosphorescent" sample, the phosphorescence intensity would rise rapidly during each pulse, and would decay between pulses. Also, that the intensity immediately following the pulse would increase steadily, as "new"intensity (that due to the latest pulse) is added to the intensity still present from the previous pulses. Again, after some number of pulses, the pulsetopulse intensity would reach some "pulsed source steady state," with the additional intensity from any pulse balancing the loss of intensity due to decay. The time required to reach this steady state should be independent of repetition rate, but should depend on the decay lifetime, T, of the phosphor. It is not improper, then, to speak of "pulsetopulse phosphorescence intensity growth," when the intensity is observed at the same time relative to each pulse. The operation of the pulsed source gated detection system of Figure 2 can now be examined further. The intensity and time axes are not to scale. The excitation pulse, of width t is an extremely short, high intensity burst of radiation, which is assumed to have the shape of a step function. That is, it goes instantaneously from zero intensity to maximum intensity, and maintains this level for t seconds. The phosphorescence intensity P grows during t and decays between pulses as previously P discussed. If the excitation pulse had sufficient dura tion, the intensity would reach I For this derivation, it is assumed that a sufficiently large number of pulses have been incident on the sample, that the "pulseto pulse steady state" has been attained. This means that in Figure 2,the loss of intensity due to decay from I P1 to I is equal to the increase in intensity from I to P3 P3 I For convenient reference, important variables are listed in Table 3. I is the instantaneous intensity at the start of 3 any excitation pulse, and includes the intensity resulting from many previous excitation pulses. During the pulse, the intensity level will continue to decay, and at the end of t the remaining intensity will be p I exp(t /T) (13) P3 p TABLE 3 DEFINITION OF PARAMETERS Symbol Definition t excitation pulse width, s p td delay time, s t gate width, s g I0 CW phosphorescence intensity I/I'0 Relative phosphorescence intensity, unitless T Phosphorescence decay lifetime, s R T Phosphorescence growth lifetime, s I Instantaneous phosphorescence intensity I I immediately following t I PI at the leading edge of t P2 P g I I at the leading edge of t p3 P P P Integrated luminescence P intensity observed (per excitation/emission cycle) However, during t ,intensity growth occurs, and the intensity added per pulse is given by Equation 12, I = 10I[lexp(t p/TR)] Therefore, the instantaneous intensity immediately following t is the sum of these two contributions, p I = I exp(t /T)+I0[lexp(t /T ] (14) p1 3 However, I is simply I after decay for a period of p3 P! time equal to the total time per cycle, 1/f, minus the pulse width, t : p I = Ip exp[(l/ft p)/T] (15) Substituting for I in Equation 14, P3 R IPl= I exp[(l/ft )/T]exp(t /T)+I[lexp(t /T)] (16) 1 1 p p 0t1e p(t/)]16 By combining exponentials and solving, one finds R) I 0[lexp(t p/T )] (17) 1 [lexp(l/f T)] I is the maximum instantaneous phosphorescence obtained per cycle. However, the instantaneous intensity present at the leading edge of the gate, IP2 is less than I , "2 1! due to decay over a period of time equal to td Thus, I = Ip exp(td/T) (18) 2and substituting into Equation 17 for I yields and substituting into Equation 17 for Ip yields "1 I [lexp(t /TR )]exp(t d/T) I = 0 d (19) 2 [lexp(l/f T)] At any time during the gate, the instantaneous intensity is given by Ip = I exp(t/r) (20) 2 The observed integrated phosphorescence intensity per cycle, P (the shaded area in Figure 2), is the integral of the intensity during the gate width: t t g g p = f I dt I exp(t/T)dt (21) p 0 0 2 t g P = I I exp(t/T)dt (22) 2 0 P = I T[lexp(t /t) ] (23) p p2 Substituting for I from Equation 19 yields "2 10 T[lexp(t /T) ] [lexp(t /TR) ]exp(td/T) (24) p = ___g___P___ P [lexp(l/f T)] The boxcar or gated average measures signal levels by averaging the intensity over each gate, and thenaverag ing the average intensity per gate over many gates (30,31). Thus, for the boxcar average the signal level is proportional to P /t Therefore, for the pulsed source gated average system, I0 T[lexp(t p/TR )] [lexp(t /T)]exp(t d/T) (25) t [lexp(l/f T)] g Equation 25 is the basis from which all remaining expressions will be derived. Thus far, no assumptions have been made regarding the relative magnitudes of the various parameters, and Equation 25 is quite general. Note that Equation 24 for P can also be validly applied to the boxcar or gated integrator. The integrator sums the integrated observed phosphorescence intensity per cycle, and I = P f t (26) p c where t is the counting time. The signal level is c simply equal to the area per gate times the number of gates summed. For the averaging DC meter (4), I = f P (27) P At this point, several assumptions will be made to simplify Equation 25 and to put it in a form more conducive to practical application. The first assumption is that the phosphorescence growth lifetime, T is approximately equal to the phosphorescence decay lifetime, T. This is done for several reasons. First, in the majority of cases, the error introduced by this assumption should be negligible. The difference between T and T could easily lie within the standard deviation of the normal lifetime determination in many cases. Also, the thrust of this work is to study primarily the relative dependencies of intensity upon experimental parameters, and an absolute relationship is not essential. Finally, a relationship containing only T would be more easily applied than if both lifetimes were required. Phospho rescence decay lifetimes are readily available in the literature for many compounds, and are easily measured with standard phosphoroscopic instrumentation, while growth lifetimes are seldom quoted and require modifica tion of the phosphorimeter for measurement. It is certainly important to realize that T and T may differ, and under what conditions this difference is maximized. As the difference between T and T increases, the expressions may begin to show error. This is the reason for including the kinetic summary in the preceding section. The second assumption is easily met by most pulsed source phosphorimeters. We assume that the excitation pulse width, t is much smaller than the sample lifetime, 4 t << T Thus, the excitation pulse is limited to 104 s P for the shortest lived phosphors (T %lms). Most pulsed sources have pulse widths of microseconds or less, and so this assumption should be valid. If the case should arise where T t Equation (25) would be necessary. %X p With the assumptions T = T and t << T the growth term P [R [lexp(t /T )] can be expanded and approximated by t /T. Therefore, Equation 25 reduces to t [lexp(t /T)]exp(td/T) (28) 1=1 _~ _________________3_____________ 0t 0 g [lexp(l/f T)] It should be possible to derive a similar expression by relying upon the additivity of intensity from pulse to pulse. Each excitation pulse yields phosphorescence intensity as given by Equation 12. Let this intensity growth per pulse be designated IG. Let the last pulse G be designated as pulse "N," and preceding pulses as "Nl," "N2," etc. At the termination of pulse N, the intensity decays resulting from preceding pulses have decayed for various periods of time, given by some number of 1/f (s) periods. Intensity resulting from pulse N has decayed for zero cycles, pulse Nl for 1 cycle, and so on. Therefore, after N pulses, the total intensity, I , could be given by IT=IG+IG[exp(l/f T)]+I G[exp(2/f T) ]+...+i G[exp(M/f T)](29) or N i/f T I = I e (30) T i=O If N is large, 00 1/f IT = IG f/ e di (31) 0 But eax dx = e ax/a (32) so, if a = 1/f T , 1= t /f T _ IT = G e 1' (f T)] 0 (33) Substitution and evaluating yields IT = IG f T (34) Since I is the intensity following t at steady T p state (N large), IT = I in Figure 2, and since I is defined by Equation 12, IP= f T I0[lexp(t /TR)] (35) The remainder of the derivation would then follow that already presented in Equations 1728. Comparing Equations 35 and 17 shows that they are not identical; however, in the limit of small 1/f T (large f or large T), the two converge. Why this difference occurs is not clear. However, the similarity of the results for the limiting case indicates that there is validity in the underlying principle of the second derivation. Applications From a practical point of view, Equation 28 is very important, for it allows one to ascertain the relative effects of tp t td f and T on the observed in p g tensity. Note that the observed intensity, I is some fraction of 10. Dividing I by I 0 would essentially normalize to a constant CW intensity level, t [lexp(t /T) ]exp(td/T) I/I =t P 2 (36) S g [lexp(l/f T)] I/I0 can be termed the "relative response" of the detection u0 system, and is actually the effective duty factor for the measurement (26,30). A plot of I/I0 versus T with t tg td and f fixed gives a plot of the relative response of the instrumentation as a function of sample lifetime. The terms "relative response" and "relative intensity" will be used interchangeably. A typical "relative response profile" resembles Figure 4. The most significant feature is that there is a lifetime corresponding to an optimum response, des ignated T Relative intensity falls off rapidly max towards longer (T ) and shorter (T ) lifetimes. The "enhancement ratios," or ratios of relative intensity values, for Tmax over T and TL can be approximated by reading off the intensities Imax IS and I and calculating Imax /IS and I max/I There is a lower 'max S max' L boundary on relative intensity at long T. This occurs when T >> 1/f t td and t Under these conditions, p g [lexp(t /T)] is approximately equal to t /T exp(td/T) approaches unity, and [lexp(l/f T)] is approximately equal to 1/f T Therefore, Equation 28 reduces to I/I0 = t f (37) P The gated detection system has enhanced response to T and discriminates against other lifetime components, max both longer and shorter. The time resolution system is, in effect, a "time filter," and the relative response profile could be compared to the wavelength response profile Figure 4. A typical relative response profile. I I max s I CO 1 I L TS max TL LIFETIME (s) of an optical filter, or the frequency response profile of an electrical filter. It would be very useful to be able to alter the shape of the response profile, and to change Tmax as desired. This would make it much easier to tailor the experimental system for a particular analysis. A way to attack this is to take the derivative of I/10 with respect to T and set the derivative equal to zero. Optimization Expression for td From Equation 28, exp (td/T) [lexp(t /T) ] (I/I0) (t/t ) = (38) 0 P [lexp(l/f T)] Taking the derivative with respect to T and setting it equal to zero, exp (t/T) [1exp(tg/) ] dI/dT = 0 = d Td (39) T [lexp(l/f T)] By using standard calculus techniques (28), we obtain [exp(td/T)(td/T2)(exp[(td+t g)/T]) (td+t )/T2 ] x [lexp(l/f T)]=[exp(l/f T)] (1/f T2) ([exp(td/T)] exp[(td+tp)/T]) (40) Factoring yields [lexp(l/f T)] [exp(td/T)] [(td/T2 )exp(t /T) (td+t)/T2 ]= [exp(l/f T)] (1/f T2) [exp(td/T] [lexp(t /T)] (41) Further simplification is algebraic, and the necessary manipulations are: (1) division by exp(td/T) 2 (2) multiplication by T (3) division by [lexp(l/f T)] (4) expansion of the first term (5) addition of t exp(t /T) to both sides; and (6) division by [lexp(t /T)] These steps yield t (1/f) [exp(l/f T)] + t [exp(t/T) (42) d [lexp(l/f T)] g [lexp(t /T)] By dividing out each term, the final result is obtained: (td)op t= [ 1 ]li/f)l 1 1 (43) g exp(t /T)l exp(l/f T)I This expression calculates the optimum delay time, (td)opt required to optiiLze the response of the instrumentation to any given lifetime, T at fixed t and f. There is no g dependence upon t due to the earlier assumption regarding t Equation 43 is also valid for the gated integrator system, since the conversion factor is multiplicative, and disappears when the derivative is set equal to zero. O'Haver and Winefordner (4) give a similar expression for the DC averaging meter system, but with the assumption that t < (td)opt = t 1 1 ] (44) iit < tg exp(t /T)li If the limitation T 1/f is applied to Equation 43, 1/f T grows large, exp(l/f T) approaches infinity, and the frequency dependent term drops out. T.hus, within the limits of Equation 44, the two expressions are identical. Equation 43 is also of practical importance, because it allows rapid evaluation of instrumental parameters for a sample of given lifetime. For further study and convenience of application, plots of (td)opt versus T at constant f and t were prepared. The plots were obtained g by programming Equation 43 into a HewlettPackard 25 calculator, and evaluating the various terms. The results were plotted on oversize sheets of loglog graph paper, and were later photographically reduced. The sets of parameters were chosen to be representa tive of the operating characteristics of practical experi mental systems, and specifically those of the source/de tection system used later in this work. Repetition rates of 1, 10, and 50 Hz were chosen, and a wide range of gate widths was used. The plots are keyed to the various gate widths as shown in Table 4. One microsecond was taken as the lower limit on gate width. The results are shown in Figures 57. Each figure gives the curves correspond ing to the various gate widths at constant repetition rate. Examination shows several interesting features. Distinct regions can be observed for each curve, roughly corresponding to long, intermediate, or short lifetimes. TABLE 4 KEY TO GATE WIDTH FOR FIGURES 57 Gate width (t), s Legend lxl05 A 5x105 B 4 ixlO04 C 5x104 D 3 lxl03 E 5x103 F lxl02 G 5x102 H 9x102 I Figure 5. Optimum delay versus lifetime (f = 1 Hz). 1C2 .10 E lo' Optimum Delay (s) Figure 6. Optimum delay versus lifetime (f = 10 Hz). 10' I Optimum Figure 7. Optimum delay versus lifetime (f = 50 Hz). Optimum Delay (s) In the 50 Hz plot, Figure 7, gate widthsH and I do not appear. This is due to the physical boundary conditions of the real system. The total time between successive excitation pulses is 1/f (s). This must be larger than the sum of the pulse width, delay time, and gate width. At 50 Hz, 1/f = 0.02 s, and therefore no gate widths larger than this are possible. At the long lifetime limit, the optimum delay is asymptotic, and shows little change with lifetime. The asymptote is gate width dependent, and shifts the optimum delay to smaller values at higher frequencies. The implication of this asymptotic behavior is that at long lifetimes, since (t d)opt is independent of lifetime, the gated detection system will not be able to discriminate between phosphors with lifetimes in this region. Mathematically, the reason for this behavior can be explained. By expanding the exponential terms in Equation 43 and retaining first and second order terms, we obtain ( [1 1 1 1 1 1 ]= 1 (45) exp(l/f T)l f + 2(f T)2 + 2fT and t 1 ]= t [ 1]= T (46) i 2 t/2T Sexp(t /T)i g t /T + (t /T)2 1 + t /2T Therefore, (t )pttT (47) dopttl9t/2Tr 1 + 1/2f T Finding the common denominator and combining terms gives 2 i/f t (td)opt = 2T [ 1f  (48) opt (2T + t ) (2T + 1/f) if the assumption is made that 2T>>t 1/f, 2 /ft 1/f t (t)opt = 2T 1[ (49) d opt 4T 2 2 Thus, for very long lifetimes (relative to t and 1/f), g (td)opt is constant, and is exactly onehalf of the maximum possible delay, 1/f t (t negligible). g p Equation 49 does predict correctly the asymptote in Figure 57. In the limit of shorter lifetimes (lefthand section), the curves are frequency independent. This is expected, because in this region, Equation 44 is valid. In the central region of the Figures, the curves for longer gate widths exhibit curvature. However, as the gate widths decrease, the curves approach linearity, with (t d) = T. This can be shown to occur when t T< 1/f. Because the lefthand boundary of the figures represents the smallest delay time attainable on a prac 06 tical level, the lifetime corresponding to (t ) 10ot s d opt is the smallest lifetime that can be realistically opti mized at that f and t As t decreases (curves I to A), the (t for smaller lifetimes becomes accessible. the (td)opt for smaller lifetimes becomes accessible. There is another physical constraint of great significance. As noted earlier, the boxcar average averages the signal over a large number of gate widths. If enough gates are averaged, random fluctuations (noise) in the signal should cancel, and the output should approach the average signal level of P /t This signal tonoise ratio (SNR) enhancement is accomplished by using an RC filter. Most measurement instruments possess a time constant, which indicates how rapidly the instrument can respond to an applied signal. The normal measurement procedure is to actually measure the signal for a period of time equal to five time constants, to insure adequate time for the instrument to respond. In the gated system, the signal is only sampled during the gate width, which is a small fraction of the total measurement time. The fraction, actual measurement time divided by total measure ment time, is known as the duty factor, Df = f x t The RC filter in the system necessitates that the signal be actually applied to the filter section for 5 x RC. Because the signal is actually sampled only a fraction, Df, of the total time, with the boxcar average the total measurement time required is 5[]RC ft g where the quantity in brackets is known as the observed time constant, OTC. Thus, the actual measurement time for the boxcar average is five timesOTC. Since the value of RC selected effectively deter mines the SNR of the measurement, if the noise is not directly related to f or t the measurement time g required to obtain the same SNR decreases as f or t g increases. Conversely, as f or t is decreased, the g OTC, and thus the actual measurement time, increases proportionately. Response Profiles If t tg, and f are known, (td)opt can be cal culated, which will give maximum enhancement to intensity at the lifetime, T, chosen. The parameters thus selected can be used in conjunction with Equation 28 to calculate response profiles with maxima at selected lifetimes, under various experimental conditions. Such profiles will be presented here, and are used to ascertain the effects of f, t and t on the observed intensity levels. The plots are prepared in a similar fashion to those shown previously. The values of the parameters represent realistic experimental conditions. It was necessary to limit the number of values studied per parameter, but those values selected for each factor cover a fairly broad range. Four repetition rates (f = 1, 10, 50, 100 Hz) and 3 4 5 three gate widths (5x103 5x10, 5x105 s) are employed. 8 The excitation pulse width, t is 10 s, and is rep resentative of the nitrogen laser pulse used later in this study. For each combination of frequency and gate width, (td)opt 's are calculated to yield a family of response profiles, with maximum response occurring at lifetimes of 9, 0.9, 9x10 2, 9x10 3, 9x10 4, and 9x10 s. The optimum delays calculated for the various combinations of f, t and T are given in Table 5, which also contains the legend used to identify the curves. Every curve marked "A" should have maximum response at T = 9 s, curves marked "B" at 0.9s, and so on. In addition, a curve marked "G" appears on one figure. For this curve, the delay time used was the maximum physically attainable delay, 1/f t (remember the asymptote at long T is g equal to 1/2 of this quantity). This was included to demonstrate that delays other than the (td)opt predicted at long lifetimes can be used. The resulting families of response profiles of relative intensity versus lifetime are presented in Figures 819. Each figure represents a fixed frequency and gate width, with the individual curves varying only in delay time. Any one curve represents the relative response of the experimental system under one fixed set of experimental conditions. T (s) = max Legend: Fig. t (s) 8 5x103 9 5x103 10 5x103 11 5x103 12 5xlO4 13 5x104 14 5x104 15 5x104 16 5x105 5 17 5xl0 5 18 5x105 19 5x105 f(Hz) 1 10 50 100 1 10 50 100 1 10 50 100 4.88x10 4.74x10 7.50x10 2.50x10 4.91x10 4.97x10 9.75x10 4.77x10 4.90x10 4.92x10 9.98x10 4.98x10 TABLE 5 PARAMETERS FOR RESPONSE PROFILES 9x10 9x102 9xl03 B C D Optimum Delays (s) ii 2 3 1 4.07xl01 8.75xl02 6.73xl03 2 2 2 3 2 4.66xl02 3.84xl02 6.73xl03 33 3 3 3 7.47xl03 7.15xl03 4.30xl03 33 3 3 3 2.49xl03 2.43xl03 1.82xl03 1 4.09xl01 8.97x102 8.75x103 *2 2 2 3 2 4.88x102 4.07xl02 8.75xl03 33 3 3 3 9.71x103 9.38xl03 6.32xl03 33 3 3 3 4.74xl03 4.66x103 3.84xl03 Ii 2 3 1 4.09xl01 9.00x102 8.98xl03 2 4.91x102 4.09x102 8.97x103 33 3 3 9.94xl03 9.60xl03 6.54x103 3 .97xl03 4.88xl3 4.07xl3 S4.97xi03 4.88x103 4.07xi0 9x104 E 1.94x105 1.94xl05 1.94xl05 1.93x105 6.73xl0~4 6.73xl04 4 6.73xl04 6.73xl04 8.75xl0~4 8. 75xl04 8.75xl04 8.75xl04 9x105 F 6 1.94x10 6 1.94x106 1.94x106 6 1. 94xl0 6 6.73x105 5 6.73x105 6.73xl05 6.73xl0~5 3 Figure 8. Response profile (t = 5x10 s, f = 1 Hz). 104 io5 i0 o 10 CD w 10I1 10 "13 i .. ..I I i ,n 1 ,tnL m il..Lf i e I(l 105 Ci4 103 102 10"2 Lifetime (s) Figure 9. 3Response profile (t = 5x s, f = 10 Hz). Figure 9. Response profile (t =5x10 s, f 1 0 Hz). g 10"r 108 I03 Lifetime (s) 102 10 I Figure 10. 3Response profile (t = 5x s, f = 50 Hz). Figure 10. Response profile (tg = 5x10 s, f = 50 Hz). 104 101.1 10E IOe 107 108 Lifetime (s) 3 Figure 11. Response profile (t = 5x10 s, f = 100 Hz). g 71 I05 105 )E SB 107_ / 08 / _1 09 _) io10 i01o 1013 I5 I04 I03 102 Lifetime (s) 3 r 4 .c C 4 a S10I Figure 12. Response profile (t = 5x10 4s, f = 1 Hz). 73 F 105_^N cc IO 106 10 1 10r 0 10' 1 1 Lifetime (s) 4 Figure 13. Response profile (t = 5x10 s, = 10 Hz). g . . . .. .. ., I I I i J L Ii I *, I 103 Lifetime (s) 104 105 106 107 108 4 in 0) _ lO9 C: )10 10)10[ 10" 1012 IC 104 102 )5 Figure 14. Response profile (t = 5x10 4s, f = 50 Hz). g Lifetime (s) Figure 15. Response profile (t = 5x10 4s, f = 100 Hz). g 100 106 107 i O8 Sj109 idr9 J I) 1012 105 104 1073 102 101 I 10 Lifetime (s) Figure 16. Response profile (t = 5x10 5s, f = 1 Hz). 81 io4 F 10"6 108 I0I cnc I~a 10 13 . .. . ..._ . ... . . .. . ... . . .. 1c.E Bo 409 10 1 105 I04 103 102 10 I 10 Lifetime (s) Figure 17. Response profile (t = 5x10 s, f = 10 Hz). g 103 IC Lifetime (s) 1013 5 Figure 18. Response profile (t = 5x10 s, f = 50 Hz). g Lifetime (s) 5 Figure 19. Response profile (t = 5x10 s, f = 100 Hz). g Lifetime Results and Discussion Initially, one figure will be discussed, before comparisons are made from figure to figure. Figure 8 shows the response for t = 5x103 s and f = 1 Hz. It g is evident that the intensity enhancement at the maximum increases as the Tmax decreases. That is, as one goes from A, optimized for T = 9s, towards E,optimized for 9x14 for T = 9x10 s. Curve A has a very broad, flat maximum, while curve E has a very sharp, well pronounced peak. It is important to note that (t d)opt is not the td of d opt  maximum attainable intensity. In all cases, decreasing td gives increased intensity, but simultaneously increases response to shorter lived components. As mentioned earlier, the degree of enhancement (or discrimination) for phosphors of various lifetimes can be estimated by comparing their relative intensities. It can be seen that in all cases, except for lifetimes lying very closely together, discrimination over shorter lived components, IT /I is drastic. The reason for this max s is simply that the chosen delay time is so long that phos phorescence intensity due to shorter lived species has decayed significantly before the gate opens to sample the intensity. At longer lifetimes, the relative intensities approach the previously described limit of t f which p 8 f is 108 for Figure 8. It is obvious that, since the intensity contributions from longlived components never drop below this level, in most cases, the ratio of IT /IT will be substantially less than the ratio max long of max/I T short This occurs because, regardless of max short where the gate is positioned for measurement of intensity from a particular lifetime component, the intensity resulting from phosphors of longer lifetime will always be present, and will always underliethe intensity decays for shortlived components. Effect of excitation pulse width, t P The effect of t is not illustrated directly in any of the figures, because the earlier assumption concerning the relative magnitude of t makes it a strictly multi P plicative factor in all cases presented here. The relative intensity is directly proportional to t as long as t << T. This simple dependency is deceptive, P however. The t factor enters the intensity expression P as the term describing phosphorescence growth during the pulse, [lexp(t /T)]. Within the limit of t T, this growth term reduces to I = I t /T. This growth factor is solely responsible for the observed intensity enhancement of short over long lifetime components. At a fixed t the phosphorescence intensity level p attained due to growth during t is inversely proportional to the phosphorescence lifetime, T Therefore, for two components of identical I1 the component of shorter lifetime is excited to a greater fraction of I and the intensity due to the shorter lived component immediately following the excitation pulse (I in Figure 2) is p1 greater than that of the longlived component. However, this intensity due to the shortlived component also decays more rapidly following t Therefore, for some p period of time immediately after the excitation pulse, the intensity contribution of the shorter lived component is greater than that due to any longer lived components. This is shown by the shaded area in Figure 20, which illustrates the phosphorescence intensity growth/decay for two phosphors of differing lifetime. Thus, the maxima in the instrumental response profiles occur because the shorter lived components actually do have greater intensity along the earlier portion of the emission decay curve. If t is increased, all lifetime components attain P a larger fraction of I As t approaches T in value, the multiplicative effect gradually becomes exponential. As t continues to increase, components with very short lifetimes will completely attain I0 and further length ening of t will not further increase the intensity due P to those components. However, longer lived components will still increase in intensity with increasing t , p until the pulse width is so long that they too attain I 0. This is, of course, what occurs in a CW system, and I/I0 = 1 for all lifetimes. Therefore if t is large, and all components reach 10 during the excitation pulse, Figure 20. Schematic representation of phosphorescence growth during the excitation pulse for two phosphors with different lifetimes. Short 