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Author(s)First Name Middle

NameSurname Role Email

Daniel McKewn Jenkins Member-Engr 324709 danielje@hawaii.edu

AffiliationOrganization Address Country

University of Hawaii, Manoa, Molecular Biosciences and Bioengineering

1955 East West Rd., Rm. 218

Honolulu, HI 96822

USA

Author(s)First Name Middle Name Surname Role Email

Chaopin Zhu non-member? czhu@spectra.eng.hawaii.edu

AffiliationOrganization Address Country

University of Hawaii, Manoa, Electrical Engineering

USA

Author(s)First Name Middle Name Surname Role Email

Wei-Wen Su non-member wsu@hawaii.edu

AffiliationOrganization Address Country

University of Hawaii, Molecular Biosciences and Bioengineering

1955 East West Rd., Rm. 218

Honolulu, HI 96822

USA

Publication InformationPub ID Pub Date

073062 2007 ASABE Annual Meeting Paper

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

An ASABE Meeting Presentation

Paper Number: 073062

A Simple Hybrid Circuit for Direct Determination of Fluorescence Lifetimes

Daniel M. JenkinsUniversity of Hawaii, Molecular Biosciences and Bioengineering, 1955 East West Rd., Rm. 218, Honolulu, HI, 96822, danielje@hawaii.edu

Chaopin ZhuUniversity of Hawaii, Electrical Engineering, czhu@spectra.eng.hawaii.edu

Wei-Wen SuUniversity of Hawaii, Molecular Biosciences and Bioengineering, wsu@hawaii.edu

Written for presentation at the2007 ASABE Annual International Meeting

Sponsored by ASABEMinneapolis Convention Center

Minneapolis, Minnesota17 - 20 June 2007

Abstract. A new circuit for the measurement of fluorescence lifetime is described. The technology may be used in sensors which rely on fluorescence quenching in the presence of chemical species such as O2 or H+. Fluorescence is excited by pulses of light from an LED modulated with a square wave. The same square wave is used to gate the resulting luminescence signal from the fluorophore in order to eliminate non-specific luminescence detected during the LED pulse, and to extract the first harmonic of the resulting train of fluorescence decays. The first harmonic is then compared to the excitation signal using simple digital logic, resulting in a pulse width modulated signal. This signal has direct trigonometric relationships to the fluorescence lifetime and to the concentration of the quenching molecule. Evaluation of a prototype of this circuit was successful; the relationships between the sensor output and quenching concentration were as predicted by theory. Observed lifetimes of the fluorophore Ruthenium(4,7-diphenyl-1,10-phenanthroline)3

2+ immobilized in a sol-gel (~3 to 13 s) exceeded the lifetimes reported for the same fluorophore dissolved in liquid solvents, indicating a stabilizing effect of the sol-gel and comparatively low values of oxygen permeability in this material. Rate constants for emission and quenching of the fluorophore by oxygen in the sol-gel were determined to be 7.6 x 104 s-1 and 2.8 x 105 (atm·s)-1, respectively. The simplicity of the circuit design compared to alternative technologies is particularly compelling where rapid multiplexing to many parallel sensors is required..

Keywords. Fluorescence quenching, fluorescence lifetime, Ruthenium (II), oxygen sensor.

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

IntroductionFluorescence quenching is a phenomenon used for the detection of molecular species such as oxygen (Bambot, et al., 1994), hydronium ion (Kosch, et al., 1998), and carbon dioxide (Liebsch, et al., 2000). Chemical sensors based on this mechanism are becoming common, especially for application in increasingly miniaturized bioreactors (Harms, et al., 2006; Kostov, et al., 2001; Zhang, et al., 2006) for basic and applied biological research. In dynamic fluorescence quenching, energy available for luminescence of a fluorophore is lost during a collision with a quenching molecule, thereby diminishing the fluorescence intensity and the lifetime of luminescence when the excitation source is extinguished (Demas, et al., 1977; Lakowicz, 1983, p. 179).

In such a system, the fluorescence intensity is a straightforward measure of the quantity of quenching molecule available (Demas, et al., 1977; Lakowicz, 1983; Mills and Thomas, 1997). However, frequent recalibration is required for intensity measurements due to photobleaching and other mechanisms of fluorophore degradation (Fuller, et al., 2003), as well as minor changes in the alignment of the optics. Because of this, it is more common to measure fluorescence lifetime in the frequency domain using a lock-in amplifier to discriminate phase lag from the excitation source (Bambot, et al., 1994; Lakowicz, 1983, pp. 53-59). Alternatively, fluorescence lifetime can be measured in the time domain (Lakowicz, 1983, pp. 51-53). By “gating” out the photodector during excitation pulses and recording only the transients due to long lifetime (on the order of s or ms) quenchable fluorophores, effects due to excitation light scattering and short lifetime (on the order of ns) background fluorescence can be eliminated (Kostov and Rao, 2003; Rowe, et al., 2002). An analogous approach can be used in the frequency-domain (Lakowicz, et al., 2000). The main drawbacks of these systems are the level of complexity inherent in the signal gating and mixing circuitry themselves (Lakowicz, et al., 2000), the processing capability required to analyze lifetimes based on signal shape (Rowe, et al., 2002), and/or mathematical complexities arising during the interpretation of sensor output (Kostov and Rao, 2003).

Here we describe a new circuit design to measure fluorescence lifetime which can be implemented with a simple digital clock and other inexpensive components. Building on earlier work (Kostov and Rao, 2003), excitation light is ‘windowed’ out of the output to prevent non-specific luminescent detection. The output of the new detector is continuous and can be easily transformed to provide a linear correlation with fluorescence lifetime. This feature is especially compelling where speed and simplicity are overriding factors, such as when many sensors must be multiplexed together in parallel bioreactors.

Materials and MethodsCircuit Design. The circuit was inspired by earlier prototypes in which phase information was collected by gating the rectified luminescence signal with the excitation signal through an XOR gate (Jenkins, et al., 2005). The primary advance of the present prototype (Figure 1) is the use of a band pass filter to extract only the first harmonic (f0) of the gated luminescent signal. The filter effectively cuts out high frequency noise sources which resulted in poor performance of earlier prototypes. In addition, phase of the resulting first harmonic is related trigonometrically to the lifetime of the fluorescence. Implementation of the filter with a switched capacitor IC (LMF100, National Semiconductor, Santa Clara, CA) allows the pass band (f0 center frequency, fhc – flc = f0/28) of the filter to scale directly with the system clock. In addition, the light source and logic components are all modulated directly from the system clock, so that no special timing circuitry is required (Figure 1).

2

For excitation of the fluorophore, an ultrabright 470 nm LED (HLMPCB28, Agilent Technology, Santa Clara, CA) is pulsed at the desired frequency with a custom made driver using emitter coupled logic (Schumate and M. DiDomenico, 1982). A hardware delay causes the illumination of the LED to be delayed by about 400 ns, thus preventing the inclusion of the start of excitation into the windowed output. The hardware delay to turn off the LED is considerably shorter due to asymmetries in the logic level for signal transition; in fact this delay is not detected in the windowed output (see representation “C” in Figure 2 below) using a 100 MHz oscilloscope (TDS 2012, Tektronix, Richardson, TX). Emission is collected through an interference filter centered at 600 nm (600/40/75-2R, Intor, Socorro, NM) and detected by a reverse biased P-I-N photodiode (S5972, Hamamatsu Corporation, Hamamatsu City, Japan). Photocurrent is amplified by a custom designed transimpedance amplifier with a bandwidth in excess of 4 MHz and gain of about 5.6x107 V/A. The luminescence signal is ‘windowed’ with a sample and hold chip, gated by the excitation signal to hold the ‘dark’ signal during LED excitation. The windowed and filtered luminescence signal is compared to the original excitation signal through an AND gate, resulting in a pulse width modulated signal proportional to the phase delay between these signals (Figure 2). The system is designed specifically for detection of the fluorescence lifetime of [Ruthenium(II)(4,7-diphenyl-1,10-phenanthroline)3]2+ (hereafter abbreviated as Ru(dpp)3), which varies by a factor of three in the range from zero to atmospheric oxygen.(Kostov and Rao, 2003) The speed of the amplifier is designed to be approximately 10x faster than the fastest relaxation expected from Ru(dpp)3 (0.7 s). For other fluorophores, the circuit may be easily adapted by using different driver frequencies, light sources, and/or optical filters.

Figure 1. Simplified system diagram of fluorescence lifetime detector. Fluorescence emission signal ‘B’ from square wave excitation is ‘windowed’ by a sample and hold chip which holds the dark signal during the excitation of fluorescence. The windowed output ‘C’ is filtered (‘D’), rectified, and gated with the excitation signal ‘A’ resulting in a pulse

width modulated signal ‘’ related to the fluorescence lifetime.

Validation of Windowed Signal Fidelity. To ensure that the windowed output ‘C’ reproduced the decay of the luminescent signal ‘B’ without any distortion (Figure 2), these signals were compared on a 100 MHz oscilloscope (Tektronix TDS-2012) under ambient conditions. No difference in the gated portions of these signals was discernible.

Preparation of the fluorescent oxygen sensor. An oxygen sensitive sol-gel was prepared in a 1.5 ml centrifuge tube immersed in a 60 ºC water bath. The water bath and sol-gel formulation were both agitated with magnetic stir bars during the synthesis. First, 250 l of tetramethyl orthosilicate (TMOS, Aldrich, Milwaukee, WI) was combined with 400 l dimethoxy dimethyl silane (DiMeDMOS, Aldrich) and 167 l of 0.03 M HCl. This mixture was stirred for 30 minutes, after which 50 l of a stock solution (77.1 mg/ml ethanol) of Ru(dpp)32+ dichloride

3

(Stock # 44123, Alfa Aesar, Ward Hill, MA) was added. This was stirred for approximately 30 minutes in the controlled temperature bath until the onset of a viscous consistency in the sol-gel. The sol-gel was then applied to the inside of a real-time PCR tube (Bio Rad Cat# TBS0201, Hercules, CA) using a #1 round brush. The resulting films were cured for 12 hours at 75 ºC on a PCR thermal cycler.

Figure 2. Timing diagram for system described in Figure 1. Increasing fluorescence lifetime relative to the excitation period T results in a filtered output less in phase with

the excitation, and therefore a smaller duty cycle on the phase output .

Analysis of circuit prototype: For testing the prototype circuit, a tube coated with oxygen sensitive sol-gel was fit over the end of the LED and placed directly above the detector. To minimize reflection of excitation light into the detector, the primary axis of the LED was oriented at about 45º from the axis between the oxygen sensor and the photodetector.

The oxygen sensor was then ventilated through a pinhole in the bottom of the tube with a mixture of O2 and N2. The composition of the test gas was controlled using two calibrated mass flow controllers (FMA-2400 series, Omega Engineering Inc., Stamford, CT) attached to compressed gas cylinders of N2 and O2. After equilibration with each new air composition, the detector output was recorded at a number of excitation frequencies f0.

Analysis of detector performance: The electronic excitation of a population of fluorophores can be regarded as a first order process dependent on the excitation intensity I0, and is limited by the extinction coefficient and quantum efficiency . Likewise, the rate of decay of the excited population can be modeled as a first order process defined by the rate for fluorescent emission and the rate for non-radiative decay such as molecular quenching.(Lakowicz, 1983) The resulting system of equations predicts that after application of a pulse of excitation light, a population of excited fluorophores N will exist which diminishes over time according to the differential equation:

, (1)

where kE is the rate constant for emission, kQ is the rate constant for quenching, and [Q] is the concentration of the quenching molecule (which is assumed constant over the short intervals involved in fluorescence emission). Since fluorescence emission F is directly related to the excited fluorophore concentration, the solution to this equation predicts an exponential decay in fluorescence emission after the excitation pulse ends at time 0:

(2)

4

where

. (3)

If excitation pulses are applied periodically at intervals of T = 1/f0, and the luminescent output during the excitation pulses is windowed out, the signal (C in Figures 1 & 2) becomes a train of time shifted decays of the form of equation 2:

(4)

for all n. The first harmonic x(t)1H (D in Figures 1 & 2) of this periodic windowed signal can readily be evaluated from the Fourier series representation. If T is sufficiently larger than :

(5)

where

(6)

and

. (7)

The cotangent of the observed phase then is linearly related to the fluorescence lifetime, and provides a convenient measure of its value. Since the lifetime is inversely related to the quencher concentration (equation 3), it follows that the tangent of phase is directly related to the quencher concentration:

. (8)

Equation 8 is a direct mathematical analog of the Stern-Volmer relationship (Lakowicz, 1983) describing the relationship between fluorescence intensity and quencher concentration. In our implementation, the final output stage is applied to a low pass filter (not shown in Figure 1) to remove jitters in the pulse widths and to provide a continuous analog output. In this case, the value of is linearly related to the output voltage Vo scaled by the fixed supply voltage Vcc:

. (9)

Results and DiscussionTo demonstrate the performance of the lifetime detector, lifetimes at different air compositions were estimated by evaluating the slope of cot against the excitation frequency according to

5

equation 7. Results of a representative analysis of lifetime for a given air composition are shown in Figure 3. A compilation of these lifetime data for different air compositions (Figure 4) demonstrates good theoretical agreement with equation 3, suggesting effective molecular quenching of the fluorophore by oxygen and successful operation of the lifetime detector. Observed fluorescence lifetimes (ranging from an excess of 10 s in the absence of oxygen to about 3 s near 1 atm of oxygen partial pressure) are approximately four times longer than those reported for the same fluorophore in water (Kostov and Rao, 2003) and 2.5x longer than reported values in methanol (Demas, et al., 1977). These discrepancies suggest that the sol-gel exerts a stabilizing effect on the excited fluorophore. Given these large lifetimes, it appears that the bandwidth designed for the photoamplifier and the speed of the sample and hold element are sufficient for this application.

Figure 3. Sensor output against excitation frequency under oxygen partial pressure of 0.471 atm (cot() = 2.8x10-5 f0, with f0 in Hz; R2 = 0.972). Fluorescence lifetime is

equivalent to the slope divided by 2, or 4.51 s.

Figure 4. Inverse of observed fluorescence lifetimes vs. partial pressure of oxygen (-1

= 0.193 ppO2 + 0.112; R2 = 0.976).

To evaluate the performance of the system for detection of oxygen, data collected at a single excitation frequency (10 kHz) was fit to equation 8. The excitation frequency was chosen so that the ‘dark’ interval exceeded the maximum observed fluorescence lifetime by a factor of about 4, thereby allowing the system to settle back to almost no fluorescence emission before initiation of the subsequent excitation pulse. Results showed reasonable linearity, indicating

6

that the system was sensitive to presence of oxygen (Figure 5). Within the range of atmospheric oxygen compositions, data were correlated with an R2 of 0.949 and a standard error of 7.7 % atmospheric composition (~0.016 atm). Over a wider range of oxygen partial pressures approaching 1 atm, the correlation improved to an R2 of 0.993, and the standard error increased to only 0.022 atm (Figure 5 inset). Based on the latter data set, the estimated values for kE and kQ for quenching of Ru(dpp)32+ by oxygen respectively were 7.6 x 104 s-1 and 2.8 x 105 (atm·s)-1. Discrepancies of these values from those inferred from other reports (Table 1) indicate that the permeability of oxygen into the sol-gel is lower than the corresponding values in water and especially methanol. These results also suggest that while the sol-gel is a good matrix to stabilize the fluorescence energy of Ru(dpp)32+ and thereby relax the constraints on the speed of the electronics to obtain reliable lifetime data, it is not a particularly effective matrix for dissolving and transporting oxygen to the fluorophore. This last property, however, is desirable if the sensor is to be used to detect high oxygen levels, especially those above ambient conditions.

Figure 5. Tangent vs. oxygen composition of air, up to atmospheric composition, with excitation frequency of 10 kHz (tan = 7.8x10-3 %atm.comp. + 1.28; R2 = 0.949; std. error = 7.7 % atmospheric composition). Inset: Same correlation, extended beyond atmospheric oxygen

content (tan = 4.48 atmO2 + 1.21; R2 = 0.993; std. error = 0.022 atm).

Table 1. Comparison of emission and quenching rate constants for Ru(dpp) 32+ in different media.

Media kE (s-1) kQ (atm-1 s-1) (O2 = 0) = kE-1 (s)

Sol-gela 0.76 x 105 0.28 x 106 13.2

Waterb 3.23 x 105 5.29 x 106 3.1

Methanolc 1.87 x 105 21.5 x 106 5.34a Data from this investigation.b Inferred from data reported in Kostov and Rao (2003)c Inferred from data reported in Demas, et al., (1977) using solubility data

for oxygen in methanol from Fischer and Wilken (2001).

The simplicity of this design is especially attractive for situations where it is desired to multiplex a large number of sensors to a single data acquisition or control system. Compared to lock-in amplifiers which are the standard technology for lifetime detection, the system described here is

7

considerably less inexpensive, and can settle on the correct output within a few excitation cycles so that multiple sensors can be polled in a short period of time.

Incremental improvements to the design of this system could be incorporated to improve selected performance criteria. For example, improvements to the bandwidth of the amplifier (Kostov and Rao, 2003) could extend the useful range of the system to superatmospheric concentrations of oxygen or allow the detection of shorter lifetime fluorophores. Substitution of an XOR gate for the AND gate would double the sensitivity to changes in oxygen by effectively doubling the pulse rate and maintaining the same sensitivity of pulse width to changes in . A slightly more sophisticated approach to implementing this technology would be to use a microcontroller to adjust the system clock in order to maintain a constant output. This would allow the sensitivity to be optimized for all values of while precluding the possibility of non-linearities arising as the value of approaches the same order of magnitude as T.

ConclusionsTesting of a new prototype for detection of fluorescent lifetimes in the microsecond range was successful, and use of the detector was demonstrated for the measurement of oxygen composition in different mixes of gas. Observed lifetimes for the oxygen sensitive fluorescent material were longer than those reported elsewhere for the same material, suggesting a stabilizing effect of the sol-gel on the fluorophore and a low permeation rate of oxygen through the sol-gel. The architecture of the new detector is significantly simpler than other detection systems for luminescent lifetime, and the detector output can be easily transformed to give a direct indication of fluorescence lifetime or quenching concentration. Substitution of alternative logic gates for the AND gate in the prototype can improve the theoretical performance without sacrificing the linearity of the transformed output against fluorescent lifetime. For example, substitution of an XOR gate for the AND would effectively double the sensitivity (change in duty cycle per change in lifetime) by inserting a second symmetrical pulse into the output waveform, while inverting the output’s general relationships to lifetime and quencher molecule concentration. In summary, the new prototype is a versatile, simple, and cost effective platform for the development of chemical sensors using fluorescence lifetime. These characteristics are especially favorable for applications where rapid multiplexing to multiple sensors is required. Finally, simple detection mechanisms like this one may become increasingly relevant as advances are made in the development of longer lifetime fluorophores (Tyson, et al., 2000, Tyson and Castellano, 2000).

Acknowledgements

We acknowledge financial support from the USDA-TSTAR program, project HAW00508-1016. We would also like express our deep appreciation to Dr. Yordan Kostov at the University of Maryland Baltimore County for his generous material and intellectual contributions to this work.

ReferencesBambot, S. B., R. Holavanahali, J. R. Lakowicz, G. M. Carter, and G. Rao. 1994. Phase

Fluorometric Sterilizable Optical Oxygen Sensor. Biotechnology and Bioengineering. 43(11):1139-1145. Online. Available: <Go to ISI>://A1994NG86500018.

Demas, J. N., E. W. Harris, and R. P. McBride. 1977. Energy-Transfer from Luminescent Transition-Metal Complexes to Oxygen. Journal of the American Chemical Society. 99(11):3547-3551. Online. Available: <Go to ISI>://A1977DG50800001.

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Fischer, K. and M. Wilken. 2001. Experimental determination of oxygen and nitrogen solubility in organic solvents up to 10 MPa at temperatures between 298 K and 398 K. Journal of Chemical Thermodynamics. 33(10):1285-1308. Online. Available: <Go to ISI>://000173601400006.

Fuller, Z. J., W. D. Bare, K. A. Kneas, W. Y. Xu, J. N. Demas, and B. A. DeGraff. 2003. Photostability of luminescent ruthenium(II) complexes in polymers and in solution. Analytical Chemistry. 75(11):2670-2677. Online. Available: <Go to ISI>://000183397500023.

Harms, P., Y. Kostov, J. A. French, M. Soliman, M. Anjanappa, A. Ram, and G. Rao. 2006. Design and performance of a 24-station high throughput microbioreactor. Biotechnology and Bioengineering. 93(1):6-13. Online. Available: <Go to ISI>://000234287400002.

Jenkins, D. M., C. Zhu, and W.-W. Su. 2005. Comparison of prototype circuits for direct measurement of fluorescence lifetime. 2005 ASAE Annual International Meeting, Tampa, FL:paper #053036.

Kosch, U., I. Klimant, T. Werner, and O. S. Wolfbeis. 1998. Strategies to design pH optodes with luminescence decay times in the microsecond time regime. Analytical Chemistry. 70(18):3892-3897. Online. Available: <Go to ISI>://000075911500027.

Kostov, Y., P. Harms, L. Randers-Eichhorn, and G. Rao. 2001. Low-cost microbioreactor for high-throughput bioprocessing. Biotechnology and Bioengineering. 72(3):346-352. Online. Available: <Go to ISI>://000166456100012.

Kostov, Y. and G. Rao. 2003. Low-cost gated system for monitoring phosphorescence lifetimes. Review of Scientific Instruments. 74(9):4129-4133. Online. Available: <Go to ISI>://000184873200027.

Lakowicz, J. R. 1983. Principles of Fluorescence Spectroscopy. Plenum Press, New York, NY.

Lakowicz, J. R., I. Gryczynski, Z. Gryczynski, and M. L. Johnson. 2000. Background suppression in frequency-domain fluorometry. Analytical Biochemistry. 277(1):74-85. Online. Available: <Go to ISI>://000085231800009.

Liebsch, G., I. Klimant, B. Frank, G. Holst, and O. S. Wolfbeis. 2000. Luminescence lifetime imaging of oxygen, pH, and carbon dioxide distribution using optical sensors. Applied Spectroscopy. 54(4):548-559. Online. Available: <Go to ISI>://000086787500014.

Mills, A. and M. Thomas. 1997. Fluorescence-based thin plastic film ion-pair sensors for oxygen. Analyst. 122(1):63-68. Online. Available: <Go to ISI>://A1997WD71300014.

Rowe, H. M., S. P. Chan, J. N. Demas, and B. A. DeGraff. 2002. Elimination of fluorescence and scattering backgrounds in luminescence lifetime measurements using gated-phase fluorometry. Analytical Chemistry. 74(18):4821-4827. Online. Available: <Go to ISI>://000178068000031.

Schumate, P. W. and J. M. DiDomenico. 1982. Semiconductor Devices for Optical Communication. Springer, Berlin.

Tyson, D. S., J. Bialecki, and F. N. Castellano. 2000. Ruthenium(II) complex with a notably long excited state lifetime. Chemical Communications. (23):2355-2356. Online. Available: <Go to ISI>://000165487300033.

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Tyson, D. S. and F. N. Castellano. 2000. Ruthenium(II) complexes with remarkably long lifetimes. Abstracts of Papers of the American Chemical Society. 220:U489-U489. Online. Available: <Go to ISI>://000166091202603.

Zhang, Z. Y., P. Boccazzi, H. G. Choi, G. Perozziello, A. J. Sinskey, and K. F. Jensen. 2006. Microchemostat - microbial continuous culture in a polymer-based, instrumented microbioreactor. Lab on a Chip. 6(7):906-913. Online. Available: <Go to ISI>://000238580900011.

AppendicesDerivation of phase and amplitude of first harmonic signal. Starting with the train of decaying fluorescence intensities described by equation (4) in the manuscript:

(4)

the function can be approximated as the Fourier Series representation:

(i)

where

(ii)

In this investigation, the signal is filtered so that only the first harmonic (k = +/- 1) is considered:

(iii)

(iv)

10

. (v)

If T is chosen to be significantly greater than (e.g., by a factor of 10, then the numerator in the first term of (v) becomes approximately , and likewise the second term in (v) becomes significantly smaller than the first, such that:

(vi)

The coefficient a-1 is merely the complex conjugate of a1:

(vii)

By defining a new coefficient B0 as

(viii)

we can substitute a1 (vi) and a-1 (vii) into the Fourier series representation (i) to find the first harmonic

(ix)

which we can expand using Eulers relation:

(ix)

Recalling that f0 = T-1 and canceling terms:

(x)

It is a straightforward exercise to use phasor analysis to demonstrate that this signal is equivalent to equation (5) in the manuscript

(5)

where

(6)

11

and

. (7)

Evaluation of other reported quenching data for comparison.

To compile the values for comparison in Table 1:

Table 1. Comparison of emission and quenching rate constants for Ru(dpp) 3

2+ in different media.

Media kE (s-1) kQ (atm-1 s-1) (O2 = 0) = kE-1 (s)

Sol-gela 0.76 x 105 0.28 x 106 13.2

Waterb 3.23 x 105 5.29 x 106 3.1

Methanolc 1.87 x 105 21.5 x 106 5.34a Data from this investigation.b Inferred from data reported in Kostov and Rao (2003).c Inferred from data reported in Demas, et al., (1977) using solubility data

for oxygen in methanol from Fischer and Wilken (2001).

From equation 3 in the manuscript , so that when the quencher concentration

([O2]) is zero, kE = -1. kE were simply evaluated from values of reported in Demas, et al., (1977) and Kostov and Rao (2003).

To find kQ, we again used equation 3. Kostov and Rao (2003), reported lifetimes in the absence of oxygen (0 = 3.1 s) and in the presence of air (air = 0.7 s). Assuming 0.209 atm partial pressure of oxygen in air, application of equation (3) results in:

Demas, et al., (1977), report the value of kQ as 2.5x109 (M·s)-1. For the conversion, we used solubility data from Fischer and Wilken (2001) for oxygen in methanol. These data indicate that at 0.1197 MPa of oxygen tension, 0.00041 mole fraction (mol O2/ total mol O2 + methanol) of oxygen dissolves at 298 K. Conversion to units reported in Table 1 then is as follows:

12