Computer experimentation in and teaching of modern instrumental techniques using circular dichroism measurement as an example

5.59

Analytica Chimica Acta, 283 (1993) 559472 Elsevier Science Publishers B.V., Amsterdam

Computer experimentation in and teaching of modern instrumental techniques using circular dichroism measurement as an example Edward Voigtman LGRT-102 (Chemktry), Universiry of Massachusetts at Amherst, Amherst, MA 010034035 (USA) (Received 2nd September 1992)

Abstract Several different circular dichroism measurement techniques and instrument schemes have been examined by means of detailed Jones calculus computer simulations. The simulations are easy to set-up, extremely realistic and accurately predict what would happen if careful, well-characterized experiments were to be performed. Students can see how experiments are supposed to work and become familiar with the operational parameters. Experts can explore instrument designs and configurations, determine parameter sensitivities, predict signal-to-noise ratios, calibration linearities, dynamic ranges, and so on. Keywords:Circular dichroism; Computer simulations

Modem chemical instrumentation is extremely powerful and sophisticated, capable of routine analyses that would have been essentially impossible as little as a generation ago. The many factors contributing to the remarkable advances in instrumentation and associated technologies are not considered further, because what is of interest here is the matter of training students, and other analysts, to use sophisticated instruments and techniques. How can we teach students to use instruments which, all too often, are simply too expensive or too delicate to be placed in teaching laboratories? How are we to teach students to use instruments, if the instruments are designed never to be “opened up” by users (and instructors)? How can we teach students how best to select among alternative techniques Comsp&ence to: E. Voigtman, LGRT-102 (Chemistry), University of Massachusetts at Amherst, Amherst, MA 010039035 (USA).

when so little quantitative performance information, of true intrinsic significance, i.e., not detection limits, is available? The standard textbooks tend not to be of much help in this regard, and the primary literature is fragmented and of highly variable quality, so what can be done to remedy the situation? There are no general answers to these questions, and related ones, but one partial solution is to use carefully crafted computer stimulations of instruments and instrumental techniques. It has recently become possible to craft such simulations in simple, powerful, and elegant fashion. The models are constructed using a commercially available simulation program named ExtendTM (Imagine That, Inc., San Jose, CA), augmented with a collection of 133 component blocks custom-programmed by the author. The libraries of custom blocks, named Voigt fxxTM,comprise a complete implementation of the Jones and Mueller optical calculi and also include an assort-

0003~2670/93/$06.00 Q 1993 - Elsevier Science Publishers B.V. All rights reserved

560

E. Voigtman /Anal. Chim. Acta 283 (1993) 559-572

ment of conventional electronic signal processing components and a versatile noise generator. The optical calculi have been described, in detail, elsewhere [1,2]. Several applications of the Voigt lx blocks have also been described [3-71. This paper details the use of Extend plus the Voigt fx software for the analysis of several published circular dichroism instruments and techniques. Circular dichroism (CD) was selected as a typical example of the type of instrumental technique which can be accurately simulated with the combination of Extend plus Voigt fx. Circular dichroism measurement is an increasingly important matter because of its utility in the structural study of both chemical and biological systems, especially polymeric systems. Yet most modem teaching curricula have ignored CD because of its instrumental costs, the cumbersomeness of describing polarized light, especially circularly and elliptically polarized light, and the difficulties in dealing with CD in quantitative fashion.

optical calculus and signal processing libraries were widely released as copyrighted shareware on January 2, 1992. Interested readers may contact the author. The coordinate system in all of the Voigt fx optical simulations is right-handed, with x being horizontal, y being vertical, and z as the light beam propagation direction. In all the simulations described below, Jones calculus was used, though Mueller calculus was equally serviceable. All Mueller matrices in the Voigt fx blocks are in standard Shurcliff form [l], including those in references using other matrix element arrangements, e.g., Jensen et al. [8]. The Appendix shows the dialog boxes, of the more complicated blocks, present in the figures in the simulations. Necessary operational parameters are entered into the appropriate dialog box entries, as may be understood by examining the dialog boxes in the Appendix, and then the simulation is performed by specifying a starting time, an ending time, and the desired number of simulation steps.

EXPERIMENTAL

All simulations were performed on a Macintosh IIfx computer (Apple, Cupertino, CA) with 20 M RAM, system 7.0.1 (enhanced), and an Extend l.ln memory allocation of 4000 Kbytes. A Macintosh Plus with 4 M RAM is a satisfactory, though much slower, alternative. The Voigt fx

RESULTS

A simplified conventional, but noiseless, circular dichroism simulation model is shown in Fig. 1. Each of the blocks in Fig. 1 is a portion of the simulation computer code, requiring appropriate

analyte concentration profile 6ource 2 nlw, +4!5” linear polarlzat.lon

.P.

ptlotocb6tic

photodetector & uan6impedancc amplifier

modulator

Fig. 1. A conventional circular dichroism measurement scheme using photoelastic modulation.

E. Vo&tman /AnaL Chh. Acta 283 (1993) 559-572

561

input parameter specification via individual dialog box parameters. The figure is the over-all simulation computer program itself. The physical principles of operation of the model are quite simple. The light source produces linearly polarized light having its polarization axis at +45” to the horizontal. The x polarizer converts the light to a pure horizontal polarization and passes it on to the photoelastic modulator (PEM). The modulation axis of the PEM is oriented at +45” relative to the x axis. With appropriate squarewave drive voltage, the PEM behaves as a quarter wave retardation plate, alternating between +90” and -90” retardation. The output is therefore circularly polarized, alternating, with 50% duty factor, between right circular polarization (RCP) and left circular polarization (LCP). The polarization-modulated beam then passes through a sample cell containing a circularly dichroic material, wherein the RCP and LCP states are absorbed unequally. The CD material may be present in a static cell, at fiied concentration, or it may flow through a dynamic cell, in

f 0.02236 + 0

which case the concentration is determined by another block. This is the situation shown in Fig. 1. The differentially absorbed circular polarizations then pass to the photodetector and preamplifier, which produce voltages proportional to the incident light intensities. The digital storage oscilloscope provides for signal acquisition and processing. Phase sensitive detection, via lock-in amplifier, is the customary signal processing option of choice. It is demonstrated in a later figure, when source and photodetector/preamplifier noise sources have been added to the model. Figure 1 is much more than simply a schematic of a simplified CD instrument: it is a computer program modeling, via the use of Jones calculus, the performance and behavior of a CD instrument. For Fig. 1, the starting time was 0 s, the ending time was 0.8 s, and 640 steps were specified. Before observing the time-domain output of the instrument, it is useful to see how the blocks accomplish their modeling tasks. A circularly dichroic medium, by definition, unequally absorbs incident RCP and LCP light. Therefore, CD may be measured by performing

ij

1 mW, +450 linear

polIlrlutJon

Jones

calculus

RCPJones vcdoroutput (

quarter wwe retarder Fig. 2. Converting

linearly polarized

ideal x polarizer light to circularly polarized

light.

562

appropriate absorbance measurements, using RCP and LCP light. The conventional method of preparing RCP and LCP light is shown in Fig. 2. The incident light beam is converted to a pure linearly polarized state, in this case the x polarization, and the resulting state is converted to circularly polarized light by passage through a suitably oriented retarder. The retardance must be !W’, i.e., quarter wave at the wavelength of the incident beam, and the handedness of the circularly polarized light depends on whether the retarder’s “fast axis”, i.e., axis of minimum index of refraction, is oriented at + 45” to x or is at - 45” to x. If it is at + 45” and the retardance is + !W’, the light is RCP, if at - 45” and + 90” retardance, the light is LCP. Figure 2 also shows the Jones vectors describing the process of converting light, in arbitrary initial polarization state, into both RCP and LCP states. In the figure, the initial polarization state is linear, oriented at + 45” to X. The Jones vector, a complex two-vector, has equal x (top) and y (bottom) polarization components. Passage through the x polarizer removes the y component, leaving a pure x state. The beamsplitter transmits 50% of the incident x state and reflects the other 50%, which is then totally reflected by an ideal mirror. Passage of the two x states through the quarter wave retarders gives the RCP and LCP states. The same results are obtained when the retarders have the same orientation, e.g., +45”, but differ only in the sign of their 90“ retardances. The component blocks in Fig. 2 can model ideal behavior and various types of non-ideal behaviors. In Fig. 2, the blocks were specified, for reasons of clarity and simplicity, as modeling ideal components. Below the simulation itself is the Jones calculus matrix calculation showing how the RCP state would be obtained. This calculation is automatically performed by the connected blocks, once for each simulation step. Having obtained Jones vectors for RCP and LCP light, it is only necessary to pass them to a block exhibiting circular dichroism, measure the resultant transmitted intensities, and use Beer’s law as appropriate. Figure 3 shows the general circular dichroism and circular birefringence (CB)

E. Voigtman /Anal. Chim. Acta 283 (1993) 559472 Jonw

e-Q-

Mudla

MM(

for clmukr dkhrokm

(CD) and oircukr blrefHqaw

co&Q -(CB - i CD) SrnbQ /2Q

&/2

m8trbc tar clrcukr dkhrokm

e-A. 1

(CB - I CD> stnbQ /2Q casbQ

(CD) and clrcukr MnMylau

cosb CD 0 0 CoScB 0 -shrCB sfnbCD 0

(Cs)

(CS)

0 sfnb CD SfncB 0 CoScB 0 0 cosb CD I

Fig. 3. The Jones and Mueller matrices for circular dichroism and optical activity (CB).

Jones and Mueller calculus matrices. Table 1 defines the terms in the matrices and relates them to the usual experimental parameters, e.g., molar ellipticity, molar optical activity, concentration and path length. Note that circular birefringence is also called optical activity or optical rotation. These matrices are subsets of the general anisotropic medium matrices, which are programmed, in full, in another block in the Voigt fx software. The matrices, rearranged into standard Shurcliff form 111,are from Jensen et al. [S].

TABLE 1 Definitions of symbols and expressions RCP: Lcp: ‘+: A,: n,: ;:: I\: n: A,: 9: 8: 4: CD: CBZ a: 6: B:

right circularly polarized light ( + subscript) left circularly polarized light ( - subscript) molar absorptivities for RCP and LCP (1 mol-’ cm-‘) absorbances for RCP and WP indices of refraction for RCP and LCP concentration (M) path length (cm) wavelength (cm) = lo-’ x wavelength (nm) (n _ + n + )/2, mean index of refraction (A, + A _ )/2, mean absorbance 2~7nl/A, phase (radians) molar elliptic&y (degree cm-’ M-l) molar optical activity (degree cm-’ M-l) In10 (e_ - c+)c1/2 = 8&/180 24&r/180=27r (n_-n+)l/A CD2-CB* 2CDCB [(a’ + 6’)” + a]0.5/2fi [(a’ + b2)‘.’ - a]0.5/2fi B + iC

E. k&man

/Anal.

Chim

Acta 283 (1993)

559-572

In Fig. 1, it was assumed that the optical activity was zero, the molar ellipticity was 100” cm-’ M-‘, the path length was 1 cm, and the reference frequency for the PEM was 40 Hz. The CD analyte concentration had a Gaussian temporal profile, with 0.4 s retention time, 0.1 s standard deviation, and peak concentration as specified below. The mean molar absorptivity was 1 I mol-’ cm-‘, unless otherwise stated. The photodetector responsivity was 0.1 A W-’ and the preamplifier’s transimpedance was lo4 V A- ‘. Figure 4 shows the effect of increasing the CD analyte concentration, holding everything else constant. The circular dichroism is clearly shown as an AC squarewave signal, modulated by an “envelope” due to the mean molar absorptivity of the analyte. With phase sensitive detection, the AC signal may be separated from the envelope, as will be seen later. Figure 5 shows the effects of varying the mean

563 1.0

0.6

z

0.6

$

0.2

0.0

+ 0.0

0:2

0:6

0:4 Time

Ol6

(s)

Fig. 5. The detrimental effects of mean molar absorptivity on circular dichroism signals. 1 Umok 00

cm mean m&r 0.2

dmrpWty 0.4

Time (S)

Fig. 4. ‘Apical circular dichroism responses as a function of concentration.

molar absorptivity while holding the mean molar ellipticity constant. It is quite evident that the CD signal is dramatically degraded by high mean molar absorptivities, a circumstance that also makes phase sensitive detection less sensitive, since the large “envelope” must be rejected while acquiring the concomitantly small CD signal. An interesting feature of the simulations is that various processes may be “turned off, as desired, to verify the causes of observed effects. In Figs. 4 and 5, it is a simple matter to specify zero molar ellipticity and see the mean absorbance envelope devoid of CD signal squarewave modulation. An unrealistic feature of Fig. 1 is the complete absence of noise in the simulation. Figure 6 shows a modified version of Fig. 1, allowing for both light source noise and photodetector/preamplifier (PD/preamp) noise. The light source had 0.1% R.S.D. of Gaussian, white noise. The

564

E. Voigtman /Anal. Chim. Acta 283 (1993) 559-572 Gaussian concentr0tlon orofile

photodttcctorfi tranblmpedance amplifier

dlgital

linear polrrfization. 2 mW, with 0.1% Gaussian. white nolee

Fig. 6. A conventional CD instrument with noise sources and lock-in amplifier detection.

PD/preamp noise was modeled by a following noise generator block. The noise was Gaussian, bandlimited (1 mHz-10 Hz) l/f noise, with approximately 5 nV HZ-~/~ noise amplitude spectral density. The average light intensity reaching the PD/preamp, in the absence of an absorbing analyte, was approximately 1 mW. The PD/pre-

amp responsivity was 0.1 A W-’ and the transimpedance was 10000 V A-‘. Therefore, the average PD/preamp output voltage, in the absence of an absorbing analyte, was approximately 1 V. The simulation had a starting time-of 0 s, an ending time of 2 s, and the number of simulation steps was 10000.

0.05 offset. phot&t&or 1

signal

/

lock-in ampAsr

output

-0

-025 0.0

I

I

I

0.2

0.4

0.6

I

Iims~;

Fig. 7. The output response of the simulation in Fig. 6.

I

I

I

1.0

12

1.4

565

E. Voigtman /Anal: Chim. Acta 283 (1993) 559-572

circular polarization

photoelastic modulator

Fig. 8. A simulation showing the use of a photoelastic modulator for polarization analysis.

Figure 7 shows the first 1.5 s, i.e., 7500 data points, of the simulation results. The PD/preamp output was offset to approximately 0 V by using - 1 V offset parameter in its dialog box. If this were not done, the lock-in amplifier would have

, :

1.2

:

, 8’

Ri3fmncs~usncy=2Hn

.-. ‘a \

, \ ,

1

0.0

responded with its step response, partially obscuring the signal peak. The step response can be avoided by simply “out waiting” it, but only at the expense of simulation time. Note that the lock-in amplifier response is quite smooth and both de-

02

I

I

I

0.4

0.6

0.8

lime

Fig. 9. The waveforms produced by Fig. 8.

(s)

I 1.0

566

E. Voigtman /Anal. Chh. Acta 283 (1993) 559-572

layed and stretched. These are necessary consequences of the use of an output filter time constant long relative to the signal duration. For the lock-in amplifier in Fig. 6, the output low pass filter was specified as being a third order RC low pass filter with 1 Hz noise bandwidth. Clearly, the photoelastic modulator does an excellent job of producing light which is circular polarization-modulated. It has other benefits as well. It may serve, for example, as a polarization analyzer [9]. Figure 8 shows a simulation in which the PEM is used to extract the linear and circular polarization components from a beam comprised of several types of polarized light. A linear component oriented at 0” is aligned with the PEM. It passes through the PEM and is attenuated, by

REP wrth O”/cm

M

CD

LEP with O’lcm M CD

intensity = 2 mW; linatiy polatized at +4F

50%, in passing through the analyzer, oriented at +45”. There is no intensity modulation impressed on this linearly polarized light component, so it simply contributes a DC offset, of 0.5 V, to the PD/preamp output. The linearly polarized light component at + 135” was combined with the 0” linearly polarized component via the beamsplitter cube and was then sent to a second beamsplitter cube, where right circularly polarized light was also added. In passing through the PEM, the linearly polarized light at 135” was converted to elliptically polarized light, circularly polarized only at the peaks of the sine wave reference frequency. Accordingly, the output of the analyzer contained a modulated intensity at twice the reference fre-

azimuth elliptlclty intensity

= 0’ = 0.008726060 = 0.9997698

mW

azimuth clliptlclty intensity

= 0’ = 0.000726060 = 0.9997690

mW

ideal rctmdec f4v ofimltation. 1°retardtion

Intensity

= 0.4990849

mW

inten&zy

= OS4990049

mW

ideal analger at +45O T

I

A

+45’ retarder orientation Right Elliptic Polarization

give6 (REP)

clnuialiy dichrolc rnrlyte

a+ib 4hc+id amme Joncs vector sink

REP wfth lo/cm M CD

azimuth ellipticity intensity

= 0’ = O.OO0735594 = 0.9997701 mW

fntcneity

= 0.499005

LEP with lo/cm M CD

azimuth elliptlcity Men&y

= 0’ = 0.000710142 = 0.9997695

Intensity

= 0.4990047

mW

Fig. 10. The simulation used to demonstrate the principles of circular dichroism measurement by ellipticity measurement.

mW

mW

E. Voigtkn /Ad

Chim. Acta 283 (1993) 559-572

567

conccntr0tim (M)

for MO (E. -E,) c

aligned with the analyzer, the other is orthogonal to it. Hence, there is an analyzer intensity component at the reference frequency. With phase sensitive detection, the two modulated components are readily found, even in the presence of a substantially larger unmodulated component. Figure 9 shows these results for Fig. 8. There are other advantages of PEM-based systems, but there are also some disadvantages. Actual PEM devices are resonantly driven, providing modulation frequencies of approximately 50 KHz. Increasing the modulation frequency requires reduction in the size of the device, with concomitant reduction in the optical throughput. There may also be problems with residual birefringence in the PEM device. Given the relative slowness of PEM devices, it is not possible, at present, to perform CD measurements, using PEM-based instruments, on nanosecond lifetime species. However, there are other ways to measure CD and it is indeed feasible to perform such measurements. One possibility involves the use of ellipticity measurement

I <<6

Fig. 11. The circular dichroism elliptic&y signal expression derived by Goldbeck and Kliger [lo].

quency, since both RCP and LCP were produced in each period of the reference frequency and these polarizations yield the maximum transmitted intensity through the analyzer. The circularly polarized component in the beam incident at the PEM was converted to elliptically polarized light, but at the peaks of the sine wave reference frequency, it is actually linearly polarized. The original retardation of 90” is either increased or decreased by 90” in transiting the PEM. One resultant linear polarization is

Lwl.

Circular Dichroiem Ellipticity

4ignal Detection phtieteotor transimped0nce

81 amplifier

difference

retio

digital storage oe4ofxope

Y

R=l

circularly dichrolc sample

+-

bum

photodeteotor& translmpedance amplifier

Fig. 12. A “double beam in space” instantiation of the Goldbeck and Kliger circular dichroism ellipticity measurement scheme.

568

The basic idea is shown in Fig. 10. Linearly polarized light is converted to elliptically polarized light having very small ellipticity, i.e., the light is described by a polarization ellipse which is very thin. The retardation is a small value, typically about l”, and the retarder is oriented at either +45” relative to the incident polarized beam or at - 45” relative to the incident beam. In each case, the elliptically polarized resultant beam has an azimuth of O”, but the +45” retarder orientation yields right elliptic polarization (REP), while the -45” retarder orientation yields left elliptic polarization (LEP). As shown in the data in the upper portion of Fig. 10, both REP and LEP light have the same ellipticity and intensity, if they pass through a medium having zero CD. The intensities, after transmission through an analyzer oriented at +45”, are also equal. The data in the lower portion of Fig. 10 shows that even a small molar ellipticity causes the REP to become more circularly polarized, i.e., its ellipticity increases, while the LEP becomes more linearly polarized. In Fig. 10, the path length was 1 cm and the analyte concentration was 1 mM, so the CD was only 1 millidegree. After transmission through the analyzer, the intensity difference is easily detected, particularly for larger CD signals. Goldbeck and Kliger [lo] gave an approximate expression, shown in Fig. 11, used to describe the ellipticity signal. Measurement of, e.g., the molar ellipticity, is possible by determining the other parameters and by making measurements of the light intensities (IREP and IrEp) for the two orientations of the 1” retarder. An advantage of the technique is that it can be used with nanosecond-pulsed light sources. Another advantage is that polychromatic operation is easily achieved. A disadvantage is that the light intensities would ordinarily be measured in succession. Thus, the retarder would be oriented at +45” and the transient I,, light intensity would be acquired, perhaps with a high speed digital storage oscilloscope. Then the retarder would be switched to -45” orientation, by 180” rotation about the x axis, and the transient ILEp light intensity would be acquired. High quality digital storage oscilloscopes readily perform file arithmetic on digitized channel data, so calculation of

E. Voigtman /Anal. Chim. Acta 283 (1993) 559-572

the normalized light intensity difference is easy, but has the drawback of requiring two light pulses, which then degrades the signal-to-noise ratio (S/N) because of pulse-to-pulse light source fluctuations. Note that the normalized light intensity difference is bounded by f 1, while the other ratios in Fig. 11 are inversely proportional to 6, and, therefore, potentially much greater than unity. Decreasing 6 is a feasible way of improving the measurement only so long as these ratios are much less than unity. If the ratios become too large, temporal distortion occurs, followed by non-linear response. Figure 12 shows a simple “double beam in space” configuration of the Goldbeck and Kliger ellipticity measurement scheme. Such an arrangement might be useful in cases where source noise was dominant. Two matched sample cells are used and the analyte is supplied by separate, but matched, reservoirs. The PD/preamp outputs would probably be acquired on two channels of a high speed digital storage oscilloscope and the normalized light intensity difference would be calculated in the oscilloscope or in a subsequent computer program. In Fig. 12, the calculation is carried out with unrealistically fast, and accurate, sum, difference, and quotient blocks, for simulation convenience.

20-

15-

S 5 a

!I0 z

J-L-A-n 0.0

0.2

0.4

0.6

0.8

1.0

hme(5)

Fig. 13. A typical elliptic&y signal waveform produced by the simulation in Fig. 12.

569

E. Voigtman /AnaL Chim. Acta 283 (1993) 559-572

The resulting ellipticity waveform is shown in Fig. 13. The concentration profile was that of an exponentially modified Gaussian (EMG), with asymmetry of 2, and the laser light source was of 2 mW constant intensity, with 1 ppm Gaussian, white noise. The waveform scales with analyte concentration and is almost completely immune to source noise: even 10% R.S.D. Gaussian, white noise on the light source causes no significant change in the waveform. Likewise, changing the light intensity by a factor of 2 has no effect on the signal. This is, of course, a benefit of the “double beam in space” configuration. In practice, it is impossible to match the arms of the instrument perfectly, but the performance should still be impressive. There are many ways in which to improve upon or change Fig. 12. Suppose the light source is a pulsed laser, with substantial laser noise and also pulse-to-pulse intensity fluctuations. Also suppose the analyte’s circular dichroism is photo-induced, with a 1 ns lag time, and suppose the PD/preamps are noisy. Figure 14 shows a modified version of Fig. 12 having these complications. The laser is modulated with the product of an EMG temporal profile and a noise generator’s output (for pulse-to-pulse fluctuations). The EMG has an amplitude of unity, retention time of 1.5 ns, standard deviation of 0.5 ns, and time

Nanosecond

20 mW, +45’ po*riution 10% Gaussian

CD Elllpticity

Detection

linear with

Fig. 14. A more realistic version of the simulation in Fig. 12.

constant of 1 ns ill]. The noise generator produces 1 point per simulation, held throughout a given simulation, having Gaussian distribution, p = 1 and (T= 0.1. The resultant product modulated the laser’s 20 mW output, which has 10% R.S.D. of Gaussian, white noise. The fluctuating laser modulation input serves as the input to an infinite impulse response filter, i.e., digital recursive filter, with 1 ns time constant. The filter is simply a single pole low pass filter. The attenuated output then serves as the “concentration” input to the two sample cells. Therefore, the concentration of CD analyte may be considered as being “photo-generated”, though the laser noise is not used. If it is desired to include the laser noise in the “photo-generation” process, this is readily accomplished by addition of a beamsplitter and PD/preamp after the 50:50 beamsplitter. It should also be noted that far more complicated “kinetics” may be modeled by custom-programming an appropriate block, if the necessary photophysical equations and data are available. The PD/preamp block has no noise, so it may be made noisy by following it with a noise generator block. As shown, the noise amplitude spectral density is 10 nV II-1/2. The PD/preamp block also has no gain-bandwidth product limitations, so IIR filters, with 1 ns time constants, are used

E. Voigtman /Arm! Chim. Acta 283 (1993) 559-572

signs and configurations, determine parameters sensitivities, predict signal-to-noise ratios, calibration linearities, dynamic ranges, and so on. It is abundantly clear, from the material presented, that many additional simulations and demonstrations are waiting to be performed. The teaching value of the simulations is enormous and obvious.

-1

11 0

I 2

I 4

I

6

I 8

I 10

lime(n5)

Fig. 15. Four consecutive ellipticity signal waveforms produced by the simulation in Fig. 14.

to roll-off the frequency response. The responsivities of the PD/preamps were lo4 A W- ’ and the transimpedances were 1000 V A-‘. How well does the simulation work? Figure 15 shows 4 consecutive ellipticity signal waveforms. The PD/preamp noise is dominant. The peak analyte concentration was approximately 1 mM, the path length was 10 cm, the mean molar absorptivity was 5 1 mol- ’ cm- ‘, and the molar ellipticity was 0.4” cm-’ M-‘. Clearly, the laser’s pulse-to-pulse intensity fluctuations are not cornpensated by the light intensity normalization calculation because the fluctuations appear twice: once in the use of the fluctuating laser pulses as the CD probes and a second time in the “photogeneration” of the CD analyte. Another normalization factor is required. conclusions Several different circular dichroism measurement techniques and instrument schemes have been examined by means of Jones calculus computer simulations. The simulations are easy to set-up, extremely realistic and accurately predict what would happen if careful, well-characterized experiments were to be performed. The simulations are useful for both novices and experts. Novices can see how experiments are supposed to work and become familiar with the operational parameters. Experts can explore instrument de-

This material is based upon work supported by the National Science Foundation under Grant No. CHE-9108707. Thanks are also due to W. Wegscheider and M. Valclrcel for providing the opportunity to participate in the 12th Zntemutional Symposium on Microchemical Techniques, in C%rdoba.

APPENDIX

POlWtZWS 0 Mueller?

lzl 0 Llnw (18) 0 Llnew (y) 0 l&mar (n: non-ideal) 0 Circular (RI 0 Clrcukr (1)

10.9999)51

* tnnsmlttance (4

IJe-00s

- trensmlttancs (y)

- szlmuth of fast snls (theta, ‘1

10

0 Elll~tlcal (RI 71 0 EllIptIcal (LB

- elllptlclty (tsnlomcgsl -b/a)

Comments Ideal I&war ‘II’ polartzstlon

I ’ Fig. Al. The dialog box for the polarizers block.

rhoto-ele*tlc motMator

q ~~~~~~~ 0

- offset angle (‘1 = moflulatlon angle (‘1

B90

= static retardance

IO

- retardance

(0)

skew (*B

OK

w (Help) ot

CommMtr 1

Fig. A2. The dialog box for the photo-elastic modulator block.

E. Voigtman/Anal. Chim. Acta 283 (1993) 559-572

Retarders

anlratmpic medium

Cbwhly r[-

D@BIIY]

- circular dlrhrolrm (‘/cm MB

- maa” lndaa “1 rslmctlon

1

- Flatardsnce (delta, ‘1

H -45

Comments

- llzlmuth of fast aals (rho.

(6)

Rmplltude

]Y]-

-

Prabablllty Dl&lbutlon Function 0 Ewponsntlal @ Sausrlan 0 Poisson

0 Constant

Moan/I

Q 6ourrlon

0

SD

MOdlflod onponontlal

I

0 Unity area?

[_)

0 Muollor?

[7 I pt/rlm?

I I

I

I

-

I

I

LLlp

Import custom nolre PSD] Polarlzatlon: Comments

Osi” II

0 Custom

I

I

[s)

I

Import custom nolso record

Comme”ts I

0 Custom

-1

Nolse Poumr Spectral Oanrlty @tUhly 0 l/f*g,amma

0 EM6

I

(2) light tourco -

Light sour%. KItI b Impulsluo)

Concantmtlon profUa

Slgms

I

produces Left Elllptlc Polarlzatlon

:ig. A6. The dialog box for the retarders block.

[Hslp)MI01(1

- Ratantlon tlms

10.4-j

Rzlmuth 01-45’ (LEP)

Confontratlon profllos _

Conrentratlon proliler gensrator /xG----j-

lt

- Elllptlclty of fart anis (tanlomogal - b/a)

Comments

Fig. A3. The dialog box for the circular activity block.

0 Clrculor (left)

0 Sonora1 olllptlcal (any a) $ :

0 Loft clrculsr (e - 90’) cm)

waoalongth (nn)

_

0 Circular (right)

0 Right circular (a - 90’)

- mea” molar absorptlulty Wnolo

IJ r\-

0 Full tuaoo plate 0 lluarter wauo plot0

0 Circular to - 180’)

- rtatlc concenlmtlon (Ml

1.01

@ 6anoral llnosr (any a)

ElliptIcal

- path length km) ‘pi

0 Muallorl

0 Half iuaoo plate

0 Muollar?

optical octlulty (‘/cm M)

100

El

Llasor

Dolou:

>

fllename:

1

Moan

&

ua

0 horizontal (a) 0 oerticol (y) 0 unpolarized

Intensity: 2 mW; polarlzotlon: nolso: 0.1% RSD, 6eurslan. white.

l4S Unoar.

Fig. A4. The dialog box for the concentration profiles block. Fig. A7. The dialog box for the light source block.

III

(7)

PlVpreampllfler

_II

Photodetector/preamplifier -

Jones uector

El

Stokes uector

(13)

Naha Oanorator

Nalso ganerator I_

.

Pmbablllty Dlrtrlbutlon Function 0 Unllona @ Sawsian 0 Polrronlan MoanlO

Responsluity WWI Ironsimpedance

output offset

(n)

t 10000

0 Mueller?

Lou,

0 Display7

gamma - []

Intensity bl3

IJ) !

Comments typical responsiuity

10.000999971

I

Noise gain 0 Custom

II 0 One polntlsim Slgnal gain II

Import custom nolsa PSD J Comments

I

High I’o]

(V]

Import custom oolso record

p transimpedance

Fig. A5. The dialog box for the PD/preampliier

(o.0011

0 Custom

(ss-0071

Nolsa Powor Spoctml Donslty 0 Ulwto 0 I /r*gamma

171

Ill) 101

EI Output saturation

SD

@wm

l

5 nU/u’Hz

I block.

Fig. AS. The dialog box for the noise generator block.

E. Voigtman /Arm! Chim. Acta 283 (1993) 559-572

0 1st order RC LPF

0 3rd order Bessel LPF

0 2nd order RC LPF

0 1X ‘Pickup’ LPf

@3rd

OTruo

order RC LPF

[Noise bondwidth

@ HornwIt

integration

] 71

Phase

I-1

D billi’s ‘tl’

0 ent*moi

0 Blbboro’S ‘K’

0 uniformly distributed

0 goursion distributed

0 roclprocol deriuotiue

0 prodotor-prey

Time conrtont optionr:

@constant

input

Chaos

0 proportionat

me time constant is(~]seconds

(IO

,Y,

Reference thre8hold [y] Comments

iiystoreslr

71

)

II

Fig. A9. The dialog box for the lock-in amplifier block.

- inltlal fllter output

Comments R rlmple dlgitol, rocunlue fitter. I.e., Infinite ImPulso roSPonso filter, tuith 1 ns time constant.

Fig. A12. The dialog box for the IIR filter block. REFERENCES

Jones vector source

[ Conuort

m

roct to polar

[E)

I

c Conusrt poior

)

to net

1

Intensity coicuiotlon

[GT---]( Comments

right clrculor polorizotlon

Fig. A10. The dialog box for the Jones vector source block.

(4)

Jonor uoctor Sink A

Jones vector sink p Display? Jones UoCtOr intonslty 0 Enable separate Outputs?

145 1011

- ozlmuth (degroorl oitipticity (0 (- b/o <-

1)

Fig. All. The dialog box for the Jones vector sink block.

1 W.A. Shurcliff, Polarized Light, Haward University Press, Cambridge, MA. 1st edn., 1%2. 2 D.S. Kliger; J.W. Lewis and C.E. Randall, Polarized Light in Optics and Spectroscopy, Academic Press, Boston, MA 1st edn., 1990. 3 E. Voigtman, Anal. Chim. Acta, 246 (19911 9. 4 E. Voigtman, Appl. Spectrosc., 45 (1991) 8%. 5 U. Kale and E. Voigtman, Appl. Spectrosc., 46 (19921 1636. 6 E. Voigtman, Spectrochim. Acta Electronica, 47l3 (19921 E1549. 7 E. Voigtman, Anal. Chem., 64 (1992) 2590. 8 H.P. Jensen, J.A. Schelhnan and T. Troxell, Appl. Spectrosc., 32 (1978) 192. 9 Hinds Instruments, Inc., Hillsboro, OR, PEM-90TM Photoelastic Modulators, brochure and data sheets, 1991. 10 R.A. Goldbeck and D.S. Kliger, Spectroscopy, 7 (1992117. 11 J.P. Foley and J.G. Dorsey, J. Chromatogr. Sci., 22 (1984) 40.