Capillary-Scale Refractive Index Detection by Interferometric

Anal. Chem. 1996, 68, 1762-1770

Capillary-Scale Refractive Index Detection by Interferometric Backscatter Hendra J. Tarigan,† Paul Neill,‡ Christopher K. Kenmore, and Darryl J. Bornhop*

Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061

We describe a novel approach for measuring fluid bulk properties such as refractive index (RI) and temperature changes in tubes of capillary dimensions based on a simple optical configuration which uses an unfocused He-Ne laser, a cylindrical tube, and a photodetector. Side illumination of a fused silica capillary produces a fan radiation in a 360° plane normal to the central axis of the capillary that is spatially well defined in the lateral direction. It is shown that, upon viewing a high-contrast interference pattern contained in the beam profile on a flat imaging plane in a direct backscattering configuration, the physical characteristics of the capillary and the bulk properties of the fluid contained within the tube can be determined. Position changes in the maxima and minima in the intensity-modulated profile (interference fringes) are directly related to the refractive index of the fluid in the tube. Measurement of the fringe shift by a slitphotodetector assembly facilitates the determination of dn/n at the level of 1.8 × 10-7, while temperature changes can be measured using the fringe centroid position at a level of 5.8 × 10-5 °C (DL ) 3σ). Each determination can be made within a probe volume of 2.6 nL. Also, a wide range of tube diameters can be employed (75-775 µm i.d.) with no modification to the optical train or measurable degradation in system performance. We report results for an optical ray trace model for predicting fringe pattern energy distributions, optimization of the optical configuration, and general system performance predictions. Comparison of our four-beam interference model with experimental results illustrates the utility of the model. Measurement of the change in refractive index (n, or RI) can be used in many applications and has been applied to the most common phases of matter: solids, fluids, and gases. Some typical applications are the detection of geometric perturbations in optical fibers,1 laser interferometric thermometry for solid substrate temperature measurement,2 construction of three-dimensional tomographic maps of turbulent flow,3 and quantification of analyte

species in flowing streams.4 Of particular interest is the application of RI measurement schemes for universal detection in separation techniques such as high-performance liquid chromatography (HPLC) and capillary electrophoresis (CE). Although it is a workhorse in conventional HPLC separation (because it is a concentration-sensitive bulk property and a nondestructive technique), the RI detector has found little acceptance in capillary chromatography.5 The limited use in capillary HPLC certainly does not stem from a lack of attempts to measure RI changes in small volumes6-11 but more likely from the inherent difficulty in miniaturizing detection schemes to volumes in the low nanoliter region without a significant loss in performance. In the work by Woodruff and Yeung,6 a Fabry-Perot interferometer provided excellent sensitivity, but it is expensive to configure and, due to a path length sensitivity, can only provide detection in low microliter volumes. Refractometric interference spectrometry can be used to measure organic pollutants in water, as demonstrated by Gaugliz and co-workers.7,8 This technique uses the change in optical path length resulting from the absorption of a solute onto a film that swells reversibly. Path length sensitivity and flow cell volume constraints limit this method to schemes larger than capillary techniques. Bornhop and Dovichi9 demonstrated the use of a laser-based, off-axis, oncapillary technique that can probe nanoliter volumes and has been applied to detect picogram quantities of sugars in micro-LC separations.10 This technique was found to be tedious to align. Bruno and co-workers further developed the forward-scatter, offaxis technique11 and showed that improved performance is possible by employing an RI-matching fluid to surround the capillary tube, active thermal control of the flow cell assembly, and position-sensitive detection. These improvements facilitated the use of the RI detector for capillary electrophoresis, yet the device still requires off-axis alignment and is limited by the need to modify the capillary tube by removing the polymer coating to aid in index matching. There is a clear need for a universal detection method with reasonable sensitivity applicable to capillary separation schemes.

* To whom correspondence should be addressed. E-mail: [email protected]. †Permanent address: PT Newmont Minahasa Raya, Jalan Wolter Monginsidi, 50, Manado, Indonesia. ‡ Department of Physics, University of Nevada, Reno, NV 89557. E-mail: [email protected]. (1) Presby, H. M. Appl. Opt. 1977, 16, 695-700. (2) Saenger, K. L.; Gupta, J. Appl. Opt. 1991, 30, 1221-1226. (3) Roggemann, M. C.; Welsh, B. M.; Gardner, P. J.; Johnson, R. L.; Pedersen, B. L. Opt. Eng. 1995, 34, 1374-1384.

(4) Munk, M. N. In Liquid Chromatography Detectors; Vickery, T. M., Ed.; Dekker: New York, 1983; Chaper 5. (5) Jorgenson, J. W.; Wit, J. D. In Detectors for Capillary Chromatography; Hill, H. H., McMinn, D. G., Eds.; John Wiley: New York, 1992; Chaper 15. (6) Woodruff, S. D.; Yeung, E. S. Anal. Chem. 1982, 54, 1174-1178. (7) Gauglitz, G.; Krause-Bonte, J.; Schlemmer, H.; Matthes, A. Anal. Chem. 1988, 60, 2609-2612. (8) Yan, H. M.; Kraus, G.; Gauglitz, G. Anal. Chim. Acta 1995, 312, 1-8. (9) Bornhop, D. J.; Dovichi, N. J. Anal. Chem. 1986, 58, 504-505. (10) Bornhop, D. J.; Nolan, T. G.; Dovichi, N. J. J. Chromatogr. 1987, 384, 181187. (11) Bruno, A. E.; Krattinger, B.; Maystre, F.; Widmer, H. M. Anal. Chem. 1991, 63, 2689-2697.

1762 Analytical Chemistry, Vol. 68, No. 10, May 15, 1996

S0003-2700(95)01145-0 CCC: $12.00

© 1995 American Chemical Society

Two of the obvious reasons behind this need for a detection system are (1) the fact that few solutes have native absorbance or fluorescence and (2) the requirement that detection be accomplished directly on the tube limits the path length of conventional methods based on absorbance. Therefore, several researchers have continued investigations aimed toward implementing RI detection methods that probe directly on-column. One such method for small-volume RI measurements is the concentration gradient method, which probes the on-axis optical perturbation produced by a transient solute band.12,13 Although somewhat insensitive to thermal noise, the concentration gradient detector seems most suitable to capillary isoelectric focusing schemes and is, therefore, somewhat limited in its application. A second technique for detecting changes in n in capillary tubes uses a holographic grating to produce two-beam interference in a forward-scatter configuration.14 In a meritorious advance for universal detection in capillary dimensions, Krattiger and coworkers were able to separate and detect metal ions by CE14 using this holographic grating, a capillary that is encapsulated in an index matching glue, and a photodiode array wired to produce position- sensitive detection. Still, there are several drawbacks to the holographic technique, as in the forward-scatter configuration of the past.9,11,14 The major drawback of grazing angle forward-scatter optical configurations is the existence of a fundamental path length dependence, which ultimately limits the level of miniaturization. The results we present here (theory and practice) show that, by using microinterferometry, a technique exists that can produce high-sensitivity RI measurements in smalldiameter capillaries with minimal path length sensitivity. Index of refraction measurements are particularly versatile and take on the duty of performing a wide spectrum of determinations. Yet, the measurement of ∆n in small volumes and at high sensitivity is a formidable task, as shown by the number of attempts made and reported in the existing literature. It is the universal response of the bulk property sensor (an RI detector is one example) that leads to the high background noise, which can often swamp the analyte signal. In measures of RI, the primary source of interference is thermal sensitivity. For most cases, n has a relatively high thermal coefficient (dn/dT), requiring very precise temperature stabilization of the system. As an example, dn/dT for H2O is on the order of 8 × 10-4 °C-1, so at a usable detection limit for ∆n, which is on the order of one part in 106, the temperature-induced signal corresponds to a change in T to one part in 102. To determine n to one part in 108, thermal stability or compensation must be accomplished at the millidegree centigrade level. Conversely, the “noise” in RI measurements can be used to the advantage of the analyst. One such example was demonstrated by Bornhop and Dovichi,15 where the inherent dn/dT sensitivity for fluids was used to perform short path length absorbance measurements using photothermal refraction. Furthermore, as shown here and in previous investigations,16,17 refractive index methods have been used to configure very

sensitive thermal sensors. In the case of the microinterferometer described here, microdegree temperature changes can be quantified noninvasively within nanoliter volumes. Presented here is the theoretical modeling and the general performance evaluation of an RI detection scheme based on laser interferometric backscatter (LIB).18,19 In LIB, an unfocused, linearly polarized He-Ne laser beam impinges on a tube of capillary dimensions producing a fan of radiation, spatially contained, in 360° around the long axis of the tube. When viewed on a flat surface, a series of light and dark spots (high contrast interference fringes) are seen. The central fringe pattern is similar in appearance to that produced by single slit diffraction. The position of these maxima and minima can be employed in the sensitive measurement of fluid bulk properties. It will be shown that this simple optical train can be used to monitor ∆n changes to two parts in 10-7 within unmodified 100 µm capillary tubes for flowing streams. The LIB is inherently alignment insensitive, with overfilling of the capillary the major requirement for significant signal generation. We show that microdegree temperature changes can be probed in subnanoliter volumes. Finally, our current investigations also confirm the previous report19 that, within the tube size range of 75-775 µm, the LIB has limited path length sensitivity, facilitating highsensitivity RI detection in small volumes. The optical configuration we employ is similar to that used previously,20-24 yet in the past the laser light was directed onto a hollow glass fiber to view radially scattered interference fringes. The novelty of the experimental technique described here is that upon slightly tilting a side-illuminated, fluid-filled capillary tube, interference fringes are produced that can be directed above or below the plane of excitation and viewed in a direct backscatter configuration. Simplicity, high sensitivity, low cost, a folded optical train producing a small footprint, and the ability to probe capillary tubes without modification are among the advantages of LIB. Either position or intensity detection schemes are applicable. For reasons related to keeping the optical configuration simple and the system cost low, we have chosen to monitor the lateral fringe shift related to the fluid bulk properties using a simple slitphotodetector assembly. The spatial shift in the position of the fringes is a measure of n for the fluid or gas contained or flowing through the capillary. Tubes with inner diameters of 75-775 µm have been probed with no modification to the polymer coated tube, no changes to the simple optical train, and no reduction in the signal-to-noise ratio (S/N).

(12) Wu, J.; Pawliszyn, J. Anal. Chem. 1992, 64, 2934-2941. (13) Wu, J.; Pawliszyn, J. Anal. Chem. 1992, 64, 224-227. (14) Kattiger, B.; Bruin, G. J. M.; Bruno, A. E. Anal. Chem. 1994, 66, 1-8. (15) Bornhop, D. J.; Dovichi, N. J. Anal. Chem. 1987, 59, 1632-1636. (16) Wang, A.; Wang, G. Z.; Murphy, K. A.; Claus, R. O. Appl. Opt. 1995, 34, 2295-2300. (17) Saenger, K. L.; Gupta, S. Appl. Opt. 1990, 30, 1221-1226.

(18) Bornhop, D. J. U.S. Patent 5325170, 1994. (19) Bornhop, D. J. Appl. Opt. 1995, 34, 3234-3239. (20) Kerker, M.; Matijevic, E. J. Opt. Soc. Am. 1961, 51, 506-508. (21) Horton, R.; Williamson, W. J. J. Opt. Soc. Am. 1973, 63, 1204-1210. (22) Presby, H. M.; Marcuse, D. Appl. Opt. 1974, 13, 2882-2885. (23) Marcuse, D. Appl. Opt. 1975, 14, 1528-1532. (24) Presby, H. M. Appl. Opt. 1977, 16, 695-700.

EXPERIMENTAL SECTION The basic optical configuration for LIB has been described in detail elsewhere18,19 and is depicted in the generalized block diagram presented in Figure 1. A linearly polarized 4 mW HeNe laser (Melles Griot, 5-LHP-111) operating at 632.8 nm, producing a beam diameter at 1/e2 of 0.59 mm, is directed onto a mirror and then onto the capillary tube, which is mounted on a flow cell assembly (Figure 2) with active thermal control. The capillary tubing employed ranges in inner diameter from 75 to

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Figure 1. Block diagram for LIB detection system. OPs is the sample I to V Op-Amp circuit used to condition the signal from Pds, which is the photodetector. M is a mirror, and FC is the thermostated flow cell. OP07 is a differential operational amplifier, DMM is a digital multimeter, and SCR is a strip chart recorder. V is a manual injection valve, and S is the syringe pump used during flowing experiments.

Figure 2. Block diagram for flow cell assembly.

775 µm (Polymicro Technologies, Phoenix, AZ). Theoretical and experimental beam shift comparisons are performed on tubes that are ∼266 µm × 370 µm, while flow injection analysis experiments are performed on 75 µm × 350 µm, 100 µm × 350 µm, 250 µm × 530 µm, and 775 µm × 1000 µm capillaries. The complete flow cell assembly is tilted at an angle that is convenient for placement of the signal photodetector and normally does not exceed a 7° angle. All determinations, except the initial beam profile experiments, are carried out using unmodified capillary tubes that have a 12-15 µm polyimide protective coating. All optical components and detectors are rigidly mounted on a 6 ft × 4 ft optical bread board (Newport Research, Irvine, CA). Manual micrometer-driven translation stages are used to provide reproducible translation of the photodetector, capillary tube, and optical components. Excluding the pump and injector, the entire experiment in enclosed in a Plexiglas box. The flow cell shown in Figure 2 is thermostated with active control using a Peltier thermoelectric cooling chip (Melcore, Trenton, NJ) controlled by a power supply (ILX Lightwave Model LDT-5412, Bozeman, MT) wired in feedback from a calibrated thermocouple. Thermal stability is discussed in detail in the Results and Discussion; it is found to be better than 5.0 × 10-3 °C over a 30 min period. Detection is accomplished using a silicon photodetector (Hamamatsu, Model S2386-5K, Japan) with an active area of 0.8 mm2 placed behind a 100 µm precision air slit (Melles Griot). An Op-Amp (OPA111, Burr-Brown)-based current-to-voltage converter conditions and amplifies the signal. The photodetector is mounted in a fixture that also holds a 632.8 nm interference filter (Optical Coating Tech., Southampton, MA), and the assembly is mounted 1764 Analytical Chemistry, Vol. 68, No. 10, May 15, 1996

Figure 3. Schematic diagram of the fringe pattern and a fixed detector at position xo. The arrows designate the relative direction of the fringe shifting.

on a high-precision translation stage. A strip chart recorder (Linear Instruments, Reno, NV) is used to record the flow injection analysis events, and a digital multimeter (Keithley, Model 197) records all other signal values. A syringe pump (MicroFlow, Isco, NE) is operated in the flow and pressure control mode providing flow to the capillary. A single 0.35 m section of capillary acts both to transfer the solute and as the capillary component of the flow cell. Calibration samples for flow injection analysis (FIA) are introduced using a manual nanoliter injection valve (Rheodyne, Inc.). All chemicals are reagent grade or better. DDI water is used as the solvent or the blank solution. Standards are 0.004, 0.008, 0.01, 0.04, 0.08, 0.10, and 0.4 (% wt/v) glycerol in water. RESULTS AND DISCUSSION Mapping. Figure 3 presents a graphical representation of the interference pattern (actual photographs can be found in ref 19) and shows the configuration of the slit-photodetector. For convenience, arrows have been added to designate how the fringes shift. Mapping the intensity profile of the beam pattern involves translation of the slit across the fringes, providing a quantitative measure of intensity versus position. The beam profile was mapped from the central region to the eigth fringe. A typical profile map for two individual fringes is depicted in Figure 4. As shown in these figures, when removing the coating from the tube, a high-frequency component can be seen on the otherwise smooth monotonic intensity variation. Initially, it was believed that simply using a coated tube would facilitate the elimination of this secondary modulation component, yet further investigations not within the scope of this paper indicate that laser polarization orientation and surface characteristics must be considered.25,26 In practice, we are able to obtain a smooth monotonic intensity variation for many fringes by using coated tubes. All results described here result from using coated tubes as supplied by the manufacturer. The principle of operation for the RI measurement can be ascertained from a study of Figures 3 and 4A. With reference to Figure 3, as the optical path length within the tube changes (as occurs when n changes for materials contained in the tube), the position of the fringes shifts. By placing the slit-photodetector assembly at x position of about 2900 µm (see Figure 4A) and integrating the intensity change as the solute RI changes, we read a signal that is proportional to analyte concentration change.19 This (25) Tarigan, H. J.; Neill, P.; Kennmore, C. K.; Bornhop, D. J. Submitted to Opt. Eng. (26) Bornhop, D. J.; Hankins, J. Anal. Chem. 1996, 68, 1677-1684 (in this issue).

Figure 5. Ray paths and angle designations for four rays traversing a side-illuminated capillary tube.

Figure 4. (A) Intensity profile for a water-filled polyimide-coated capillary of dimensions 530 µm × 775 µm. (B) Intensity profile for a water-filled uncoated capillary of dimensions 530 µm × 775 µm.

simple intensity-based detection method is inexpensive and easy to implement yet will ultimately limit the dynamic operation range. Consequently, we are investigating the use of diode array detection and fringe counting to improve detector performance and further simplify beam-detector alignment. Theory. Several researchers have provided insightful models for forward-scattering by clad fibers,20-23 deflection by a cylindrical tube,27,28 and the interference for a pair of collinear beams focused onto the wall and center of the capillary, respectively.14 Van de Hulst29 has discussed the scattering of plane electromagnetic waves by dielectric cylinders, and Kerker and Matijevic20 derived the solution for the scattering of plane electromagnetic waves by two isotropic concentric cylinders. While Watkins30 has performed calculations for forward-scattering clad fibers using this theory and a geometric ray-trace, he did not apply his analysis to scattering angles in the 0-7° range. Marcuse23 reported an investigation on light scattering from unclad fibers that is most like the direct backscatter configuration of the LIB detector, yet in his three-ray model, the results (27) Krattiger, B.; Burno, A. E.; Widmer, H. M.; Geiser, M.; Dandliker, R. Appl. Opt. 1993, 32, 956-965. (28) Synovec, R. E. Anal. Chem. 1987, 59, 2877-2884. (29) Van de Hulst, H. C. Light Scattering by Small Particles; Wiley: New York, 1981. (30) Watkins, L. S. J. Opt. Soc. Am. 1974, 64, 767-773.

correspond poorly with experimental observations. Below we present a four-beam geometric ray theory to predict the backscatter intensity profile from a fluid-filled, side-illuminated fused silica capillary tube, with a focus on small scattering angles (03°). Here we show that the ray trace theory can be used to predict changes in the scatting intensity pattern due to fluid RI (n2) changes. In a related report,25 we extend the use of the fourbeam model to predict the effects on beam profile by the variables of outer wall radius (R), inner wall radius (r1), and refractive index of the tube (n1). Figure 5 shows the geometric ray paths for the four rays traced. Rays 1 and 3 are incident on the left side of the focal line. They traverse the fused silica capillary wall and enter the sample fluid. Ray 3 is reflected at the sample fluid-tube interface. Ray 1 passes through this interface and is reflected at the fused silicaair interface. Ray 2 and 4 are incident on the right side of the focal line. Ray 4 is reflected at the fused silica-sample fluid interface. The four rays emerge from the tube on the right-hand side of the focal line. The rays are chosen that exit parallel to each other. By applying Bouguer’s formula from Born and Wolf,31 the following relation is obtained for ray 1:

n0R sin u ) n1R sin v ) n1r1 sin s ) n2r1 sin t

(1)

where R is the outer wall radius, r1 is the inner wall radius, n0 is the refractive index of air, n1 is the RI of fused silica, and n2 is the sample fluid refractive index. From the relation above, several equations are obtained:

sin v )

sin u R , sin s ) sin u n1 n1r1

(2)

R sin u, n0 ) 1 n2r1

(3)

sin t )

For small scattering angles φ, the angles t, u, and v are small. (31) Born, M.; Wolf, E. Principles of Optics; Pergamon Press: New York, 1975.

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Therefore, a small-angle approximation can be applied:

v)

tangent to the capillary and normal to the incident and scattered directions.

u R , s) u n1 n1r1

(4)

R u n2r1

(5)

t)

Using trigonometric identities, the following relations can be derived:

ab ) R - r1, bc ) 2r1 cos t

(6)

bc ) 2r1(1 - t2)1/2

(7)

Angle u can be expressed as a function of the scattering angle φ:

[(

) ]

1 R R + -1 r1n2 n1 r1n1

u ) φ/ 2

(8)

The incidence angles for rays 3 and 4 are w and z, respectively. For rays 3 and 4, the following equations can be derived:

A)

R R w , C) w, D ) w n1 n1r1 n2r1

(

w ) φ/

)

1 R 2R + -1 r1n2 n1 r1n1

G)

R z z, F ) n1r1 n1

(

z ) φ/

(9)

(10)

(11)

)

1 R - +1 r1n1 n1

kl ) R - r1

(13)

lm ) 2r1 cos D

(14)

pq ) R - r1

(15)

The optical path lengths of rays 1-4 between entering and exiting the capillary are given by

∆1 ) 4abn1 + 2bcn2 + 2R(1 - cos) - λ0/4

(16)

∆2 ) 2R(1 - cos φ) + λ0/2

(17)

(18)

ray 2:

2R(1 - cos φ)

(21)

ray 3:

2R(1 - cos w)

(22)

ray 4:

2R(1 - cos z)

(23)

Θi )

2π ∆ , i ) 1-4 λ0 i

(24)

The total backscattered intensity can be calculated using the following equation:32

I)

∑I

n

+

∑∑(I I

1/2 n m)

cos(Θn - Θm)

(25)

where

n ) 1-4, m ) 1-4, and n * m, and In and Θn are the intensity and phase, respectively, of the four rays. The In for each ray takes into account reflection and transmission coefficients at each interface encountered by the ray. The backscattered intensity of each ray can be calculated by using appropriate combinations of the reflectivity, R, and the transmissivity, T, calculated using the following equations at each interface:

R)

(nn +- 11) , 2

T)

nt 4n , R + T ) 1, n ) 2 ni (n + 1)

(26)

(19)

An additional optical path length for each ray is needed to allow for the curved wall of the capillary. These distances are from the tangential line l1 to the entrance points and from the tangential line l2 to the exit points for all four rays. The tangential lines are Analytical Chemistry, Vol. 68, No. 10, May 15, 1996

(20)

The reflection of ray 1 inside the capillary wall at the fused silica-air interface does not result in a phase change for ray 1 (Fresnel’s law of reflection). However, ray 1 suffers a quarterwavelength decrease in path length because it crosses the focal line.29 Ray 2 is reflected at a medium of higher refractive index and experiences a half-wavelength phase shift. Ray 3 decreases its optical path length by a quarter-wavelength because it also crosses the focal line. Ray 3 is reflected inside the sample fluid, the less dense medium, at the sample fluid-fused silica interface. This reflection will increase its path length by a half-wavelength. It should be noted that the theory presented in this paper is limited to sample fluids whose refractive indexes are less than the refractive index of fused silica at the laser wavelength of 632.8 nm, (nfused silica ) 1.45702). In the absence of this limitation, the half-wavelength phase shifts on reflection for rays 2 and 3 would no longer be valid. Further, the sample solutions used in this experiment satisfied this constraint. The phase angle for each optical path length can be calculated as follows:

∆3 ) 2kln1 + 2lmn2 + 2R(1 - cos w) + (λ0/2 - λ0/4)

1766

2R(1 - cos u)

(12)

The angles w and z are expressed as functions of the scattering angle φ. Using the geometry of Figure 5, the following relations can be obtained:

∆4 ) 2pqn1 + 2R(1 - cos z)

ray 1:

Here, ni and nt are the refractive indexes of the incident and transmitted ray media, respectively. In the following section, the predicted scattered intensity profiles are plotted as a function of the fluid refractive index, n2, (32) Klein, M. V.; Furtak, R. E. Optics, 2nd ed.; Wiley: New, York, 1986.

Figure 6. Calculated scattered intensity profile as a function of n2 (RI of fluid in tube).

Figure 7. Calculated scattered intensity profiles upon changing n2 by 1 × 10-4 RIU and using a tube with dimensions of 266 µm × 369 µm placed 0.28 m from the detector. 9, n2 ) 1.3330; O, n2 ) 1.33290.

for R ) 369.5 µm, r1 ) 266.3 µm, n1 ) 1.45702, and d ) 0.28 m (d is the screen to capillary tube distance). Scattered Intensity Profile as a Function of the Sample Refractive Index, n2. Figure 6 demonstrates the ability of the model to predict the previously discussed general characteristics of the scattered intensity profile. As n2 is increased, the peaks shift to larger angles and a peak begins to displace the central minimum to appear at the center (φ ) 0°) of the fringe pattern. The result shows that, as the RI of the fluid contained in the tube changes, the position of any given fringe shifts. This movement

is used to monitor changes in n or temperature noninvasively. Figure 7 is used to depict the fringe shift predicted by our fourbeam theory more clearly. For a 1 × 10-4 ∆n change, the maxima for the first fringe from the center shifts by ∼1.5 mm. A more detailed confirmation of our theoretical model is currently under way, yet our initial experimental comparisons shown here are quite encouraging. Figure 8 presents the experimentally determined fringe map for a change in RI of one part in 104. The optical configuration in the experiment is made to match those used in the calculation (for R ) 369.5 µm, r1 ) Analytical Chemistry, Vol. 68, No. 10, May 15, 1996

1767

Figure 8. Experimentally determined map of the scattered intensity profiles for water and a solution that produces a change in n2 of 1 × 10-4 RIU. Optical configuration includes using a tube with dimensions of 266 µm × 369 µm placed 0.28 m from the detector.

266.3 µm, n1 ) 1.45702, and d ) 0.28 m) and plotted in Figure 7. The intensity versus position map shown in Figure 8 is obtained by performing a stepwise translation of the slit-photodetector assembly across the fringes of interest while recording the intensity related voltage values at each position. Several observations can be made through comparison of the two figures. First, the general form of the interference pattern predicted by the four-beam model (Figure 7) and that observed experimentally (Figure 8) correlate well. Second, when an aqueous glycerol solution is used to provide an RI change of 1 × 10-4 experimentally, the corresponding spatial shift of a particular fringe is found to be nearly equivalent to that predicted by the model (1.5 mm versus 1.45 mm). In other words, there is an excellent correlation between the experimental positional shift of the interference fringes and that calculated by four-beam interference. Third, there is an obvious nonuniformity or noise seen in the experimental beam profile intensity that is not indicated by our four-beam model. We are currently investigating this anomaly and now believe it to result from a polarization sensitivity that produces a second-order modulation component or another interference pattern at higher frequency. Initial investigations indicate that this higher order component results from a polarization sensitivity26 and could indicate the use of LIB for small-volume polarimetry. Our initial experiments demonstrate a reasonable correlation between the theory and experiment. Further detailed investigations regarding various optical parameters using the four-beam method and LIB have been performed and can be found elsewhere.25 The predictive capabilities of the four-beam model are now demonstrated, yet we believe that we must expand the fourbeam model. This extension is underway and includes a fifth beam that carries polarization and reflection coefficient information, allowing the model to better fit the experimental observation and to more accurately predict the contribution of the highfrequency interference component sometimes observed during operation of the LIB. FIA and Temperature Determinations. Two additional experiments are presented here that demonstrate the analytical utility of the LIB technique: FIA and noninvasive thermometry. 1768 Analytical Chemistry, Vol. 68, No. 10, May 15, 1996

If the LIB is to be useful for techniques such as CE and C-HPLC, then detection of transient events is required. To test the application of LIB for flowing samples, we have configured the system shown in Figure 1. Recall that alignment (see Figure 3) is accomplished by selecting a set of fringes with high contrast and placing the slit-photodetector assembly on the front edge of one of the spots. As the RI of the fluid in the tube changes, a positional change of the fringe ensues, and an intensity change is detected by the photodetector. A syringe pump is used to provide a flowing stream through a capillary tube, with the inner diameter of 75, 100, 250, or 775 µm, to the detection zone used on the same capillary. Plugs of sample, glycerol solutions in increasing concentration, are introduced to the sample stream as in a flow injection analysis experiment. The chromatographic peaklike response is presented in Figure 9 as recorded on a strip chart recorder. Duplicate injections are made for each solution, and a calibration curve is constructed, as shown in Figure 10. Detector response is linear over a dynamic range of about 3 decades. Above this value, a differential response is seen, because the peak maximum shifts past the center of the slit so that the detector senses the inflection point of the fringe. Array detection and peak counting are under investigation to compensate for this limitation. The spike in the tracing between solutions 6 and 7 can be attributed to a transient noise event (scattering) resulting from a particle traversing the laser beam. Peak heights are quite reproducible for multiple injections, as demanded in a quantitative separation analysis scheme. Detection limits are determined for the FIA experiment by determining the short-term noise (voltage signal variation in a 10 s period) and applying the accepted relationship of DL ) 3σ/ slope. As a representative illustration, we calculate the detection limits for the traces shown in Figure 9, where a 100 µm i.d. tube is used. At 3 times the standard deviation (3σ), the minimal detectable quantity of glycerol was determined to be 1.24 × 10-6 g/mL, corresponding to a 1.89 × 10-7 RIU change. At this detection limit, in a probed volume of ∼2.6 × 10-9 L (2.6 nL), there is about 3.2 pg of glycerol present. Detection limits for the various tube sizes are presented in Table 1. These detection limits compare well with previous reports for on-capillary universal

Table 1. Detection Limits for Different Size Capillaries Using FIA

a

Figure 9. Flow injection analysis peaks for glycerol solutions. These FIA experiments are performed using a 100 µm i.d. × 250 µm o.d. capillary, a 100 nL injection loop, and a sample stream flow rate of 602 µL/min at a pressure of 330 psi. Duplicate peaks are standards at concentrations of 0.004, 0.008, 0.01, 0.04, 0.08, 0.10, and 0.4 (% wt/v) glycerol in water. Chart speed is 1 cm/min, vertical scale for peaks 1-4 is 0.0078 V/cm, for 5 and 6 is 0.019 V/cm, and for 7 is 0.078 V/cm.

Figure 10. Calibration curve for FIA experiment.

detection10,11,14 and, considering the simplicity of the optical configuration, should facilitate the use of refractive index detection in capillary-based separation schemes. To utilize LIB, it is necessary to understand the limitations on detection imposed by fluid bulk properties such as changes in temperature. Since changes in n as a function of temperature can be significant for fluids, e.g., dn/dT of H2O is on the order of one part in 104 per degree centigrade, thermal perturbations can

tube dimensions (µm)

limit of detection (∆n)a

75 × 350 100 × 350 250 × 530 775 × 1000

1.94 × 10-7 1.89 × 10-7 2.23 × 10-7 1.96 × 10-7

Determined at 3σ.

Figure 11. Plot of fringe centroid position as of function of temperature change, demonstrating detection of small temperature changes.

significantly limit the usefulness of RI detection. On the other hand, this thermal sensitivity can be used to determine minute temperature changes in small-volume flowing streams and can be applied to noninvasive process stream monitoring. We have evaluated the thermal response of the LIB system for static water using a 100 µm i.d. × 250 µm o.d. capillary tube incorporated into the flow cell shown in Figure 2. The experimental configuration for the thermal measurements is shown in Figure 1, with the exceptions that the sample is static, so the pump is not employed, and the centroid position is determined by translation of the slit-photodetector assembly across a single fringe. Thermoelectric cooling chips allow the temperature of the flow cell assembly to change, thus causing the fringes in the interference pattern to shift due to the temperature dependence of n. Figure 11 shows the plot for centroid position of a selected fringe as a function of temperature. The actual flow cell temperature is determined by measuring the resistance of a calibrated thermistor in an open loop and in contact with the flow cell housing and the capillary tube. The thermistor is placed about 3 mm from the laser beam spot at the capillary tube, and the resistance is measured using a digital multimeter. The independent temperature measurement corresponds well with that indicated by the Peltier controller. Figure 10 shows, as expected, that the relationship between dn and dT is linear. The slope of this curve is 3.1 × 104 µm/°C. The rate of change of n with temperature, dn/dT is estimated using slopes calculated from linear calibration (dc/dx ) 26 300 Analytical Chemistry, Vol. 68, No. 10, May 15, 1996

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µm/(% g/cm3) and Figure 11. A simple calculation yields a dn/ dT value of 1.7 × 10-3 RIU/°C. At a detection limit for dn of 1 × 10-7, a temperature change of 5.9 × 10-5 °C can be detected for the fluid contained or flowing through a probe volume of 2.6 nL. It is clear that the microinterferometer described here can be used both to measure changes in temperature in small volumes at the level of six parts in 105 and for the determination of ∆n values for species such as hazardous liquids which must be monitored in a noninvasive format. SUMMARY It is shown that the backscatter microinterferometer can be modeled by a four-beam optical ray trace. This model can be used to predict positional changes in the interference pattern and to define the outcome of modifying the optical train or changing the tube physical parameters. The optical configuration is simple, facilitates the use of unmodified capillaries as desired in CE, and can be constructed inexpensively. LIB is sensitive to small changes in refractive index (picogram quantities can be detected currently) and responds in a predictable manner to solutes which are flowing. In addition, the simple optical device can be used to measure thermal changes at a microdegree centigrade level and (33) Lee, S. S.; Lin, L. Y.; Pister, K. S. J.; Wu, M. C.; Lee, H. C.; Grodzinski, IEEE Photon. Technol. Lett. 1994, 6, 1031-1033. (34) Lin, L. Y.; Lee, S. S.; Pister, K. S. J.; Wu, M. C. Appl. Phys. Lett. 1995, 66, 2946-2948.

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to determine dn/dT for fluids which must be contained in a tube. Finally, it should be possible to configure the entire detector onto a single chip by employing solid-state excitation sources and recently reported attachment techniques.33,34 Current investigations in our laboratories at Texas Tech include the application of LIB detection to CE and C-HPLC, the extension of our theoretical model to include a fifth beam containing polarization information, the use of a second-order anomaly (high-frequency inference component) to perform polarimetry in capillary dimensions,26 and the miniaturization the LIB detector to the size of a single chip. ACKNOWLEDGMENT Some of the results presented here appear in the Masters Thesis of H.T. (Department of Physics, University of Nevada, Reno). Part of this work was supported by a grant from the College of Arts and Sciences of Texas Tech University (Research Enhancement Fund). The authors thank Neven Steinmetz (TTU Undergraduate Research Associate) and David Tarnowski for their assistance in preparing the figures. Received for review November 27, 1995. February 19, 1996.X AC9511455 X

Abstract published in Advance ACS Abstracts, April 1, 1996.

Accepted