Effect of Capillary Properties on the Sensitivity Enhancement in

Liquid-core low-refractive-index-contrast Bragg fiber sensor. Hang Qu , Maksim Skorobogatiy. Applied Physics Letters 2011 98 (20), 201114 ...
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Anal. Chem. 1996, 68, 183-188

Effect of Capillary Properties on the Sensitivity Enhancement in Capillary/Fiber Optical Sensors Vincent Benoit and M. Cecilia Yappert*

Department of Chemistry, University of Louisville, Louisville, Kentucky 40292

The sensitivity enhancement observed in fluorescence signals when a conventional fiber optical sensor is coupled with a quartz or glass capillary results from the partial reflection of the radiation at the sample/internal wall interface and from the internal reflection of the refracted portion within the capillary wall. Thus, the length and absorbing properties of the capillary as well as the nature of the surrounding medium affect the enhancement significantly. To interpret the dramatic changes in enhancement observed experimentally when the absorbing properties of the capillary were changed, a partial reflective waveguide model is reported. We recently reported sensitivity enhancements of almost 2 orders of magnitude in the fluorescence signals acquired with capillary/fiber optical sensors (C/FOSs) as compared to those obtained with conventional optical sensors without the capillary.1 The improvement in the sensitivity of signals acquired with optical sensors and the understanding of factors that affect the sensitivity have been and continue to be investigated.2-7 Several articles have reported the enhancements obtained in absorbance,8-12 fluorescence,13 and Raman14-16 scattering signals when the sample is contained in a capillary tube. These capillary/sample cells, some of which were longer than a meter,10-13 have been denoted long capillary cells or liquid-core waveguides. In most cases, the use of solvents of refractive index greater than that of the capillary material was required to trap the radiation within the sample volume by total internal reflection. In colorimetric measurements, the increase in detectability was demonstrated in aqueous samples contained in long aluminum- and silver-coated capillary tubes.8,9 In these reports, however, the theoretical discussion did not evaluate quantitatively the effect of the optical properties of the capillaries on the measured absorbance. As these factors affect (1) Zhu, Z. Y.; Yappert, M. C. Anal. Chem. 1994, 66, 761-764. (2) Hirschfeld, T.; Deaton, T.; Milanovich, F.; Klainer, S. Opt. Eng. 1983, 22, 527. (3) Deaton, T. Instrumentation and Methodology for Remote Fiber Fluorimetry. Ph.D. Dissertation, University of California at Davis, 1984. (4) Louch, J.; Ingle, J. D., Jr. Anal. Chem. 1988, 60, 2537-2539. (5) Komives, C.; Schultz, J. S. Talanta 1992, 39, 429-441. (6) Zhu, Z. Y.; Yappert, M. C. Appl. Spectrosc. 1992, 46, 912-918. (7) Zhu, Z. Y.; Yappert, M. C. Appl. Spectrosc. 1992, 46, 919-925. (8) Lei, W.; Fujiwara, K.; Fuwa, K. Anal. Chem. 1983, 55, 951-955. (9) Dasgupta, P. K. Anal. Chem. 1984, 56, 1401-1403. (10) Fuwa, K.; Lei, W.; Fujiwara, K. Anal. Chem. 1984, 56, 1640-1644. (11) Fujiwara, K.; Fuwa, K. Anal. Chem. 1985, 57, 1012-1016. (12) Wei, W.; Qushe, H.; Tal, W. Anal. Chem. 1992, 64, 22-25. (13) Fujiwara, K.; Simeonsson, J. B.; Smith, B. W.; Winefordner, J. D. Anal. Chem. 1988, 60, 1065-1068. (14) Walrafen, G. E. Appl. Spectrosc. 1972, 26, 585-589. (15) Ross, H. B.; McClain, W. C. Appl. Spectrosc. 1981, 35, 439-442. (16) Schwab, S. D.; McCreery, R. L. Appl. Spectrosc. 1985, 41, 126-130. 0003-2700/96/0368-0183$12.00/0

© 1995 American Chemical Society

considerably the enhancement of fluorescence signals acquired with C/FOSs, a model including these parameters was deemed necessary. The commercial availability of uniform and small-diameter capillaries has allowed this study of the effect of capillary or sample length and its absorbance on the enhancement of fluorescence signals in nonideal waveguide systems. EXPERIMENTAL SECTION Sensor Construction. Double-fiber optical sensors were constructed from 98-µm-diameter core, 140-µm-diameter cladding, 0.30 numerical aperture glass fiber optics (F-MLD-50, Newport Corp., Fountain Valley, CA). The sensors were made by removing the buffer or jacket of both the excitation and collection fibers over a certain length from the tip. The bare clads were then glued together with instant glue so that the flat ends of the fibers were in the same plane, perpendicular to the fiber’s axis. The capillary tubes used in all experiments were sections of 320-µm-i.d., 440-µm-o.d. fused silica tubing (Polymicro Technologies Inc., Phoenix, AZ). This tubing was coated with an 18-µmthick, brown-colored polyimide jacket. The clear capillary tubes were obtained by removing the brown polyimide jacket from the coated tubes by soaking them in hot sulfuric acid. Cleaning and Filling of the Capillary. As previously reported,1 the reproducibility of the measurements was significantly affected by the cleanliness of the walls of the capillary. Furthermore, the cleanliness of the inner wall also affected the filling of the capillary. The inner and outer walls were thoroughly cleaned with nitric acid and then rinsed with copious amounts of water and methanol. The smoothness and cleanliness of the external wall were checked under microscope magnification. After the methanol was completely dried, the capillary tubes were rinsed and filled by capillary action with the sample solution. C/FOS Setup and Measurements. Figure 1 shows a schematic representation of the instrumental setup. The excitation radiation was provided by the 488 nm line of an argon ion laser (Innova 90-6, Coherent Inc., Auburn, CA). The fluorescence signals were spectrally analyzed by a monochromator (Instruments SA Inc., Edison, NJ; Model HR-320, 150 grooves/mm holographic grating) and detected by a photomultiplier tube (PMT). The fluorophore used in all experiments was Rhodamine 6G (R6G) (LC 5900, Lambda Physik). Aqueous solutions with 10 ng/ mL and 1 µg/mL R6G concentrations were prepared. Each capillary was mounted on a holder consisting of a microscope glass slab and two pieces of double-sided mounting tape, denoted spacers in Figure 1. This arrangement allowed the outside of the capillary to be in contact with nothing but the surrounding air over a length of at least 100 mm. Analytical Chemistry, Vol. 68, No. 1, January 1, 1996 183

Figure 1. Schematic representation of the experimental setup. MC, monochromator; PMT, photomultiplier tube; c, capillary tube; f, fibers for excitation and collection; g, glass slab; p, plunger; s, spacer.

The optical fiber sensor, mounted on an X-Y-Z micropositioner, was introduced into the tube so that its tip was located just beyond the first spacer. This location defined the origin (z ) 0) of the sample length scale. A plunger made from a piece of optical fiber was used to vary the sample length in the length-dependence studies. The tip of the plunger was blackened with enamel paint to avoid any reflection or scattering of radiation. The plunger was mounted on a high-resolution translation stage to allow precise control of the sample length. To minimize photodecomposition of the sample, the excitation beam was blocked at all times except during measurement of the signal. To assess the reproducibility of the measurements, the length-dependence study was carried out with three different capillary tubes, and three independent runs were performed with each of the capillaries. The sensitivity enhancement was calculated as previously described,1 as the ratio of the signals acquired with the C/FOS and the reference signals obtained with the very same doublefiber optical sensor but without the capillary. The effects of capillary absorbance and sample length on the enhancement were studied using the brown polyimide-coated capillaries as well as clear capillaries that were blackened in small length increments. The absorbance of the polyimide-coated capillary per unit length was evaluated by measuring with a Si photodiode the amount of laser excitation radiation reaching the distal end of the coated capillary as the optical sensor was introduced into the capillary. A similar approach was used to measure the absorbance over the wavelengths of fluorescence emission. The source of radiation in this case was a Xe arc lamp. RESULTS AND DISCUSSION Fluorescence Dependence with Capillary Length in Clear C/FOSs. All the experimental results presented in this section were obtained with the two-fiber optical sensor and the clear, i.e., polyimide coat removed, 320-µm-i.d. capillary tube. Figure 2 shows the averages and the 95% confidence intervals for the experimental fluorescence signals obtained for a 10 ng/mL solution of R6G as a function of sample length. To evaluate these averages, three independent runs were carried out for each of three different capillary tubes. Unlike for conventional FOS without the capillary,6,7 the fluorescence signals did not reach a maximum value even at 100 mm, the maximum sample length 184 Analytical Chemistry, Vol. 68, No. 1, January 1, 1996

Figure 2. Relative fluorescence signal acquired with a clear C/FOS versus the sample length for a 10 ng/mL R6G sample solution. (- - -) Evaluated with totally reflective waveguide (TRW) model. (×) Evaluated with partially reflective waveguide (PRW) model. Bars represent the average and 95% confidence intervals of experimental measurements.

investigated. Although not as high as in the first 20 mm, the rate of increase of the fluorescence (FL) with sample length observed at longer lengths indicates that fluorescence can be excited and collected from lengths which are almost an order of magnitude longer that those “viewed” with the conventional FOS. To understand and characterize this behavior, predictions based on two different models are included in Figure 2. Totally Reflective Waveguide Model. The curve in dotted lines is based on the perfect or totally reflective waveguide (TRW) model described by eq 10 of ref 1. The TRW model assumes that all the fluorescence excitation and emission rays are trapped within the internal volume of the waveguide. Thus the only source of attenuation is related to primary and secondary absorption effects caused by the analyte(s) and sample matrix components. In the case of a sample with negligible absorbance, each fluorescent species is expected to have the same contribution to the overall signal, regardless of its distance from the sensor tip. Consequently, the fluorescence signal increases linearly with sample length in this ideal waveguide model. The agreement between the theoretical and experimental curves observed over the first 10 mm diminishes considerably as the sample length increases. The observed disparity suggests that the intensity of the differential fluorescence signal due to a sample “slice” decreases when the position of this slice with respect to the sensor tip increases. In other words, the farther the fluorescent volume is from the sensor tip, the smaller its contribution to the total signal. Partially Reflective Waveguide Model. The second set of predicted values is represented by crosses in Figure 2. These values were calculated with a more realistic model in which the capillary/sample cell behaves as a partially reflective waveguide (PRW). Figure 3 shows the schematic representation of a singlefiber C/FOS used in our model. The PRW Model Development section summarizes the mathematical expressions developed. In this model, the excitation and collection fibers were assumed to be located coaxially in the center of the capillary, just as in the case of a single-fiber sensor. As previously reported in our characterization of double-fiber optical sensors,7 this assumption does not describe correctly the excitation/collection properties of the double-fiber sensor in the vicinity of the fiber tips. However,

Figure 3. Sensor configuration and propagation of excitation (left) and emission (right) rays for the PRW model. Regions I, II, and III: fluorescence emission zones, see text for details.

as the sample length increases, the double-fiber sensor behaves as a single-fiber one, as the cones of excitation and collection overlap almost completely. Only meridional rays were considered for the excitation and the collection of the fluorescence. Consequently, the model C/FOS exhibited a cylindrical geometry in which the optical axis is the axis of symmetry over the entire sample length. Therefore, all coaxial planes were assumed to be equivalent. This allowed for a simple mathematical description of the model. The experimental values for the numerical aperture of the optical fibers (NA ) 0.30) and refractive indices of the sample solution (ηs ) 1.33), the capillary (ηc ) 1.46), and its surrounding medium, air in this case (ηa ) 1.00), were used to predict the ray trajectory for the fluorescence excitation and emission. Briefly, a portion (predicted by Fresnel’s law of reflectivity) of each ray is partially reflected at the first sample/internal capillary wall interface, while the rest is refracted into the capillary wall. Because of the values of the fiber’s angle of semiaperture, θ, in the sample solution and of the refractive indices of the capillary and its surrounding medium, the refracted portion is internally reflected at the capillary outer wall and reaches the inner wall/sample interface. At this point, part of the beam is refracted back into the sample solution and the rest is reflected within the capillary wall. The relative amounts of refracted and reflected radiation are controlled by the launching angle, R, and the refractive indices of the media. As the angle R increases, the reflectivity decreases, and the number of reflections per unit length increases within both the capillary walls and the capillary internal volume. The relative intensity of the rays at the tip of the fiber is related to R and the angular excitation efficiency, Ee, of the fiber. As the launching angle increases, the excitation efficiency decreases. Thus rays with angles R greater than θ/2 exhibit relatively small intensity and do not contribute significantly to the overall excitation of fluorescence within the sample. These contributions become even smaller as the sample length increases. We used the experimentally measured values for the angular excitation efficiency.6 The intensity, IR(z), of a primary ray with a launching angle R at a distance z from the fiber tip was evaluated by summing the contributions from all its associated rays resulting from the partial reflection of the primary ray at the m location(s) at the inner capillary wall (solid-line rays in Chart 1 in the next section) and from the refraction back into the capillary after n internal reflections at the outer capillary wall (broken-line rays in Chart 1 in the next section). The proper selection of m and n values for a given ray at a distance z was based on the z-criterion listed in the next section. The total excitation intensity, I(z), at a distance z from the sensor tip was calculated as the sum of the contributions from each ray over a discrete range of R values between 0 and θ/2. The PRW model assumes that the FL emission from a given plane perpendicular to the C/FOS axis is condensed into a single

point source of fluorescence located on that axis. Because of the collection characteristics of the sensor, only emission rays in zone I, whose angular orientation is within the cone of acceptance of the collection fiber, were considered to contribute to the signal. In addition, the weight of this contribution is affected by the angular collection efficiency of the fiber. Rays in zone II reach the proximal end of the capillary by partial reflections and refractions, as described for the excitation ray. But, since these rays reach the collection fiber at an angle greater than the fiber’s acceptance angle, they do not contribute to the FL signal. Rays emitted within angular zone III include those that travel toward the distal end of the capillary and those that escape the capillary because their angle of incidence at the outside wall/air interface is smaller than the critical angle. In Figure 2, except for the first 5 mm, in which the experimental signals were greater than those predicted, the values obtained using the PRW model lay within the confidence interval obtained for the 10 ng/mL solution of R6G for every sample length. The discrepancy observed in the vicinity of the sensor (z < 5 mm) is believed to arise from improper subtraction of the background signal, which was mostly due to elastic scattering and whose magnitude was affected by the exact position and angular orientation of the sensor with respect to the capillary. Most of this scattering originates at the fibers/blank interface. No additional source of scattering was detected when the analyte species were present. The agreement of the predicted and experimental values at longer lengths (z > 5 mm) suggests that the sample/capillary cell behaves as a nonperfect, partially reflective waveguide. The reflections within the sample volume and the capillary walls allow the effective excitation and collection of FL signals at long sample lengths. These partial reflections and refractions cause the signal enhancement in C/FOSs with respect to conventional FOSs. It is relevant to note that this cause of enhancement only requires a medium of greater refractive index (fused silica in this case) than the sample refractive index. Unlike other reports, in which the sample matrix is limited to solvents of refractive indices greater than that of glass or quartz, so as to serve as a sample internal waveguide,10,11 in the C/FOS reported here, the capillary itself is an integral part of the sensor, for it behaves as a conduit for the radiation and emission radiation. Therefore, the refractive index of the sample matrix must be smaller than that of the capillary. This allows for a much greater selection of solvents, including aqueous ones. Figure 4 shows both the experimental results and the curve predicted with the PRW model for the relative fluorescence of a 1000 ng/mL R6G solution. As intuitively expected, the length dependence of the more concentrated solution shows a greater curvature than that for the 10 ng/L solution shown in Figure 2. The greater curvature seen for the very concentrated solution Analytical Chemistry, Vol. 68, No. 1, January 1, 1996

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Figure 4. Relative fluorescence signal acquired with the clear C/FOS versus sample length for a 1000 ng/mL R6G sample solution. (-) experimental values. (‚‚‚) Evaluated with PRW model. Bars represent the 95% confidence intervals of experimental measurements.

Figure 5. Relative fluorescence signals acquired experimentally with the clear C/FOS for different blackening patterns of the capillary. Total sample length, 100 mm. (9) blackening from proximal end, sample solution, R6G 10 ng/mL. (]) Blackening from distal end; sample solution, R6G 10 ng/mL. (4) blackening from distal end; sample solution, R6G 1000 ng/mL.

indicates that the contribution from volumes far from the sensor tip was, as expected, relatively smaller due to greater attenuation of both the excitation reaching that volume and the emission originating from that volume. This figure also shows significant discrepancy between the experimental and calculated values for the 1000 ng/mL solution of R6G. In the evaluation of the FL excitation in the PRW model, primary absorption effects were taken into account. Yet, the observed disagreement suggests that the relative contribution of FL emitted from longer lengths is greater than that predicted by the model. To evaluate this possibility, relative fluorescence signals were acquired for 10 and 1000 ng/mL R6G solutions with a sample length of 100 mm as the capillary tube was being sequentially blackened with enamel paint from the distal end. The blackening of portions of the capillary outer wall resulted in the absorption of excitation and emission rays internally reflected in that portion of the wall; thus, their contribution to the overall signal was canceled. Over the blackened length, only those rays traveling through the sample by partial reflections on the inner wall of the capillary continued to contribute to the fluorescence signal. These results are shown in Figure 5. The solid box curve shows a substantial decrease in the signals as the first few millimeters of capillary wall were blackened. This decrease is greater than that predicted by the PRW model and suggests that more than the expected amount 186

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of fluorescence from longer lengths is being collected by the sensor. As the model takes into account only meridional rays, it is possible that the observed discrepancy could be related to the presence of skew rays traveling within the sample volume and partially reflecting at the capillary walls. This could account for a greater portion of the fluorescence excitation and emission traveling along the capillary walls. The quantification of this contribution cannot be formulated at this time, as the relative amount and characteristics of these skew rays are not known. Furthermore, imperfections in the internal and external capillary walls could also result in directional changes of the meridional rays not taken into consideration in the present PRW model. Effect of the Capillary Absorbance and the Surrounding Medium on the Sensitivity Enhancement. Unlike in the lengthdependence studies with clear capillaries, a plateau was reached at sample lengths shorter than 15 mm when the polyimide-coated capillaries were used. The effective depth, zeff, as defined in ref 1, was found to be about 8 mm. This length was much shorter than that with the clear capillary, which exceeded 100 mm. The more rapid attenuation of the signal can be explained by the partial, yet significant, absorption at the capillary outer wall (coated with polyimide) of the excitation and emission radiations traveling through the capillary walls. The absorption due to the capillary at the excitation wavelength (488 nm) was measured to be 0.036 AU mm-1. Over the fluorescence emission range (500-700 nm), the absorption was 0.028 AU mm-1. This attenuation reduces considerably the sensitivity enhancement. The enhancement values for clear capillaries, as well as the reproducibility, are very similar and statistically not different from those previously reported by us. The enhancement measured for the 100-mm-long clear capillary with a 10 ng/mL R6G solution was 81 ( 13 (n ) 28). We reported an enhancement of 85 ( 13 for C/FOSs made with capillary tubes drawn by hand with an internal diameter of 280 µm.1 The enhancement values obtained experimentally from the ratio of the signals acquired by the same optical sensor with and without the polyimide-coated capillary were 1.5 ( 0.1 (n ) 9) and 1.4 ( 0.1 (n ) 9) for 1 and 2 mg/mL R6G solutions, respectively. The values obtained for the two sample solutions are very close to one another. This is expected because of the relatively small absorption of the R6G (0.0075 AU mm-1 at 488 nm, and 0.023 AU mm-1 for the emission range for a 1 µg/mL solution) compared to that measured for the capillary (0.036 AU mm-1 at 488 nm and 0.028 AU mm-1). The weakness of these enhancements relative to those reported for clear capillaries results from the partial absorption of the excitation and emission radiation at the outside wall of the capillary. The loss in the enhancement points out the crucial role that the nature of the capillary and its external surface plays in the effectiveness of the transmission of radiation in C/FOS. When the clear capillaries were surrounded by water (ηH2O ) 1.33), the average enhancement for seven measurements was reduced to 16 ( 2. This significant reduction with respect to the enhancement values observed in air can be attributed to the relatively greater amount of fluorescence excitation and emission that refracts out into the water medium. The sensitivity enhancements reported here are based on the ratio of the signals collected by the capillary sensor and by the conventional sensor at the same sample length. Yet the sampling volumes for a given sample length are indeed quite different. In

Table 1. Definition of the Variables Used in the PRW Model symbol

description

expression

I0 R Ee(R) Ri Rr F ri re m

intensity of excitation beam at z ) 0 (tip of the optical fibers) launching angle angular excitation efficiency of the fiber incidence angle at the solution/silica interface refraction angle at the solution/silica interface reflectivity at the solution/silica interface internal radius of the capillary external radius of the capillary number of partial reflections undergone at the interface between the solution and the inner wall of the capillary number of total internal reflections undergone at the interface between the outer wall of the capillary and air

set equal to 1 for the computation 0 e R e θ (θ, angle of semiaperture)a see ref 1 Ri ) 90° - R Rr ) arcsin(ηs sin Ri/ηc) F ) 1/2(sin2(Ri - Rr)/sin2(Ri + Rr) + tan2(Ri - Rr)/tan2(Ri + Rr))

n

see Chart 1b see Chart 1c

a Discrete set of values used in the computation: 0.01, 0.75, 1.50, 2.25, 3.00, 3.75, 4.50, 5.24, 5.99, 6.74. b For the computation, 1 e m e 9 (for greater values, the excitation intensity became negligible). c For the computation, 0 e n e 20 (for greater values, the excitation intensity became negligible).

Chart 1

Table 2. Expressions Used To Evaluate the Intensity of Each Excitation Ray at a Reflection/Refraction Point symbol Am,n D z(Am,n) Fp i(Am,n)

description

expression

point at which a ray undergoes a reflection/refraction at the inner wall of the capillary distance between two successive reflections of the same ray on the inside wall of the capillary position of point Am,n along the z-axis attenuation factor due to primary absorption effects between two reflections on the inner wall of the capillary intensity of a ray with launching angle R at the distance z(Am,n)

see Chart 1 D ) 2ri/sin R (see Table 3) z(Am,n) ) (m - 1/2)D cos R + 2n(re - ri) tan Ri Fp ) 10-cD m ) 1, n ) 0: m > 1, n ) 0: m ) 2, n > 0: m > 2, n > 0:

i(A1,0) ) I0EeFp1/2 i(Am,0) ) I0EeF(m-1)Fp(m-1/2) i(A2,n) ) (1 - F)2F(n-1)I0EeFp3/2 i(Am,n) ) [Fi(Am-1,n) + (1 - F)2i(Am-1,n-1)]Fp

Table 3. Expressions Used To Evaluate the Intensity of Excitation at Any Sample Length z symbol

description

expression

dm,n(z) fm,n(z) IR(z)

pathlength correction between z and z(Am,n) compensation factor contribution to the excitation intensity in a plane at distance z from the ray with lauching angle R total excitation intensity in a plane at distance z from the fiber’s tipa

dm,n(z) ) (z(Am,n) - z)/cos R fm,n(z) ) 10cdm,n(z) IR(z) ) ∑ i(Am,n)fm,n(z) (m and n such that z e z(Am,n) e z + D

I(z)

m,n

I(z) ) ∑IR(z) R

a

z was incremented by step of 1 from 0 to 10 and by step of 5 from 10 to 100.

the case of the conventional sensor, the volume viewed can be approximated to a cone whose semiaperture angle is related to the numerical aperture of the fibers used. For a 10-mm sample length, the signal acquired with a double-fiber sensor made with 100-µm fibers was shown to reach a maximum.7 The approximate volume of the viewed cone is 56 mm3. For the C/FOS configuration, the sampling volume is a cylinder whose dimensions are those of the capillary. If a length of 100 mm is considered, this volume is 8 mm3. Thus, the actual sample volume needed for a measurement with the C/FOS is 7 times smaller, and yet the sensitivity is almost 2 orders of magnitude greater.

PRW MODEL DEVELOPMENT Table 1 lists and defines the variables used in the PRW model. Upon reflection or refraction on the inside wall of the capillary, a ray undergoes a reduction of its intensity which is directly related to the value of the reflectivity, F, at the reflection/refraction point. Chart 1 graphically summarizes the excitation ray trajectories assumed in the C/FOS system described herein. Besides, in the presence of primary absorption effects, the intensity of the ray is attenuated between two successive partial reflections as a function of the traversed distance, D, between these two points of reflection. Each of the rays used in this Analytical Chemistry, Vol. 68, No. 1, January 1, 1996

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evaluation corresponds to the R values indicated above (Table 2). The intensity at any sample length z is evaluated by correcting the intensity at the immediately following reflection/refraction point, Am,n, for the path length difference, d, between the point Am,n and the point intersection of the considered ray with a plane at z. The correction is based on the compensation factor fm,n. In Table 3, the proper values for m and n (i.e., for which the portion of ray between Am-1,n and Am,n actually intersects with the plane at z) are those which satisfy the criterion z e z(Am,n) e z + D. CONCLUSIONS Compared to conventional double-fiber sensors, the C/FOSs described here offer greater sensitivity (enhancement of almost 2 orders of magnitude) and a reduction of the sampling volume. The capillary tube acts as both a partially reflective waveguide and a sample cell, which makes it an integral part of the sensor. Indeed, the capillary allows the partial trapping of the excitation and emission radiations inside its volume, and it also provides a cell of definite volume in which the sample is confined. The angular excitation and collection efficiencies are important factors in the behavior of the C/FOS, since they affect both the excitation and collection processes. On one hand, the excitation rays with the greater launching angles are the ones which undergo

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a greater number of partial reflections, but they are also the less intense ones, which limits the advantage provided by the capillary in the respect of the light trapping. On the other hand, the efficiency of the collection process is limited by the small acceptance angle of the collection fiber and its angular collection efficiency, since most of the excited fluorescence is inefficiently collected or not collected at all. Unlike other reported capillary sensor designs, which require particular sample solvents with high refractive indices, the C/FOS presented in this work can be used with most common solvents, including water. This is particularly interesting in the prospect of developing this sensor as a tool for bioanalysis. However, the sensitivity of the sensor is also affected by the value of the refractive index of the surrounding medium. The use of the sensor in, for example, a water stream, would result in the “leakage” of a portion of the radiation into the medium and a loss in sensitivity. Further steps in the development of the C/FOSs using nonglass capillary tubes are under consideration in our laboratory. Received for review June 5, 1995. Accepted October 2, 1995.X AC950541K X

Abstract published in Advance ACS Abstracts, November 15, 1995.