Anal. Chem. 1997, 69, 1496-1503
A Spectroscopic Refractometer for Temperature-Independent Refractive Index Detection Anders Hanning* and Johan Roeraade
Department of Analytical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden
This paper presents the working principles of spectroscopic refractive index detection. The method is based on measurement of the differences in the wavelength dispersion of the refractive index of a solute and a solvent. The basic theory of the method is outlined, and it is shown that spectroscopic refractive index detection has the potential to eliminate the thermal noise that is connected with conventional refractive index detection. The design and testing of a spectroscopic refractometer are described. The device is based on light deflection in a liquid prism and utilizes a deuterium lamp and a CCD detector in order to measure the deflection at several wavelengths simultaneously. When thermal variations of 4-5 °C are evoked, the noise observed corresponds to 4 × 10-3 °C, while the gain obtained in the signal-to-noise ratio is a factor 40. It is also shown that the sensitivity and selectivity of the method can be controlled by spectrochemical modification of the refractive index spectrum of the solvent. In this mode, similar or better signal-to-noise ratios can also be obtained at wavelengths where there is little or no difference in refractive index dispersion between the analyte and the solvent. Spectroscopic refractive index detection combines low noise with universal and concentration sensitive response and should therefore have a considerable potential in liquid chromatography and process analysis, particularly in applications where it is difficult to accurately control the temperature. Since spectroscopic refractive index detection is well suited for miniaturization, it should be of special interest for small refractometric sensors and in microcolumn separations. Refractometry is a widely used detection method. The three most important application areas are detectors for liquid separation methods, chemical sensors, and process analyzers. The two most common types of refractive index (RI) detectors in liquid chromatography are the prism deflection refractometer and the Fresnel reflection refractometer.1-3 In recent years, new kinds of RI detectors for capillary electrophoresis (CE) have also been developed and are expected to become of growing importance.4-15 (1) Munk, M. In A Practical Guide to HPLC Detection; Parriott, D., Ed.; Academic Press: San Diego, CA, 1993; Chapter 2. (2) Yeung, E. S. In Detectors for Liquid Chromatography; Yeung, E. S., Ed.; Wiley: New York, 1986; Chapter 1. (3) Munk, M. N. In Liquid Chromatography Detectors; Vickrey, T. M., Ed.; Marcel Dekker: New York, 1983; Chapter 5. (4) Zimmermann, E.; Da¨ndliker, R.; Souli, N.; Krattiger, B. J. Opt. Soc. Am. A 1995, 12, 398-403.
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Chemical sensing is an application area that has emerged in recent years. Characteristic for such sensors is that a form of chemical discrimination mechanism is exploited to obtain the desired selectivity, while a surface-sensitive refractometric principle is used as the physical signal transduction method. A few examples are pH sensors,16 ion-selective optodes,17 and sensors based on selective partitioning of analytes.18,19 Several biosensors, utilizing biochemically selective surfaces or thin films, and surfacesensitive refractometric techniques, such as surface plasmon resonance20,21 or frustrated total internal reflectance,22,23 have also been developed and are becoming of significant commercial importance. Refractometry is well established in process analysis, e.g., in the pulp and paper, food and beverage, and chemical industries. Most such refractometers are based on the critical angle design,24 where the more recent variants utilize CCDs or diode arrays for light detection. The most advantageous property of refractometry is its universal response. Refractometry does not demand that the (5) Krattiger, B.; Bruin, G. J. M.; Bruno, A. E. Anal. Chem. 1994, 66, 1-8. (6) Saz, J. M.; Krattiger, B.; Bruno, A. E.; Maystre, F.; Widmer, H. M. Anal. Methods Instrum. 1994, 1, 203-7. (7) Krattiger, B.; Bruno, A. E.; Widmer, H. M.; Geiser, M.; Da¨ndliker, R. Appl. Opt. 1993, 32, 956-65. (8) Maystre, F.; Bruno, A. E. Anal. Chem. 1992, 64, 2885-7. (9) Bruno, A. E.; Krattiger, B.; Maystre, F.; Widmer, H. M. Anal. Chem. 1991, 63, 2689-97. (10) Tarigan, H. J.; Neill, P.; Kenmore, C. K.; Bornhop, D. J. Anal. Chem. 1996, 68, 1762-70. (11) Kasyutich, V. L.; Mahnach, I. I. Proc. SPIE-Int. Soc. Opt. Eng. 1995, 2208, 94-102. (12) Chen, C.-Y.; Demana, T.; Huang, S.-D.; Morris, M. D. Anal. Chem. 1989, 61, 1590-3. (13) Dovichi, N. J.; Zarrin, F.; Nolan, T. G.; Bornhop, D. J. Spectrochim. Acta B 1988, 43, 639-49. (14) Synovec, R. E. Anal. Chem. 1987, 59, 2877-84. (15) Bornhop, D. J.; Nolan, T. G.; Dovichi, N. J. J. Chromatogr. 1987, 384, 1817. (16) Gauglitz, G.; Kraus, G. Fresenius J. Anal. Chem. 1993, 346, 572-6. (17) Freiner, D.; Kunz, R. E.; Citterio, D.; Spichiger, U. E.; Gale, M. T. Sens. Actuators B 1995, 29, 277-85. (18) Foster, M. D.; Synovec, R. E. Anal. Chem. 1996, 68, 1456-63. (19) Synovec, R. E.; Sulya, A. W.; Burgess, L. W.; Foster, M. D.; Bruckner, C. A. Anal. Chem. 1995, 67, 473-81. (20) Jo ¨nsson, U.; Fa¨gerstam, L.; Ivarsson, B.; Johnsson, B.; Karlsson, R.; Lundh, K.; Lo ¨fås, S.; Persson, B.; Ståhlberg, R.; Urbaniczky, C.; O ¨ stlin, H.; Malmquist, M. Biotechniques 1991, 11, 620-7. (21) Liedberg, B.; Nylander, C.; Lundstro ¨m, I. Sens. Actuators 1983, 4, 299304. (22) Cush, R.; Cronin, J. M.; Stewart, W. J.; Maule, C. H.; Molloy, J.; Goddard, N. J. Biosens. Bioelectron. 1993, 8, 347-54. (23) Buckle, P. E.; Davies, R. J.; Kinning, T.; Yeung, D.; Edwards, P. R.; PollardKnight, D. Biosens. Bioelectron. 1993, 8, 355-63. (24) Fishter, G. E. In Applied Optical Engineering, Volume IV, Optical Instruments, Part I; Kingslake, R., Ed.; Academic Press: New York, 1967; Chapter 10. S0003-2700(96)01111-0 CCC: $14.00
© 1997 American Chemical Society
analyte possesses specific properties, such as absorbance, fluorescence, or electrochemical activity, but will respond universally to all kinds of analytes, albeit with different response factors. Another important advantage of refractometry is that it is a true concentration measuring technique, which is independent of optical path length. In other words, the RI is an intensive property of the optical medium, and the RI does not decrease on miniaturization. This is in contrast to absorbance, which is an extensive property of the optical medium; i.e., the absorbance decreases linearly with optical path length according to the Lambert-Beer law. The main drawback of refractometry is that the sensitivity is limited by thermal noise. The most sensitive, commercially available liquid refractometers, which are differential RI detectors for HPLC, offer a short-term RI noise of ∼2.5 nRIU (RIU ) refractive index unit).25,26 However, since the temperature dependence of the RI of water is ∼100 µRIU/°C at 25 °C, and as much as 600 µRIU/°C for organic solvents,1,3 it is obvious that such high-sensitivity RI measurements require extensive thermal equilibration, and in practice it is therefore hard to obtain very high sensitivities. The situation is particularly difficult for CE, since the generated Joule heat constitutes an inherent source of thermal variations. The sensitivity of RI detectors is impaired also in process analysis, since the temperature of process liquids may vary several degrees, and in-line process monitoring does normally not permit thermostating. Therefore, temperature-corrected RI monitoring is frequently employed in process applications. However, it is seldom possible to measure the temperature more precisely than 0.1 °C, corresponding to 10 µRIU for water. Consequently, it is highly desirable to develop a refractometer that is less sensitive to thermal noise, without compromising the advantages of universal and concentration sensitive response. In the present paper, we show how this can be achieved by using spectroscopic refractive index detection (SRID). The method is based on the fact that the RI is not a constant for a given optical medium but is highly dependent on wavelength. By measuring and comparing the RI response at two or more wavelengths simultaneously, it is possible to cancel the thermal noise. This is confirmed by experiments. It is also demonstrated that the sensitivity and the selectivity of SRID can be further controlled by spectrochemical modification of the solvent. THEORY Wavelength Dependence of the Refractive Index. The optical properties of any homogenous medium are completely described by the complex refractive index, N:
N ) n + ik
(1)
where n is the (real) refractive index, k ) λR/(4π), λ is the wavelength, and R is the absorption coefficient. The imaginary part (k) of the complex refractive index describes the absorption of electromagnetic energy as a light wave propagates through the medium, while the real part (n) of the complex refractive index describes the phase velocity of the light wave. N is a function of the wavelength, and so are k and n. k and n are not independent properties but are interrelated as (25) Product information, Erc Inc., Kawaguchi-City, Japan. (26) Product information, Showa Denko K. K., Tokyo, Japan.
Figure 1. (a) Graphical representation of the relation between k (absorption) and n (refractive index) as expressed by the KramersKronig relations. (b) Spectrochemically modified dispersion (solid line) of a solvent with normal dispersion (dashed line) through addition of a small amount of a substance with anomalous dispersion.
described by the Kramers-Kronig relations or dispersion relations:27,28
k(ω) ) -(2ω/π)P
∫
n(ω) - 1 ) (2/π)P
∫
∞
0 ∞
0
[n(Ω)/(Ω2 - ω2)] dΩ
(2)
[Ωk(Ω)/(Ω2 - ω2)] dΩ
(3)
where P denotes a principal value integral in the complex plane and ω and Ω denote angular frequency (ω ) 2πc/λ, where c is the speed of light). A graph of the relation between k and n is shown in Figure 1a. The variation of n (the refractive index) with wavelength is related to as dispersion: normal dispersion when dn/dλ < 0 and anomalous dispersion when dn/dλ > 0. For isolated, Gaussian absorption peaks some approximate statements are as follows: n has maximum and minimum values where k has inflection points, and the difference between the maximum and the minimum of n is proportional to the maximum value of k. A corollary of the Kramers-Kronig relations is that for every medium that has an absorption peak at some wavelength in the electromagnetic spectrum, the RI will vary with wavelength. (A medium that does not absorb at any wavelength does not exist from an optical point of view.) The variation of RI extends over a much broader wavelength interval than the variation of absorption. Even for a sharp absorption peak at one specific wavelength, the RI variation extends, in principle, throughout the entire electromagnetic spectrum. The RI value of uncolored substances (27) Bohren, C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983; Chapter 2. (28) Ashcroft, N. W.; Mermin, N. D. Solid State Physics; Saunders: Philadelphia, PA, 1976; Appendix K.
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in the visible region depends on the wavelengths and intensities of absorptions in the ultraviolet region. Water, for example, exhibits several strong absorption peaks below 170 nm, which causes the RI of water to vary throughout the entire UV-visible region. SRID is based on the measurement of RI as a function of wavelength. In regions of anomalous dispersion, strong and abrupt RI variations are present. In regions of normal dispersion, substance-related dispersion differences (caused by absorptions outside of the measurement range) are weaker but still fully measurable. Temperature and Concentration Dependence of the Refractive Index. The RI of a medium as a function of wavelength and temperature may approximately be expressed as29
n(λ,t) ≈ 1 + NAF(t)R(λ)/(2M0)
(4)
where t is temperature, NA is Avogadro’s constant, F is density, R is molecular polarizability, M is molecular weight, and 0 is vacuum permittivity. The molecular polarizability is a molecular property that is largely independent of temperature but strongly dependent on wavelength. The density is a bulk property that is independent of wavelength but dependent on temperature. For small temperature variations, the density may be considered a linear function of the temperature (Taylor expansion). Thus, for a given wavelength of light, eq 4 may be simplified:
n(λ,t) ) n0(λ) + γ(λ)∆t
(5)
where n0 is the RI at a fixed temperature, γ is a wavelengthdependent factor, and ∆t is the deviation from the fixed temperature. The RI of a solvent as a function of concentration of added analyte at a fixed temperature may be expressed as
n(λ,c) ) n0(λ) + R(λ)c
(6)
where c is the concentration, n0 is the RI of the pure solvent, and R is the (molar) refractive index increment for a given solvent/ analyte pair. The linear dependence on concentration is valid for dilute solutions (Henry’s law). Since temperature and concentration are independent properties, eqs 5 and 6 may now be combined:
n(λ,t,c) ) n0(λ) + γ(λ)∆t + R(λ)c
(7)
From eq 7, a temperature-independent quantity can be derived, for example, by dividing the equation by γ(λ) and taking the derivative with respect to λ. Since d(∆t)/dλ ) 0, the result is
d(n/γ)/dλ ) d(n0/γ)/dλ + c d(R/γ)/dλ
(8)
A somewhat simpler expression is obtained if only two wavelengths, λ1 and λ2, are considered: (29) Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University Press: Oxford, U.K., 1983; Chapter 13.
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n(λ1,t,c) ) n0(λ1) + γ(λ1)∆t + R(λ1)c
(9)
n(λ2,t,c) ) n0(λ2) + γ(λ2)∆t + R(λ2)c
(10)
γ12n(λ1,t,c) - n(λ2,t,c) ) γ12n0(λ1) - n0(λ2) + c(γ12R(λ1) - R(λ2)) ≡ ndiff(λ,c) (11) where γ12 ) γ(λ2)/γ(λ1). The defined quantity ndiff in eq 11 is a measurable property, which may be termed the differential RI with respect to wavelength. It represents a weighted difference of refractive indices measured at different wavelengths. The factor (γ12R(λ1) - R(λ2)), which is a characteristic of the chosen wavelengths and the chosen solvent/analyte pair, may be termed the differential RI increment. The weight factors γ(λ) can be derived theoretically from eqs 4 and 5, or experimentally obtained through calibration. The quantity ndiff has the desired properties of universal and concentration-sensitive response, while being independent of temperature variations. Likewise, since the pressure as well as the temperature influences the density of the liquid, a similar method may be used to cancel RI noise caused by pressure variations. By replacing the ∆t term in eq 5 with a more general ∆F term, variations in both pressure and temperature are covered by the factor γ(λ). Pressure variation is a common source of noise in RI detection when viscous solutions are used, for example, in gel permeation chromatography of polymers. Pulsating pumps and flow restrictors downstream of the detection cell may also cause pressure variations in chromatography. EXPERIMENTAL SECTION Design of the Spectroscopic Refractometer. In order to evaluate the SRID concept, a spectroscopic refractometer as shown in Figure 2 was designed. In brief, light from a broad-band light source was first passed through a prismatic flow cell and then dispersed by a grating, and finally, the deflection of the light beam at each separate wavelength was monitored by a CCD. The light source was a high-brightness deuterium lamp with a 0.5 mm aperture (Hamamatsu L5499-50, Toyooka-Village, Japan) and a regulated current power supply (Hamamatsu C4545). The light was reflected and focused by a concave aluminum mirror (f ) 150 mm, custom design). The light first passed a 1.0 mm pinhole (Melles Griot 04PPM025, Irvine, CA) and then a 0.4 mm pinhole (Melles Griot 04PPM019). The distance from the lamp to the mirror was 150 mm, from the mirror to the first pinhole 200 mm, and from the first to the second pinhole 100 mm. The aim of this arrangement was to obtain a small, intense, polychromatic light beam with low divergence. The light beam then passed through a 45° prismatic flow cell (Knauer, Berlin, Germany). This is a standard, two-chamber HPLC flow cell,1-3 but made of high optical quality fused silica. The volume of a single cell is ∼8 µL. The cell was mounted in a specially designed Teflon holder and connected to the liquid flow system by means of PEEK tubing. The cell was mounted with the liquid flow horizontally (in the y direction), so that the light beam was deflected vertically (in the z direction) by the two liquid prisms. The light then passed a shutter (Melles Griot 04IES001) with an electronic shutter controller (Melles Griot 04ISC501). The role of the shutter was to protect the CCD from light during readout. The light was then horizontally dispersed (in the y direction) by
Figure 2. Block diagram of the spectroscopic refractive index detector. x is the direction of the light beam, y is the direction of wavelength resolution, and z (perpendicular to the plane of the paper) is the direction of refractive index resolution. The flow through the prismatic cell is also in the y direction, i.e., along the long axis of the prism.
a 25 × 25 mm holographic grating (Spectrogon P150 25 × 25 × 6 VIS, Ta¨by, Sweden). The dispersed beam was horizontally focused by a cylindrical fused-silica lens (Melles Griot 01LQC006) onto the CCD chip. Between the lens and the CCD a glass filter (Schott WG 360, Mainz, Germany) was mounted to reject higherorder UV light. The distance from the flow cell to the grating was ∼725 mm, and the distance from the grating to the CCD chip was ∼275 mm. This long optical axis was used to obtain an adequate deflection of the light beam at the position of the CCD chip. The CCD system was an InstaSpec IV (Oriel, Stratford, CT), consisting of a UV-sensitive CCD chip with 1024 × 256 pixels of 27 × 27 µm size (EEV 15-11) mounted in a CCD detector head, which was connected to a computer via an interface card. The detector head was used without any cooling in the present work. The system was controlled by InstaSpec IV software. The software also controlled the shutter, so that the operation of the shutter and the CCD was synchronized. The CCD chip was mounted with its long axis (28 mm) vertically (in the z direction). Thus, the deflection of the light by the flow cell (i.e., the position of the light spot) was monitored along the long axis, while the wavelength dispersion by the grating was monitored along the short axis (7 mm) of the CCD (the y direction). All components were mounted on a 0.6 × 1.2 m optical breadboard (Melles Griot UltraPerformance 07OBC507) using standard mounting equipment. The mirror, pinholes, lens, filter, and CCD were adjustable in the y and z directions, utilizing standard positioning devices. The flow cell and the shutter were adjustable in the z direction. Likewise, the grating was adjustable in the z direction and might be rotated about the z axis. The total distance from the lamp to the flow cell was ∼475 mm, and the distance from the flow cell to the CCD was ∼1000 mm. The lamp, mirror, and first pinhole were contained within a lamp housing to protect the operator from UV light. The grating, lens, filter, and CCD were contained within a light-tight black housing to carefully protect the CCD from stray light. The only entrance for light to the detector housing was through the shutter. The flow cell apartment between the lamp housing and the detector housing was only superficially protected from excessive daylight or lamplight. Operation of the Spectroscopic Refractometer. At first, the optical setup was adjusted, so that the first-order spectrum in the region 200-700 nm was collected, and the intensity of the beam hitting the CCD and the symmetry of the light spot were
Figure 3. Refractive index as a function of the wavelength on the CCD chip. The light spot is actually ∼200 pixels wide in the z direction, but only the position of the calculated center of gravity is shown.
optimized. Wavelength calibration was performed by means of interference filters. The CCD was operated with pixel binning. In the wavelength (y) direction, 8 pixels were binned together, so the wavelength scale consisted of 32 superpixels, each corresponding to ∼15 nm. The CCD system used is rather slow: the read out time for one wavelength row consisting of 1024 position pixels is ∼0.025 s, so the total readout time with the chosen wavelength resolution was ∼0.8 s. In order to obtain sufficient counts to ensure highprecision counting statistics, exposure times were at least a few tenths of a second, and the subsequent processing of data also demanded a few tenths of a second. The resulting total cycle time was in the order of at least 1 s. In the position (z) direction, no binning was used in order to obtain maximum position resolution. The image on the CCD can be viewed as a series of 32 light spots of different wavelength, each experiencing a certain deflection in the flow cell, due to the RI at that specific wavelength (Figure 3). The spots had an approximate Gaussian intensity distribution in the position (z) direction, the width of which was in the order of 200 pixels fwhm with the chosen pinholes. The exact position of each spot was determined by a center of gravity algorithm. This algorithm allowed a high degree of interpolation between pixels, so the obtainable position resolution was far better than 1 pixel (27 µm). The result was a graph of RI versus wavelength. For a dual-cell arrangement with pure liquid in the reference cell and liquid containing a low concentration of analyte in the sample cell, the deflection of the beam as a function of the RI change in the sample cell is approximately2
dn ) dβ ) dz
(12)
where dn is the RI change, dβ is the deflection angle, and dz is Analytical Chemistry, Vol. 69, No. 8, April 15, 1997
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Table 1. Refractive Index Signal, Noise, and Signal-to-Noise Ratio for Single-Wavelength Measurements and for Dual-Wavelength Differential Measurement of 1% Sucrose in Water without temp variation (Figure 4) signal, z (pixel) noise, s.d. (pixel) S/N
RI 210 nm 63.9 0.273 234
64.1 3.76 17
signal, z (pixel) noise, s.d. (pixel) S/N
RI 590 nm 54.6 0.273 200
54.8 3.69 15
signal, zdiff (pixel) noise, s.d. (pixel) S/N weight factor noise improvement S/N improvement Figure 4. Refractive index trace of the injection of 1% sucrose in water into a pure water carrier stream. Single-wavelength measurements at 210 and 590 nm on the left ordinate and differential measurement (zdiff) on the right ordinate.
the position deviation in meters of the light spot in the z direction at the CCD, using a 1 m optical axis. Thus, 1 pixel ) 27 µm corresponds to ∼27 µRIU. In all experiments, the reference cell was filled with water and sealed, while liquid was continuously pumped through the sample cell by a peristaltic pump (Bifok FIA-08, Sollentuna, Sweden) without any pulse dampening. The reason for using a liquid-filled reference cell was not to obtain thermal compensation (as in conventional RI detectors) but to simplify the geometry of the optical setup. In principle, an air-filled reference cell may be used (or no reference cell at all), but this leads to a very large net deflection of the beam and may even lead to total reflection of the light under certain conditions. A liquid or solid prism reference cell counterbalances this large deflection. Chemicals. Deionized water was used throughout. Sucrose (Sigma S-9378, 99.5%, St. Louis, MO) was used as the analyte. Sodium benzoate (Aldrich 10916-9, 99%, Milwaukee, WI) was used as a spectrochemical modifier. All solutions were used without filtration or degassing. RESULTS AND DISCUSSION Baseline Noise and Signal-to-Noise Ratio of Sucrose. In a first series of experiments, the obtainable noise level and signalto-noise ratio using dilute sucrose solutions in water were determined. Figure 4 shows the results for a 1% solution of sucrose. The refractive indices were recorded at 210 and 590 nm. The RI changes are not displayed in RI units but as changes of the position in pixel units of the light spots on the CCD in the z direction. The exposure time per data point was 3 s. The data were passed through a simple three-point boxcar smoothing. The peak height was evaluated, while the baseline noise was calculated as the standard deviation for data points 1-30. The results are summarized in the first column of Table 1. A weighted difference between the two refractive indices was computed in order to reduce the baseline noise and increase the signal-to-noise ratio. The RI difference, expressed in pixel units, 1500 Analytical Chemistry, Vol. 69, No. 8, April 15, 1997
with temp variation (Figure 5)
Differential RI 9.7 0.0111 876 1.007 25× 4.4×
8.1 0.0130 625 0.982 285× 42×
is denoted zdiff (corresponding to ndiff in eq 11). The best result was obtained with the weight factor 1.007, i.e., zdiff ) 1.007z(210 nm) - z(590 nm). The weight factor corresponds to the theoretical ratio γ12 in eq 11. The signal and the baseline noise were calculated as before. The data obtained are also summarized in Table 1. It can be seen from these results that the noise of the differential signal corresponds to 0.011 pixel, i.e., 25 times less than the noise of the single-wavelength signals. This is due to the noise-canceling characteristics of the differential RI response. On the other hand, the height of the differential RI peak for the sucrose solution is only 18% of the single-wavelength peak at 590 nm. Therefore, the gain in signal-to-noise ratio for the present example is only a factor 4.4. The potential of the SRID method is particularly visible in the example shown in Figure 5, where the sample was subjected to deliberate temperature variations in the order of 4-5 °C by means of a hot-air gun. The baseline noise was calculated as the standard deviation for the data points 60-100. The results are summarized in Table 1. The noise of the differential signal is reduced by a factor 285 in this example, while a 42-times gain in signal-to-noise ratio is obtained. The absolute noise level is 0.013 pixel ) 0.35 µRIU, corresponding to a temperature noise of ∼3.5 × 10-3 °C. Although the absolute noise level obtained in the present experiments is not up to the performance of the best commercial single-wavelength RI detectors,25,26 it is clear that the differential method is more robust. The results were obtained without any thermostating, with liquid flow in the sample cell, with a pulsating peristaltic pump without any pulse dampening, without filtering or degassing of the samples, and without any lengthy equilibration of the system before the readings were taken. It is further believed that the demonstrated noise levels could have been obtained without using a reference cell. Linearity. In order to evaluate to linearity of the differential method, seven different solutions of sucrose in water were prepared, ranging from 100 ppm to 1%. The solutions were measured by the spectroscopic refractometer as described above, with pure water as the baseline. The exposure time per data point was 1 s. The results are shown in Figure 6.
Table 2. Refractive Index Signal, Noise, and Signal-to-Noise Ratio for Single-Wavelength Measurements and for Dual-Wavelength Differential Measurement of 0.1% Sucrose in Water in the Presence of a Spectrochemical Modifier (Sodium Benzoate) RI 280 nm signal, z (pixel)
3.8 RI 590 nm
signal, z (pixel) Differential RI signal, zdiff (pixel) noise, s.d. (pixel) S/N
Figure 5. Refractive index trace of the injection of 1% sucrose in water into a pure water carrier stream with deliberate temperature variations in the order of 4-5 °C. Single-wavelength measurements at 210 and 590 nm on the left ordinate and differential measurement (zdiff) on the right ordinate.
Figure 6. Linearity test with seven different concentrations, ranging from 100 ppm to 1%, of sucrose in water. Single-wavelength measurements at 210 and 590 nm on the left ordinate and differential measurement (zdiff) on the right ordinate.
Since the RI at a single wavelength is a linear function of concentration for dilute solutions, the RI difference zdiff is also expected to behave linearly. This is confirmed by the experiments. The coefficient of determination (r2) is 0.9999 for the two single-wavelength measurements and 0.9998 for the differential measurement over the two studied decades, including the origin. The slope of the fitted straight line is 0.005 48 pixel/ppm at 590 nm. With the nominal value 1 pixel ) 27 µRIU, this equals 0.148 µRIU/ppm or 0.148 mL/g, which is in fair agreement with the reported value (0.145 mL/g) for the RI increment of sucrose in water at 590 nm.30 The slope of the differential signal zdiff is 0.000 983 pixels/ppm, which again is ∼18% of the signal at 590 nm.
4.2 -1.1 0.0080 138
Spectrochemical Modification of the Solvent. For some pairs of analyte/solvent with closely resembling RI spectra, it may be difficult to obtain an acceptable differential RI increment at easily accessible wavelengths. In the present example, sucrose in water, the highest sensitivity can be expected at wavelengths below 210 nm. However, we propose a method, which may be termed spectrochemical modification of the solvent, to improve the sensitivity for all substances even at longer UV or visible wavelengths. In this method, the RI spectrum of the solvent is modified through addition of a substance with specially selected RI spectral properties. The effect of this modification is graphically explained in Figure 1b. The RI and the RI dispersion of water decrease with wavelength from 200 nm and upward, and the same is true for sucrose. This means that the obtainable differential RI increment (dndiff/dc) also decreases with wavelength, if the long wavelength is fixed at 590 nm and the short wavelength is shifted toward longer wavelengths, e.g., from 210 to 280 nm. If a substance that absorbs light slightly above 200 nm is added to the water, the RI of the solvent at 280 nm will increase, and so will the RI dispersion between 280 and 590 nm. As a consequence, the differential RI increment between 280 and 590 nm for the system sucrose/solvent will also change. The sign and magnitude of the change are dependent on the RI, the RI dispersion, and the concentration of the added substance. In order to test the validity of this principle, a solvent consisting of 2% sodium benzoate (maximum absorptivity 9000 M-1 cm-1 at 224 nm) in water was prepared, and the RI change on addition of 0.1% sucrose to this solvent was studied at 590 and 280 nm. (Preliminary experiments had shown that the differential RI increment for pure water and sucrose was very small between 590 and 280 nm.) The exposure time per data point was 1 s. The results are summarized in Table 2. Several effects are noted as compared to the earlier obtained results (Table 1). The RI increment at 280 and 590 nm both decrease, since the RI of the solvent increases. On the other hand, the differential RI increment between 280 and 590 nm increases. In fact, due to the high dispersion of the benzoate molecule, the sign of the differential RI (ndiff) is reversed, since the RI increment becomes larger at 590 nm than at 280 nm. With the weight factor employed, 0.804, the response is 11 pixels/% sucrose. Clearly, the spectral modification of the solvent yields a response at 280 nm, which is higher than the previously obtained response at 210 nm. The baseline noise in this experiment was 0.0080 pixel, corresponding to 7 ppm sucrose. (30) Weast, R. C., Ed. Handbook of Chemistry and Physics, 59th ed.; CRC Press: West Palm Beach, FL, 1978; p E-358.
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General Discussion. It is somewhat worrying that only 1518% of the original signal remains after differentiation, since this limits the obtainable signal-to-noise ratio. The signal strength depends on the difference in molar RI increment for the chosen solvent/analyte pair at the chosen wavelengths (cf. eq 6). The system water/sucrose was chosen since it represents a common and a difficult case in chromatography as well as in process analysis. Both substances show only normal dispersion in the wavelength region above 200 nm, and the two RI spectra closely resemble each other, so the obtainable differences in molecular RI increment are rather small. The way to obtain a stronger differential signal would be to utilize a wavelength shorter than 210 nm, but this was not possible with the present apparatus. It is believed that when the measuring wavelength is brought down below 210 nm, the differential RI signal will strongly increase and may even exceed that of conventional single-wavelength measurements. This is explained by the strongly increasing dispersion of sucrose in this region (cf. Figure 1). The highest sensitivity is obtained when measurements are made close to an absorption band of the analyte, where the dispersion is large.31,32 This is especially true in regions of anomalous dispersion, i.e., “across” absorption bands. In such cases, absorption detection may also be used, but the advantage of SRID is obvious in analytical separations of mixtures of absorbing and nonabsorbing substances, where a SRID detector may replace an absorption detector and an RI detector in series. Even though the best sensitivity is obtained close to absorption bands, SRID is not limited to such wavelength regions. High sensitivity may also be obtained well outside absorption bands, since RI spectral features are much broader than absorption features. The way to decrease noise is by improving the optical design of the detector. Some of the most important factors are as follows: increasing the light source intensity, replacing the mechanical shutter with an electronic shutter, improving the noise, speed, and pixel-to-pixel response of the CCD, and optimizing the algorithm to determine the position of the light spot. It is probably easier to design a low-noise detector with a few fixed wavelengths than a full spectroscopic detector. A fixed-wavelength detector could utilize the intense light from a line source and could utilize diode arrays instead of a CCD, which would result in higher speed and lower noise of the light detection. With such improvements in the optical design, it should be possible to reach a noise level in the order of a few nRIU. For chromatography applications, it is necessary to increase the sampling frequency of the detector. By increasing the light throughput and decreasing the wavelength resolution, it should be possible to decrease the exposure time to ∼0.1 s. By utilizing an electronic shutter, by utilizing a CCD chip with free format binning and read-out, or by replacing the CCD with a number of diode arrays, the readout time should get neglectable. Finally, by performing the computations in parallel with the exposure of light (instead of in series, as in the present experiments), it should also be possible to drastically decrease the computing time. Such improvements would allow a sampling frequency in the order of 10 Hz. For process analysis, a sampling frequency of 1 Hz may (31) Gauglitz, G.; Krause-Bonte, J.; Schlemmer, H.; Matthes, A. Anal. Chem. 1988, 60, 2609-12. (32) Hanning, A. Swedish Patent 9300231-9, 1993.
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be sufficient, and in such cases, it would be possible to further decrease the noise through signal averaging. For example, when an 11-point boxcar smoothing was applied to the raw data of the run presented in Table 2, the noise was brought down to 1 × 10-7 RIU. Spectrochemical modification of the solvent is an indirect technique that shows promise in increasing the sensitivity and controlling the selectivity. Such modification of the solvent is not so compatible with process analysis but can be readily applied in liquid chromatography and capillary electrophoresis. The optimal measuring wavelengths are dependent on the spectral properties of the modifying agent. Using a visible dye as the modifying agent, measuring wavelengths within the visible range may be used. This would permit the use of lasers as light sources, which is expected to yield an additional improvement in sampling speed and noise reduction. When two closely spaced wavelengths in the visible range are used in conjunction with a visible modifying agent, the dispersion of the solvent as well as the analyte may, to a first approximation, be neglected. This implies that all analytes will show the same response per volume concentration unit, since the signal only originates from the volume fraction of modifying agent that is being displaced by the analyte. In this mode, SRID could therefore offer a universal calibration graph for all substances. This is not the case for absorption detection, which depends on the absorptivity of the analyte, nor for single-wavelength RI detection, which depends on the RI of the solvent and the analyte, respectively. When the system solvent/modifier/analyte is being designed, care should be taken not to introduce any nonideal molecular interactions that may result in nonlinear calibration graphs. Work is currently ongoing in our laboratory to optimize the system with respect to applicable wavelengths, signal strength, and linearity. Perhaps the most exciting area of development for SRID is miniaturization. There is a strong trend to develop miniaturized refractometers for use as sensors and as detectors for microcolumn separations. The most sensitive microrefractometers reported are developed by Bruno, Krattiger and co-workers,4-9 who obtained a noise of 3×10-8 RIU using 50 µm i.d. capillaries. Further decrease of the noise was claimed to be limited by thermal fluctuations, but it was predicted that it would be possible to obtain a noise level on the order of 1 nRIU if the thermal noise could be canceled. By designing a miniaturized spectroscopic refractometer, such thermal noise limitations could effectively be eliminated. The cell length at which the signal-to-noise ratio of SRID is expected to exceed that of absorption detection can be theoretically estimated. The calculation utilizes an absorption detector with a noise level of 10-5 AU (absorption units) and a refractometer with a noise level of 2.5 × 10-9 RIU. Such noise levels are commonly specified for commercial detectors. The ratio between the peak-to-peak differential RI increment (dndiff/dc) and the peak absorptivity () in the region of anomalous dispersion for a given substance is estimated from literature data.32,33 This ratio is found to be ∼10-7 m. Combining the Lambert-Beer law A ) bc with the corresponding law for SRID yields (33) Brackmann, U. Lambdachrome Laser Dyes; Lambda Physik: Go¨ttingen, Germany, 1986; Chapter III.
ndiff ) (dndiff/dc)c
(13)
b ) (A/ndiff)((dndiff/dc)/) )
supported by the Swedish National Board for Industrial and Technical Development, the Swedish Natural Science Research Council, and the SAF-LO Employment Security Found.
(10-5/2.5 × 10-9)10-7m ) 0.4 mm (14) Thus, at cell dimensions less than 0.4 mm, SRID has the potential to be more sensitive than absorption detection.
Received for review October 30, 1996. Accepted February 6, 1997.X AC961111C
ACKNOWLEDGMENT We gratefully acknowledge the help of Lars Eriksson, BPT Optik AB, in designing the optics. This work was financially
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Abstract published in Advance ACS Abstracts, March 15, 1997.
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