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Anal. Chem. 1984, 56, 1467-1469
Liquid Chromatography Detection at the Second Harmonic of the Modulated Thermal Lens Teng-Ke Joseph P a n g a n d Michael D. Morris* Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109
A new form of thermal lens spectroscopy Is descrlbed. A CW laser beam Is modulated and the thermal lens is detected as the frequency component induced at the second harmonic of the modulation frequency. The second harmonlc response is linear in analyte concentration. Laser power of 35-80 mW Is usable. SignaVnoise ratios are shown to be sllghtly below those obtainable by the twdaser pump/probe technique. The technique Is applied to ilquld chromatography detectlon wlth a 1 mm path length cell and Is proposed for appilcatlon to short path length or restricted-volume experiments In general.
Thermal lens spectroscopy is emerging as a powerful technique for high-sensitivity solution-phase absorption measurements (1). The technique is especially useful for measurements in short path length or restricted-volume systems because much of the effect is generated over a few confocal distances (2). Liquid chromatographydetection (3-7) has received substantial attention. Thermal lens systems have already been shown to work well with microbore columns (6) and have been proposed for use with capillary columns. The appeal of the technique is that it is entirely optical. While an optical window into the effluent is needed, there is no need to insert anything or attach anything to a system whose dead volume must remain well below 1 pL. There are two major experimental approaches to thermal lens spectroscopy. Both, unfortunately, are difficult, or even impractical, for systems requiring real-time response and submicroliter working volume. Excellent performance can be obtained by monitoring the growth of a thermal lens over a period of 0.5-1 s and fitting a data set of several hundred points to the governing equation (8). However, the governing equation is nonlinear and a fit requires about 1min on a PDP 11/23. For chromatographic work, this approach has been replaced by an approximate fit, with substantial degradation of the signal to noise ratio (2). The approximation is necessary in order to reduce the computation time to 0.25 s. Other investigators employ the pump/probe method (1,9), in which the thermal lens generated by a modulated laser is detected as the modulation component induced on a much weaker probe laser. Lock-in amplifier demodulation provides good signal/noise ratio with a time constant of about 1s. The pump/probe experiment is easy to carry out in a long-path system, where loose focusing can be employed. Unfortunately, if tight focusing must be used, as in microbore chromatography, alignment of the two lasers becomes critical (6). Careful alignment is necessary to obtain good signal/noise ratios even in a 1mm path length cell. This alignment is destroyed by pointing instabilities in either laser. It is doubtful that the pump/probe technique is practical, even if feasible, for shorter path lengths. Interferometric variants on the pump/probe experiment have been described (4). While elegant, these experiments have some computational constraints and suffer alignment problems similar to those encountered in other pump/probe configurations. 0003-2700/84/0356-1467$01.50/0
We do not wish to argue the merits of the various approaches to thermal lens detection. Recently, the pump/probe and time evolution methods have been shown to provide essentially identical signal/noise ratios in practice and to be theoretically equivalent if pump and probe lasers have the same wavelength (10). It is clear that there may be applications where one technique or the other will be preferred. Chromatographic detection does not seem to be the ideal domain for either approach. In this paper, we describe thermal lens detection as the second harmonic component induced on a single modulated laser beam. The technique uses lock-in amplifier demodulation and provides high signal/noise ratios with short time constants and no need for high-speed computations. Because only one laser is used, the alignment problems of conventional pump/probe experiments do not exist. We are exploiting a general property of modulated systems. That is, if the system response lags the excitation, then a response at the second harmonic of the modulation frequency is observed. Second harmonic response is readily observed with sinusoidal modulation or with square-wave modulation. A square wave consists of the fundamental and all odd harmonics in amplitude ratio 1:1/3:1/5, etc. Here, too, the second harmonic response is generated as a result of the modulation. Second harmonic system response has not previously been employed in thermal lens measurements. It should be noted that the thermal lens equation itself contains linear and quadratic terms (I). The weak quadratic term can become important in a pump/probe experiment a t high absorbance and generate a significant second harmonic component on the probe intensity. This response has been observed by Carter and Harris (10). They have measured the second harmonic induced on a DC probe beam in a conventional (9) pump/ probe experiment. At absorbance of 0.05 the second harmonic intensity is about 30% of the fundamental response.
THEORY We present here an approximate theory of the second harmonic experiment. The key assumption is that the thermal response is linear in time. In a steady-state experiment, such as we perform, the linearity assumption is valid at low absorbance (1,9,10) but becomes increasingly inadequate at high absorbance (10). Consider a thermal lens experiment in which the lens is detected conventionally as the intensity change generated at a detector placed beyond a far-field limiting aperture. If the laser is modulated at frequency w with a square wave, eq l a
describes the time evolution of laser-on focal length, F ( t ) ,of the thermal lens during each half-cycle (9). Here dn/dT is the temperature coefficient of refractive index, cy is the absorption of the solution, P is the laser power, 1 is the sample length, w1 is the beam radius at focus, J is the mechanical equivalent of heat, k is the thermal conductivity of the solution, t is the on time of the modulated laser, and t , is the 0 1984 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
critical time, or response time of the solution, given by t, = wI2/4D, where D is the thermal diffusivity. Equation l a contains only the steady-state ac terms. The dc “memory” terms have been omitted. A similar equation, eq Ib, can be
written to describe the decay of the thermal lens during the off half-cycle. The intensity change, as measured in the far field, is given by eq 2. Here, z’ is the distance from beam focus to the -W = -t ) I(0)
1
F( t ) / 22’
(2)
1
(3)
However, the laser beam itself is modulated. Again, we consider only the fundamental frequency, as in eq 4.
P ( t ) = P cos (ut)
(4)
Here P(t)is the time dependence of the laser power, whose unmodulated power is P. For simplicity, phase-angle terms have been omitted from this equation. If mechanical chopping is used, the modulation function is a square wave and contains odd harmonics only. The detector response, as conventionally measured, is proportional to the product of 1/F and P(t). By inspection of eq 3 and 4, we see that the thermal lens response contains a component, R ( t ) ,a t 2w.
R ( t ) = K”aP[cos 2ut]
c rn n L
0
m
n
sample. Because the lens is generated by a sinusoidally or squarewave modulated laser, 1/F(t) can be represented as a Fourier series in the modulation frequency, w. We consider only the fundamental, since terms due to odd harmonics will be small and will be further attenuated or rejected by the lock-in amplifier. For convenience we lump all of the nonvarying terms into one constant, K’, as in eq 3.
- = K P a cos (ut + 4) F
aJ 0
(5)
In eq 5, all constants are lumped into K” and the dc and phase-angle terms are omitted. Thus, monitoring the thermal response at twice the modulation frequency, 2 w , provides a direct measurement of the thermal lens signal. Lock-in amplifier detection of the second harmonic response is the most convenient experimental technique. A similar response could be obtained with sinusoidal modulation of the laser beam or with any other periodic modulation which did not directly introduce a second harmonic component onto the laser beam intensity.
EXPERIMENTAL SECTION The thermal lens apparatus is a modification of the apparatus previously described (5,6). The probe laser was omitted and the sharp-cut glass filter was replaced with a neutral density filter. The filter was chosen to provide a dc voltage of 2-5 V when the laser was focused onto the optical fiber. For the several experiments, lenses of 30-,50-, and 73-mm focal lengths were employed. The PARC 5101 lock-in amplifier was employed in its second harmonic (2f) mode. An active notch filter (PARC 5101/98) was added to the instrument to improve rejection of the fundamental. The chromatography system employed the LDC minipump, 4.6 x 250 mm column packed with 10 W r n Licrosorb RP-18, and 80% methanol used previously. The test compound was onitroaniline. Samples were made up in methanol/water and injected onto the system in 1.0-pL aliquots. The flow rate was 1.0 mL/min. The detector cell was a short length of 1-mm i.d. x 1.2-mm 0.d. quartz tubing connectedvia a 4-cm length of Teflon tubing to the outlet of the chromatographic column. The cell was
a
il 0.00
1.50
3.00
4.50
6.00
T i m e , minutes Flgure 1. Thermal lens detection of 22 ng of o-nitroaniline. Laser power, 80 mW. Focusing lens 30-mm focal length. Elution of I-pL sample at 1.0 mL/min. (a)Pump/probe method (b) second harmonic
detection using Ar’ laser only. mounted on translation stages for positioning in the laser beam. All data were taken by using the Ar+ 458-nm line. The laser power was maintained at 80 mW and attenuated with neutral density filters as necessary. The system was adjusted by maximizing the oscilloscope trace of the second harmonic signal generated with the pump and column disconnected and the cell g/L of o-nitroaniline, absorbance 0.03. filled with 2.2 X
RESULTS AND DISCUSSION The major departure from our previous chromatographic apparatus is the use of a quartz capillary in place of a commercial flow cell. The commercial 1-pL cell available to us employs sharp right-angle turns to provide maximum path length with minimum dead volume. This design introduces uncontrollable turbulence into the system at 1mL/min flow rates. Turbulence prevented formation of a reproducible thermal lens with this cell. The straight-through design of a capillary cell reduced but did not completely eliminate turbulent flow. To minimize turbulence effects we used high chopping frequencies, typically about 315 Hz. This frequency was found to be the best compromise between losing the signal at very high frequencies and turbulence-induced noise at low frequencies. Figure 1 shows conventional pump/probe and second harmonic thermal lens chromatograms obtained sequentially with this system. That the signal in curve b is truly the second harmonic was readily verified. First, the signal appears at the same retention time and with the same band shape as the pump/probe signal. Second, only a constant output was obtained in the one laser configuration with the lock-in amplifier operated in its fundamental mode, representing the transmitted intensity of the chopped laser. The transmitted intensity change is negligible at the low absorbances, 0.005 and below, encountered here. We have observed linear response with o-nitroaniline concentration over the range 0.9-46 ng/pL. The slope of a linear regression has a standard deviation of f2.1%, with the data set heavily weighted toward noisy, low concentration points below 10 ng/WL. We observe a small positive intercept because of the solvent absorbance, which is uncompensated. We have not examined response at higher concentrations than 46
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
ng/pL. However, at sufficiently high concentration, the nonlinearity of the thermal lens phenomenon itself will cause deviation from linearity in this experiment (IO). We have also verified the laser power squared dependence of eq 5. Linear dependence of chromatographic peak height with laser power squared was observed over the range tested, 15-80 mW. A least-squares fit of peak height vs. power squared was linear with a slope standard deviation of f3.5%. This linearity is within the experimental error expected because uncalibrated neutral density filters were used to attenuate the laser beam. The signal to noise ratio generally increases with laser power. The variation is only about a factor of 2 over the range 35-80 mW, but decreases rapidly below 30 mW power. The signal/noise ratio obtained by the second harmonic technique is about a factor of 2-3 worse than that obtained with the same laser power, sample, and chromatographic conditions by the pump/probe technique. The loss in signal/noise ratio appears to be largely due to the presence of residual subharmonic (i.e., fundamental) response in our lock-in amplifier. The lock-in available to us has a 1-2% response to the fundamental when operated in the second harmonic mode. To obtain acceptable response it was necessary to operate the instrument with its internal notch filter (Q = 5). The effect of varying the focal length of the focusing lens was examined. Best performance was obtained with a 30-mm focusing lens, although theory ( I , 2 ) says that the confocal parameter of the system should be much longer than the sample cell length. Performance was slightly worse with a 50-mm focal length lens and discernibly worse with a 73-mm focal length lens. There are two possible sources for the observed dependence on focal length. First, conventional thermal lens theory assumes a truly Gaussian beam. However, in our system the sample cell itself is a strong cylindrical lens, which converts the laser beam to a pencillike form as it leaves the cell. It is quite probable that the observed response comes primarily from the component along the beam axis, which is not perturbed by the cell curvature. Second, the cell walls themselves have a significant thickness, about 20% of the thickness of the liquid inside. Any residual absorption by the cell walls or by impurities adsorbed on any wall surface can cause deviations from the expected performance. Which of these effects predominates is not yet clear.
CONCLUSIONS Second harmonic response appears to be an especially convenient thermal lens measurement scheme. It is computationally simple and avoids the alignment problems inherent in two-laser techniques. Although the signal/noise ratio is
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slightly worse than that obtainable by the pump/probe technique, this appears to be a consequence of the use of a basic broad-band lock-in amplifier with only moderate ability to reject subharmonics. Use of a heterodyning lock-in or addition of an active or passive high-pass filter to provide at least 40-dB rejection of the fundamental should make second harmonic measurements equivalent to pump/probe or time evolution results. In particular, better rejection of the fundamental should allow operation of the system at lower laser power. With these modifications, second harmonic thermal lens measurements should prove especially attractive for microbore or capillary liquid chromatography. The second harmonic technique can be considered as one case of the pump/probe system in which both functions are combined in one laser. Other systems in which pump and probe functionsare derived from the same laser may also prove attractive. These include forming the probe beam with a beam splitter and encoding it by rotating its plane of polarization and/or by modulating it at a high frequency. In the former case a polarizing beam splitter serves as a beam combiner and a Glan prism will separate pump and probe. In the latter case cross polarization and Glan prism prefiltering can also be used, but the thermal lens response will appear only at the intermodulation frequencies and can be processed there by demodulation at either of those frequencies. Any of these systems, once aligned, would be expected to remain in alignment indefinitely, since pump and probe components would undergo small pointing drifts together. Constructionof improved second harmonic instrumentation and evaluation of alternative modulation systems are currently under way. These results will be reported in subsequent communications.
ACKNOWLEDGMENT We thank Earl Klugman, EG&G Princeton Applied Research Corp., for the loan of the notch filter used in this work.
LITERATURE CITED (1) Fang, H. L.; Swofford, R. L. In "Ultrasensitive Laser Spectroscopy"; Kliger, D. S., Ed.; Academic Press: New York, 1983; pp 175-182. (2) Carter, C. A.; Harris, J. M. Appl. Spectrosc. 1983, 37, 166-172. (3) Leach, R. A.; Harris, J. M. J . Chromatogr. 1981, 218, 15-19. (4) Woodruff, S. D.; Yeung, E. S. Anal. Chem. 1982, 5 4 , 1174-1178. (5) Morris, M. D.; Buffett, C. E. Anal. Chem. 1982, 54, 1824-1825. (6) Morrls, M. D.; Buffett, C. E. Anal. Chem. 1983, 55, 376-378. (7) Morris, M. D. Proc. Soc. Photo-Optlcal Instrum. Eng. 1983, 426, 116-120. (8) Harris, J. M.; Carter, C. A. Anal. Chem. 1981, 53, 106-109. (9) Swofford, R. L.; Morreii, J. A. J . Appl. f h y s . 1978, 49, 3667-3774. (IO) Carter, C. A.; Harris, J. M. Anal. Chem. 1983, 55, 1256-1261.
RECEIVED for review November 28, 1983. Accepted March 26, 1984. This work was supported by a research grant, GM28484, from the National Institutes of Health.
