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Anal. Chem. 1981, 53, 689-692
were analyzed. Long-term reproducibility was achieved. This method has all the advantages of modified thermal decomposition method (3) and also some additional ones: (i) the temperature of reaction is significantly reduced; (ii) time consuming purification to remove COP and H2O may be omitted because of the high purity of SO2;(iii) it can be used for all natural and precipitated sulfates and proceasing of these samples is performed under identical conditions; (iv) the same apparatus may be used for both sulfate and sulfide preparation; (v) its simplicity makes it suitable for the preparation of native sulfur and also, in some difficult cases, of sulfides converted into BaS04 as advised. ACKNOWLEDGMENT We thank J. R. ONeil of the US.Geological Survey, Menlo Park, for valuable comments on methodsof SO2 preparation and R. 0. Rye of the US. Geological Survey, Denver, for
sending us special information on use of the thermal decomposition procedure. Thanks are also due to J. W. Case and H. R. Krouse of the Physics Department, University of Calgary, for comments on the final version of the manuscript. LITERATURE CITED Hok, B. D.; Engeikemeir, A. G. Anal. Chem. 1070, 42, 1151-1453. Bailey, S. A.; Smith, J. W. Anal. Chem. 1972, 44, 1542-1543. Coleman, M. L.; Moore, M. P. Anal. Chem. 1078, 50, 1594-1595. Erdey, L.; Pauiik, F. Acta Chim. Acad. Scl. Hung. 1054, 4 , 37. Vinogradov, A. P.; Chupakhin, M. S.; Grinienko, V. A.; Trofimov, V. A. Geokhimiya 1058, 96. Oana, S.; Ishikawa, H. Geochem. J . 1066, 1 , 45-50. Halas, S. Isotopenpraxis 1977, 13, 321-324. Robinson, 6. W.; Kusakabe, M. Anal. Chem. 1075, 47, 1179-1161. Halas, S.; Lis, J.; Saran, J.; Trembaczowski, A. Ann. Univ. Marlee Curie-Sklodowska, Sect. AAA, in press.
RECEIVED for review November 13,1978. Resubmitted December 10, 1980. Accepted December 10, 1980.
Thermal Lens Calorimetry for Flowing Samples N. J. Dovichl and J. M. Harris' Department of Chemistry, University of Utah, Salt Lake City, Utah 84 112
I n order to utlllre thermal lens calorimetry as a sensitive means of detection for liquid chromatography or automated analysis, we must conslder the behavlor of a thermal lens In a flowing sample. The major disturbance of the calorimetric response by the flow is caused by turbulent mixing In the lllumlnated region of the sample. At large flow rates, a loss of sensltlvlty, due to Increased thermal conduction, and an additional source of proportional nolse, from flow pulsations, are observed. The degradation of performance Is not severe at flow velocities suitable for most appllcatlons.
case of a motionless sample, is governed primarily by radial thermal diffusion (7,8).Following the onset of illumination by the laser beam, the temperature gradient approaches a steady-state condition where the rate of heating by the laser, which depends on laser power density and sample absorbance, equals the rate of heat loss, which depends on thermal conductivity and the temperature change produced. The time dependence of the focal length of the resulting lens has been derived (7)
f(t) = f ( a ) ( 1+ t,/2t)
(1)
where f(-), the steady-state focal length, is The introduction of laser sources into spectrometric detectors for liquid chromatography (1-3) has produced significant gains in sensitivity and detection limits. The improvements over conventional sources arise not only from the increased intensity of the laser but also from the unique spatial coherence of the beam which facilitates focusing through small volume flow cells. The detection of LC samples having insignificant fluorescence quantum yields could be improved, similarly, by a calorimetric absorbance measurement using a laser source ( 4 , 5 ) . This idea was first proposed by Kreuzer (6) where the heat produced in the eluent by absorption of a pulsed COz laser would be detected by a thermistor downstream from the laser beam; unfortunately, no details of performance were provided. In this work, the suitability of a related technique, thermal lens calorimetry, for detection of samples in a flowing stream is considered. The thermal lens effect, unlike other laser techniques, relies on the modification of the spatial coherence of the laser beam by the temperature distribution within the sample. It is important to consider, therefore, how the disturbance of the temperature profile by the flow will effect the thermal lens response. In a thermal lens calorimeter, a lenslike element is formed within the sample by absorption of radiation from a TEM, laser beam, having a radially symmetric, Gaussian intensity distribution. The resulting temperature distribution, in the 0003-2700/81/0353-0689$01.25/0
f(m)
= dw2/2.303P(dn/dT)A
(2)
and t, is the characteristic time constant given by
t, = w 2 p C p / 4 k
(3)
where k is thermal conductivity in W cm-l K-l, w is the beam spot size in cm, P is the laser power in W, (dn/dT) is the variation in refractive index with temperature, A is the sample absorbance, p is the density, and C, is the specific heat in J g-' K-'. The thermal lens acts to change the divergence of the laser beam, which is detected as a change in the intensity of the beam center in the far-field, zbc. When the sample is located one confocal length beyond a waist in the laser beam, the time dependence of Ibc is given by
where E is the enhancement of the linear portion of the response compared to Beer's law (9),E = -P(dn/dT)/Xk. From the relative change in I& caused by the lens, an expression linear in absorbance may be obtained
+
( 2 M b c / I b ~ ( ~ ) 1)'" - 1 = 2.303EA
(5) A quantitative model of thermal lens behavior for a flowing sample is considerably more complex. A complete treatment 0 1981 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
F W e 1. Flow components effecting thermal lens response in a typical
flow cell. Solid curved arrows indicate mixing, solid straight arrows are transverse bulk flow, and the dashed arrow is longitudinal bulk Row. would require a solution of the Navier-Stokes equations (10) to determine the flow profile within the cell, inclusion of the result into the heat equation as a heat loss term (11), and analysis of the resulting time-dependent temperature (refractive index) profile with diffraction theory (12) to obtain the time-dependent intensity of the beam center in the farfield. The solution of the Navier-Stokes equations is considerably complicated by the boundary conditions associated with sample introduction and removal from the flow cell. Although the flow profile may be laminar a t very slow flow rates, the sharp corners commonly encountered in the flow cell can induce secondary flow at very low Reynold's numbers (10). This secondary flow, arising from the destabilizing effect of the velocity difference across the cell corners, takes the form of motion in vortices which results in efficient mixing within the cell. This mixing is superimposed upon the bulk from the cells, as shown in Figure 1. For the purpose of discussion, it is convenient to consider the two effects separately. Bulk flow from the cell may be divided into two components: one directed parallel to the cell axis and the other directed transverse to the axis. Axial bulk flow cools the sample by removing heated material from the exit and introducing unheated material at the entrance. This cooling results in a decreased temperature gradient at the beam axis, which increases the focal length of the thermal lens thereby reducing the enhancement of the effect. The time scale necessary for axial flow to influence thermal lens behavior is given by the residence time of the cell, which for either plug or turbulant flow is the cell volume divided by the flow rate; laminar flow would produce somewhat shorter effective residence times presuming the laser beam probes the center of the cell. The case of transverse bulk flow has been treated by several investigators (13-16), and its ramifications for thermooptical effects in jet-stream dye lasers has been studied (17,18). Transverse flow should be present in most flow cell designs since the sample introduction and removal are generally perpendicular to the beam axis. Transverse flow results in a movement of heat into the direction of flow, yielding a skewed temperature distribution within the cell. This distribution acts as a prism to deflect the beam against the direction of flow which results in a translation of the far-field profile from the initial beam center. The thermal lens effect of a flowing sample influenced by mixing is considerably more complex than for simple bulk flow. The time dependence of the effect could be obtained by convolution of the thermal lens impulse response (19) for a static sample with a correlation function which describes the time-dependent decrease in coherence of the temperature distribution due to random mixing within the cell (10). This correlation function decreases monotonically to zero after a characteristic mixing time and therefore results in a more rapid approach to steady state. If mixing occurs over times much longer than t,, the correlation function resembles a step function, so that flow has little influence on the thermal lens.
In the opposite case, where mixing occurs over much shorter times than t,, the thermal lens behavior is governed entirely by the time integral of the correlation function and not thermal diffusion. Although an exact mathematical model which accounts for bulk flow effects might be derived for very simple flow geometries, it is unlikely that it would be successful in describing typical flow cells where turbulence is dominant. Nevertheless, on the basis of the above qualitative description of the anticipated effects of mixing and bulk flow on the temperature distribution, several general predictions can be made. Since flow in a medium of constant refractive index has no effect on beam propagatiop (20), the initial intensity, Ih(O), is constant, independent of flow rate. At later times, the turbulant and bulk flow both act as an additional thermal transport mechanism, which has two results. First, the increased rate of thermal transport produces a more rapid approach to steady state. Second, the steady-state intensity change is smaller than that observed from a static, thermal diffusion limited case. These results follow by analogy to chemical kinetics, where the introduction of an additional reaction mechqnism increases the rate of reactant removal and decreases the equilibrium concentration. Overall, flowing the sample will, in general, decrease the observed enhancement, E, and increase the rate of approach to steady state. Further complications could arise if the flow severely distorts the radial symmetry of the temperature distribution, which could lead to an aberrant far-field beam profile. EXPERIMENTAL SECTION The argon ion laser based, thermal lens calorimeter has been described previously (21). The laser is operated for this work at X = 514.5 nm with a power measured at the sample of 160 mW regulated optically. A 40-cm focal length lens focuses the beam through a flow cell located one confocal distance beyond the beam waist and centered on the beam axis with x-y microscope translation stage. Two flow cells are used in the study: a 1-cm pathlength, 7 0 - ~ Lcell (Precision cells), and a 1-cm pathlength, 8KL cell (Gilson). The optical quality of the windows on the latter cell was found to be poor; they were replaced by carefully cut, borosilicate glass microscope slides. The spot size of the beam, calculated from the variation in thermal lens effect with position along the propagation axis (9),is smaller by a factor 0.3 than the radius of the flow cell, which minimizes diffraction from the edges of the cell. Aqueous solutions of CoClz are used in the study because they are stable (22)and the small absorptivity of the Co(HzO)B2+ion allows sufficiently large concentration samples to be prepared that errors in sample handling are minimal. The samples are pumped through the flow cell using a peristaltic pump (Gilson),calibrated by weighing the eluent. To observe the effect of flow on the temporal behavior of the thermal lens, a 100-point transient is sampled from Z&) at a l-k& sampling rate. One hundred replicates are averaged, and the result is fit to eq 4 by using a Marquardt algorithm (23). For determination of the effects of flow on the analytical response, a series of seven-point calibration curves are constructed at flow rates from 0.00 to 1.23 mL/min where the solution absorbance is varied at each flow rate from the solvent blank A = 1.7 X lo4 (determined by calibrating the enhancement with standard Twenty-five replicate measurements samples) to A = 6.0 X of Zb(0) and Zh(m) are made, and AZk/Zk(m) is the function that is averaged. The averaged result is converted to an expression, linear with absorbance, using eq 5. RESULTS AND DISCUSSION A study of the time-dependent behavior of the thermal lens in a flowing sample is carried out a t several flow rates, the results of which are presented in Figure 2. Since the initial intensity reflects the propagation of the laser beam through the unheated sample, its response does not change with flow, as expected. The signal at later times clearly shows the influence of flow on heat transport in the sample. For small
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
891
0
n
m
-
0
..
H
0 0
n
m 0
20
40
60
80
TIME (mS)
!
Table I. Time-Dependent Thermal Lens Response, Fit of Data to Diffusion Model enhancement, flow rate, residence E time constant mL/min time,a s (dimensionless) t,, ms
a
m
3.04 1.15
10.7 6.2 4.5
I
I
I
I
I
02
04
06
08
IO
IO0
Flgure 2. Timedependent thermal lens behavlor for flowin sample. The sample Is aqueous 2.0 X lo3 M CoCI,, A = 9.8 X 10- , and the flow cell volume Is 70 pL; pathlength Is 1 cm. The data represent 100 averages of 100 data points gathered at 1 kHz.
0 1.40 3.70
I
0
44 25 20
Residence time of the cell is defined as the cell volume
(70 pL) divided by the flow rate.
flow rates, the data may be fit to a thermal diffusion response, eq 4, where the flow increases the effective thermal conductivity of the sample. The results of this study, shown in Table I, point out the reduction in enhancement and time constant with increasing flow rate, where the ratio t , / E = 4.2 (k0.2) ms remains constant. This is consistent with an increase in the effective thermal conductivity, k , since k appears in the denominator of the expressions for both E and t,. Beyond a flow rate of 4 mL/min, the time dependence does not follow a perturbed thermal diffusion model as the flow becomes the dominant thermal transport process. The results in Table I are useful further in identifying the major heat conduction mechanism effecting the calorimetric response. Since the time constants determined are more than an order of magnitude shorter than the residence time, axial bulk flow can be ruled out as a significant contribution to the response. The effect of transverse bulk flow was investigated by observing the far-field beam profile for a strongly absorbing sample, where expansion in spot size was clearly visible to the eye. Since no beam deflection was observed under these conditions, transverse bulk flow can also be eliminated as a significant contributor to thermal transport. This leaves mixing to account for the observed flow response. As a check on this hypothesis, a partially mixed water-glycerol solution was pumped through the flow cell in order to visualize the flow profile as a schlieren pattern. A turbulent flow profile, indeed, was observed where the streamlines took the form of helices through the cell which would result in efficient mixing within the path of the laser beam. The analytical performance of the thermal lens under flowing sample conditions was evaluated by constructing a series of calibration curves over a range in sample absorbance from A = 1.7 X 10” to A = 6.0 X using the 8-pL flow cell. The thermal lens response (EA)converted from the raw data by using eq 5 , was found to be linear with absorbance ( R 2 0.994) for each of the six flow rates tested. The enhancement was determined for each flow rate from the slope of a linear
12
Flow R a t e (ml/min)
Figure 3. Variation in enhancement with sample flow rate. Enhancement was determined from the slope of the calibration curves. Cell volume is 8 pL; pathlength is 1 cm.
Table 11. Thermal Lens Analytical Results for Flowing Samples flow rate, std dev in dE/dv, detection min/mL limits, A mL/min EA, us 2.7 x 10-4 0 4.2 x 10-5 0 4.0 x 10-4 1.7 6.4 x 10-5 0.21 6.8 X 3.8 1.1 x 10-4 0.45 0.70 9.1 x 10-4 4.8 1.7 X 0.96 1.23
8.5 X 6.2 X
4.8 4.8
1.8 X
1.4 x 10-4
least-squares fit of the data, the results of which are shown in Figure 3. The onset of flow perturbation is initially small, until the characteristic mixing time is of the same order as the time constant for thermal diffusion. Beyond this point, the flow dominates the thermal conduction, and the change in enhancement with increasing flow is approximately linear. Although the reduction in enhancement due to flow represents a loss of sensitivity, the decrease observed is not particularly great for the flow rates used and could be overcome by an increase in laser power or the use of a solvent having more favorable thermooptical properties. The flowing sample significantly increases, however, the detection limits of the measurement defined as twice the standard deviation of the solvent blank converted to units of absorbance, as in Table 11. The increase arises from two sources: the first is the small loss of sensitivity (enhancement) and second is the large increase in the noise on the thermal lens response, EA, also listed in Table 11. This additional noise appears to be primarily due to the pulsed nature of the peristaltic pump, wherein fluctuations in flow rate are translated into fluctuations in enhancement by a change in the rate of thermal transport. Assuming this is the major flow dependent noise source, an expression for the observed variance in the thermal lens response, 02,would include a static contribution, ut, and a flow-dependent contribution
= go2 + A2(dE/dU)2g$ (6) where (dE/du) is the variation of enhancement with flow rate and:u is the variance in the flow rate. By use of the signal variance of the static sample as an estimate of go2and determination of (dE/du) by the slope of the curve in Figure 3, the standard deviation of the flow rate was calculated for each of the experiments by using eq 6. The results, a, = 0.94 (k0.07) mL/min, was observed consistently at each flow rate. The actual value obtained for u, is larger than expected but is probably biased by the fact that the distribution of flow variation is not Gaussian. An additional confirmation of the effect of flow fluctuation on enhancement was visible to the eye, for strongly absorbing samples, in the expansion and contraction of the far-field spot size, synchronous with the :g
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Anal. Chem. 1981, 5 3 , 692-695
mandrels of the peristaltic pump contacting the manifold tubing.
CONCLUSIONS The results of this study have shown that thermal lens calorimetry is tolerant of flowing samples at flow velocities which would be suitable for applications in liquid chromatography or automated analysis. Although some reduction in sensitivity is observed, the major loss in performance is the increase in detection limits due to flow pulsations adding to the proportional noise. Several improvements in the system could reduce this problem. The peristaltic pump provides a worst-case example of pulsations; a pulse-damped, dual-piston pump or a syringe pump would greatly improve the situation. Furthermore, a differential thermal lens calorimeter (24), where reference and sample cells are placed on opposite sides of the beam waist, has been shown to exhibit excellent immunity to enhancement fluctuations and could be applied to a flowing sample experiment. One possible advantage of flowing the sample could be expected when the solvent composition is changed or otherwise unknown. Under static conditions, the sensitivity (enhancement) of a thermal lens measurement is governed by the thermal conductivity, K, and (dn/dT) of the solvent. When the mixing process induced by flow dominates heat transport, however, the enhancement should be less significantly effected by the thermal conductivity of the solvent. This could, therefore, reduce the dependence of sensitivity on solvent composition.
LITERATURE CITED (1) Freeman, N. K.; Upham, F. T.; Wlndsor, A. A. Anal. Lett. 1973, 6 , 943-950.
(2) Deiboid. G. J.; Zare, R. N. Sclence 1977, 196, 1439-1441. (3) Yeung, E. S.; Steenhock, L. E.; Woodruff, S. D.; Kuo, J. C. Anal. Chem. 1980, 52, 1399-1402. (4) Hu, C.; Whlnnery, J. R. Appl. Opt. 1973, 12, 72-79. (5) Hordvlk, A. Appl. Opt. 1977, 76, 2827-2833. (6) Kreuzer, L. B. US. Patent 4048499, 1977. (7) Gordon, J. P.; L e k , R. C. C.; Moore, R. S.; Porto, S. P. S.; Whinnery, J. R. J. Appl. PhyS. 1965, 36,3-8. (8) Whinnery, J. R. Acc. Chem. Res. 1974, 7 , 225-231. (9) Harris, J. M.; Dovlchl, N. J. Anal. Chem. 1980, 52, 695A-706A.
( I O ) Hunt, J. N. "Incompressible Fluid Dynamlcs"; American Elsevkr: New York, 1964. (11) Carslaw, H. S.; Jaeger, J. C. "Operatlonal Methods In Applled Mathematics", 2nd ed.;Oxford University Press: London, 1948; Chapter VI. (12) Dabby, F. W.; Gustafson, T. K.; Whinnery, J. R.; Kohanzandeh, Y.; Kelley, P. L. Appl. Phys. Lett. 1970, 16, 362-388. (13) Akhamanov, S. A.; Krindach, D. P.; Migulin, A. V.; Sukhorukov, A. P.; Khokhlov, R. V. I€€€ J . Quantum Electron. 1966, QE-4, 568-575. (14) Gebhardt, F. G.; Smlth, D. C. Appl. Phys. Lett. 1969, 74, 52-54. (15) Smith, D. C.; Gebhardt, F. G. Appl. Phys. Lett. 1970, 16, 275-278. (16) Gebhardt, F. G.; Smlth, D. C. Appl. Opt. 1972, 1 7 , 244-248. (17) Wellegehausen, B.; Laepple, L.; Welling, H. Appl. Phys. 1975, 6 ,
335-340. (18) Teschke, 0.; Whlnnery, J. R.; Dlenes, A. I€€€ J. Quantum Electron. 1978, QE-12, 513-515. (19) Twarowski, A. J.; Kliger, D. S. Chem. Phys. 1977, 20, 253-258. (20) Rohde, R. S.; Buser, R. G. Appl. Opt. 1979, 18, 898-704. (21) Dovlci, N. J.; Harris, J. M. Anal. Chem. 1981, 53, 108-109. (22) Burke, R. W.; Deardorff, E. R.; Menls, 0. J. Res. Nat. Bur. Stand., Sect. A 1972, 76, 469-478. (23) Bevington, P. R. "Data Reductlon and Error Analysis for the Physlcal Sclences"; McGraw-Hill: New York, 1989; Program 11-5. (24) Dovichl, N. J.; Harris, J. M. Anal. Chem. 1980, 52, 2338-2342.
RECEIVED for review November 4, 1980. Accepted January 12,1981. This material is based upon work supported by the National Science Foundation under Grant CHE79-13177. Fellowship support (N.D.) by the Phillips Petroleum Co. and the American Chemical Society, Division of Analytical Chemistry (sponsored by General Motors), is acknowledged.
Enrichment of Nickel and Cobalt in Natural Hard Water by Donnan Dialysis Robert L. Wilson and James E. DINunzio" Department of Chemistry, Wright State University, Dayton, Ohio 45435
Donnan dlalysis enrichment was used for the determination of nlckel in natural rlver water by flame atomic absorptlon spectrophotometry. The optimum receiver electrolyte composition was found to be a compromlse between maxlmum enrlchrnent and the effects of the electrolyte on the signal to nolse ratio. The presence of phosphate In the sample was found to influence both the precision and accuracy of the method. However, adjustment of the sample pH prior to enrichment eiimlnated this problem. The use of cobalt as an internal standard Improved the preclslon and ellmlnated matrlx interferences.
Ion-exchange membranes have been used under conditions of Donnan dialysis ( I ) for a number of anlytical applications. In this process an ion-exchange membrane is used to separate solutions of differing ionic strength. As the system approaches Donnan equilibrium, trace level ions in the dilute sample soluton will migrate into the more concentrated receiver solution (2, 3). If the volume of the receiver solution is much
less than that of the sample, an enrichment of these ions can be accomplished. Since the rate of transfer of these ions is directly proportional to concentration, enrichment for a prescribed time can be used as a method of preconcentration prior to analysis. This technique has been used for the enrichment of both anions ( 4 , 5 )and cations (6, 7). Although Donnan dialysis enrichment has been used successfully as a preconcentration method prior to chemical analysis, few applications of the technique to natural samples have been reported. This may be due to the fact that a number of interferences are present in natural waters. The interferences include surfactants which can foul the membrane (8),chelating agents (9, IO),and an unknown and usually high ionic strength. These factors can interfere with the enrichment technique by altering the ion transfer rate across the membrane. The purpose of this paper is to report on the successful application of Donnan dialysis enrichment for the preconcentration of heavy metals from natural hard water. In this study Ni(I1) and Co(I1) were chosen as test species; however, since the enrichment process is nonspecific and operates on
0003-2700/61/0353-0692$01.25/00 1981 American Chemlcal Society
