680 OPTICS LETTERS / Vol. 34, No. 5 / March 1, 2009

Current-induced thermal-lens spectrometry

Pavel A. Gorkin,1 Mikhail A. Proskurnin,2,* Boris K. Zuev,1,3 Andrei A. Zhirkov,1 and Vladimir V. Yagov1

1Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, ul. Kosygina,d. 19, 119991 Moscow, Russia

2Department of Chemistry, M.V. Lomonosov Moscow State University, Vorob’evy gory, d. 1 Stroen 3,119991 Moscow, Russia

3“Dubna” International University of Natural, Social, and Human Sciences, ul. Universitetskaya, d. 19, Dubna,141980 Moscow Region, Russia

*Corresponding author: michael@analyt.chem.msu.ru

Received November 10, 2008; revised January 4, 2009; accepted January 23, 2009;posted February 3, 2009 (Doc. ID 103938); published February 26, 2009

A new spectroelectrochemical method using the thermal-lens effect from electrolytes using regular jouleheat generation by current focusing in a small-sized channel is proposed. The experimental dependences ofthe signal on the analyte concentration and applied voltage are in good concordance with the theoreticalestimations. A cell design providing good reproducibility and sensitivity of measurements is proposed.© 2009 Optical Society of America

OCIS codes: 120.1880, 120.6810, 300.6430, 350.6830, 350.5340.

Thermal-lens spectrometry (TLS) is a highly sensi-tive method for determining trace substances in awide range of materials [1,2]. Laser-induced TLS(LITLS) is based on the formation of a regular tem-perature field as a result of nonradiative relaxationof the absorbed radiation, which is similar in actionto that of a divergent lens and is referred to as a ther-mal lens [1,3]. The overall sensitivity of quantifica-tion using TLS depends not only on the effectstrength but rather on the regularity of the actingtemperature field [2,4].

Nowadays, photoinduced thermo-optical effects aredominant. However, alike in luminescence spectros-copy, the nature of the external source excitingthermo-optical phenomena is not restricted; the onlyrequirement is a regular temperature field that canbe related to the concentration of a sample compo-nent [1]. In our opinion, joule heating is a good can-didate for an alternative excitation source forthermo-optical measurements of conducting ana-lytes. In this case, the action of the excitation laser[1,5,6] is replaced with a similar effect from an elec-tric current, which is focused in a small volume (Fig.1) [7]. Thus the aim of this Letter is a theoretical es-timation of parameters of current-induced TLS(CITLS) and its experimental verification on a modelsystem.

In TLS, the signal is expressed as a probe-beam in-tensity change on a thermal lens [1,8]:

� �Ip�0� − Ip�t�

Ip�t�, �1�

where Ip�0� and Ip�t� are intensities at the center ofthe probe beam at a distant detector plane before theformation of a thermal lens and at a moment t, re-spectively.

The deduction of the equation for CITLS was madefor short-current pulses (up to 1 ms to avoid diffusioneffects) in a narrow cylindrical channel in a dielectricmembrane dividing the cell with two electrodes in

which the current is focused (Fig. 1). The first tests

0146-9592/09/050680-3/$15.00 ©

using finite-element analysis modeling showed (Fig.1, inset) that isothermal lines from current-inducedheating resemble a point heat source, which simpli-fies the deduction. Apart from short excitation times,we used the following assumptions: (1) The resis-tance of the solution is much higher than that of elec-trodes and (2) the heat emerging at electrode sur-faces is much lower than the heat dissipating in thechannel. (These conditions are readily met if the elec-trode surface area is much larger than the channelcross-section area.) (3) The channel diameter is muchsmaller than the size of the other parts of the cell(current density in these parts is negligible). (4) Theresistance of the membrane material is infinitelyhigh (an ideal dielectric). (5) The solution is consid-ered dilute (equivalent conductivity � can be equaledto ion mobility). Under these conditions, the emerg-ing heat Q is determined by joule heating (takinginto account the interconnection of the specific con-ductivity � and electrolyte concentration �=�c) [9]:

Q = U2�lt = U2�lct, �2�

where U is the voltage at the electrodes, l is channellength, and t is heating time. The temperature rise is

Fig. 1. Schematics of the experimental setup for current-induced thermal-lens measurements with an inset showinga numerically calculated temperature field (COMSOL Mul-tiphysics) in the working channel (along the optical axis,1 mm; diameter, 1.5 mm). See the text for other experimen-

tal parameters.

2009 Optical Society of America

March 1, 2009 / Vol. 34, No. 5 / OPTICS LETTERS 681

�T =Q

�CpV= �T

U2�ct

�Cprcs2 , �3�

where V=�lrcs2 is channel volume and rcs is its cross-

section radius. The due account for the experimentalparameters of the cell can be made by adding a heatyield �T. This factor is a function on the membranematerial, channel dimensions, and the distancesfrom electrodes to the channel. As the nature ofthermo-optical phenomena principally affects the so-lution of the temperature field only, all the existingtheories on calculating the field of the refractive in-dex [1,2,4] and photothermal-element probing [8,10]are not affected by the heating source and can beused in CITLS as in LITLS. Thus, using Eq. (3) as atemperature field for generic mathematical appara-tus of TLS, which is discussed elsewhere [1], and sim-plifying it with the expressions for the thermal-lensenhancement factor E0=−�dn /dT� /�pk (k is thermalconductivity) [4] an thermal diffusivity DT=k /�Cp(where Cp is isobaric heat capacity and � is density)by multiplying and subtracting Eq. (3) by k�p, pro-duces the sought-for expression

�CITLS = B�p��TU2/rcs2 �tE0DT�c, �4�

where B�p is the term combining all the geometryconstants of the probe beam [10]. Equation (4) pre-dicts a linear dependence of the signal on the concen-tration of the target electroconducting substance.The signal is also proportional to the power density ofthe source U2 /rcs

2 . The E0DT term, which gathersthermo-optical parameters of the solvent, predictsthe same level of influence of thermo-optical proper-ties on the amplitude and development of the signalin CITLS as in LITLS.

The cell (protected with a patent [7]) is a polymeth-ylmethacrylate cylinder with a radius of 30 mm andwall thickness of 5 mm with glass windows with a ra-dius of 20 mm, which is divided in the middle by aninsulating fluoroplastic membrane (thickness,1 mm), which has a working channel with a radius of0.75 mm. Each compartment has a platinum elec-trode of the length of 18 mm (the distance betweenelectrodes is 66 mm, and the distance from the opti-cal axis is 5 mm). A He–Ne 632.8 nm laser (SP 106-1,Spectra-Physics, Eugene, Ore.; 632.8 nm, 5 mW inthe sample; beam waist, 110 m) beam is directedthrough both windows and the center of the channel,and the changes in beam divergence Ip�t� [Eq. (1)] ismeasured at the center of the beam by a far-fieldFD-7K photodiode (Russia) (sample-to-detector dis-tance, 40 cm) with a KS-11 stained-glass bandpassfilter and a 2-mm-diameter pinhole (see [10] for pa-rameter selection). Data collection is controlled by apersonal computer through an ADC–DAC board. Foreach sample, the signal was derived from the averageof 7–11 replicate measurements.

Sodium chloride (pa grade) solutions in distilled(specific resistance, 5 M cm) water served as model

electrolytes. At this stage, we did not succeed in

deducing the analytical form of the dependence of �Ton the cell parameters, and only a numerical estima-tion was possible. Such an estimation for the selectedgeometry using finite-element simulation (which waspreviously used for similar tasks in LITLS [11]) withCOMSOL Multiphysics v. 3.4 (COMSOL, Inc., Mass.)gives �T=0.7±0.1.

To estimate the sensitivity of the setup, we used acriterion taking 1 mK as a minimum heating thatcan be reliably measured with a change in the diver-gence of the probe beam as a thermal-lens effectagainst other environmental factors affecting tem-perature and refractive index in solution [1]. FromEq. (3) we calculated that the specific resistance pro-viding a constant heating rate of 1 mK/s for a voltageof 100 V are about 50 M cm, which corresponds to aconcentration of 10−7 M of a common electrolyte likeNaCl. However, the real sensitivity of the methodshould be degraded owing to the own specific resis-tance of water of 26.3 M cm [12]. Thus concentra-tions that can be measured at 100 V in an aqueoussolution are about 10−6 M, unless a background-subtraction technique to compensate solvent signal isused. This estimation can be used as a minimumlimit of detection achieved with this simplest ap-proach to a CITLS experiment with an electrolyte inwater.

To estimate the interfering effects that can accom-pany CITLS, we estimated the effects from the diffu-sion and electrochemistry. Under the experimentalconditions, the electrochemical reaction producinghydrogen and oxygen gases at the electrodes takesplace. The heat effect of this reaction is 0.07 J for 7�10−2 M and 1�10−5 J for 1�10−5 M NaCl. This ef-fect cannot be neglected compared with the jouleheating in the channel. However, as electrodes are lo-cated �5 mm above the channel, the electrochemicalheating is 0.1 K for the maximum concentration of7�10−2 M and 2�10−5 K for 1�10−5 M NaCl, whichis insignificant compared with CITLS. The electro-chemical processes at electrodes may also produce apH gradient between the anode and cathode compart-ments of the cell. The pH will increase at the cathodewhere the hydrogen gas is produced and decrease atthe anode. Under the selected conditions, the charac-teristic time for this process is 1700 s, which is muchlonger than the experiment time, and electro-osmoticflow through the channel can be considered negli-gible.

The relation between thermal-lens signal calcu-lated from Eq (1) for 10–90 V, with a 0.07 M NaCl(Fig. 2) revealed that the signal is proportional to thesquare of the applied voltage with the coefficient ofcorrelation of 0.9961, which is in good concordancewith Eq. (4). The reproducibility of measurementswas investigated for 10–90 V and 0.005 M NaCl andshowed (Fig. 3) that the minimum signal that can bemeasured with relative standard deviation (RSD)�0.3 is achieved for �CITLS 0.04; thus the corre-sponding voltage should be above 40 V. However, afurther increase in the voltage is unsuitable, as it de-creases the linear dynamic range of the setup. There-

fore the voltage of 41.6 V was set as working.

682 OPTICS LETTERS / Vol. 34, No. 5 / March 1, 2009

The calibration plot is obtained for c= �1�10−5�− �7�10−2�M NaCl (Fig. 3, inset). The equation�U=41.6 V� is

�CITLS = �860 ± 10�c + �0.4 ± 0.1��r = 0.998,n = 37,P

= 0.95�. �5�

Fig. 3. RSD for CITLS and LITLS for the same probe-beam geometry as a function of the signal (error curve).The data for LITLS are previously recorded for the sameprobe-beam geometry and reproduced from [13]; the datafor CITLS were collected for the voltage 10–80 V for0.005 M NaCl. The inset shows a calibration plot ofthermal-lens signal on NaCl concentration at applied volt-

Fig. 2. Dependence of the thermal-lens signal [Eq. (1)] onthe applied voltage for 0.07 M NaCl for three replicate ex-periments marked with similar marks and a parabolic ap-proximation of the whole series of the results. The insetshows a development of thermal lens signal (a decrease inthe probe-beam light intensity), with time upon increasingthe voltage, in one of these replicate measurements (setupsoftware capture screen).

The linear range covers at least 3 orders of magni-tude. The theoretical calibration slope, Eq. (4), is950±50 L/mol, which is in good agreement with theexperiment. The limit of detection of NaCl for 90 V is5�10−6 M, which is fivefold higher than the aboveestimated value, which correlated with the ratio ofspecific resistances of the pure and used water�26.3/5�5.3�. The blank signal from Eq. (5) corre-sponds to the specific resistance 4 M cm, which is insatisfactory agreement with the value of specific re-sistance of the used distilled water.

Thus CITLS expands the possibilities of photother-mal spectroscopy to spectroelectrochemical methods.The correctness of the deduced theoretical equationof CITLS is confirmed by model experiments, and thesuitable sensitivity for the first experiments with anew method is achieved. It was experimentally con-firmed that CITLS gives a more reproducible signalthan LITLS under the same probing conditions. Weshould emphasize that the evaluation of the maxi-mum sensitivity of CITLS principle was out of thescope of this Letter, and the theoretical and practicallimits of detection are rather figures of merit for theused setup and solvent. As a whole, CITLS can beused as a tool for more complex investigation of pho-tothermal and thermo-optical phenomena and showssome potential in chemical-analysis applications asregular and simple schematics.

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