Combined Photothermal Lens and Photothermal Mirror Characterization of Polymers Odon S. Are´stegui,a Patricia Y.N. Poma,a Leandro S. Herculano,a Gustavo V.B. Lukasievicz,a Francine B. Guimara˜es,a Luis C. Malacarne,a Mauro L. Baesso,a Stephen E. Bialkowski,b Nelson G.C. Astratha,b,* a b

Departamento de Fı´sica, Universidade Estadual de Maringa´, Maringa´, PR 87020-900 Brazil Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322 USA

We propose a combined thermal lens and thermal mirror method as concurrent photothermal techniques for the physical characterization of polymers. This combined method is used to investigate polymers as a function of temperature from room temperature up to 170 8C. The method permits a direct determination of thermal diffusivity and thermal conductivity. Additional measurements of specific heat, linear thermal expansion, and temperature-dependent optical path change are also performed. A complete set of thermal, optical, and mechanical properties of polycarbonate and poly (methyl methacrylate) samples are obtained. Methods presented here can be useful for in situ characterization of semitransparent materials, where fast and non-contacting measurements are required. Index Headings: Photothermal mirror; Photothermal lens; Photothermal methods; Material characterization.

INTRODUCTION Photothermal methods have been extensively used to measure the thermal, optical, and mechanical properties of a variety of solids, liquids, and gases for many decades.1-5 The photothermal methods are based on light-induced heat generation in the sample, followed by changes in temperature or related thermodynamic properties of the sample. The thermally induced perturbations are detected by measuring, for instance, internal changes in refractive index, surface deformation, and pressure, comprising together a group of very sensitive spectroscopic tools for material characterization.1–5 The light-induced changes in the refractive index of the sample initially follow the spatial distribution of the excitation laser beam, and a time-dependent optical element is formed in the excited volume of the sample. The spatial distribution has a radial profile and a thermal lens (TL) effect.6,7 This effect can be probed using another laser beam passing through the optical excited volume. The TL affects the propagation of the probe beam, and the signal is measured by analyzing the timedependent far-field probe beam focusing or defocusing.6 The TL method has been used as a highly sensitive technique in optical absorption.8–16 Its strength is related to the optical absorption coefficient, the temperature dependence of the optical path change, and the analyte concentration. The time evolution of the TL effect Received 28 November 2013; accepted 7 February 2014. * Author to whom correspondence should be sent. E-mail: astrathngc@ pq.cnpq.br. DOI: 10.1366/13-07404

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depends on the heat diffusion properties of the sample. Transient signal analysis gives direct quantitative access to thermal and optical properties of the sample.7,12-15 In addition, the remote characteristics of the TL method make this appropriate for measurements in a controlled environment, where temperature changes or other external fields are applied.14,17,18 Thermal lens measurements require the transmission of both the probe and the excitation beams through the sample, thus limiting the applications to semitransparent materials. An alternative detection based on surface deformation can be used for material characterization of semitransparent and opaque materials. 1 9 – 2 9 Surface deformation occurs when an excitation laser beam irradiates a solid sample, resulting in expansion/contraction of the surface. A reflected probe laser is used to detect the deformation in the thermal mirror (TM) effect.30 The TM effect has been exploited in several photothermal techniques that are fast, non-contacting, and highly sensitive tools for material characterization.1,20,24,29 The effect can be measured as the TL is measured, by analyzing the focusing/defocusing far-field probe beam reflected off the sample surface.29,31,32 Its amplitude is directly related to the optical absorption and thermal expansion coefficients. Like the TL effect, the time evolution of the deformation depends on the heat diffusion properties of the sample. Thus, measuring the transient effect allows direct quantitative access to thermal, optical, and mechanical properties of the material.24–29 In addition, recent theoretical developments opened the way for the application of these methods for analytical characterization of transparent to opaque solids,1,6 considering the effects of population lens in fluorescent materials and photochemical reactions and mass diffusion during laser excitation.33–36 The TM method can be used concurrently with the TL method.37 The apparatus can be compact and fully automated, making this especially interesting for in situ measurements. In situ testing is indispensable for preproduction control and quality monitoring. Measuring and investigating materials at production conditions is, in fact, pointed out as the single most challenging issue among polymer and materials laboratories.38 This paper uses a concurrent photothermal method for fast polymer characterization. Since physical properties of polymers may be strongly dependent on temperature, it is desirable to measure their absolute values as a function of temperature. Here, TL and TM methods are used

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concurrently to investigate polymers as a function of temperature, from room temperature up to 170 8C. Thermal diffusivity and thermal conductivity are measured in addition to specific heat, linear thermal expansion, and temperature dependence of optical path change. A complete set of thermal, optical, and mechanical properties of polycarbonate and poly (methyl methacrylate) samples is obtained. It is shown that the concurrent method presented here can be a useful tool for in situ characterization of semitransparent materials where fast and non-contacting measurements are required.

THEORY The basic principle of the photothermal techniques employed in this work is the photoinduced heat generation using nonradiative decay processes following optical excitation of a sample. In this work, a singlemode TEM00 laser beam is used to excite a solid sample, and another single-mode TEM00 laser beam, nearly collinear to the excitation beam, is used to probe the TL and TM effects. Figure 1 shows a schematic diagram of the laser beams at the sample. The probe beam travels through the sample and probes the change in the refractive index resulting in the TL effect. The reflected probe beam fraction is affected by surface deformation resulting in the TM effect. The radii of the excitation and probe beams at the sample are w0e and w1p , respectively. The probe beam propagates along the z direction and the sample is located at z = 0. Photodetectors are used to monitor the transmitted and reflected probe beam intensity variations in the far-field. The distance between the sample and the photodetector plane is Z2, and the distance between the sample and the probe beam waist of radius w0p is Z1. The theoretical descriptions for the TL and TM effects entails calculations of the sample temperature change and the effects of this temperature change on the optical path change (TL) and the thermoelastic surface deformation.39,40 Thermal state perturbations produce phase shifts in the probe beam wave front, altering the complex amplitude of the probe beam at the detector plane. The probe beam intensity changes past a pinhole spatial filter. Only the central part of the probe beam is monitored at the detector, leading to further simplifications in the modeling.6,29 Concerning the transparent polymers investigated in this work, the low optical absorbing TL and TM models

could be used.6,31 The advantage of using the weak absorbing approximation is that modeling becomes relatively simple, and semianalytical expressions can be used to describe the TL and TM transient signals. This approximation has been extensively tested and used to model previous experiments.6,7,12–17,29–31 The semianalytical expressions have been shown to produce accurate results for TL and TM effects in the semitransparent materials studied to date. Also assumed is that the dimensions of the sample are large compared with the excitation beam radius, avoiding edge effects, and that the optical absorption of the sample is low enough that the excitation laser intensity is not attenuated along the direction of travel. The laser induced temperature change in the sample, DT(r,t), is given by the solution of the heat diffusion equation.6 Sample deformation caused by the temperature gradient described evolves following the Navier-Stokes thermoelastic equation.38 The axially symmetric radial nature of the Gaussian heat source requires the problem to be treated in cylindrical coordinates, and, in the quasistatic approximation, the solution for the surface displacement uz (r,t) for a sample of thickness L has been proposed by introducing displacement potential functions.30,38 The strength of the TM effect is hTM ¼ 

Pe Ae aT ð1 þ mÞ/ kp k

ð1Þ

where aT is the linear thermal expansion coefficient, m is the Poisson ratio, kp is the probe beam wavelength, k is the thermal conductivity, Pe = P0 (1  R), P0 is the excitation power, R is the sample surface reflectivity, Ae is the optical absorption coefficient at the excitation beam wavelength ke, and / is the heat yield: the amount of absorbed energy converted to heat. In addition to the surface deformation, the sample’s temperature rise distribution produces a refractive index change. Both effects act as optical elements causing phase shifts to the transmitted (TL) and reflected (TM) probe beam. In two limiting cases, the plane stress and the plane strain approximations, the phase shift for the TL effects is directly proportional to the temperature change, UTL = (2p/kp) L(ds/dT)TL [DT(r, t)  DT(0, t)], with (ds/dT)TL describing the temperature coefficient of the optical path change.39 For the TM effect, the phase shift is related to the surface deformation by UTM = (2p/kp) 2[uz(r,t)  uz(0,t)], with uz(r,t).31 The produced phase shifts are thus7,32    Z t 1 2mg 1  exp  UTL ðg; t Þ ¼ hTL d s ð2Þ 1 þ 2s=tc 0 tc þ 2s and Z w20e ‘ coshðLaÞ  1 UTM ðg; t Þ ¼ hTM tc 0 La þ sinhðLaÞ Z t  w20e ð1þ2s=tc Þa2 =8 3 e ds 0

FIG. 1. Geometrical representation of the laser beams for the TL and TM experimental setups.

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  pffiffiffiffiffiffiffi 3 J0 ðaw0e mg Þ  1 d a

ð3Þ

Here, J0(x) represents the Bessel function of the first kind, g ¼ ðr =w1p Þ2 , m ¼ ðw1p =w0e Þ2 , tc ¼ w20e =4D is the characteristic thermal time constant, D = k/qCp is the thermal diffusivity of the sample, and Cp and q are specific heat and mass density of the sample, respectively. The strength of the TL effect is given by hTL ¼ 

Pe Ae Lðds=dT ÞTL / kP k

ð4Þ

The transmitted and reflected probe beams propagate to the detector plane in the far-field at a distance Z2 from the sample. The propagation can be treated using Fresnel diffraction theory. The time-dependent intensity variation of the central portion of the probe beam at the detector is dependent on the phase shift Uj (g,t) produced by either the thermal lens (j  TL) or the th R ‘e r m a l m i r r o r ( j  T M ) e f f e c t s a s I ( t ) = j 0 exp½ð1 þ iV Þg  iUj ðg; t Þdgj2 :6,29 The geometrical parameter V = Z1/Zc þ Zc [(Z1/Zc)2 þ 1]/Z2, and Zc is the confocal distance of the probe beam. I(t) is calculated by substituting one of the equations for the phase shift, Eqs. 2 or 3, into I(t) and carrying out numerical integration over a, s, and g. Though it is convenient in most applications to simplify the TL signal by assuming that the phase shift induced is very small, i.e., UTL(g, t)  1, and the approximation e iUðg;t Þ  1  iUðg; t Þ holds, leading to the well-known analytical expression6 8 < hTL tan1 Iðt Þ ¼ Ið0Þ 1  : 2 2

2mV

3

g

2

5 34 tc ½ð1 þ 2mÞ2 þ V 2 =2t þ 1 þ 2m þ V 2

ð5Þ The temperature changes induced in a sample are generally small in the TL and in the TM experiments, ,1 8C, which, in turn, produce similarly small surface refractive index changes. Consequently, changes in the probe beam intensity due to surface reflectivity effects can be safely neglected without affecting the accuracy.

EXPERIMENTAL SECTION The TL and TM experiments can be concurrently arranged in a way that both measurements can be performed simultaneously. The schematic diagram of the TL–TM apparatus used in this work is presented in Fig. 2. The method is represented in the dual beam mode-mismatched experimental configuration, in which the sample is excited and probed using beams of different diameters. The experiments are very similar in essence to apparatuses previously described in many reports.6–17,29,33 The excitation source is a continuouswave single-mode TEM00 Arþ ion laser at ke = 514.5 nm (Coherent, Innova 90). A mechanical shutter (ThorLabs, Model SH05) controls the exposure of the excitation beam on the sample. The excitation beam was focused in the sample using a 0.25 m focal length lens. A

FIG. 2. Schematic of the TL and TM experimental setup. Mi, Li, and Pi stand for mirrors, lenses, and photodiodes, respectively. The experimental parameters are w0e = 79 lm, w1P = 515 lm, m = 42.5, and V = 6.0.

continuous-wave single-mode TEM00 He–Ne laser at kp = 632.8 nm (Melles Griot, Model 25-LHR-151-249), nearly collinear to the excitation beam (angle ,18), is used to probe both the TL and the TM effects. After being reflected off of the sample surface, the probe beam propagates to the photodetector P2 positioned in a far-field (Z2 . 4 m) and probes the TM effect. Its transmission through the sample propagates to the photodetector P3 and probes the TL effect. P2 and P3 (ThorLabs, Model DET100A/M) were assembled with pinholes and probe beam laser line filters. Only the central part of the probe beam is then detected using either photodiode and recorded using a digital oscilloscope (Tektronix, Model TDS1001B). The oscilloscope is triggered by P1 (ThorLabs, Model PDA10A). The response time of the photodiodes is ,50 ls. The experimental parameters are shown in the caption of Fig. 2, which were measured as described elsewhere.6,14 A computer was used to control (using Labview) the experimental apparatus and the measurements. A sample holder containing a heater and a heat sink device was used for temperature data measurements.16 Thermal paste was used to improve the thermal contact between the sample and the thermal reservoir. The heater temperature was controlled using a temperature controller (LakeShore, Model 340) with a resolution of 0.01 8C. Polymers of different thicknesses were investigated in this work. Polycarbonate (PC from Sigma-Aldrich Inc.) and poly(methyl methacrylate) (PMMA from Diamond Inc.) samples were prepared for the TL–TM measurements in cylinders of radius of 10 mm and polished in different thicknesses. In addition to the photothermal measurements, a homemade thermal relaxation calorimeter41 and a

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FIG. 3. Normalized TL and TM signals, I(t)/I(0), for PC and a TL signal for PMMA at room temperature.

commercial dilatometer (Netzsch, Model DIL402PC) were used to measure the specific heat and the linear thermal expansion coefficient, respectively, as a function of temperature. The temperature dependence of the optical path change was measured using an optical interferometer,42 and mass density and refractive index measurements were performed using a standard Archimedes method and an interferometer,43 respectively.

RESULTS AND DISCUSSION The samples were first characterized at room temperature. For the TL–TM experiments, the samples were excited at different excitation power levels. More than 100 transients were averaged at each excitation power. Figure 3 shows examples of TL and TM transients for PC (L = 1.00 mm) and a TL transient for PMMA (L = 1.82 mm) samples. For the normalized TL signal, Fig. 3a, the transients results from a decreasing intensity at the photodetector. A decreasing signal is a result of a defocusing thermal lens forming in the sample. A divergent thermal lens results from (ds/dT)TL , 0. Most polymers presented in this report exhibit a divergent thermal lens. As for the normalized TM signal, Fig. 3b, the decreasing signals arise from surface expansion due to the positive linear thermal expansion coefficient of the polymer samples. The expansion produces a convex mirror, which in turn defocuses the probe beam intensity at the pinholedetector plane. The transients were obtained with excitation power levels of up to 150 mW, and a few examples are displayed in Fig. 3b. TM measurements were performed only on PC samples. The signal decay times depend directly on the heat diffusion properties of the samples, while the amplitude

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of both the TL and the TM effects depend on the optical path change and thermal expansion of the sample, respectively. The thermal diffusivity D and the parameter hTL and hTM were obtained from regression using the theoretical models, Eq. 5 for TL, and I(t) with Eq. 3 for TM. Regression with the TM model was performed using the ‘‘NonlinearModelFit’’ function in Wolfram Mathematica 7. Thermal diffusion constants are presented in Table I. The thermal constants are found to be D = (1.8 6 0.1) 3 107 m2 s1 for PC and D = (0.8 6 0.1) 3 107 m2 s1 for PMMA. These are within the range of values expected for these materials.44 The signal amplitudes hTL and hTM depend on the excitation power. Figures 3c and 3d shows the excitation power dependence of these amplitudes. From the linear fit, the coefficients hTL Pe1 L1 and hTM Pe1 are obtained. Average values are presented in Table I. hTL and hTM are directly related to the optical absorption coefficient, heat yield parameter, thermal conductivity, and optical path change for hTL, or the linear thermal expansion coefficient for hTM. Thus, amplitude measurements of TM and TL effects allow quantitative access to thermal, optical, and mechanical properties of the material. In order to ensure the accuracy and repeatability of the measurements, several TL and TM transients were recorded at room temperature. The accuracy of the measurements was then evaluated using the standard deviation of the measurements with a 90% confidence interval. The determined parameters, D and hj, reported in this study are then the average of all the repeated measurements within 90% confidence levels. The temperature dependence of D and hj were obtained by performing TL and TM measurements from room temperature up to 170 8C. The experiments were performed using a heating rate of 0.5 8C/min. Each consecutive excitation time interval was 30 s, which was an adequate delay to obtain the complete TL or TM signal relaxation between each measurement. The TL and TM transients were fit to the models, and the resulting parameters are shown in Figs. 4 and 5. Figure 4a presents the temperature dependence of the thermal diffusivity, D(T), obtained using TL and TM for PC and PMMA. The D(T) shows a slight decrease with temperature below 150 8C for PC and 75 8C for PMMA. The thermal diffusion varies between 1.82 3 107 m2 s1 and 1.48 3 107 m2 s1 for PC and 0.88 3 107 m2 s1 and 0.84 3 107 m2 s1 for PMMA. Large D(T) variations are observed near the glass transition temperatures. Note the difference between the onset of the transition observed on the thermal diffusivity data for PC as measured using TL and TM results. This could be a result of the temperature dependence of the physical properties of the sample near the glass transition. The thermal conductivity, k(T), can be determined by independently measuring the specific heat (Cp) and the mass density as a function of temperature using the relation k(T) = q(T)Cp(T)D(T). The volumetric thermal expansion coefficients of these polymers at room temperature are on the order of 2 3 104 K1 and around 10% larger near the glass transition. Thus, the variations in the volumes in the considered temperature interval here are less than 2% for both samples. Also, the mass

TABLE I. Physical properties of PC (L = 2.3 mm) and PMMA (L = 2.0 mm) at room temperature.

7

2

1

D (10 m s ) hTL Pe1 L1 (103 W1 m1) hTM Pe1 (103 W1 m1) q (kg m3) Cp (J Kg1 K1) k (Wm1 K1) Ae @514.5 nm (m1) m44 n (ds/dT)OI (106 K1) (ds/dT)TL (105 K1) dn/dT (105 K1) aT (105 K1) u (105 K1) DSO (105 K1) Tg (8C)

PC

PMMA

1.8 6 0.1 4.6 6 0.5 2.8 6 0.5 1201 6 4 1320 6 45 0.28 6 0.02 6.3 6 0.3 0.414 1.584 6 0.001 2.9 6 0.1 13.0 6 0.9 10.1 6 0.8 6.6 6 0.9 5.7 6 0.9 2.9 6 0.3 150 6 2

0.8 6 0.1 0.5 6 0.1 — 1198 6 4 1650 6 50 0.17 6 0.01 3.0 6 0.2 0.343 1.480 6 0.001 1.0 6 0.1 1.8 6 0.2 10.6 6 0.9 7.2 6 0.9 3.0 6 0.6 8.7 6 0.9 83 6 2

density can be considered approximately constant in our calculations for temperatures below 150 8C for PC and 75 8C for PMMA. Cp(T) and k(T) are shown in Fig. 4b. The mass densities measured at room temperature are listed in Table I. Cp(T), k(T) increase monotonically within the considered temperature interval. Figure 5 shows the result of the temperature dependence of the TL and TM signals amplitudes normalized by the excitation power, hj/Pe. The amplitudes are strongly affected near the glass transitions. The temperature derivative of hj(T) has been used to calculate the glass transitions in previous works16,17 and here yielded Tg = (150 6 2) 8C for PC and Tg = (83 6 2) 8C for PMMA. Note that for the samples of different

FIG. 4. Temperature dependence of the (a) thermal diffusivity and (b) thermal conductivity of the polymer samples. The inset in (b) shows the specific heat.

thicknesses, the TL amplitudes normalized by the thickness, hTLP1 L1, are slightly different. The difference is a consequence of the combined effects leading to the lens signal, i.e., the thermo-optic effect, thermal expansion, and the stress-optic effect, which present a complex dependence with thickness.39 If the thickness is larger than the radius of the region affected by the thermoelastic effect, the TL plane–strain approximation could be safely employed. The temperature dependence of the optical path change (ds/dT)TL can be calculated from hTL(T) using Eq. 4. The optical absorption coefficients of the samples were determined in the same temperature range by measuring the transmission at 514.5 nm, and the results were found to be approximately constant with temperature from 25 to 150 8C for PC and 25 to 75 8C for PMMA (Table I). Using k(T) and / = 1 for both samples, (ds/ dT)TL(T) was calculated, and the results are presented in Fig. 6a. The values found at room temperature are listed in Table I. The parameter hTM(T) is related to thermal conductivity k(T) and linear thermal expansion coefficient aT(T) of the sample by Eq. 1. As an example, we calculated the thermal expansion of PC using the measured hTM (T) and k(T), and the results are presented in Fig. 6b. The Poisson ratio was assumed to be constant within this temperature range (Table I). aT(T) determined from the TM measurements and measured using a commercial dilatometer are in good agreement. The linear thermal expansion coefficient for the PMMA sample was found to be approximately constant below the glass transition.

FIG. 5. Temperature dependence of (a) TL amplitude, hTL/Pe, and (b) TM amplitude hTM/Pe.

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(2.9 6 0.1) 3 106 K1 for PC and (1.0 6 0.1) 3 106 K1 for PMMA. These values are very small compared with (ds/dT)TL, indicating the competition between the negative dn/dT and aT. In fact, (ds/dT)OI can be written as41   ds dn þ naT ¼ ð7Þ dT OI dT Using aT(T) for both samples, and n as given in Table I, dn/dT was calculated for PC, and the results are displayed in Fig. 6c. The variation of aT(T) between 25 and 75 8C for PMMA was less than 5%, and it was considered constant in the calculation. Additionally, the difference between (ds/dT)OI and (ds/dT)TL can be used to calculate thermo-optical properties for the sample. These parameters can be related as     ds ds  ¼ DSO  naT ð8Þ dT TL dT OI

FIG. 6. Temperature dependence of (a) temperature coefficient of optical path length, (ds/dT)TL; (b) linear thermal expansion coefficient, aT, and thermal coefficient of the electronic polarizability, u; and (c) the temperature coefficient of refractive, dn/dT. The uncertainties in the calculations of these parameters are less than 15%.

Regarding (ds/dT)TL, the subscript TL is necessary here to distinguish this from the ds/dT measured with the optical interferometer, (ds/dT)OI. (ds/dT)TL accounts for the stress effects due to the nonuniformity of the excitation laser beam. In the case of plane–strain approximation,39 (ds/dT)TL can be written as   ds dn n 3 Y aT þ ðqjj þ 3q? Þ ¼ ð6Þ dT TL dT 4ð1  mÞ in which dn/dT is the temperature coefficient of refractive index, n is the refractive index, Y is the Young’s modulus, and qjj and q? are the stress-optical coefficients parallel and perpendicular to the beam direction, respectively. As a consequence of the temperature profile across the sample, thermal stress effects can be generated, giving rise to the second term in Eq. 6. This term is much smaller than dn/dT in many systems and can be omitted.17,39 An optical interferometer was employed to determine the temperature dependence of the (ds/dT)OI. In this method,41 the temperature change is homogeneous throughout the sample, eliminating any stress effect during heating. The interference pattern is detected as described in detail elsewhere.41 A He–Ne laser at 632.8 nm was used as the optical source, and the sample was heated using the same furnace used in the TL–TM measurements. (ds/dT)OI values were approximately constant (,5% variation) in the temperature range below the glass transition for both samples, yielding

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The stress-optic parameter is DSO = n3Y aT(qjj þ 3q?)/4(1  m). Using the parameters listed in Table I, we estimated DSO  2.9 3 105 K1 for PC and DSO  7.6 3 105 K1 for PMMA at room temperature. In addition, dn/dT is related to the temperature coefficient of the electronic polarizability / by17 dn ðn 2  1Þðn 2 þ 2Þ ¼ ð/  3aT Þ dT 6n

ð9Þ

The negative values of dn/dT show that the expansion term on the right side of Eq. 9 is dominant over the electronic polarizability. The temperature dependence of /(T) is presented in Fig. 6b for PC.

CONCLUSIONS We propose a quantitative method for the in situ evaluation of thermal, optical, and mechanical properties of polymers. The thermal lens and thermal mirror methods are used as a concurrent photothermal technique. This combined method was used to investigate polymers as a function of temperature, from room temperature up to 170 8C. A complete set of thermal, optical, and mechanical properties of polycarbonate and poly (methyl methacrylate) samples were obtained. The concurrent method presented here can be a useful tool for in situ characterization of semitransparent materials, where fast and non-contacting measurements are required. ACKNOWLEDGMENTS The authors are thankful to the Brazilian Agencies CAPES, CNPq, FINEP, and Fundac¸a˜o Arauca´ria for the financial support of this work. NGCA also thanks Fulbright and CAPES for financial support under the process BEX 17572/12. 1. S.E. Bialkowski. ‘‘Photothermal Spectroscopy Methods for Chemical Analysis’’. In: J.D. Winefordner, editor. Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications. New York: John Wiley and Sons, 1996. Vol. 134. 2. D.P. Almond, P.M. Patel. Photothermal Science and Techniques. London, UK: Chapman and Hall, 1996. 3. H. Vargas, L.C.M. Miranda. ‘‘Photoacoustic and Related Photothermal Techniques’’. Phys. Rep. 1988. 161(2): 43-101.

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