Photothermal device for water dynamics measurement and thermophysical characterization: Application on textile samples

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 73, NUMBER 3 MARCH 2002 Photothermal device for water dynamics measurement and thermophysical characterization: Application on textile samples T. Duvaut a) Laboratoire d Energétique et d Optique, Faculté des Sciences, Moulin de la Housse BP 1039, 51687 Reims Cedex 2, France A. Limare and J. M. Bachmann b) Institut Français du Textile et de l Habillement 270, rue du Faubourg Croncels 10042 Troyes Cedex, France Received 27 August 2001; accepted for publication 17 December 2001 The photopyroelectric method in a noncontact configuration excitation source: diode laser at 1.94 m is capable of yielding information on the water content of a textile sample and on its influence on the thermal properties. A one-dimensional theoretical model was developed assuming the sample thermally homogeneous and taking into account the optical absorption and scattering. The experimental setup designed for this purpose included an excitation source resonant with water absorption, signal and data processing units and cells for conditioning the samples. We optimized the experimental conditions in order to identify the parameters related to the water content in the sample, and to monitor the dynamics of the process. The effective thermal conductivity and the volume specific heat were determined at different moments of time while the sample was taking up water. Two thermal parameters related to the comfort of a fabric were also calculated: the thermal effusivity and the thermal resistance. 2002 American Institute of Physics. DOI: 10.1063/1.1448902 I. INTRODUCTION One problem of general interest that could be solved using photothermal methods is the study of migration dynamics of water. Humidity modifies a number of parameters that influence processes like drying, printing, dyeing, preservation and having a considerable impact in industries like textile, paper, packaging and cosmetic. There is a number of methods already used in the industry for assessment of moisture content that give information on its global value. 1 In the particular case of textiles the thermal insulation and water transport properties are the major factors defining the comfort. The studies in literature concern different situations such as the liquid wetting and retention properties 2 or the nonisothermal heat and water vapor transport in textile. 3 The effective thermal conductivity measurement of fabrics containing water related the insulation properties to fiber sorption. 4 The goal of this work was to explore the potential of the photopyroelectric method for the water content measurement in textiles, the study of its migration dynamics and the measurement of thermal properties function of water content. Our studies were done in isothermal conditions which are far from use conditions, but they can be useful for the classification of materials function of their hydrothermal properties and eventually for quality assessment of multilayered fabrics. Here we report only on the results obtained on single layer, cotton fabrics. The PhotoPyroElectric PPE method in a noncontact configuration was chosen for the study of water migration a Electronic mail: thierry.duvaut@univ-reims.fr b Electronic mail: jmbachmann@ifth.org due to the fact that it satisfies several conditions. The method allowed the water uptake in vapor phase. Due to the capability of the pyroelectric sensors to respond to very low temperature variations, very low levels of excitation radiation could be used which prevented unwanted phenomena like desorption of water. The depth profiling capabilities of the noncontact PPE method were also proven for nonscattering samples upon the study of blood sedimentation 5 and on PVC samples with a known profile of dye 6 or for water migration measurements in starch films used as packaging material, 7 9 provided that the number of unknown parameters is limited. The one-dimensional 1D model 8 developed for the water migration in starch was modified to take into account the scattering of the incoming radiation. Introducing the scattering into the modeling of the PPE signal added another parameter to identify. This is the reason why an eventual water profile in the sample becomes difficult to detect due to the strong correlation of parameters. Here we present results obtained during water uptake by initially dry cotton samples. The water content in time and the thermal properties are identified from the photopyroelectric signal amplitude and phase. II. EXPERIMENT The pyroelectric effect consists in the change of spontaneous polarization of a ferroelectric material, as a result of a temperature variation. All pyroelectric materials are also piezoelectric but at low frequencies the pyroelectric effect is dominant. The schematic of the experimental setup is shown in Fig. 1. A diode laser emitting at 1.94 m SDL-6432-P2 was used as excitation source, corresponding to an absorption 0034-6748/2002/73(3)/1299/5/$19.00 1299 2002 American Institute of Physics

1300 Rev. Sci. Instrum., Vol. 73, No. 3, March 2002 Duvaut, Limare, and Bachmann FIG. 1. Schematic diagram of PPE experiment. FIG. 2. Experimental setup: 1-diode laser ( 1.94 m), 2-Peltier element, 3-optical fiber, 4-collimator, 5-beam splitters, 6-photodiode, 7-energy attenuators barrel, 8-focusing lenses barrel, 9-reference pyroelectric sensor, 10-PPE cell, 11-balance. band of the water contained in the material, in a region where dry cotton is less absorbing. The experimental cell was provided with a CaF 2 window of high transmittance in IR. Two heat sources are generated by the optical absorption of the modulated incident radiation: one due to the absorption into the sample and the second one due to the absorption into the sensor s electrode of the radiation transmitted by the sample. We are mainly interested in the first heat source which contains information on the sample s thermal properties. Therefore, in order to reduce the second heat source, the electrode should be highly reflecting. A 200 m thick and 20 mm in diameter PZT ceramic thermal diffusivity 3.7 10 7 m 2 /s, and thermal conductivity 1.2 W/m/K provided with high reflectance gold electrodes, was used as a pyroelectric sensor. In the two containers various relative humidities can be imposed around the textile samples by saturated salt solutions. The upper container is provided with a hole to allow the passing of the incident optical excitation. The textile sample is a disk clamped between two PVC rings. The PPE signal data were measured by a Stanford Research SR850 lock-in amplifier. The diode laser was electronically modulated by the internal generator of the lock-in. The experiment was computer controlled via a RS 232 interface and a LabView 6.01 program. Figure 2 shows a photograph of the laboratory prototype. The diode laser 1 is fixed on a temperature controlled Peltier element 2. The temperature control unit serves to stabilize the output power of the diode laser and it can be also used for small range tuning of the wavelength. In our case the temperature was fixed at 8 C. The diode laser is connected to an optical fiber 3 and then to a collimator 4. The collimated beam passes through the first beam splitter 5 before reaching the photodiode 6 and the barrel containing the energy attenuators 7. After passing through a barrel containing focusing/defocusing lenses 8 and another beam splitter, the beam reaches the experimental cell. The photodiode 6 and the reference pyroelectric sensor 9 give information on the output stability of the diode laser. The average power of the incident collimated beam was about 1 mw with a spot diameter of about 5 mm. Samples were prepared with the aim of studying the water uptake on macroscopic scale, over the thickness of the textile between 0.5 and 2 mm. Here we report results on only one kind of textile sample: a knitted textile fabric single jersey made of cotton, with a one layer construction consisting of one yarn/stitch, of a yarn number of 50 and an absorbed stitch length of 32. The yarn number represents the length in km of 1 kg of yarn while the absorbed stitch length is the length of yarn in cm of 100 stitches. The surface weight of the sample at 20 C and 65%RH was 157 g/m 2. The thickness in the same conditions of temperature and relative humidity was measured for two applied pressures: of 1 g/cm 2 and 10 g/cm 2 and the obtained values were 1.07 mm and 0.81 mm, respectively. The sample, previously dried in an oven at 80 C for 2 days, was accommodated in the measurement cell and the surface facing the sensor was exposed to a relative humidity of 98%. The first spectrum was obtained for the dry material, using silica gel in the two containers of the measurement cell, in order to keep it dry during the measurement. Then the sample was exposed to 98%RH for 18 h from one side while on the other side was left the container filled with silica gel. After 18 h silica gel from the upper side was replaced by another 98%RH salt solution. The PPE signal amplitude and phase was measured in the range 0.01 100 Hz. Each spectrum took half an hour and the time interval between two consecutive spectra was 1 h. The signal-to-noise ration was better than 100 for the amplitude and the phase noise was smaller than 1 deg.

Rev. Sci. Instrum., Vol. 73, No. 3, March 2002 Photothermal device for water dynamics 1301 FIG. 3. Successive amplitude a and phase b spectra for a dry cotton sample 1 exposed to a humid atmosphere (RH 98%) with the surface facing the sensor curves 2 to 6 and from both sides curves 7-11. Also shown is the response of the pyroelectric sensor alone. Points: experiment; lines: fit. III. RESULTS AND DISCUSSION The PPE results function of modulation frequency for the cotton sample are shown in Fig. 3 together with the spectrum obtained when the sensor is illuminated directly without sample. With the sample present, the amplitude signal at low frequencies is mainly given by the thermal component generated by the heat diffusion from the sample to the sensor. As the frequency increases, the heat waves are damped out and the signal is given only by the optical absorption of the transmitted radiation: the optical component. The phase lag reaches a minimum in the region where the amplitude is strongly attenuated and approaches the sensor s phase lag at high frequencies. The preamplifier acts as a low pass filter, so that at frequencies higher that 20 Hz it produces an attenuation and a dephasing of the signal. From the amplitude spectra we observe that as the sample is taking up water, the thermal component at low frequencies is increasing slightly due to higher absorption in the sample, while the optical component at high frequencies which is proportional to transmission through the sample, is decreasing. The phase minimum at intermediate frequencies becomes wider and is moving to higher frequencies. This indicates that the water is penetrating more into material and that the sample is deforming, so the heat source is moving closer to the sensor. A temperature rise is produced upon absorption generating heat diffusion. The heat diffusion equation for each layer is solved taking into account optical reflections, absorption and scattering. 10 The pyroelectric signal is given by the temperature increase averaged over the sensor s thickness and it was calculated numerically using Mathematica 3.1 Package. The best fits between experimental and theoretical curves were determined according to the least-square minimization criterion. 11 The fitting was conducted according to a Levenberg Marquardt algorithm. 12 16 The unknown parameters related to water uptake are the following: optical absorption coefficient, scattering coefficient, thermal conductivity and thermal diffusivity. The full lines in Fig. 3 are the results of the model. The choice of using either the amplitude or the phase lag or both depends on the information provided by the estimation that limits the maximum number of parameters that could be simultaneously determined. The latter depends on several factors. First, the signal amplitude or phase has to be sensitive with respect to the parameter variation. But even if the contributions of the parameters to the signal are important, the parameters could be too correlated to be identified. Finally, the noise of the experimental data is the end-limiting factor. We used the K criterion to calculate the maximum number of parameters. 12,16 K is the global measure of the statistical correlation expressed as a number of decimal digits. A simultaneous identification of parameters is possible if K is smaller than the number of significant digits accuracy of the experimental data divided by 2. The air gap thickness cannot be known a priori with a sufficient precision because the sample is slightly deforming while taking up water and therefore we had to consider this parameter as unknown. The effect of the number of experimental points on the parameters estimation was tested too. A compromise between the duration of experiment and the resolution of the identified parameters had to be done. In our case we have chosen 5 points/decade of frequency. The study of the sensitivity coefficients showed that at high frequencies the amplitude is very sensitive to the extinction coefficient ( K abs scatt ), and it is not sensitive to the thermal parameters and to the air gap thickness. The optical spectra of cotton samples equilibrated at different relative humidity obtained from a spectrophotometer equipped with a integrating sphere Lambda 9 Perkin-Elmer showed that the optical absorption coefficient is increasing with the water content from 200 m 1 to 500 m 1 from dry material to the one equilibrated at 98%RH while the scattering coefficient is decreasing from 3630 m 1 to 3350 m 1, respectively. The sorption isotherm for cotton i.e., the water content function of the relative humidity was measured by gravimetry. The extinction coefficient can be calculated directly from the transmitted light amplitude at high frequencies. Then the water content can be calculated. The evolution of the water content in time expressed as the mass of water divided by the mass of dry sample is shown in Fig. 4.

1302 Rev. Sci. Instrum., Vol. 73, No. 3, March 2002 Duvaut, Limare, and Bachmann FIG. 4. Time evolution of the water content. The experimental points were fit by exponential functions of the form W W 0 W max W 0 1 exp, t where W 0 is the initial value of the water content 1.5% for the first curve and 4.9% for the second one, W max is the saturation value of the water content 4.9% and 13.5%, respectively and is the time constant of the water uptake 2 and 7 h, respectively. The value of the time constant is much smaller for the first curve, a dry sample is taking up water much quicker than an already wet sample. The final water content is approaching the equilibrium value 15% for a relative humidity of 98%. Statistical evaluation of the signal and noise K criterion showed that the maximum number of parameters that can be evaluated from the phase is 3. If we consider no optical profile in the sample i.e., constant absorption coefficient, we can estimate the evolution of the effective thermal parameters of the sample: the thermal conductivity and the volume specific heat and C and the air gap thickness (d air ). For the thermal parameters identification we have to assume a sample thickness. Since it depends on the pressure applied during the measurement, we calculated the thermal FIG. 6. Time evolution of the volume specific heat of the cotton sample during water uptake considering two values of sample thickness. parameters for both values. In Fig. 5 is represented the thermal conductivity and in Fig. 6 are the values of the volume specific heat function of the water content for the two values of thickness. The two curves differ only by a factor depending on the ratio of the calculated densities. In other words, the specific heat: c C/ is the same for the two identifications within the errors of calculated values. We observe in Fig. 5 that the thermal conductivity is larger when we consider a larger thickness. N.B. The real thickness is the same. The thermal resistance R th defined as the ratio between the sample thickness and its thermal conductivity is shown in Fig. 7. We observe that the thermal resistance is the same within the errors for the two identifications, meaning that we can apparently obtain a larger conductivity when considering a larger value for the thickness but the result in terms of thermal insulation is the same. This is not the case for the only method Alambeta used up to now for textile insulation characterization, 17 where the sample is placed between two metal plates and a pressure is applied during measurement. In this case the real thickness varies function of pressure. The Alambeta method can classify fabrics function of their insulation properties, but the values are subject to large errors. The calculated thermal effusivity e (C ) 1/2 function of the water content is insensitive to the value of the thickness Fig. 8. This could be explained by the fact that the effusiv- FIG. 5. Time evolution of the thermal conductivity of the cotton sample during water uptake considering two values of sample thickness. FIG. 7. Time evolution of the thermal resistance of the cotton sample during water uptake considering two values of sample thickness.

Rev. Sci. Instrum., Vol. 73, No. 3, March 2002 Photothermal device for water dynamics 1303 FIG. 8. Time evolution of the thermal effusivity of the cotton sample during water uptake considering two values of sample thickness. ity is a parameter related to interfaces and it should not depend on the thickness of the sample. This observation is important for the comfort estimation, the thermal effusivity being easily related to the warm cool feeling quality. Moreover, in the handle estimation of a tissue by the method of Kawabata, 18 the only thermal parameter taken into account is the thermal effusivity among some other 10 mechanical parameters. For such an inhomogeneous sample like a knitted textile we could expect to obtain only average, effective values of the thermal parameters, nevertheless the only important ones are in the use conditions. For the particular case of migration dynamics, better concentration sensitivity is obtained if a selective wavelength is employed. For the wavelength 1.94 m water has more than 10 times larger absorption coefficient than cotton. If appropriate excitation source is used, the method is applicable to study the dynamics of other agents such as solvents, inks, drugs or cosmetics in other matrices. Our approach contained obviously some simplifying assumptions: the sample was considered thermally homogeneous and the optical parameters absorption and scattering coefficients were global values characterizing the sample as a whole. We also had to define the thickness of the sample, which is not trivial for a textile. These assumptions are however justified since in practice, the comfort of a fabric with respect to water is given by the warm cool feeling quantified by the thermal effusivity and by the insulation properties. The latter is well characterized by the effective thermal conductivity and its dependence on water content. The PPE approach is not a true noncontact method, the distance between sensor and sample has to be controlled in the submillimeter range. This is the reason why the PPE method will always remain at laboratory device level. The main advantage of our laboratory prototype rely on its reproducible and pressure independent results. A study is currently being conducted for defining a data base of thermal properties of textiles function of yarn, structure, material composition, and water content. ACKNOWLEDGMENT This work was financially supported by the region Champagne Ardenne, France. 1 H. A. Slight, Meas. Control 22, 42 1989. 2 Y. L. Hsieh, B. Yu, and M. M. Hartzell, Text. Res. J. 62, 697 1992. 3 T. Yasuda and M. Miyama, Text. Res. J. 62, 227 1992. 4 A. M. Schneider, B. N. Hoschke, and H. J. Goldsmid, Text. Res. J. 62, 61 1992. 5 J. S. Antoniow, J. F. Henry, M. Egée, and M. Chirtoc, High Temp.-High Press. 29, 549 1997. 6 J. S. Antoniow, J. F. Henry, D. Paris, and M. Chirtoc, AIP Conference Proceedings 463, edited by F. Scudieri and M. Bertolotti AIP, Woodbury, New York, 1999, pp. 567 569. 7 D. Paris, A. Frandas, C. Bissieux, J. S. Antoniow, M. Chirtoc, and M. Egée, AIP Conference Proceedings 463, edited by F. Scudieri and M. Bertolotti AIP, Woodbury, New York, 1999, pp. 679 681. 8 D. Paris, Ph.D. thesis, University of Reims, France, 1998. 9 A. Frandas, T. Duvaut, and D. Paris, Appl. Phys. B: Lasers Opt. 70, 77 2000. 10 J. F. Henry, C. Bissieux, S. Marquié, and Y. Gillet, High Temp.-High Press. 29, 159 1997. 11 J. V. Beck and K. J. Arnold, Parameter Estimation in Engineering and Science Wiley, New York, 1977. 12 P. Comon, Signal Process. 36, 287 1994. 13 T. Duvaut, D. Georgeault, and J. L. Beaudoin, Infrared Phys. Technol. 36, 1089 1995. 14 K. Levenberg, Quant. Appl. Math. 2, 164 1944. 15 D. W. Marquardt, J. Soc. Ind. Appl. Math. 2, 431 1963. 16 C. Martinsons and M. Heuret, Thin Solid Films 317, 455 1998. 17 L. Hess and I. Dolezal, J. Text. Mach. Soc. Jpn. 42, 124 1989. 18 S. Kawabata and Y. Akagi, J. Text. Mach. Soc. Jpn. 23, 51 1977.