NDT.net • July 2004 • Vol. 9 No.07

Variation of Thermal Diffusivity of PMA on Ultrasonication Period by Photoacoustic Phase Measurements

M.A.Jothi Rajan, FDP Research Scholar, School of Physics, Madurai Kamaraj University, Madurai-625 021, India
T.S. Vivekanandam, School of Chemistry, Madurai Kamaraj University, Madurai-625 021, India.
S.Umapathy, School of Physics, Madurai Kamaraj University, Madurai-625 021, India

Corresponding Author Contact:
Email: anjellojothi@yahoo.co.in


Polymethylacrylate (PMA) is synthesized by free radical addition polymerization in the presence of ultrasound of frequency 35MHz and intensity 100W/cm2 for various ultrasonication periods, at 58°C. Using Photoacoustic (PA) spectrometer available in our laboratory, depth profile analysis is made on the various PMA samples synthesized by measuring the amplitude and phase of the photoacoustic signal. From the amplitude the characteristic frequency of the sample is found out. Knowing the characteristic frequency the thermal diffusivity (a) of the sample is calculated from the phase of the photoacoustic signal. Thus the thermal diffusivity for all the samples (eleven) is found out. A graph is plotted between the thermal diffusivity and sonication period. The experimental result is compared with the available literature values and discussed.


Viscoelastic properties, optical properties and thermal properties of poly-methyl-metha-acrylate (PMMA) synthesized by conventional methods have been reported in literature [1-5]. Still a complete thermal study on polymethylacrylate(PMA) for thermal diffusivity is sparse. So, here we report our measurements on the thermal property in the view of the study on conducting polymers. The PA technique is the simplest NDT tool in studying the thermal diffusivity of the polymers. Also thermal effusivity measurements are possible with this technique.
The thermal diffusivity of the polymer PMA synthesized by the monomer methylacrylate and potassium peroxodisulphate as initiator at different sonication periods at moderately high power is reported here.


Polymerization is carried out by keeping the experiment solution mixtures in a flat bottom glass test tube of capacity. 100ml. Immersed in a transonic digital ultrasonic water bath model (Elma T490DH). The ultrasonic water bath, which is a rectangular metallic tub filled with water to three-fourth of its total capacity gives out ultrasonic waves of fixed frequency 20KHz which can be varied for various powers starting from 20W/cm2 to 140W/cm2 in steps of 20W/cm2. a frequency of 20KHz and a power of 100 W/cm2 at a constant temperature of 58°C is employed throughout our experiment.

Methylacrylate solution of strength 0.33M is mixed with a solution of potassium peroxodisulphate of strength 0.005M in a clean flat bottom glass test tube with the total volume as 25ml. A solution of Methylacrylate 20ml and potassium peroxodisulphate 5ml is used throughout our studies. Ultrasound is passed for a period of 30 minutes continuously and stopped exactly at the end of the 30th minute. The reaction test tube is taken out from the ultrasonic bath and a fixed volume (75ml) of sulphuric acid of strength 2N is slowly and gently added to the reaction mixture and is allowed to settle down.

After an interval of 48 hours we get a thin solid layer of polymethylacrylate (PMA) settled at the bottom of the test tube. The remaining liquid mixture is poured out the thin layer of PMA is taken out gently from the test tube and placed over a filter paper, which absorbs all the liquid content and dries the thin layer of PMA. This thin layer is washed with distilled water and dried in atmosphere air conditions.

Thus we obtain PMA wafer, which is semitransparent, and colorless. Using the same procedure as given above we synthesize PMA by varying the period of sonication for 60,90,120,150,180,210,240,300 and 330 minutes. There are eleven PMA samples of thickness of 0.35mm for eleven different sonication periods that are available for further studies. The sample is cut to have uniform size of 4 x 4mm and thickness 0.35mm in a highly symmetric direction.


The principle of photoacoustic spectroscopy (PAS) is when fraction of incident chopped optical radiation, when absorbed by the sample, raises the molecules of the sample from the ground electronic state to the excited electronic state and these excited molecules relax to the ground state through non-radiative de-excitation, i.e., periodic heat emission. This periodic heat emission produced in the sample is diffused through an air medium in front of the sample. This temperature variation changes the pressure in the PA cell, which is detected as acoustic signal by a sensitive electret microphone. Many experiments and theoretical investigations are available for conducting polymers elsewhere[6,7]. The PA measurements for conducting polymers such as thermal effusivity, specific heat capacity and thermal conductivity for both vinyl and conducting polymers of different molecular weights are of our research interest.

The present PA spectrometer for measurement of thermal diffusivity, is set up with a Xenon lamp (450W, SPEX), monochromator (100-1000nm, SPEX), electromechanical chopper (EG &G, model 601-1), an innovatively designed photoacoustic cell which is kept inside a vibration free metallic cylindrical vessel of length 45cm and diameter 21cm weighing nearly 40kg with slits and adjustable screws. A sensitive electret microphone, a lock-in amplifier (EG &G Model 7225) in which provisions are made to measure amplitude and phase difference between incident modulating light signal and emitted acoustic signal for different chopping frequencies.

The experimental setup is shown in figure 1. As we keep the PMA sample in the PA cell, the light absorbed by the sample would generate thermal waves and subsequently the sensitive electret microphone detects the acoustic waves. The weak signal is fed into the lock-in-amplifier for amplification and also for noting down the readings. The frequency of the chopper can be varied from 0.1Hz to 999.9Hz.

Fig 1: Schematic diagram of the PA setup


Now the photoacoustic spectra on one of these PMA samples are recorded in the following way.


Here the wavelength is fixed and the chopping frequency is varied. For every chopping frequency the amplitude and the phase of the PA signal are recorded in the same lock-in amplifier setup. We start from 10Hz and end at 70Hz as the signal became constant in phase and amplitude above 70Hz. A graph is plotted between Ln (amplitude of the PA signal) and Ln (chopping frequency). From this curve the characteristic frequency, fc of the sample is found out. This procedure is shown in figure 2.

Fig 2: Ln(frequency) Vs Ln( signal amplitude)

This frequency fc is that point at which the PMA sample goes from thermally thin to thermally thick state i.e., the PA signal varies as 1/f with the chopping frequency after this point as required for a thermally thin sample[8]. The characteristic frequency for all the eleven samples is found out by following the above procedure.

Now thermal diffusivity (a) is calculated from

a = l2 fc m2 s-1       (1)

Thermal diffusivity can also be found by measuring the phase of the PA signal for various chopping frequencies. A graph is drawn between Ln (2pf )and Ln (phase). The slope of this curve is related to thermal diffusivity as

a = l2 / (slope)2 · 1/2 m2 s-1      (2)

Where l is the thickness of the sample. This is shown in figure 3. in this work equation (2) is finding thermal diffusivity of the PMA samples.

Fig 3: Ln (Phase ) Vs Ln [ Sqrt (2 x 3.15 x f)]

The results are shown in Table 1.

Power of Sonication W/cm2 Temperature °C Period of sonication min. Thickness of the sample mm Characteristic Frequency Hz Thermal diffusivity x 10-6 m2/sec
100 58 30 0.35 18.17 2.510
100 58 60 0.35 22.63 2.647
100 58 90 0.35 24.50 2.647
100 58 120 0.35 24.77 2.647
100 58 150 0.35 25.01 2.761
100 58 180 0.35 25.79 2.761
100 58 210 0.35 27.10 2.833
100 58 240 0.35 29.94 2.870
100 58 270 0.35 31.48 2.998
100 58 300 0.35 38.45 3.423
100 58 330 0.35 38.84 3.790
Table 1: Thermal diffusivity for various sonication period

A graph is plotted between thermal diffusivity (physical property) and sonication period. This is shown in figure 4. An analysis of the graph shows that the period of sonication from 45 to 200 minutes is the optimum period for the preparation of PMA, since in this region the thermal diffusivity of PMA seems to be stable. This method of synthesis and this period of sonication is of engineering importance.

The graph (figure 4) can be divided into three parts namely the first from 5min to 45min and secondly 46 min to 200 min and thirdly 201 min to 330 minutes.

Fig 4: Sonication Period Vs Thermal Diffusivity

The first may be due to the increasing molecular weight of the polymer since the rate of polymerization increases as sonication period is increased and then drops in general. Such a gradual increase in thermal diffusivity may be due to the changes in molecular weight.

During the sonication period (46-200 minutes) the change in molecular weight of the polymer formed may be slow and hence thermal diffusivity almost remains constant for this time interval and also the addition of monomer units or depletion of monomer units may be in the same order.

For further period of sonication (above 200minutes) if any depolymerization occurs, the monomer radical will be formed. This monomer radical may combine with the monomers present in excess to form a polymer of different kind, due to side reactions or cross linking . Such a side reaction/ cross linking will definitely alter the molecular size, viscosity, thermal diffusivity etc., like any other physical property. Such a cross linking and chain reaction may occur and this may cause the changing trend in the physical property in the case of PMMA and PS [9].

The different monomer units from PMMA are involved and hence there is a change in the relative viscosity [9]. Such a trend may also be possible here in our system, namely polymethylacrylate generates methylacrylate and/or macromonomer radical of different size which will combine to give the polymer of different molecular size having different thermal diffusivity. This latter process may increase the rate of thermal diffusivity and hence the properties of the polymer.

In order to justify the present PA measurement we report here the recently available thermal diffusivity measurements for polymer-carbon composites[10], high density polyethylene[11], and poly vinyl acetate/poly aniline solution [12], in Table 2.

Polymer Process Thermal diffusivity m2/sec Reference
Polymer-carbon fibre composites Modulated photothermal device 6.0x10-6 [10]
High density polyethylene Unsteadystate technique 2.05x10-7 [11]
Polyvinylacetate/polyaniline solution Thermal lens measurements 1.05x10-7 [12]
Table 2: Thermal diffusivity from other references


The authors acknowledge UGC-DRS AND COSIST, India for the financial support and setting up the PA spectrometer. One of the authors (MAJ) acknowledges UGC, India for awarding FIP fellowship to carry out this work.


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