ULTRASONIC STUDIES OF SOME POLYMERS AT LOW TEMPERATURES

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1 ULTRASONIC STUDIES OF SOME POLYMERS AT LOW TEMPERATURES G. Federle, S. Hunklinger To cite this version: G. Federle, S. Hunklinger. ULTRASONIC STUDIES OF SOME POLYMERS AT LOW TEMPERATURES. Journal de Physique Colloques, 1982, 43 (C9), pp.c9505c9508. < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1982 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE Colloque CS, supplement au n 12, Tome 43, decembve 1982 page C9505 ULTRASONIC STUDIES OF SOME POLYMERS AT LOW TEMPERATURES G. Federle and S. Hunklinger MaxPlanakInstitut fiir Festkorperforsahung, Heisenbergstr. 1, 7000 Stuttgart 80, F.R.G. Résumé. La vitesse du son et l'absorption acoustique ont été mesurées dans le polyméthylméthacrylate (PMMA),l e polyéthylméthacrylate (PEMA) et le polycarbonate (PC) de 60 mk à 10 K. Des propriétés élastiques similaires sont observées pour les trois polymères. A basse température, contrairement à des mesures précédentes, nous trouvons une absorption proportionnelle a (0 T et une variation logarithmique de la vitesse, comme le prévoit le modèle tunnel. A plus haute température l'absorption atteint un plateau. Ceci constitue la première observation du plateau prédit par le modèle tunnel, dans un matériau amorphe. Abstract. The sound velocity and acoustic absorption have "been measured in polymethylmethacrylate (EMMA.), polyethylmethacrylate (PEMA), and polycarbonate (PC) from 60mK to 10K. For all three polymers similar acoustic properties are observed. At low temperatures, in contrast to earlier measurements, we find an absorption proportional to 0) TV and a logarithmic variation of the sound velocity, as expected from the tunneling model. At higher temperature the absorption reaches a plateau. This is for the first time the plateau, predicted in the tunneling model, has been observed in an amorphous material. The low temperature acoustic, dielectric and thermal properties of amorphous solids have been investigated extensively in recent years. These efforts are directed mainly to elucidate the dynamics and eventually the microscopic origin of the twolevel systems found in dielectric as well as in metallic materials. Generally these twolevel systems (TLS) are thought to arise from quantum mechanical tunneling /'[f of atoms or small groups of atoms between two potential minima. According to the tunneling model there exists a broad spectrum of relaxation times (T) of the TLS. If x is the relaxation time of the fastest TLS one can distinguish between two regions m.. o)t» 1 and LOT «1. At low temperature or high frequency urr» 1. In this regime, in an insulating glass the relaxational sound absorption /2/ varies as u> T: This has been observed experimentally in silica based glasses /3/. In contrast to this expectation, previous acoustic and hypersonic measurements done on jpolymers polystyrene (PS) /h/ and polymethylmethacrylate (PMMA) /5,6/ down to O.UK reported a relaxational sound absorption which varies as tot. This result was rather puzzling for PS and PMMA have thermal properties similar to other insulating glasses /T/. This observation would imply two things. Either the polymers with their unique structure and bonding have anomalous acoustic properties or it may imply that the temperature O.UK is not low enough to reach the regime IOT» 1 in these glasses. To clarify the above problem and also to investigate the effect of polymer structure on low temperature acoustic properties we have carried out a systematic study of three polymers PMMA, PEMA, and PC in the temperature range 60mK to 10K. The experiments were carried out using both longitudinal and transverse waves in the frequency range 15 ^00 MHz. The acoustic power used was about 10 7 W/cm 2 at 15 MHz and W/cm 2 at i*00 MHz. The power was varied to check for intensity dependence of the absorption which will arise either from heating effect or from the resonant absorption /3/. No detectable intensity dependence was found. The results on PMMA are shown in Fig. 1 and 2. For other materials the results look similar. In Fig. 1, it can be seen the acoustic absorption below 0.2K follows a co T 3 law as expected. So we reach the regime U)T» 1 in the polymers at much lower temperature. And it is then obvious why previous measurements made down to O.ltK did not show a 60 T 3 law. According to theory /2/ the attenuation in the regime (tor» 1) is given by: m Article published online by EDP Sciences and available at

3 CS506 JOURNAL DE PHYSIQUE Fig. 1: The acoustic absorption versus temperature in polyrnethylmethacrylate for various frequencies. For each frequency a constant background absorption has been subtracted. A 410 MHz 0.m1 1 * i I TEMPERATURE [KI > 0 > 15 MHz..* **.., tronsveisol 3 Fig. 2: Relative variation of sound velocity as a function of temperature in polymethylmethacrylate for longitudinal and transverse waves. 4 W FI.. A 4 L!i! 0 I I A**.A A A* A r ' longitudinal * A A A I OD TEMPERATURE ( K) PMMA long. w. Fy2/pv2 from sound velocity eq.2 ~.IO~ pyl/pv2 from absorption eq ' 7 (ev) from eq. 1 and sound velocity at 4K (m/s) 3150 density (g/cm3) 1.18 PMMA transv. w. 3.7 ' ' I PEMA long. w PC long. W. Ps long. w. (ref. 4) 1.8 a ' Table 1: Paramezers characterizing the twolevel syste s in various amorphous polymers. y is defined as [~y2/v5>/(1/v5+2/v~)] l?p 1

4 where is the density of states, y is the deformation potential which represents coupling of TLS to the lattice, v ig the sound velocity, p is the density and <y2/v5> represents an average% coupling constant. e stands for polarization index. Values for the averaged coupling constant can be derived from the experimental data using Eq. 1 once ~y'/pv' is known. At the lowest temperatures ($ < 0.3K) the sound velocity (see Fig. 2) increases logarithmically as expected from the theory /3/ following the relation: Here T is some arbitrary reference temperature. Py2/pv2 obtained for all the materigls for both longitudinal and transverse pola$iza?ions are shown in table 1. At higher temperature ( depending on the measuring frequency) we enter the regime wt << 1. It can be seen that the attenuation approaches a "plateau", also predicted m in the tunneling model. The attenuation at the plateau /2/ is given by: The value of 6(2/pv: obtained from the plateau is also given in table 1. The observation of the prateau deserves comments. The plateau, as predicted in the tunneling model, arises because of a wide distribution of relaxation times and is a crucial prediction of the model. It is for the first time the plateau has been observed in an amorphous solid. In silica based glasses one enters the regime wr << 1 at higher temperature where interference due to other processes mask th8 plateau. The observation, that the low temperature acoustic properties of polymers are qualitatively similar to other glasses, establishes the fact that even with their unique bonding and structure they are not different from network inorganic glasses like silica. The only difference is the crossover wr = loccurs at lower. f: em g erat yes. In view of extremely low transverse sound velocitymof the polymers (vs1 lc /vp0 ymer 2.4) it seems quite expected, since r a v:. It can be seenfrom table 1 that py'/$v2 for polymers are very similar to silica glasses. Also Py2/pvL obtained from sound velocity and plateau attenuation agree to within a factor of 2. The coupling constant 7 calculated from Eq. 1 is 0.3ev and significantly lower than that of silica glasses. ( 1.6ev). Though one cannot draw any definite conclusion about the microscopic nature of the tunneling unit in glasses, we can, however, draw certain conclusions when we compare different polymers. When the methyl side group in PMMA is replaced by the heavier ethyl side group to obtain PEMA no big change in the quantity Py2/pv2 is observed. This therefore excludes side group motion or torsion of backbone chain within a single monomeric unit as responsible for the tunneling states. Quite probably the tunneling motion involves motion of several monomeric units together. In conclusion, we have shown that polymers have similar acoustic properties as network glasses at low temperature.

5 JOUEWAL DE PHYSIQUE References /1/ P.W. Anderson, B.I. Halperin, C.M. Varma ; Phil. Mag. 5, 1 (1972) W.A. Phillips, J. Low Temp. Physics 1, 351 (1972) /2/ J. Jackle, Z. Phys. z, 212 (1972) /3/ S. Hunklinger, W. Arnold in Physical Acoustics, Ed. by W.P. Mason and R.N. Thurston (Academic Press, New York) 1976, Vol. XII, p. 155 /4/ J.Y. Duquesne, G. Bellessa; J. de Physique Lett. 4, L193 (1979) /5/ G. Federle, S. Hunklinger; Proc. Conf. Fundamentals and Applications of Nonmetallic Materials at Low Temp. Ed by G. Hartwig, D. Evans, R.L. Kolek (Plenum Press, New ~ork) 1980 /6/ R. Vacher, J. Pelous, H. Sussner, M. Schmidt, S. Hunklinger; Proc. Ann. Conf. Cond. Mat. Div. EPS, Antwerpen, 1980 /7/ R.B. Stephens, G. S. Cieloszyk, G. L. Salinger; Phys. Lett. 38, 215 (1972)