Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityRelation Between Thermodynamic and Dynamic Properties inGlass FormersThe investigation of the glass transition phenomenonis a central topic in the field of amorphous condensedmatter. In fact, the understanding of the glasstransition phenomenon can improve the knowledgeof materials used in the fields of pharmaceutical andmedical applications, food-packaging, plasticelectronics, and more generally amorphousmaterials. Several investigations performed bystudying dynamic properties of glass formerssystems varying pressure, P, and temperature, T,revealed that reduction of thermal energy and ofdensity play an equally important role in thevitrification process [1]. The Adam and Gibbs (AG)theory of glass transition includes both thesecontributions since it relates the increase ofstructural relaxation time, τ, occurring onapproaching the glass transition, to the reduction ofconfigurational entropy, S c, by [2],⎛ CT,P)= τ exp⎜⎝ TSc⎞⎟⎠AGτ (0(1)log(1/τ max[s -1 ])log(1/τ max[s -1 ])log(1/τ max[s -1 ])4.0TPC3.53.02.52.01.51.00.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04543265432101.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.401.5x10 -3 2.0x10 -3 2.5x10 -3 3.0x10 -3 3.5x10 -3 4.0x10 -310 4 X [J -1 mol]OTPPMMAFig. 1: Logarithmic of the inverse of relaxation timelog(1/τ max) (symbols) as a function of X∝(TS C) -1 , forTPC (0.1-69 MPa), OTP (0.1-79 MPa), and PMMA(0.1-200 MPa). Different symbols for the samesystem correspond to different values of pressure.where τ 0 the value of τ in the limit of infinite (TS c),and C AG assumed as a constant. Since the AG theoryincludes the contributions of the thermal energy andof the density, it appears as a suitable theory for theinterpretation of the glass transition phenomenon.Unfortunately, the configurational entropy is not aquantity that can be experimentally determined, andthis shortage represented a big limitation in theapplicability of this theory.Recently, we proposed a phenomenological model toestimate the configurational entropy as a function oftemperature and pressure, basing on calorimetricand thermal expansion data [4]. By this expressionof S c we extended the use of the AG Eq. (1), whichat the beginning was used to consider temperaturevariations, to take into account also the effect ofpressure on the dynamic properties of the materials.The relation we proposed relates thermodynamicquantities, such as molecular volume and heatcapacity, to dynamic ones (relaxation dynamics).The proposed equation, tested on systems wherethermodynamics and dynamics data were available,revealed to relate such quantities. In Fig. 1 a fewexamples of the obtained results are shown for threedifferent materials: o-terphenyl (OTP),triphenylchloromethane (TPC) and poly (methylmethacrylate) (PMMA). The logarithm of the inverseof relaxation time, measured for different values oftemperature and pressure, is plotted as a function ofa quantity inversely proportional to S c. Each symbolrefers to a different value of pressure. For eachsystem all the data can be reproduced by a singlelinear equation. Due to the good quantitativeagreement with experimental data, the model can beused to predict the dynamic properties at highpressure when few quantities (isothermalcompressibility, ambient temperature calorimetriccurve, relaxation time at ambient pressure) areknown.References[1] M. L. Ferrer, et al. J.Chem.Phys. 109, 8010(1998); C.M. Roland, R. Casalini Macromol. 36, 1361(2003).[2] G.Adam, J.H.Gibbs J.Chem.Phys. 28,139 (1965).[3] D. Prevosto, S. Capaccioli, R. Casalini, M.Lucchesi, P.A. Rolla Phys. Rev. B 174202, 67(2003) ; D. Prevosto, S. Capaccioli, M. Lucchesi, D.Leporini, P.A. Rolla, J. Phys.: Condens. Matter 16,6597 (2004); S. Capaccioli, M. Lucchesi, D. Prevosto,R. Casalini, P.A. Rolla, Philosophical Magazine B, 84,1513-1519, (2004)Authors:S. Capaccioli (a), D. Prevosto (b), M. Lucchesi (b), P.Rolla (b)(a) CNR-INFM, CRS-Soft and Dip. Fisica “E. Fermi”Univ. Pisa. (b) Dip. Fisica “E. Fermi” Univ. Pisa andCNR-INFM Polylab Largo B. Pontecorvo 3, Pisa.SOFT Scientific Report 2004-0662