Scaling of the local dynamics and the intermolecular potential

Abstract

The experimental fact that relaxation times, τ, of supercooled liquids and polymers are uniquely defined by the quantity TV γ , where T is temperature, V specific volume, and γ a material constant, leads to a number of interpretations and predictions concerning the dynamics of vitrification. Herein we examine means to determine the scaling exponent γ apart from the usual superpositioning of relaxation data. If the intermolecular potential can be approximated by an inverse power law, as implied by the TV γ scaling, various equations are derived relating γ to the Grüneisen parameter and to a common expression for the pressure derivative of the glass temperature. In addition, without assumptions, γ can be obtained directly from pressure-volumetemperature data. These methods for determining γ from molecular or thermodynamic properties are useful because they enable the P-and V-dependences of τ to be obtained, and thereby various analyses of the dynamics to be explored, without the need to carry out relaxation measurements beyond ambient pressure.2

Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

“…40 There have been suggestions of how to connect the socalled density scaling exponent 24,25 -the one controlling the relaxation time via the variable ␥ / T-with the Grüneisen parameter, notably by Roland and co-workers. [41][42][43] In Ref. 41, equality of ␥ G and ␥ was argued theoretically by reference to the Avramov model.…”

Entropy basis for the thermodynamic scaling of the dynamics ofo-terphenyl

“…where C p is the isobaric heat capacity and We compare this exponent to γ G , based on the connection between these quantities [26,28]. Note that while γ G is a strong function of temperature close to 0 K and well below T g , at higher temperature it becomes approximately constant [33,34].…”

“…(2) is accurate, thermodynamics properties in general will depend only on the scaled variable TV n [23,24]. This scaling breaks down for the equation of state, due to neglect of the longer range attractions [26]. However, we have shown for three glass-forming materials, propylene carbonate, salol, and polyvinylacetate, that the entropy is well represented by [27] S S f(TV )…”

Thermodynamic interpretation of the scaling of the dynamics of supercooled liquids

“…(8), it is assumed that α p is inversely proportional to P. This expression gives a satisfactory description of experimental τ(T,P) data and also yields an expression for the pressure-dependence of the glass transition temperature identical to the empirical Andersson equation 57,58 , the latter widely used to fit T g (P) results. (The Andersson equation can also be derived from the Simon equation 59,76 .) One shortcoming, however, is that the value of the Avramov parameters calculated from thermodynamic quantities can differ from the values obtained by fitting of experimental relaxation times.…”