Scaling the $\alpha $ -relaxation time of supercooled fragile organic liquids

Abstract

:It was shown recently [1] that the structural α-relaxation time τ of supercooled o-terphenyl depends on a single control parameter Γ, which is the product of a function of density E(ρ), by the inverse temperature T -1 . We extend this finding to other fragile glassforming liquids using light-scattering data. Available experimental results do not allow to discriminate between several analytical forms of the function E(ρ), the scaling arising from the separation of density and temperature in Γ. We also propose a simple form for τ(Γ), which depends only on three material-dependent parameters, reproducing relaxation times over 12 orders of magnitude. I-IntroductionThe steady increase over more than 12 orders of magnitude of the shear viscosity η, or of the structural α-relaxation time τ measured by dielectric or light-scattering spectroscopic methods, is among the spectacular features that accompany the liquid-glass transition [2]. The latter can take place in a large variety of liquids ranging from mineral oxides, salts, organic polymers, metallic alloys, to simple molecular liquids. Under cooling, these liquids avoid crystallisation at the melting temperature T m and become a glass at a lower temperature T g .For low molecular weight glassforming materials, a glass is usually defined as a liquid whose relaxation times τ are larger than 10 2 seconds, a phenomenon that takes place at some temperature T g . In spite of its frequent occurrence and of continuous theoretical and experimental efforts over the last fifty years, this transition remains one of the least understood phenomena in condensed matter physics. In particular, one still does not fully grasp how and on which parameters, usually called control parameters, these relaxation times τ depend [3,4]. Obviously, in simple glassforming colloids the only control parameter is the density. Conversely, would the structural relaxation of a liquid at equilibrium be only due to jumps over energy barriers that are independent from temperature and density, τ might have a simple Arrhenius behaviour and the only control parameter would be temperature. The Angell plot [2], which represents the logarithm of relaxation times τ (or viscosity η) as a function of orders of magnitude, they showed that the data can be scaled using control parameters of the same form as in OTP, n becoming material dependent. Previously, a scaling was shown to hold in glycerol by . Also ref. [24] showed that the domain of density explored in the experiments was too small to ascertain the analytical form of E(ρ Table 1. At each pressure and temperature, the corresponding density can be obtained from the Tait interpolation formula, whose form and parameters are also collected in Table 1. Table 2 as well as that obtained from unpublished PCS data on BMPC (1,1-bis(p-methoxyphenyl)cyclohexane ) [25]. We add also the n value obtained by the scaling of the dielectric α-relaxation time in KDE (cresolphtaleine-dimethyl ether) [26].The values of n vary from 3.8 to 7.5.We note that similar result...

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