IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 20 (2008) 244103 (11pp) doi:10.1088/0953-8984/20/24/244103 On the pressure evolution of dynamic properties of supercooled liquids Aleksandra Drozd-Rzoska 1 , Sylwester J Rzoska 1 , C Michael Roland 2 and Attila R Imre 3 1 Institute of Physics, Silesian University, ulica Uniwersytecka 4, 40-007 Katowice, Poland 2 Naval Research Laboratory, Chemistry Division, Code 6120, Washington, DC 20375-5342, USA 3 KFKI Atomic Energy Research Institute, 1525 Budapest, POB 49, Hungary Received 4 April 2008 Published 29 May 2008 Online at stacks.iop.org/JPhysCM/20/244103 Abstract A pressure counterpart of the Vogel–Fulcher–Tammann (VFT) equation for representing the evolution of dielectric relaxation times or related dynamic properties is discussed: τ( P ) = τ P 0 exp[ D P  P ( P 0 −  P )], where  P = P − P SL , P 0 is the ideal glass pressure estimation, D P is the pressure fragility strength coefficient, and the prefactor τ P 0 is related to the relaxation time at the stability limit ( P SL ) in the negative pressure domain. The discussion is extended to the Avramov model (AvM) relation τ(T , P ) = τ 0 exp[ε(T g ( P )/ T ) D ], supplemented with a modified Simon–Glatzel-type equation for the pressure dependence of the glass temperature (T g ( P )), enabling an insight into the negative pressure region. A recently postulated (Dyre 2006 Rev. Mod. Phys. 78 953) comparison between the VFT and the AvM-type descriptions is examined, for both the temperature and the pressure paths. Finally, we address the question ‘Does fragility depend on pressure?’ from the title of Paluch M et al (2001 J. Chem. Phys. 114 8048) and propose a pressure counterpart for the ‘Angell plot’. 1. Introduction On cooling a liquid to the glass transition a tremendous change in dynamic properties occurs [1–6]. A decade ago it was postulated that [3] ‘determining the general behavior of liquids near glass temperature (T g ) at high pressures is the key problem in the challenging field of viscous liquids and the glass transition’. Indeed, in subsequent years it was shown that many phenomenological and theoretical predictions can be verified only by means of comprehensive temperature and pressure investigations [1, 4–50]. A fundamental prerequisite in such studies is a reliable parameterization of the pressure evolution of the dynamic properties. For their temperature dependence under atmospheric pressure, the Vogel–Fulcher– Tammann (VFT) relation is most often used [1–6, 51]: τ(T ) = τ T 0 exp  B T − T 0  = τ T 0 exp  D T T 0 T − T 0  (1) where D T is the fragility strength coefficient and T 0 is the VFT-based estimate of the ideal glass temperature. Similar dependences can be written for the dielectric (structural) relaxation time τ(T ), viscosity η(T ), DC conductivity σ(T ), and diffusion coefficient d (T ) [1, 4–10]. It is noteworthy that Johari [52] questioned the validity of the substitution B = D T T 0 , since ‘this form does not yield the Arrhenius equation for T = 0 K’. Despite this objection, the coefficient D T estimated via equation (1) remains one of basic parameters characterizing the fragility of glassy systems [1–6]. The validity of the VFT equation (1) for non-atmospheric isobars ( P  0.1 MPa) has also been tested ([4, 5] and references therein). A simple extension of equation (1) for portraying both the temperature and the pressure ( P ) behavior was used by several groups [10, 53–57]: τ(T , P ) = τ T 0 exp  B  + aP T − (T 0 + bP )  . (2) However, the linear pressure dependences of T 0 ( P ) and B( P ), assumed in equation (2), are valid only over a narrow range of pressures, mainly for so-called ‘strong’ glass formers. It is worth recalling that in 1967, Greet and Turnbull [58] introduced the following relation for portraying the isothermal pressure behavior of the viscosity of supercooled o-terphenyl: η(T ) = η P 0 exp  B P 0 − P  . (3) 0953-8984/08/244103+11$30.00 © 2008 IOP Publishing Ltd Printed in the UK 1 Downloaded from http://polymerphysics.net Downloaded from http://polymerphysics.net