Experimental evidence against the existence of an ideal glass transition Sindee L. Simon * , Gregory B. McKenna Department of Chemical Engineering, Texas Tech University, P.O. Box 43121, Lubbock, TX 79409-3121, USA article info Article history: Available online 9 April 2009 PACS: 61.25.hk 61.43.Fs 65.40.Ba 65.40.gd Keywords: Glass transition Polymers and organics Calorimetry abstract The absolute liquid heat capacity of poly(a-methyl styrene) was determined at temperatures far below T g and T K in previous work by use of pentamer/polymer athermal mixtures. Here the data is compared to data compiled by Wunderlich and coworkers from 0 K to above T g in order to obtain the absolute entropy for the polymer in its equilibrium state at temperatures as much as 180 K below the glass temperature or 130 K below the Kauzmann temperature. The results provide no evidence of a second-order transition or of a smeared transition in the entropy. In addition, we find no evidence that the entropy would become negative at a finite temperature. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction The glass transition has been said to the most important unre- solved problem in condensed matter physics [1]. For the last 50 years, an important framework for the glass transition has been the postulated existence of an ideal thermodynamic glass transi- tion below the experimentally accessible transition [2,3]. The ideal glass transition was invoked by Gibbs and DiMarzio in part to re- solve the Kauzmann paradox [4], the observation that the entropy of glass-forming liquids often extrapolates to zero at a finite tem- perature. However, several recent works suggest that, in fact, there is no need to invoke an ideal glass transition to resolve the Kauz- mann paradox [5–11], including modeling of the equilibrium heat capacity of amorphous polyethylene by Pyda and Wunderlich [7,8], Monte Carlo simulations by Binder and coworkers [9,10], and work by Stillinger and coworkers [11]. A major obstacle to resolving whether or not there is an ideal glass transition is the lack of suitable experimental methods to determine the equilibrium liquid response of a glass-forming material below its glass temperature (T g ). The difficulty lies in the inordinately long times required to achieve equilibrium den- sity as temperature is reduced below T g . For example, although the nominal T g is often taken to be the value corresponding to a relaxation time of approximately 100 s, the time required to reach equilibrium only 10 K below T g increases by four orders of magni- tude for the typical glass former, polystyrene [12]. In fact, the log- arithmic increase in the relaxation times as one approaches and goes below T g has been well-known for decades [13,14]. Conse- quently, it is, practically, impossible to obtain equilibrium proper- ties in the vicinity of the Vogel (T 1 ) or Kauzmann (T K ) temperatures – even though it has been demonstrated [15–17] that relaxation times do not diverge at these temperatures and it has been argued recently that the general body of literature does not support the divergence of timescales in glass-forming liquids [18,19]. However, although it is not possible to reach equilibrium density and directly measure liquid properties far below T g , we have recently developed a novel experimental approach [20] that exploits the properties of athermal polymer/oligomer blends and makes possible the determination of the equilibrium liquid heat capacity of a polymer at temperatures far below T g . Blends of a polymer with its own oligomer are unique because chemically, the two components are identical except for molecular weight differences and except for potential differences caused by the end groups on the oligomer that depend on the synthesis method. An exceptional blend system is poly(a-methyl styrene) and its pentamer because the oligomer can by synthesized without chemically different initiator groups at the ends of the molecules. Consequently the only difference between the poly(a-methyl sty- rene) and its specially synthesized oligomer is molecular weight, and since the chemical structure is identical, it is expected that these blends are athermal. Furthermore, based on work on both poly(a-methyl styrene) and a homologous alkane series [20,21], we have shown that if the oligomer has ten atoms in its backbone 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.11.027 * Corresponding author. Tel.: +1 806 742 1763. E-mail addresses: sindee.simon@ttu.edu (S.L. Simon). Journal of Non-Crystalline Solids 355 (2009) 672–675 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol