Is there a connection between fragility of glass forming systems and dynamic heterogeneity/cooperativity? L. Hong a , V.N. Novikov b,c,d , A.P. Sokolov b,c, ⁎ a Department of Polymer Science, The University of Akron, OH 44325, USA b Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, TN 37996, USA c Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA d IA&E, Russian Academy of Sciences, Novosibirsk, 630090, Russia abstract article info Article history: Received 18 April 2010 Received in revised form 14 June 2010 Keywords: Glass transition; Fragility; Cooperativity Although fragility of glass forming liquids is traditionally related to cooperativity in molecular motion, the connection between those parameters remains unclear. In this paper we present the estimates of cooperativity (heterogeneity) length scale ξ obtained from the boson peak spectra. We demonstrate that ξ agrees well with the dynamic heterogeneity length scale for the structural relaxation estimated by 4- dimensional NMR, justifying the use of ξ. Presented analysis of large number of materials reveals no clear correlation between ξ and fragility. However, there is a strong correlation between the cooperativity volume ξ 3 and the activation volume measured at T g . This observation suggests that only the volume (pressure) dependence of structural relaxation time correlates directly with the cooperativity size. However, the pure thermal (energetic) contribution to the structural relaxation, the so-called isochoric fragility, exhibits no correlation to the heterogeneity length scale ξ, or the amount of structural units in ξ 3 . The presented results call for a revision of traditional view on the role of cooperativity/heterogeneity in structural relaxation of glass forming systems. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Understanding the microscopic mechanism governing the glass transition remains one of the most challenging problems in the condensed matter physics [1–4]. At high temperatures liquids exhibit a simple Arrhenius behavior of the structural relaxation time τ α . At lower temperatures, however, the relaxation time increases much faster than the Arrhenius law. In another words, the apparent activation energy of the structural relaxation increases strongly with decrease in temperature close to the glass transition T g . Following the Adam–Gibbs idea [5], many researchers ascribe this non-Arrhenius temperature dependence of τ α to a significant increase in molecular cooperativity involved in the structural relaxation. The deviation from the Arrhenius dependence is traditionally quantified by the fragility index m, that is the slope of the log τ α vs. T g /T at T g [2]: m = d logτ α dT g = T j T =T g : ð1Þ This concept leads to the intuitive connection between fragility and cooperativity: more fragile systems are expected to have higher cooperativity involved in the structural relaxation. The studies of cooperativity, however, face the problem of experi- mental estimates that would not involve convoluted and model- dependent assumptions. In many cases researchers measure dynamic heterogeneity and relate the obtained heterogeneity length scale to the cooperativity involved in structural relaxation [6–9]. These studies reveal no particular correlations between fragility and dynamic heterogeneities. According to many models [10–16] the length scale of dynamic heterogeneities ξ can be also estimated from the low-frequency vibrational spectrum, the so-called boson peak: ξ≈S V T ν BP : ð2Þ Here V T is the transverse sound velocity, ν BP is the boson peak frequency and S is a constant ~ 0.5–1, depending on the model. Although this length is estimated from the vibrational spectra, i.e., dynamic measurements, it reflects the size of frozen in fluctuations in elastic constants, i.e. static structure. It is not obvious how this length relates to the length scale of dynamic heterogeneities. Wolynes and coworkers showed in the framework of the Random first-order transition theory that the vibrational modes of the domain walls of the entropic droplets constitute the boson peak with the frequency described by Eq. (2) Journal of Non-Crystalline Solids 357 (2011) 351–356 ⁎ Corresponding author. Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, TN 37996, USA. E-mail address: sokolov@utk.edu (A.P. Sokolov). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.06.071 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol