Molecular cooperativity in the dynamics of glass-forming systems: A new insight

Abstract

The mechanism behind the steep slowing down of molecular motions upon approaching the glass transition remains a great puzzle. Most of the theories relate this mechanism to the cooperativity in molecular motion. In this work, we estimate the length scale of molecular cooperativity xi for many glass-forming systems from the collective vibrations (the so-called boson peak). The obtained values agree well with the dynamic heterogeneity length scale estimated using four-dimensional NMR. We demonstrate that xi directly correlates to the dependence of the structural relaxation on volume. This dependence presents only one part of the mechanism of slowing down the structural relaxation. Our analysis reveals that another part, the purely thermal variation in the structural relaxation (at constant volume), does not have a direct correlation with molecular cooperativity. These results call for a conceptually new approach to the analysis of the mechanism of the glass transition and to the role of molecular cooperativity.

Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. II. Thermal liquids

“…Given Eq. (39), and that prior experiments [13] generically found V # (T )  ln  (T ) in the deeply supercooled regime consistent with our theory, an effective barrier proportional the "number of correlated molecules" can be viewed as a logical inference of the ECNLE approach. However, the notion of a number of correlated particles determining the barrier, a central concept of models based on compact domains of re-arranging particles, does not directly enter ECNLE theory.…”

“…Very interestingly, the activation volume appears to be tightly correlated with measures of dynamic heterogeneity and correlation. Specifically, the cube root of the activation volume at T g has been shown to correlate with the characteristic length scale of the Boson peak [13,14]. In addition, V # (T ) appears to have the same temperature dependence as the number of correlated molecules, N corr (T ) , as extracted from nonlinear dielectric measurements for glycerol [62].…”

“…The similarities and differences between our approach and the phenomenological shoving model [11,12] are established in section V, including the relative role of the shear modulus and a growing dynamical length scale in determining the collective barrier in the deeply supercooled regime. Section VI presents calculations for the effect of pressure on the alpha relaxation, and also analyzes an "activation volume" that grows with cooling and is strongly correlated with the number of cooperatively moving molecules and other measures of dynamic heterogeneity [13,14]. Connections of our approach with diverse alternative theories and models, including Arrhenius, mode coupling theory (MCT) [15], entropy crisis [16,17], dynamic facilitation [18], and phenomenological two-barrier approaches [19][20][21][22] is the subject of section VII.…”

String model for the dynamics of glass-forming liquids

“…also accords with the typical "cooperative motion scale" from neutron and Raman scattering, Boson peak, and NMR measurements. 75 In addition, the inset of Fig. 8 shows that the predicted low T limit of G/ μ = L/L A from our model is compatible with the experimentally observed behavior of several glass-forming liquids.…”

Measurement of Segmental Mobility during Constant Strain Rate Deformation of a Poly(methyl methacrylate) Glass

“…As a result, simulations are likely to miss some of the complex features associated with highly cooperative 44 and spatially heterogeneous dynamics 43,[45][46][47] . For example, while constant stress experiments have shown that polymer segmental dynamics during plastic flow become substantially more spatially homogeneous 20 , this feature is much less prominent in computer simulations 48 .…”