Dynamic Heterogeneity and Cooperative Length Scale at Dynamic Glass Transition in Glass Forming Liquids

Abstract

Understanding the evolution of the cooperative molecular mobility as a function of time and temperature remains an unsolved question in condensed matter research. However, recently great advances have been made within the framework of the Adam–Gibbs theory on the connection between cooperatively rearranging regions, or dynamic heterogeneities, i.e., domains of the supercooled liquid whose relaxation is highly correlated. The growth of the size of these dynamic domains is now believed to be the driving mechanism for different experimental parameters like relaxation times and viscosity of supercooled liquid approaching the glass transition. Recent studies have shown the evolution of cooperative motions in supercooled liquids using different experimental tools and models. In this work, broadband dielectric spectroscopy and modulated temperature differential scanning calorimetry were carried out on six different amorphous glass-forming systems in order to scan a wide range of relaxation times and temperatures. Two different models based on four point dynamic susceptibilities and the thermodynamic fluctuation approach, have been used to compare the temperature evolution of the number of molecules dynamically correlated during the α-relaxation process. Divergences and convergences between these two models are discussed.

Rotational Dynamics of a Probe in Rubbery Polymers Characterized by Time‐Resolved Fluorescence Anisotropy Measurement

“…A slight difference between C p by the quasi‐isothermal mode and C ′ p by the heat–cool mode can be recognized. This is actually seen in the literature for several polymers . Thus, Δ C p −1 was determined from C p and δT in C ″ p for both PI and NBR.…”

“…A method widely used for characterizing the ξ CRR is TM‐DSC, which simultaneously detects the real and imaginary parts ( C′ p and C ″ p ) of the heat capacity ( C p ) for polymers, and is given by where Δ C p −1 is the difference in the inverse between the glassy and liquid heat capacities at T g , k B is the Boltzmann constant, ρ is the density of the sample at T g , and δT is the temperature fluctuation in CRR. The ρ values of PI and NBR at room temperature were found to be ≈0.92 and 0.97 g cm −3 , respectively, and slightly increased to 0.98 and 1.01 g cm −3 at their respective T g values .…”

“…The TM‐DSC (Q200 TA Instruments) measurements for PI and NBR were performed in quasi‐isothermal and heat–cool modes. The former mode has been demonstrated to examine the heat capacity of a sample more accurately than that in conventional calorimetric measurement . In this mode, the heat capacity ( C p ) was obtained with a modulation amplitude of ±1 K and an oscillation period of 100 s. The latter mode was used to determine the real and imaginary components ( C ′ p and C ″ p ) of the dynamic heat capacity.…”

“…The measurements in the heat–cool mode were performed with a modulation amplitude of ±1 K, an oscillation period of 60 s, and a cooling rate of 0.5 K min −1 . These conditions were well established in the literature for determining the size of the cooperatively rearranging region (CRR) for various amorphous polymers using the Donth's model as discussed later with Equation …”

“…The former mode has been demonstrated to examine the heat capacity of a sample more accurately than that in conventional calorimetric measurement. [30][31][32][33] In this mode, the heat capacity (C p ) was obtained with a modulation amplitude of ±1 K and an oscillation period of 100 s. The latter mode was used to determine the real and imaginary components (C′ p and C″ p ) of the dynamic heat capacity. The measurements in the heat-cool mode were performed with a modulation amplitude of ±1 K, an oscillation period of 60 s, and a cooling rate of 0.5 K min −1 .…”