Thermodynamic scaling of dynamics in polymer melts: Predictions from the generalized entropy theory

Abstract

Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ γ /T , where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ∼ 50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.

Influence of Cohesive Energy and Chain Stiffness on Polymer Glass Formation

“…In particular, the chains in the more realistic model have the structure of poly(n-α-olefins) where the terminal segments on the side chains are assigned different, specific van der Waals interaction energies with other united atom groups. The greater realism introduced into the LCT and the GET by this new model enables testing the limits of validity of the present model with a single monomer averaged van der Waals energy [9,10,22,[25][26][27][28][29][30]. In addition, the subsequent work will study how the variation of the specific interactions can be used to exert greater control over the properties of designed materials.…”

Generalized Entropy Theory of Glass Formation in Polymer Melts with Specific Interactions

“…To this end, the new extension of the LCT is combined with the AG theory [16,17], thereby providing a similar generalization of the GET to describe polymer glass formation. Moreover, the greater realism introduced into the LCT and the GET by the new physical model enables testing the limits of validity of the simpler LCT model with a single monomer averaged van der Waals energy [13,14,[18][19][20][21][22][23][24][25], which is also discussed in detail in the present paper.…”

Scaling of the dynamics of flexible Lennard-Jones chains

“…Tsolou et al [63] found γ = 2.8 from power-law density scaling of simulation data of a united atom model of cis-1,4-polybutadiene. A possible explanation for this low value of γ has been given by Xu [64] who showed using the generalized entropy theory that polymer rigidity significantly decreases the density scaling exponent γ. Xu quantified polymer rigidity y the bending energy of the angle between two bonds.…”