Density-functional theory of the crystallization of hard polymeric chains

Abstract

We study how connectivity influences the crystallization of fully flexible model polymers by applying a recently advanced amalgamation of the Green-function description of polymers, and the density-functional theory of simple liquids. Our calculations show that the model polymers only crystallize if the effective Kuhn length of the chains is sufficiently large compared with the range of the hard-core interaction between the segments. Also shown is the importance of bond-length fluctuations for the stability of the crystal phase.

Static and dynamic scaling behavior of a polymer melt model with triple‐well bending potential

“…From theoretical perspective, attempts have been made to understand thermodynamics of polymer crystallization. These efforts include lattice-based model [5], Landau-de Gennes types of approach [6] and density functional theory [7,8]. Among these, the density-functional theory is a particularly promising approach as it can predict equilibrium features of inhomogeneous semicrystalline structure from the homogeneous melt structure provided that a suitable free-energy functional is employed and accurate information about chain conformations and structure of * Correspondence to: sjabbari@uni-mainz.de polymeric liquids is supplied [9].…”

Theory of the Crystallization of Hard Polymeric Chains in an Orienting Field

“…We apply a recently proposed polymeric density functional theory (DFT). The model polymers consist of N beads that interact through a hard-core repulsive potential and that are connected by freely hinged phantom bonds with an adjustable bond stiffness.…”

“…It is a model-dependent quantity. For our model polymer we define this probability, such that it interpolates between the standard Gaussian and Kuhn models, where l is a mean length of the bonds and ξ is a root-mean-square deviation from this length. The effective Kuhn length l K of the model may be expressed in terms of l and ξ, as l K = .…”

“…For our model polymer we define this probability, such that it interpolates between the standard Gaussian and Kuhn models, where l is a mean length of the bonds and ξ is a root-mean-square deviation from this length. The effective Kuhn length l K of the model may be expressed in terms of l and ξ, as l K = . We distinguish two regimes: one where our model behaves like a freely hinged chain model for ξ ≪ l with fixed bond length l K = l and one where it becomes equivalent to the standard Gaussian-chain model with a root-mean-square bond extension l K = ξ, corresponding to the limit ξ ≫ l .…”

“…For use in a DFT of the crystal phase, it turns out useful to expand the density ρ( r ) = ρ L + Δρ( r ) around that of the liquid state, ρ L , and neglect the terms of higher than second order in perturbation Δρ. Applying the methodology presented in ref , we find for difference between the configurational free energy of the solid and that of the melt where the first two terms are the free energies of the ideal solid and melt and the third term enters due to the connectivity of the polymers. A consequence of the ground-state approximation is that eq 6 only describes (positional) ordering on short wavelengths, although the coupling to the external field described next does not preclude long-range configurational effects.…”