Phase transition behaviours of a single dendritic polymer

Morphology and thermodynamics of polymers with monofunctional hydrogen bonding ends in dilute and semidilute concentration

Rheological properties of supramolecular polymers (SMPs) depend on their equilibrium structure including the size, the number, and the topology of aggregates. A polymer with a hydrogen bonding (H-bonding) motif at both ends is one widely used precursor to build SMPs. Due to the complex interplay between chain stiffness, H-bonding interaction, polarity along a chain, and polymer conformational entropy, it is difficult to theoretically predict the structure of SMPs. In this work we investigate thermodynamics of SMPs with H-bonding ends in a wide range of densities. A replica exchange stochastic approximation Monte Carlo method with coarse-grained models for polyethylene and polybuthylene glycols is used. Our simulation shows that SMPs have two morphological transition lines with increasing temperature, a ring-linear transition, and a linear-free chain transition. The latter is a thermodynamic transition and turns out to be continuous. Comparing the two different spacers, we find that ring-linear transition temperatures differ from each other at the constant volume fraction due to different looping probabilities, which can be calculated from the average polymer size by mean field. However, the linear-free chain transition temperatures are similar because the entropic penalty to form a hydrogen bond mainly depends on the probability of finding H-bonding groups in a system, which is the same for both systems at a given volume fraction.

Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.