Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

Abstract

The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length N = 64 with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the “conformational” microcanonical ( N V U , where U is the potential energy) and the true microcanonical ( N V E , where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature.

Crystallisation in Melts of Short, Semi-Flexible Hard-Sphere Polymer Chains: The Role of the Non-Bonded Interaction Range

“…The 2D DOS as well as the conditional probabilities are a priori unknown and should be calculated during a simulation. However, since even the estimation of a 1D DOS requires a long computational time, an estimation of a 2D DOS similar to [ 23 , 24 ] is practically impossible for this model. We perform a productive run with the fixed 1D entropy instead of the time-expensive SAMC simulation and accumulate a visitation histogram .…”

Efficient Implementation of Liquid Crystal Simulation Software on Modern HPC Platforms

“…Second, these methods often do not require storing and exchanging any additional data between threads (in contrast to the molecular dynamics, for example). The most common approaches used for the physical problems formulated on cubic lattice are solutions of transport equations (for example, lattice Boltzmann methods used for computational fluid dynamics, CFD [43]), Newtonian-like function optimization [10], and Monte Carlo methods (used for wide range of statistical physics problems in soft matter, bio-chemistry and quantum physics [24,26,31,36,48], and also for function optimization [30]).…”

On the Size Effect of Additives in Amorphous Shape Memory Polymers

“…Crucial to shape memory effect in polymers is the change of chains’ conformation upon deformation and the tendency to recover a high entropic state during structural relaxation. These high entropic conformations have been recently studied for quiescent copolymers of different architectures at low temperatures and under poor-solvent conditions [ 18 , 19 , 20 ].…”