The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore.

Waldemar Nowicki

doi:10.3390/polym12122931

Abstract

The structure and dynamic properties of polymer chains in a confined environment were studied by means of the Monte Carlo method. The studied chains were represented by coarse-grained models and embedded into a simple 3D cubic lattice. The chains stood for two-block linear copolymers of different energy of bead–bead interactions. Their behavior was studied in a nanotube formed by four impenetrable surfaces. The long-time unidirectional motion of the chain in the tight nanopore was found to be correlated with the orientation of both parts of the copolymer along the length of the nanopore. A possible mechanism of the anomalous diffusion was proposed on the basis of thermodynamics of the system, more precisely on the free energy barrier of the swapping of positions of both parts of the chain and the impulse of temporary forces induced by variation of the chain conformation. The mean bead and the mass center autocorrelation functions were examined. While the former function behaves classically, the latter indicates the period of time of superdiffusive motion similar to the ballistic motion with the autocorrelation function scaling with the exponent t5/3. A distribution of periods of time of chain diffusion between swapping events was found and discussed. The influence of the nanotube width and the chain length on the polymer diffusivity was studied.

Highlights

In most cases, the self-diffusion process can be described as a relation between the mean square displacement (MSD) and time, expressed as a scaling law with the exponent equal to 1
Function: in the initial region where ν = 1 and diffusion coefficient is smaller than monomer, relationship described by scaling exponent
The results presented above allow the following description of the phenomena occurring in results presented above allow the following symmetrical description ofdiffusion the phenomena in the the The studied system

Summary

Introduction

The self-diffusion process can be described as a relation between the mean square displacement (MSD) and time, expressed as a scaling law with the exponent equal to 1. The origin of the discrepancy between the properties of the system, and the scaling law with the exponent 1 is that its derivation requires that the Brownian particle should move in an infinite structureless medium. This assumption is generally incorrect when the Brownian motion takes place in a complex medium or when the diffusively migrating objects should be treated as structured species whose structural elements’ motions are only partly independent, but mutually correlated in general. The diffusion of the theta chain (Zimm model [6,7])

Objectives

Results

Conclusion