Linear and ring polymers in confined geometries

Zoryana Usatenko,Hassan Chamati,Dirk Romeis,Piotr Kuterba

doi:10.1140/epjst/e2016-60335-0

Abstract

A short overview of the theoretical and experimental works on the polymer-colloid mixtures is given. The behaviour of a dilute solution of linear and ring polymers in confined geometries like slit of two parallel walls or in the solution of mesoscopic colloidal particles of big size with different adsorbing or repelling properties in respect to polymers is discussed. Besides, we consider the massive field theory approach in fixed space dimensions d = 3 for the investigation of the interaction between long flexible polymers and mesoscopic colloidal particles of big size and for the calculation of the correspondent depletion interaction potentials and the depletion forces between confining walls. The presented results indicate the interesting and nontrivial behavior of linear and ring polymers in confined geometries and give possibility better to understand the complexity of physical effects arising from confinement and chain topology which plays a significant role in the shaping of individual chromosomes and in the process of their segregation, especially in the case of elongated bacterial cells. The possibility of using linear and ring polymers for production of new types of nano- and micro-electromechanical devices is analyzed.

Highlights

Polymer-colloid mixtures have attracted a great deal of interest during the last few decades because of practical relevance, as well as for fundamental reasons [1,2,3,4,5]
The validity of the universal density-force relation proposed by Joanny, Leibler and de Gennes [14] for the different cases of a single polymer with one end fixed in the half space bounded by the wall, a single chain trapped in a slit geometry of two parallel walls, for the case of a dilute and semi-dilute solution of free polymers in a half space and for the case of polymer in a half space containing a mesoscopic colloidal particle of arbitrary shape was discussed initially in [23]
In a series of our papers [29, 30] the universal density-force relation is analyzed by analogy as it was proposed by Eisenriegler [23] and the corresponding universal amplitude ratio was obtained in the framework of the massive field theory approach directly in fixed space dimensions d = 3

Summary

Introduction

Polymer-colloid mixtures have attracted a great deal of interest during the last few decades because of practical relevance, as well as for fundamental reasons [1,2,3,4,5]. The question of influence of the polymer chain topology on the depletion interaction potentials and the depletion forces was investigated in a series of our papers [56–58], where we performed the investigation of a dilute solution of ring polymers immersed in a confined geometry like slit of two parallel walls with different boundary conditions and in a solution of mesoscopic colloidal particles of one sort or two sorts which can be both attractive, both repulsive for polymers or discuss the mixed case when one sort of mesoscopic colloidal particles is attractive for ring polymers and the other one is repulsive It should be mentioned, that our investigation and calculation of the respective depletion interaction potentials and the depletion forces for linear and ring polymers with the EVI in a good solvent immersed in confined geometries is based on one of the powerful analytical method: the massive field theory approach in fixed space dimensions d = 3 (see [25, 29, 30, 59]) up to one-loop order, which demonstrates quite good agreement with the results of numerical calculations and experimental data

The thermodynamic description and the model

Dilute solution of ideal polymers in a slit geometry

Dilute solution of linear and ring polymers with the EVI in a slit geometry

Conclusions and discussions