Molecular simulation of 2-dimensional microphase separation of single-component homopolymers grafted onto a planar substrate

Abstract

-The structural phase behavior of polymer brushes, single-component linear homopolymers grafted onto a planar substrate, is studied using the molecular Monte Carlo method in 3 dimensions. When simulation parameters of the system are set in regions of macrophase separation of solution for the corresponding nongrafted homopolymers, the grafted polymers also prefer segregation. However, macrophase separation is disallowed due to the spatially-fixed grafting points of the polymers. Such constraints on the grafting are similar to connecting points between blocks of non-grafted diblock copolymers at the microphase separation in the melt state. This results in "microphase separation" of the homopolymer brush in the lateral direction of the substrate. Here we extensively search the parameter space and reveal various lateral domain patterns that are similar to those found in diblock copolymer melts at microphase separation.Polymer chains grafted onto substrates, i.e. polymer brushes, have been extensively studied in physics, chemistry, materials science, and other scientific and industrial fields. Polymer brushes are widely utilized for applications such as wetting, adhesion, surface patterning, and colloidal stabilization. Recently, sophisticated polymer brushes, such as brushes composed of diblock copolymers and of binary mixture of homopolymers, have drawn significant attention [1,2]. Polymer brushes on spherical substrates, which are referred to as polymer-grafted colloidal particles, have also attracted wide interest in various scientific and industrial fields [3][4][5].The phase behavior of these complicated brushes is significantly dependent on the molecular architecture, shape of the substrate, ratios between the numbers of polymers of each polymer species, and other characteristics of each system. In the present work, the most basic and simplest polymer brush, i.e. single-component linear homopolymers homogeneously grafted onto a planar substrate, is simulated using the molecular Monte Carlo method to determine the universal and structural phase behavior of polymer brushes.The phase behavior of a solution of single-component nongrafted homopolymers underlies the phase behavior of the present brush. When the chemical and physical parameters of this polymer solution are set in regions within binodal lines of the phase diagram, the non-grafted polymers are segregated into a low-density domain and a high-density domain, which indicates macrophase separation. When the parameters of a layer of the grafted polymers are set in these regions within the binodal lines of the non-grafted polymers, the grafted polymers also prefer segregation. However, due to a topological constraint of the spatially-fixed grafting points of each polymer, macrophase separation of the grafted polymers is disallowed. This constraint has similarity to the topological constraint of connecting points between blocks of non-grafted diblock copolymers at phase separation in the melt state. These non-grafted diblock copolymers exhibit microp...

Conducting transition analysis of thin films composed of long flexible macromolecules: Percolation study

“…This 3-dimensional (3-D) model was also utilized in our recent works [10,11,15], so that the present simulation results can be compared with the ones of these recent works, especially the results of the brush [10], in the equal condition when the simulation conditions are set at the equal values. The validity of the recent work [11] using the solvent-free model is also confirmed in another experimental work [16]. This model is briefly summarized here.…”

“…ρ p(label) (r) and ρ p(unlabel) (r) are the dimensionless local molecular densities of the labelled and unlabelled molecules, respectively. Equation (2) indicates that both the molecular species identically interact with each other, and that the system is equivalent to the single-component solvent-free model [10,11,14]. This is the same as the relation between deuterated and non-deuterated polymers in experiment.…”

“…Here, the phase behaviour of bulk systems of the singlecomponent solvent-free model is quickly summarized [10,11,14]. ρ p = n p R 3 e /V is the dimensionless average volumetric molecular density of the system, where V denotes the system volume and n p is the number of molecules in the system.…”

“…These values are compared with those of the homopolymer brushes. The system of these brushes is the same as the present system except that the polymers of the brushes are grafted onto the hard planar substrate [10,11], so that the dependence of the phase behaviour on the topological constraints, i.e. grafting, is obtained.…”

Preparation and characterization of looped polydimethylsiloxane brushes

“…Such a microphase separation of the homopolymer brush in the lateral direction of the substrate is in good agreement with the results of molecular Monte Carlo simulations that we have previously reported. 30 On the other hand, dewetting-induced aggregation is hindered in looped polymer brushes, because both polymer termini are tethered to the substrate (Figure 5a). This is a possible explanation for why the looped polymer brush surface morphology was unaffected by the environmental (solvent) change.…”