SCFT Study of Microphase Separation in Mixed Polymer Brushes Grafted on Cylindrical Surface

Abstract

We report on microphase separation behaviors of mixed polymer brushes grafted onto an infinitely long cylindrical rod by performing polymer self-consistent field theory (SCFT) calculation with "masking" technique. The "masking" technique is especially suitable to deal with systems of confined polymers grafted onto curved surfaces. We have developed a method to solve the morphology of block copolymers confined into complicated topographic surfaces with SCFT. In this paper, this unique technique is extended to solve the SCFT for nanorod grafted by mixed polymer brushes. Furthermore, the use of simple Cartesian grids in a cubic computational cell with periodic boundary conditions makes it possible to solve diffusion equations in SCFT by utilizing an efficient and highly accurate pseudo-spectral method involving fast Fourier transform. Both parallel rippled phase and ring-shaped phase are predicted. We have investigated the influences of the cylinder radius, grafting density and interaction between the two incompatible grafting polymers on the stability of the two typical phases. Our results show that the system prefers the ring-shaped phase with the increase of the cylinder radius, grafting density and interaction between the two grafting polymers. Phase diagrams involving these parameters are constructed, and we explain the reason of the transition between the parallel rippled phase and ring-shaped phase in terms of the degree of phase segregation. Again, the degree of phase segregation is higher with larger cylinder radius, grafting density and interaction between the two grafting polymers. By comparing the degree of phase segregation and free energy of the parallel rippled and ring-shaped phases at the same condition, we found that the ring-shaped phase favors the entropic part of the free energy while the parallel rippled phase significantly reduces the enthalpy. Therefore, when the degree of phase segregation is low, the free energy of the system is dominated by the enthalpy, leading to the parallel rippled phase; when the degree of phase segregation is high, the free energy of the system is dominated by the entropic part and the ring-shaped phase is stable. We also found that the domain numbers of parallel rippled phase and the period of alternating ring-shaped phase vary with the radius of cylinder. These predictions are expected to be helpful in rational design and fabrication of such novel polymer brushes.

Hierarchical Superstructures Assembled by Binary Hairy Nanoparticles

“…Fortunately, more efficient two-dimensional (2D) calculations are helpful to deal with this problem. Our previous work 19 showed that the basic physical rule governing the microphase behavior of mixed polymer-grafted particles is essentially the same in 2D. In this case, the balance between the A/B interface interaction and the chain stretching will result in rippled phases with optimal domain numbers for the isolated symmetric binary hairy particle.…”

“…Their results suggest a new method to manipulate nanoparticles with precisely controlled numbers and locations of active sites. Recently, by incorporating the “masking” technique into the SCFT, we systematically investigated the morphology of isolated binary hairy nanoparticles. − Our method to solve the SCFT equations on a spherical surface in a simple Cartesian coordinate system utilizes the efficient and highly accurate pseudospectral method . Meanwhile, Zhao and Zhu − carried out a series of experiments to study the microphase structures of mixed poly­( tert -butyl acrylate) (P t BA)/polystyrene (PS) brushes grafted on a silica particle.…”

“…In this case, the balance between the A/B interface interaction and the chain stretching will result in rippled phases with optimal domain numbers for the isolated symmetric binary hairy particle. 19,49 The optimal domain numbers at different size ratios R/( N b) are shown in Figure S2.…”

Binary hairy nanoparticles: Recent progress in theory and simulations

“…In addition, the difference of the free energy between the two phases has a strong dependence on solvent entropy, and hence they predicted that both the parallel ripple and ring phases are possible to be observed in experiments. Subsequently, they also investigated the microphase separation of mixed brushes on an infinitely long cylinder . Without the spatial constraint of the two semi‐spherical caps, regular parallel ripple phase and ring phase can be obtained more easily.…”

Ripple structures of mixed homopolymer brushes grafted on cylindrical surfaces: controlling the orientation of the pattern by attuning the substrate curvatures

“…17 However, it was found that the free energy of the system is mainly determined by the entropy of the solvent, which means that a slight change of the solvent selectivity could reverse the relative stability of perpendicular and parallel ripple structures. 18 In this paper, to simplify the system, we removed the solvent, and investigated a brush consisting of two chemically incompatible homopolymers graed onto cylindrical surfaces (in reality this corresponded to mixed brushes in contact with a neutral polymer melt composed of much longer chains, ensuring a dry brush condition). We assumed that the chain end segments were xed by covalent connection to the graing site, i.e., the system could only undergo microphase separation.…”