Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush

Abstract

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

Perspectives on Theoretical Models and Molecular Simulations of Polymer Brushes

“…However, there exist some differences in the density distribution of individual monomers and free chain ends of grafted polymers in the direction perpendicular to the grafting plane when comparing scaling approaches, 42 Flory-type approaches, 43 and SCF approaches. 45 Both scaling and Florytype approaches utilize a step function to depict the monomer density distribution. This function linearly decreases to zero as one moves from the substrate (h = 0) to the top of the brush.…”

“…Pioneering theoretical research on polymer brushes, initiated by Alexander and de Gennes, closely paralleled experimental investigations. Single-chain mean-field theory (SCMFT) and its associated models (worm-like chain model, self-consistent field model) have been developed to elucidate the grafting density and conformation of polymer brushes. − SCMFT allows for the use of a simplified parameter, ∑ = σπ R g 2 , to effectively describe and differentiate tethered polymer chains across three principal regimes: (1) the mushroom regime, characterized by highly flexible polymer chains (∑ < 1), (2) the crossover regime (∑ ≈ 1), and (3) the brush regime, marked by highly stretched polymer chains (∑ ≫ 1). This model not only elucidates the mushroom-to-brush transition from a single grafted chain to a polymer brush but also accounts for the influence of the solvent on grafting density in relation to this transition.…”