Compression of finite size polymer brushes

TL;DR

This paper investigates edge effects in compressed finite-size polymer brushes, deriving scaling laws for penetration depth and border chain extension, and calculating effective line tension and force variation.

Contribution

It introduces a scaling framework for edge effects in finite polymer brushes using local Flory theory, providing new quantitative insights.

Findings

Penetration depth scales as $\xi\, ext{proportional to}\, h_0(h_0/h)^{1/2}$.

Border chain extension follows a scaling law $u_S = \xi \, ext{phi}(S/\xi)$.

Effective line tension and force variation with compression are quantified.

Abstract

We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $\xi\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a disk), the lateral extension $u_S$ of the border chains follows the scaling law $u_S = \xi \phi (S/\xi)$. The scaling function $\phi (x)$ is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small $x$, $\phi (x)$ decays as a power law in agreement with simple arguments. The effective line tension and the variation with compression height of the force applied on the brush are also calculated.