Phase transitions in single grafted molecules*

We use Brownian dynamics simulations and analytical theory to study and compare
different phase transitions in single molecules that are grafted to a bare or
polymer-functionalized surface.

In the first part, we compare two prominent types of transitions on bare
substrates: One is the adsorption transition of a loop (a chain with two ends
bound to an attractive substrate) driven by an attraction parameter ε, and the
other is the loop-stretch transition in a chain with one end attached to a
repulsive substrate, driven by an external end-force F applied to the free end.
Close to the transition points, both the static and the dynamic behavior of
chains with different length are very well described by a scaling Ansatz with
the scaling parameters (ε−ε_c)N^φ (adsorption transition) and (F−F_c)N^ν
(loop-stretch transition), respectively, where φ is the crossover exponent of
the adsorption transition, and ν the Flory exponent. Explicit crossover
functions are based on an Ansatz for the analytical form of the order parameter
distributions at the respective transition points. The transition between the
adsorbed state and the stretched state is first order. Nevertheless, the
characteristic relaxation time is found to grow according to a power law as the
transition point is approached. We present a dynamic effective interface model
which reproduces these observations an provides an excellent quantitative
description of the simulation data.

In the second part, we discuss the adsorption transition of a single
adsorption-active polymer embedded in a polymer brush. This transition
is first order and can serve as a basis for the design of a polymer-based
sensor or switch with sharp switching transition and fast response time.
We discuss in particular the influence of polydispersity in the brush,
and show how it can be used to tune the characteristics of the switch,
i.e., the sharpness of the transition and the response time.