Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains.
We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, 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. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition, and the mean position of the chain end in the case of the loop-stretch transition. Clo…
Anomalous critical slowdown at a first order phase transition in single polymer chains
Using Brownian Dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order, (in the infinite chain length limit, the stretching degree of the chain jumps discontinuously), 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 and provides an excellent quantitaive description of the simulations data. The generic nature of the theoretical model suggests that the unconventional mixing of features that are characteri…
Contour-Variable Model of Constitutive Equations for Polymer Melts
Based on a modified expression of the rate of the convective constraint release, we present a new contour-variable model of constitutive equations in which the non-uniform segmental stretch and the non-Gaussian chain statistical treatment of the single chain are considered to describe the polymer chain dynamics and the rheological behavior of an entangled system composed of linear polymer chains. The constitutive equations are solved numerically in the cases of steady shear and transient start-up of steady shear. The results indicate that the orientation and stretch, as well as the tube survival probability, have strong dependence on the chain contour variable, especially in the high-shear-…