Entropic trapping and polymer dynamics in static, quasi-periodic arrays of obstacles in two dimensional media - Nixon, Grant Ian (University of Ottawa (Canada), 2003)
Using the bond fluctuation algorithm of Carmesin and Kremer (Carmesin and Kremer 1988), we investigate the static and dynamic properties of self-avoiding linear polymers embedded in static, two-dimensional (d=2), quasi-periodic arrays of obstacles with entropic traps. The phenomenon of polymer collapse, the closely related enrichment and depletion of polymer configurations, the conformational relaxation, and the diffusive behaviour are all investigated within the framework of the lattice Monte Carlo method. Several distinct dynamical regimes are encountered: the (obstacle-free) Rouse-like regime (obstacle sub-array concentration c=0), the reptation regime for chains in perfectly periodic obstacle sub-arrays (c=1), and, in the presence of disorder and entropic traps (0<c<1), the anomalous regimes where the scaling properties differ from those predicted by the Rouse and reptation theories. Prior to the onset of normal diffusion, even systems characterized by very slight disorder (i.e., the existence of random isolated void spaces) are shown to lead to long, transient, subdiffusive regimes where the mean square displacement of the centre of mass scales as RCM 2∼D*tbeta where 0.5<beta<1 is the anomalous diffusion exponent and D* is the anomalous diffusion coefficient. In such disordered systems, conformational relaxation is shown to be coupled with centre of mass subdiffusion, resulting in long, time-stretched, exponential relaxation of the Rouse coordinates, viz. exp.[-(t/tau) alpha]. The stretching exponents 0.5<alpha<1 are shown to be closely related to the anomalous diffusion exponents beta and where the alpha, for a given chain, are shown to decrease with increasing mode number and with strong disorder. The molecular size-dependence of the steady-state diffusion coefficient, as well as that of the conformational relaxation time, is shown to be greatest when the concentration of obstacles is large and when that of the voids is non-vanishing (c ≲ 1). Thus, the dynamical scaling in entropic trapping systems is non-monotonic with respect to the concentration of obstacles. Polymer reptation dynamics thus appears to be intrinsically unstable with respect to static disordered systems of obstacles. Having demonstrated the coupling of centre of mass subdiffusion and conformational relaxation, we introduce a new relaxation length scale, lambda=(2dD*t alpha)1/2, that is more appropriate for characterizing disordered systems than is the ubiquitous radius of gyration used in both the Rouse and reptation theories. However, lambda could not be distinguished from the radius of gyration in terms of the molecular size scaling given the uncertainty in our data. Finally, having proposed a theoretical dynamic model of entropic trapping for dilute polymer solutions in embedded mesoscopic voids, we investigate the effect of polymer solution concentration on the dynamics for both monodisperse and polydisperse polymer solutions. New, unexplored dynamical behaviours are manifest as the conformational and translational entropies compete to minimize the system free energy.
Keywords: Physics, Molecular.; Physics, Fluid and Plasma.