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.

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Many interesting problems in cellular biophysics involve the dynamics of filamentary elastic objects with bend and twist degrees of freedom, moving in a viscous environment. Motivated by the mysterious macrofiber formation in B. subtilis and the rotational dynamics of bacterial flagella, we have sought to establish a general theoretical structure to deal with elastic filament dynamics, analyze these equations for model systems, and to determine the important physical parameters that set the dynamical scales for these systems. We first studied the novel problem of a rotationally forced elastic filament in a viscous fluid [1] to examine the competition between twist injection, twist diffusion, and writhing motions. Two dynamical regimes separated by a Hopf bifurcation were discovered: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. Next, we extended elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality [2]. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom was developed using the natural frame of space curves, spanning from the inviscid limit to the viscously-overdamped regime applicable to cellular biology. To be able to measure the elastic properties of cell-sized objects, such as bacterial fibers [3], we utilized an optical trapping system to study the relaxation of a single fiber of B. subtilis which was bent and then released. By analyzing the relaxation time, the bending modulus of the bacterial cell wall was measured to be 1.6 ± 0.6 x 10⁻¹² erg·cm. This number is important in understanding the scales of forces and torques that are present in macrofiber formation and motion, lending insight into the mechanism behind these phenomena.

Two models are presented to describe the immediate environment surrounding negatively charged contaminants in an idealized plasma. The first model uses Poisson's equation to determine the contaminant charge and voltage. This model predicts a critical radius of 40 microns or less below which Poisson's equation is no longer valid. For contaminant radii less than 40 microns, the Coulomb potential is used to find the contaminant charge and voltage. Both models predict negative charges on the order of 10-14 Coulombs, and voltages on the same order of magnitude as the electron energy.