Abstract:
We present a numerical solution of the Worm-Like Chain (WLC) model for semi-flexible polymers. We display graphs for the end-to-end distance distribution and the force-extension relation expected from the model. We predict the expected level of fluctuations around the mean value in force-extension curves. Our treatment analyses the entire range of polymer lengths and reproduces interesting qualitative features seen in recent computer simulations for polymers of intermediate length. These results can be tested against experiments on single molecules. This study is relevant to mechanical properties of biological molecules.

Abstract:
We directly visualize single polymers with persistence lengths ranging from $\ell_p=0.05$ to 16 $\mu$m, dissolved in the nematic phase of rod-like {\it fd} virus. Polymers with sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of semi-flexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract both the Odijk deflection length and the elastic constant of the background nematic phase from the data.

Abstract:
We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin.

Abstract:
Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase diagram for the complete range of semi-flexible polymers, from flexible to stiff. Although a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Changing the internal bending stiffness, the model exhibits different pseudo phases like bent, hairpin or toroidal. In particular, we find thermodynamically stable knots and transitions into these knotted phases with a clear phase coexistence, but almost no change in the mean total energy.

Abstract:
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: \textit{uniform} stretching by external forces and \textit{non-uniform} stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g. fluid in uniform motion, or uniform electric field) by a universal physical framework which leads to general conclusions on different types of polymers. We derive analytical results both for the freely-jointed chain and the worm-like chain models based on classical statistical mechanics. Moreover, we provide a Monte Carlo numerical analysis of the mechanical properties of flexible and semi-flexible polymers anchored at one end. The simulations confirm the analytical achievements, and moreover allow to study the situations where the theory can not provide explicit and useful results. In all cases we evaluate the average conformation of the polymer and its fluctuation statistics as a function of the chain length, bending rigidity and field strength.

Abstract:
We study the model of a partially directed flexible or semi-flexible homopolymer on a square lattice, subject to an externally applied force, in a direction either parallel to, or perpendicular to the preferred direction. The polymer is self-interacting and can therefore undergo a collapse transition. We show that this model can be solved and we obtain the force-temperature phase diagrams which, for the case of flexible polymers, agree with that of Brak et al obtained using a different method. At sufficiently low temperatures, the polymer conformation changes from compact to coil state as the force is increased beyond a critical value. This transition is second or first order for the completely flexible or semi-flexible polymer, respectively.

Abstract:
We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P , its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. At the blob size P/a^2 , where a is the size of a monomer, the statistics becomes that of an ideal chain. As the blob size further decreases to below the persistence length P, the statistics is that of a rigid rod. We argue that semi-flexible polymer in translocation should include the three regions: a self-avoiding region, an ideal chain region and a rigid rod region, under uneven tension propagation, instead of a uniform scaling picture as in the case of a completely flexible polymer. In various regimes under the effect of weak, intermediate and strong driving forces we derive equations from which we can calculate the translocation time of the polymer. The translocation exponent is given by \alpha=1+\mu, where \mu is an effective exponent for the end-to-end distance of the semi-flexible polymer, having a value between 1/2 and 3/5, depending on the total contour length of the polymer. Our results are of relevance for forced translocation of biological polymers such as DNA through a nanopore.

Abstract:
We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.

Abstract:
Necking or cold drawing is a smoothed jump in cross-sectional area of long and thin bars (filaments orfilms) propagating with a constant speed. The necks in polymers, first observed about seventy years ago, arenow commonly used in modern processing of polymer films and fibers. Yet till recently there was a lack infundamental understanding of necking mechanism(s). For semi-crystalline polymers with co-existingamorphous and crystalline phases, recent experiments revealed that such a mechanism is related tounfolding crystalline blocks. Using this idea, this paper develops a theoretical model and includes it in ageneral continuum framework. Additionally, the paper explains the forced (reversible) elasticity observedin slowly propagating polymeric necks, and also briefly analyses the viscoelastic effects and dissipative heatgeneration when polymer necks propagate fast enough.

Abstract:
A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.