Related papers: Elastic Lattice Polymers
We give two different, statistically consistent definitions of the length l of a prime knot tied into a polymer ring. In the good solvent regime the polymer is modelled by a self avoiding polygon of N steps on cubic lattice and l is the…
We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase…
The entropic pressure in the vicinity of a cubic lattice knot is examined as a model of the entropic pressure near a knotted ring polymer in a good solvent. A model for the scaling of the pressure is developed and this is tested numerically…
The negative internal energetic contribution to the elastic modulus (negative energetic elasticity) has been recently observed in polymer gels. This finding challenges the conventional notion that the elastic moduli of rubberlike materials…
Exact results for the scaling properties of compact polymers on the square lattice are obtained from an effective field theory. The entropic exponent \gamma=117/112 is calculated, and a line of fixed points associated with interacting…
We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to…
We present a detailed study of the static and dynamic behavior of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [{\it Zhang et al.} ACS Macro Lett. 3,…
We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain.…
We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Bl\"ote and Nienhuis in J. Phys. A. {\bf 22}, 1415 (1989) and it describes polymers with some attraction, providing thus…
We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…
We compare Monte Carlo simulations of knotted and unknotted polymers whose ends are connected to two parallel walls. The force $f$ exerted on the polymer is measured as a function of the separation $R$ between the walls. For unknotted…
Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and Molecular Dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
We investigate the Rouse dynamics of a flexible ring polymer with a prime knot. Within a Monte Carlo approach, we locate the knot, follow its diffusion, and observe the fluctuations of its length. We characterise a topological time scale,…
In this paper we present simulations of a surface-adsorbed polymer subject to an elongation force. The polymer is modelled by a self-avoiding walk on a regular lattice. It is confined to a half-space by an adsorbing surface with attractions…
We study the static properties of a semiflexible polymer exposed to a quenched random environment by means of computer simulations. The polymer is modeled as two-dimensional Heisenberg chain. For the random environment we consider hard…
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…
We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of $t$ teeth, also modelled as…
We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of "interacting elastic lattice polymers" and allows a sufficiently good sampling of long and…
The distribution of monomers in a coating of grafted and adsorbing polymers is modelled using a grafted staircase polygon in the square lattice. The adsorbing staircase polygon consists of a bottom and a top lattice path (branches) and the…