arXiv subjects

Marcin R. Piątek

Publications and source records attributed to Marcin R. Piątek.

3 recordsLinked to original sources

arXiv2026

SPOCK*: A simple program for simulating knotted and concatenated polymer rings off-lattice

The purpose of this work is to present SPOCK*, a Monte Carlo code specifically written to investigate the thermodynamic and mechanical properties of polymers in the presence of topological constraints. The interactions between the monomers are described by a Lennard-Jones potential. Pulling forces can be applied to one or more monomers. Simple and fast algorithms have been implemented to preserve the topology and to compute the energy of the sampled conformations. After a new conformation is accepted, only the difference of energy between the new and the old conformations needs to be evaluated. In this way the simulation time grows linearly with the polymer size. A strategy based on the fluctuations of the specific heat capacity has been developed in order to avoid bottlenecks like the trapping of the system in a deep local minima at low temperature. Currently, the averages of the following observables are computed: specific heat capacity, elongation and gyration radius.

cond-mat.soft↗

arXiv2026

On the thermal properties of knotted block copolymer rings

We investigate the thermal and structural properties of knotted diblock copolymer rings using a coarse-grained lattice model in an implicit solvent. The system is studied by means of the Wang--Landau Monte Carlo algorithm, allowing us to analyze thermodynamic and conformational responses over a wide temperature range. Different knot topologies, including the unknot, trefoil, figure-eight, and pentafoil knots, are considered for both symmetric and asymmetric monomer compositions. In the AB model employed here, A-type monomers are self-repulsive, B-type monomers are self-attractive, and A-B interactions are neutral, such that the solvent is effectively good for A-type monomers and poor for B-type monomers at low temperatures. We analyze several key observables, including the heat capacity, the radius of gyration, and its temperature derivative for both the entire copolymer ring and the individual blocks, and the probability that a monomer belongs to the knotted region. Our results show that the interplay between knot topology, monomer composition, and temperature strongly influences polymer conformations. Small variations in the B-block length induce nonmonotonic, reentrant-like conformational behavior as a function of temperature, including transitions between knot localization and delocalization at low temperatures. These effects arise from the competition between energetic and entropic contributions imposed by topological constraints.

cond-mat.soft↗

arXiv2025

Single [2]catenanes in solution forming ${\sf 4}$-plats: a combined field theoretical and numerical approach

The statistical mechanics of [2]catenanes in a solution with constrained number of maxima and minima along a special direction (the height) is discussed. The interest in this system comes from the fact that, in the homopolymer case, it has analogies with self-dual anyon field theory models and has conformations that minimize the static energy and bear particular symmetries and properties. In the first part of this work we provide a procedure for deriving the equations of motion in the case of replica field theories in the limit of zero replicas. We compute also the partition function of the [2]catenane at the lowest order in the frame of the so-called background field method. In the second part the statistical mechanics of the system is investigated using numerical simulations based on the Wang-Landau Monte Carlo method. At equilibrium, independently of the temperature, it turns out that the conformations of the system are elongated in the height directions. The two rings composing the [2]catenanes have approximately the same heights and are aligned. The thermodynamic properties of the system are discussed and the results coming from the field theoretical approach are compared with those of the numerical simulations.

cond-mat.soft↗