arXiv subjects

MC Tesi

Publications and source records attributed to MC Tesi.

4 recordsLinked to original sources

arXiv2026

Thermodynamics of Confined Knotted Lattice Polygons

A ring polymer in a confining space may exhibit at least two phases, namely an expanded (or solvent-rich phase) if its concentration is small, or a collapsed (or polymer-rich phase) when it is concentrated and compressed. These phases are discussed in reference \cite{deG79}, and have been modelled, traditionally, in the mean field using Flory-Huggins theory \cite{Flory42,Huggins42}. In three dimensions the ring polymer may also be knotted, or linked, and have its conformational degrees of freedom constrained by its topology. In a lattice model of confined knotted ring polymers there are indications that the thermodynamic properties of the ring polymer (for example, the osmotic pressure \cite{GJvR18,JvR19}) is a function of its topology. In this paper we explore a lattice knot model of a confined ring polymer as a function of its chemical potential. We show that a well-defined phase transition occurs between solvent-rich and polymer-rich phases when the lattice knot exhibits either the unknot topology or any other fixed knot type. Furthermore, we observe small yet significant variations in the free energy near the critical point when comparing trefoil knots with other non-trivial knot types. These findings indicate that the thermodynamic properties of confined ring polymers depend on their topological entanglement characteristics (namely, their knot type).

cond-mat.soft↗

arXiv2025

Mixing, segregation, and collapse transitions of interacting copolymer rings

A system of two self and mutual interacting ring polymers, close together in space, can display several competing equilibrium phases and phase transitions. Using Monte Carlo simulations and combinatorial arguments on a corresponding lattice model, we determine three equilibrium phases, two in which the rings segregate in space and are either extended (the segregated-expanded phase) or compact (the segregated-collapsed phase). The third is a mixed phase where the rings interpenetrate. The corresponding phase boundaries are located numerically and their critical nature is discussed. Finally, by looking at the topological properties of the three phases, we show that the two rings are likely to be linked in the mixed phase and knotted in the segregated-collapsed phase.

cond-mat.soft↗

arXiv2025

Relative knot probabilities in confined lattice polygons

In this paper we examine the relative knotting probabilities in a lattice model of ring polymers confined in a cavity. The model is of a lattice knot of size $n$ in the cubic lattice, confined to a cube of side-length $L$ and with volume $V=(L{+}1)^3$ sites. We use Monte Carlo algorithms to approximately enumerate the number of conformations of lattice knots in the confining cube. If $p_{n,L}(K)$ is the number of conformations of a lattice polygon of length $n$ and knot type $K$ in a cube of volume $L^3$, then the relative knotting probability of a lattice polygon to have knot type $K$, relative to the probability that the polygon is the unknot (the trivial knot, denoted by $0_1$), is $\rho_{n,L}(K/0_1) = p_{n,L}(K)/p_{n,L}(0_1)$. We determine $\rho_{n,L}(K/0_1)$ for various knot types $K$ up to six crossing knots. Our data show that these relative knotting probabilities are small so that the model is dominated by lattice polygons of knot type the unknot. Moreover, if the concentration of the monomers of the lattice knot is $\varphi = n/V$, then the relative knot probability increases with $\varphi$ along a curve that flattens as the Hamiltonian state is approached.

cond-mat.soft↗

arXiv2022

Thermodynamic and topological properties of copolymer rings with a segregation/mixing transition

Two ring polymers close to each other in space may be either in a segregated phase if there is a strong repulsion between monomers in the polymers, or intermingle in a mixed phase if there is a strong attractive force between the monomers. These phases are separated by a critical point which has a $θ$-point character. The metric and topological properties of the ring polymers depend on the phase, and may change abruptly at the critical point. In this paper we examine the thermodynamics and linking of two ring polymers close in space in both the segregated and mixed phases using a cubic lattice model of two polygons interacting with each other. Our results show that the probability of linking is low in the segregated phase, but that it increases through the critical point as the model is taken into the mixed phase. We also examine the metric and thermodynamic properties of the model, with focus on how the averaged measures of topological complexity are related to these properties.

cond-mat.soft↗