Related papers: Mean Field and the Single Homopolymer
In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in the $3D$ space at a range of chain lengths $N$. The…
The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…
We derive the mean-field theory of disordered block-copolymers composed of two monomeric species, combining Edwards' functional method with the replica technique of disordered systems. In the absence of disorder we recover the canonical…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…
Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n\leq d$ in spaces of…
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…
The adsorption of a single multi-block $AB$-copolymer on a solid planar substrate is investigated by means of computer simulations and scaling analysis. It is shown that the problem can be mapped onto an effective homopolymer adsorption…
Adsorption of dimers is modelled using random sequential adsorption algorithm. The interaction between molecules is given by screened electrostatic potential. The paper focuses on the properties of adsorbed monolayers as well as the…
The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…
In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as…
The de Gennes' blob model is extensively used in different problems of polymer physics. This model is theoretically applicable when the number of monomers inside each blob is large enough. For confined flexible polymers, this requires the…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
The shape of a polymer plays an important role in determining its interactions with other molecules and with the environment, and is in turn affected by both of them. As a consequence, in the literature the shape properties of a chain in…
The confinement mechanism proposed earlier and then applied successfully to meson spectroscopy by one of the authors is interpreted in classical terms. For this aim the unique solution of the Maxwell equations, an analog of the…
Using molecular dynamic simulation, we study the stretching of an adsorbed homopolymer in a poor solvent with one end held at a distance $z_e$ from the substrate. We measure the vertical force $f$ on the end of the chain as a function of…
We study the phase transitions of a random copolymer chain with quenched disorder. We apply a replica variational approach based on a Gaussian trial Hamiltonian in terms of the correlation functions of monomer Fourier coordinates. This…
Protein sequences are believed to have been selected to provide the stability of, and reliable renaturation to, an encoded unique spatial fold. In recently proposed theoretical schemes, this selection is modeled as ``minimal frustration,''…
Associative polymers are a class of polymers containing attractive stickers that can reversibly bind to each other. Their fully-bonded state gives rise, in dilute conditions, to a fluid phase of so-called single-chain nanoparticles (SCNPs).…