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Jaroslaw Paturej

Publications and source records attributed to Jaroslaw Paturej.

12 recordsLinked to original sources
arXiv2025

Shape spectra of elastic shells with surface-adsorbed semiflexible polymers

The shape of biological shells, such as cell nuclei, membranes, and vesicles, often deviates from a perfect sphere due to an interplay of complex interactions with a myriad of molecular structures. In particular, semiflexible biopolymers adsorbed to the surfaces of such shells seem to affect their morphological properties. While the effect of a single, long, semiflexible chain is relatively well characterized, the mechanisms by which a high density of such surface-adsorbed polymers can alter the morphology of a spherical, soft confinement, akin to biological shells, remain relatively poorly understood. Here, we use coarse-grained molecular dynamics simulations to investigate how surface adsorption of many semiflexible polymers affects the morphology of a pressurized bead-spring shell, which is spherical in the absence of these chains. By varying the attraction strength between the chains and the shell surface, chain concentration, and the polymerization degree of chains, we demonstrate that strong surface localization of the chains can induce severe shape distortions and shrinkage, depending on the chain length and concentration. Conversely, weak localization does not induce significant shape fluctuations, yet nematically ordered phases appear on the surface. Notably, these ordered phases lead to elliptic shell shapes for chains with sizes comparable to or longer than the radius of the confinement when the elastic shell is composed of extensible, harmonic bonds. Overall, our findings offer a strategy to control the shape of synthetic shells by manipulating peripheral localization and length of semiflexible polymers while suggesting a mechanism for non-spherical shapes appearing in some biological systems.

cond-mat.soft↗
arXiv2023

The size and shape of snowflake star polymers in dilute solutions: analytical and numerical approaches

We investigate the conformational properties of a multi-branched polymer structure with a dendrimer-like topology, known as a snowflake polymer. This polymer is characterized by two parameters: $f_s$, which represents the functionality of the central star-like core, and $f$, which represents the functionality of the side branching points. To analyze the conformational properties, we have employed various approaches, including analytical methods based on direct polymer renormalization and the Wei's approach as well as numerical molecular dynamics simulations. These methods have allowed us to estimate a size and shape characteristics of the snowflake polymer as functions of $f$ and $f_s$. Our findings consistently demonstrate the effective compactification of the typical polymer conformation as the number of branching points increases. Overall, our study provides valuable insights into the conformational behavior of the snowflake polymer and highlights the impact of branching parameters on its overall compactness.

cond-mat.soft↗
arXiv2023

Molecular conformations of dumbbell-shaped polymers in good solvent

We study conformational properties of diluted dumbbell polymers which consist of two rings that are attached to both ends of a linear spacer segment by using analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We investigate the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers are much more compact than linear polymers. Oppositely, we observe that the influence of side rings on the size of dumbbells becomes negligible with increasing length of a spacer. Consequently dumbbell molecules with long spacers become comparable in size with corresponding linear chains. Our analytical theory predicts quantitative cross-over between short- and long-spacer behavior and is confirmed by numerical simulations.

cond-mat.soft↗
arXiv2011

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time $<τ>$ decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 ÷4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time $<τ>$ declines with growing contour length $L$ as $<τ>\propto L^{-0.17}$, and with side chain length as $<τ>\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.

cond-mat.soft↗
arXiv2009

Diffusion of Brownian particles and Liouville field theory

In this work we review a recently proposed transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field. The used methodology is illustrated with the help of the simple case of a particle performing a random walk in a delta function potentials.

hep-th↗
arXiv2009

Dynamics of a three-dimensional inextensible chain

In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the $z-$axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is similar to the reduction of the statistical mechanics of a directed polymer to the random walk of a two-dimensional particle.

cond-mat.stat-mech↗
arXiv2008

On the connection of the generalized nonlinear sigma model with constrained stochastic dynamics

The dynamics of a freely jointed chain in the continuous limit is described by a field theory which closely resembles the nonlinear sigma model. The generating functional $Ψ[J]$ of this field theory contains nonholonomic constraints, which are imposed by inserting in the path integral expressing $Ψ[J]$ a suitable product of delta functions. The same procedure is commonly applied in statistical mechanics in order to enforce topological conditions on a system of linked polymers. The disadvantage of this method is that the contact with the stochastic process governing the diffusion of the chain is apparently lost. The main goal of this work is to reestablish this contact. To this purpose, it is shown here that the generating functional $Ψ[J]$ coincides with the generating functional of the correlation functions of the solutions of a constrained Langevin equation. In the discrete case, this Langevin equation describes as expected the Brownian motion of beads connected together by links of fixed length.

cond-mat.stat-mech↗
arXiv2008

Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain

Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.

cond-mat.soft↗
arXiv2008

A path integral approach to the dynamics of a random chain with rigid constraints

In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.

cond-mat.stat-mech↗