Polymer unfolding and motion synchronization induced by spatially correlated noise

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Thermodynamically consistent Langevin dynamics with spatially correlated noise predicting frictionless regime and transient attraction effect

While the origins of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of spatially correlated noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, starting from the microscopic, deterministic model, we derive the analytical formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by the Gaussian SCN and calculate the adequate fluctuation-dissipation relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g., the singular behavior for certain types of interactions. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a nonequilibrium mechanism facilitating the molecular binding of the like-charged particles.

Non-Gaussian polymers described by alpha-stable chain statistics: Model, effective interactions in binary mixtures, and application to on-surface separation

The Gaussian chain model is the classical description of a polymeric chain, which provides analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse-grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the α stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of α-stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the α-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains described by the heavy-tailed distributions of persistence length; polymers adsorbed to the surface; and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the α-stable chain and construct the coarse-grained interaction potential between two chains. These results are employed to discuss the model of binary mixture consisting of the α-stable chains. In what follows, we establish the spinodal decomposition condition generalized to the mixtures of the α-stable polymers. This condition is further applied to compare the on-surface phase separation of adsorbed polymers (which are known to be described with heavy-tailed statistics) with the phase separation condition in the bulk. Finally, we predict the four different scenarios of simultaneous mixing and demixing in the two- and three-dimensional systems.

Analytical theory of effective interactions in binary colloidal systems of soft particles

While density functional theory with integral equations techniques are very efficient tools in the numerical analysis of complex fluids, analytical insight into the phenomenon of effective interactions is still limited. In this paper, we propose a theory of binary systems that results in a relatively simple analytical expression combining arbitrary microscopic potentials into effective interaction. The derivation is based on translating a many-particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language, which turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. As a result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the following: the effective attraction as a demixing factor in the binary systems of Gaussian particles, the screening of charged spheres by ions, which proves equivalent to Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, effective interactions in the binary mixtures of Yukawa particles, and the system of particles consisting of both a repulsive core and an attractive/repulsive Yukawa interaction tail. For this last case, we reproduce the "attraction-through-repulsion" and "repulsion-through-attraction" effects previously observed in simulations.