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Nail Fatkullin

Publications and source records attributed to Nail Fatkullin.

7 recordsLinked to original sources
arXiv2026

Dynamics of ring polymer melts: Memory function approach

We investigated the static and dynamic properties of a Rouse ring polymer modified by introducing an effective, spherically symmetric, attractive potential of entropic nature and a memory function describing the effect of dynamic entanglement. Renormalized Rouse formalism is used to approximate the time dependence of the memory matrix. The results obtained are in good agreement with existing experimental data and the results of computer simulations of ring polymer ring with , , where N_e is the number of Kuhn segments in linear polymer melts between neighboring entanglements and , the number of Kuhn segments. For large molecular weights, a refined self-consistent approximation is proposed to describe the time dependence of the memory function. It is shown that this approximation allows us to describe an exponential decrease in the self-diffusion coefficient with molecular weight of the rings, i.e., the effect of dynamic localization.

cond-mat.soft↗
arXiv2025

The Rouse ring chain with attractive harmonic potential of spherical symmetry

The static and dynamic properties of a cyclic Rouse chain modified by the introduction of an effective, spherically symmetric, attracting potential of entropic nature is studied. It is shown that a relatively weak potential can lead to a strong contraction of the polymer chain: the radius of gyration becomes much smaller compared to the size of free cyclic chain. The pronounced decrease in the terminal relaxation time of cyclic macromolecules compared to the Rouse relaxation time leads to a lengthening of the time interval for the transition to the normal, i.e. the Fickian, diffusion regime, generating a pseudo-plateau at increasing molecular mass for the time dependence of segmental mean squared segmental displacement.

cond-mat.soft↗
arXiv2016

Short-time diffusion behavior of Brownian particles in confining potentials

Diffusion behavior of Brownian particles in confined spaces was studied for the displacements notably shorter than the confinement size. The confinements, resembling structure of porous solids, were modeled using a spatially-varying potential field with an infinitely large potential representing the solid part and zero potential in the void space. Between them, a smooth transient mimicking the interaction potential of the tracer molecules with the pore walls was applied. The respective Smoluchowski equation describing diffusion of tracer particles in the thus created force field was solved under certain approximations allowing for a general analytical solution. The time-depended diffusion coefficient obtained was found to agree with that obtained earlier using the Fick's diffusion equation, but with a different numerical constant. Numerical solution of the Smoluchowski equation with selected interaction potentials was used to clarify the origin of this discrepancy. The conditions under which the solutions obtained within these two approaches converge were established.

cond-mat.dis-nn↗
arXiv2011

Generalized Bloch-Wangsness-Redfield Kinetic Equations

We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short correlation times and large heat capacity of the lattice are sufficient to derive the kinetic equations without the use of perturbation theory for the spin-lattice interaction operator. The perturbation theory is only applied for calculation of the kinetic coefficients, for which we obtain general and compact expressions. We argue that kinetic equations for the density matrix elements are not essential for derivation of the generalized Bloch-Wangsness-Redfield equations for the expectation values of any set of physical quantities, and the latter may be obtained directly under the weak assumptions of mutual orthogonality and completeness. We show that existence of a unity operator in the algebra of spin operators is a necessary condition for convergence of the spin subsystem to thermodynamic equilibrium with the temperature equal to that of the lattice. Finally, as an application of the general theory, we discuss some features of spin relaxation in heterogeneous systems for I=1/2.

cond-mat.stat-mech↗
arXiv2010

Why Does the Rouse Model Works at Least Satisfactorily at Polymer Molecular Masses M<M_c ?

Generalization of the Rouse model without any use of the postulates concerning the Gaussian distribution of the vector connecting the ends of segments is advanced. In the initial (in general, nonlinear) Langevin equations, self-averaging over continuous fragments of a macromolecule naturally defines a linear term for the tagged chain, and this term differs from the entropy term of the classical Rouse model only by the numerical coefficient. According to the inertia-free approximation, the initial decay rates of correlation functions for the normal modes are described by the Rouse model independently of the character of fluctuations of the vector connecting the ends of the Kuhn segment. This statement is valid for any moment if the initial Langevin equations are treated in terms of the approximation of dynamic self-consistency. Simulation of the Fraenkel chains by the method of Brownian dynamics shows that decay of autocorrelation functions of shortwave normal modes is fairly described by the linearized equations for a given model of a chain and that the Rouse equation can be used for the longwave modes. The results of this study make it possible to explain a marked difference between the lengths of the Kuhn and Rouse segments that is estimated from static and dynamic experiments.

cond-mat.soft↗
arXiv2010

The Corset Effect, Field-Cycling NMR Relaxometry, Transverse NMR Relaxation, Field-Gradient NMR Diffusometry, and Incoherent Neutron Scattering

The corset effect is an experimentally established dynamic confinement phenomenon first observed by field-cycling NMR relaxometry and transverse NMR relaxation in polymer melts in pores with dimensions ranging from a few nanometers up to 0.06 micrometers or even more. The techniques employed are specifically sensitive to rotational fluctuations of polymer segments. It will be shown that neutron scattering and other methods probing translational fluctuations are not suitable for the detection of this phenomenon.

cond-mat.mes-hall↗