arXiv subjects

Timur Aslyamov

Publications and source records attributed to Timur Aslyamov.

30 records · Page 2Linked to original sources

arXiv2023

Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds

Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.

cond-mat.stat-mech↗

arXiv2022

Analytical solution to the Poisson-Nernst-Planck equations for the charging of a long electrolyte-filled slit pore

We study the charging dynamics of a long electrolyte-filled slit pore in response to a suddenly applied potential. In particular, we analytically solve the Poisson-Nernst-Planck (PNP) equations for a pore for which $λ_D\ll H\ll L$, with $λ_D$ the Debye length and $H$ and $L$ the pore's width and length. For small applied potentials, we find the time-dependent potential drop between the pore's surface and its center to be in complete agreement with a prediction of the celebrated transmission line model. For moderate to high applied potentials, prior numerical work showed that charging slows down at late times; Our analytical model reproduces and explains such biexponential charge buildup.

cond-mat.soft↗

arXiv2021

Relation between charging times and storage properties of nanoporous supercapacitors

Investigating the correlations between dynamic and static storage properties of nanoporous electrodes is beneficial for further progress of supercapacitors-based technologies. While the dependence of the capacitance on the pores' sizes is well described by classical Density Functional Theory (c-DFT), the lack of dynamic c-DFT extension capable for correct estimation of the charging time has been noted in the literature. Here, we develop a dynamic model of the electrolyte inside nanopores based on c-DFT and realistically describing both the time-dependent charging process and maximum static capacitance. Our calculations show that the charging starts with a square-root dependency of the total charge on time and then follows two subsequent exponential trends with significantly different time scales that agree with published simulations. We demonstrate that the full charging time corresponds to the timescale of either the first or the second exponential trend depending on the pores' size. Also, we find analytical expressions to fit the timescales for a wide range of parameters. Derived correlations provide the relation of charging time to pores' size, applied voltage, and final ions' densities inside the pore, making these expressions useful to design supercapacitors with an optimal combination of power and energy characteristics.

cond-mat.stat-mech↗

arXiv2021

Electrolytes structure near electrodes with molecular size roughness

Understanding the electrodes' surface morphology influence on the ions' distribution is essential for designing the supercapacitors with enhanced energy density characteristics. We develop a model for the structure of electrolytes near the rough surface of electrodes. The model describes an effective electrostatic field's increase and associated intensification of ions' spatial separation at the electrode-electrolyte interface. These adsorption-induced local electric and structure properties result in notably increased values and sharpened form of the DC dependence on the applied potential. Such capacitance behavior is observed in many published simulations, and its description is beyond the capabilities of the established flat-electrodes theories. The proposed approach could extend the quantitatively verified models providing a new instrument of the electrodes surface-parameters optimization for specific electrolytes.

cond-mat.stat-mech↗

arXiv2020

Branching random graph model of rough surfaces describes thermal properties of the effective molecular potential

Fluid properties near rough surfaces are crucial in describing fundamental surface phenomena and modern industrial material design implementations. One of the most powerful approaches to model real rough materials is based on the surface representation in terms of random geometry. Understanding the influence of random solid geometry on the low-temperature fluid thermodynamics is a cutting edge problem. Therefore this work extends recent studies bypassing high-temperature expansion and small heterogeneity scale. We introduce random branching trees whose topology reflects the hierarchical properties of a random solid geometry. This mathematical representation allows us to obtain averaged free energy using a statistical model of virtual clusters interacting through random ultrametric pairwise potentials. Our results demonstrate that a significant impact to fluid-solid interface energy is induced by the hierarchical structure of random geometry at low temperature. These calculations coincide with direct Monte Carlo simulations. Due to the study's interdisciplinary nature, the developed approach can be applied to a wide range of quenched disorder systems on random graphs.

cond-mat.dis-nn↗

arXiv2020

Disjoining pressure oscillations causing height discretization in graphene nanobubbles

Recent experiments and computer simulations observe various geometrical formations of nanobubbles in van der Waals heterostructures. Among the well studied dome and tent geometries, there is yet least understood pancake graphene nanobubbles (GNB). This more exotic form exhibits discrete values of vertical sizes around just a few diameters of the molecules trapped inside the GNBs. We develop a model based on the membrane theory and confined fluids thermodynamics. Our approach describes the equilibrium properties of such flat GNBs. We show that discrete pancake geometry is the result of disjoining pressure induced by the trapped fluid inside GNB. The calculated total energy defines a discrete series of the metastable states with the pancake heights, which are multiple to molecular diameter. We observe that the value and the distribution of the total energy minima crucially depend on the temperature. The energy barriers between metastable states decrease as the temperature becomes larger. Also, we demonstrate that the pancake forms are favorable in the cases of sufficiently low membrane-substrate adhesion energy and the small number of trapped molecules. These properties are in agreement with the published simulations and experiments. The numerical comparison of our result with molecular dynamics results additionally shows the adequacy of the proposed model.

cond-mat.soft↗

arXiv2019

Zeros of partition functions in the NPT-ensemble

Lee-Yang and Fisher zeros are crucial for the study of phase transitions in the grand canonical and the canonical ensembles, respectively. However, these powerful methods do not cover the isothermal-isobaric ensemble (NPT ensemble), which reflects the conditions of many experiments. In this work we present a theory of the phase transitions in terms of the zeros of the NPT-ensemble partition functions in the complex plane. The proposed theory provides an approach to calculate all the partition function zeros in the NPT ensemble, which form certain curves in the thermodynamic limit. To verify the theory we consider Tonks gas and van der Waals fluid in the NPT ensemble. In the case of Tonks gas, similarly to the Lee-Yang circle theorem, we obtain an exact equation for the zero limit curve. We also derive an approximated limit curve equation for van der Waals fluid in terms of the Szegö curve. This curve fits numerically calculated zeros and correctly describes how the phenomenon of phase transition depends on the temperature.

cond-mat.stat-mech↗

arXiv2019

Detailed Characterization of Rough Surfaces for Silica Materials

We propose a new approach to obtain the nanoscale morphology of rough surfaces from low-temperature adsorption experiments. Our method is based on one of the most realistic models of rough surfaces formulated in terms of random correlated processes and random surface density functional theory (RS-DFT) as a theoretical adsorption model. We consider the roughness in the normal direction, the correlation length of the lateral surface structure and the specific surface area as tuning parameters of RS-DFT to fit the experimental data in the low pressure range, where the influence of the surface geometry is the most crucial. One of the major advantages of the proposed approach over published methods is the best-fit detailed geometry of rough surfaces, which provides full information for further atomistic modeling. The obtained geometry correctly reflects how the nanoroughness of silica materials depends on the synthesis conditions. We demonstrate that the surface fractal dimension observed in many experiments is natural for the correlated random surface model. We investigated the surface geometry of popular silica materials synthesized at different conditions. The obtained roughness parameters and fractal dimensions coincide well with the published experimental data. Analysis of the best fit specific surface area reveals the mechanism of adsorption on rough surfaces and provides a new strategy for the search of optimal storage materials.

cond-mat.mtrl-sci↗

arXiv2018

Random Surface Statistical Associating Fluid Theory: Adsorption of n-Alkanes on Rough Surface

Adsorption properties of chain fluids are of interest from both fundamental and industrial points of view. Density Functional Theory (DFT) based models are among the most appropriate techniques allowing to describe surface phenomena. At the same time Statistical Associating Fluid Theory (SAFT) successfully describes bulk PVT properties of chain-fluids. In this publication we have developed novel version of SAFT-DFT approach entitled RS-SAFT which is capable to describe adsorption of short hydrocarbons on geometrically rough surface. Major advantage of our theory is application to adsorption on natural roughs surfaces with normal and lateral heterogeneity. For this reason we have proposed workflow where surface of real solid sample is analyzed using theoretical approach developed in our previous work [1] and experimentally by means of low temperature adsorption isotherm measurements for simple fluids. As result RS-SAFT can predict adsorption properties of chain fluids taking into account geometry of the surface sample under the consideration. In order to test our workflow we have investigated hexane adsorption on carbon black with initially unknown geometry. Theoretical predictions for hexane adsorption at 303K and 293K fit corresponding experimental data well.

cond-mat.stat-mech↗

arXiv2017

Density Functional Theory Formulation for Fluid Adsorption on Correlated Random Surfaces

We provide novel random surface density functional theory (RSDFT) formulation in the case of geometric heterogeneous surface of solid media which is essential for description of thermodynamic properties of confined fluids. The major difference of our theoretical approach from existing ones is stochastic model of solid surface which takes into account the correlation properties of geometry. The main building blocks are effective fluid-solid potential developed in work (J. Stat. Phys, 2017,167(6), 1519-1545) and geometry based modification of Helmholtz free energy for Lennard-Jones fluids. Efficiency of RSDFT is demonstrated in calculation of argon and nitrogen low temperature adsorption on real heterogeneous surfaces (BP280 carbon black). These results are in good agreement with experimental data published in the literature. Also several models of corrugated materials are developed in the framework of RSDFT. Numerical analysis demonstrates strong influence of surface roughness characteristics on adsorption isotherms. Thus developed formalism provides connection between rigorous description of stochastic surface and confined fluids thermodynamics.

cond-mat.stat-mech↗

arXiv2016

Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid-Solid Interaction

Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarse-grained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations shows good qualitative agreement with the theory predictions. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.

cond-mat.stat-mech↗

arXiv2016

Analytical expression for radial distribution function of hard sphere system: density derivative and application to perturbation theories

Model of hard sphere system is important part of modern theories of liquids. Radial distribution function of hard sphere fluid represented in form of explicit analytical expression allows to obtain thermodynamic potentials in analytical form, which is very helpful for further analysis and applications. A new analytical expression of radial distribution function of hard sphere fluid is developed. The density derivative of the radial distribution function and the first two terms of Barker-Henderson perturbation theory are derived as analytical expressions. The obtained results agree well with published simulation data. These results have important implications for real fluid modeling using density functional theory and perturbation theories.

cond-mat.stat-mech↗