arXiv subjects

Iskander Akhatov

Publications and source records attributed to Iskander Akhatov.

6 recordsLinked to original sources

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

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↗

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

Neural network interpolation of exchange-correlation functional

Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.

physics.comp-ph↗

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

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 Szeg\"o curve. This curve fits numerically calculated zeros and correctly describes how the phenomenon of phase transition depends on the temperature.

cond-mat.stat-mech↗