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Research Interests
Statistical Thermodynamics, Molecular dynamics simulation, Monte Carlo simulation, Brownian Dynamics simulation, Langevin Dynamics simulation, Multidimensional Non-Markovian rate theory, Chemical Kinetics, Linear response theory, Hydrodynamics theory, Projection operator techniques, Liquid State Properties, Structure & Dynamics of Bio molecules, Scaling relations, Quantum chemical calculation, Phase transition, Machine learning, Density functional theory, AIMD simulation, Polymer chemistry, etc.
(a) Study of Diffusion-Entropy Scaling Relations in Deterministic Systems
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study and any derivation of an algebraic relation between the two do not seem to exist. Here, we explore the nature of this entropy–diffusion relation in three deterministic systems where an accurate estimate of both can be carried out. We study three deterministic model systems: (a) the motion of a single point particle with constant energy in a two-dimensional periodic potential energy landscape, (b) the same in the regular Lorentz gas where a point particle with constant energy moves between collisions with hard disk scatterers, and (c) the motion of a point particle among the boxes with small apertures. These models exhibit diffusive motion in the limit where ergodicity is shown to exist. We estimate the self-diffusion coefficient of the particle by employing computer simulations and entropy by quadrature methods using Boltzmann’s formula. We observe an interesting crossover in the diffusion–entropy relation in some specific regions, which is attributed to the emergence of correlated returns. The crossover could herald a breakdown of the Rosenfeld-like exponential scaling between the two, as observed at low temperatures. Later, we modify the exponential relation to account for the correlated motions and present a detailed analysis of the dynamical entropy obtained via the Lyapunov exponent, which is rather an important quantity in the study of deterministic systems.
Figure 1: We study diffusion-entropy scaling relation in three model systems. (a) A schematic representation of the potential energy function. The range and color codes are given on the right side of the plot. (b) The location of fixed hard-scatterers in a periodic Lorentz model. The blue shaded region denotes a trapping region of triangular symmetry. W is the separation parameter between hard disks. (c) A schematic diagram of the box-hole model where the point particle (i.e., red-colored circle) moves among the boxes with small holes of width W1 allowing the long distance motion only in one direction. In (c), L indicates the length of the box.
(b) Formulation and applications of multidimensional non-Markovian theory
Multidimensional rate theory provides a theoretical framework for understanding chemical reactions that occur in systems with more than one reaction coordinate, such as isomerization reactions, protein folding, or electron transfer reactions. Although recent years have seen many computational studies employing advanced simulation techniques, like umbrella sampling and metadynamics, to construct the reaction-free energy surface in terms of several reaction coordinates, less effort has been directed to calculate the rate by quasi-analytical means. In this context, we formulate a non-Markovian multidimensional rate theory, explicitly considering coupling at the level of Hamiltonian and friction between reactive and non-reactive modes. The formulation is quite general, allowing recovery of other theoretical approaches, such as Langer's theory, Pollak's Hamiltonian formulation, and van der Zwan-Hynes theory, under appropriate conditions. We then use the non-Markovian theory to calculate the rate in several interesting systems, namely (i) the isomerization rate of stilbene molecule in hexane solvent, (ii) the escape rate of a particle moving on a two-dimensional periodic potential energy landscape, (iii) dissociation rate of insulin dimer in water and (iv) homogeneous gas-liquid nucleation rate in LJ system. The rate predicted by the non-Markovian theory is found to be in good agreement with experimental and theoretical findings. An intriguing interplay between dimensionality and memory effects was observed in rate calculations. In this context, we unveil the microscopic mechanism for the early stage of insulin dimer dissociation and the role of water molecules in explicitly facilitating the hydrophobic disentanglement.
(c) Emergence of Non-Linear Response in Liquid at Molecular Length Scales Studied by Pulling of a Tagged Particle
The time correlation function representation of transport properties like diffusion and viscosity is based on the assumption of linear response of the liquid to an external perturbation. However, the range of the validity of this linear response and the onset limit of significant non-linearity have remained somewhat ill-understood. Here we probe these limits by calculating the friction coefficient directly by using Stokes law of hydrodynamics, where we pull a tagged molecule by a constant force and find the friction from the velocity created by the drag. Einstein’s relation gives the alternate independent estimate through diffusion at equilibrium conditions, either from velocity TCF or mean square displacement. We find that while the relation holds quantitatively at a low pulling force, it breaks down when the pulling force exceeds a certain critical value. We find that the attractive interaction between the particles plays a vital role in enhancing the deviation from linearity by studying the soft sphere and LJ system separately. The reason is discovered to be the onset of fluid motion that helps lower friction. We discuss the possible microscopic reasons for such a departure.
(Top) Schematic diagram of the system consisting of LJ particles. We randomly pick one particle and pull it along the Z-direction with a constant force FZ. Below, the plot of the Z-component of the drift velocity of the tagged LJ and soft sphere (SS) particle against the applied force FZ along the Z-direction. We calculate the drift velocity and plot it against the applied force, as shown by the solid black line. We perform a linear fit to obtain the effective friction using the Stokes relation established by the red dotted line. We observe a deviation from the linearity when the perturbative force is high.
(d) Enhancement of reaction rate in small sized droplets
A schematic diagram of the theoretical model employed in our study. Initially, the reactants (blue) and the targets (red) are uniformly distributed inside the droplet. Because of the high ionic mobility of the targets (hydronium ions), almost all of them reach the surface at a faster rate. However, the reactants exhibit slower random walk in the bulk.
In this study, we provide a brief analytical theory of the rate enhancement of organic reactions inside charged microdroplets. An analytical model is developed to derive the expression for the mean search time for a reactant to find a target located on the surface in both two- and three-dimensional droplets. This is then compared with Brownian dynamics simulations across various droplet sizes. The analysis in this part effectively elucidates the origins of the observed rate enhancement.
(e) Altered Polar Character of Dipolar Fluid under Nano-confinement
Plot of the static dielectric constant against the inverse of the number of molecules (1/N) for aqueous nanocavities with (a) LJ-12,6 atomistic walls, (b) LJ-10,4,3 walls, (c) and LJ-9,3 walls (d) SF with LJ-9,3 wall.
We investigate the dielectric relaxation of dipolar fluids under spherical confinement, such as water and Stockmayer fluid. The study finds that the static dielectric constant shows a significant system size dependence along with ultrafast relaxation of total dipole-dipole correlation functions under confinement.
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