arXiv subjects

Anirudhha Chakraborty

Publications and source records attributed to Anirudhha Chakraborty.

6 recordsLinked to original sources

arXiv2017

Exact solution of long-range electron transfer through conjugated molecular bridge

Intermolecular electron transfer reaction often occurs over long range distances (i.e. up to several tens of angstroms) and plays a key role in various physical, chemical and biological processes. In these reactions the rate constant of long range electron transfer depends upon electronic coupling between the donor and acceptor. The coupling between donor and acceptor may increases by the atoms located between them which form a kind of bridge for electron tunneling. By using exact analytical method we calculated the value of electronic coupling for the above said processes in which the interaction of an electron with the donor, acceptor are represented as Dirac delta functions and conjugated bridge is represented by finite square well.

physics.chem-ph↗

arXiv2017

Exploring the relaxation time, bond length and length of the polymer chain in the kinetics of end-to-end looping of a long polymer chain

We present a theoretical model for understanding the kinetics of a long polymer in solution. A Smoluchowski-like equation has been used to model the problem of polymer looping with a Dirac delta function sink of finite strength. The results for rate constants have been obtained by using Green's function. In this model, the rate constants for end-to-end looping of polymer exhibits simple Arrhenius behavior. The rate constants are sensitive to relaxation time, bond length and chain length dependence of the looping probability. In particular, for short term rate constant, relaxation time makes loop formation between two ends of a polymer chain slower but has a direct dependence with long term rate constant. We also show that for shorter polymer strands looping is slower as compared to polymer having longer chain length. The long term rate constant shows inverse square root dependence on the length of the chain. The bond length strongly affects the probability of loop formation as for long constructs of polymer, the end-to-end distance is found to exhibit inverse power law relationship to bond length. We also observe that the short term rate constant for flexible polymer shows stronger affinity for loop formation.

cond-mat.stat-mech↗

arXiv2017

Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delocalized sink model

The fundamental understanding of loop formation of long polymer chains in solution has been an important thread of research for several theoretical and experimental studies. Loop formations are important phenomenological parameters in many important biological processes. Here we give a general method for finding an exact analytical solution for the occurrence of looping of a long polymer chains in solution modeled by using a Smoluchowski-like equation with a delocalized sink. The average rate constant for the delocalized sink is explicitly expressed in terms of the corresponding rate constants for localized sinks with different initial conditions. Simple analytical expressions are provided for average rate constant.

cond-mat.stat-mech↗

arXiv2016

Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delta function sink model

A diffusion theory for intramolecular reactions of polymer chain in dilute solution is formulated. We give a detailed analytical expression for calculation of rate of polymer looping in solution. The physical problem of looping can be modeled mathematically with the use of a Smoluchowski like equation with a Dirac delta function sink of finite strength. The solution of this equation is expressed in terms of Laplace Transform of the Greens function for end to end motion of the polymer in absence of the sink. We have defined two different rate constants, the long term rate constant and the short term rate constant. The short term rate constant and long term rate constant varies with several parameters such as length of the polymer, bond length and the relaxation time. The long term rate constant is independent of the initial probability distribution.

cond-mat.stat-mech↗

arXiv2015

Diffusion under a flat potential with time dependent sink

The Smoluchowski equation for a free particle with a time dependent sink is solved exactly for many special cases. In this method by knowing the probability distribution at the origin P(0,t), one may derive the probability distribution at all positions i.e. P(x,t)

quant-ph↗

arXiv2015

Exact results on diffusion in a piecewise linear potential with a time dependent sink

The Smoluchowski equation with a time dependent sink term is solved exactly. In this method by knowing the probability distribution at the origin P(0,s), one may derive the probability distribution at all positions i.e., P(x,s). Further the exact solution for Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse and exponential variation in time.

quant-ph↗