Particle diffusion in elastically coupled narrow parallel channels

[摘要] ENGLISH ABSTRACT: We investigate a model system for particle diffusion in elastically coupled one-dimensionalnarrow channels. The elastic coupling of the channels is such that channels mutually affectthe stochastic dynamics of particles. This kind of constrained and coupled stochastic diffusionmay occur in supramolecular lattices where pore occupancy by guest particles mayinduce a reversible mechanical deformation of the lattice hence, affecting particle evolutionin neighbouring pores. The model is explored first for out-of-equilibrium conditions, wherewe look mainly at the kinetic properties of the system, and thereafter under equilibriumconditions, where we try to understand the nature of dynamic correlation within the coupledchannel system. For an out-of-equilibrium version of the model the focus is placed onthe steady state behaviour of the two elastically coupled finite channels. The channels arekept in contact with particle reservoirs at the boundaries. Three current-density regimesof different distinct behaviour are identified using a simulation experiment. The sensitivityof the system mean occupancy profile and the steady state particle flux to small and largecoupling parameter strength are explored. We find that, for small coupling strength, thesystem steady state profile and flux behaviour can be approximated by a simple meanfield theory ignoring density-density correlations. We present the analytic description ofthe system using a cellular automaton formalism and then we generalize the theory fora multi-coupled channel system using a hopping particle dynamics approach. For smallcoupling parameter values, the analytic results are confirmed by the stochastic simulation.From the equilibrium perspective, we model the elastically coupled channel systemas a system of infinite narrow channels having a uniform guest particle occupancy andwe calculate density fluctuation correlation functions. The elastic coupling between channelsis modelled as short range interacting potential and the particle evolution is modelledthrough Langevin dynamics. The dynamics are cast into the functional integral formalismexpressed in terms of the collective particle number density, current density and theassociated density response fields. The resulting generating functional takes these fieldsinto consideration within the random phase approximation (RPA) up to second order. Fora short range interaction potential, we uncover the behaviour of the system by looking at the influence of the inter-channel interaction strength on the dynamic density-densitycorrelation functions. We conclude that the system long time limit effective friction coefficientis reduced with increase in the coupling parameter values while the strength of thermal forces for the effective system becomes renormalized. We also find out that theRPA breaks down under certain conditions, signalling a transition to a behaviour that isno longer characterised by a homogeneous density. The work presented here provides thebeginnings for microscopic insights into the filling, filtering and storage processes for whichcertain types of microporous materials can be utilised.

[发布机构] Stellenbosch University