Coarse grained modelling of nanopore systems

Nanopore devices are a class of nanofluidic systems which involve the trans- port of mass and ions through a nanometer sized pore. These systems are widely studied for their attractive applications, ranging from biological analysis (e.g. real-time study of enzyme kinetics, macromolecule detection or sequencing), to blue energy harvesting. Despite their widespread potential applications and the increasing interest of the scientific community, the actual design of nanopore based devices remains a major challenge in the field. In fact, most analytical models fail the quantitative prediction of experimental data, since the assumptions on which they are based often fail in the extremely small nanopore region. The relevant effects to be taken into account in order to model nanopore systems with reasonable accuracy are: i) at the nanometer scale, thermal fluctuations play a major role in the dynamics of mass and ion transport, consequently, the fluid cannot be treated with a deterministic set of equations. ii) the presence of the confining boundaries at nanoscale induces additional effects due to hydrodynamic interactions with particles moving in the pore region. iii) the presence of surface charges modify the equilibrium ionic distribution, giving rise to peculiar electrohydrodynamic phenomena such as current rectification and electroosmosis. iv) when dealing with large biological molecules such as proteins, the additional complexity of dealing with their complicated structure has to be considered. A well-known approach which takes into account these physical features is all-atoms Molecular Dynamics, which has been thoroughly used to study many different nanopore systems. Despite their undeniable usefulness, Molecular Dynamics simulations are limited both in the size of the systems which can be simulated and in the total simulated time. In this thesis, Coarse Grained models are employed to study the dynamics of confined systems on time and space scales not easily accessible to all-atoms Molecular Dynamics. The Coarse Graining of the system is performed by retaining only some of its degrees of freedom, dropping the remaining ones considered not relevant for the desired level of description. The equations of motion are then written for the selected variables, while the action of the dropped variables is introduced as a proper random forcing in the equations of motion. In this thesis, two different levels of Coarse Graining are considered. The first one is Brownian Dynamics for confined rigid particles, the second is a particle based model of the electrolyte fluid based on Dissipative Particle Dynamics. For what concerns Brownian dynamics of confined rigid particle, the Langevin equation governing the translations and rotations in confined environment is derived. The rotational motion of the particle is based on the quaternion formulation. The effect of confinement is introduced via a configuration dependent mobility matrix. A Brownian code which integrates the equation of motion has been set up, and the dynamics of a spherical rigid particle diffusing in a nanochannel is studied. The effect of confinement as well as the effect of different force fields on the diffusion of the particle is investigated. The results are in good agreement with experimental evidence. The second Coarse Grained approach analyzed in this thesis concerns the description of the hydrodynamics of electrolyte solutions including the coupling between hydrodynamic and ionic transport in the nanopore (i.e. electrohydrodynamics), which is crucial in several applications. A new Coarse Grained model based on Dissipative Particle Dynamics is proposed and validated. The model considers each particle to carry a quantity of positive or negative ions. The energy of the system, including the chemical potential due to the concentration of each specie and to the presence of the electric potential, is written as a function of the Coarse Grained variables (positions, velocities and number of ions). A set of ordinary stochastic differential equations has been derived for which the equilibrium distribution is the Boltzmann distribution associated to the chosen thermodynamic potential. The model has been implemented into the LAMMPS software and has been validated against a number of cases for which the analytical solution is available.