Dynamic model of biomolecular diffusion through two-dimensional nanochannels

The molecular diffusion dynamics in unconstrained cases has been studied thoroughly during the last two centuries, leading to the well-known Fick's diffusion laws and Stokes-Einstein equation. More recently, a new impulse to the study of this topic has been provided by the necessity of understanding the behavior of solute particles in the presence of environmental constraints of size comparable to the molecular dimensions. In this work, we investigate the diffusion kinetics of biomolecules, such as bovine serum albumin, interferon, and lysozyme, through microfabricated silicon membranes, having pores of nanometric size in only one dimension, in the range from few to tens of nanometers (the other dimensions are in the mu m range). Experimental results show that the diffusion profiles, in some cases, deviate substantially from those predicted by Fick's laws. In light of these results, a new diffusion mathematical model is proposed, which can reasonably explain the phenomenon and, at the same time, recovers the classical diffusion laws in the unconstrained case. Moreover, a physical description, derived from van der Waals equation of state, is presented, and it is compared with the results obtained by the mathematical model.