Modeling and simulating electrostatic, diffusive, and hamaker inelastic collisions for two charges in an ionic solution

The mechanisms governing the attraction of biological molecules remain an open question in biophysics and chemistry, particularly in the case of actin and myosin. These molecules have characteristic lengths on the order of 10 nm, suggesting that they are subject to thermal agitation, Hamaker, and electrostatic forces over small enough length scales. However, as intracellular fluid contains significant concentrations of free ions, these proteins also gather ion clouds creating an electric double layer on and near their boundaries. This causes electrostatic shielding - a characteristic that limits the strength of electrical attraction between binding sites on complementary molecules. However, that energy is stored in a concentration gradient of opposing counterions in the molecules' respective ion clouds. Here, we explore how the concentration gradients of the ions in solution in addition to the forces already listed may affect the dynamics of nanoparticles.