Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles.

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Random sequential adsorption (RSA) models particle aggregation and jamming in various contexts.
• Asymptotic jamming coverage in RSA models exhibits algebraic time dependence (∼t^{-ν}).
• The exponent ν is analytically known only for monodisperse spheres on a line (ν=1).

Purpose of the Study:

• To analytically solve the long-standing problem of the scaling exponent ν for RSA of nonspherical particles in one dimension (d=1).
• To investigate the dependence of the jamming exponent on particle shape.
• To resolve discrepancies between empirical simulations and theoretical conjectures regarding ν.

Main Methods:

• Analytical solution of the 1D Random Sequential Adsorption (RSA) problem, referred to as the 'Paris car parking problem'.
• Derivation of the asymptotic jamming coverage exponent ν for general particle shapes.
• Classification of particle shapes into universality classes based on their contact distance properties.

Main Results:

• The scaling exponent ν for 1D RSA is proven to be dependent on particle shape, contrary to prior conjectures.
• Two universality classes for ν are identified: ν=1/(1+d[over ˜]/2) for smooth contact distance shapes (e.g., ellipsoids) and ν=1/(1+d[over ˜]) for singular contact distance shapes (e.g., spherocylinders, polyhedra).
• The derived exact solutions explain observed empirical scalings that fall between theoretical limits.

Conclusions:

• The jamming exponent in 1D RSA is not universal but depends on particle geometry.
• The study establishes a theoretical framework for understanding shape-dependent jamming phenomena in RSA.
• This work provides an exact solution for the 1D 'Paris car parking problem,' resolving a key challenge in particle adsorption and jamming.