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There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities. [12]
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Typically, the diffusion constant of molecules and particles defined by Fick's equation can be calculated using the Stokes–Einstein equation. In the ultrashort time limit, in the order of the diffusion time a 2 /D, where a is the particle radius, the diffusion is described by the Langevin equation.
A damping constant = / is frequently used for the inverse momentum relaxation time (time needed for the inertia momentum to become negligible compared to the random momenta) of the diffusive object. For spherical particles of radius r , Stokes' law gives ζ = 6 π η r , {\displaystyle \zeta =6\pi \,\eta \,r,} where η {\displaystyle \eta } is ...
In practice, the diameter of gas molecules is not well defined. In fact, the kinetic diameter of a molecule is defined in terms of the mean free path. Typically, gas molecules do not behave like hard spheres, but rather attract each other at larger distances and repel each other at shorter distances, as can be described with a Lennard-Jones ...
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
The thermal motions of the atoms or molecules in a gas are allowed to move freely, and the interactions between the two (the gas and the atoms/molecules) can be neglected. In physics , a partition function describes the statistical properties of a system in thermodynamic equilibrium .
Collision frequency describes the rate of collisions between two atomic or molecular species in a given volume, per unit time. In an ideal gas, assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B is: [1]