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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 ]
For the diffusive collision, at the infinite time limit when the molecular flux can be calculated from the Fick's laws of diffusion, in 1916 Smoluchowski derived a collision frequency between molecule A and B in a diluted solution: [4] = where:
The plasma collisionality is defined as [4] [5] =, where denotes the electron-ion collision frequency, is the major radius of the plasma, is the inverse aspect-ratio, and is the safety factor. The plasma parameters m i {\displaystyle m_{\mathrm {i} }} and T i {\displaystyle T_{\mathrm {i} }} denote, respectively, the mass and temperature of the ...
Thus, this Smoluchowski frequency represents the lower limit of the real collision frequency. In 2022, Chen calculates the upper limit of the collision frequency between A and B in a solution assuming the bulk concentration of the moving molecule is fixed after the first nearest neighbor of the target molecule. [17]
At a resonance frequency , called the plasma frequency, the dielectric function changes sign from negative to positive and real part of the dielectric function drops to zero. ω p = n e 2 ε 0 m {\displaystyle \omega _{\rm {p}}={\sqrt {\frac {ne^{2}}{\varepsilon _{0}m}}}} The plasma frequency represents a plasma oscillation resonance or plasmon .
In effect, the free energy of activation takes into account both the activation energy and the likelihood of successful collision, while the factor k B T/h gives the frequency of molecular collision. The factor (c ⊖) 1-M ensures the dimensional correctness of the rate constant when the transition state in question is bimolecular or higher.
For that reason, it is often called frequency factor. According to collision theory, the frequency factor, A, depends on how often molecules collide when all concentrations are 1 mol/L and on whether the molecules are properly oriented when they collide. Values of A for some reactions can be found at Collision theory.
Also called the probability factor, the steric factor is defined as the ratio between the experimental value of the rate constant and the one predicted by collision theory. It can also be defined as the ratio between the pre-exponential factor and the collision frequency, and it is most often less than unity.