Brownian Motion of Polyatomic Molecules: The Coupling of Rotational and Translational Motions

Abstract

Articles you may be interested inInertial and bias effects in the rotational Brownian motion of rodlike molecules in a uniaxial potential J. Chem. Phys. 134, 044530 (2011); 10.1063/1.3524534 Rotational Brownian motion of a pair of linear molecules or dipoles with anisotropic interaction Fokker-Planck equation and the grand molecular friction tensor for coupled rotational and translational motions of structured Brownian particles near structured surfacesThe coupling of rotational and translation Brownian motions is examined from several points of view. The first is a phenomenological theory based upon generalized Langevin equations of motion and a Markoff integral equation. Next, a more detailed statistical-mechanical theory is fashioned after the pattern of Kirkwood's theory for nonequilibrium processes in monatomic liquids. Both schemes lead to a generalized Fokker-Planck-Chandrasekhar equation for the singlet-distribution function. This equation includes terms that account for separate rotational and translational motions as well as two mutually symmetric contributions which are descriptive of their coupling. The friction tensors associated with the uncoupled components of these motions are found to be proportional to the autocorrelations of the environmental force and torque which act upon a given molecule. The frictional coupling is related to the cross correlation of force and torque. From the principle of microreversibility it is possible to establish a reciprocal relationship between the two coupling tensors. A third approach is to derive the generalized Fokker-Planck equation from the Boltzmann equation for a dilute solution of rotating molecules. This has been done for the model of perfectly rough spheres and also for "loaded spherocylinders." In both cases explicit formulas are obtained for the various friction tensors. The last section of the paper is devoted to the application of these theories to problems of diffusion.2

The Smoluchowski diffusion equation for structured macromolecules near structured surfaces

“…The form of the SM equation was shown to follow those derived previously in the absence of external surfaces. 5 There are, however, subtle but important differences in the definitions of diffusion tensor and external force terms that appear in the SM equation when an external surface is present. These terms account for the fluid mediated interactions between the macromolecule and external surface, and they constitute the molecular-based definitions of the so-called ''hydrodynamic interactions'' in continuum theories.…”

“…͑22͒ is in agreement with the FP equation given by Condiff and Dahler. 5 Now, following Wilemski, 7 we will derive the Smoluchowski ͑SM͒ equation from a regular perturbation expansion of the FP equation. This formality will allow us to set definite limits on the applicability of the SM equation, which is important in applications and in establishing higher order corrections.…”

“…5 We note that the smallness parameter ⑀(ϭN ST ) can be recast in terms of the dimensionless diffusion, D 0 ϵkT/ 0 , as…”

Symmetry analysis of non-equilibrium time correlation functions

“…This has consequences for the Onsager--Casimir reciprocal relations [- [39][40][41], which require symmetry in the exchange of indices of quantities such as diffusion coefficients which are integrals over time correlation functions. Well known examples are provided in textbooks such as Landau and Lifshitz [42] which state that kinetic coefficients (~) satisfy the Onsager-Casimir symmetry principle ri~ = ~;ji.…”

An Integrated Reaction-Transport Model for DNA Surface Hybridization: Implications for DNA Microarrays

“…The distribution P is governed by a diffusion equation containing terms describing both translational and rotational diffusion, respectively characterized by a translational diffusion coefficient D(z 0 ) and a rotational diffusion coefficient D r 8,9,13,36 :…”