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Beginning with the molecular-based Fokker–Planck equation obtained previously [M. H. Peters, J. Chem. Phys. 110, 528 (1999); J. Stat. Phys. 94, 557 (1999)], the Smoluchowski diffusion equation is derived here to describe the spatial and orientational dynamics of molecularly structured macromolecules near molecularly structured surfaces. The formal scaling and perturbation methods employed allow the establishment of definite limits on the use of the Smoluchowski equation when surfaces are present. It is shown that the Smoluchowski equation reduces to that given previously [D. W. Condiff and J. S. Dahler, J. Chem. Phys. 44, 3988 (1966)] in the absence of external surfaces. A specific example application is given involving a spherical macromolecule with electrostatic charge segments near a planar surface with an arbitrary charge distribution. Finally, we show that the short-time solution to the Smoluchowski equation obtained here yields a Brownian dynamics method consistent with that given previously [E. Dickinson, S. A. Allison, and J. A. McCammon, J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)] for orientable, interacting Brownian particles. This study has applications to problems involving site-specific adsorption of orientable, structured Brownian particles, such as association or adsorption of biological macromolecules to cellular surfaces and enzyme–substrate docking kinetics, to name a few.

The Fokker-Planck equation and molecular-based grand friction tensor are derived for the problem of rotational and translational motions of a structured Brownian particle, including the presence of a structured wall. Using the method of multiple time scales, it is shown that the time independent, grand friction tensor for the Brownian particle includes, in a general way, terms that account for the fluid molecular mediated interactions with the wall. The resulting Fokker-Planck equation has important applications in processes involving site-specific adsorption of macromolecules, such as affinity chromotography, biological separations, and numerous cellular processes involving attachment of macromolecules.

In this study, the grand (translational) friction tensor for free‐molecule (large Knudsen number) flows over two, unequal‐size cylinders is obtained analytically considering both ‘‘shielding’’ effects and multiple collisions off cylinder surfaces, as well as including both diffuse and specular molecule‐surface boundary conditions. A perturbation solution is used where the leading‐order term accounts for molecular collisions from the free‐streaming gas including all shielding effects. The first‐order correction term is also obtained here and accounts for collisions by molecules reflected off neighboring surfaces from the free‐stream gas. It is shown that the grand friction tensor is symmetric under the conditions of small ratios of the free‐stream gas velocity to the thermal gas velocity, the same type of molecular reflection boundary condition on both cylinders, and constant temperature. It is also shown that the two‐term expansion formula is accurate under isothermal conditions in the so‐called ‘‘far‐fie...

In two previous studies [J. Chem. Phys. 91, 1287 (1989); 95, 1234 (1991)] we had examined the dynamics of coupled, internal translational, and rotational motions in a rigid or pseudorigid N‐sphere macromolecular model using the rotational–translational Brownian dynamics algorithm of Dickinson et al. [J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)]. In the present study, those works are generalized to include all possible internal flexible motions in an N‐sphere macromolecular model. In general, for the N‐sphere system there are 6(N‐1) degrees of configurational freedom, although not all modes may be active in any particular application. Using the language of small oscillation theory, the deviations in the generalized coordinates associated with the ‘‘joints’’ connecting the spheres to one another are described in terms of quadratic potentials. From these potentials, the components of the generalized forces (torques and forces) are obtained for subsequent use in the Brownian dynamics algorithm. The degree o...

A former investigation [R. Ying and M. H. Peters, J. Chem. Phys. 9 1, 1287 (1989)] on the rotational dynamics of rigid and partially flexible macromolecules in solution by means of Brownian dynamics simulation methods is extended to a trimer or three‐body macromolecular model. We present expressions for the torque constraints in rigid and semirigid trimer systems that allows for a comprehensive simulation of the translational, rotational, and coupled translational–rotational motions of the three interacting spherical Brownian particles comprising the trimer (trumbell). The torque constraint expressions are verified by comparisons of the Brownian dynamics simulation results to exact analytical results for a rigid trimer system (Appendix). Computer simulations and analytical solutions for the rigid trimer system indicate that the inclusions of rotational motions of the model’s elements can have an appreciable effect on macromolecular dynamics. Macromolecular flexibility can also be easily introduced into the model through varying the parameters of the torque and force constraint expressions. Extensions to an N‐body macromolecular model are also outlined based on the trimer system studied here.

This work investigates the rotational dynamics of rigid and partially flexible macromolecules in solution by means of Brownian dynamics simulation techniques. In a previous study by Diaz et al. [J. Chem. Phys. 87, 6021 (1987)] on the rotational correlation functions of rigid models, the effect on rotational dynamics from pure rotations of the model’s elements has been neglected due to the difficulty of introducing rotational constraints in the simulations. We present expressions for rotational constraints in a rigid dimer system, which makes it possible to completely describe the translational, rotational, and coupled translational–rotational motions for interacting spherical Brownian particles by employing the generalized algorithm of Dickinson et al. [J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)]. Theoretical studies indicate, and our simulation calculations confirm, that the pure rotational effects are appreciable. The torque constraint expressions are verified by comparison of the simulation results ...