Asymmetrical Free Diffusion With Orientation-dependence Of Molecule In Finite Timescales

Diffusion is a very common matter transport phenomenon. Classic theory of thediffusion treats the target particle as a ball surrounded by continuously distributed solvent.Through the establishment of such a simple theoretical model, the classical diffusiontheory can understand the diffusion of the target particle in uniform continuous solvent.Within the macro-scale, the classical diffusion theory explains the diffusion phenomenonwell. But at the microscopic scale, the approximation of the theoretical model (uniformcontinuous solvent) is no longer applicable. So the thermodynamics statistical methodsbased on molecular kinetic theory are used for researching the diffusion at micro-scale,like Brownian motion. Although whose basic idea is from the discrete molecfular kinetictheory, thermodynamics and statistical methods are based on the statistics from a largenumber of samples for long time, the physical variables in which are usually obtained byaveraging a large number of samples and always associated with the probability. Theresults obtained by calculation are also the statistical average states associated with theprobability instead of realistic dynamics details. There are diffusion phenomena within veryshort period in reality, for example the molecular diffusion between cells, where thedistance of diffusion is only several nanometers and the time of diffusion also lasts severalnanoseconds. In this case, both the classical theory with the approximation of uniformcontinuous solvent and the statistical methods calculated from a large number of samplesfor long time have issues of applicability on understanding and analyzing the details of thediffusion within short time interval.In this paper, using classical molecular dynamics methods we simulate and analyzethe details of the molecular diffusion in short time interval. From a large number ofcomputer simulations, asymmetrical diffusion with orientation-dependence of molecules isfound within limited time. At a certain direction based on the structure of molecule itself,the mean diffusion distance is longer than those at the other directions. Such asymmetry accumulates as the correlation of the molecular orientation decays. After the correlation ofthe molecular orientation decays to zero, the asymmetry of the mean diffusion distancedoes not accumulate any longer. The attenuation of the correlation of the molecularorientation is very fast (about10ps). During such short time interval, the moleculardiffusion is not very far away (about0.5nm). The difference between these asymmetricalmean diffusion distances is also very small (about0.1nm). Compared with the diffusiondistance for long time, this difference can be ignored, that is why the classical theoryexplains the diffusion phenomenon well without considering molecular orientation. But insome diffusion within short time interval, for example, as mentioned above, the moleculardiffusion between cells. Since the diffusion distance is only several nanometers, thedifference is notable compared to the short diffusion distance (~10%). So the asymmetricaldiffusion with orientation-dependence of molecules can not be ignored as the macroscopictheory.Through further analysis, it is obtained that the reason of the asymmetrical diffusionwith orientation-dependence of molecules in limited time scale is the asymmetricalstructure of the molecule itself. Due to the asymmetrical structure of the molecule itself, theinteractions between the target molecule and the discrete solvent molecules surroundingare different at different direction of the molecular structure, which affects the moleculardiffusion in different directions. This also explains that the classical diffusion theory has noasymmetry since we treat the molecule as a sphere or a point in which. In case of diffusionat nanometer scale in short time, the structure of the molecule itself can not be ignored.Finally, simulations with different molecules manifest that the asymmetrical diffusionwith orientation-dependence of molecules is reliable in limited time interval, and accordingto the analyzation and our theoretical model, it is suggested that this asymmetry is mainlydue to the structure of the molecule itself, which is not ignored in the diffusion atnanometer scale for limited time.