摘要
扩散现象是一种常见的物质输运现象。传统经典理论将扩散行为等效为目标颗粒在均匀连续分布的介质中的动力学行为,通过建立这样一个简单的理论模型,经典扩散理论可以理解并推导得到目标颗粒在均匀连续分布介质中扩散行为的规律。在宏观尺度内的,经典扩散理论较好的符合真实的扩散现象,但在微观尺度内,由于理论模型中均匀连续分布介质的近似条件不再适用,所以使用与真实情况较接近的、基于分子运动论产生的热力学统计方法来研究类似布朗运动的微观尺度扩散行为。热力学统计方法基于大量长时间样本统计,虽然其基本思想是基于离散的分子运动论,但所使用的物理量通常都是大量样本平均得到的与概率相关的平均值,通过计算所能得到的结果也往往只限于跟概率相关的统计平均状态量,得不到较真实的动力学过程细节。而在实际情况中,存在时间很短的扩散行为,例如分子在细胞之间的扩散,往往只有纳米尺度,在纳秒的时间内就已经完成,在这种情况下,无论是将环境近似为均匀连续介质的经典理论,还是基于大量样本长时间平均统计的热力学统计方法,在理解和分析短时间内扩散行为的动力学细节方面,都存在适用性问题。
本文从经典分子动力学研究方法出发,模拟并分析分子在短时间内扩散行为的动力学细节信息。通过大量的计算模拟,发现在有限时间内,分子的扩散行为具有与其自身指向相关的不对称现象。在基于分子自身结构的某一个方向上,相同时间间隔内其平均扩散距离要比其他方向上的平均扩散距离要远。这样的不对称现象会随着分子自身指向关联的衰减不断的积累,分子自身指向关联衰减到零之后,平均扩散距离的不对称现象不再积累,而是一直保持,但由于分子自身指向关联衰减的很快(10ps量级),在这样短的时间内,分子扩散的距离并不是很远(0.5nm量级),所以平均扩散距离的不对称现象积累的差值并不是很大(0.1nm量级),这样小的不对称扩散行为差值相比随着时间推移不断增大的扩散距离来说,长时间后确实可以被近似忽略,这也就是经典理论中没有考虑分子指向得到的扩散理论仍能较好的符合宏观扩散现象的原因,但在某些短时间扩散行为中,例如上文所提到的分子在细胞之间的扩散,由于扩散距离只有纳米量级,所以与分子指向相关的不对称扩散差值相比而言具有不可忽视的比例(-10%),所以在短时间的分子扩散行为中,分子指向相关的不对称扩散现象不能象宏观理论被近似忽略。
通过进一步的分析研究发现,这种在有限时间尺度内分子指向相关的不对称扩散现象发生的原因在于分子自身结构的不对称。由于分子自身不对称的结构,所以在不同方向上与周围离散的介质分子发生相互作用的情况不同,从而影响到分子在不同方向上扩散行为的不同。这也说明了近似分子为球形或质点的宏观经典理论没有得到不对称扩散行为的原因,因为在短时间纳米尺度下,分子自身结构不能被近似忽略。
最后,通过对多种不同分子进行模拟统计,验证了有限时间尺度内分子指向相关的不对称扩散现象的真实性,并通过建立模型分子和理论计算,证明这种不对称扩散现象产生的主要原因就是分子自身结构在短时间纳米尺度下的扩散行为中不能被近似忽略。
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 But at the microscopic scale, the approximation of the theoretical model (uniformcontinuous solvent) is no longer applicable.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.
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