球形表面上粒子密集堆积中的能量有利缺陷
Energetically favoured defects in dense packings of particles on spherical surfaces
摘要：
相互作用的粒子在球体上的密集堆积已被证明是病毒衣壳和胶体体的有用模型。事实上，在病毒衣壳中观察到的二十面体对称性对应于发生幻数的势能最小值，例如，12、32和72个相同的Lennard-Jones颗粒，对于这些颗粒，填充具有正好最小数量的12个五重缺陷。然而，目前还不清楚这些结构对热搅动的稳定性如何。我们调查这个属性通过盆地跳跃的全球优化和朗之万动力学粒子数在10和100之间。一个重要的测量是点缺陷的数量和类型，即没有六个最近邻居的粒子。我们发现，小的二十面体结构是最强大的对热波动，表现出较少的过剩缺陷和重排的一个很宽的温度范围。此外，我们提供的证据表明，在低的非零温度下出现的多余的缺陷降低的熵为代价的势能。在较高的温度下，缺陷，如预期的那样，热激发，从而熵稳定。如果我们用一个非常短程的（Morse）势来代替Lennard-Jones势，我们会发现，同样的粒子数会给出势能的最小值，尽管对于更大的粒子数，这些最小值对应于不同的堆积。此外，缺陷是更难以激发热的短程电位，这表明短程相互作用进一步稳定平衡结构。
英文摘要：
The dense packing of interacting particles on spheres has proved to be a useful model for virus capsids and colloidosomes. Indeed, icosahedral symmetry observed in virus capsids corresponds to potential energy minima that occur for magic numbers of, e.g., 12, 32 and 72 identical Lennard-Jones particles, for which the packing has exactly the minimum number of twelve five-fold defects. It is unclear, however, how stable these structures are against thermal agitation. We investigate this property by means of basin-hopping global optimisation and Langevin dynamics for particle numbers between ten and one hundred. An important measure is the number and type of point defects, that is, particles that do not have six nearest neighbours. We find that small icosahedral structures are the most robust against thermal fluctuations, exhibiting fewer excess defects and rearrangements for a wide temperature range. Furthermore, we provide evidence that excess defects appearing at low non-zero temperatures lower the potential energy at the expense of entropy. At higher temperatures defects are, as expected, thermally excited and thus entropically stabilised. If we replace the Lennard-Jones potential by a very short-ranged (Morse) potential, which is arguably more appropriate for colloids and virus capsid proteins, we find that the same particle numbers give a minimum in the potential energy, although for larger particle numbers these minima correspond to different packings. Furthermore, defects are more difficult to excite thermally for the short-ranged potential, suggesting that the short-ranged interaction further stabilises equilibrium structures.
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