Department of Zoology, La Trobe University, Melbourne, Victoria 3083, Australia.
J Theor Biol. 2011 May 7;276(1):8-15. doi: 10.1016/j.jtbi.2011.01.046. Epub 2011 Feb 3.
Electrically charged long-chain macromolecules in an electrolyte can form an ordered lattice whose spacing is greater than their diameter. If entropic effects are neglected, these nematic structures can be predicted from a balance of Coulomb repulsion and van-der-Waals attraction forces. To enhance the utility of such theories, this paper extends existing results for the interaction between charged filaments, and gives approximate formulae for the screened Coulomb and van-der-Waals potentials over the whole range of their centre-to-centre spacing d. The repulsive Coulomb potential is proportional to exp(-λd)/λd for all spacings when the Debye screening length 1/λ is smaller than the sum of the filament radii. The attractive van-der-Waals potential is asymptotic to d⁻⁵ at large d. For smaller spacings, the potential is calculated by numerical integration and compared with published formulae: the series expansion of Brenner and McQuarrie converges too slowly, whereas the interpolation formula of Moisescu provides reasonable accuracy over the whole range of d. Combining these potentials shows that there is a finite range of charge densities for which a nematic crystal lattice is stable, but this conclusion ignores entropic effects associated with motile filaments. The role of electrostatic forces in aligning filaments and stabilizing a nematic liquid-crystal phase is discussed, in conjunction with other mechanisms such as motor proteins, crosslinkers or scaffolding structures.
在电解质中，带电荷的长链大分子可以形成一个有序的晶格，其间距大于它们的直径。如果忽略熵效应，这些向列结构可以从库仑斥力和范德华吸引力的平衡中预测出来。为了增强这些理论的实用性，本文扩展了已有带电细丝相互作用的结果，并给出了在它们的中心到中心间距 d 的整个范围内屏蔽库仑和范德华势的近似公式。当德拜屏蔽长度 1/λ小于细丝半径之和时，对于所有间距，排斥库仑势与 exp(-λd)/λd 成正比。在较大的 d 时，吸引力范德华势渐近于 d⁻⁵。对于较小的间距，通过数值积分计算势，并与已发表的公式进行比较：Brenner 和 McQuarrie 的级数展开收敛太慢，而 Moisescu 的插值公式在整个 d 范围内提供了合理的精度。将这些势结合起来表明，存在一个有限的电荷密度范围，在这个范围内向列晶格是稳定的，但这个结论忽略了与运动细丝相关的熵效应。本文讨论了静电力在排列细丝和稳定向列液晶相方面的作用，以及其他机制，如马达蛋白、交联剂或支架结构。
