Rechtsman Mikael C, Stillinger Frank H, Torquato Salvatore
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 1):021404. doi: 10.1103/PhysRevE.74.021404. Epub 2006 Aug 7.
Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures [M. C. Rechtsman, Phys. Rev. Lett. 95, 228301 (2005); Phys. Rev. E 73, 011406 (2006)], we present an isotropic pair potential V(r) for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors, and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered-cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.
传统观点认为，低配位晶体基态需要定向相互作用。利用我们最近引入的优化程序来实现目标结构的自组装[M. C. 雷克茨曼，《物理评论快报》95, 228301 (2005); 《物理评论E》73, 011406 (2006)]，我们给出了一个三维多粒子系统的各向同性对势V(r)，其经典基态是低配位简单立方晶格。这一结果是作者正在进行的一项研究的一部分，该研究旨在开发分析和计算工具，以解决统计力学逆问题，从而实现目标自组装。这些方法的目的是设计粒子间相互作用，以使具有技术重要性的目标结构自组装，用于光子学、催化、分离、传感器和电子学等应用领域。我们还表明，利用对关联函数信息的标准液态近似积分方程理论不能以反向模式用于预测正确的简单立方势。我们顺便报告了产生体心立方晶格和简单六方晶格的优化各向同性势，它们提供了可以使用各向同性对相互作用进行组装的非密排结构的其他示例。
