Growth of copolymer chains and mixed CRYSTALS—TRIAL-AND-ERROR statistics
Growth of copolymer chains and mixed CRYSTALS—TRIAL-AND-ERROR statistics
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共聚物链和混合晶体的增长——试错统计
DOI：
10.1070/pu1970v013n01abeh004200
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发表时间：
1970
期刊：
影响因子：
2.7
通讯作者：
A. Chernov
中科院分区：
文献类型：
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作者：
A. Chernov
我们知道，生长中的晶体的表面原子结构和内部结构不同于平衡结构。例如，不同的面以不同的方式结合杂质（晶体的扇形结构），并且它在晶体中的量不是由普通相图确定的。在生长过程中产生的亚稳态实际结构是高度持久的。所有这些对于保持单体的顺序和浓度的共聚物链也是如此。因此，结晶和聚合不仅必须在统计热力学的框架内处理，而且统计动力学。晶体表面上的原子通过热力学和动力学意义上的集体相互作用而结合在一起：态的分布（原子表面构型）及其变化率取决于整个表面的结构。在单组分体系中，尤其是在混合体系中，这种协同动力学的困难使得晶体生长理论沿着热力学路线发展。最重要的是，这一发展产生了科塞尔-斯特兰斯基-凯舍夫分子动力学理论（见'4”7 3）。后者主要基于分析不同表面粒子的能量。Frenkel对台阶和表面结构的热力学分析开始了解释熵项和复杂构型的实践，导致了原子光滑和粗糙表面的概念。巴顿和卡布雷拉19 '10· 1利用与二维铁磁材料性质的类比，考虑了基本表面层中的集体相互作用。他们表明，结合能和温度之间存在着一种临界关系，这种关系是从有序的、光滑的结构过渡到无序的、粗糙的结构所必需的。研究的进一步发展使得有可能处理跨越数十个原子间距离的表面波动，从而根据结晶熵提出任何特定表面结构存在的标准，十二年143找到简单的近似方法，用于确定从光滑表面过渡到粗糙表面的条件115 '163，并推广这样一个过渡到二元系统，C17> 125'12 e3提出和研究的可能性，无障碍运动的相边界，' 18”211和开始分析表面结构的离子晶体。22· 1所有这些研究构成了结晶理论的大部分工作，
A S we know, the atomic structure of the surface and the internal structure of a growing crystal differ from the equilibrium structures. For example, different faces incorporate an impurity in different ways (the sectorial structure of a crystal'1" 3· 1), and the amount of it in the crystal is not determined by the ordinary phase diagram. The metastable actual structure arising during growth is highly persistent. All of this is also true of copolymer chains that maintain a sequential order and concentration of monomers. Hence, crystallization and polymerization must be treated not only within the framework of statistical thermodynamics, but also that of statistical kinetics. The latter is the topic of this review.The atoms on the surface of a crystal are bound by collective interaction, both in the thermodynamic and the kinetic sense: the distribution of states (atomic surface configurations) and their rates of variation depend on the structure of the entire surface. The difficulties involved in this cooperative kinetics in single-component systems, and a fortiori in mixed systems, have led the theory of crystal growth to develop along the thermodynamic line. Above all, this development has given rise to the Kossel-Stranskii-Kaishev molecular-kinetic theory (see'4" 7 3). The latter is based mainly on analyzing the energies of different surface particles. Frenkel's thermodynamic analysisC8] of step and surface structure started the practice of accounting for entropy terms and complex configurations, leading to the concepts of atomically-smooth and rough surfaces. Barton and Cabrera19'10· 1 have taken into account collective interactions in an elementary surface layer, using the analogy with the properties of a two-dimensional ferromagnetic material. They showed that there is a critical relation between the binding energy and the temperature necessary for transition from an ordered, smooth structure to a disordered, rough structure. Further development of the studies'8" 103 has made it possible to treat surface fluctuations spanning tens of interatomic distances,'1" to propose criteria for the existence of any particular surface structure in terms of entropy of crystallization,'12" 143 to find simple approximate methods for determining the conditions for transition from a smooth to a rough surface115'163 and to generalize the concept of such a transition to binary systems, C17> 125'12e3 to propose and study the possibility of barrier-free motion of a phase boundary,'18" 211 and to begin to analyze the surface structure of ionic crystals.'22· 1 All these studies, which have constituted the bulk of the work on the theory of crystallization,