We introduce a toy model that contains the basic features of microphase separation in polymer gels: a stretched elastic network of Lennard-Jones particles, studied in two dimensions. When temperature is lowered below some value T*, attraction between particles dominates over both thermal motion and elastic forces, and the network separates into dense domains of filaments connected by three-fold vertices, surrounded by low-density domains in which the network is homogeneously stretched. The length of the filaments decreases and the number of domains increases with decreasing temperature. The system exhibits hysteresis characteristic of first-order phase transitions: pre-formed filaments thin upon heating and eventually melt at a temperature T** (>T*). Although details may vary, the above general features are independent of network topology (square or hexagonal), system size, distribution of spring constants, and perturbations of initial conditions.
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机译：我们介绍了一种玩具模型，该模型包含聚合物凝胶中微相分离的基本特征：二维研究的Lennard-Jones粒子的拉伸弹性网络。当温度降低到低于某个值T *时，粒子之间的吸引力在热运动和弹性力上都占主导地位，并且网状结构分成细丝的密集区域，该区域由三折顶点连接，并被低密度区域包围，其中网络均匀分布舒展。随着温度降低，细丝的长度减小，并且畴的数量增加。该系统表现出一阶相变的磁滞特性：预成型的长丝在加热时变细，最终在温度T **（> T *）下熔化。尽管细节可能有所不同，但上述一般特征与网络拓扑结构（正方形或六边形），系统大小，弹簧常数的分布以及初始条件的扰动无关。
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