We continue our theoretical study of a recently proposed two-dimensional colloidal system with attractive critical Casimir and repulsive magnetic dipole forces that can be tuned easily and independently from each other via the temperature and the strength of an external magnetic field, respectively [K. Marolt, M. Zimmermann, and R. Roth, Phys. Rev. E 100, 052602 (2019)]. Using this freedom, it is possible to construct a competing interaction potential that causes microphase separation featuring spatially inhomogeneous cluster, stripe, and bubble phases in the bulk, i.e., in an infinite system without an external potential. In the present work, we demonstrate by means of density functional theory that microphase separation can also occur in finite geometries. In a square cell with a side length of 20 or 30 colloid diameters, we observe the emergence of highly structured cluster and ring phases at intermediate bulk densities in addition to almost uniform fluid phases for lower and higher bulk densities. We then employ dynamic density functional theory to determine how the system reacts when the temperature and the magnetic field are altered over time, and we show how to induce a transition from the liquid to the cluster/ring phase and also from the cluster directly to the ring phase. We find that often a slowly varying and nontrivial path in parameter space is required to reach a stable state, whereas abrupt changes are prone to lead to metastable configurations.

中文翻译：

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具有竞争吸引力的临界卡西米尔和排斥磁偶极子相互作用的有限二维胶体系统的静力学和动力学

我们继续对最近提出的二维胶体系统进行理论研究，该系统具有诱人的临界卡西米尔和排斥磁偶极力，可以分别通过外部磁场的温度和强度轻松地且彼此独立地进行调整[K。Marolt，M.Zimmermann和R.Roth，物理学。E 100版，052602（2019）]。利用这种自由度，有可能构建竞争性的相互作用势，该相互作用势将导致微相分离，其特征是在本体中，即在无外部势能的无限系统中，空间上不均匀的簇，条纹和气泡相。在目前的工作中，我们通过密度泛函理论证明了微相分离也可以在有限的几何形状中发生。在具有20或30胶体直径的边长的正方形单元中，我们观察到在较低的和较高的堆积密度下，除了几乎均匀的流体相以外，在中等堆积密度下还出现了高度结构化的团簇和环相。然后，我们采用动态密度泛函理论确定温度和磁场随时间变化时系统的反应，并且我们展示了如何诱导从液相到团簇/环相以及从团簇直接到环相的转变。我们发现，通常需要在参数空间中缓慢变化且不平凡的路径才能达到稳定状态，而突然的变化则容易导致亚稳构型。