Phase Behavior Of Soft-core Systems:Two-dimensional Melting And Self-assembly Of Quasicrystals

The most prominent feature of soft matter-softness and complexity,makes the soft material phase behavior particularly rich and interesting.The complexity of the soft matter makes it self-assembling into more complex structures under certain conditions,and its softness causes the properties of the soft matter to be influenced by a variety of interactions.The in-depth study of self-assembly of soft matter not only helps us to understand the phase transition behavior between different phases,but also provides a new way to design materials with special functions.In many research directions,two-dimensional melting and the formation of soft quasicrystal has always been a hot content of soft condensate physics.In this article,we mainly study the two-dimensional solid-liquid phase transition properties and quasicrystal self-assembly behavior of soft-core systems.In the first chapter of the introduction,we first introduced the development of soft matter,and its important characteristics and the main research direction.Then we in-troduce the self-assembly of soft matter from its classification,the form of soft matter self-assembly and its research status.In many self-assembly research directions,we fo-cus on two-dimensional melting and self-assembly of quasicrystal.KTHNY theory is an important theoretical basis for understanding and analysis of two-dimensional melt-ing.We from the 2D solid,KTHNY theory hypothesis and conclusions,as well as the integrated KTHNY theory and some research results to understand the 2D melting,and then introduce some methods which are commonly used to identify the two-dimensional melting and various different states from structural and dynamical properties.Finally,we introduce the history of quasicrystal,high-dimensional space model,important phys-ical characteristics and two important quasicrystal structures.It is an important way to study and solve a series of problems in the field of quasicrystal by associating quasicrys-tal and soft matter into soft quasicrystal.Particles with different physical properties have a significant effect on the macro-scopic properties of soft matter.In the second chapter,we first introduce two commonly used soft particle model,hard core shell model and ultrasoft model,and the typical phase behaviors.Then we have a superficial analysis of a typical ultrasoft system and its phase behaviors.In the third chapter,we study two-dimensional melting of three typical soft-core systems which could occur reentrant phenomena.There is a maximum melting temper-ature of Tm in the phase diagram of these system,with a corresponding density of ?m.By analyzing the isothermal equations of state and its finite size effect,and using the ori-entational correlation functions and the positional correlation functions to determine the phases,we find that the hexatic phase-liquid phase transition is discontinuous on the side of ?<?m,there exists coexistence phase,and the density interval of coexistence phase decreases with increasing temperature,and tends to disappear at the maximum melting temperature of Tm.On the side of ?>?m,the phase transition properties be-tween the hexatic phase-liquid is continuous.Furthermore,by analyzing the maximum correlation length of the liquid phase,we determine that the maximum melting temper-ature T,may be the transition point between the two type of phase transition.More directly,we clearly see the coexistence phase and pure hexatic phase by intuitionistic instantaneous bit patterns.These results show that the soft-core system with the max-imum melting temperature can exhibit two different phase transition between hexatic phases and liquid phase.In the traditional method of quasicrystal formation,a variety of competing length scales are considered indispensable,either directly provided by the interaction potential or hidden in the particle size or shape.In the fourth chapter,we use the purely repul-sive,homogeneous soft-core model,and surprisingly discover the existence of eight-fold and twelve-fold quasicrystals.By analyzing the quasicrystal structure,we find that the pentagon is the key element for the formation of quasicrystal.The importance of the pentagon is further confirmed by analyzing the dynamical properties of quasicrys-tals and the analysis of the structure of the liquid before transform to(quasi)crystals.Then,we found route independence of the formation of quasicrystals,and the compari-son of the potential energy of different solid structures determine that our quasicrystal is stable.Finally,we simply analyze the phase transition properties and vibrational prop-erties of quasicrystals.Our results provide an incredible simple path for the formation of quasicrystals and presents a challenge to the theoretical understanding of alignment.In the fifth chapter,we summarize this paper and look forward to the future work.