In the framework of the density functional theory of freezing proposed in our previous works, we calculate the phase diagram of two-dimensional system of particles interacting through the repulsive shoulder potential. This potential consists of the hard core and repulsive shoulder of the larger radius. It is shown that at low densities the system melts through the continuous transition in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario, while at high densities the conventional first order transition takes place.A large number of papers studying the melting transition in two dimensions have been published during last decades. They include results of real experiments, computer simulations and various theoretical approaches. This is dictated by the growing interest to the behavior of the nanoconfined systems. Confining drastically changes the spatial distribution and the ways of dynamic rearrangement of the molecules in the system. The confined fluids microscopically relax and flow with characteristic times that differ from the bulk fluids. These effects play important role in the thermodynamic behavior of the confined systems and can considerably change the topology of the phase diagram. In general, the motivation for the study of the confined systems follows from the fact that there are a lot of real physical, chemical and biological processes which drastically depend on the properties of such systems [1][2][3][4][5][6].It is not surprising that the spatial ordering of molecules depends on the dimensionality of the space to which it is confined. Mermin [7] has shown that in in two dimensions (2D) the long-range crystalline order can not exist because of the thermal fluctuations and transforms to the quasi-long-range order. On the other hand, the real long range bond orientational order does exist in this case. At high temperatures one can find the conventional isotropic fluid.The melting scenario in two dimensions is a subject of long lasting controversy. Now it is widely believed that the Kosterlitz, Thouless, Halperin, Nelson, and Young theory (KTHNY theory) [8][9][10][11] correctly describes the melting transition in 2D. In the framework of the KTHNY theory the two-dimensional melting occurs in the way which is fundamentally different from the melting transition of three-dimensional systems. In 2D, the bound dislocation pairs dissociate at some temperature T m transforming the quasi-long range translational order in the short-range, and long-range orientational order into the quasi-long range order. The new phase with the quasi-long range orientational order is called the hexatic phase. After consequent dissociation of the disclination pairs at some temperature T i the system transforms into the isotropic liquid. Both transitions are continuous, in contrast with the conventional first order three dimensional melting.The unambiguous confirmations of the KTHNY theory have been obtained, for example, from the recent experiments on the colloidal model system with repulsive magnetic di...
Рассмотрено плавление двумерной системы коллапсирующих твердых дисков (система с потенциалом твердых дисков, к которому добавлена отталкивающая ступенька) для различных значений ширины отталкивающей ступеньки. Фазовая диаграмма системы рассчитана методом функционала плотности в теории кристаллизации с использованием уравнений теории Березинского-Костерлица-Таулесса-Хальперина-Нельсона-Янга для определения линии устойчивости по отношению к диссоциации дислокационных пар, которая соответствует непрерывному переходу из твердой в гексатическую фазу. Показано, что кристаллическая фаза может плавиться как посредством непрерывного перехода при низких плотностях (переход в гексатическую фазу), с последующим переходом из гексатической фазы в изотропную жидкость, так и посредством перехода первого рода. С помощью решения уравнений ренормгруппы, учитывающих наличие в системе сингулярных дефектов (дислокаций), рассмотрено влияние перенормировки упругих модулей на вид фазовой диаграммы.
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