vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"vestifm-265Research ArticleФИЗИКАPHYSICSДИНАМИКА ФАЗОВЫХ ПЕРЕХОДОВ 1-ГО РОДА В ФИНСЛЕРОВОМ КОНФИГУРАЦИОННОМ ПРОСТРАНСТВЕ ЛЕНГМЮРОВСКОГО МОНОСЛОЯFIRST-ORDER PHASE TRANSITION DYNAMICS IN THE FINSLER CONFIGURATION SPACE OF THE LANGMUIR MONOLAYERКрыловаН. Г.KrylovaN. G.

научный сотрудник научно-исследовательской лаборатории диэлектрической спектроскопии гетерогенных систем, физический факультет

Researcher of the Laboratory of Dielectric Spectroscopy of Heterogeneous Systems, Physics Facul ty

krylovang@bsu.byГрушевскаяГ. В.GrushevskayaH. V.

кандидат физико-математических наук, ведущий научный сотрудник научно-исследовательской лаборатории диэлектрической спектроскопии гетерогенных систем, физический факультет

Leading Researcher of the Laboratory of Dielectric Spectroscopy of Heterogeneous Systems, Physics Faculty

grushevskaja@bsu.byРедьковВ. М.Red’kovV. M.

доктор физико-математических наук, главный научный сотрудник центра теоретической физики 

D. Sc. (Physics and Mathematics), Chief Researcher of the Center of Theoretical Physics

redkov@dragon.bas-net.byБелорусский государственный университетBelarusian State UniversityИнститут физики им. Б. И. Степанова Национальной академии наук БеларусиB. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus201709102017036677Copyright © Крылова Н.Г., Грушевская Г.В., Редьков В.М., 20172017Крылова Н.Г., Грушевская Г.В., Редьков В.М.Krylova N.G., Grushevskaya H.V., Red’kov V.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/265 

 

В работе получены уравнения Эйлера – Лагранжа, описывающие динамику фазового перехода 1-го рода в конфигурационном финслеровом пространстве ленгмюровского монослоя. Развит приближенный метод анализа полученных уравнений, который основан на сочетании аналитического и численного исследований с использованием нулевого приближения при фиксированном времени релаксации и более точного приближения с модельным распределением времен релаксации. Показана гетерогенность динамики системы, что соответствует метастабильному состоянию монослоя при наличии зародышей фаз с различными временами релаксации. Распределение времен релаксации характеризуется наличием максимума, причем его высота зависит от скорости сжатия монослоя. Рост максимума в распределении времен релаксации при повышении скорости сжатия ассоциируется с появлением выраженного плато на изотерме. На этой основе теоретически обосновано характерное поведение изотерм сжатия монослоя в области фазового перехода. Аналитически исследована динамика двумерного фазового перехода при малых скоростях сжатия и проведен сравнительный анализ поведения системы в двух приближениях: в приближении одного времени релаксации и в приближении модельного распределения времен релаксации. Показано, что существование зародышей фаз с различными временами релаксации приводит к появлению эффективной центробежной силы, величина которой зависит от градиента электрокапиллярных сил.

 

 

 

 

 

 

 

 

In the article, the Euler – Lagrange equations, which describe first-order phase transition dynamics in a con-figuration Finsler space of a Langmuir monolayer, have been obtained. An approximate method for analysis of the equations has been developed. The method is based on a combination of analytical and numerical calculations using the zero-order approximation with a fixed relaxation time and the more exact approximation with a model distribution of relaxation times. Heterogeneous dynamics of the system has been demonstrated. Such dynamics corresponds to the monolayer metastable state with different relaxation times of phase nuclei. The relaxation time distribution has a maximum and a maximum height depends on a monolayer compression rate. The increase of the maximum height at enhancement of a compression rate is accompanied by an explicit plateau of the isotherm that displays the characteristic behavior of the monolayer isotherm in the region of phase transition. The dynamics of a two-dimensional phase transition has been numerically studied at the compression rate as being sufficiently low, and a comparative analysis of the system behavior at two approximations (the approximation of fixed relaxation time and the approximation of model distribution of relaxation times) has been made. It has been found that the presence of phase nuclei with different relaxation times causes an effective centrifugal force, the magnitude of which depends on the gradient of electrocapillary forces.

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The authors declare that there are no conflicts of interest present.