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"10.29235/1561-2430-2018-54-1-84-96vestifm-302Research ArticleФИЗИКАPHYSICSГЕОМЕТРИЧЕСКОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ СЖИМАЕМОСТИ ЛЕНГМЮРОВСКОГО МОНОСЛОЯGEOMETRICAL MODELING OF COMPRESSIBILITY DYNAMICS 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 of the Physics Faculty

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

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

Ph. D. (Physics and Mathematics), Leading Researcher of the Laboratory of Dielectric Spectroscopy of Heterogeneous Systems of the Physics Faculty

grushevskaja@bsu.byБелорусский государственный университет, МинскBelarusian State University, Minsk2018050420185418496Copyright © Крылова Н.Г., Грушевская Г.В., 20182018Крылова Н.Г., Грушевская Г.В.Krylova N.G., Grushevskaya H.V.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/302

Развивается ранее построенная геометрическая модель, описывающая динамику фазового перехода 1-го рода в конфигурационном финслеровом пространстве ленгмюровского монослоя. Изучено поведение вектора Картана и кривизны Бервальда финслерового пространства монослоя. Показано, что кривизна Бервальда существенно изменяется на этапе фазового перехода жидкости в кристаллическое состояние. Установлено соответствие между поведением кривизны Бервальда и динамикой термодинамических параметров монослоя: поверхностного давления и сжимаемости. Найденные теоретические зависимости хорошо согласуются с экспериментальными данными. Получено приближенное аналитическое выражение для сжимаемости как функции кривизны Бервальда при малых скоростях сжатия. Сравнение результатов численного моделирования с экспериментальными изотермами сжатия показывает, что образование зародышей фаз с большими временами релаксации определяет динамику фазового перехода при формировании монослоя с высокими скоростями сжатия.

 

In the article, the previously constructed geometrical model, which describes the first-order phase transition dynamics in the configuration Finsler space of the Langmuir monolayer, is developed. The behavior both of a Cartan vector and a Berwald curvature of the Finsler space is studied. The Berwald curvature is found to change significantly during the first-order phase transition from liquid to crystal. The correspondence between the Berwald curvature behavior and the dynamics of monolayer thermodynamic parameters: surface pressure and compressibility, is established. The agreement between theoretical dependences and experimental data is shown. An approximate analytical expression is found for compressibility, as a function of the Berwald curvature at low compression rates. Comparison of numerical simulation results with the experimental isotherms reveals that the formation of phase nuclei with large relaxation times determines the phase transition dynamics during the monolayer formation with large compression rates.

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