Компьютерное моделирование ионных и неионных обратных мицелл тема диссертации и автореферата по ВАК РФ 02.00.04, кандидат наук Копаничук Илья Владимирович

• Копаничук Илья Владимирович
• кандидат наук
• 2019

Оглавление диссертации кандидат наук Копаничук Илья Владимирович

ОГЛАВЛЕНИЕ

ВВЕДЕНИЕ

ГЛАВА 1. ОБЗОР ЛИТЕРАТУРЫ

1.1. Компьютерное моделирование обратных мицелл ионных ПАВ

1.2. Компьютерное моделирование обратных мицелл неионных и цвиттер-ионных ПАВ

ГЛАВА 2. МОДЕЛИ И МЕТОДЫ

2.1. Основы молекулярной динамики

2.2. Детали моделирования 27 ГЛАВА 3. ВЛИЯНИЕ СОСТАВА СИСТЕМЫ НА ФОРМУ АГРЕГАТОВ В

ОБРАТНЫХ МИКРОЭМУЛЬСИЯХ

3.1. Размер и форма агрегатов в обратных микроэмульсиях АОТ

3.2. Оценка эллиптичности каплеобразных обратных мицелл AOT

3.3. Размер и форма обратных мицелл СПЭН 80/ТВИН 80 45 ГЛАВА 4. РАСПРЕДЕЛЕНИЕ КОМПОНЕНТОВ ВНУТРИ ОБРАТНЫХ

МИЦЕЛЛ

4.1. Внутренняя структура обратных мицелл AOT

4.2. Внутренняя структура обратных мицелл СПЭН 80/ТВИН 80 60 ГЛАВА 5. ВЛИЯНИЕ РАЗМЕРА И СОСТАВА ОБРАТНЫХ МИЦЕЛЛ НА

ИХ ЭЛЕКТРИЧЕСКИЕ СВОЙСТВА

5.1. Локальное электрическое поле в обратных мицеллах AOT

5.2. Средний квадрат дипольного момента обратных мицелл AOT 71 ГЛАВА 6. СОЛЮБИЛИЗАЦИЯ АРОМАТИЧЕСКИХ СОЕДИНЕНИЙ В

ОБРАТНЫХ МИЦЕЛЛАХ AOT И СПЭН

ОСНОВНЫЕ РЕЗУЛЬТАТЫ

ВЫВОДЫ

СПИСОК ЛИТЕРАТУРЫ

Введение диссертации (часть автореферата) на тему «Компьютерное моделирование ионных и неионных обратных мицелл»

ВВЕДЕНИЕ

Обратные микроэмульсии представляют собой оптически прозрачные, термодинамически стабильные смеси воды, неполярного компонента и поверхностно-активных веществ. Структуры агрегатов (обратных мицелл), которые образуются в обратных микроэмульсиях, могут быть различными: сферические или удлиненные капли, черви или биконтинуальные сетки[1]. Обратные мицеллы привлекают внимание исследователей благодаря широкому применению в различных практических целях. Они используются в качестве матрицы для приготовления металлических наночастиц[2], полимерных материалов[3], ультрадисперсных порошков неорганических солей[4], и нанокристаллов лекарственных препаратов[5], доставки лекарств в живые организмы[6] и экстракции белков[7]. Обратные мицеллы находят широкое применение в пищевой, косметической и топливной промышленности[8]. Крайне перспективным представляется использование обратных микроэмульсий в качестве сред для проведения химических реакций между реагентами различной полярности, так как в них значительно увеличена площадь контакта областей, занятых гидрофильными или гидрофобными компонентами. Увеличение контактной поверхности приводит к существенному изменению скорости химической реакции. Проведение реакции в микроэмульсии, кроме изменения скорости реакции, позволяет управлять выходом и механизмом реакции, ее регио- и стереоселективностью[9]. Для успешного проведения катализа важно знать, в какой части системы (ядро мицеллы, поверхность мицеллы, неполярная фаза) концентрируются реагенты. Использование методов компьютерного моделирования, одним из которых является метод молекулярной динамики, позволяет явно установить предпочтительное относительно мицеллы расположение молекул реагентов и влияние на это расположение особенностей строения молекул солюбилизируемых веществ. В синтезе наночастиц, как и в процессе солюбилизации большую роль играет двойной электрический слой, формирующийся на поверхности обратных мицелл. С помощью метода молекулярной динамики можно в явном виде

получить данные об электрическом поле в обратных мицеллах и вкладе флуктуаций заряженных частиц, составляющих мицеллу, в межмицеллярные взаимодействия.

Актуальность работы определяется необходимостью получения данных о недоступных прямому экспериментальному исследованию внутренних областях обратных мицелл, распределении в них компонентов и генерируемых ими электрических полей, а также о влиянии структуры молекулы и типа обратной мицеллы на возможность использования обратных мицелл для катализа органических реакций и управляемого синтеза неорганических наночастиц.

Степень разработанности темы исследования. В первых работах по моделированию обратных мицелл использовали примитивную модель агрегата в виде сферической полости, расположенной в сплошной среде углеводородного растворителя и гидрофобных хвостов молекул поверхностно-активного вещества[10-13]. Были получены данные о структуре ядра, мобильности компонентов, двойном электрическом слое обратной мицеллы и проведена оценка силы межмицеллярных взаимодействий. Ионные обратные мицеллы бис(2-этилгексил)сульфосукцината (АОТ) активно изучались методами компьютерного моделирования. Форма и структура обратных мицелл АОТ были изучены методом молекулярной динамики в рамках примитивного[14], гибридного[15], объединенно-атомного[16] и полноатомного[17] подходов. В работах [18,19] был смоделирован процесс самосборки обратных мицелл АОТ в углеводородах. Активно исследовался процесс солюбилизации пептидов в обратных мицеллах АОТ[20,21]. В настоящее время методами моделирования решаются проблемы, связанные с распределением размеров обратных мицелл АОТ[22] и их поведении при низких температурах[23]. Активно исследуются электрические свойства ионных обратных мицелл[24-26]. Неионные обратные мицеллы СПЭН 80 и ТВИН 80 на момент написания этой работы практически не исследованы методами компьютерного моделирования. Было смоделировано поведение обратных мицелл СПЭН 80 во внешнем электрическом

поле[27], созданы атомистические и грубозернистые модели для исследования прямых мицелл ТВИН 80 [28] и моно- и бислоев СПЭН 80[29].

В диссертационной работе представлены результаты по моделированию обратных мицелл АОТ, СПЭН 80 и ТВИН 80 с добавками различных солей и органических веществ. Целью диссертации являлось установление зависимости внутренней структуры и морфологии агрегатов, образующихся в обратных микроэмульсиях, в том числе ионных и неионных обратных мицелл, от состава системы, расчет численных характеристик электрических свойств (распределения электрического поля и среднего квадрата дипольного момента) ионных обратных мицелл; определение вклада компонентов в различные свойства обратных мицелл и влияния типа обратной мицеллы, структуры и полярности молекулы на результат солюбилизации молекулы в обратной мицелле.

Для достижения поставленной цели было необходимо решить следующие задачи:

1. собрать подходящую модель для описания компонентов обратной микроэмульсии;

2. определить условия моделирования, при которых системы наиболее полно проявляют изучаемые свойства;

3. подобрать вещества, на примере которых можно определить влияние структуры и полярности молекулы на ее способность к солюбилизации в обратных мицеллах;

4. разработать алгоритмы анализа полученных траекторий и расчета средних значений параметров систем.

Научная новизна работы заключается в том, что:

1. впервые созданы модели обратных мицелл неионных ПАВ ТВИН 80 и его смеси со СПЭН 80;

2. установлена внутренняя структура обратных мицелл неионных ПАВ ТВИН 80, СПЭН 80 и их смеси;

3. рассчитаны распределения электрического потенциала и поля в обратных мицеллах АОТ№ и АОТ2Са с добавкой соли и без;

4. выделены вклады воды и ионов в средний квадрат дипольного момента обратных мицелл АОТ;

5. предложена формула, аппроксимирующая зависимость среднего квадрата дипольного момента от размера обратной мицеллы АОТ, показаны преимущества объединенно-атомной модели над примитивной при оценке электрических параметров мицеллы;

6. смоделирован процесс солюбилизации бензола, пиридина и их гидроксильных производных в обратных мицеллах АОТ№ и СПЭН 80, определено их стационарное положение относительно обратной мицеллы в системе.

Практическая значимость работы заключается в том, что полученные данные о свойствах ионных и неионных обратных мицелл важны для использования их в органическом и неорганическом синтезе. Предсказание результата солюбилизации той или иной молекулы в мицелле позволяет более эффективно использовать обратные мицеллы для катализа органических реакций. Средний квадрат дипольного момента мицеллы вносит существенный вклад в межмицеллярные взаимодействия, что важно при синтезе в обратных мицеллах наночастиц.

Положения, выносимые на защиту:

1. Найдены составы систем, в которых методом молекулярной динамики может быть воспроизведен процесс самоагрегации обратных мицелл различной морфологии;

2. Классифицированы типы обратных мицелл, определены связи между соотношением компонентов системы и формой ионных обратных мицелл АОТ№ и неионных обратных мицелл СПЭН 80 и/или ТВИН 80. Разработан улучшенный алгоритм аппроксимации поверхности ионных обратных мицелл.

3. При сравнении радиальных и собственных профилей неионных мицелл СПЭН 80 и/или ТВИН 80, обнаружены существенные различия в относительном распределении веществ только для рыхлых мицелл, содержащих ТВИН 80.

4. На основе локального электрического потенциала в ионных мицеллах показано, что двойной слой обратной мицеллы сосредоточен в ее поверхностном слое и характеризуется высокими значениями интенсивности электрического поля (порядка 108-109 В/м), при которых на практике может наблюдаться ионизация молекул воды. Добавление соли оказывает заметное влияние на интенсивность двойного слоя.

5. Показано, что средний квадрат дипольного момента мицеллы зависит в основном от ее размера и увеличивается с увеличением радиуса как Ла^2.5. И хотя смена противоиона и добавление в систему соли влияет на электрическое поле мицелл, средний квадрат дипольного момента остается практически неизменным.

6. Проведено сравнение сил межмицеллярных взаимодействий с таковыми, рассчитанными в рамках примитивной модели. Показано, что неучет молекулярной структуры воды в электрические свойства обратных мицелл приводит к более, чем двукратной недооценке силы взаимодействия между обратными мицеллами.

7. При сравнении солюбилизации различных органических молекул показано, что самыми важными факторами, позволяющими однозначно предсказать успешную солюбилизацию молекулы, являются как наличие стерически незатрудненной гидроксильной группы в ее структуре, так и ее ионогенность. Полярность молекулы не играет большой роли при солюбилизации в неионных мицеллах, но очевидно более сильное электрическое поле ионной мицеллы заставляет принимать ее во внимание. Наличие гетероатома азота в структуре важно для предсказания положения уже солюбилизированной молекулы в обратной мицелле.

Апробация работы. Результаты работы докладывались на конференциях, перечисленных в таблице 1.

Таблица 1. Конференции, на которых проводилась апробация работы.

Название конференции Статус Время и место проведения Тип доклада

6th International Colloids Conference международная 19-22.06.2016, Берлин стендовый доклад

16th European Students Colloids Conference международная 19-22.06. 2017, Флоренция стендовый доклад

XXI International Conference on Chemical Thermodynamics in Russia (RCCT-2017) международная 26-30.06.2017, Новосибирск устный доклад

10th Liblice Conference on the Statistical Mechanics of Liquids международная 17-22.06.2018, Срни стендовый доклад

Публикации. По материалу диссертации было опубликовано 5 статей в

рецензируемых международных журналах, индексируемых Scopus и Web Of Science:

1. Kopanichuk, I.V., Vanin, A.A., Ostras', A., Brodskaya, E.N. // Computer Simulation of Luminophore Solubilization in Reverse Micelles (2018) Colloid Journal, 80 (3), pp. 266-271. DOI: 10.1134/S1061933X18030067 [30].

2. Kopanichuk, I.V., Vanin, A.A., Brodskaya, E.N. // The Dipole Moment of Reverse Micelles according to Computer Simulation Data (2018) Colloid Journal, 80 (2), pp. 184-188. DOI: 10.1134/S1061933X18020059 [31].

3. Kopanichuk, I.V., Vedenchuk, E.A., Koneva, A.S., Vanin, A.A. // Structural properties of Span 80/Tween 80 reverse micelles by molecular dynamics simulations

(2018) Journal of Physical Chemistry B, 122 (33), pp. 8047-8055. DOI: 10.1021/acs.jpcb.8b03945 [32].

4. Kopanichuk, I.V., Ochkalova, S.D., Vanin, A.A. // The Effect of Hydroxyl Groups on Solubilization of Pyridine Derivatives in Span 80-Water-n-Decane Reverse Micelles (2018) Colloid Journal, 80 (4), pp. 389-393. DOI: 10.1134/S1061933X18040051 [33].

5. Kopanichuk, I.V., Vanin, A.A., Brodskaya, E.N. // The effect of water on the shape of aggregates in water-in-oil microemulsions according to data of computer simulation (2017) Colloid Journal, 79 (3), pp. 328-332. DOI: 10.1134/S1061933X1703005X [34].

Личный вклад автора состоял в активном участии в постановке задач, исследовании, планировании, подготовке и проведении расчетов, а также в анализе, интерпретации и обобщении полученных результатов, подготовке докладов и публикаций.

Работа выполнена в Федеральном Государственном Бюджетном Образовательном Учреждении Высшего Образования «Санкт-Петербургский Государственный Университет» (Институт химии, кафедра физической химии) в соответствии с планом научно-исследовательских работ по теме: «Компьютерное моделирование ионных и неионных обратных мицелл»

ГЛАВА 1. ОБЗОР ЛИТЕРАТУРЫ

Эта глава содержит обзор наиболее важных исследований обратных мицелл, выполненных с помощью моделирования методом молекулярной динамики и имеющих отношение к заявленной цели исследования. Проведение компьютерного моделирования - лучший способ получить информацию о форме обратных мицелл, их внутренней структуре и других свойствах, которые зависят от распределения компонентов внутри обратных мицелл. Кроме того, компьютерное моделирование было использовано для изучения поведения различных соединений, солюбилизированных в обратных мицеллах.

Есть несколько предыдущих обзоров по изучению молекулярного моделирования обращенных мицелл. Самосборка амфифилов в отсутствие воды рассматривается в [35]. Был сделан вывод, что АОТ чаще всего используется для образования обратных мицелл, содержащих неводные полярные органические растворители, а ТХ-100 преобладает в системах, содержащих ионные жидкости комнатной температуры. Другие поверхностно-активные вещества могут обеспечивать эффективное или, возможно, даже более эффективное эмульгирование неводных полярных органических растворителей. Несмотря на то, что АОТ великолепно удается инкапсулировать воду, другие поверхностно-активные вещества могут оказаться более эффективными для инкапсулирования неводных полярных растворителей. Ионные жидкости могут выступать в качестве полярной фазы для создания обратных мицелл и могут демонстрировать интересное альтернативное поведение из-за значительных взаимодействий с поверхностно-активными веществами. Ясное понимание взаимодействия между ионными жидкостями и полярными растворителями с различными поверхностно-активными веществами на молекулярном уровне имеет решающее значение для потенциальных новых применений неводных мицеллярных систем в качестве нанореакторов. Влияние внешнего неполярного растворителя на образование и свойства неводных обратных мицелл не было исследовано в достаточном объеме (на момент написания обзора).

Большинство исследователей не анализировали сходства и различия между системами для изучения влияния внешнего растворителя.

Основные структурные и термодинамические свойства, а также динамика компонентов обратной мицеллы, полученные молекулярным моделированием, рассматриваются в [36]. Был сделан вывод, что полно-атомные модели наиболее эффективны для воспроизведения реальных свойств обратных мицелл в растворах. Показана эффективность метода молекулярной динамики для исследования обратных мицелл. Атомистический молекулярно-динамический подход позволяет определить свойства ядра мицеллы, структуру и форму обратных мицелл, их поверхностные флуктуации и возможные конформации углеводородных хвостов в молекулах ПАВ. Разработка и применение упрощенных моделей важны для расчета электрических и термодинамических свойств мицелл из-за значительного временного фактора при проведении полно-атомного моделирования.

Исследования червеобразных обратно-мицеллярных агрегатов освещены в [37]. Была рассмотрена структура только червеобразных обратных мицелл на основе лецитина в масле, поскольку структура ионных червеобразных обратных мицелл широко не изучалась. Был сделан вывод, что изменений в природе растворителя достаточно для изменения мицеллярной связности и фазового поведения. Разветвленные мицеллы образуют живые сетки, динамика которых в значительной степени определяется быстрой рекомбинацией через образование переходных замыканий. Полностью разветвленные живые сетки разделяются на плотную сетку и разбавленный раствор при добавлении избытка воды.

Наиболее эффективные способы компьютерного моделирования обратных мицелл методом молекулярной динамики, в том числе полно-атомный и упрощенный подходы, рассмотрены в [38-40]. Был сделан вывод о важности роли зарядов и полярной головы ПАВ в процессе самосборки. Общая стабильность прямых и обратных мицелл, как в конденсированной фазе, так и в вакууме, в значительной степени зависит от силы полярных взаимодействий. Результаты изучения обратных

мицелл методом молекулярной динамики следует анализировать с осторожностью: не всякие обратные мицеллы, полученные в результате моделирования, даже существующие бесконечно долго, могут быть соотнесены с реальным химическим экспериментом. Если открытые участки контактов между водой и неполярным растворителем составляют значительную часть поверхности моделируемой мицеллы, доля таких мицелл мала в химическом эксперименте, и такие мицеллы не представляют интереса для тщательного исследования. Моделирование, выполненное с использованием различных исходных расположений молекул (случайным образом распределенных или объединенных в предварительно собранную мицеллу), дает одинаковые мицеллы. Кроме того, результат расчета не зависит от типа используемой модели растворителя. При применении предварительно собранных мицелл, наиболее существенные изменения в мицелле происходят (или могут иметь место) в течение начальных 2 нс; после этого обратимо изменяется только форма мицеллы.

Этот обзор не претендует на то, чтобы содержать все статьи о компьютерном моделировании обратных мицелл, а только самые важные. Эта диссертация посвящена сравнительным исследованиям различных типов поверхностно-активных веществ, которые образуют обратные мицеллы. Следовательно, существует необходимость в классификации предыдущих работ по темам, которые в них рассматривались. Анионные обратные мицеллы, образованные поверхностно-активным веществом АОТ, в настоящее время в основном рассматриваются в исследованиях компьютерного моделирования. Катионные, цвиттер-ионные и неионные обратные мицеллы и обращенные мицеллы, образованные ионными жидкостями, также важны.

1.1. Компьютерное моделирование обратных мицелл ионных ПАВ

Наиболее упрощенный подход моделирования обратной мицеллы основан на представлении мицеллы в виде сферической полости, возникающей в сплошной среде углеводородного растворителя и гидрофобных хвостов молекул поверхностно-активного вещества[10-13]. Представлены данные о структуре ядра мицеллы и

диффузионных характеристиках компонентов. Несмотря на используемые упрощения, полученные результаты полезны для интерпретации данных ЯМР для растворов полиэлектролитов, микроэмульсий и жидких кристаллов. Был также исследован двойной электрический слой обратной мицеллы. Определялись электростатические вклады от взаимодействий частиц, принадлежащих мицелле, с объемным водным раствором поверхностно-активного вещества между соседними агрегатами одинакового размера, числа агрегации и степени ионизации. Изучалось взаимодействие двух похожих мицелл, было показано, что сила взаимодействия двух бесконтактных мицелл уменьшается логарифмически от расстояния между ними. Сила существенно зависит от размеров мицелл, числа и валентности ионов и диэлектрической проницаемости системы.

Первое компьютерное моделирование обратной ионной мицеллы в рамках грубозернистого подхода провели Brown и Clarke в 1988[41]. Одну предварительно собранную обратную мицеллу со слабо оформленным водным ядром помещали в неполярную среду растворителя, затем уравновешивали в течение 120 пс. Для всех молекул, кроме воды был использован грубозернистый подход. Было выбрано катионное поверхностно-активное вещество с нейтральными гидрофобными хвостами, силовые центры которых описывались потенциалом Леннард-Джонса, положительно заряженными головами и подвижными анионами. Использовалась модель воды SPC, а неполярный растворитель был представлен одноцентровой молекулой. Используемая в работе модель слишком проста для представления какого-либо конкретного поверхностно-активного вещества. Интересно, что не было наложено периодических граничных условий, потому что число молекул ПАВ, воды и растворителя в сферической полости континуума растворителя составляло 36, 72 и 1079, соответственно, и не было необходимости в периодических границах для стабилизации системы. Несмотря на примитивность используемой модели, были получены очень важны данные. Средние радиальные плотности для всех компонентов показали их предпочтительное расположение в системе. Среднеквадратичные

смещения растворителя и компонентов обратной мицеллы показали, что подвижность внутри мицеллы очень мала. Форма поверхности обратной мицеллы была описана рядами сферических функций. Этот математический метод хорошо описывал форму обратной мицеллы, но не использовался никакими более поздними исследователями, возможно, из-за его сложности.

В работах [42,43] изучались катионные обратные мицеллы на основе солей аммония. Обратные мицеллы на основе цетилтриметиламмоний бромида и воды в хлороформе рассматривались при температурах около и ниже нуля по Цельсию[42]. Данные молекулярной динамики подтвердили данные ЯМР-спектроскопии о размере агрегатов и дополнили их данными о форме. Несферичность обратных мицелл цетилтриметиламмонийбромида/воды возрастает с увеличением количества воды в ядре. В работе [43] были смоделированы обратные мицеллы на основе цетилтриметиламмоний бромида, гексанола и воды. Размер обратной мицеллы определяли методами малоуглового рассеяния рентгеновских лучей и нейтронов. Обнаружено уменьшение вращательной и поступательной диффузии в направлении от центра мицеллы к поверхности водяного ядра. Интересно, что вместо обычного эксцентриситета была рассчитана несферичность.

Анионные обратные мицеллы, образованные сульфатами и сульфонатами, широко изучены методом молекулярно-динамического моделирования. Компьютерное моделирование анионных обратных мицелл на атомистическом уровне впервые было проведено в работе [44]. Обратные мицеллы содержали ядро из карбоната кальция, стабилизированное фенолятом или сульфонатом, молекулы которого образовывали оболочку вокруг этого ядра. Такие агрегаты отличаются тем, что, в отличие от обратных мицелл на водной основе, они имеют твердую форму, которая очень мало изменяется во времени. Они также относительно устойчивы к изменениям температуры и кислотности среды. Было показано, что структура этих агрегатов и их свойства определяются геометрией содержащихся в них молекул поверхностно-активного вещества, поскольку структурные и динамические различия

между агрегатами, основанными на сульфонате с одним хвостом, и агрегатами, основанными на феноляте с двумя хвостами, были очевидны. В вакууме сульфонатные мицеллы гораздо более сферические, чем основанные на солях фенолов, и их ядро лучше закрыто для внешней среды. В неполярном растворителе это различие несколько сглаживается из-за проникновения растворителя между молекулами поверхностно-активного вещества, но форма обратных мицелл фенолята по-прежнему сильно отличается от сферической. Методом компьютерного моделирования был воспроизведен процесс самосборки обратных мицелл, состоящих из воды и (C7F15)(C7H15)CHSO4Na в сверхкритическом диоксиде углерода[45]. Лучшее понимание процесса должно было помочь решить проблему молекулярного дизайна поверхностно-активных веществ, пригодных для промышленного использования в сверхкритическом CO2. Было обнаружено, что мицеллизация в сверхкритическом СО2 происходит намного быстрее, чем в растворителях, жидких при стандартных условиях. Рассчитаны профили локальной плотности компонентов обратной мицеллы, что позволило сравнить результаты с данными, полученными методами рассеяния.

Poghosyan et al. [46] изучили систему, содержащую обратные мицеллы додецил сульфата натрия в смешанном растворителе толуол/пентанол. Для полноатомного моделирования с использованием силового поля CHARMM27 и размера ячейки 15^15x15 нм3, время моделирования очень короткое и составляет всего 15 нс благодаря использованию предварительно собранных агрегатов. Были изучены эффекты присутствия хлорида полидиаллилдиметиламмония в системе: ионы натрия практически не подвержены его влиянию, что свидетельствует о высокой ионной силе вблизи голов додецил сульфата натрия.

Ионные обратные мицеллы, образованные поверхностно-активным веществом бис(2-этилгексил)сульфосукцинат (АОТ), были смоделированы в многочисленных исследованиях. Форма и структура обратных мицелл АОТ изучались в работе [17] методом полно-атомной молекулярной динамики. Abel et. al. [17] уделили большое

внимание обеспечению согласованности результатов численного и реального эксперимента. Моделировались системы, содержащие мицеллы АОТ/вода в изооктане, состав и размер систем были взяты непосредственно из данных, полученных с использованием методов малоуглового рассеяния рентгеновских лучей и нейтронов. Параметры силового поля для поверхностно-активного вещества и растворителя были взяты из СН^^ММ27, для воды была использована модель Т1Р3Р. Все мицеллы были предварительно собраны, чтобы сэкономить время расчета. Структура обратной мицеллы была тщательно описана с использованием профилей локальной плотности компонентов. Для характеристики формы мицеллы и ее водяного ядра был предложен алгоритм их аппроксимации эллипсоидом, равным по массе и компонентам тензора инерции. Было показано, что форма обратных мицелл АОТ и их ядер далека от сферической (эксцентриситет порядка 0.6-0.7 для мицелл и 0.8 для их ядер), и менее 1% воды на поверхности ядра вступает в контакт с неполярным растворителем. Систематическое исследование размера РМ было выполнено с помощью молекулярно-динамического моделирования с целью определения размера обратных мицелл для заданного водного числа и согласования результатов с экспериментальными измерениями[22]. Результаты для водного числа, равного 7,5, показывают, что энергия взаимодействия между анионами АОТ и другими компонентами системы минимальна, когда в каждой обратной мицелле находится 62 аниона АОТ-. Работа [47] также посвящена детальному рассмотрению обратных мицелл АОТ/вода в изооктане. Молекулы ПАВ были представлены гибридным силовым полем ТгаРРе/СНАКММ. В дополнение к обычным профилям локальной плотности относительно центра масс были рассчитаны собственные профили плотности. Поверхность обратной мицеллы определялась расположением атомов серы. Были получены парные функции распределения между атомами натрия, водорода, серы и кислорода, распределение углов между различными векторами, связывающими атомы с положительными и отрицательными эффективными зарядами, и распределение водородных связей в воде.

Список литературы диссертационного исследования кандидат наук Копаничук Илья Владимирович, 2019 год

СПИСОК ИСПОЛЬЗОВАННОЙ ЛИТЕРАТУРЫ

[1] K. Krauel, L. Girvan, S. Hook, T. Rades, Characterisation of colloidal drug delivery systems from the naked eye to Cryo-FESEM, Micron. 38 (2007) 796-803. doi: 10.1016/j.micron.2007.06.008.

[2] L. Podhorska, D. Delcassian, A.E. Goode, M. Agyei, D.W. McComb, M.P. Ryan, I.E. Dunlop, Mechanisms of Polymer-Templated Nanoparticle Synthesis: Contrasting ZnS and Au, Langmuir. 32 (2016) 9216-9222. doi:10.1021/acs.langmuir.6b01900.

[3] V.S.S. Gon?alves, P. Gurikov, J. Poejo, A.A. Matias, S. Heinrich, C.M.M. Duarte, I. Smirnova, Alginate-based hybrid aerogel microparticles for mucosal drug delivery, Eur. J. Pharm. Biopharm. 107 (2016) 160-170. doi:10.1016/j.ejpb.2016.07.003.

[4] A.I. Bulavchenko, M.G. Demidova, D.I. Beketova, Preparation of Ultradispersed KNO 3 Powders in Mixed Reverse Micelles of Tergitol NP-4 + AOT by Isothermal Evaporation Crystallization, Cryst. Growth Des. 13 (2013) 485-490. doi: 10.1021/cg300721q.

[5] S. Rozner, I. Popov, V. Uvarov, A. Aserin, N. Garti, Templated cocrystallization of cholesterol and phytosterols from microemulsions, J. Cryst. Growth. 311 (2009) 40224033. doi:10.1016/j.jcrysgro.2009.06.027.

[6] M.D. Chatzidaki, K.D. Papavasileiou, M.G. Papadopoulos, A. Xenakis, Reverse Micelles As Antioxidant Carriers: An Experimental and Molecular Dynamics Study, Langmuir. 33 (2017) 5077-5085. doi:10.1021/acs.langmuir.7b00213.

[7] M. Vasudevan, J.M. Wiencek, Mechanism of the Extraction of Proteins into Tween 85 Nonionic Microemulsions, Ind. Eng. Chem. Res. 35 (1996) 1085-1089. doi: 10.1021/ie950328e.

[8] B.-J. Lin, W.-H. Chen, W.M. Budzianowski, C.-T. Hsieh, P.-H. Lin, Emulsification analysis of bio-oil and diesel under various combinations of emulsifiers, Appl. Energy.

178 (2016) 746-757. doi:10.1016/j.apenergy.2016.06.104.

[9] S. Ta§cioglu, Micellar solutions as reaction media, Tetrahedron. 52 (1996) 1111311152. doi: 10.1016/0040-4020(96)00669-2.

[10] P. Linse, B. Halle, Counterion N.M.R. in heterogeneous aqueous systems, Mol. Phys. 67 (1989) 537-573. doi:10.1080/00268978900101281.

[11] A. Luzar, D. Bratko, Electric double layer interactions in reverse micellar systems: A Monte Carlo simulation study, J. Chem. Phys. 92 (1990) 642-648. doi: 10.1063/1.458415.

[12] D. Bratko, A. Luzar, S.H. Chen, Electrostatic model for protein/reverse micelle complexation, J. Chem. Phys. 89 (1988) 545-550. doi:10.1063/1.455443.

[13] D. Bratko, C.E. Woodward, A. Luzar, Charge fluctuation in reverse micelles, J. Chem. Phys. 95 (1991) 5318-5326. doi:10.1063/1.461671.

[14] J. Faeder, B.M. Ladanyi, Molecular Dynamics Simulations of the Interior of Aqueous Reverse Micelles, J. Phys. Chem. B. 104 (2000) 1033-1046. doi:10.1021/jp993076u.

[15] G. V Mudzhikova, E.N. Brodskaya, Molecular simulation of an Aerosol OT reverse micelle: 1. The shape and structure of a micelle, Colloid J. 68 (2006) 729-737. doi: 10.1134/s1061933x06060093.

[16] M. Freda, G. Penna, V. Minicozzi, S. Morante, G. Salina, Molecular dynamics and hybrid Monte Carlo simulations of a sodium bis(2-ethylhexyl)-sulfosuccinate reverse micelle, in: V. Buckin (Ed.), Trends Colloid Interface Sci. XIV, Springer Berlin Heidelberg, Berlin, Heidelberg, 2000: pp. 20-24. doi:10.1007/3-540-46545-6_5.

[17] S. Abel, F. Sterpone, S. Bandyopadhyay, M. Marchi, Molecular Modeling and Simulations of AOT-Water Reverse Micelles in Isooctane: Structural and Dynamic Properties, J. Phys. Chem. B. 108 (2004) 19458-19466. doi:10.1021/jp047138e.

[18] M. Marchi, S. Abel, Modeling the Self-Aggregation of Small AOT Reverse Micelles from First-Principles, J. Phys. Chem. Lett. 6 (2015) 170-174. doi:10.1021/jz5023619.

[19] A. V Nevidimov, V.F. Razumov, Molecular dynamics simulations of AOT reverse micelles' self-assembly, Mol. Phys. 107 (2009) 2169-2180. doi: 10.1080/00268970903203736.

[20] J. Tian, A.E. Garcia, An Alpha-Helical Peptide in AOT Micelles Prefers to be Localized at the Water/Headgroup Interface, Biophys. J. 96 (2009) L57-L59. doi: 10.1016/j.bpj.2009.03.014.

[21] S. Abel, M. Waks, W. Urbach, M. Marchi, Structure, Stability, and Hydration of a Polypeptide in AOT Reverse Micelles, J. Am. Chem. Soc. 128 (2006) 382-383. doi: 10.1021/ja053043u.

[22] G. Eskici, P.H. Axelsen, The Size of AOT Reverse Micelles, J. Phys. Chem. B. 120 (2016) 11337-11347. doi:10.1021/acs.jpcb.6b06420.

[23] G. Neganova, E.N. Brodskaya, Computer simulation of the AOT reverse micelle at freezing temperature, Colloids Surfaces A Physicochem. Eng. Asp. 510 (2016) 122128. doi:10.1016/j.colsurfa.2016.07.061.

[24] M. Senske, Y. Xu, A. Bäumer, S. Schäfer, H. Wirtz, J. Savolainen, H. Weingärtner, M. Havenith, Local chemistry of the surfactant's head groups determines protein stability in reverse micelles, Phys. Chem. Chem. Phys. 20 (2018) 8515-8522. doi: 10.1039/c8cp00407b.

[25] V.R. Hande, S. Chakrabarty, Exploration of the presence of bulk-like water in AOT reverse micelles and water-in-oil nanodroplets: the role of charged interfaces, confinement size and properties of water, Phys. Chem. Chem. Phys. 18 (2016) 2176721779. doi: 10.1039/C6CP04378J.

[26] M. Schmollngruber, D. Braun, D. Oser, O. Steinhauser, Dielectric depolarisation and

concerted collective dynamics in AOT reverse micelles with and without ubiquitin, Phys. Chem. Chem. Phys. 18 (2016) 3606-3617. doi:10.1039/C5CP07112G.

[27] M. Mannoor, S. Kang, Y.K. Suh, Molecular Dynamics Simulation of Aggregates in the Dodecane / span80 System and Their Behaviour in an Electric Field, Adv. Condens. Matter Phys. 2015 (2015) 1-19.

[28] A. Amani, P. York, H. de Waard, J. Anwar, Molecular dynamics simulation of a polysorbate 80 micelle in water, Soft Matter. 7 (2011) 2900-2908. doi: 10.1039/c0sm00965b.

[29] S. Han, Molecular Dynamics Simulation of Sorbitan Monooleate Bilayers, Bull. Korean Chem. Soc. 34 (2013) 946-948. doi:10.5012/bkcs.2013.34.3.946.

[30] I. V. Kopanichuk, A.A. Vanin, A. Ostras', E.N. Brodskaya, Computer Simulation of Luminophore Solubilization in Reverse Micelles, Colloid J. 80 (2018) 266-271. doi: 10.1134/S1061933X18030067.

[31] I. V. Kopanichuk, A.A. Vanin, E.N. Brodskaya, The Dipole Moment of Reverse Micelles according to Computer Simulation Data, Colloid J. 80 (2018) 184-188. doi: 10.1134/S1061933X18020059.

[32] I. V. Kopanichuk, E.A. Vedenchuk, A.S. Koneva, A.A. Vanin, Structural properties of span 80/tween 80 reverse micelles by molecular dynamics simulations, J. Phys. Chem. B. 122 (2018) 8047-8055. doi:10.1021/acs.jpcb.8b03945.

[33] I. V. Kopanichuk, S.D. Ochkalova, A.A. Vanin, The Effect of Hydroxyl Groups on Solubilization of Pyridine Derivatives in Span 80-Water-n-Decane Reverse Micelles, Colloid J. 80 (2018) 389-393. doi:10.1134/S1061933X18040051.

[34] I. V. Kopanichuk, A.A. Vanin, E.N. Brodskaya, The effect of water on the shape of aggregates in water-in-oil microemulsions according to data of computer simulation, Colloid J. 79 (2017) 328-332. doi:10.1134/S1061933X1703005X.

[35] N.M. Correa, J.J. Silber, R.E. Riter, N.E. Levinger, Nonaqueous Polar Solvents in Reverse Micelle Systems, Chem. Rev. 112 (2012) 4569-4602. doi: 10.1021/cr200254q.

[36] G. V. Mudzhikova, E.N. Brodskaya, Computer simulation of reverse micelles and water-in-oil microemulsions, Colloid J. 74 (2012) 269-279. doi: 10.1134/s1061933x1203009x.

[37] G. Palazzo, Wormlike reverse micelles, Soft Matter. 9 (2013) 10668. doi: 10.1039/c3sm52193a.

[38] A. V Nevidimov, V.F. Razumov, Molecular dynamics simulation of reverse micelles: A search for the most efficient strategy, Colloid J. 75 (2013) 191-197. doi: 10.1134/S1061933X13010080.

[39] A. V Nevidimov, Molecular dynamics simulation of reverse micelles: Standing problems after 25 years of research, Russ. J. Phys. Chem. B. 8 (2014) 554-558. doi: 10.1134/S199079311404023X.

[40] S. Indelicato, D. Bongiorno, V. Calabrese, U. Perricone, A.M. Almerico, L. Ceraulo, D. Piazzese, M. Tutone, Micelles, Rods, Liposomes, and Other Supramolecular Surfactant Aggregates: Computational Approaches, Interdiscip. Sci. Comput. Life Sci. 9 (2017) 392-405. doi:10.1007/s12539-017-0234-7.

[41] D. Brown, J.H.R. Clarke, Molecular dynamics simulation of a model reverse micelle, J. Phys. Chem. 92 (1988) 2881-2888. doi:10.1021/j100321a036.

[42] L. Klicova, E. Muchova, P. Sebej, P. Slavicek, P. Klan, Nature of CTAB/Water/Chloroform Reverse Micelles at Above- and Subzero Temperatures Studied by NMR and Molecular Dynamics Simulations, Langmuir. 31 (2015) 82848293. doi:10.1021/acs.langmuir.5b01776.

[43] B. Fuglestad, K. Gupta, A.J. Wand, K.A. Sharp, Characterization of

Cetyltrimethylammonium Bromide/Hexanol Reverse Micelles by Experimentally Benchmarked Molecular Dynamics Simulations, Langmuir. 32 (2016) 1674-1684. doi:10.1021/acs.langmuir.5b03981.

[44] J.A. Griffiths, D.M. Heyes, Atomistic Simulation of Overbased Detergent Inverse Micelles, Langmuir. 12 (1996) 2418-2424. doi:10.1021/la950816r.

[45] S. Salaniwal, S. Cui, H.D. Cochran, P.T. Cummings, Molecular Dynamics Simulation of Reverse Micelles in Supercritical Carbon Dioxide, Ind. Eng. Chem. Res. 39 (2000) 4543-4554. doi:10.1021/ie000144m.

[46] A.H. Poghosyan, L.H. Arsenyan, H.H. Gharabekyan, S. Falkenhagen, J. Koetz, A.A. Shahinyan, Molecular dynamics simulations of inverse sodium dodecyl sulfate (SDS) micelles in a mixed toluene/pentanol solvent in the absence and presence of poly(diallyldimethylammonium chloride) (PDADMAC), J. Colloid Interface Sci. 358 (2011) 175-181. doi: 10.1016/j.jcis.2011.01.091.

[47] J. Chowdhary, B.M. Ladanyi, Molecular Dynamics Simulation of Aerosol-OT Reverse Micelles, J. Phys. Chem. B. 113 (2009) 15029-15039. doi:10.1021/jp906915q.

[48] G. V Mudzhikova, E.N. Brodskaya, Molecular simulation of an aerosol OT reverse micelle: 2. Energy and kinetic characteristics, Colloid J. 68 (2006) 738-742. doi: 10.1134/S1061933X0606010X.

[49] G. V Mudzhikova, E.N. Brodskaya, Study of mechanism of micellization in nonpolar media, Colloid J. 73 (2011) 676-682. doi:10.1134/S1061933X11050097.

[50] G. V. Mudzhikova, E.N. Brodskaya, Molecular dynamics simulation of surfactant microaggregates in the apolar medium of n-octane, Colloid J. 67 (2005) 451-458. doi: 10.1007/s10595-005-0118-0.

[51] G. V Mudzhikova, E.N. Brodskaya, An AOT reverse micelle in a medium of supercritical carbon dioxide, Colloid J. 77 (2015) 306-311.

doi: 10.1134/S1061933X15030126.

[52] G. Longhi, S. Abbate, L. Ceraulo, A. Ceselli, S.L. Fornili, V. Turco Liveri, A molecular dynamics study of structure, stability and fragmentation patterns of sodium bis(2-ethylhexyl)sulfosuccinate positively charged aggregates in vacuo, Phys. Chem. Chem. Phys. 13 (2011) 21423. doi:10.1039/c1cp21740b.

[53] G. Longhi, S. Abbate, A. Ceselli, L. Ceraulo, S.L. Fornili, V. Turco Liveri, Structure, Stability, and Fragmentation of Sodium bis(2-ethylhexyl)Sulfosuccinate Negatively Charged Aggregates In Vacuo by MD Simulations, J. Am. Soc. Mass Spectrom. 25 (2014) 1642-1649. doi:10.1007/s13361-014-0942-8.

[54] G. Longhi, A. Ceselli, S.L. Fornili, S. Abbate, L. Ceraulo, V.T. Liveri, Molecular dynamics of electrosprayed water nanodroplets containing sodium bis(2-ethylhexyl)sulfosuccinate, J. Mass Spectrom. 48 (2013) 478-486. doi: 10.1002/jms.3179.

[55] G. Longhi, S.L. Fornili, V. Turco Liveri, Structural organization of surfactant aggregates in vacuo: a molecular dynamics and well-tempered metadynamics study, Phys. Chem. Chem. Phys. 17 (2015) 16512-16518. doi:10.1039/C5CP01926E.

[56] G. Longhi, S.L. Fornili, V.T. Liveri, S. Abbate, D. Rebeccani, L. Ceraulo, F. Gangemi, Sodium bis(2-ethylhexyl)sulfosuccinate self-aggregation in vacuo: molecular dynamics simulation, Phys. Chem. Chem. Phys. 12 (2010) 4694. doi: 10.1039/b924146a.

[57] J. Faeder, B.M. Ladanyi, Solvation Dynamics in Aqueous Reverse Micelles: A Computer Simulation Study, J. Phys. Chem. B. 105 (2001) 11148-11158. doi: 10.1021/jp010632n.

[58] J. Faeder, M. V Albert, B.M. Ladanyi, Molecular Dynamics Simulations of the Interior of Aqueous Reverse Micelles: A Comparison between Sodium and Potassium

Counterions, Langmuir. 19 (2003) 2514-2520. doi:10.1021/la026755w.

[59] J. Faeder, B.M. Ladanyi, Solvation Dynamics in Reverse Micelles: The Role of Headgroup-Solute Interactions, J. Phys. Chem. B. 109 (2005) 6732-6740. doi: 10.1021/jp045202m.

[60] M.R. Harpham, B.M. Ladanyi, N.E. Levinger, The Effect of the Counterion on Water Mobility in Reverse Micelles Studied by Molecular Dynamics Simulations, J. Phys. Chem. B. 109 (2005) 16891-16900. doi: 10.1021/jp052773l.

[61] M.R. Harpham, B.M. Ladanyi, N.E. Levinger, K.W. Herwig, Water motion in reverse micelles studied by quasielastic neutron scattering and molecular dynamics simulations, J. Chem. Phys. 121 (2004) 7855. doi:10.1063/1.1792592.

[62] M.H. Alaimo, T.F. Kumosinski, Investigation of Hydrophobic Interactions in Colloidal and Biological Systems by Molecular Dynamics Simulations and NMR Spectroscopy, Langmuir. 13 (1997) 2007-2018. doi:10.1021/la961070f.

[63] A. Gardner, V.R. Vasquez, A. Clifton, O.A. Graeve, Molecular dynamics analysis of the AOT/water/isooctane system: Effect of simulation time, initial configuration, and model salts, Fluid Phase Equilib. 262 (2007) 264-270. doi: 10.1016/j.fluid.2007.09.013.

[64] V.R. Vasquez, B.C. Williams, O.A. Graeve, Stability and Comparative Analysis of AOT/Water/Isooctane Reverse Micelle System Using Dynamic Light Scattering and Molecular Dynamics, J. Phys. Chem. B. 115 (2011) 2979-2987. doi: 10.1021/jp109202f.

[65] M.H.H. Pomata, D. Laria, M.S. Skaf, M.D. Elola, Molecular dynamics simulations of AOT-water/formamide reverse micelles: Structural and dynamical properties, J. Chem. Phys. 129 (2008) 244503. doi:10.1063/1.3042275.

[66] W. Shi, L. Hong, K. Damodaran, H.B. Nulwala, D.R. Luebke, Molecular Simulation

and Experimental Study of CO 2 Absorption in Ionic Liquid Reverse Micelle, J. Phys. Chem. B. 118 (2014) 13870-13881. doi:10.1021/jp509282h.

[67] F.M. Agazzi, R.D. Falcone, J.J. Silber, N.M. Correa, Non-aqueous reverse micelles created with a cationic surfactant: Encapsulating ethylene glycol in BHDC/non-polar solvent blends, Colloids Surfaces A Physicochem. Eng. Asp. 509 (2016) 467-473. doi: 10.1016/j.colsurfa.2016.09.070.

[68] S. Palchowdhury, B.L. Bhargava, Glycine molecules in ionic liquid based reverse micelles: Investigation of structure and dynamics using molecular dynamics simulations, J. Mol. Liq. 230 (2017) 384-394. doi:10.1016/j.molliq.2017.01.034.

[69] T.H. Ibrahim, R.D. Neuman, Nanostructure of Open Water-Channel Reversed Micelles. I. 1 H NMR Spectroscopy and Molecular Modeling, Langmuir. 20 (2004) 3114-3122. doi: 10.1021/la036422e.

[70] L.Y. Lu, M.L. Berkowitz, Molecular dynamics simulation of a reverse micelle self assembly in supercritical CO2, J. Am. Chem. Soc. 126 (2004) 10254-10255. doi: 10.1021/ja048670i.

[71] S. Senapati, J.S. Keiper, J.M. DeSimone, G.D. Wignall, Y.B. Melnichenko, H. Frielinghaus, M.L. Berkowitz, Structure of Phosphate Fluorosurfactant Based Reverse Micelles in Supercritical Carbon Dioxide, Langmuir. 18 (2002) 7371-7376. doi: 10.1021/la025952s.

[72] S. Senapati, M.L. Berkowitz, Computer simulation studies of water states in perfluoro polyether reverse micelles: Effects of changing the counterion, J. Phys. Chem. A. 108 (2004) 9768-9776. doi:10.1021/jp048954p.

[73] A.V. Martinez, E. Malolepsza, L. Domínguez, Q. Lu, J.E. Straub, Role of Charge and Solvation in the Structure and Dynamics of Alanine-Rich Peptide AKA 2 in AOT Reverse Micelles, J. Phys. Chem. B. 119 (2015) 9084-9090. doi:10.1021/jp508813n.

[74] A.V. Martinez, E. Malolepsza, E. Rivera, Q. Lu, J.E. Straub, Exploring the role of hydration and confinement in the aggregation of amyloidogenic peptides Ap 16-22 and Sup35 7-13 in AOT reverse micelles, J. Chem. Phys. 141 (2014) 22D530. doi: 10.1063/1.4902550.

[75] S. Abel, M. Waks, M. Marchi, Molecular dynamics simulations of cytochrome c unfolding in AOT reverse micelles: The first steps, Eur. Phys. J. E. 32 (2010) 399409. doi: 10.1140/epje/i2010-10635-x.

[76] B. Qiao, T. Demars, M. Olvera De La Cruz, R.J. Ellis, How Hydrogen Bonds Affect the Growth of Reverse Micelles around Coordinating Metal Ions, J. Phys. Chem. Lett. 5 (2014) 1440-1444. doi:10.1021/jz500495p.

[77] D.E. Rosenfeld, C.A. Schmuttenmaer, Dynamics of the Water Hydrogen Bond Network at Ionic, Nonionic, and Hydrophobic Interfaces in Nanopores and Reverse Micelles, J. Phys. Chem. B. 115 (2011) 1021-1031. doi:10.1021/jp109599q.

[78] J. Tian, A.E. Garcia, Simulations of the confinement of ubiquitin in self-assembled reverse micelles, J. Chem. Phys. 134 (2011) 225101. doi:10.1063/1.3592712.

[79] A.V. Martinez, S.C. DeSensi, L. Dominguez, E. Rivera, J.E. Straub, Protein folding in a reverse micelle environment: The role of confinement and dehydration, J. Chem. Phys. 134 (2011) 055107. doi:10.1063/1.3545982.

[80] B. Smit, P.A.J. Hilbers, K. Esselink, L.A.M. Rupert, N.M. Van Os, A.G. Schlijper, Structure of a water/oil interface in the presence of micelles: a computer simulation study, J. Phys. Chem. 95 (1991) 6361-6368. doi:10.1021/j100169a052.

[81] R. Allen, S. Bandyopadhyay, M.L. Klein, C12E2 reverse micelle: A molecular dynamics study, Langmuir. 16 (2000) 10547-10552. doi:Doi 10.1021/La001182d.

[82] S. Abel, M. Waks, M. Marchi, W. Urbach, Effect of Surfactant Conformation on the Structures of Small Size Nonionic Reverse Micelles: A Molecular Dynamics

Simulation Study, Langmuir. 22 (2006) 9112-9120. doi:10.1021/la060978v.

[83] J. Rodriguez, J. Martí, E. Guàrdia, D. Laria, Protons in Non-ionic Aqueous Reverse Micelles, J. Phys. Chem. B. 111 (2007) 4432-4439. doi:10.1021/jp0703410.

[84] W. Yu, Y. Liu, J. Yin, Separation of 1,3-propanediol using supercritical CO2microemulsion with non-ionic surfactant Ls-54: Experiment and simulation, Chem. Eng. J. 273 (2015) 197-204. doi:10.1016/j.cej.2015.03.082.

[85] S. Vierros, M. Sammalkorpi, Phosphatidylcholine reverse micelles on the wrong track in molecular dynamics simulations of phospholipids in an organic solvent, J. Chem. Phys. 142 (2015) 094902. doi:10.1063/1.4914022.

[86] S. Vierros, M. Sammalkorpi, Role of hydration in phosphatidylcholine reverse micelle structure and gelation in cyclohexane: A molecular dynamics study, Phys. Chem. Chem. Phys. 17 (2015) 14951-14960. doi:10.1039/c5cp01799h.

[87] S. Abel, N. Galamba, E. Karakas, M. Marchi, W.H. Thompson, D. Laage, On the Structural and Dynamical Properties of DOPC Reverse Micelles, Langmuir. 32 (2016) 10610-10620. doi:10.1021/acs.langmuir.6b02566.

[88] Allen M.P., Tildesley D.J., Computer simulation of liquids, Clarendon Press, 1987.

[89] D. Frenkel, B. Smit, Understanding molecular simulation: From algorithms to applications., Academic Press, 2001.

[90] C. Oostenbrink, A. Villa, A.E. Mark, W.F. Van Gunsteren, A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS force-field parameter sets 53A5 and 53A6, J. Comput. Chem. 25 (2004) 1656-1676. doi: 10.1002/jcc.20090.

[91] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, J. Hermans, Intermolecular Forces, Reidel, Dordrecht, The Netherlands, 1981.

[92] A. Ritwiset, S. Krongsuk, J. Johns, Molecular structure and stability of the sorbitan monostearate (Span60) monolayers film at the water-air interface: A molecular dynamics simulation study, J. Mol. Liq. 195 (2014) 157-164. doi: 10.1016/j.molliq.2014.02.032.

[93] M.J. Abraham, T. Murtola, R. Schulz, S. Pall, J.C. Smith, B. Hess, E. Lindah, E. Lindahl, GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers, SoftwareX. 1-2 (2015) 19-25. doi: 10.1016/j.softx.2015.06.001.

[94] U. Essmann, L. Perera, M.L. Berkowitz, T. Darden, H. Lee, L.G. Pedersen, A smooth particle mesh Ewald method, J. Chem. Phys. 103 (1995) 8577-8593. doi: 10.1063/1.470117.

[95] W. Humphrey, A. Dalke, K. Schulten, VMD: Visual molecular dynamics, J. Mol. Graph. 14 (1996) 33-38. doi:10.1016/0263-7855(96)00018-5.

[96] M. Münz, P.C. Biggin, JGromacs: A Java Package for Analyzing Protein Simulations, J. Chem. Inf. Model. 52 (2012) 255-259. doi:10.1021/ci200289s.

[97] L. Bai, D. Breen, Calculating Center of Mass in an Unbounded 2D Environment, J. Graph. Tools. 13 (2008) 53-60. doi:10.1080/2151237X.2008.10129266.

[98] J.J. Morales, M.J. Nuevo, L.F. Rull, Statistical error methods in computer simulations, J. Comput. Phys. 89 (1990) 432-438. doi:10.1016/0021-9991(90)90151-P.

[99] B. Tamamushi, N. Watanabe, The formation of molecular aggregation structures in ternary system: Aerosol OT/water/iso-octane, Colloid Polym. Sci. 258 (1980) 174178. doi:10.1007/BF01498277.

[100] C.A. Bearchell, D.M. Heyes, Mesoscale modelling studies of microemulsions, Phys. Chem. Chem. Phys. 3 (2001) 5255-5265. doi:10.1039/b105096f.

[101] S.-L. Yuan, Z.-T. Cai, G.-Y. Xu, Y.-S. Jiang, Mesoscopic simulation study on phase diagram of the system oil/water/aerosol OT, Chem. Phys. Lett. 365 (2002) 347-353. doi: 10.1016/S0009-2614(02)01494-X.

[102] G.N. Smith, P. Brown, C. James, S.E. Rogers, J. Eastoe, The effect of solvent and counterion variation on inverse micelle CMCs in hydrocarbon solvents, Colloids Surfaces A Physicochem. Eng. Asp. 494 (2016) 194-200. doi: 10.1016/j.colsurfa.2016.01.020.

[103] H.-F. Eicke, J. Rehak, On the Formation of Water/Oil-Microemulsions, Helv. Chim. Acta. 59 (1976) 2883-2891. doi:10.1002/hlca.19760590825.

[104] A. Maitra, Determination of size parameters of water-Aerosol OT-oil reverse micelles from their nuclear magnetic resonance data, J. Phys. Chem. 88 (1984) 5122-5125. doi: 10.1021/j150665a064.

[105] N.T. Southall, K.A. Dill, A.D.J. Haymet, A View of the Hydrophobic Effect, J. Phys. Chem. B. 106 (2002) 521-533. doi:10.1021/jp015514e.

[106] A.S. Koneva, E.A. Safonova, P.S. Kondrakhina, M.A. Vovk, A.A. Lezov, Y.S. Chernyshev, N.A. Smirnova, Effect of water content on structural and phase behavior of water-in-oil (n-decane) microemulsion system stabilized by mixed nonionic surfactants SPAN 80/TWEEN 80, Colloids Surfaces A Physicochem. Eng. Asp. 518 (2017) 273-282. doi:10.1016/j.colsurfa.2017.01.020.

[107] G. V. Mudzhikova, E.N. Brodskaya, Effect of counterions on the structure of reverse micelles according to the data of molecular-dynamic simulation, Colloid J. 71 (2009) 803-809. doi: 10.1134/S1061933X0906009X.

[108] D.T. Allen, C.D. Lorenz, A novel method for constructing continuous intrinsic surfaces of nanoparticles, J. Mol. Model. 23 (2017) 219. doi:10.1007/s00894-017-3378-9.

[109] V. V. Zakharov, E.N. Brodskaya, A. Laaksonen, Surface tension of water droplets: A

molecular dynamics study of model and size dependencies, J. Chem. Phys. 107 (1997) 10675-10683. doi:10.1063/1.474184.

[110] E.N. Brodskaya, V. V. Zakharov, Computer simulation study of the surface polarization of pure polar liquids, J. Chem. Phys. 102 (1995) 4595-4599. doi: 10.1063/1.469507.

[111] Р.Н. Вадзинский, Справочник по вероятностным распределениям, Наука, Санкт-Петербург, 2001.

[112] R.A. Fisher, Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population, Biometrika. 10 (1915) 507. doi:10.2307/2331838.

[113] T. Pham-Gia, V. Choulakian, Distribution of the Sample Correlation Matrix and Applications, Open J. Stat. 04 (2014) 330-344. doi:10.4236/ojs.2014.45033.

[114] Y.-J. Sheng, H.-K. Tsao, Ion Fluctuations within an Aqueous Microdroplet in an Apolar Medium, Phys. Rev. Lett. 87 (2001) 185501. doi: 10.1103/PhysRevLett.87.185501.

St. Petersburg State University

Manuscript copy

KOPANICHUK Ilia Vladimirovich Computer simulations of ionic and nonionic reverse micelles

Qualification: 02.00.04 - Physical chemistry

This thesis is submitted in conformity with the requirements for the candidate degree in

chemistry

Academic supervisor:

Prof., Dr.

Brodskaya Elena Nikolaevna

St. Petersburg 2019

111

CONTENTS

INTRODUCTION 112

CHAPTER 1. LITERATURE REVIEW 119

1.1. Computer simulations of reverse micelles of ionic surfactants 121

1.2. Computer simulations of reverse micelles of nonionic and zwitter-ionic surfactants 130

CHAPTER 2. MODELS AND METHODS 133

2.1. Basics of molecular dynamics 133

2.2. Details of simulations 134 CHAPTER 3. THE EFFECT OF THE COMPOSITION OF THE SYSTEM ON

THE SHAPE OF AGGREGATES IN REVERSE MICROEMULSIONS 136

3.1. The size and shape of aggregates in AOT reverse microemulsions 137

3.2. The evaluation of ellipticity of dropletlike AOT reverse micelles 145

3.3. The size and shape of Span 80/Tween 80 reverse micelles 151 CHAPTER 4. THE DISTRIBUTION OF COMPONENTS INSIDE THE

REVERSE MICELLE 158

4.1. The internal structure of AOT reverse micelles 158

4.2. The internal structure of Span 80/Tween 80 reverse micelles 166 CHAPTER 5. THE EFFECT OF THE SIZE AND THE COMPOSITION OF

REVERSE MICELLES ON THEIR ELECTRICAL PROPERTIES 170

5.1. The local electric field inside AOT reverse micelles 170

5.2. The mean square dipole moment of AOT reverse micelles 177 CHAPTER 6. THE SOLUBILIZATION OF AROMATIC SUBSTANCES IN

AOT AND SPAN 80 REVERSE MICELLES 186

MAIN RESULTS

CONCLUSIONS

REFERENCES

198 200 202

112

INTRODUCTION

Reverse microemulsions are optically transparent, thermodynamically sable mixtures of water, non-polar component and surfactants. The structures of the aggregates (reverse micelles), which are formed in reverse microemulsions, can be of different kind: spherical or elongated droplets, worms, or bicontinual networks[1]. Reverse micelles attract the attention of researchers due to their widespread application for various practical purposes. They are used as a matrix for the preparation of metallic nanoparticles[2], polymeric materials[3], ultrafine powders of inorganic salts[4], and nanocrystals of drugs[5], drug delivery to living organisms[6], and protein extraction[7]. Reverse micelles are widely used in food, cosmetic and fuel industries[8]. The use of reverse microemulsions as a medium for chemical reactions between reagents of different polarity seems extremely promising, since they significantly increase the contact area between hydrophilic or hydrophobic components. An increase in the contact surface leads to a significant change in the rate of a chemical reaction. Performing the reaction in a microemulsion, in addition to changing the reaction rate, allows one to control the yield and reaction mechanism, its regio- and stereoselectivity^]. For successful catalysis it is important to know in which part of the system (the core of the micelle, the surface of the micelle, the nonpolar phase) the reactants are concentrated. The use of computer simulation methods, one of which is the molecular dynamics method, makes it possible to explicitly determine the location of reagent molecules relative to micelles and the influence of structural properties of molecules of solubilizing substances on this location. In the synthesis of nanoparticles, as in the process of solubilization, an important role is played by the electric double layer (EDL) formed on the surface of reverse micelles. Using the molecular dynamics method, one can explicitly obtain data on the electric field in reverse micelles and on the contribution of the fluctuations of charged particles into intermicellar interactions.

The relevance of the work is determined by the need to obtain data on reverse micelles internal area inaccessible to direct experimental research, the distribution of the components and the electric fields inside them, as well as the influence of the solubilized molecule

structure and the type of its on the possibility of using the reverse micelles to catalyze organic reactions and in controlled synthesis of inorganic nanoparticles.

The degree of elaboration of the research topic. A primitive model of an aggregate in the form of a spherical cavity, located in a continuous medium of a hydrocarbon solvent and hydrophobic tails of surfactant molecules, was used in the first works on modeling the reverse micelles[10-13]. Data was obtained on the structure of the nucleus, the mobility of the components, the electrical double layer of the reverse micelle, and the strength of intermicellar interactions was estimated. Ionic reverse micelles of bis(2-ethylhexyl)sulfosuccinate (AOT) have been extensively studied by computer simulation methods. The shape and structure of the AOT reverse micelles were studied by the molecular dynamics method by using the primitive[14], hybrid[15], united-atom[16], and all-atom[17] approaches. In the works [18,19] the process of self-assembly of AOT reverse micelles in hydrocarbons was simulated. The process of peptide solubilization in reverse AOT micelles was actively investigated in [20,21]. Currently, simulation methods solve problems of the size distribution of AOT reverse micelles [22] and their behavior at low temperatures[23]. The electrical properties of ionic reverse micelles are actively studied[24-26]. The nonionic inverse micelles of Span 80 and Tween 80 at the time of writing this work have not been practically studied yet by the computer simulation methods. The behavior of Span 80 reverse micelles in an external electric field was simulated in [27], atomistic and coarse-grained models for the study of direct micelles Tween 80[28], mono- and bilayers of Span 80 were created in [29].

The thesis presents the results on simulation of reverse micelles AOT, Span 80 and Tween 80 with the addition of various salts and organic substances. The purpose of the thesis was to establish the dependence of the internal structure and morphology of the aggregates formed in reverse microemulsions, including ionic and nonionic reverse micelles, on the composition of the system; calculating the numerical characteristics of the electrical properties (distribution of the electric field and the average square of the dipole moment) of the ion reverse micelles; determining the contribution of the system components to various

properties of reverse micelles; the influence of the type of reverse micelle, the structure and

polarity of the solubilized molecule on the result of the solubilization of the molecule in the

reverse micelle.

To achieve this goal it was necessary to solve the following tasks:

1. Assemble a suitable molecular model to describe the components of the reverse microemulsion.

2. Determine the modeling conditions under which the systems most fully exhibit the studied properties.

3. Select substances, by the example of which one can determine the influence of the structure and polarity of a molecule on its solubilizing ability in reverse micelles.

4. Develop algorithms for analyzing the obtained trajectories and calculating the average values of the system parameters.

The scientific novelty of the work consists in:

1. Models of reverse micelles of nonionic surfactants Tween 80 and its mixtures with Span 80 were created for the first time.

2. The internal structure of reverse micelles of nonionic surfactants Tween 80, Span 80 and their mixtures was found.

3. Electric potential and field distributions were calculated for AOTNa and AOT2Ca reverse micelles with and without salt addition.

4. The contributions of water and ions to the mean square of the dipole moment of the AOT reverse micelles were distiguished.

5. A formula is proposed that approximates the dependence of the mean square of the dipole moment on the size of the AOT reverse micelle, and shows the advantages of the united-atom approach over the primitive one when estimating the electrical parameters of the micelle.

6. The process of solubilization of benzene, pyridine and their hydroxyl derivatives in AOTNa reverse micelles and Span 80 was simulated, their stationary position relative to the reverse micelle in the system was determined.

The practical significance of the work consists in that the data obtained on the properties of ionic and non-ionic reverse micelles is important for their use in organic and inorganic synthesis. Predicting the result of solubilization of a particular molecule in a micelle makes it possible to a more effective use of reverse micelles to catalyze organic reactions. The mean square of the dipole moment of a micelle makes a significant contribution to intermicellar interactions, that is important for synthesizing nanoparticles in reverse micelles.

Statements to be defended:

1. Compositions of systems were found in which the self-aggregation of reverse micelles of various morphology can be reproduced using the molecular dynamics method.

2. The types of reverse micelles were classified, the relationships between the ratio of the system components and the shape of AOTNa ionic micelles and nonionic Span 80 and/or Tween 80 micelles were determined. An improved algorithm for approximating the surface of ionic reverse micelles was developed.

3. When comparing the radial and intrinsic profiles of non-ionic micelles Span 80 and/or Tween 80, significant differences were found in the relative distribution of substances only for loose micelles containing Tween 80.

4. Basing on the local electric potential in ionic micelles, it has been shown that the double layer of the reverse micelle is concentrated in its surface layer and is characterized by high values of the electric field (about 108-109 V/m), at which ionization of water molecules can be observed in practice. The addition of salt has a significant effect on the intensity of the double layer.

5. It was shown that the average square of the dipole moment of a micelle depends mainly on its size and increases with the increase in the radius of Ragg as Ragg25. Although the

change of the counterion and the addition of salt to the system affects the electric field of the micelles, the average square of the dipole moment remains almost unchanged.

6. The intermicellar interaction forces were compared with those calculated by using the primitive model. It is shown that the neglect of the molecular structure of water in the electrical properties of reverse micelles leads to a more than double underestimation of the interaction force between reverse micelles.

7. When comparing the solubilization of various organic molecules, it was shown that the most important factors that unambiguously predict the successful solubilization of the molecule are both the presence of a sterically free hydroxyl group in its structure and its ionogenicity. The polarity of the molecule does not play a major role in solubilization in non-ionic micelles, but it is apparently that the stronger electric field of the ionic micelle requires it to be taken into account. The presence of a nitrogen heteroatom in the structure is important for predicting the position of an already solubilized molecule in the reverse micelle.

Approbation of work. The results of the work were reported at the conferences listed in Table 1.

Table 1. Conferences at which the work was reported.

Name of the conference Status Time and place Type of presentation

6th International Colloids Conference international 19-22.06.2016, Berlin poster presentation

16th European Students Colloids Conference international 19-22.06. 2017, Florence poster presentation

XXI International Conference on Chemical Thermodynamics in Russia (RCCT-2017) international 26-30.06.2017, Novosibirsk oral presentation

10th Liblice Conference

17-22.06.2018, poster

on the Statistical international

Srni presentation

Mechanics of Liquids

Publications. As the base of the dissertation, 5 articles were published in peer-

reviewed international journals, indexed by Scopus and Web Of Science:

1. Kopanichuk, I.V., Vanin, A.A., Ostras', A., Brodskaya, E.N. // Computer Simulation of Luminophore Solubilization in Reverse Micelles (2018) Colloid Journal, 80 (3), pp. 266-271. DOI: 10.1134/S1061933X18030067 [30].

2. Kopanichuk, I.V., Vanin, A.A., Brodskaya, E.N. // The Dipole Moment of Reverse Micelles according to Computer Simulation Data (2018) Colloid Journal, 80 (2), pp. 184-188. DOI: 10.1134/S1061933X18020059 [31].

3. Kopanichuk, I.V., Vedenchuk, E.A., Koneva, A.S., Vanin, A.A. // Structural properties of Span 80/Tween 80 reverse micelles by molecular dynamics simulations (2018) Journal of Physical Chemistry B, 122 (33), pp. 8047-8055. DOI: 10.1021/acs.jpcb.8b03945 [32].

4. Kopanichuk, I.V., Ochkalova, S.D., Vanin, A.A. // The Effect of Hydroxyl Groups on Solubilization of Pyridine Derivatives in Span 80-Water-n-Decane Reverse Micelles (2018) Colloid Journal, 80 (4), pp. 389-393. DOI: 10.1134/S1061933X18040051 [33].

5. Kopanichuk, I.V., Vanin, A.A., Brodskaya, E.N. // The effect of water on the shape of aggregates in water-in-oil microemulsions according to data of computer simulation (2017) Colloid Journal, 79 (3), pp. 328-332. DOI: 10.1134/S1061933X1703005X [34].

The personal contribution of the author consisted in active participation in setting tasks, researching, planning, preparing and conducting calculations, as well as analyzing, interpreting and summarizing the results, preparing reports and publications.

The work was performed in the Federal State Budgetary Educational Institution of Higher Education "St. Petersburg State University" (Institute of Chemistry, Department of Physical Chemistry) in accordance with the research plan on the topic: "Computer simulations of ionic and nonionic reverse micelles"

CHAPTER 1. LITERATURE REVIEW

This Chapter contains the review of the most important studies of reverse micelles carried out by molecular dynamics simulations and concerning the claimed aim of this study. Performing computer simulations is the best way to obtain information about the shape of reverse micelles, their internal structure and other properties that depend on the distribution of components inside the reverse micelles. Also, computer simulations were used to study the behavior of different substances solubilized inside the reverse micelles.

There is a few methods of previous reviews on the molecular simulation study of the reversed micelles. Studies on the self-assembly of amphiphiles in the absence of water are reviewed in [35]. It was concluded that AOT has most commonly been used to form reverse micelles encapsulating nonaqueous polar organic solvents and TX-100 dominates systems encapsulating room temperature ionic liquids. Other surfactants may provide as (or possibly more) effective emulsification for nonaqueous polar organic solvents. Although AOT succeeds gloriously to encapsulate water, other surfactants may prove even more efficient for encapsulation of nonaqueous polar solvents. Ionic liquids have been demonstrated as the polar phase for reverse micelles and may provide interesting alternative behavior due to significant interactions with surfactants. A clear understanding at the molecular level of the interaction between ionic liquids and polar solvents with the different surfactants is crucial for the potential novel applications of the nonaqueous micelle systems as nanoreactors. The effect of the external nonpolar solvent on the nonaqueous reverse micelle formation and their properties was not clearly analyzed. Most of researchers have not explored similarities or differences between the systems to learn the effect of the external solvent. The main structural and thermodynamic properties, as well as the dynamics of reverse micelle components obtained by molecular simulation are considered in [36]. It was concluded that full-atom models are the most efficient for reproducing real properties of reverse micelles in solutions. The efficiency of the molecular dynamics method for investigating reverse micelles was demonstrated. Atomistic molecular dynamics approach enables one to determine the properties of a micelle core, the structure and the shape of

reverse micelles, their surface fluctuations, and possible conformations of hydrocarbon tails in surfactant molecules. The development and application of simplified models is important to calculate the electrical and thermodynamic properties of micelles due to significant time factor of performing the all-atomic simulations.

Studies on wormlike reverse aggregates are highlighted in [37]. Only the structure of wormlike reverse micelles made by lecithin in oil was considered, because the structure of ionic wormlike reverse micelles was not studied widely. It was concluded that changes in the solvent nature are sufficient to change the micellar connectivity and phase behavior. Branched micelles form living networks whose dynamics is fast due to rapid recombination through the formation of transient junctions. Fully branched living networks is separated into a dense network and a dilute solution upon water overloading.

The most efficient ways to perform computer simulation of reverse micelles by the molecular dynamics method, including all-atomic and simplified approaches have been considered in [38-40]. It also studied the prominent role of the charges and of the polar head to the self-assembling process. The overall stability of direct and reverse micelles, both in condensed phase and in vacuum, largely depends on the strength of polar interactions. Results of studying reverse micelles by the molecular dynamics method should be processed carefully: not each reverse micelle obtained in simulations, even existing for an infinitely long time, is of relevance to a real chemical experiment. If the open regions of contacts between water and nonpolar solvent constitute a considerable part of the surface of the simulated micelle, the fraction of such micelles is small in chemical experiment, and such micelles are of no interest for a detailed study. The simulation performed with the use of different initial arrangements of molecules (randomly distributed or gathered into a preassembled micelle) yields similar micelles. Moreover, the calculation result is independent on the type of solvent model used. When preassembled micelles are applied, the most substantial changes in a micelle take place (or can take place) within the initial 2 ns; then, only the micelle shape reversibly varies.

This review does not pretend to contain all articles on computer simulations of reverse micelles but only on the most important ones. This thesis focuses at comparative studies of different types of surfactants that form reverse micelles. Hence, there is a need in the classification of previous works according to the subjects that were considered in them. By now, anionic reverse micelles formed by AOT surfactant are mostly considered in computer simulations studies. Cationic, zwitter-ionic, and nonionic reverse micelles, and reversed micelles formed by ionic liquids are also important.

1.1. Computer simulations of reverse micelles of ionic surfactants The most simplified approach of modelling the reverse micelle is based on the representation of a micelle as a spherical cavity occurring in a continuous medium of a hydrocarbon solvent and hydrophobic tails of surfactant molecules[10-13]. Data on the structure of a micelle core and diffusion characteristics of the components were presented. Despite the simplifications used, the results obtained in are useful for interpretation of NMR data on polyelectrolyte solutions, microemulsions, and liquid crystals. The electric double layer of a reverse micelle was also investigated. The electrostatic contributions from the interactions of particles belonging to a micelle with bulk aqueous surfactant solution were determined as well as between adjacent aggregates of the same sizes, aggregation numbers, and degrees of ionization. Interaction between two similar micelles was studied and it was shown that the interaction force between two non-contacting micelles decreases in logarithmic law on the distance between them. The force substantially depends on the micelle sizes, the number and the valence of ions, and the permittivity of the system.

The first computer simulation of coarse-grained reverse ionic micelle was performed by D. Brown and J. H. R. Clarke in 1988[41]. A preassembled single reverse micelle with poorly defined water core was set in an apolar solvent medium, then it was equilibrated during 120 ps. A coarse-grained approach was used for all molecules, except water. The surfactant was chosen to be cationic with Lennard-Jones centers of neutral hydrophobic tails, positively charged heads, and mobile anions. SPC water model was used and the apolar solvent was represented by a single-site interaction center. The model used in that work is

too simple to represent any specific surfactant. It is interesting that no periodic boundary conditions were used: the numbers of the surfactant, water, and solvent molecules are 36, 72, and 1079, respectively, in a spherical cavity of a solvent continuum and there was no need in periodic boundaries to stabilize the system. Despite the primitivism of the used model, the obtained data was very important. Average radial densities for all components showed their preferable locations in the system. Mean square displacements of the solvent and of components of the reverse micelle showed not only that that there is very weak mobility within the micelle. The shape of the reverse micelle was described with a series in spherical harmonics for its surface. This mathematically strong method was not used by any later researchers to describe the shape of the reverse micelle, may be due to its complexity.

Cationic reverse micelles based on ammonium salts were studied in works [42], [43]. Cetyltrimethylammonium bromide/water reverse micelles in chloroform were considered at temperatures around and below zero Celsius[42]. The molecular dynamics data confirmed the NMR spectroscopy data on the size of the aggregates and supplemented it with the shape data. The non-sphericity of reverse micelles of cetyltrimethylammonium bromide / water increases with the increasing amount of water in the core. In the work [43] CTAB / hexanol / water mixed reverse micelle was modelled. The size of the reverse micelle was determined by SAXS and SANS methods. A decrease in rotational and translational diffusion in the direction from the center of the micelle to the surface of the water core was detected. It is interesting that non-sphericity was calculated instead of the usual eccentricity.

Anionic reverse micelles formed by sulfates and sulfonates are widely studied by the molecular dynamics simulation method. Computer simulations of the anionic reverse micelles at the atomistic level were first carried out in the work [44]. Reverse micelles contained a calcium carbonate core stabilized with phenolate or a sulfonate, the molecules of which formed a shell around this core. Such aggregates are notable for the fact that, unlike water-based reverse micelles, they have the hard shape, which fluctuates very weak in time. They are also relatively resistant to changes in temperature and acidity of the medium. It was shown that the structure of these aggregates and their properties are determined by the

geometry of the surfactant molecules contained in them, since the structural and dynamic differences between the aggregates based on the single-tail sulfonate and the aggregates based on the double-ended phenolate were obvious. In vacuum, sulfonate micelles are much more spherical than phenol salts, and their core is better closed to the external environment. In a non-polar solvent, this difference is somewhat smoothed due to the penetration of the solvent between the surfactant molecules, but the shape of the phenolate reverse micelles is still very different from the spherical one.

The process of self-assembly of reverse water/(C7F1s)(C7H1s)CHSO4Na micelles in supercritical carbon dioxide was reproduced by computer simulation[45]. A better understanding of the process was supposed to help to solve the problem of molecular design of surfactants suitable for industrial use of the supercritical CO2. It was found that micellization in supercritical CO2 occurs much faster than in a liquid solvents under standard conditions. The local density profiles of the components of the reverse micelle were calculated that made it possible to compare the results with the data obtained by the scattering methods.

Poghosyan et al. [46] studied a system containing inverse micelles of sodium dodecyl sulfate (SDS) in a mixed solvent (toluene/pentanol). For a full-atom simulation with a CHARMM27 force field and the box size of 15x15x15 nm3, the simulation time is extremely short and is only 15 ns, thanks to the use of pre-assembled aggregates. The effects of the presence of polydiallyldimethylammonium chloride in the system were studied: sodium ions are practically unaffected that indicates a high ionic strength near the SDS heads.

Ionic reverse micelles formed by bis(2-ethylhexyl)sulfosuccinate (AOT) surfactant were simulated in numerous studies since 1997. The shape and the structure of AOT RMs were studied in the work [17] by all-atomic molecular dynamics simulation technique. Abel et. al. paid a lot of attention to ensuring consistency between the results of a numerical and a real experiment. Systems containing AOT / water micelles in isooctane were modeled, and the composition and the size of the systems were taken directly from data obtained using SAXS and SANS. The parameters of force field for the surfactant and the solvent were taken

from CHARMM27, TIP3P model was used for water. All micelles were pre-assembled to save the calculation time. The structure of the reverse micelle was carefully described using the profiles of the local density of the components. In order to characterize the shape of the micelle and its water core, an algorithm was proposed for their approximation with an ellipsoid equal to them in mass and in components of the inertia tensor. It was shown that the shape of AOT reverse micelles and their nuclei is far from spherical (eccentricity of the order of 0.6-0.7 for micelles and 0.8 for nuclei), then less than 1% of water on the surface of the core comes into contact with a non-polar solvent. A systematic study of RM size was performed by MD simulation with the aims of determining the size of an RM for a given water number, and of reconciling the results with experimental measurements[22]. Results for a water number of 7.5 indicate that the interaction energy between AOT anions and other system components is at a minimum when there are 62 AOT anions in each reverse micelle. The work [47] is also devoted to detailed consideration of reverse AOT/water micelles in isooctane. The surfactant molecules were represented by the TraPPe/CHARMM hybrid force field. In addition to the usual local density profiles relative to the center of mass, the intrinsic density profiles were calculated. The surface of the RM were defined by the locations of sulfur atoms. Pair distribution functions between atoms of sodium, hydrogen, sulfur and oxygen, the distribution of angles between different vectors connecting atoms with positive and negative effective charges, and the distribution of hydrogen bonds in water were obtained.

A hybrid coarse-grained/atomic approach was used in works [15,48,49] for the AOT/water/hexane ternary system. Molecules of surfactants and hydrocarbons were modeled in a coarse-grained approximation, and SPC/E model was taken for water. The shape of the micelle, the distribution function of molecules over position and orientation, the local electrostatic potential, the normal component of the pressure tensor, rotational and translational diffusion and water mobility, the influence of the size and charge of counterions on the micelle structure, the mechanism of micelle formation and the effect of the solvent were investigated in details. Effects of the freezing temperature on the internal structure of

AOT RM in hexane were considered[23]. AOT RMs in different solvents: n-octane and supercritical CO2 were simulated by the same approach[50,51].

Longhi et al. published series of studies considering isolated AOTNa aggregates in vacuum[52-56]. The surfactant model was created on the basis of the GAFF (AMBER) force field. Positively and negatively charged non-aqueous AOTNa RMs were simulated. The processes of growth of the aggregate and internalizing of the molecules were shown. As well as positively charged ones, negatively charged aggregates grow linearly with the addition of NaAOT molecules. The effects of counterions on structural organization and shape of the RM were estimated.

The process of self-assembly of AOT reverse micelles in hydrocarbons was simulated in works [18,19]. Three ternary AOTNa / water / isooctane, systems were considered in [18]. Each system contained 140 AOTNa molecules, 700 water molecules, and 10147 isooctane molecules; that means more than 2.75-105 interactions centers in total. All-atomic CHARMM force field was used for the hydrocarbon and surfactant, and SPC/E model for water. The total simulation time exceeds 1000 ns. The mechanism of self-aggregation of the micelles, their geometry, and the degree of polydispersity were considered. Estimated aggregation number and self-diffusion coefficients are in a good agreement with experimental data[18]. This study of the reverse micelles' self-assembly was designed in order to optimize calculation strategy. A single-center hexane molecule was used as a solvent. The force field topology for AOTNa was taken from CHARMM27 as well as in the work [18], but the efficient charges of the interaction centers of the AOT head were obtained from quantum-chemical calculations in terms of the MP2 theory using basis set 6-311+G**. TIP3P model was used for water. All molecules were placed into a sphericalbox(9 nm in radius) with repulsion potential (spherical boundary conditions). Analysis of the shape, the composition, and the internal structure of RMs was performed. Two different theoretical approaches for describing the reverse micelle were considered. One with hydrated surfactant molecules' heads in the water core and another with the surface of the core being limited to surfactant heads. Expressions for dependence of the composition and size of AOT micelle

on parameter wo were suggested. The first approach and consequent expressions is better for use in molecular dynamics simulation of pre-assembled AOT reverse micelles because it allows one to make more accurate choice of micelle radius and composition at a given value of w0. However, the second approach is significantly easier in practice.

A detailed analysis of the structure and dynamics of water in the internal cavity of the reverse micelle was carried out in [14]. Only hydrophilic constituents: the water core, the heads of anionic surfactants, and counterions, were modeled. The polarization density of water, the pair distribution functions of ions and water, the diffusion coefficients of ions and water were calculated. Water dynamics inside the interior of the AOT reverse micelle and the interactions of the surfactant heads and counterions with water were considered in works [57-61] for the coarse-grained model of the micelle. To determine the effects of solute-headgroup interactions on solvation dynamics, the results for charge localization in model ionic diatomic chromophores were compared. Differences in the solvation responses for anionic and cationic chromophores were found. Solvation dynamics for the cationic chromophore are considerably slower and more strongly depends on the water number than those for the anionic chromophore[59]. The dependence of water mobility on the water number was investigated and found weak[57]. The effect of counterion size on the structure of the ionic layer at the interface was described. The larger counterions display greater coordination with the anionic headgroups, thus are more effective at excluding water from the interfacial layer, and are much less likely to dissolve into the core of the reverse micelle. More favorable packing of the larger K+ counterions at the interface is responsible for these trends. In addition, the counter-ion density as a function of distance from the interface displays less sensitivity to increasing RM size and does not split into two peaks as observed in the Na+ reverse micelles[58].

The effects of different solvents and additives are very important to predict the behavior of such complicated objects like AOT reverse micelles. In the work [62] computer simulation was used to study the role of hydrophobic interaction in the formation of reverse micellar aggregates. Changes in hydrophobic interactions were studied on the example of the

conformations of a model polypeptide based on L-lysine. This work did not solve the problem of the duality of the physical nature of the hydrophobic interaction, but it confirmed the importance of taking it into account in order to be able to predict the behavior of amphiphilic molecules in various media.

Vasquez et. al. studied the effect of different salt additions on AOT reverse micelles in isooctane[63,64]. Systems with a low water number (w0 < 10) contained cylindrical reverse micelles with a significantly fluctuating form. The shape fluctuations decreased markedly when water was added to the system and the water number increased. The average radius of the aggregates increased nonlinearly, reaching a maximum at w0 = 15. When salt was added to the system, the size of the micelles increased, but the shape oscillations decreased compared to the variations in the ternary system. Molecular dynamics complements the data of dynamic light scattering. With a small water number w0 = 3, self-assembly of an AOT reverse micelle with broken spherical symmetry was observed, more closely shaped to a torus than to a sphere or an ellipsoid. The effects of the presence of the zirconyl chloride salt on the size distribution of reverse micelles were studied. A significant asymmetry of the distribution of AOT reverse micelles in size was found, significant fluctuations of the shape of reverse micelles were observed, which increase with increasing salt concentration.

Three types of AOT reverse micelles in cyclohexane were modeled in the work [65]. The first type contained only water, the second one - only formamide, and the third one contained their equimolar mixture. All three types of aggregates were characterized by a highly distorted elliptical shape with an eccentricity about 0.75. In aggregates of mixed composition, the concentration of formamide in the center of the core exceeded the concentration of water.

Another one important group of ionic reverse micelles consists of reverse micelles based on ionic liquids. Ionic liquids have a lot of desired properties, such as negligible volatility, high thermal stability, non-flammability, and large CO2 solubility. However, ionic liquids have some drawbacks such as the high viscosity and large hygroscopicity. Ionic liquid reverse micelle systems potentially can overcome the above two drawbacks. In the

work [66] reverse micelles stabilized by several ionic liquids were considered with the aim of studying the solubilization of CO2 in them. Tetrafluoroborate 1-butyl-3-methylimidazolium acted as a main component of the core, benzylhexadecyl-methylimidazolium chloride acted as a surfactant, and benzene as a solvent. Reverse micelles self-assembled under standard conditions in the NpT ensemble. After self-assembly, self-diffusion of aggregates was simulated in the NVE ensemble. Ion exchange between the core and the shell of the reverse micelle was detected. Both experimental and calculated data showed that the mobility of the ionic liquid in the aggregate exceeds that for the ionic liquid in the bulk phase from 5 to 26 times, that is partly due to the high mobility of the aggregate in benzene. The carbon dioxide molecule was absorbed primarily by benzene, and by the micelle core. Reverse water/benzylhexadecylammonium chloride (BHDC) micelles in benzene were modeled in the work[67]. The eccentricity of the considered aggregates is close to 0.9, that indicates their significant ellipticity. Even with wo = 10, the density of water in the core reached only 80% of the density of water in the bulk phase, that indicates a significant hydration of the surfactant heads. Basing on the density profiles, the authors also conclude that solvent has penetrated deep into the core of the micelle, that most likely has no relation to reality. The overlapping profiles of the local density of water, surfactant and solvent is explained by a significant deviation of the micelle shape from spherical, while the profile has spherical symmetry. Intermicellar interactions in benzene and in the benzene / heptane mixture were studied by calculating the Helmholtz free energy profiles during coalescence. For this, the adaptive biasing force algorithm was used. In the work [68] reverse micelles [C1C10Im][Br]/water in nonane with the addition of glycine were modeled. The sphericity of the obtained aggregates and the formation of hydrogen bonds between the molecules of the solubilizate and the components of the aggregate were shown. Volume limitation stabilizes hydrogen bonds as compared to the bulk phase.

There are also simulation studies of ionic RMs where surfactants could not be included in any of the groups above. In the work [69] molecular modeling complements the data of NMR spectroscopy in the study of rod-shaped reverse micelles formed by the

di(ethylhexyl)phosphate nickel II. It was confirmed that, unlike AOT reverse micelles, micelles formed by di(ethylhexyl)phosphate have an open water channel, and the hydrophilic-hydrophobic character of micelles can be controlled by adding a co-surfactant, for example, octanol. In the work [70] the process of self-assembly of reverse micelles of perfluorinated polyester CF3-(O-CF2-CF(CFs))3-O-CF2-COO" NH4+ (PFPE) in supercritical CO2 was considered. The contact area of the water core and solvent in the case of the non-perfluorinated PFPE analog was found to be large enough due to the uneven distribution of the polyester molecules, so that it was found unsuitable for industrial use as a surfactant in supercritical CO2. In works [71,72] reverse micelles based on perfluorinated polyester and phosphate, respectively, were modeled. The data on the internal structure of the aggregates and the dynamics of water in them were obtained.

The solubilization of different substances inside the RM and the effect of the confinement on the interactions between these substances and water molecules was studied in [20,21,24,73-79]. The explanation for the stability of the polypeptide in the reverse micelles was found as the competition for hydration water between the AOT headgroup and the peptide. The alanine-lysine AKA2 peptide was observed in the AOT reverse micelle. Peptide remains in a helical conformation within a spherically constrained reverse micelle and partially unfolds when being simulated in an unconstrained reverse micelle environment, in agreement with experiment[73,79]. Hydration dynamics and protein stability inside sodium bis(2-ethylhexyl)sulfosuccinate (AOT) and cetyltrimethylammonium bromide (CTAB) reverse micelles were studied. It was found that water inside anionic AOT and cationic CTAB reverse micelles is characterized by a strong dielectric depolarization giving rise to a very low relative permittivity compared to an unconfined solution. Protein stability correlates rather with the local chemistry of the hydrated head groups than with the excluded volume effect or the low global permittivity[24]. The reduced form of horse cytochrome c confined in reverse micelles (RM) of sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) in isooctane were simulated. It was shown that the protein secondary structure and the heme conformation both depend on micellar hydration. The observed slowing-down of water

molecules at the protein surface were considered as a marker of the microenvironment experienced by them[75]. The quaternary system polypeptide/AOT/water/isooctane was simulated in [21]. Stability of the polypeptide in the reverse micelle was explained by the competition for hydration water between the AOT headgroup and the peptide. Molecular dynamics simulations of the encapsulation of ubiquitin and alpha-helical peptide into self-assembled protein/surfactant reverse micelles were performed in [20,78]. The positioning and interactions of proteins with the RM were studied. It was found that ubiquitin binds to the RM interface at low salt concentrations. The peptides prefer the constrained hydration environment of the AOT headgroups. It was demonstrated that the confinement of protein can result in altered protein dynamics due to the interactions between the protein and the surfactant.

1.2. Computer simulations of reverse micelles of nonionic and zwitter-ionic surfactants The first simulation of nonionic reverse micelle were performed in 1991 by Smith et. al.[80]. The existence of two types of particles was assumed: "oil-like" o particles and "water-like" w particles. These two types of particles were used to model three types of molecules, namely oil molecules, water molecules, and surfactant molecules. An oil molecule consists of a single o particle, and a water molecule consists of a single w particle. A surfactant molecule is made up of one or more o particles and one or more w particles; these are joined together by harmonic potentials. The formation of micelles was observed. It was shown that self-assembly in surfactant systems does not require the presence of hydrogen bonds. Pronounced oscillations of the density profile of water and surfactants in the water phase were found. Since then, simulation studies of nonionic reverse micelles mostly considered oxyethylene (EO)-based surfactants, the so called CmEn, where m is a number of carbon atoms in a tailgroup and n is the length of the headgroup (EO oligomer chain); formula: CH3-(CH2)n-1-(O-(CH2)2)m-OH. In the work [81] reverse C12E2 micelles in decane and in vacuum were modeled. The difference in the behavior of the core and the surfactant headgroups between these two media was not detected, unlike the surfactant tails. In the absence of a solvent, the surfactant tails adjoin close to the core, as if facilitating it.

The relaxation time of the fluctuations of the aggregate shape was about 150 ns. Water molecules form hydrogen bonds, acting as a bridge between pairs of oxygen atoms from oxyethylene groups. The influence of the conformation of the amphiphilic C12E4 molecule on the structure of small (w0 = 3) reverse micelles of nonionic surfactants was studied in the work [82]. CHARMM force field and SPC water model were used. EO oligomer chains were modelled by the force filed of Tasaki. Data on the size of the water core, the specific surface area of the core per one surfactant head, the hydration of the surfactant headgroup, and the translational diffusion of water for the trans-conformation of the surfactant molecule is in a better agreement with the experimental data than for the cis-conformation. It was shown that the surfactant head plays a key role in all properties of the reverse micelle associated with water capture. In the work [83] the structures arising from the addition of excess proton to the aqueous reverse micelle of the non-ionic C12E2 surfactant in vacuum were considered. The calculations were performed by the molecular dynamics method using the MS-EVB model. The equilibrium constant between ZDL [H2O-H-OH2] and EGN [H3O(H2O)s+] configurations was calculated. It was found that this constant is two times larger for bulk water than for reverse micelles. Density profiles, pair functions and correlations in time were obtained. In the work [84] the phase behavior and micro-structure of the supercritical CO2 microemulsion system with nonionic dodecyl (poly(ethylene-methylethylene glycol)) ether Ls-54 as a surfactant were studied. The results not only indicate the formation of the thermodynamic stable microemulsion system, but also demonstrate that 1,3-PDO can be selectively solubilized from dilute aqueous solution using the supercritical CO2 microemulsion system with Ls-54 as surfactant by easily controlling the operating pressure. Moreover, the simulation results reveal that the microemulsion formation depends on the interaction between the water cluster and head groups of surfactant. A new formation mechanism of the supercritical CO2 microemulsion system with nonionic surfactant was proposed.

Zwitter-ionic amphiphiles form another major group of surfactants that was studied recently by computer simulation methods. Vierros et al. modeled reverse micelles based on

various phospholipids in cyclohexane: DPPC, DOPC, DLPC, DGPC, and DSPC[85]. The mechanism of the effect of water on the formation of organic gels in the DSPC-water-lecithin system in cyclohexane was investigated. The role of hydrogen bonds in this process is small. Cylindrical reverse micelles are actively involved in the process[86]. In the work [87] an approach to the modeling of DOPC reverse micelles in benzene was developed in detail. Based on the DLS data, the sizes of micelles and their aggregation numbers in the w0 range from 1 to 16 were calculated. The calculations of the inertia tensor showed that DOPC micelles are extremely close to spherical. In small micelles with w0 < 4, the core is disordered, whereas in large micelles the structure is clearly pronounced. Calculations of the infrared spectrum of water showed a red shift with a decrease in the water number, which indicates significant water interactions with surfactant heads in this area of the microemulsion formulations.

CHAPTER 2. MODELS AND METHODS 2.1. Basics of molecular dynamics Molecular dynamics method based on the numerical solution of the equations of classical particle motion - the Newton equations of the ensemble of atoms that makes up the molecular system:

d2r F

- = - (1)

dt2 m w

where r is the radius vector of the atom, F is the total force from all other atoms, m is the mass of the atom. Atomic velocities are the first-order derivatives of the coordinates:

dr . .

v = — (2)

dt v '

Coordinates of atoms are calculated step-by-step by numerical integration. Infinitesimal dt are replaced with finite differences At, named the time step of integration. There are different algorithms to perform numerical integration of (1) and (2). The Verlet algorithm is one of the most popular algorithms. Coordinates of atoms are calculated through the Taylor series with time as an argument. For each atom:

r(t + At) = r(t) + v(t)At + 1a2(t)At2 +1b3(t)At3 + - (3)

r(t- At) = r(t)- v(t)At + 1a2(t)At2 -1b3(t)At3 + - (4)

After the addition of these equations the coordinate of the atom at t + At moment will be obtained without a need in the calculation of the velocity:

r(t + At) = 2r(t) - r(t - At) + a2(t)At2 + - (5)

Accelerations are calculated by using the equation (1), velocities by the equation (2). Forces are determined by the interactions between the atoms:

F = -VU(r) (6)

Hence, the most important part of the preparation of the molecular dynamics simulations are the choice of the intermolecular and intramolecular potentials. Lennard-Jones 12-6 potential are usually used to describe the intermolecular interactions in liquids:

then the problem of the correct description of the intermolecular potential is reduced to the choice of Lennard-Jones parameters a and e. Intramolecular interactions are described as harmonical bonds (or angles):

U = lK(x-x0)2 (8)

where K is the constant, and x0 is the length of the bond (or the cosine of the angle) between the atoms (or bonds)[88-90]. The total of intramolecular constants and intermolecular parameters are the force field. The force fields and algorithms that were used in this work are described in the next Section 2.2.

2.2. Simulations details The united atom approach was used to represent AOT, Tween 80, Span 80, n-decane, and isooctane molecules, and calcium, chloride, and sodium ions with the parameter set 53A6 for all interactions from GROMOS96 force field[90]. The methylene (CH2) and methyl (CH3) groups were represented as unified atoms. SPC model was used for water molecule[91]. Charges on the polar head of AOT located on the ester and the sulfonate groups were taken from Nevidimov et. al. [19]. Atomic partial charges for all other molecules were derived using the CHELPG technique by the B3LYP/6-31G**[92]. The molecular dynamics simulations were performed using GROMACS 2016[93]. Equations of motion were integrated by the leapfrog algorithm with a time step of 2 fs. For electrostatic interaction, the Particle Mesh Ewald method was used with interpolation of the fourth order and the maximum spacing of 0.25 for the fast Fourier transform grid[94]. Both the Lennard-Jones and the real part of the Coulombic interactions were truncated at 1.0 nm. Verlet cutoff scheme was used for the latter. The tolerance (ewald_rtol)[93] was set to 10-5 for all systems. All configurations and trajectories were analyzed with the aid of VMD software[95]. Software for creating the starting configuration and analysis of the obtained trajectories was written using JGROMACS source code[96] and the algorithm for calculating the center of mass for a set of point masses that are distributed in an unbounded environment[97]. The systems considered in Chapters 3 and 6, and in Section 4.2 were created in two stages. At the first stage, optimal box size L was determined for a required composition of the

examined system under isothermal-isobaric conditions at temperature T = 298.1 K and pressure p = 1 bar. The initial configuration contained random mixture of uniformly distributed components. The calculation in the NpT isothermal-isobaric ensemble was carried out for approximately 200-400 ps. The temperature of the whole system was supported by scaling the rates at each step (v-rescale), and the pressure was preset by a Berendsen barostat[15]. After the box was stabilized, its average edge length <Lprev> was calculated. Then a new initial configuration was preset in the created box with size L = <Lprev>. To obtain an equilibrium structure of isolated aggregates, the system was simulated for 400 ns in the case of AOTNa systems and for 35-50 ns in the case of Span 80/Tween 80 systems in the NVT canonical ensemble at T = 298.15 K. Then 10-20 ns NVT simulation was performed to obtain ensemble averages. The trajectory was written to file through every 10 ps to minimize statistical inefficiency[98].

All the considered in Section 4.1 and Chapter 5 AOTNa and AOT2Ca reverse micelles were pre-assembled. The initial configuration was created with the spherical drop of water with ions in the center of the simulation box, the layer of the surfactant around this drop, and isooctane molecules which were randomly uniformly distributed in the rest part of the box. The size of the box L was calculated as the cubic root of the sum of the volumes of components determined by their bulk densities. The initial 15-20 ns NVT simulation was run for the equilibration, then the 20 ns simulation was performed to obtain average values.

CHAPTER 3. THE EFFECT OF THE COMPOSITION OF THE SYSTEM ON THE SHAPE OF AGGREGATES IN REVERSE MICROEMULSIONS This Chapter discusses aspects related to the morphology of reverse micelles -aggregates that self-assemble into hydrocarbon-water-surfactant systems. The types of reverse micelles were classified, the relationships between the ratio of the components of the system and the shape of the AOTNa ionic reverse micelles and Span 80 and/or Tween 80 nonionic reverse micelles were determined. Assumptions were made concerning the causes of fluctuations in the shape of the aggregates. An improved algorithm for approximating the surface of ionic reverse micelles with ellipsoids has been developed.

It is very difficult to model correctly the reverse micelles without distorting their shape relative to the shape of real reverse micelles in the real system of a given composition. The first reason is that the size of the reverse micelle model significantly depends on the size of the simulation cell. It is impossible to get a large reverse micelle in a small cell. Another reason is the long-range Coulomb interactions. The interactions of the model reverse micelle with its virtual copies are significant through periodic boundary conditions. These interactions lead to shape distortion in the direction of one or more axes of the simulation box. These problems can be solved by using the largest box of the simulation, but its size is also limited by the available computer resources. Because of these problems, the reverse micelle models considered in this work cannot be directly correlated with real reverse microemulsions of the same composition. Instead of literal comparison with experimental data, the models under consideration are compared with each other in order to find the effect of composition changes on the shape of reverse micelles and offer possible explanations for the behavior of the entire system. Computer simulation of real reverse microemulsions is still a difficult problem. This work offers solutions only for some particular cases and does not claim to solve the problem as a whole.

3.1. The size and the shape of aggregates in AOT reverse microemulsions

O

H3C CH'

Fig. 3.1.1. Structure of anion of bis(2-etylhexyl)sulfsuccinate (AOT-).

In order to study the morphology and topology of the model anionic reverse microemulsion, a molecular dynamics simulation was performed by using the aggregateed-atomic approach. Sodium bis (2-ethylhexyl) sulfosuccinate was chosen as a surfactant (AOTNa, see Fig. 3.1.1), water as a polar component, and isooctane as a nonpolar component (2,2,4-trimethylpentane, C8H18). Each system was simulated for 200 ns. The time of formation of the aggregate ranged from 1 ns go 15 ns, assembly speed increases with increasing the surfactant and/or water concentration. For confidence in the stability of the aggregates, some systems were simulated for 400 ns, the collapse of the aggregates was not observed. The phase diagram of the AOTNa/water/isooctane system has been thoroughly studied both experimentally and by simulations[99-101]. However, the structure of AOTNa reverse micelles in isooctane was studied before in a rather narrow concentration range, usually with a very high concentration of the nonpolar component. Figure 3.1.2 shows a triple phase diagram of the AOTNa/water/isooctane system. Only the L2 region of the phase diagram was investigated, where the existence of water-in-oil microemulsions were previously observed by mesoscopic simulations and experiments[99,101]. All the considered systems and their parameters are listed in Table 3.1.1. The ratio of mole fractions of water and surfactant or the water number w0 = xwat/xaot is the most important characteristic when describing reverse micelles. To exactly determine the location of the system on the phase diagram, one parameter is not enough; therefore, by analogy with the water number, another

parameter was introduced i. e. h0 = xiso/xwat - the ratio of the molar fraction of isooctane to the molar fraction of water (see Fig. 3.1.2). Systems with w0 in the range from 0 to 20 and h0 in the range from 1 to 10 were considered. As it is shown in Table 3.1.1, both characteristics are important for predicting the morphology of the simulated aggregate. Four main types of aggregates were found in the L2 region of the phase diagram,. Dropletlike (spherical) reverse micelles are formed at relatively low surfactant concentrations. (see Fig. 3.1.3). Reverse micelles, which are formed in the absence of water, can be considered as a special case of classical dropletlike reverse micelles. And increase in the amount of surfactant leads to the formation of wormlike reverse micelles. When interconnect by bridges they form a certain similarity to the networks, in the L2 area with a low concentration of water. Borders between regions with a predominance of one type of aggregate are very smooth, but obvious (see Fig. 3.1.2).

For utility of the description of the calculation results, the systems were renamed with the regard to their composition, as described in Table 3.1.1. If the system name is 132_330_495, this means that it contains 132 AOTNa molecules, 330 water molecules and 495 molecules of surfactants. Accordingly, its parameters from Table 3.1.1: w0 = 2.5, h0 = 1.5, the structure type is a network.

Table 3.1.1. Parameters of systems with AOTNa reverse micelles. L is the size of the simulation box, Naot is the number of AOT- anions, Niso is the number of isooctane molecules, Nwat is the number of water molecules, h0 is the number of isooctane molecules per one water

molecule, w0 is the water number (number of water molecules per one AOTNa molecule).

Naot Nwat Niso wo ho L, nm structure type

200 22 220 0.11 10 5.703 network

250 100 100 0.4 1 5.773 network

210 84 252 0.4 3 5.868 network

130 52 520 0.4 10 6.010 network

140 98 490 0.7 5 6.011 network

120 120 600 1 5 6.158 network

200 300 300 1.5 1 5.970 network

130 195 585 1.5 3 6.190 network

160 240 360 1.5 1.5 5.925 network

116 290 580 2.5 2 6.132 network

132 330 495 2.5 1.5 6.042 network

110 605 605 5.5 1 6.240 network

150 225 450 1.5 2 6.013 network

60 90 900 1.5 10 6.470 Y-closure

90 135 675 1.5 5 6.157 Y-closure

78 78 780 1 10 6.311 Y-closure

66 165 825 2.5 5 6.364 Y-closure

92 230 690 2.5 3 6.225 Y-closure

100 70 700 0.7 10 6.253 Y-closure

38 95 950 2.5 10 6.459 wormlike

50 275 825 5.5 3 6.310 wormlike

80 440 660 5.5 1.5 6.172 wormlike

70 385 770 5.5 2 6.329 wormlike

68 374 1870 5.5 5 6.455 perforated dropletlike

20 110 1100 5.5 10 6.670 dropletlike

31 310 930 10 3 6.435 dropletlike

43 430 860 10 2 6.382 dropletlike

55 550 825 10 1.5 6.322 dropletlike

22 440 880 20 2 6.408 dropletlike

36 720 720 20 1 6.122 dropletlike

28 560 840 20 1.5 6.301 dropletlike

Fig. 3.1.2. The ratio between the compositions of simulated reverse microemulsions in molar fractions.

Fig. 3.1.3. Snapshots of equilibrated configurations of systems with dropletlike reverse micelles. (a) - spherical micelle 31_310_930, (b) - perforated dropletlike micelle 68_374_1870, (c) - non-aqueous micelle 15_1000.

Non-aqueous AOTNa reverse micelles are of special interest (see Fig. 3.1.3c). Their formation in a non-polar hydrocarbon environment was experimentally confirmed[102]. The shape and the structure of non-aqueous AOT reverse micelles in vacuum was studied by the molecular dynamics method[52,53,55,56]. The main reason for the formation of reverse micelles in the absence of water is the solvophobic effect[102]. However, if it was the single reason for the formation of anhydrous reverse micelles, their shape should be close to spherical in order to minimize the interface area. The non-aqueous reverse micelles of AOTNa in isooctane obtained in this work (see Table 3.1.2) are not spherical. Their shape is more similar to the shape of analogous aggregates in vacuum. They have an extended core that contains counterions located between the head groups of AOT and connected to them in a freely bending ionic chain (see Fig. 3.1.4). In the complete absence of water or other polar solvents, a chain of positively charged sodium ions and negatively charged sulfonate ions is formed in the system. In the polar group of the AOT- anion, the partial positive charge is localized on the sulfur atom, and the partial negative charge is on the oxygen atoms. In the ionic chain, oxygen atoms are usually located between sulfur atoms and sodium ions as a result of electrostatic interactions between them.

Fig. 3.1.4. The positively charged part of the core of the micelle of 20 AOTNa molecules in the non-aqueous system 20_1000 (top) and its schematic representation (bottom). Sodium ions are yellow, sulfur atoms are red.

Fig. 3.1.5. Images of equilibrium configurations for systems with wormlike micelles. (a) - cylindrical micelle 50_275_825, (b) and (c) - micelles with Y-junctions, systems 80_440_660 and 92_230_690, respectively.

Aqueous AOT reverse micelles characterized by a variety of forms are presented in Figures 3.1.3, 3.1.5 and 3.1.6. Dropletlike micelles are formed (see Fig. 3.1.3a) at a high value of water number w0 > 6. Wormlike micelles are formed at a lower water number i. e. from 2.5 to 5.5. The transition between these forms occurs through an intermediate version. When the water number is not too small (about 5-6), and h0 is not too large (about 5), the formation of a reverse micelle with perforation is possible, in other words, a wormlike micelle being closured in a ring. A similar object was observed previously by simulations[64]. With further decrease in the water number to 1-2.5 and an increase in h0 to 3-10, wormlike micelles start to form Y-junctions, that is, branching wormlike reverse micelles (see Figs. 3.1.5a and 3.1.5b). The decrease in the content of isooctane in the system of a low water number (0.4-2.5, but also possible at w0 = 5.5) leads to further branching of wormlike micelles and formation of networks (see Figs. 3.1.6a and 3.1.6b). The decrease in h0 leads to the decrease in the distances between the formed wormlike micelles and a higher probability for the formation of stable closures in the system.

On the basis of the data obtained, it can be concluded that the transition from dropletlike reverse micelles to networks occurs gradually and it is caused not so much by the ratio of water and isooctane, as by the ratio between water and surfactant w0. In order to

determine the reasons for this transition, five different compositions of microemulsions in the range of water number w0 from 5.5 to 0 (see Table 3.1.1) were studied and the specific surface areas of the reverse micelle per head surfactant a0 were calculated. For a dropletlike reverse micelle in the system 20_55_10 (w0 = 5.5) the occupied volume was 7 nm3, and the surface area was 12 nm2. The area per polar head was about 0.6 nm2, while the minimum area of the head itself was estimated at 0.55 nm2[103]. After reducing the water number to w0 = 2.5 in the system 38_25 a wormlike micelle was formed. Its occupied volume was about 7 nm3, and the surface area was approximately 20 nm2. Water formed a coherent structure: a flexible framework around which AOT- ions were located. Surface per head of surfactant molecule was about 0.5 nm2. This means that the surface of the water is completely occupied by a dense layer of AOT- ions. By further reducing the water content to w0 = 1.5 in the system 60_15 the shape of the wormlike micelle became distorted. Compared to systems with higher w0 the surfactant heads were packed even more densely: the surface area was approximately 25 nm2, and the surface per head was about 0.4 nm2, much less than 0.55 nm2 - minimal packing area of the head of the molecule. This leads to the displacement of individual ions AOT- from the surface, which, however, do not detach from the aggregate, but begin to form a branch. The volume occupied by the aggergate was about 9 nm3, that is, the concentration of water inside the aggregate has dropped to 10 nm-3 in comparison with 13 nm-3 in the previous case. In this case, the surfactant and water molecules could not be assembled into the wormlike aggregate without increasing the water concentration inside it, which led to the formation of a Y-shaped defect with a branch (Y-junction). The water in such system still serves as a framework for the structure, but it is not enough for the formation of a single coherent extended core. Obviously, with a slightly higher water content in the network, a continuous aqueous pseudophase will arise, which can ensure the conductivity of the solution. For a system with a water number of 0.4 a single water channel was not formed. Instead, the water acted as an equal participant in the construction of chains that formed in a three-dimensional grid. Although the surfactant ions are in contact mainly through water

molecules, in some parts of the grid it does not exist at all, and the heads of the surfactant ions are connected through sodium ions.

Thus, with a decrease in the content of water in the system relative to the surfactant, or, equivalently, with an increase in the content of the surfactant relative to water, the formation of Y-junctions becomes possible. When the concentration of worm-like micelles reaches the required value, all substances are closed, forming a grid. The closures can slide along the micellar contour therefore, the entire interconnected dynamic structure is a living mesh[37]. Molecular dynamics is a good instrument for observing closures formed directly through periodic boundary conditions (see Fig. 3.1.6). A small increase in the amount of water does not have a significant effect on the shape of the network: when the water content is not enough to form a cluster with the observed core, the water molecules are only parts of the chain. Additional water molecules cause the formation of an extended water core. It may be continuous if the amount of water is large or intermittent, if there is not enough water in the system.

Fig. 3.1.6. Snapshots of equilibrated configurations with reverse micellar networks, systems 110_605_605 (a) and 116_290_580 (b).

3.2. The evaluation of ellipticity of dropletlike AOT reverse micelles In Section 3.1, it was shown that wormlike micelles have a much lower specific surface area per surfactant head than dropletlike micelles. It is possible that the distortion of the shape of reverse micelles relative to the representational spherical shape of the water cluster is due to the same reasons for droplike reverse micelles.

Table 3.2.1. Parameters of systems with AOTNa reverse micelles. L is the size of the simulation box, Naot is the number of AOT- anions, Niso is the number of isooctane molecules, NWat is the number of water molecules, ao is the specific surface area per head of the surfactant, Ragg is the radius of the reverse micelle, e is the eccentricity of the reverse

micelle.

2 ao, nm2 Ragg, nm Naot Nwat Niso L, nm e

0.5 1 25 140 1100 6.703 0.79

0.5 1.5 57 474 1100 6.932 0.86

1 1 13 140 1100 6.646 0.67

1 1.25 20 274 1100 6.723 0.63

1 1.5 28 474 1100 6.807 0.61

1.5 1 8 140 1100 6.630 0.68

1.5 1.25 13 274 1100 6.690 0.57

1.5 1.5 19 474 1100 6.772 0.57

0.75 1 17 140 1100 6.659 0.67

0.75 1.25 26 274 1100 6.732 0.68

0.75 1.5 38 474 1100 6.833 0.67

0.625 1 20 140 1100 6.673 0.75

0.625 1.25 31 274 1100 6.756 0.71

0.625 1.5 45 474 1100 6.864 0.70

0.875 1 14 140 1100 6.645 0.61

0.875 1.25 22 274 1100 6.715 0.66

0.875 1.5 32 474 1100 6.805 0.61

0.375 0.5 9 18 1100 6.594 0.90

0.375 0.75 19 59 1100 6.651 0.93

0.5 0.75 14 59 1100 6.634 0.89

0.5 1.25 39 274 1100 6.838 0.85

0.625 0.75 11 59 1100 6.624 0.74

0.625 1.75 62 752 1650 7.865 0.70

0.625 2 80 1123 2200 8.670 0.66

2 ao, nm2 Ragg, nm Naot Nwat Niso L, nm e

0.75 1.75 51 752 1650 7.831 0.62

0.875 1.75 44 752 1650 7.811 0.57

0.875 2 57 1123 2200 8.607 0.55

1 1.75 38 752 1650 7.789 0.57

1 2 50 1123 2200 8.588 0.57

1.125 1 11 140 1100 6.648 0.65

1.125 1.25 17 274 1100 6.709 0.62

1.125 1.5 25 474 1100 6.794 0.62

1.125 1.75 34 752 1650 7.774 0.58

1.125 2 45 1123 2200 8.575 0.55

1.25 1 10 140 1100 6.639 0.63

1.25 1.25 16 274 1100 6.698 0.60

1.25 1.5 23 474 1100 6.792 0.58

1.25 1.75 31 752 1650 7.766 0.56

1.25 2 40 1123 2200 8.560 0.54

1.5 1.75 26 752 1650 7.747 0.55

1.5 2 34 1123 2200 8.544 0.52

In order to determine more accurately the effect of the system composition on the shape of the dropletlike reverse micelle, a series of systems (see Table 3.2.1) containing various concentrations of surfactants and water with a fixed amount of isooctane were simulated. Thus, one can check the dependence for the deviation of the shape of the reverse micelle from the spherical one basing on the initial specific surface area a0 and the radius of the aggregate Ragg. These two parameters were calculated with formulas obtained by Eicke [103] and Maitra [104], which were based on simple theoretical assumptions on the sphericity of reverse micelles:

Ragg = R1Nwat, (1)

a0 = ^ (2)

Naot

here NWat and Naot are numbers of molecules of water and surfactant, respectively, and R1 is the radius of the aggregate containing only one water molecule (the volume of such aggregate is equal to 0.03 nm3). These formulas are exact in the case of perfectly spherical

reverse micelles, with clearly separated regions of the core and the surface. Consequently, they are representational for describing the composition of the system, as far as they immediately give a basic representation of the size of the reverse micelle and its surface surfactant density, which can be specified after the calculation. In order to estimate the distortion of the shape of the micelle from a spherical one, the so-called elliptic

approximation is commonly used for reverse micelles, first described by Abel et. al.:[17]

2 2 2

£! + Z! + £! = I (3)

a2 b2 c2 1 ' K J

where a, b and c are semi-axes of respective ellipsoid.

The best way to describe correctly the shape of the reverse micelle within the framework of the elliptical approximation is to select such an appropriate ellipsoid for which the sum of squares of distances between the surfactant heads and the surface of which will be minimal. However, the formula for the distance between a point and the ellipsoid surface in a three-dimensional space is too complicated to be used in practice, because the number of iterations for selecting an representational object can be extremely large and so the researchers suggest other ways. In work [17] the ellipsoid semi-axes were calculated on the basis of the diagonal components of the inertia tensor for the reverse micelle as a whole. This approach allows the one to choose the shape of the micelle in accordance with the ellipsoid of the same mass and inertia tensor, though it does not take into account the mass distribution inside this ellipsoid, and therefore gives a distorted description of the surface of the micelle. In this paper, another method is proposed for describing the shape of the reverse micelle in the framework of the elliptic approximation. It is based on the following principles:

• the ellipsoid semi-axes are coinside with the axes of inertia for the reverse micelle as a whole;

• the surface of the micelle is defined as the geometric location of the highest density of surfactant heads in the system.

The algorithm checks ellipsoids with semi-axes a, b, and c, chooses an elliptic layer of 5 thickness based on these semi-axes which contains the largest number of surfactant heads compared to other layers. This layer is specified by the following system of inequations:

v2 z2

(a-0.55)2 (b-0.58)2 (c-0.58)2

*2 + ()

V(a+0.515)2 (b+0.5S)2 (c+0.5S)2

The optimal layer thickness was chosen so as to correspond to the standard deviation in the distribution of the density of the surfactant heads relative to the center of the reverse micelle, which in the case of AOT is equal to 0.3 nm. Figure 3.2.1 shows how the ellipsoid is located relatively to the surfactant heads in a particular micelle.

The eccentricity of the ellipsoid e expresses the measure of the shape distortion of the micelle from the spherical one:

e=J1-C* (5)

<

Fig. 3.2.1. The elliptical approximation of the surface for the reverse micelle 31 274 1100.

Figure 3.2.2 summarizes the results of all calculations of the parameters for micelles from Table 3.2.2 and shows how the eccentricity e depends on a0 and Ragg. The eccentricity increases with decreasing both a0 and Ragg, and vice versa. The lowest observed eccentricity was 0.52. Reverse micelles with a small specific surface area per surfactant molecule a0 < 0.5 nm2 and a small radius of the reverse micelle Ragg < 1.0 nm are the most elliptical with e > 0.8. Reverse micelles with a0 < 0.5 nm2 and Ragg > 1.0 nm are wormlike and cannot be approximated using finite-size ellipsoids. The distortion of the shape for the reverse micelle from spherical is the greatest for aggregates with low a0 and decreases with increasing a0. These data allow us to conclude that the eccentricity of the reverse micelle depends on the specific surface area per the surfactant head, and therefore on the distance between the AOT heads. On the other hand, an increase in the proportion of the surface of the reverse micelle, which is in direct contact with the oil, leads to the decrease in the eccentricity of the reverse micelle. It can be assumed that the shape of the reverse micelle is the result of a struggle between two main interactions in the system: electrostatic repulsion of the heads and entropy solvophobicity of water or the hydrophobic effect. The hydrophobic effect forces the water core to minimize its surface area[105], which leads to the formation of spherical drops, because the sphere is an object with a minimum surface area among all other objects with the equal volume. On the other hand, the electrostatic repulsion between the head surfactant groups increases simultaneously with the decrease in a0. As far as hydrogen bonds hold water molecules in the core, the only way to increase the surface area is to change the shape of the aggregate (see Fig. 3.2.3). The struggle between two competing interactions leads to the oscillations observed earlier in the simulation[63]. However, there are other reasons for the distortion of the micelle shape, such as hydration of the surfactant heads. The dependence of the morphology of AOT reverse micelles on the degree of hydration of the surfactant heads is not considered in this paper, since it has already been described in [19] and [104] .

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