Theoretical and Computational Study of Ionic Liquids Confined in Topologically Complex Micro and Nano Structures

TESIS DE DOCTORADO THEORETICAL AND COMPUTATIONAL STUDY OF IONIC LIQUIDS CONFINED IN TOPOLOGICALLY COMPLEX MICRO AND NANO STRUCTURES Hadrián Montes Campos ESCUELA DE DOCTORADO INTERNACIONAL PROGRAMA DE DOCTORADO EN CIENCIA DE MATERIALES SANTIAGO DE COMPOSTELA 2020 DECLARACIÓN DEL AUTOR DE LA TESIS Theoretical and computational study of ionic liquids confined in topologically complex micro and nano structures D. Hadrián Montes Campos Presento mi tesis, siguiendo el procedimiento adecuado al Reglamento, y declaro que: 1) La tesis abarca los resultados de la elaboración de mi trabajo. 2) En su caso, en la tesis se hace referencia a las colaboraciones que tuvo este trabajo. 3) La tesis es la versión definitiva presentada para su defensa y coincide con la versión enviada en formato electrónico. 4) Confirmo que la tesis no incurre en ningún tipo de plagio de otros autores ni de trabajos presentados por mí para la obtención de otros títulos. En Santiago de Compostela., 21 de Septiembre de 2020 Fdo.: Hadrián Montes Campos AUTORIZACIÓN DEL DIRECTOR / TUTOR DE LA TESIS Theoretical and computational study of ionic liquids confined in topologically complex micro and nano structures D. Luis Miguel Varela Cabo, catedrático del área de Física da Materia Condensada, del Departamento de Física de Partículas de la Universidade de Santiago de Compostela, INFORMA: Que la presente tesis, corresponde con el trabajo realizado por D/Dña. Hadrián Montes Campos, bajo mi dirección, y a utorizo su presentación , considerando que reúne l os r equisitos exigidos en el R eglamento de Estudios de Doctorado de la USC, y que como director de ésta no incurre en las causas de abstención establecidas en Ley 40/2015. En Santiago de Compostela, 21. de Septiembre de 2020 Fdo.: Luis Miguel Varela Cabo Resumo Os líquidos iónicos (LIs), ou sales fundidas a temperatura ambiente, son considerados hoxe en día como un dos materiais avanzados máis prome tedores e están a atraer moita atención nas últimas dúas décadas debido as súas interesantes propiedades. Os LIs son materiais formados unica mente por ións que se atopan en estado líquido a temperaturas inferiores a 100 ◦C. É xeralmente admitido que esta baixa temperatura de fusión obtense debido as grandes asimetrías entre anións e catións, as cales de bilitarían a enerxía de rede evitando así obter un sólido cunha lata sime tría. As súas propiedades, tales como a súa baixa presión de vapor, a súa nano estructuración ou a sía gran resistencia a diferencias de potencial os fan desexables para aplicacións tales como a catálise, fluídos térmi cos, lubricantes ou dispositivos electroquímicos. É nesta última aplica ción a que será obxecto de estudo preferente nesta tese. Ademais, os LIs son considerados disolventes de deseño, debido a que é posible combi nar diferentes anións e catións dando lugar a millóns de combinacións posibles. Debido a isto é posible escoller a combinación que reúna as propiedades óptimas para unha tarefa en concreto. O interese do uso de LIs en dispositivos electroquímicos debese a que teñen unha gran ventá electroquímica, é dicir, se manteñen estables baixo un amplo rango de diferencias de potencial. Esto debería permitir en teoría a fabricación de dispositivos electroquímicos con un rango de voltaxe de funcionamento maís amplo e, no caso concreto de dispositi vos para o almacenamento de enerxía, permitiría unha maior potencia e capacidade. Nestas aplicacións a rexión do espazo onde ten lugar as interaccións maís relevantes é na interfase eléctrodolíquido. Ademais, para conseguir un rendemento maior é frecuentemente desexable traba llar con eléctrodos que teñan un cociente superficie volume grande. Polo tanto, resulta imprescindíbel coñecer detalladamente como se compor tarán os LIs cando se atopen confinados en recintos con poros nanomé tricos. Este será polo tanto o obxectivo principal da tese, o análise da estructura e dinámica d LIs baixo condicións de nanoconfinamento. O estudo do confinamento será realizado por partes, comezando polo es vii DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ tudo de como a propia nano estruturación inherente dos LIs afecta a súa estrutura, pasando polo análise da estrutura dos LIs en interfases planas e rematando co estudo de LIs próticos e apróticos confinados dentro de unha nano estructura topoloxicamente complexa. Para obter istos resultados foron utilizadas ferramentas computacio nais, isto nos permite ter una ccesaccesoo directo ás propiedades micros cópicas dos LIs. Para este estudo utilizaremos diferentes técnicas depen den da da precisión coa que necesitemos traballar. En concreto as dúas ferramentas que foron maís utilizadas foron a simulación por dinámica molecular clásica (MD) e a simulación usando a teoría do funcional den sidade cuántica (DFT). As simulacións por MD foron as utilizadas para para estudar as propiedades dos LIs en escalas espaciais de decenas de nm e temporais de decenas de ns. Neste método non se incluen de forma os electróns dos átomos e polo tanto se asume que non hay unha va riación das densidades electrónicas durante o transcurso da simulación. Para a realización destas simulacións se utilizou a suite de simulación de código aberto GROMACS1xunto co campo de forzas OPLSAA,2 o cal é amplamente utilizado para simulacións de líquidos. Pola outra banda, os cálculos DFT foros os empregados para a obtención e carac terización de estruturas de equilibrio cunha gran precisión en escalas espaciais subnanométricas. O programa escollido para á realización de ditos cálculos DFT foi o programa comercial VASP.3Este programa resolve as ecuacións de KohnSham utilizando unha expansión da den sidade electrónica do sistema en ondas planas. Para á execución deste programa empregáronse diferentes funcionais de intercambio e corre lación dependendo do sistema a estudar, en concreto empregáronse os funcionais PBE e B3LYP. 1Mark James Abraham, Teemu Murtola, Roland Schulz, Szilárd Páll, Jeremy C Smith, Berk Hess, and Erik Lindahl, GROMACS: High performance molecular simulations through multilevel parallelism from laptops to supercomputers, SoftwareX, 1(19–25), 2015 (.) 2William L Jorgensen, David S Maxwell, and Julian Tirado Rives, Development and testing of the OPLS allatom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc., 118(45), 11225–11236 (1996). 3GeorgKresse and Jürgen Furthmüller, Efficient iterative schemes for ab initio total energy calculations using a planewave basis set, Phys. Rev. B, 54(16), 11169 (1996). viii Resumo Comezamos o estudo da estructura baixo confinamento dos LIS no Capítulo 4 cunha avaliación da validez do campo de forzas a empre gar durante os seguintes estudos. En concreto se avaliaron as diferen cias na estructura en na dinámica dunha mistura de bis(trifluorometil sulfonil)amida (TFSI) 1butil3metilimidazolio (BMIM) con bis(tri fluorometilsulfonil)amida de litio. Para elo realizaronse simulacións MD con campos de forzas polarizables e nonpolarizables. O campo de forzas nonpolarizable que escollimos para o estudo foi o OPLS AA, mentras que para o campo de forzas polarizable escollimos o AP PLE&P.4Ademais, se engadiu unha versión do campo de forzas AP PLE&P cos términos de polarización desactivados (APPLE&PNP), pe ro se modificar ningún outro parámetro do potencial co fin de avaliar se é preciso recalcular os parámetros de un campo de forzas ao acender ou apagar os termos de polarización. A escolla de este sistema debeuse a que, debido ña elevada densidade electrónica presente non ións de litio, a polarizabilidade do campo de forzas debería xogar un papel moi im portante nas propiedades deste sistema. Para istos sistemas analizáronse tanta a estructura como a dinámica monoparticular. A primeira avaliá ronse a través da función de distribución radial (RDF) e a súa integral, a cal se corresponde co número de coordinación a unha determinada distancia. A dinámica, polo outra banda, avaliouse utilizando os despra zamentos cadráticos medios, a función de autocorrelación da caixa de solvatación a función de autocorrelación de velocidades e a súa trans formada de Fourier, a densidade vibracional de estados. A estructura mostrou estruturas moi similares para os dous campos de forzas com pletamente optimizados (OPLSAA e APPLE&P), mostrando só peque nas diferencias nas distancias de equilibrio entre o litio eo LI. Pola outra banda, o campo de forzas APPLE&PNO mostrou unha coordinación do litio moi diferente á obtida mediante os outras campos de forzas. No tocante á dinámica a polarizabilidade xoga un papel moi relevante, con grandes diferencias no desprazamento cadrático medio entre o campo de forzas polarizable e o nonpolarizable. A propiedade máis afectada resultou ser a función de correlación da caixa de solvatación. Dita fun 4O. Borodin, Polarizable force field development and molecular dynamics simulations of ionic liquids, J. Phys. Chem. B, 113(33), 11463–11478 (2009). ix Resumen Los líquidos iónicos (LIs), o sales fundidas a temperatura ambiente, se consideran hoy uno de los materiales avanzados más prometedores y han ganado mucha atención en las últimas dos décadas debido a sus interesantes propiedades. Los LIs son materiales formados únicamente por iones que se encuentran en estado líquido a temperaturas inferio res a 100 ◦C. Es generalmente admitido que esta baja temperatura de fusión se obtiene debido a las asimetrías entre aniones y cationes, las cuales debilitarían la energía de red evitando obtener un sólido con alta simetría. Sus propiedades, tales como su baja presión de vapor, su nano estructuración o su gran resistencia a diferencias de potencial los hacen deseables para aplicaciones tales como la catálisis, fluidos térmicos, lu bricantes o dispositivos electroquímicos. Es esta última aplicación la que será objeto de estudio preferente en esta tesis. Además, los LIs son considerados disolventes de diseño, debido a que es posible combinar diferentes aniones y cationes dando lugar a millones de combinaciones posibles. Debido a esto es posible escoger la combinación que reúna las propiedades óptimas para una tarea en concreto. El interés del uso de LIs en dispositivos electroquímicos se debe a que tienen una gran ventana electroquímica, es decir, se mantienen es tables bajo un amplio rango de diferencias de potencial. Esto debería permitir en teoría la fabricación de dispositivos con un mayor voltaje de funcionamiento y, en el caso de dispositivos para almacenamiento de energía, una mayor potencia y capacidad. En estas aplicaciones la región del espacio donde tienen lugar las interacciones mas importan tes es la interfase electrodolíquido. Además, para conseguir una mayor rendimiento es frecuentemente deseable trabajar con electrodos con un amplio cociente superficievolumen. Por lo tanto, resulta imprescindible conocer como se comportarán los LIs cuando se encuentren confinados en recintos nanoporosos. Este será por lo tanto el objetivo principal de la tesis, el análisis de la estructura y dinámica de LIs nanoconfinados. El estudio del confinamiento será realizado por partes, empezando por como la propia nanoestructuración de los LIs afecta a su estructura, pa xvii DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ sando por el análisis de la estructura de los LIs en interfases planas y finalizando con el estudio de LIs próticos y apróticos confinados dentro de una nanoestructura topológicamente compleja. Para obtener estos resultados utilizaremos herramientas compu tacionales, que nos permiten un acceso directo a las propiedades microscópicas de los LIs. Para el estudio utilizaremos diferentes técnicas según la precisión con la que necesitemos trabajar. En concreto las dos herramientas que más hemos utilizado fueron la simulación por dinámica molecular (MD) y la simulación usando la teoría del funcional densidad cuántica (DFT). Las simulaciones por MD fueron utilizadas para estudiar los LIs en escalas espaciales de decenas de nm y temporales de decenas de ns. En este método no se incluyen de forma explícita los electrones de los átomos y se asume que no hay variación de las densidades electrónicas en la simulación. Para realizar estas simulaciones se usó la suite de simulación de código abierto GROMACS1y el campo de fuerzas OPLSAA,2el cual es ampliamente utilizado para simulaciones de líquidos. Por otro lado, los cálculos DFT fueron utilizados para la obtención y caracterización de estructuras de equilibrio con gran precisión en escalas subnanométricas. Para la realización de dichos cálculos DFT hemos utilizado el programa co mercial VASP.3Este programa resuelve las ecuaciones de KohnSham utilizando una expansión de la densidad electrónica en ondas planas. Se han utilizado diferentes funcionales de intercambio y correlación dependiendo del sistema de estudio, en concreto se ha utilizado los funcionales PBE y B3LYP. Comenzamos el estudio de la estructura bajo confinamiento de los LIs en el Capítulo 4 con una evaluación de la validez de los métodos 1Mark James Abraham, Teemu Murtola, Roland Schulz, Szilárd Páll, Jeremy C Smith, Berk Hess, and Erik Lindahl, GROMACS: High performance molecular simulations through multilevel parallelism from laptops to supercomputers, SoftwareX, 1(19–25), 2015 (.) 2William L Jorgensen, David S Maxwell, and Julian Tirado Rives, Development and testing of the OPLS allatom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc., 118(45), 11225–11236 (1996). 3GeorgKresse and Jürgen Furthmüller, Efficient iterative schemes for ab initio total energy calculations using a planewave basis set, Phys. Rev. B, 54(16), 11169 (1996). xviii Resumen utilizados. En concreto se evaluaron las diferencias en la estructura y la dinámica de una mezcla de bis(trifluorometilsulfonil)amida (TFSI) 1butil3metilimidazolio (BMIM) con bis(trifluorometilsulfonil)ami da de litio usando simulaciones MD con campos de fuerza polarizables y nopolarizables. El campo de fuerza nopolarizable utilizado fue el OPLSAA, mientras que el polarizable fue el APPLE&P.4Además, se añadió una versión del campo de fuerzas APPLE&P con la polarización apagada (APPLE&PNP), pero sin modificar ningún otro parámetro del potencial con el fin de evaluar si es necesario recalcular los parámetros de un campo de fuerza al encender o apagar los términos de polariza ción. Este sistema fue escogido ya que, debido a la elevada densidad electrónica de los iones de litio, la polarizabilidad del campo de fuerzas debería jugar un papel muy importante en las propiedades del sistema. Para estos sistemas se analizaron la estructura y la dinámica monoparti cular. La primera fue evaluada a través de función de distribución radial (RDF) y su integral, la cual nos da el número de coordinación a una de terminada distancia. La dinámica, por otro lado, fue evaluada utilizando desplazamientos cuadráticos medios, la función de autocorrelación de la caja de solvatación, la función de autocorrelación de velocidades y su transformada de Fourier, la densidad vibracional de estados. La estruc tura mostró estructuras muy similares para los dos campos de fuerzas completamente optimizados (OPLSAA y APPLE&P), con solo peque ñas diferencias en las distancias de equilibrio del litio. Por otro lado, el campo de fuerzas APPLE&PNP mostró una coordinación del litio muy diferente a la obtenida con los otros campos de fuerzas. En lo to cante a la dinámica la polarizabilidad juega un papel muy relevante, con grandes diferencias en el desplazamiento cuadrático medio. La propie dad más afectada es la función de correlación de la caja. Dicha función muestra un tiempo de residencia del litio en su caja de solvatación órde nes de magnitud mayor en el caso del campo de fuerzas nopolarizable que en el del polarizable. La función de autocorrelación de velocidades muestra un menor tiempo de colisión en el caso del campo de fuerzas nopolarizable, lo cual puede asociarse con una mayor fuerza promedio 4O. Borodin, Polarizable force field development and molecular dynamics simulations of ionic liquids, J. Phys. Chem. B, 113(33), 11463–11478 (2009). xix DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ en la configuración de equilibrio. Sin embargo un análisis de la densidad vibracional de estados muestra que ambos campos de fuerza producen distribuciones similares, pero con un corrimiento hacia el azul para el campo de fuerzas no polarizable. Este estudio nos permite concluir que los campos de fuerza nopolarizables son adecuados para estudiar la es tructura, pero no la dinámica y que tras añadir la polarización a un campo de fuerzas es necesario recalcular sus parámetros. Con el campo de fuerzas apropiadamente validado continuamos nuestro estudio analizando la nanoestructura propia del LI (Capítulo 5). Esta nanoestructura impone un confinamiento en regiones polares y apolares intrínseco al LI. Dicho confinamiento da lugar al paradig ma de la solvatación nanoestructurada, según el cual otras molécu las son disueltas en las diferentes regiones del seno del LI atendien do a su polaridad. Por lo tanto moléculas polares se disolverán en los nanodominios polares del LI y las apolares en los nanodominios apo lares. Para comprobar este paradigma se realizaron simulaciones de MD de nitrato de etilamonio (EAN) y nitrato de butilamonio (BAN) mez clado con 1propanol, 1butanol y 2pentanol. La particularidad de es tos alcoholes es que muestran una cabeza polar y una cadena alquíli ca apolar. Dado que son anfifílicas, según el paradigma de la solvata ción nanoestructurada deberían ser disueltas en la interfase entre los nanodominios polar y apolar. Además, este comportamiento anfifílico lo comparte con el catión del LI, por lo que deberíamos ver una compe tición entre ambas moléculas por la misma región del seno del LI. Para evaluar esta competición estudiamos la estructura y la dinámica mono particular de dichas mezclas. La estructura fue evaluada utilizando la RDF, la función de distribución espacial y el número de enlaces de hi drógeno por molécula. La dinámica fue evaluada utilizando la función de correlación de velocidades y su transformada de Fourier. Las RDFs no mostraron cambios significativos al añadir alcohol frente a la dis tribución del LI puro. Por otro lado, la función de distribución espacial mostró que, efectivamente, tanto el alcohol como el catión compiten por la misma región del espacio alrededor de los aniones, con la salvedad de que la capacidad de formar múltiples enlaces de hidrógeno del ca tión le permite acceder a una configuración bidentada. El análisis del xx Resumen número de enlaces de hidrógeno por molécula corroboró dicha imagen mostrando un reemplazo gradual de las moléculas del catión por mo léculas de alcohol a medida que la concentración de alcohol aumenta. Por otro lado, la dinámica no mostró diferencias significativas para el LI puro y el mezclado con alcohol. Esto nos permitió concluir que la ima gen propuesta por la solvatación nanoestructurada es correcta y que en LIs con una amplia red de enlaces de hidrógeno esta interacción es tan importante como la interacción de Coulomb entre aniones y cationes. A continuación procedimos a estudiar la interfase electrodoLI para sistemas con electrodos planos (Capítulos 6, 7 y 8). Comenzamos estu diando la estructura de la interfase en las direcciones paralelas a la in terfase (Capítulo 6). Para ello utilizamos simulaciones de [BMIM][BF4] con diferentes aditivos confinados entre dos electrodos de grafeno. El análisis de la estructura en dichas direcciones mostró la existencia de dos conformaciones diferentes para los aniones en el ánodo. Depen diendo de la composición exacta del LI, este se configuraba siguiendo un patrón hexagonal o uno de bandas. Para estudiar dicho fenómeno planteamos un modelo teórico basado en la teoría fenomenológica de LandauBrazovskii. Este modelo predice la existencia de diferentes fa ses, incluyendo patrones de bandas, hexagonales y una homogéneos. La configuración final del sistema según este modelo depende solo de la densidad de carga efectiva en la interfase y el tipo de patrones posibles debería ser, por lo tanto, independiente del electrodo y del LI. Además, para confirmar estos resultados realizamos simulaciones de Monte Carlo de modelos genéricos de iones sobre una red. Usando este modelo pudi mos obtener un diagrama de fases de que patrón debería ser el resultante dependiendo de las interacciones anióncatión y cuyos resultados con cuerdan con los de MD. Estos resultados teóricocomputacionales pre dicen por lo tanto la existencia de al menos dos patrones posibles para los iones en la interfase eletrodoLI. Además, dichos patrones deberían ser modificables externamente por cualquier interacción que pueda mo dificar la densidad de carga efectiva en el electrodo. Con el fin de estudiar como se produce el cambio entre estos patro nes, en el Capítulo 7 realizamos un estudio extensivo de las propiedades xxi DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ de dichos patrones para una mezcla de [BMIM][BF4] con LiBF4confi nada entre dos electrodos de grafeno. A estos electrodos se le añadieron defectos de vacantes con el fin de crear modificaciones locales de la densidad de carga en la interfase. Estos cambios en las densidades de carga deberían, según el estudio anterior, ser capaces de modificar la es tructura bidimensional de la interfase. Para ello comenzamos realizando un estudio de cómo se ve modificada la estructura y distribución de car ga del grafeno al añadir vacantes. Este estudio preliminar mostró que el grafeno se mantiene plano tras quitar uno de sus átomos. Además, usan do dichos resultados creamos un modelo sencillo de redistribución de la carga de la vacante entre sus átomos vecinos. Usando este modelo rea lizamos simulaciones de MD con diferentes fracciones de defectos dis tribuidos aleatoriamente. Los resultados de dichas simulaciones fueron analizados usando la distribución de la densidad, tanto en la dirección perpendicular como en las direcciones paralelas a la interfase, funciones de correlación de la densidad y distribuciones de energía potencial en el electrodo. Además, se utilizó el algoritmo de Otsu para dividir la inter fase en regiones con y sin aniones para una evaluación más profunda de las propiedades de los patrones. Este estudio mostró que los defectos no son capaces de alterar significativamente la estructura del LI en la dirección perpendicular a la interfase. Sin embargo, estos defectos son capaces de modificar el patrón en las direcciones paralelas a la interfase. Además, dicho cambio no se produce de forma gradual, sino que se pro duce de forma repentina al superar una fracción crítica de defectos. Este estudio mostró además que la transición entre patrones bidimensionales puede modificar propiedades macroscópicas del sistema. Acabamos el estudio de interfases planas en el Capítulo 8 estudian do mezclas de [BMIM][BF4] con LiBF4confinado entre dos electrodos de borofeno. Estos electrodos tienen la particularidad de ser rugosos a nivel atómico. Este estudio fue pionero en el estudio de interfases de borofeno con LI y nos permite evaluar los efectos que las rugosidades puedan tener en el LI. Comenzamos el estudio con un cálculo DFT de la distribución de cargas de una monocapa de borofeno cargado. Es tas distribuciones de carga fueron usadas a continuación para realizar simulaciones de MD del sistema. En estas simulaciones analizamos la xxii Resumen estructura del LI a través de las distribuciones de densidad (tanto en la dirección perpendicular a la interfase como en las direcciones paralelas) y de la orientación de los iones en la interfase. Además, la dinámica mo noparticular fue analizada usando la densidad vibracional de estados. La distribución de la densidad en la dirección perpendicular a la interfase y la orientación de los iones mostró resultados muy similares a las de las simulaciones de grafeno, lo cual indica que la estructura es a grandes ras go similar a la del LI confinado entre electrodos de grafeno. El análisis de la densidad bidimensional mostró sin embargo notables diferencias entre ambos sistemas con una transición de un patrón hexagonal para el grafeno a un patrón de bandas en el borofeno. Este cambio parece estar inducido por las nanorugosidades del electrodo. Por lo tanto podemos concluir que las rugosidades del electrodo afectan solo a la primera capa de LI junto a la interfase, pero que no producen efecto alguno en el seno del fluído. Antes de proceder al estudio de LIs dentro de una estructura topoló gicamente compleja realizamos un modelo teórico para explicar el trans porte en LIs (Capítulo 9). Este modelo intenta explicar las diferencias experimentales para la conductividad con el modelo de BaheVarela5 para altas concentraciones de materia iónica. Nuestro modelo modela el seno del fluido como una mezcla de regiones de alta y baja movilidad, de la misma forma que el modelo original de BaheVarela. Sin embar go, introdujimos una dependencia extra a las frecuencias de salto entre regiones. Mientras que en el modelo original las frecuencias dependían únicamente del tipo de celda inicial, en el nuevo modelo dependen tan to de la celda inicial como de la final. Esto conlleva la inclusión de un nuevo término en la teoría que tiene en cuenta el exceso de frecuencia de salto entre celdas de diferente tipo. Este modelo puede ser utilizado para explicar la conductividad de mezclas de LIs y disolventes mole culares y de disoluciones electrolíticas en general en todo el rango de concentraciones con éxito. 5L M Varela, J Carrete, M García, L J Gallego, M Turmine, E Rilo, and O Cabeza, Pseudolattice theory of charge transport in ionic solutions: Corresponding states law for the electric conductivity, Fluid Phase Equilibria, 298(2), 280–286 (2010) xxiii DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Finalmente procedimos al estudio del comportamiento de LIs próticos y aproticos dentro estructuras topológicamente complejas con multiples poros interconectados (Capítulo 10). Para ello hemos realizado simulaciones MD de un LI prótico (EAN) y un LI aprótico ([EMIM][BF4]) dentro de nanotubos de carbono (CNT) y dentro de una estructura de carbono templado en zeolita (ZTC). Esta estructura ZTC contiene poros en diferentes direcciones del espacio que se interconec tan formando cavidades. Esto le confiere un gran cociente superficie volumen deseable en electrodos reales. El estudio incorporó dos partes. En la primera se analizan las propiedades estructurales y dinámicas de los LIs dentro de CNTs de diferentes radios para usar como referencia de las propiedades dentro de la ZTC. A continuación se estudiaron las mismas propiedades dentro de la ZTC. Para las propiedades estruc turales se utilizó la densidad, la RDF, así como su integral tanto para los CNTs como para la ZTC. Además, para los CNTs se estudió su factor de estructura y la densidad radial de partículas. Para la dinámica monoparticular se estudiaron los desplazamientos cuadráticos medios y las densidades vibracionales de estado. La estructura de los LIs dentro de los CNTs muestra dos regímenes diferentes, uno cuando el radio del CNT es inferior al tamaño típico de un par iónico y otro cuando es superior. En los CNTs más estrechos la estructura está dominada por efectos estéricos y ambos LIs muestran estructuras puramente unidimensionales. Cuando se supera el tamaño típico de un par iónico las interacciones coulombianas anióncatión empiezan a ser importantes y se aprecian diferencias estructurales entre ambos LIs a medida que se incrementa el radio y la estructura deja de ser unidimensional. Los LIs dentro de CNTs muestran además una dinámica acelerada con respecto al seno del fluido, con un desplazamiento cuadrático medio mayor y un desplazamiento hacia el azul de la densidad vibracional de estados. Por otro lado, los mismos LIs dentro de la ZTC muestran una estructura más parecida a la del interior del fluido, lo cual deja entrever que el aumento de la dimensionalidad dentro de dichas estructuras tiene un papel fundamental. Además, la estructura del LI prótico es más parecida a la del seno del fluido que a la del LI aprótico. Esta recuperación acelerada de la estructura del LI libre parece estar causada xxiv Resumen por la red de enlaces de hidrógeno presente en LI prótico. La dinámica por otro lado muestra un comportamiento parecido a la de los CNTs para la densidad vibracional de estados, mientras que en el rango de estudio el desplazamiento cuadrático medio se mantuvo en régimen subdifusivo. Además, proponemos estudiar la ZTC como una estructura de dimensionalidad intermedia entre uno y tres. Esto nos permite modelar la estructura del LI dentro de la ZTC como la combinación de una estructura puramente unidimensional (obtenida de las simulaciones de los CNTs) y una tridimensional. Este modelo es capaz de predecir la densidad del sistema y la coordinación de los iones utilizando la distribución de tamaño de poro de la estructura ZTC. La dinámica sin embargo no es sencilla de calcular utilizando dicho modelo y es necesario desarrollar trabajo adicional en esta dirección (similar al presentado en el Capítulo 9). La tesis finaliza con unas conclusiones generales y con potenciales lineas de investigación futuras (Capítulo 11). Además se presenta una lista de publicaciones relacionadas, pero no contenidas, en la tesis. xxv DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ tential energy distribution in the electrode. Moreover, Otsu’s algorithm was used to divide he interface in regions with and without anions in order to perform a deeper evaluation of the properties of the patterns. This study showed that the defects are not able to significantly modify the IL structure in the direction perpendicular to the interface, However, these defects are able to modify he pattern in the directions parallel to the interface. Moreover, that change is not produced in a gradual way, but it changes suddenly once a critical fraction of defects in achieved. This study showed also that the transitions between the twodimensional patterns can modify macroscopic properties of the system. We finish the study of planar interfaces in Chapter 8 with the study of the same mixtures of [BMIM][BF4] with LiBF4confined between borophene electrodes. This electrodes have the particularity of having roughness at the atomic level. This study is pioneer in the analysis of ILborophene interfaces and allow us to evaluate the effects that rough ness may have on the IL. We start the study with a DFT calculation fo the charge distribution of a charged borophene layer. This charge distri bution is used then to perform MD simulations of the system. In these simulations we analyzed the structure of the IL using the density distri bution (both in the perpendicular and parallel directions to the interface) and the orientation of the ions at the interface. Moreover, the single particle dynamics was analyzed using the vibrational density of states. The density distribution in the directions perpendicular to the interface showed very similar results to the graphene ones, which indicates that the structure is pretty much the same than the one of IL confined between graphene electrodes. The analysis in the parallel direction, however, showed notable differences between both system with a transition from an hexagonal pattern in the case of graphene to an stripped pattern for the borophene. This change sees to be induced by the nanoroughness of the electrode. Thus, we can conclude that the roughness of the electrode only affect to the first layer of IL next to the interface, but they do not produce any effect in the bulk IL. Before proceeding to the study of IL inside a topologically complex structure, we designed a theoretical model to predict the transport in ILs xxxii Summary (Chapter 9). This model tries to explain the experimental differences of the conductivity with the BaheVarela model5for high concentrations of ionic matter. Our model treats the IL bulk as a mixture of high and low mobility regions, in the same way than the original BaheVarela model. However, we introduce an extra dependence to the jumping frequencies between the regions. While in the original model, jumping frequencies were only dependent on the mobility of the initial region, in this new model they depend on both the initial and final regions. This leads to the inclusion of a new parameter in the theory that accounts for the jumping frequency excess between region of different type. This model can be successfully used to predict the conductivities of mixtures of ILS and molecular solvents and electrolytic mixtures in the whole concentration range. Finally we proceed to the study of the behaviour of protic and aprotic ILs inside topologically complex structures with multiple interconnected pores (Chapter 10). For this study we performed MD simulations of a protic (EAN) and an aprotic ([EMIM][BF4]) IL inside carbon nanotubes (CNTs) and inside a zeolitetemplated carbon (ZTC) framework. This ZTC framework have multiple pores in different directions that interconnect creating cavities. This gives a large surface to volume ratio with is desirable in real electrodes. The study is split in two parts. In the first one the structural and dynamic properties of ILs inside CNTs of different radii to be used as a reference for the properties inside the ZTC. Then the same properties properties are analyzed inside the ZTC. The structural properties are analyzed using the density, the RDF and its integral fo the ILs inside the CNTs and the ZTC framework. Moreover, inside the CNTs the structure factor and the radial density are also analyzed. The singleparticle dynamics of the ILs inside the ZTC and the CNTs is analyzed using the mean squared displacement and the vibrational density of states. The structure of the ILs inside the CNTs show two different regimes, one when the radius of the CNT is smaller than the typical ion pair size and another 5L M Varela, J Carrete, M García, L J Gallego, M Turmine, E Rilo, and O Cabeza, Pseudolattice theory of charge transport in ionic solutions: Corresponding states law for the electric conductivity, Fluid Phase Equilibria, 298(2), 280–286 (2010). xxxiii DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ when it is higher. In the narrower CNTs the structure is dominated by steric effects and both ILs show purely onedimensional structures. When the radius is higher than the typical ion pair size the anioncation Coulombic interactions start to be relevant and structural differences between both ILs appear as the CNT radius increases and the structure stops being purely onedimensional. The ILs inside the CNTs show also an accelerated dynamics with respect to the bulk one, showing a higher mean square displacement and a blueshift of the vibrational density of states. On the other hand, the same ILs inside the ZTC structure show a structure more similar to he bulk one, which suggest that the increase of dimensionality inside those structures have a fundamental role. Moreover, the structure of the protic IL is closer to its bulk one that the aprotic IL. This accelerated recovery of the bulk structure seems to be caused by the extensive hydrogenbonding network present in the protic IL. On the other hand, the dynamics shows a behaviour similar to the CNTs for the vibrational density of states, while the mean squared displacement slowed down and showed a subdiffusive regime in the whole range of study. Moreover, we studied the ZTC as an structure with a fractional dimensionality between one and three. This allows us to model the structure of the IL inside the ZTC as a combination of a purely onedimensiona structure (obtained from the CNT simulations) and threedimensional one. Using this model we are able t predict the density of the system and the ionic coordination using the pore size distribution of the ZTC framework. The dynamics, however, cannot be calculated easily using that model and more work in this direction (similar to the present in Chapter 9) is required. The thesis ends with some general conclusions to the thesis and po tential future research lines (Chapter 11). Moreover a list of publications related, but not included, in this thesis is presented. xxxiv Cargando contenido… Por favor, manténgase a la espera. Agradecimientos Esta tesis representa mi trabajo de los últimos 4 años, sin embargo, este no sería posible sin la presencia de personas que me han apoyado du rante el camino. Es por ello que quiero dedicar las siguientes lineas a agradecerles su contribución a esta tesis. • A mi familia, mis padres y mi hermano, por su continuo apoyo, especialmente en los momentos más duros. Sin ellos esta tesis no habría sido posible. • A Yara, por darme su apoyo y aguantarme con mis estreses, es pecialmente durante estos últimos meses. Además, por ser una compañera perfecta para el confinamiento. • A mi director de tesis, Luis, por su apoyo y consejos, tanto cien tíficos como personales. • A Txema, como compañero de trabajo y amigo. Sin nuestras con versaciones y nuestros planes para automatizar todo hasta niveles absurdos muchos de los resultados de esta tesis no existirían. • A Víctor y Alex, por sus interminables conversaciones en el des pacho. • A mis amigos, especialmente a Carlos y Adrián, por estar ahí y apoyarme siempre que lo he necesitado, además de las cañas de los fines de semana. • A Jesús Carrete, por su apoyo, conversaciones y conocimiento sobre cervezas mostrado durante mi estancia en Viena. • A Luis Javier Gallego, por su apoyo, consejos y discusiones cien tíficas, así como al resto de compañeros de Nafomat (Trini, Borja, Julio, …) por su apoyo constante. xxxvii DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Además, también agradezco la financiación y recursos aportados por las siguientes entidades. Agradezco al Centro de Supercomputación de Galicia los recursos disponibles a mi disposición y al Ministerio de Educación por su financiación mediante una ayuda para formación de profesorado universitario (FPU). Además, la tesis fue realizada con las ayudas de los proyectos MAT201457943C31P, MAT 201457943C32P, MAT201457943C31P, MAT201457943C32P, MAT201789239C21P, MAT201789239C212P, CTQ201565816 R and PGC2018093745BI00 y FIS201233126 del Ministerio de Economía y Competitividad. Además, esta tesis recibió financiación de la Xunta de Galicia a través de la red gallega de líquidos iónicos (REGALIS CN 2014/1015), AGRUP 2015/11, ED431D 2017/06, ED431E 2018/08 y GRC ED431C 2016/001. También se recibió apoyo de la Unión Europea a través de acciones COST (CM1206 y MP1303). La tesis fue financiada parcialmente con fondos FEDER. xxxviii Contents List of Figures 4 List of Tables 14 List of publications included in this thesis 15 List of publications related to this thesis 17 I Introduction and Methods 19 1 Introduction 21 1.1 Motivation and purpose . . . . . . . . . . . . . . . . . 21 1.2 Properties of ionic liquids . . . . . . . . . . . . . . . . 25 2 Methods 29 2.1 Computational tools . . . . . . . . . . . . . . . . . . . 29 2.2 Pseudolattice theory of charge transport in ionic solutions 46 II Results 51 3 Summary of the Results 53 1 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ 4 Molecular dynamics analysis of the effect of electronic po larization on the structure and singleparticle dynamics of mixtures of ionic liquids and lithium salts 57 4.1 Introduction....................... 69 4.2 Theoretical section . . . . . . . . . . . . . . . . . . . 71 4.3 Simulation details . . . . . . . . . . . . . . . . . . . . 75 4.4 Results and discussion . . . . . . . . . . . . . . . . . 78 4.5 Conclusions....................... 90 5 Nanostructured solvation in mixtures of protic ionic liquids and longchained alcohols 93 5.1 Introduction....................... 105 5.2 Computational procedure . . . . . . . . . . . . . . . . 108 5.3 Experimental measurements . . . . . . . . . . . . . . 108 5.4 Results and discussion . . . . . . . . . . . . . . . . . 109 5.5 Large scale structure . . . . . . . . . . . . . . . . . . 120 5.6 Conclusions....................... 121 6 Twodimensional pattern formation in ionic liquids con fined between graphene walls 125 6.1 Introduction....................... 135 6.2 Computational Details . . . . . . . . . . . . . . . . . 137 6.3 Results and Discussion . . . . . . . . . . . . . . . . . 139 6.4 Conclusions....................... 152 7 Mixtures of Lithium Salts and Ionic Liquids at Defected Graphene Walls 155 7.1 Introduction....................... 165 7.2 Simulation Details . . . . . . . . . . . . . . . . . . . 168 7.3 Results and Discussion . . . . . . . . . . . . . . . . . 171 7.4 Conclusions....................... 181 8 Borophene vs. Graphene Interfaces: Tuning the Electric Double Layer in Ionic Liquids 185 8.1 Introduction....................... 195 8.2 Computational details . . . . . . . . . . . . . . . . . . 198 2 CONTENTS 8.3 Results and discussion . . . . . . . . . . . . . . . . . 198 8.4 Conclusions....................... 211 9 Randomalloy Model for the Conductivity of Ionic Liquid–Solvent Mixtures 213 9.1 Introduction....................... 221 9.2 Pseudolattice theory for ionic conductivity . . . . . . 222 9.3 Conductivity of ionic systems . . . . . . . . . . . . . 226 9.4 Conclusion ....................... 232 10 Structure of protic and aprotic ionic liquid inside carbon nanotubes and zeolite templated carbon structures 235 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 249 10.2 Computational details . . . . . . . . . . . . . . . . . . 251 10.3Results.......................... 255 10.4Conclusions....................... 272 IIIConclusions 277 11 Conclusions and Future Perspectives 279 11.1Conclusions....................... 279 11.2 Future Perspectives . . . . . . . . . . . . . . . . . . . 281 A Supplementary Information 283 A.1 Supplementary information for: Mixtures of Lithium Salts and Ionic Liquids at Defected Graphene Walls . . 285 A.2 Supplementary information for: Randomalloy Model for the Conductivity of Ionic Liquid–Solvent Mixtures 299 A.3 Supplementary information for: Ionic liquids nanocon fined in zeolitetemplated carbon: a computational study 311 Bibliography 317 3 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ 8.7 Orientational probability density functions as a function of cos(θ)and the zdistance to the wall for the IL cations in the first layer, P(cos(z,θ)), for LiBF4+[BMIM][BF4] near graphene (left) and borophene (right) walls of different sur face charges: (a) negative, (b) neutral. . . . . . . . . . . . 208 8.8 Average distance of closest approach to the wall of salt cations, for all the wall charges and surfaces considered in this paper. Dashed lines are guides to the eye. . . . . . . . 209 8.9 vDOS (S(ν)) comparison of lithium salt cations in bulk (shaded in blue) and near a graphene wall (a) or borophene wall(b)............................ 210 9.1 Randomalloy and ideal models for the conductivity of BMIMPF6in 2(N,Ndimethylamino)ethanol (dMAEt). (a) Conductivity of BMIMPF6dissolved in dMAEt at T=288.15K as a function of the volume fraction of BMIMPF6. The idealsolution model is given by Eq. (9.2) and the randomalloy model by Eq. (9.8). (b) The same as (a) but expressed in the scaled form, where σmax is the maximum conductivity and φmax is the corresponding BMIMPF6volume fraction. (c)(d) The same as (a)(b) but for T=323.15K. For comparison, solid lines in (b) and (d) show the universal scaling form given by Eq. (9.4). All fitting parameters are listed in Supplementary Table S1. See also Fig. 9.2. The experimental data have been taken fromref.329. ....................... 227 10 List of Figures 9.2 Temperature dependence of the randomalloy model for BMIMPF6in 2(N,Ndimethylamino)ethanol (dMAEt). Experimental data for various values of temperature have been fitted to the randomalloy model, Eq. (9.8) (see Fig. 9.1 for examples). The fitting parameters σIL,˜νBand ∆νare shown by symbols as functions of temperature. (a) Temperature dependence of σIL (conductivity of neat BMIMPF6) and ˜νB. The lines show the fit of σIL and ˜ν to the Arrhenius law. (b) Temperature dependence of ∆ν. The line shows the result of fitting ∆νto Eq. (9.10). The shaded areas mark the regions in which we have applied the Arrhenius law. All fitting parameters are listed in Supplementary Tables S1 and S2. See also Supplementary Fig. S1. The experimental data have been taken from ref. 329. ............................. 229 9.3 Effect of alkyl chain length (n) on the conductivity of EMIMAlkyl sulphates in water and ethanol. Conductivity of neat EMIMAlkyl sulphates σIL (a), and jumping frequencies ˜νB(b) and ∆ν(c), as functions of the alkyl chain length. The parameters σIL,˜νand ∆νhave been oobtained by fitting the experimental data from ref. 323 to the randomalloy model, Eq. (9.8). The deviations for water and ethanol in (a) are due to experimental inaccuracy. For the fitting results see Supplementary Table S3 and Supplementary Fig. S2 and S3; see also Supplementary Fig.S4. ........................... 230 9.4 Conductivity of aqueous aluminium bromide (AlBr3). The conductivity is shown as a function of AlBr3volume fraction. The ideal model is given by Eq. (9.2) and the randomalloy model by Eq. (9.8). The vertical dash line denotes the highest AlBr3concentration soluble in water, φsolv ≈0.26, which was obtained by treating φsolv as an additional fitting parameter. The remaining parameters are σIL ≈23 mS cm−1,˜νB≈26 and ∆ν≈−2.9. The experimental data have been taken from ref. 330. . . . . . 232 11 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ 10.1 Representation of the ZTC showing some of its nanopores. 251 10.2 Representation of the two ILs used in the study. . . . . . . 252 10.3 Pore size distribution of the ZTC. The yellow region corres ponds to the range of CNTs radii studied in this article. . . 253 10.4 Snapshots of the setup used for filling the CNTs (a) and the ZTC (b). In the latter, the hydrogen atoms have been removed from the visualization and the ZTC atoms are colored orange for an easier viewing. . . . . . . . . . . . . 254 10.5 Comparison between the simulated density for the nan otube and the different models of the density. Circles correspond to the densities calculated in this article (blue for [EMIM][BF4] and orange for EAN), squares to the data of Ref.356 for a LennardJones fluid, the dotted line corresponds to the fitting of the IL densities to Eq. 10.1 and the dashed one to the model of Ref.356. . . . . . . . . 256 10.6 Structure factor for EAN (top) and [EMIM][BF4] (bottom) in the z direction inside CNTs of different radii. . . . . . . 258 10.7 Radial density of the confined ILs. The grey area corres ponds to the fraction of the radius that is occupied by car bons of the CNT wall (i.e σc/2). The cation tail and cation head correspond to the alkyl tail and the charged region of the cations, respectively (see Fig. 10.2). . . . . . . . . . . 259 10.8 Integral of the radial distribution function between anions and cations for EAN (top) and [EMIM][BF4] (bottom) for different nanotube radius. The value for the bulk simulation is in the background as reference. . . . . . . . . . . . . . . 261 10.9 Vibrational density of states for cations (left) and an ions (right) in nanotubes filled with EAN (top) and [EMIM][BF4] (bottom) for different nanotube radius. . . . 262 10.10Mean square displacement in the z direction inside the nanotube for the IL cations, in top plot for EAN and for [EMIM][BF4] in the bottom one. . . . . . . . . . . . . . . 263 10.11Position of the wall that pushed the IL inside the zeolite template as function of time. The wall starts at position z=−10 nm and the zeolite is placed at z=0nm. . . . . 265 12 List of Figures 10.12Radial distribution function for EAN (left) and [EMIM][BF4] (right). From top to bottom: cationcation, anioncation and anionanion. . . . . . . . . . . . . . . . . . . . . . . 266 10.13Comparison between the anioncation coordination num bers of EAN (top) and [EMIM][BF4] (bottom) inside the ZTC and inside some of the carbon nanotubes. . . . . . . . 268 10.14Coordination between anions and cations modeled by Eq. 10.11 compared to the actual coordination inside the ZTC template. The results for the purely 1D coordination given by Eq. (10.10) and the 3D bulk coordination are shown for completeness......................... 270 10.15Vibrational density of states for EAN (left) and [EMIM][BF4] (right). On top, density of states of cations and on the bottom row for the anions. . . . . . . . 271 10.16Comparison between the vibrational density of states of the cations of EAN (top) and [EMIM][BF4] (bottom) inside the zeolite template and inside some of the carbon nanotubes. . 272 10.17Mean squared displacement for the cations and anions of EAN (top) and [EMIM][BF4] (bottom). A dashed straight line with slope 1 in loglog scale is represented for compar ison with the diffusive regime. . . . . . . . . . . . . . . . 273 13 List of Tables 4.1 Dynamic properties of the ions as a function of the force field.............................. 88 6.1 Number of molecules used in the reported MD simulations. 138 6.2 Values of the average fraction of surface covered by anions (η) in mixtures of [BMIM][BF4]. The vacancy percentages correspond to those in the positively charged graphene wall. 142 8.1 Comparison of Minkowski cluster parameters, Coverage Factor (CV) and Mean Cluster Size (MCS), as well as Shannon entropy (H), calculated for BF – 4anions dens ity maps in LiBF4+[BMIM][BF4] near graphene and borophene walls for different surface charges: negative (), neutral (0) and positive (+). . . . . . . . . . . . . . . . . . 203 10.1 Effective number density of IL per unit volume of the ZTC, bulk number density and ratio between the effective and bulk densities for both ionic liquids. . . . . . . . . . . . . 264 14 List of publications included in this thesis •Molecular dynamics analysis of the effect of electronic polar ization on the structure and singleparticle dynamics of mix tures of ionic liquids and lithium salts, Volker Lesch, Hadrián MontesCampos, Trinidad MéndezMorales, Luis Javier Gallego, Andreas Heuer, Christian Schröder, & Luis M Varela, J. Chem. Phys., 145(20), 204507 (2016). Journal information: Impact factor: 2,965. Cathegory: Physics. Atomic, Molecular & Chem ical. Ranking inside cathegory: 10/36 (Q2). •Nanostructured solvation in mixtures of protic ionic liquids and longchained alcohols, Hadrián MontesCampos, José M OteroMato, Trinidad MéndezMorales, Elena LópezLago, Olga Russina, Oscar Cabeza, Luis J Gallego & Luis M Varela, J. Chem. Phys., 146(12), 124503 (2017). Journal information: Impact factor: 2,843. Cathegory: Physics, Atomic, Molecular & Chem ical. Ranking inside cathegory: 13/36 (Q2). •Twodimensional pattern formation in ionic liquids con fined between graphene walls, Hadrián MontesCampos, José Manuel OteroMato, Trinidad MéndezMorales, Oscar Cabeza, Luis J Gallego, Alina Ciach, & Luis M Varela , Phys. Chem. Chem. Phys., 19(36), 24505 (2017). Journal information: Impact factor: 3,906. Cathegory: Physics, Atomic, Molecular & Chemical. Ranking inside cathegory: 9/36 (Q1). •Mixtures of Lithium Salts and Ionic Liquids at Defected Graphene Walls, Hadrián MontesCampos, Jose Manuel Otero Mato, Roberto Carlos Longo, Oscar Cabeza, Luis Javier Gallego, & Luis Miguel Varela, J. Mol. Liq., 289, 111083 (2019). Journal information: Impact factor: 5,065. Cathegory: Physics, Atomic, Molecular & chemical. Ranking inside cathegory: 4/37 (Q1). •Borophene vs. graphene interfaces: Tuning the electric double layer in ionic liquids, Víctor GómezGonzález, J 15 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Manuel OteroMato, Hadrián MontesCampos, Xabier García Andrade, Amador GarcíaFuente, Andrés Vega, Jesús Carrete, Oscar Cabeza, Luis J Gallego, & Luis M Varela, J. Mol. Liq., 303, 112647 (2020). Journal information:*Impact factor: 5,065. Cathegory: Physics, Atomic, Molecular & chemical. Ranking inside cathegory: 4/37 (Q1). •RandomAlloy Model for the Conductivity of Ionic Liquid– Solvent Mixtures, Hadrián MontesCampos, Svyatoslav Kondrat, Esther Rilo, Oscar Cabeza, & Luis M Varela, J Phys. Chem. C, 124(22), 11754 (2020). Journal information:∗Impact factor: 4,404. Cathegory: Materials Science, Multidisciplinary. Ranking inside cathegory: 90/314 (Q2). •Structure of protic and aprotic ionic liquid inside carbon nanotubes and zeolite templated carbon structures, Hadrián MontesCampos, Trinidad MéndezMorales, Jose Manuel Otero Mato, Oscar Cabeza, Luis Javier Gallego, Enrique Lomba, & Luis Miguel Varela, J. Mol. Liq., 318, 114264 (2020). Journal information:∗Impact factor: 5,065. Cathegory: Physics, Atomic, Molecular & chemical. Ranking inside cathegory: 4/37 (Q1). *The journal information for the articles published in 2020 corresponds to the data of 2019 due to the yearly nature of this information. 16 List of publications related to this thesis •Molecular dynamics simulation of the behaviour of water in nanoconfined ionic liquid–water mixtures, Borja Docampo Álvarez, Victor GómezGonzález, Hadrián MontesCampos, José M OteroMato, Trinidad MéndezMorales, Oscar Cabeza, LJ Gal lego, Ruth M LyndenBell, Vladislav B Ivaništšev, Maxim V Fe dorov & Luis M Varela, J. Phys.: Cond. Matt., 28(46), 464001 (2016) •Solvation of Al 3+ cations in bulk and confined protic ionic liquids: a computational study, Víctor GómezGonzález, Borja DocampoÁlvarez, Hadrián MontesCampos, Juan Carlos Otero, Elena López Lago, Oscar Cabeza, Luis J Gallego, & Luis M Vare la, Phys. Chem. Chem. Phys., 20(28), 19071 (2018) •3D structure of the electric double layer of ionic liquid–alcohol mixtures at the electrochemical interface, José M OteroMato, Hadrián MontesCampos, Oscar Cabeza, Diddo Diddens, Alina Ciach, Luis J Gallego, & Luis M Varela, Phys. Chem. Chem. Phys., 20(48), 30412 (2018) •GADDLE Maps: General Algorithm For Discrete Object Deformations Based on Local Exchange Maps, J Manuel OteroMato, Hadrián MontesCampos, Martin Calvelo, Rebeca GarciaFandino, Luis J Gallego, Ángel Piñeiro, & Luis M Varela, J. Chem. Theory Comput., 14(2), 466 (2018) •Molecular dynamic simulation, molecular interactions and structural properties of 1butyl3methylimidazolium bis(trifluoromethylsulfonyl)imide + 1butanol/1propanol mixtures at (298.15–323.15) K and 0.1 M Pa, Urooj Fatima, Naushad Anwar, Hadrián MontesCampos, & Luis M Varela, Fluid Phase Equilibria, 472, 9 (2018) •Solvation in ionic liquidwater mixtures: A computational study, Jose M OteroMato, Volker Lesch, Hadrián Montes 17 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Campos, Jens Smiatek, Diddo Diddens, Oscar Cabeza, Luis J Gallego, & Luis M Varela, J. Mol. Liq., 292, 111273 (2019) •Experimental and MD simulation investigation on thermo physical properties of binary/ternary mixtures of 1butyl3 methylimidazolium trifluoromethanesulfonate with molecu lar solvents, Urook Fatima, Riyazuddeen, Hadrián MontesCam pos, & Luis M. Varela, J. Mol. Liq, 302, 112481 (2020) •Thermoswitchable de novo ionogel as metal absorbing and curcumin loaded smart bandage material, Muzammil Kuddushi, Nehal K Patel, Santosh L Gawali, Jitendra P Mata, Hadrian MontesCampos, Luis M Varela, Puthusserickal A Hassan, & Naved I Malek, J. Mol. Liq., 306, 112922 (2020) •Microstructure, dynamics and optical properties of metal doped imidazoliumbased ionic liquids, Carlos Damián RodríguezFernández, Hadrián MontesCampos, Elena López Lago, Raúl de la Fuente, & Luis M Varela, J. Mol. Liq, 317, 113866 (2020) •Nanoconfined ionic liquids: A computational study, José M. OteroMato, Hadrián MontesCampos, Oscar Cabeza, Luis J. Gallego, & Luis M. Varela, J. Mol. Liq, 320, 114446 (2020) 18 Part I Introduction and Methods 19 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ N N R1R2 Dialkylimidazolium Pyridinium CholineSulfonium S R2 R1 R3 N R1R2 N,N-dialkylpyrrolidinium NH3 R Alkylammonium N R2 R3 R4 R1 N OH S O O OO R Methanesulfonate Hexafluorophosphate Tetrafluoroborate Nitrate bis(trifluoromethyl-sulfonyl)imide N S S O O O O CF3CF3 PF6 -BF4 -NO3 - Cations Anions Figure 1.2: Some of the most common cations and anions that form ILs. very relevant classification of ILs that arise from the method used in their synthesis. When the IL is created by a protontransfer reaction between an acid and a base without any solvent in the process, it is called a protic ionic liquid,50;51 in contrast with aprotic ILs which are synthesized with different methods. Protic ILs usually present many hydrogenbonds which heavily modify their properties.52. Most of these novel solvents show interesting and unique properties as: •Very low vapour pressure/volatility: Due to strong interactions 26 1. Introduction inside the IL, and to the requirement of forming ionic pairs before vapourizing, their vapour pressure is very low, almost undetect able. Experimental measurements of ILs from the imidazolium family show vapour pressures lower that 1 Pa,53;54 i.e. less than one thousand that of water. This makes ILs good candidates for their use as thermal fluids and in situations in which temperature increases are expected. •Low toxicity: ILs have a toxicity in line with other organic ma terials.55 However, their extremely low vapour pressures make them safer to handle and avoids toxic emissions to the atmosphere. Moreover, when used in catalytic processes they can be recovered by distillation.56 For these reason they are usually classified as green solvents. •High viscosity: ILs have in general higher viscosities than other common solvents due to being a highly charged medium. Their viscosities range between 10 and 500 cP. This magnitude usually shows a strong dependence with temperature. For instance, the viscosity of [BMIM][PF6] changes from 286 cP at 293 K to 29 cP at 343 K.57. •Great thermal stability: Due to the previously discussed low va pour pressure, ILs remain in liquid state for a very broad range of temperatures, compared to other molecular solvents. Their max imum temperature of practical operation is usually controlled not by evaporation but by chemical instability. •High electrochemical stability and good ionic conductivity: Due to being composed only by ions and to their large liquid range, ILs are capable of redistributing their charges under an electric find allowing a fast migration of ions which provide a good ionic conductivity. Moreover, they show high redox po tential, and, therefore, they are able to withstand high voltages. The range of voltage than an IL can withstand is generally much higher than other common solvents like water, with electrochem ical windows of more than 6 V having been reported.12 Their 27 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ conductivities are also greater than for most common solvents (∼10−1S/m). Moreover, in protic ILs the Grotthuss mechanism may be present58 greatly enhancing electrical conductivity. These two properties are they key ones for their use in electrochemical devices, such as batteries, supercapacitors or fuel cells. •Solvation and variable chemical polarity: The large number of cations and anions that form ILs provides a wide range of chem ical polarities and chemical groups to choose in order to design an IL. This large number of possibilities allows tuning ILs to solvate a huge variety of molecules. Moreover, most ILs contain both po lar and apolar regions which generates a nanostructuration inside the bulk IL. This nanostructure is composed of two segregated nanodomains with clearly defined chemical polarities. This am phiphilicity is the reason behind the high adaptability of ILs to solvate a great number of substances. Moreover, it is possible to tune the ability to solvate a specific material in order to make it fully miscible or immiscible.46 This property grants ILs the title of designer solvents, and it is behind the huge increase of the number of available solvents. •Nanostructured Solvation: Due to the previously discussed se gregation in two nanoregions with different chemical polarities, the solvation of molecules inside ILs is selective.59 The nanodo mains inside ILs are quite stable and therefore solvated materials must accommodate to this underlying structure. Moreover, the highly polar/apolar character of these nanodomains, forces the solute to be placed in a nanodomain with similar polarity. The presence of a robust hydrogenbond network in many ILs also conditions the ability to solvate other molecules. For example water may create clusters in ILs that lack such hydrogenbond net work,60 while it is easily accommodated into the polar domains of hydrogenbonded ILs.61 This nanostructure also endows ILs with the ability to solvate amphiphilic molecules without significant impact on the IL structure itself, as we will see later in the results of this thesis. 28 2 Methods In this chapter we will detail the main aspects of the methods used in this thesis. The chapter is divided in two subsections: in the first one we will detail the different computational tools (which are the main tools used in this thesis), and in the second one we will show the basis of the pseudolattice theory of ionic transport which will be used later in Chapter 9. ғ*Ғ ?ҩҧҪүҮқҮңҩҨқҦ ҮҩҩҦҭ The main computational tools used in this thesis can be classified as computer simulations. Computer simulations are complementary tools to experimental measurements that allow us to access properties that are not directly accessible using experiments. Moreover, computer simula tions can also be used as a cheap alternative to screen the properties of a given set of materials due to the low cost of replicating the simulation for different materials. Computer simulations can be used to study systems in almost any scale, from nuclear reactions62 to gravitational waves.63 However, the timescale that computer simulations are able to deal with is strongly tied to the spatial resolution (see Fig. 2.1). Therefore, in or der to simulate systems during long times, the spatial resolution must be very low. This means that in all simulations we must find a compromise between the length and time scales involved. All the computer simulations in this thesis can be classified as atom istic simulations. In this kind of simulations the length scale goes from pm, when making quantum simulation of the electronic density of atoms and molecules, to µm in coarse grained molecular dynamics simulations. On the other hand, time scales go from some ps for quantum simulations to µs for molecular dynamics simulations. In this thesis the following simulation methods were used and will be discussed in the following pages: 29 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ MC Kinetic-MC Finite Elements Computational Fluid Dynamics Accelerated MD QC DFT MD CG-MD Ab Initio MD nm μm Length Scale mm m smsμsns ps Time Scale Atomistic Mesoscale Continous Macroscale Figure 2.1: Most widely used computer simulation methods according to their time and length scales of application. • Molecular dynamics. • Quantum density functional theory. • Monte Carlo simulations. 2.1.1 Molecular dynamics Molecular dynamics (MD) is the main technique used in this thesis, in particular classical MD. In classical MD we obtain the time evolu tion of the motion of a series of atoms through numerical integration of Newton’s classical equations of motion. Despite the apparent sim plicity of MD, the method allows for a lot of flexibility including the implementation of barostats, thermostats, algorithms for setting con straints (e.g. SHAKE algorithm),… Moreover, there are several open source packages that allow for an easy setup of MD simulations, in clude tools for the analysis of the results and allow to parallelize the 30 2. Methods simulations. Among these simulation packages we want to highlight GROMACS64;65 (GROningen MAchine for Chemical Simulations) for its simplicity, great performance and builtin tools for postprocessing and LAMMPS66 (Largescale Atomistic/Molecular Massively Parallel Simulator) for its modularity and flexibility to add and modify atomic interactions. For these reasons, we chose GROMACS as our reference suite for this thesis. In order to follow the motion of the atoms we must discretize the simulation time. The usual approach is to divide the whole simulation in timesteps of constant size. Therefore, at the end of the simulation we will have a trajectory consisting of different snapshots of the system. These frozen images of the system are obtained in an algorithmic way by numerical integration of the Newton equation of motion: d2(r i dt2=( Fi mi =−1 mi ∂V ∂(ri ,i=1,...,N, (2.1) where Vis the potential energy of the system comprising all the relevant interactions in it. There are several integration algorithms that can be used in order to obtain the next snapshot of the trajectory. One of the most frequently used is the Velocity Verlet algorithm. In this algorithm the positions and velocities are updated from the previous configuration using the following transformations: (a i(t)=−1 mi ∂V((xi(t)) ∂(ri (2.2) (x i(t+∆t)=(x i(t)+(v i(t)∆t+1 2(ai(t)∆t2(2.3) (v i(t+∆t)=(v i(t)+1 2[(a i(t)+(a i(t+∆t)] ∆t. (2.4) Note that before updating the velocities we must recalculate the acceler ations using the updated positions for recalculating the forces. Another common algorithm, and the one we will be using in the simulations con tained in this thesis, is the leapfrog algorithm. This algorithm has the particularity that velocities are calculated at half timestep, i.e. they are 31 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ not evaluated for same simulation time than the positions. However, this is not usually a problem because the velocities are not stored in the trajectory for all the simulation frames. The equations for updating the positions and velocities in this algorithm are: (a i(t)=−1 mi ∂V((x i(t)) ∂(ri (2.5) (vi!t+∆t 2"=(v i!t−∆t 2"+(a i(t)∆t(2.6) (x i(t+∆t)=(x i(t)+(v i!t+∆t 2"∆t. (2.7) The basic algorithm for an MD simulation with a generic integration algorithm is summarized in Fig. 2.2. There are, however, some topics that must be taken into account before performing a MD simulation. In order to start our simulation, we need an initial configuration with well defined positions and velocities. This is no minor task, as this might very well condition the results of the simulation. A usual approach for simulating liquids is to start with a random distribution of molecules in side a volume, such that there is no overlapping between the atomic van der Waals spheres, and a distribution of velocities that follows Max well’s distribution for the desired temperature. The volume is chosen such that the system has a density similar to the expected one. After that, an energy minimization is performed in order to avoid configura tions with unrealistic energies. Finally, an MD simulation in the NPT ensemble is performed in order to relax the system. Usually a good value for the density is achieved in less than 1 ns and in less than 10 ns the sys tem is usually fully relaxed. The final configuration obtained from this last simulation can now be used to perform the production simulation run. Another important topic are border effects. In order to avoid hav ing borders in our simulation and being able to simulate bulk material, periodic boundary conditions are applied. These conditions create an infinitely replicated system where the molecules that exit the simulation box through one side reenter the system by the opposite one. 32 2. Methods Initial Configuration {r⁰}{v⁰} Simulation Loop NO YES Current Frame {r }{v} Force Calculation {f } New Configuration {r } {v} i+1 i+1 Trajectory {r⁰} {v⁰} {r¹} {v¹} {r²} {v²} {r³} {v³} {r } {v } ff Final Configuration {r } {v } ff Update i=i+1 Motion Integration Figure 2.2: Scheme of the basic algorithm for MD simulations. 33 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Finally, the choice of a proper model for the potential energy, and therefore the interactions, of the system is a crucial part of a classical MD simulation, as the accuracy of the results is directly conditioned by the accuracy of the force field modeling of the interactions in the system. This potential energy must include all the interactions present in the sys tem (see Fig. 2.3 for a scheme of the most usual interaction present in MD simulations of classical liquids). The collection of physical models and the parameters used to define the potential energy of the system is what constitutes a force field. There are several force fields available in the literature including OPLS,67;68 CL&P,69 APPLE&P,70 GROMOS,71 AMBER,72 CHARMM.73 In this thesis, our reference force field will be the OPLSAA68 (Optimized Potentials for Liquid Simulations, All Atom), whose components will be summarized in the following. Note that these models are not exclusive of this force field, but are shared by many of the other force fields. The OPLSAA force field includes intermolecular and intramolecu lar interactions defined as:68 V=Vbonded +Vnonbonded (2.8) Vbonded =Vbonds +Vangles +Vdihedrals (2.9) Vnonbonded =VLJ +VCoulomb .(2.10) The bonded interactions are made up of the interactions between two bonded atoms separated a distance r K r eq r Vbonds =# bonds Kr(r−req)2,(2.11) the interactions between three atoms forming an angle θ 34 2. Methods Dispersive Interactions Electrostatic Interactions -+ Bonds Angles Dihedrals Improper Dihedrals Polarization Embedded Atom Many-Body Intermolecular Intramolecular Interactions Figure 2.3: Scheme of the most common interactions present in a classical MD simulation. 35 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ •Hybrid functionals: This functionals are composed by an empir ical mixing of exact energy given by HartreeFock’s theory and one (or several) of the previously mentioned functionals. For in stance, one of the most widely used hybrid functionals, the B3LYP hybrid functional, is calculated as: EB3LY P xc =ELDA x+a0'EHF x−ELDA x(+ax'EGGA x−ELDA x( +ELDA c+ac'EGGA c−ELDA c(,(2.31) with a0=0.20,ax=0.72 and ac=0.81. The GGA energy is computed using the exchange functional Becke 8880 and Lee’s ex change functional,81 while the LDA correlation is computed using the VWN functional.82 Note that there are spin polarized versions of these approximations that instead of using the total electronic density in the *xc depend on the up and down electronic spin densities: *LDA x[ρ]→*LDA x[ρ↑,ρ ↓](2.32) *GGA xc +ρ((r),( ∇ρ,→*GGA xc +ρ↑,ρ ↓,( ∇ρ↑,( ∇ρ↓,(2.33) *MGGA xc +ρ,( ∇ρ,( ∇2ρ,→ *MGGA xc +ρ↑,ρ ↓,( ∇ρ↑,( ∇ρ↓,( ∇2ρ↑,( ∇2ρ↓,.(2.34) In this thesis we have used the commercial software VASP83;84 for the DFT calculations. Moreover the PBE GGA functional85 and the B3LYP hybrid functional86 were chosen as the exchange and correlation functionals. 42 2. Methods 2.1.3 Monte Carlo simulations Monte Carlo (MC) simulations, and Monte Carlo methods in gen eral, are a collection of techniques based on random processes that are widely used for integration and simulation processes. The common characteristic of these methods is that instead of exploring the phase space in a deterministic manner, it is done in an stochastic one. These methods are specially powerful to analyze the phase space of multidi mensional system as the convergence ratio is O(N−1/2)independently of the dimensionality of the data. This makes MC simulations a very interesting method to study systems with a large number of degrees of freedom. MC simulations are used in material science in order to simulate different properties. The resulting values from MC simulations con verge to the results from MD simulations if the ergodicity of the system is granted. In general terms, a system can be said to be ergodic if after a long enough time a system in evolution is able to reach any point in the phase space. If this condition is met, then the average value meas ured following the time evolution of the system and integrating over the phase space coincide. In a conventional MC simulation we are going to produce an stochastic trajectory in the phase space in order to calculate average values,*these values will be equivalent to the ones that would be calculated using a time dependent method (see Fig. 2.4 for a visual representation of the equivalence of deterministic and stochastic tra jectories). However, for these values to be equivalent, we must traverse the phase space in a way that preserves the probability distribution of the points in it. For physical systems coupled to a thermostat the probability of a state lof the phase space is given by the Boltzmann *It is possible to produce a trajectory which reproduces the correct time evolution using Kinetic MC as we will discuss later. 43 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Time Dependent Evolution Stochastic Evolution Figure 2.4: Example of the equivalence between an deterministic and a stochastic evolution for an ergodic process. distribution Pl∝e−El/kBT.(2.35) The MetropolisHastings algorithm87;88 gives an implementation to gen erate configurations that follows a given distribution. The sequence of samples is obtained by simulating a Markov chain.88 Let W={wij}be the transition probability matrix of an irreducible Markov chain and Pi the probability of the state i. If this matrix is to represent the probabil ities of a stationary configuration, then it must hold that: dPi dt =# j [Piwij −Pjwji]=0.(2.36) A sufficient condition for this is: Piwij =Pjwji ,(2.37) which is known as the detailed balance condition and is based on the microscopic time reversibility.88. We can write the transition probability between both states as: wij =qijαij (2.38) 44 2. Methods where qij is the probability that a system in the state itries to go from state ito state jand αij is the probability of success of such trans ition. Obviously, Eq. (2.37) implies that this probability of success must verify: αij αji =Pj Pi qji qij .(2.39) A way of fulfilling this relation is to use the following acceptance ratio: αij =min !1,Pj Pi qji qij ",(2.40) which warrants than either αij or αji is 1. If we assume that qij =qji and using the Bolztmann distribution we obtain that in order to generate random configurations that follow the Boltzmann distribution at a given temperature Tthe acceptance ratio must be: αij =min !1,e −Ej−Ei kBT",(2.41) where Eiand Ejare the energies of the iand jconfigurations respect ively. With this acceptance ratio, the MetropolisHastings algorithm† produces a Markov chain in which the following element of the chain is produced from a given configuration iusing the following rules: 1. Select one of the accessible configurations jwith a probability of qij. 2. Calculate the energy of configuration j. 3. Accept the change from ito jwith a probability given by Eq. (2.41). 4. If the change is accepted jbecomes the next element of the chain. If it is rejected, then iis added to the chain. †Note that the detailed balance condition allows the determination of the stationary distri bution Piif wij are known (ensemble theory) and of wij if Piis known (MetropolisHastings algorithm). 45 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ This process is repeated the desired number of times in order to map the phase space. It is important to note that following this algorithm, and most MC algorithms, the time evolution information is completely missing and no dynamic properties can be observed. There are how ever some algorithms that include time dependent information that can be used to analyze dynamical properties.89 However, these algorithms usually need be fed with accurate transition times for all the possible process in the system in order to match actual chronological trajectories and reproduce the dynamics. Further details about the specific methods used in each of the studies are given in their corresponding methods section. ғ*ғ LҭҟүҞҩҦқҮҮңҝҟ ҮҢҟҩҬҳ ҩҠ ҝҢқҬҡҟ ҮҬқҨҭҪҩҬҮ ңҨ ңҩҨңҝ ҭҩҦүҮңҩҨҭ The pseudolattice theory of charge transport in ionic solutions90 aims to explain and predict the ionic conductivity of ionic solutions in systems for ionic solutions with high concentrations of ionic matter. This the ory extends the concentration range beyond the classical DebyHückel theory,91 which is not suitable to study mixtures of ILs and solvents due their inherent high charge density. This theory consider the mixture of N=N++N−IL molecules‡ and N0solvent molecules as a 3D pseudolattice with coordination num ber s, lattice constant aand M=N+N0nodes. Ions are embedded in this pseudolattice and move between adjacent cells by means of hops activated by the action of an external electric field ( E. These hops are considered statistically independent and, therefore, there is no correla tion between two consecutive hops. Two adjacent cells are considered to be separated by an energy barrier. Due to the ergodic nature associated to the short characteristic times present in liquid systems, these energy barriers are the product of averaging all the possible molecular environ ments. In this model only two different kind of ionic environment are considered: βcells, where no ions are present in the adjacent cells; and ‡We will consider only binary ILs for simplicity. 46 2. Methods αcells, where ions are present in the adjacent cells. These cells have two different potential well depths, *βfor the βcells and *αfor the β ones. The distribution of αand βcells is considered to be random and no correlation between them is imposed. Therefore the probabilities of having an αor βcells are given by: χα=φα,χ β=φβ,(2.42) where φαand φβare the volume fractions of ions and solvent respect ively. The volume fractions are used instead of the molar ones to take into account the size differences between substances. In the absence of an electric field, the probability per unit time that an ion jumps a barrier is:92 ¯νi=1 3 (kBT)3 h3ν2 si e−$i/kBT;i=α,β,(2.43) where his Planck’s constant and νsi is the vibrational frequency of an ion in the two directions of the saddle point perpendicular to the flow in a cell of itype. Under the effect of an electric field ( Ethese hopping frequencies are altered in the direction parallel to the electric field by an ammount: ¯νpi =1 3 (kBT)3 h3ν2 si )e−($i−(aqE/2))/kBT−e−($i+(aqE/2))/kBT* =2¯νisinh !aqE 2kBT";i=α,β,(2.44) where qis the charge of the ions. This expression can be easily approx imated for weak electric fields as: ¯νpi ≈¯νi aqE kBT;i=α,β.(2.45) Using this expression and the probabilities given by Eq. 2.42, it is possible to calculate the weighted average excess probability of jumping 47 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ in the direction parallel to the field as: ¯νp=# i=α,β φi¯νpi =qa kBT(φα¯να+φβ¯νβ)E. (2.46) Each ionic jump has an associated polarization qa. Thus, the total cur rent density is given by j=nαqa¯νp, where nαin the number density of ions. This number density can be approximated, due to the low excess volume of ILs, as nα≈φα/Vα, where Vαis the ionic volume. Therefore the ionic conductivity is finally given by: κ=q2a2 VαkBT)φ2 α¯να+(1−φα)φα¯νβ*.(2.47) Moreover, if the values from this expression are normalized by the maximum conductivity (κmax) and the volume fraction at which this maximum appears (φmax), the resulting expression has no parameters and, therefore, it defines a universal behaviour for the conductivity. This universal conductivity can be written as: ¯κ=2¯ φ!1−¯ φ 2",(2.48) where ¯κ=κ/κmax and ¯ φ=φα/φmax. As can be seen in Fig. 2.5, this model correctly predicts the conductivity at low and medium concen trations of IL. However, at nearly pure ILs, the experimental values of the conductivity deviate from the prediction of the model. In Chapter 9 we will present an extension of this model with 2cell dependences of the jumping frequency in order to improve the predictions at nearly pure ILs. 48 2. Methods 0.0 0.5 1.0 1.5 2.0 0.0 0.4 0.8 1.2 BMIMBF 4 HMIMBF 4 MOIMBF 4 k/k max f/f max Figure 2.5: Normalized conductivity vs. scaled concentration for IL‐ethanol mix‐ tures. Reproduced from Ref.[ 90] 49 Part II Results 51 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ meters. This analysis showed that after switching off the polarization the structure and dynamics of the IL is severely impacted. Therefore we conclude that in order to add polarizability to a nonpolarizable force field, the rest of its parameters must be refitted in order to obtain accur ate results. The contribution of the author of this thesis to this publication, us ing the CRediT contribution classification,94;95 was: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing  Original Draft, Writing  Review & Editing, Visualization. 58 THE JOURNAL OF CHEMICAL PHYSICS 14, 204507 (2016) Molecular dynamics analysis of the effect of electronic polarization on the structure and single-particle dynamics of mixtures of ionic liquids and lithium salts Volker Lesch,1,2,a),b) Hadri´ an Montes-Campos,3,a) Trinidad M´endez-Morales,3 Luis Javier Gallego,3Andreas Heuer,2,4 Christian Schr¨oder,5and Luis M. Varela3,b) 1Helmholtz-Institute M¨unster (IEK-12): Ionics in Energy Storage, Forschungszentrum J¨ulich, orrensstrasse , 1 M¨unster,ermany 2Institute o hysical hemistry, est¨alische ilhelms-niersit¨at M¨unster, orrensstrasse 2, 1 M¨unster,ermany 3ruo e anomateriais e Materia rana, eartamento e Fsica a Materia onensaa, niersiae e Santiago e omostela, amus ia sn, E-12 Santiago e omostela, Sain 4enter or Multiscale heory an omutation, orrensstrasse , 1 M¨ unster,ermany 5eartment o omutational iological hemistry, niersity o ienna, ¨ahringerstrasse 1, -1 ienna, ustria (Receive 20 Je 2016 ccee  Nvee 2016 ie ie 30 Nvee 2016) DOI: https://doi.org/1.1/1. 5 Nanostructured solvation in mixtures of protic ionic liquids and longchained alcohols With the limitations of nonpolarizable force fields correctly character ized, we started our study of nanoconfinement of ILs analyzing their internal nanosegregation. The nanosegregation of the IL in polar and apolar nanodomains acts as an intrinsic nanoconfinement of the IL. In this study we analyzed the applicability of the nanostructured solvation paradigm to the solvation of amphiphilic molecules inside the IL. Ac cording to this paradigm, molecules are relatively solvated inside the ionic liquid according to their chemical polarities. Therefore, polar mo lecules are solvated in the polar domains, the apolar in the apolar ones and amphiphilic molecules place themselves in the border between these two regions. In order to test this, we simulated alcohols with different chain lengths (1propanol, 1butanol and 2pentanol) solvated in two protic ionic liquids with different cation sizes (ethylammonium nitrate and butylammonium nitrate). These cations have a marked amphiphilic behaviour and will, therefore, compete with the alcohol molecules in order to be located at the border between the polar and apolar nanodo mains. Our study concluded that the structural results were compatible with the nanostructured solvation paradigm. This picture was further proven by analyzing the hydrogen bonding between the anions and both the cations and the alcohol molecules. The hydrogen bonding revealed that alcohol molecules are able to replace the IL cations in the structure and, therefore, adding alcohol does not significantly alter the properties of the pure IL. Moreover, experimental small angle xray scattering meas urements of these mixtured showed large scale structural heterogeneities (ca. 10 nm). Due to the size of these heterogeneities their study is out side the scope of this thesis, but work towards simulating this effect is currently planned. The contribution of the author of this thesis to this publication, us ing the CRediT contribution classification,94;95 was: Conceptualization, 93 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing  Original Draft, Writing  Review & Editing, Visualization. 94 THE JOURNAL OF CHEMICAL PHYSICS 14, 124503 (2017) Nanostructured solvation in mixtures of protic ionic liquids and long-chained alcohols Hadri´an Montes-Campos,1,a) Jos´eM.Otero-Mato,1,a) Trinidad M´endez-Morales,1 Elena L´opez-Lago,1Olga Russina,2Oscar Cabeza,3Luis J. Gallego,1 and Luis M. Varela1,b) 1Grupo de Nanomateriais, Fot´ onica e Materia Branda, Departamentos de F´ısica de Part´ıculas e de F´ısica Aplicada, Universidade de Santiago de Compostela, Campus Vida s/n,  Santiago de Compostela, Spain 2Dipartimento di Cimica, Sapiena Universita di oma, Piaale Aldo Moro ,  oma, tal 3Facultade de Ciencias, Universidade da Coruna, Campus A apateira s/n,  A Coruna, Spain (Received 5 J 2017 cceed 7 Mc 2017 ied ie 2 Mc 2017) DOI: https://doi.org/1.1/1. 6 Twodimensional pattern formation in ionic liquids confined between graphene walls In this paper we started the study of the solidliquid interface. This study will span for three articles, in which efforts were devoted to properly characterize the structural properties of the interface, specially in the directions parallel to the electrodes. The structure of this interface is of key importance for any electrochemical device, as it is the region where reactions and/or the charge start to happen. However, this lateral structure has been much less studied that in the direction perpendicular to the interface. Moreover, previous experimental and computational results had suggested the possibility of two different arrangements of anions and cations in these directions. In this first study of the interface we will analyze the possible structural conformations that can appear at the electrode. Analyzing the structure in the lateral direction for different composition of the electrolyte showed that two different patterns can arise: one with the ions arranged in an hexagonal pattern and another one creating stripes. These results are backed up by a theoretical model based on the Landau–Brazovskii phenomenological theory which predicts the same structures. Moreover, Monte Carlo simulations of a simple IL model are able to replicate the same conformations. We finally conclude that the pattern that the IL will should adopt depends on the charge density of the first layer of IL at the interface and therefore, we can tune the structure of this layer by modifying any external parameter that couples to such density. The contribution of the author of this thesis to this publication, us ing the CRediT contribution classification,94;95 was: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing  Original Draft, Writing  Review & Editing, Visualization. 125 DOI: https://doi.org/1.1/ DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ ware, Formal Analysis, Writing  Original Draft, Writing  Review & Editing, Visualization. 186 Journal of Molecular Liquids 303 (2020) 112647 Contentslistsavailable at ScienceDirect Journal of Molecular Liquids jornal oeae elseviercolocateolli Borophene vs. graphene interfaces: Tuning the electric double layer in ionic liquids Víctor Gómez-Gonzáleza,1, J. Manuel Otero-Matoa,1, Hadrián Montes-Camposa, Xabier García-Andradea,AmadorGarcía-Fuenteb,f,AndrésVegac,JesúsCarreted, Oscar Cabezae, Luis J. Gallegoa, Luis M. Varelaa,* aGrupo de Nanomateriales, Fotónica y Materia Blanda, Departamento de Física de Partículas, Facultade de Física, Universidade de Santiago de Compostela, Campus Vida s/n, Santiago de Compostela E-15782, Spain bDepartamento de Física, Universidad de Oviedo, Oviedo E-33007, Spain cDepartamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, Valladolid E-47011, Spain dInstitute of Materials Chemistry, TU Wien, Vienna A-1060, Austria eDepartamento de Física y Ciencias de la Tierra, Facultade de Ciencias, Universidade da Coruña, Campus A Zapateira s/n, A Coruña E-15071, Spain fNanomaterials and Nanotechnology Research Center CINN, CSIC-Universidad de Oviedo, El Entrego, Spain DOI: https://doi.org/1.11/.oi..11 9 Randomalloy Model for the Conductivity of Ionic Liquid–Solvent Mixtures The following work tries to close the gap in the understanding of trans port in ILs and other ionic systems. It is wellknown that for systems with low ionic concentrations, DebyeHückel equilibrium theory can be used to explain the transport, which leads to Onsager’s limiting law for ionic conductance, which predict a conductance proportional to the square root of the ionic concentration. However, ILs and other charged fluids fall completely outside the range of applicability of this theory. An alternative approach to this model was proposed by Varela et al.90 based on a pseudolattice structural model of the ionic fluid, which mod els the liquid as a random mixture of low and high mobility cells. This theory is able to explain ionic conductivity up to very high concentra tions, but it showed failures at nearly pure ILs. In order to account for the deviations that the model proposed by Varela et. al. had at extremely large ionic concentrations, we proposed a modification of this model based on independent ion hops in a 2cell mode with second order hopping frequencies, opposed to the original 1cell model. As we showed in this work, this model is able to cor rectly predict the high concentration deviations from the original model. Moreover, the model also predicts how does the conductivity change with temperature and brings new insights into the ionsize dependence. This models seems to be able to correctly predict the ionic conductivity of ionic mixtures throughout the whole concentration range. The supplementary information for this work can be seen on ap pendix A.2. The contribution of the author of this thesis to this publication, using the CRediT contribution classification,94;95 was: Methodology, Soft ware, Formal Analysis, Investigation, Data Curation, Writing  Original Draft, Writing  Review & Editing, Visualization. 213 DOI: https://doi.org/1.11/s.p.1 10 Structure of protic and aprotic ionic liquid inside carbon nanotubes and zeolite templated carbon structures This last work is the culmination of all the previous studies on the prop erties of nanoconfined ILs presented in this thesis. In this study we present simulations of protic and aprotic ILs inside carbon nanotubes as a prior step to the study of their confinement inside a zeolitetemplated carbon (ZTC) framework. The key difference between this systems and those presented in the previous studies is that they are made up only of interfaces, i.e. there is no region in which the bulk 3D structure of flu ids can be adopted inside the confining structure. The zeolitetemplated carbon framework is a structure with narrow interconnected pores in dif ferent spatial directions. This provides the structure with a high surface to volume ratio, which makes them ideal for their use in many electro chemical. However, in order to correctly characterize the properties of ILs confined in ZTC frameworks, we previously simulated the same ILs inside carbon nanotubes of different radii in order to use them for further predictions in the most complex ZTC structure. ILs inside carbon nanotubes show a highly structured arrangement that goes from a purely 1D configuration in the narrowest nanotubes, to arrangements of higher dimensionality in the widest ones. This change in dimensionality appears when the radius of the nanotube is greater than the typical ion pair size and, therefore, multiple rings of IL appear inside the carbon nanotube. Using the results for the structural prop erties of ILs confined inside these nanotubes we were able to predict their properties when confined inside ZTC frameworks using its pore size distribution. In order to do that we modeled the structure as having a fraction of 1D regions and a fraction of 2D ones, which is equivalent to an effective noninteger dimensionality, corresponding to pores with a purely 1D arrangement and cavities formed where the pores meet which have a higher dimensionality. We showed that his model correctly pre dicts the structure of nanoconfined ILs, but it is not able to predict the 235 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ dynamics, but if combined with a model similar to the presented in the previous article with hopping probabilities between regions of different dimensionality. This method for calculating the structure opens the door to predicting the same properties in other carbon frameworks without the need of complex and timeconsuming simulations. The supplementary information for this article can be found in ap pendix A.3. The contribution of the author of this thesis to this publication, us ing the CRediT contribution classification,94;95 was: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing  Original Draft, Writing  Review & Editing, Visualization. 236 DOI: https://doi.org/1.11/.oi..11 DқҞҬңҷҨ IҩҨҮҟҭ ?қҧҪҩҭ 3. Continuation of the study of IL inside nanoporous frameworks, specifically of mixtures of ILs with other substances. 4. 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