Apesar de sua familiaridade e simplicidade, a água apresenta um conjunto propriedades termodinâmicas, dinâmicas e estruturais que são ainda objeto de intensa pesquisa. O aumento da densidade com a temperatura, da difusão com a densidade, ou ainda do ordenamento com a temperatura são exemplos de alguns de seus comportamentos não usuais. Com a finalidade de melhor compreender tais propriedades inúmeras abordagens têm sido utilizadas, tais como o uso geometrias de confinamento, modelos simplificados ou até mesmo misturas. Dentre as geometrias confinantes frequentemente usadas, encontra-se, nanoporos, placas paralelas e meio porosos. Os meios porosos são formados por obstáculos fixos que impõem efeitos de volume excluído adicionais ao sistema. Já no caso de misturas quando elas ocorrem entre líquidos capazes de formar ligações de hidrogênio, o comportamento não usual da água dá origem a um conjunto ainda maior de propriedades anômalas. A mistura água-metanol por exemplo, é munida de um conjunto propriedades de excesso incapazes de serem descritas pelas teorias usuais. São alguns exemplos, o máximo no calor específico e o mínimo no volume e entalpia de excesso. Neste projeto de doutoramento, nós estudamos por simulações numericas o confinamento por meio poroso (desordem queched) e misturas de água com solutos interagentes. O primeiro estudo é realizado usando um modelo 2D tipo-água que é largamente conhecido na literatura. No segundo estágio, estamos a influência de solutos interagentes nas propriedades de modelos em rede e contínuos. Para o modelo em rede, nós desenvolvemos um modelo de soluto e posteriormente uma técnica capaz de simular misturas de modelos em rede a pressão constante. De posse desta técnica estudamos as propriedades de excesso da mistura. / Although the familiarity and simplicity, the water show a set of thermodynamic, dynamics and structural properties which are still subject to intense research. The increase of density as the temperature, of diffusion as the density, or even of ordering with the temperature are examples of some of its unusual behavior. In order to better understand these properties numerous approaches have been used, such as the use of confinement geometries, simplified models, or ever mixtures. Among the confinement geometries used, are those, nanopores, parallel plates and porous media. The porous media are formed by fixed obstacles that impose the additional excluded volume effects to the system. In the case of mixtures, when they occur between liquids able to form hydrogen-bonds, the unusual behavior of water give rise to a set even higher anomalous properties. The water-methanol mixture, for example, has a set of excess properties unable to be described by usual theories. Some examples are the maximum in the specific heat and minimum in excess volume and enthalpy. In this Ph.D. project, we study by numerical simulations, the confinement of water by porous media(or under quenched disorder) and the mixture of water with interacting solutes. The first study is performed using a 2D lattice model which is widely known in the literature. In a second stage, we study the influence of interacting solutes on the properties of lattice and continuous models. For the lattice model, we develop a solute model and a technique to simulate mixtures of lattice models at constant pressure. Using this technique, we study the excess properties of the mixture. For the continuous model we study the influence of a dimeric solute on the TMD of a water-like model and posteriorly we study the excess properties of this type of mixture.

A polymer is a large molecule constructed from many smaller structural units calledmonomers joined together by covalent bonds. Polymers have existed in natural formsince life began and those such as DNA, RNA, proteins and polysaccharides are someof the most important macromolecules found in plant and animal life. From the earliesttimes, the man has used many of these polymers as materials for providing clothing,decoration, tools, weapons and other requirements. However, the origins of today'spolymer industry commonly are accepted as being in the nineteenth century whenimportant discoveries were made concerning to the modification of certain naturalpolymers, as cellulose. The use of synthetic and natural polymers as stabilisers forcolloid systems (sols, dispersions, microemulsions, etc.) is becoming more importanteveryday in contemporary life. Polymer additives can be applied in preconcentrationsand dehydration of suspensions in mineral processing, purification of wastewater andeven in nutritional and pharmaceutical emulsions being their importance related to thecharacteristics of the process and the properties that they show. The present work aimsto develop appropriate numerical and analytical modelling techniques, which candescribe (considering the formation of loops and tails) the structure of a polymeric layeradsorbed on heterogeneous surfaces; this adsorbed layer is an relevant factor in theproperties showed by this kind of materials. Taking into account this, the methodologyknown as Single Chain Mean Field (SCMF) (originally used to study micellaraggregates and grafted polymers) was modified to apply on polymer adsorptionproblems. In this way, it was possible to calculate numerically properties that can beexperimentally measured, such as total monomer volume fraction profiles, loop and tailvolume fraction profiles, adsorbance or the thickness of the adsorbed layer. Thestructure of the polymeric layer was examined both for flat and spherical (colloidalparticles) surface geometries. When compared with other well establishedmethodologies for the numerical simulation of polymeric systems, this new version ofSCMF was found to be more efficient due to the improved sampling of the polymerchain configuration space.Thus, SCMF method results, in the case of the adsorption on flat surfaces, compare wellwith those obtained either with Monte Carlo simulations or with the method developedin the 80s by Scheutjens and Fleer (SCF). Due to the lack of studies focusing to polymeradsorption on colloidal particles, our results have been the first to present quantitativepredictions of the structure of the polymeric layer adsorbed on a spherical surface. Thus,we have demonstrated the dependence of the adsorbed polymer layer with the size ofthe colloidal particle as well as the characteristic lengths that influence on it. Finally, inthis work an analytical approach for the description of polymer-colloidal mixtures hasbeen developed which compares well with the numerical results obtained from theSCMF methodology. Furthermore, the analytical approach is able to predict systembehaviours, as for example the formation of gels. / Un polímero es una molécula de grandes dimensiones formada de pequeñas unidadesllamadas monómeros, los cuales se encuentran unidos por medio de enlaces covalentes.Los polímeros han existido de forma natural desde el comienzo de la vida, y aquelloscomo el DNA, RNA o las proteínas son algunos de los polímeros más importantesencontrados tanto en la vida animal como en la vegetal. Desde siempre el hombre hautilizado muchos de estos polímeros como materiales para hacer ropa, decoración,herramientas, etc. Sin embargo, el origen de la industria de polímeros que conocemoshoy en día se produjo en el siglo 19, gracias a importantes descubrimientos dentro de lamodificación de ciertos polímeros naturales, como la celulosa. El uso de polímerossintéticos y naturales como estabilizadores de sistemas coloidales (dispersiones,microemulsiones, etc.) juega en nuestros días un papel importante. Los polímerosutilizados como aditivos, pueden ser aplicados en preconcentraciones y deshidrataciónde suspensiones dentro de procesos minerales, tratamiento de aguas residuales e inclusolos podemos encontrar dentro de la industria farmacéutica y alimentaria, donde suimportancia es debida a la procesabilidad y propiedades que ellos exhiben. El trabajoque se presenta es orientado al desarrollo de técnicas de modelización, tanto analíticascomo computacionales, y su aplicación en la descripción (por medio de la formación debucles y colas) de la estructura de la capa de polímeros adsorbida en superficiesheterogéneas, siendo dicha capa de polímeros un factor importante en las propiedadesque este tipo de materiales presentan. Con este propósito, la metodología conocidacomo Single Chain Mean Field, utilizada anteriormente tanto para el estudio deagregados micelares como de polímeros anclados en superficies, ha sido modificadapara describir la adsorción de polímeros en superficies. Así se han podido calcularnuméricamente propiedades medibles experimentalmente como los perfiles de lafracción en volumen de monómeros totales, además de los pertenecientes a los bucles ycolas, adsorbancia o el espesor de la capa adsorbida, para geometrías de la superficieabsorbente tanto plana como esférica (partículas coloidales). En su comparación conotras metodologías, ya establecidas para la simulación numérica dentro de la física depolímeros, la aplicación de esta nueva versión del Single Chain Mean Field (SCMF)ha resultado ser más eficiente debido a un mejor muestreo del espacio deconfiguraciones de las cadenas poliméricas. De este modo, comparando los resultadosobtenidos a partir del SCMF, con aquellos obtenidos mediante técnicas de simulaciónMonte Carlo o la teoría desarrollada en los años 80 por Scheutjens y Fleer (SCF), se hapodido encontrar un buen acuerdo en las propiedades calculadas para el caso de laadsorción en superficies planas. Debido a la dificultad intrínseca del estudio de laadsorción en superficies curvadas, nuestros resultados son los primeros que presentanpredicciones cuantitativas sobre la estructura de la capa que se forma sobre unapartícula coloidal. Así hemos podido comprobar la dependencia de la estructura de lacapa de polímeros adsorbidos con el tamaño de la partícula sobre la que se encuentranadsorbidos además de las longitudes características de las cuales depende. Finalmente,en este trabajo se ha desarrollado, también, una teoría analítica para la descripción de lamezcla polímero-coloide. De este modo, los resultados numéricos obtenidos con elSCMF han podido ser comparados con dicha teoría, obteniendo, de nuevo, un buenacuerdo y predecir, además, comportamientos colectivos como la formación de geles.

Apesar de sua familiaridade e simplicidade, a água apresenta um conjunto propriedades termodinâmicas, dinâmicas e estruturais que são ainda objeto de intensa pesquisa. O aumento da densidade com a temperatura, da difusão com a densidade, ou ainda do ordenamento com a temperatura são exemplos de alguns de seus comportamentos não usuais. Com a finalidade de melhor compreender tais propriedades inúmeras abordagens têm sido utilizadas, tais como o uso geometrias de confinamento, modelos simplificados ou até mesmo misturas. Dentre as geometrias confinantes frequentemente usadas, encontra-se, nanoporos, placas paralelas e meio porosos. Os meios porosos são formados por obstáculos fixos que impõem efeitos de volume excluído adicionais ao sistema. Já no caso de misturas quando elas ocorrem entre líquidos capazes de formar ligações de hidrogênio, o comportamento não usual da água dá origem a um conjunto ainda maior de propriedades anômalas. A mistura água-metanol por exemplo, é munida de um conjunto propriedades de excesso incapazes de serem descritas pelas teorias usuais. São alguns exemplos, o máximo no calor específico e o mínimo no volume e entalpia de excesso. Neste projeto de doutoramento, nós estudamos por simulações numericas o confinamento por meio poroso (desordem queched) e misturas de água com solutos interagentes. O primeiro estudo é realizado usando um modelo 2D tipo-água que é largamente conhecido na literatura. No segundo estágio, estamos a influência de solutos interagentes nas propriedades de modelos em rede e contínuos. Para o modelo em rede, nós desenvolvemos um modelo de soluto e posteriormente uma técnica capaz de simular misturas de modelos em rede a pressão constante. De posse desta técnica estudamos as propriedades de excesso da mistura. / Although the familiarity and simplicity, the water show a set of thermodynamic, dynamics and structural properties which are still subject to intense research. The increase of density as the temperature, of diffusion as the density, or even of ordering with the temperature are examples of some of its unusual behavior. In order to better understand these properties numerous approaches have been used, such as the use of confinement geometries, simplified models, or ever mixtures. Among the confinement geometries used, are those, nanopores, parallel plates and porous media. The porous media are formed by fixed obstacles that impose the additional excluded volume effects to the system. In the case of mixtures, when they occur between liquids able to form hydrogen-bonds, the unusual behavior of water give rise to a set even higher anomalous properties. The water-methanol mixture, for example, has a set of excess properties unable to be described by usual theories. Some examples are the maximum in the specific heat and minimum in excess volume and enthalpy. In this Ph.D. project, we study by numerical simulations, the confinement of water by porous media(or under quenched disorder) and the mixture of water with interacting solutes. The first study is performed using a 2D lattice model which is widely known in the literature. In a second stage, we study the influence of interacting solutes on the properties of lattice and continuous models. For the lattice model, we develop a solute model and a technique to simulate mixtures of lattice models at constant pressure. Using this technique, we study the excess properties of the mixture. For the continuous model we study the influence of a dimeric solute on the TMD of a water-like model and posteriorly we study the excess properties of this type of mixture.

Apesar de sua familiaridade e simplicidade, a água apresenta um conjunto propriedades termodinâmicas, dinâmicas e estruturais que são ainda objeto de intensa pesquisa. O aumento da densidade com a temperatura, da difusão com a densidade, ou ainda do ordenamento com a temperatura são exemplos de alguns de seus comportamentos não usuais. Com a finalidade de melhor compreender tais propriedades inúmeras abordagens têm sido utilizadas, tais como o uso geometrias de confinamento, modelos simplificados ou até mesmo misturas. Dentre as geometrias confinantes frequentemente usadas, encontra-se, nanoporos, placas paralelas e meio porosos. Os meios porosos são formados por obstáculos fixos que impõem efeitos de volume excluído adicionais ao sistema. Já no caso de misturas quando elas ocorrem entre líquidos capazes de formar ligações de hidrogênio, o comportamento não usual da água dá origem a um conjunto ainda maior de propriedades anômalas. A mistura água-metanol por exemplo, é munida de um conjunto propriedades de excesso incapazes de serem descritas pelas teorias usuais. São alguns exemplos, o máximo no calor específico e o mínimo no volume e entalpia de excesso. Neste projeto de doutoramento, nós estudamos por simulações numericas o confinamento por meio poroso (desordem queched) e misturas de água com solutos interagentes. O primeiro estudo é realizado usando um modelo 2D tipo-água que é largamente conhecido na literatura. No segundo estágio, estamos a influência de solutos interagentes nas propriedades de modelos em rede e contínuos. Para o modelo em rede, nós desenvolvemos um modelo de soluto e posteriormente uma técnica capaz de simular misturas de modelos em rede a pressão constante. De posse desta técnica estudamos as propriedades de excesso da mistura. / Although the familiarity and simplicity, the water show a set of thermodynamic, dynamics and structural properties which are still subject to intense research. The increase of density as the temperature, of diffusion as the density, or even of ordering with the temperature are examples of some of its unusual behavior. In order to better understand these properties numerous approaches have been used, such as the use of confinement geometries, simplified models, or ever mixtures. Among the confinement geometries used, are those, nanopores, parallel plates and porous media. The porous media are formed by fixed obstacles that impose the additional excluded volume effects to the system. In the case of mixtures, when they occur between liquids able to form hydrogen-bonds, the unusual behavior of water give rise to a set even higher anomalous properties. The water-methanol mixture, for example, has a set of excess properties unable to be described by usual theories. Some examples are the maximum in the specific heat and minimum in excess volume and enthalpy. In this Ph.D. project, we study by numerical simulations, the confinement of water by porous media(or under quenched disorder) and the mixture of water with interacting solutes. The first study is performed using a 2D lattice model which is widely known in the literature. In a second stage, we study the influence of interacting solutes on the properties of lattice and continuous models. For the lattice model, we develop a solute model and a technique to simulate mixtures of lattice models at constant pressure. Using this technique, we study the excess properties of the mixture. For the continuous model we study the influence of a dimeric solute on the TMD of a water-like model and posteriorly we study the excess properties of this type of mixture.

This work addresses properties of two-component lipid membranes on the experimentally relevant spatial scales of order of a micrometer and time intervals of order of a second by means of lattice-based Monte Carlo (MC) simulations. To be able to do that with reasonable computational efforts the lipid membrane is modeled as a square lattice of lipid molecules with next-neighbor interaction. This allows for efficient computation and thus provides a large-scale simulation with which it was possible to obtain important results previously not reported in simulation studies of lipid membranes. After properly tuning the next-neighbor interaction energies the simulation reproduces the experimental phase diagram of the DMPC/DSPC lipid system which is used as a model system in this work. Beyond that, the MC simulation provides a more detailed description of the phase behavior of the lipid mixture than the experimental data. It is found that, within a certain range of lipid compositions, the phase transition from the fluid phase to the fluid–gel phase coexistence proceeds via near-critical fluctuations, while for other lipid compositions this phase transition has a quasi-abrupt character. The complete combined state and component phase diagram is constructed by structure function analysis which confirms the existence of a critical point in the system. The dynamics of membrane coarsening after an abrupt temperature quench to the fluid–gel coexistence region of the phase diagram are studied. In this context, it is found that lateral diffusion of lipids plays an important role in the fluid–gel phase separation process. Dynamic scaling is observed only if the ratio of gel and fluid phase in the membrane stays constant in time. The line tension characterizing lipid domains in the fluid–gel coexistence region is found to be in the pN range thus matching values both predicted theoretically and measured experimentally. When approaching the critical point, the line tension, the inverse correlation length of fluid–gel spatial fluctuations, and the corresponding inverse order parameter susceptibility of the membrane vanish in agreement with recent experimental findings for model lipid membranes. By simulating single particle tracking and fluorescence correlation spectroscopy experiments it is found that in the presence of near-critical fluctuations lipid molecules show transient subdiffusive behavior, which is a new result important for understanding the origins of subdiffusion in cell membranes which are believed to be close to a critical point. The membrane–cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion is established.

This work addresses properties of two-component lipid membranes on the experimentally relevant spatial scales of order of a micrometer and time intervals of order of a second by means of lattice-based Monte Carlo (MC) simulations. To be able to do that with reasonable computational efforts the lipid membrane is modeled as a square lattice of lipid molecules with next-neighbor interaction. This allows for efficient computation and thus provides a large-scale simulation with which it was possible to obtain important results previously not reported in simulation studies of lipid membranes. After properly tuning the next-neighbor interaction energies the simulation reproduces the experimental phase diagram of the DMPC/DSPC lipid system which is used as a model system in this work. Beyond that, the MC simulation provides a more detailed description of the phase behavior of the lipid mixture than the experimental data. It is found that, within a certain range of lipid compositions, the phase transition from the fluid phase to the fluid–gel phase coexistence proceeds via near-critical fluctuations, while for other lipid compositions this phase transition has a quasi-abrupt character. The complete combined state and component phase diagram is constructed by structure function analysis which confirms the existence of a critical point in the system. The dynamics of membrane coarsening after an abrupt temperature quench to the fluid–gel coexistence region of the phase diagram are studied. In this context, it is found that lateral diffusion of lipids plays an important role in the fluid–gel phase separation process. Dynamic scaling is observed only if the ratio of gel and fluid phase in the membrane stays constant in time. The line tension characterizing lipid domains in the fluid–gel coexistence region is found to be in the pN range thus matching values both predicted theoretically and measured experimentally. When approaching the critical point, the line tension, the inverse correlation length of fluid–gel spatial fluctuations, and the corresponding inverse order parameter susceptibility of the membrane vanish in agreement with recent experimental findings for model lipid membranes. By simulating single particle tracking and fluorescence correlation spectroscopy experiments it is found that in the presence of near-critical fluctuations lipid molecules show transient subdiffusive behavior, which is a new result important for understanding the origins of subdiffusion in cell membranes which are believed to be close to a critical point. The membrane–cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion is established.