During my thesis work I have investigated the problem of polyelectrolyte characterization and in particular how to interpret the experimental data to obtain the mass and gyration radius of short polyelectrolytes. This is usually a challenging problem for experimentalists to deal with. For example, the interpretation of the static light scattering data to obtain the gyration radius becomes increasingly inaccurate as the size of the chain becomes very much smaller then the light wavelength. Also, the interpretation of membrane osmomometry data is complicated by the leakage of the solute of low molecular weight polymers and so forth. There are, however, a number of approaches to deal with these problems. In the first chapter of my thesis I obtained a crossover formula of the second virial coefficient of polyelectrolytes that correctly reproduces the perturbative and asymptotic polymer regimes in addition to the salt concentration dependence at high-to-medium salt concentrations. This formula will then be combined with similar crossover formula for the radius of gyration to interpret the later from the second virial coefficient measurement. On the technical side of the story, the crossover formula was obtained by combining the renormalization group equation(to the first nontrivial order in epsilon) with the direct d=3 computation of the perturbative expansion( to the second order in the two coupling constants) obtained from double inverse Laplace transform. The second chapter of my dissertation is about the translocation phenomena. Translocation is a phenomena of threading a polymer through narrow pores and/or channels. This is very promising technique to measure the molecular weight of every individual polymer in the solution. Indeed, the polymer chain threading through the pore blocks the flow of electric current that also flows through the pore. By the duration of the current blockade the length of polymer chain can be obtained. Unfortunately, there are a number of problems this approach encounters. One of them is that the only so far practically obtainable nanometer-size pore is the alpha hemolysine one which has a complicated internal layout- a spherical(more or less) vestibule. This nasty feature makes current blockade vs time data harder to interpret. There is a way to bypass this problem. Recently a number of research groups began to modify the pore via the directed mutagenesis to reduce the time the chain spends in the vestibule. In my work I theoretically investigated translocation of the polyelectrolyte chain through a spherical cavity with tunable charge. The results provide some guidelines on how to reduce the influence of the vestibule on the translocation time if we are to medify the chain in addition to the decorating the pore with charges. This work includes a number of interesting techniques. It is based on the self-consistent field theory which gives us nonlinear Schroedinger and Poisson-Boltzmann equations. These equations are then solved numerically via a finite difference schemes. Lets point out possible extensions of this work. The SCFT technique is a primary computational tool for polyelectrolyte brushes and melts. Those things can be useful for the rapidly developing technology of pore gating, brush filtration and brush lubrication, just to name a few.

This research focuses on the modeling of dendrimer molecules for their application as delivery vectors within drug and gene therapy systems. We examine how the architecture and composition of dendrimers affect their drug and gene binding efficacies along with their interactions with anionic bilayers. We specifically focus on how the weakly basic nature of dendrimer monomers and the addition of neutral grafts to dendrimer surface groups affect their interactions with drugs, linear polyelectrolytes, and bilayers. By using polymer self-consistent field theory (SCFT) to model such systems, we develop a computationally efficient means to provide physical insights into these systems, which are intended to guide dendrimer design for delivery applications.We study the conformational properties of weakly basic (annealed) polyelectrolyte dendrimers by developing a SCFT model that explicitly accounts for the acid-base equilibrium reaction of the weakly basic monomers. We specifically focus on the role of local counterion concentration upon the charge and conformations of the annealed polyelectrolyte dendrimers. We compare our results to existing polymer scaling theories and develop a strong stretching theory for the dendrimer molecules.We extend the previous study to model the interactions between weakly basic dendrimers and weakly acidic, hydrophobic drug molecules. We specifically examine the effects of excluded volume, electrostatic, and enthalpic interactions on the binding efficacies between dendrimers and drugs under a variety of dendrimer generations, solution pOH conditions, drug sizes, and Bjerrum length values.We study the role of neutral dendrimer grafts on the conformations and drug binding efficacies of dendrimers. We then elucidate how the observed conformational changes affect the charge of the dendrimers. Furthermore, we examine how the presence of grafts affects the steric, electrostatic, and hydrophobic interactions between the drugs and dendrimers under a variety of solution conditions. We compare our results with the binding efficacies observed for non-grafted dendrimers to delineate the conditions under which the grafted dendrimers are better suited as drug hosts.We include semi-flexible, anionic linear polyelectrolyte (LPE) molecules in our grafted dendrimer SCFT framework to model the interactions between dendrimers and negatively charged genetic materials. Specifically, we examine how neutral dendrimer grafts, LPE stiffness, and solution pOH affect the interactions between dendrimers and LPEs. We then use our SCFT potential fields as input into Monte Carlo simulations in order to determine the dendrimer-LPE potentials of mean force and the resulting loop and tail statistics of the dendrimer-adsorbed LPE chains.We incorporate a negatively charged bilayer into our grafted dendrimer SCFT framework to model dendrimer interactions with a cellular membrane. We specifically examine the role of dendrimer grafting length, solution pH, and membrane tension on such interactions. By comparing our results with SCFT calculations of fixed dendrimer conformations and hard sphere nanoparticles in the presence of membranes, we delineate the role of dendrimer flexibility and porosity on the interactions between dendrimers and anionic bilayers. / text

Les dispersions colloïdales ont beaucoup d’applications technologiques importantes. A cause du mouvement brownien, les particules ont des collisions fréquentes entre elles. Les forces d’attraction de van der Waals,dérivant de potentiels à longue portés, conduisent à l’agrégation et à la précipitation des particules. Plusieurs méthodes ont été proposées pour diminuer ou contrebalancer l’effet d’attraction de van der Waals et augmenter la stabilité colloïdale. Par exemple, le choix du solvant possédant l’indice de réfraction le plus proche possible de celui des particules peut diminuer les forces de van der Waals. D'autres facteurs influencent la stabilité comme les interactions électrostatiques et les interactions spécifiques liées aux chaînes de polymères. Dans le cas des polymères, les chaînes peuvent être greffées à la surface des particules ou être dissoutes dans le solvant (chaînes libres). Dans ce travail de thèse, nous avons étudié l’effet de la stabilisation par déplétion dans le cas des chaînes de polymères libres (FPI, "free polymer induced interaction"). Des modèles théoriques précédents portent un caractère trop simplifié et utilisent des approximations sans vérification. De plus, l’influence des paramètres de la solution, c’est-à-dire, de la structure de polymères et de son interaction avec la surface de particule, n’a pas été étudiée.Les chaînes polymères libres ont été modélisées comme des marches aléatoires dans un champ moléculaire auto-cohérent qui satisfait à l'équation intégro-différentielle de diffusion. Pour le domaine moléculaire, nous avons utilisé un potentiel chimique qui, pour la solution de polymère semi-dilué, peut être représenté comme une expansion du viriel où nous n’avons pris en considération que les deuxième et troisième coefficients du viriel de la solution de polymère. En variant des paramètres tels que la rigidité du polymère, la longueur du polymère, la concentration en polymère et le régime du solvant (comme le solvant thêta), que ce soit pour une surface colloïdale purement répulsive, pour une surface adsorbée ou pour la surface d'une couche de polymère greffé, nous avons été en mesure d'améliorer la barrière répulsive due aux polymères libres entre les particules et donc nous avons trouvé des conditions de la stabilisation cinétique du système. / Stable colloidal dispersions with evenly distributed particles are important for many technological applications. Due to Brownian motion colloidal particles have constant collisions with each other which often lead to their aggregation driven by the long range van der Waals attraction. As a result the colloidal systems often tend to precipitate. A number of methods have been devised to minimize the effect of long-range van der Waals attraction between colloidal particles or to override the influence of the attraction in order to provide the colloidal stability.In the PhD thesis we investigated the colloidal stabilization in solutions of free polymers which is commonly referred to as depletion stabilization. Previous theoretical studies of free-polymer induced (FPI) stabilization were based on oversimplified models involving uncontrolled approximations. Even the most basic features of the depletion stabilization phenomenon were unknown. It was unclear how the PI repulsion depends on the solution parameters, polymer structure and monomer/surface interactions.The free polymer chains were modeled as random walks in a self-consistent molecular field that satisfied to diffusion-like integro-differential equation. As the molecular field we used the chemical potential that for semi-dilute polymer solution can be represented as a virial expansion where we took into account only second and third virial coefficients of the polymer solution. Varying the parameters like polymer stiffness, polymer length, polymer concentration and solvent regime (like theta solvent) whether it is for purely repulsive colloidal surface, adsorbed surface or surface with grafted polymer layer we were able to enhance the repulsive barrier due to the free polymers between the particles and therefore found conditions for kinetic stabilization of the system.

<p>The bending moduli and line tension of bilayer membranes self-assembled from diblock copolymers was calculated using the self-consistent field theory. The limitation of the linear elasticity theory (Helfrich model) was evaluated by calculating fourth- order curvature moduli in high curvature systems. It was found that in highly curved membranes, the fourth-order contributions to the bending energy becomes comparable to the low-order terms. The line tension (γL) of membrane pores was also investigated for mixtures of structurally different diblock copolymers. The line ten- sion was found to depend sensitively on the diblock chain topology. Addition of short hydrophobic copolymers was found to reduce the line tensions to negative values, showing that lipid mixtures may be used as pore stabilizers.</p> / Master of Science (MSc)

<p>The phase behavior of AB diblock copolymers mixed with C homopolymers (AB/C), in which A and C are capable of forming hydrogen-bonds, is examined using self-consistent field theory. The study focuses on the modeling of hydrogen-bonding in polymers. Specifically, we examine two models for the formation of hydrogen-bonds between polymer chains. The first commonly used model assumes a large attractive interaction parameter between the A/C monomers. This model reproduces correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C homopolymers. The second model is based on the fact that hydrogen-bonding leads to A/C complexation. We show that the interpolymer complexation model predicts correctly the order-order phase transition sequences and the decrease of lamellar spacing for strong hydrogen-bonding. Our analysis demonstrates that hydrogen-bonding of polymers should be modeled by interpolymer complexation.</p> / Master of Science (MSc)

In this project we review the method of using c-extremization and computing anomalies to obtain AdS/CFT theories. We start with a quick introduction to CFT's and AdS/CFT correspondence which gives us the tools to later understand the 2D N= (2,0) SCFT and its gravity duals in particular AdS_5xS^5 and AdS_7xS^4 compactified on Riemann surfaces.