Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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The self-consistent field theory (SCFT) has reveived a great success in prediction of the physical properties of a variety of polymeric systems in the recent two decades. However, the traditional SCFT is based on the Gaussian chain model, completely neglecting the chain rigidity effects, which is ascribed to one of the intrinsic properties of polymer chains. This thesis concentrates on the development of SCFT in the framework of the wormlike chain model and studies the influence of the chain rigidity on the chain configuration which directly determines properties of polymer materials in the mesoscale. Firstly, considering Onsager-type, orientational-dependent repulsive interactions, we study a model for the isotropic-nematic interface in liquid-crystals. Through adjusting the ratio of total contour length L to the persistence length lambda, we consider systems consisting of molecules with various degrees of flexibility: from rods to flexible chains. Physical properties such as the surface tension, interfacial width and density- and order-parameter profiles were numerically calculated as functions of the flexibility L/lambda and tilt angle, which is defined as the angle between the interfacial normal and the nematic director. Secondly, We examine the influence of persistency on the phase diagram of AB diblock copolymers and the properties of the phase transition as a function of volume fraction, Flory-Huggins parameter and chain rigidity, covering a broad regime spanning from Gaussian chains to rigid rodlike chains. On one hand, we demonstrate that results from a Gaussian-weight based theory can be recovered in the long-chain limit, and on the other hand, we display that significant revisions to the phase diagram, due to the persistency effects, exist for shorter chains. To achieve this, an efficient numerical scheme is designed for implementing the calculations of the wormlike-chain SCFT in a full six-dimensional space.

The self-consistent field theory (SCFT) has reveived a great success in prediction of the physical properties of a variety of polymeric systems in the recent two decades. However, the traditional SCFT is based on the Gaussian chain model, completely neglecting the chain rigidity effects, which is ascribed to one of the intrinsic properties of polymer chains. This thesis concentrates on the development of SCFT in the framework of the wormlike chain model and studies the influence of the chain rigidity on the chain configuration which directly determines properties of polymer materials in the mesoscale. Firstly, considering Onsager-type, orientational-dependent repulsive interactions, we study a model for the isotropic-nematic interface in liquid-crystals. Through adjusting the ratio of total contour length L to the persistence length lambda, we consider systems consisting of molecules with various degrees of flexibility: from rods to flexible chains. Physical properties such as the surface tension, interfacial width and density- and order-parameter profiles were numerically calculated as functions of the flexibility L/lambda and tilt angle, which is defined as the angle between the interfacial normal and the nematic director. Secondly, We examine the influence of persistency on the phase diagram of AB diblock copolymers and the properties of the phase transition as a function of volume fraction, Flory-Huggins parameter and chain rigidity, covering a broad regime spanning from Gaussian chains to rigid rodlike chains. On one hand, we demonstrate that results from a Gaussian-weight based theory can be recovered in the long-chain limit, and on the other hand, we display that significant revisions to the phase diagram, due to the persistency effects, exist for shorter chains. To achieve this, an efficient numerical scheme is designed for implementing the calculations of the wormlike-chain SCFT in a full six-dimensional space.

We develop a self-consistent field theory of polymer dynamics, based on a functional integral approach, which is analogous to the existing equilibrium self-consistent field theory for polymers. We apply a saddle-point approximation to the exact dynamical theory, which generates a set of mean-field equations for the time-dependent density and mean force field. We also develop a method of treating the single-chain dynamics exactly, subject to this mean-field, resulting in a functional Fokker-Planck equation that must be solved along with the mean-field equations in a self-consistent manner. To test the self-consistency, we apply the theory to the simple but non-trivial case of np Brownian particles in one dimension interacting via a short-range repulsion in a harmonic external potential. Results for the non-interacting case agree with the literature. The interacting case demonstrates physically sensible interaction-dependent dynamics, such as an increased broadening of the density field when the repulsion is increased. We also examine the dynamics of a binary system with two distinct particle species. We calculate the center-of-mass trajectories for colliding distributions of species A and B, and observe that when the difference of repulsion strengths between like and unlike species chi is greater than a threshold value (between chi = 0.3 and chi = 0.4), the two species do not mix (indicating the onset of phase segregation).

A common strategy employed to destroy harmful bacteria is to disrupt the bacterial membrane through the action of pore-forming anti-microbial peptides. The manner in which the peptides arrange themselves spatially to form a pore in the membrane, which is important for understanding both the mechanism of pore formation and pore function, is a topic of current debate. We contrast the response of a model membrane bilayer to the presence of solid, cylindrical nanoparticle insertions, when the bilayer is composed of persistent worm-like chains and when it is composed of flexible Gaussian chains. We use self-consistent field theory, with the appropriate single-chain propagator, to describe the amphiphilic star-like triblock copolymers composing the membrane and the solvent. The nanoparticle surfaces are designed to have patches that prefer either the solvent or the tail groups of the copolymers, and the nanoparticles are fixed in space. Using this model with polymers in the lamellar phase, we investigate the question of pore-formation, nanoparticle insertion and hydrophobic mismatch in lipid bilayers and the effect that chain rigidity has on these particular interactions. We find that the main effect of increased chain rigidity is that it increases the free energy scaling and the significance of the energy barriers associated with these pore-forming processes. These results demonstrate the importance of using a more realistic persistent chain when modelling pore formation. / NSERC, CFI, SHARCNET

We develop a coarse-grained model of lipids and proteins in which the lipids are modelled as diblock copolymers and the proteins as rigid cylinders. The generic protein model allows the possibility of amphipathic proteins with intrinsic curvature. Self-consistent field theory (SCFT) is used to determine the morphology of the lipid bilayer in the vicinity of the proteins. In particular, we focus on the case of a long transmembrane protein inserted perpendicular to the bilayer. For this system we use SCFT to determine the mechanical properties of the membrane and the thickness profile as a function of distance from the protein inclusion. The mechanical constants are also used in an elastic theory to predict the thickness profile. Good agreement between the full SCFT and elastic theory is obtained. We also use SCFT to determine systematic trends of the boundary conditions for the thickness profile at the protein interface. Such results could be used as boundary conditions for the description of bilayers using elastic theory. We show that this system undergoes a second order wetting transition as the interaction strength between the protein and membrane is varied. / Thesis / Master of Science (MSc)

In this thesis, we use the self-consistent field theory (SCFT) to study neutral and charged block copolymer melts and blends in thin films and bulk. We showcase the utility of the SCFT by applying it to a number of different model systems. In our first study, we examined the elastic properties of multi-component bilayer membranes composed of amphiphilic AB/ED diblock copolymers. We focused on the effects of chain architecture and interactions between the amphiphilic molecules on the line tension or edge energy of a membrane pore. We discovered a direct relationship between the effective volume of the amphiphilic molecules, which is dictated by their architecture, and the line tension. We found that the addition of cone-shaped molecules to the membrane results in a decrease in the line tension. The opposite effect is seen for inverse cone-shaped amphiphiles, where an increase in their concentration results in an increase of the line tension. Studies two and three fall under the theme of directed self assembly of block copolymer thin films. First we examined the effects of ion concentration on the strength of the external electric field required to reori- ent lamellar domains from the parallel to the perpendicular orientation. The change in the critical electric field is found to be dependent on whether the neutral or charged polymer species is favoured by the top and bottom surfaces. In the second study, we examined the mechanism of using the entropic effect to direct the self assembly of micro domains in star block copolymer thin films. We control the architecture of star block copolymers by varying the number of arms, ranging from a linear chain with 1-arm to 4-arm star block copolymers. Using both experiments and SCFT, we showed that the entropic effect is enhanced in star block copolymer blends with greater number of arms. Furthermore, we showed that the entropic effect can be used to direct the self assembly of micro domains perpendicular to the substrate. In our last study, we examined the unbinding transition of the α-BN phase in pentablock terpolymer/ homopolymer blends. We constructed a phase diagram of the system as a function of homopolymer con- centration. We discovered that the unbinding transition is preempted by the macrophase separation of the blends into block copolymer rich/ homopolymer rich domains. The results presented in this thesis help advance our understanding of various properties of polymeric systems, such as the elastic properties of multi-component membranes, directed self assembly in block copolymer thin films and the phase behaviour of block copolymers in bulk. / Thesis / Doctor of Philosophy (PhD)

In this project, the sensitivity of the phase behaviour of AB diblock copolymers to the addition a single C-monomer is investigated using self-consistent mean-field theory. The reference diblock copolymers are composed of the minority A block with N_A = 12 monomers and the majority B block with N_B monomers. The blocks are mutually repulsive and their interaction is characterised by χ_{ij} and acts over range σ_{ij}, where i and j represent the monomer species. When a C-monomer is added to the junction of the diblock copolymers, we observe a notable shift of the phase boundaries to the larger NB and smaller χ_{AB}. The shift to larger NB is due to an increased polymer stretching. When the C-monomers is nearly-neutral, the shift does not strongly depend on the interaction strength. Similarly, the shift is not visibly affected by changing σ_{AC} and σ_{BC}. However, when the the strength of the interaction is selective such that χ_{AC} = χ_{AB} + α and χ_{BC} = χ_{AB} − α, the shift size decreases with increasing α. Conversely, when the selective C-monomer is added to the majority end, the phase boundaries are shifted to the smaller N_B, with the smallest α giving the largest shift. The shifts can be generically understood to be cause by the interplay between the changes in the interfacial tension and polymer stretching due to the C-monomer. These results demonstrate sensitivity of phase behaviour of AB diblock copolymers to the addition of a C-monomer and may provide a useful link between experiment and theory. / Thesis / Master of Science (MSc)

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