Part I: The Theory of Brownian Vacancy Driven Walk We analyze the lattice walk performed by a tagged member of an infinite 'sea' of particles filling a d-dimensional lattice, in the presence of a single vacancy. The vacancy is allowed to be occupied with probability 1/2d by any of its 2d nearest neighbors, so that it executes a Brownian walk. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. Thus, the tagged particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a random walk "driven" by the Brownian vacancy. The probability distributions for its displacement and for the number of steps taken, after n-steps of the vacancy, are derived. Neither is a Gaussian! We also show that the only nontrivial dimension where the walk is recurrent is d=2. As an application, we compute the expected energy shift caused by a Brownian vacancy in a model for an extreme anisotropic binary alloy. In the last chapter we present a Monte-Carlo study and a mean-field analysis for interface erosion caused by mobile vacancies. Part II: One-Dimensional Periodic Hopping Models with Broken Translational Invariance.Case of a Mobile Directional Impurity We study a random walk on a one-dimensional periodic lattice with arbitrary hopping rates. Further, the lattice contains a single mobile, directional impurity (defect bond), across which the rate is fixed at another arbitrary value. Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. Analytic solution for the distributions in the steady state limit is obtained. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. As an application, we extend the Duke-Rubinstein reputation model of gel electrophoresis to include polymers with impurities and give the exact distribution of the steady state. / Ph. D.

Ionomeric polymer transducers exhibit electromechanical coupling capabilities. The transport of charge due to electric stimulus is the primary mechanism of actuation for a class of polymeric active materials known as ionomeric polymer transducers (IPTs). The research presented in this dissertation focuses on modeling the cation transport and cation steady state distribution due to the actuation of an IPT. Ion transport in the IPT depends on the morphology of the hydrated Nafion membrane and the morphology of the metal electrodes. Recent experimental findings show that adding conducting powders at the polymer-conductor interface increases the displacement output. However, it is difficult for a traditional continuum model based on transport theory to include morphology in the model. In this dissertation, a two-dimensional Monte Carlo simulation of ion hopping has been developed to describe ion transport in materials that have fixed and mobile charge similar to the structure of the ionic polymer transducer. In the simulation, cations can hop around in a square lattice. A step voltage is applied between the electrodes of the IPT, causing the thermally-activated hopping between multiwell energy structures. By sampling the ion transition time interval as a random variable, the system evolution is obtained. Conducting powder spheres have been incorporated into the Monte Carlo simulation. Simulation results demonstrate that conducting powders increase the ion conductivity. Successful implementation of parallel computation makes it possible for the simulation to include more powder spheres to find out the saturation percentage of conducting powders for the ion conductivity. To compare simulation results with experimental data, a multiscale model has been developed to increase the scale of Monte Carlo simulation. Both transient responses and steady state responses show good agreement with experimental measurements. / Ph. D.

Miniaturization has become a driving force in different areas of technology including microelectronics, sensoric- and bio-technologies and in fundamental science. Because of the well-known limitations of conventional lithographic methods, newly emerging bottom-up approach, utilizing self-assembly of various nanoobjects including single polymer molecules and carbon nanotubes constitutes a very promising alternative for fabrication of ultimately small devices. Carbon nanotubes are attractive materials for nanotechnology and hold much promise to revolutionize fundamental science in a investigation of phenomena, associated with the nanometer–sized objects.It was found in this work that grafted chains of poly(2-vinylpyridine) form a shell covering the carbon nanotubes that makes them dispersible in organic solvents and in acidic water (CNTs-g-P2VP).The positively charged poly(2-vinylpyridine) shell is responsible for the selective deposition of carbon nanotubes onto oppositely charged surfaces. It was established that the deposition CNTs-g-P2VP from aqueous dispersions at low pH is an effective method to prepare ultra-thin films with a tunable density of carbon nanotubes.It was shown that poly(2-vinylpyridine) grafted to carbon nanotubes is a universal support for the immobilization of various nanoclusters at the carbon nanotube's surface. Prussian Blue nanoparticles were selectively attached to the surface of CNTs-g-P2VP.Conducting polymer nanowires are another very promising kind of nanomaterials that could be also suitable for applications in nanodevices and nanosensors. In this work was developed a simple method to control the conformation and orientation of single adsorbed polyelectrolyte molecules by co-deposition with octylamine. A simple chemical route to conductive polypyrrole nanowires by the grafting of polypyrrole from molecules of polystyrensulfonic acid was developed. The dc conductivity of individual polypyrrole nanowires approaches the conductivity of polypyrole in bulk.The conductivity can be described using variable-range hopping model.

Miniaturization has become a driving force in different areas of technology including microelectronics, sensoric- and bio-technologies and in fundamental science. Because of the well-known limitations of conventional lithographic methods, newly emerging bottom-up approach, utilizing self-assembly of various nanoobjects including single polymer molecules and carbon nanotubes constitutes a very promising alternative for fabrication of ultimately small devices. Carbon nanotubes are attractive materials for nanotechnology and hold much promise to revolutionize fundamental science in a investigation of phenomena, associated with the nanometer–sized objects.It was found in this work that grafted chains of poly(2-vinylpyridine) form a shell covering the carbon nanotubes that makes them dispersible in organic solvents and in acidic water (CNTs-g-P2VP).The positively charged poly(2-vinylpyridine) shell is responsible for the selective deposition of carbon nanotubes onto oppositely charged surfaces. It was established that the deposition CNTs-g-P2VP from aqueous dispersions at low pH is an effective method to prepare ultra-thin films with a tunable density of carbon nanotubes.It was shown that poly(2-vinylpyridine) grafted to carbon nanotubes is a universal support for the immobilization of various nanoclusters at the carbon nanotube's surface. Prussian Blue nanoparticles were selectively attached to the surface of CNTs-g-P2VP.Conducting polymer nanowires are another very promising kind of nanomaterials that could be also suitable for applications in nanodevices and nanosensors. In this work was developed a simple method to control the conformation and orientation of single adsorbed polyelectrolyte molecules by co-deposition with octylamine. A simple chemical route to conductive polypyrrole nanowires by the grafting of polypyrrole from molecules of polystyrensulfonic acid was developed. The dc conductivity of individual polypyrrole nanowires approaches the conductivity of polypyrole in bulk.The conductivity can be described using variable-range hopping model.