In this thesis, we study the classical-quantum correspondence of polyatomic molecules to further understand their rotational and vibrational behavior. More specifically, we focus on two different scenarios: (1) completely rigid asymmetric top molecules and (2) molecules with purely vibrational behavior. In the first part, we study the dynamics of the two asymmetric top molecules ortho-aminobenzonitrile (OABN) and para-aminobenzonitrile (PABN) in a static electric field. These structural isomers feature differing asymmetries and dipole moments. We show that the dynamics of each molecule depends on the region of phase space of the initial rotational state, the asymmetry of the molecule, and the direction of the dipole. We also show that the ergodicity of the system varies gradually with energy, except where the rotational energy of the initial state is much less than the Stark interaction. We find that both molecules are far from full chaos for total angular momentum quanta $J\in[0,45]$, which counters the results presented in reference 1. However, the initial rotational states in OABN access much more of the available phase space than in PABN, which is a strong cause for the experimental discrepancies observed in the molecular beam deflection experiment of reference 1. In the second part, we address the 0.01-0.1 cm$^{-1}$ peak splittings found in high-resolution IR spectra of polyatomic molecules. Narrow splittings lead to energy flow on extremely long time scales. For polyatomics molecules, there are two main competing mechanisms that occur over such time scales: (1) dynamical tunneling, which connects classically disconnected regions of phase space by tunneling through dynamical barriers, and (2) Arnol'd Diffusion, which describes diffusion in phase space along a resonance network called the Arnol'd web. As a result of the ubiquitous numerical errors that accumulate during numerical studies of Arnol'd Diffusion, we use a physically motivated non-convex Hamiltonian that features fast diffusion along the Arnol'd web. Fast diffusion is a worst case scenario as a competitor to dynamical tunneling. We show how dynamical tunneling dominates fast diffusion, suggesting that dynamical tunneling is the prime culprit of the narrow peak splittings in high-resolution IR spectra of polyatomic molecules. / Physics

This thesis investigates the basic interactions of energetic ions with the top atoms on a clean surface. This information is of relevance to impact collision ion scattering spectroscopy (ICISS) investigations of surface structure. Using a variety of ions with energies in the keV range e.g. C$\rm\sp+,\ N\sp+,\ O\sp+,\ F\sp+,\ Ne\sp+,\ P\sp+,\ S\sp+,\ Cl\sp+$ and Ar$\sp+,$ incident upon a clean amorphous silicon surface, the outgoing particles were found to contain a significant fraction of multiply charged ions. Note that the ejected ions were energy analysed with a cylindrical electrode electrostatic analyser, designed and built by us, which had a sufficiently large solid angle of acceptance so that good energy spectra could be obtained with beam fluxes which did not significantly damage the surface structure. To explain the appearance of these multicharged ions, a charge exchange model is described that considers the interaction domain to be divided into three steps: the incoming trajectory, the close encounter and the outgoing trajectory. A definite threshold distance of closest approach for the production of each of the multicharged ion species was found. These threshold distances directly confirm the model in which multiply charged ions are created in binary encounters by molecular orbital electron promotion, and then are partially neutralized as they leave the surface. The molecular orbital correlation diagram can associate particuliar crossings responsible for each multicharged ion species observed.

We present a molecular dynamics study of the activation energy of a vacancy in a monolayer of xenon with two and three degrees of freedom, in the latter case in the presence of a Ag(111) substrate. The large activation energy decreases with the third degree of freedom. The minimum energy trajectory between two lattice positions is given. In the three dimensional case the activated atom dips while the neighboring atoms rise. With temperature the activation energy increases by about 10 percent from 5 to 65K in both the two dimensional and three dimensional cases. The interaction between two vacancies has been investigated. This interaction is attractive, long-range and strong, similar in depth to the interparticle interaction.

For many years, the international scientific community has invested enormous efforts in the Human Genome sequencing project. The sequencing of the 23 human chromosomes is almost completed. This demonstrates that we now have to aim our efforts at improving their efficiency, and therefore resolution and speed are now the key issues. First, the effect of attractive analyte-gel interactions (we will study globular analytes here, proteins for example) will be examined within the framework of the Guo-Mercier-Slater model. It will be shown that it is possible to take into account such interactions and still calculate exact mobilities for various analytes and gel structures. Next, we will concentrate on the problems associated with the separation of chromosomal DNA (very long chains). Using Monte Carlo simulations, we will try to reproduce the dynamics of long DNA chains in three different experimental systems. (Abstract shortened by UMI.)

(1) Static Structure Factor and Shape of Reptating Telehelic Ionomers in Electric Fields: We calculate the static structure factor of reptating block copolymers which have a neutral middle block and charged ends. In the presence of an electric field, these telehelic ionomers reptate randomly in their "tubes" but the latter tend to orient along the field axis. If the two ends have different charges, competition between many length scales occurs. The resulting scattering function shows unusual features that are normally characteristic of highly polydisperse mixtures. (results published in Macromolecules, volume 26, number 8, pages 1905-1913). (2) Reptation, Entropic Trapping, Percolation and Rouse Dynamics of Polymer Chains in "Random" Environments: We report the simulation study of the dynamics of linear polymer chains in two-dimensional periodic arrays of obstacles where a fraction 1-c of obstacles are removed. We find Rouse dynamics when c is small, reptation dynamics when c = 1, as well as two other regimes between these two limits. Surprisingly, the diffusion coefficient actually decreases when we start removing obstacles. A study of the sites visited by the polymer molecules indicates that the latter are then entropically trapped in large but isolated voids. When about 60% of the obstacles are removed, the large voids form a percolation path and diffusion is easier when further obstacles are removed. Our results thus predict that the diffusion coefficient can vary in a non-monotonic way with concentration.

Polymeric and biological disordered materials are characterized by unique dynamical features. Although the details of the physical dynamical mechanisms are different, the disorder seems to be a common cause for non-exponential relaxation in these materials. The numerous experimental results which reveal a rather universal form of relaxation, namely a KWW or stretched exponential type function ( e-t/tb , beta < 1) have not yet been adequately explained by a unified theory. Such a disordered polymeric system is studied in this thesis and its relaxation is analysed in the framework of the well known Rouse model. This model allows for exact solutions and different types of disorder are analysed here. Exact solution and a good control over the disorder provide us with a fundamental description of the transition towards KWW behaviour. Our results favor a theory of relaxation based on parallel relaxation modes. The second part of the thesis focuses on the elasticity of a single polymer chain. The correct statistical mechanical ensemble associated with an experimental measurement probing single chain properties is an issue of great interest given the breakthroughs in the development of methods which can directly probe single chain mechanics. The complicated force-extension expressions obtained for a chain subjected to spatial constraints are available only as approximations, even for ideal models. The use of such relations in theoretical studies as well as in computer simulations is cumbersome and time consuming. A systematic method to construct simpler but still accurate expressions for the force function is given. As we demonstrate, these approximations can provide expressions with an arbitrary degree of accuracy and the proper mean statistical properties.

Advances in microfluidics have led to the development of devices which can perform simple operations on fluids with the aim of developing a fully integrated "lab-on-a-chip". Of prime importance to this procedure is the efficient operation of each individual component. Using theoretical prediction sand two-dimensional Molecular Dynamics (MD) simulations, we have explored the operation of two such devices: one which forces a cavity of fluid into rotational motion and one to mix two different fluid species. For the rotational operation, we have referred to experimental results for a circular cavity coupled to a microfluidic channel in which a laminar flow is induced. This flow causes the fluid in the cavity to rotate which we model with MD simulations. We examine the role of wall-fluid interactions and its effect on enhancing the amount of angular momentum generated in the cavity. The reduction in wall-fluid interaction allows the fluid to slip along the wall and acquire a greater level of spin. We hope this technique can be applied experimentally to enhance the rotation in these devices. For the mixing operation, we examined a previously studied theoretical system where the authors claim obstacles in microchannels increase mixing efficiency for a fluid composed of two species. We make theoretical predictions to the contrary and demonstrate, using MD simulations, that our predictions are correct. Our results show that obstacles have two effects. First, obstacles increase the amount of contact between fluid species which only has a negligible effect on increasing the mixing efficiency. Second, the obstacles flatten the normally Poiseuille (quadratic) flow profile over a finite channel length which decreases the distance required for partial but not complete mixing. We demonstrate that all channels of at least a certain length, defined by the diffusive properties of the channel, will reach full mixing at the same point. Both projects illustrate the utility of MD simulations in predicting fluid behaviour in microfluidic systems. Our aim is that these studies can be integrated into the greater body of knowledge pertaining to microfluidics.

Working towards the goal of recovering single-bonded nitrogen at ambient conditions, the approach taken in this work is to subject nitrogen-rich molecular and ionic azides (specifically, cyanuric triazide and ammonium azide) to high pressures to induce transitions to phases that contain single-bonded nitrogen. The samples were subjected to extreme pressures using a diamond anvil cell and subsequently studied using high-resolution synchrotron powder x-ray diffraction and vibrational Raman spectroscopy. The experimental results indicate that both cyanuric triazide and ammonium azide undergo a pressure-induced first order structural phase transition at 30 and 3.0 GPa, respectively. The analyses and characterizations of these dense energetic materials are discussed in detail, and will be used to explore the possibility of recovering single-bonded nitrogen at ambient conditions.

Gas clathrate hydrates are inclusion compounds in which a guest gas molecule is trapped within a host cage made up of hydrogen-bonded water molecules 1. Sequestration of CO2 in dense hydrate form has been proposed as one solution for rising levels of CO 2 in Earth's atmosphere2. Recent research has predicted the existence of a high-density clathrate structure capable of realizing this goal3. In this thesis, powder x-ray diffraction of the CO 2-H2O system as a function of increasing pressure (0 to 2.5 GPa) at sub-ambient temperatures (250 to 260 K) was performed in pursuit of discovering novel high-density hydrates of CO2. In addition to previously reported clathrate structures4, CO2 FIS Ih, a non-clathrate structure previously unobserved in the CO 2-H2O system but reported in other systems5, was identified and characterized. Using similar experimental techniques, unrelated work on the structural stability of dickite, a layered silicate mineral, is also presented. *Please refer to dissertation for footnotes.

The study of single polymer dynamics has, in the past few years, undergone a resurgence. This has been spurred on by the emergence of the fields of micro- and nanofluidics and their associated applications, especially by their ability to promise revolutionary techniques to, for example: rapidly sequence DNA, analyze proteins, carry out large-scale laboratory techniques in centimeter sized devices (lab-on-a-chip) and test and verify fundamental concepts related to the statistical physics of single molecules in fluids. In particular, the study of (typically single, isolated) polymers and the development of theoretical methods and computational tools to examine these polymers in microfluidic environments is a key challenge. In this thesis, we examine several different phenomena related to the dynamics of polymers in either microfluidic environments or related applications to DNA sequencing or separation. A recurrent theme throughout this work is the use of Molecular Dynamics (MD) simulations with an explicit solvent. Explicit solvent is an important aspect of our simulations and contrasts much work in the current literature which either artificially includes solvent or neglects it all together. This explicit inclusion of solvent allows us to explore phenomena (related to hydrodynamics) that is not observable with, for example, Brownian (or Langevin) Dynamics or Monte Carlo simulations. Chapter 2 contains a primarily computational examination of the friction coefficients of uncharged polymers. We explore the effects of deforming polymer chains on their friction coefficients along with examining several fundamental concepts of polymer friction (including hydrodynamic permeability). A key result is a verification of the hydrodynamic coupling of polymer chains resulting from a net reduction in the friction of polymer chains in hairpin (or folded) conformations. We also show that polymers undergo frictional transitions as they are stretched by an external force applied to the middle of the molecules. In chapter 3 we use some of the concepts and results from chapters 1 and 2 to explore the problem of a polymer chain migrating under the influence of an external force (or fluid flow) through a molecular obstacle course. These polymers collide with either fixed obstacles (or other polymers) and can be trapped in meta-stable long-lived, pulley-like conformations. This method can be used to separate polymers by molecular weight. We use both MD simulations and a general classical theory for the collisions to explore several different collision regimes. We also show that a classic experimental result, the formation of so-called V-shaped states, can occur in single polymer collision events, contrary to the popular assumption that it was necessary for a polymer to collide with multiple polymers. In chapter 4 we build on the results and ideas from the first three chapters and examine another phenomenon related to polymer transport, that of (Brownian) ratchets. A ratchet is essentially a method to rectify the thermal noise in a system in order to perform work, for example, to generate net transport. We use our MD simulations to examine the behaviour of polymers in the presence of an asymmetric saw tooth ratchet potential. We also show that existing ratchet models, where the ratchet widths are on the order of a polymer gyration radius, neglect an important effect of chain relaxation and thus underestimate optimal operating parameters. We propose and derive equations illustrating a new operational mode for a ratchet which inherently uses the deformation of polymer chains induced by the application of a ratcheting potential. We present a simple mathematical expression to incorporate time-dependent diffusion coefficients D (t) into ratchets. The final chapter presents work done in collaboration with Annelise Barron's group at Northwestern University and examines the breaking of polymer chains in extensional flow fields as a method to systematically and predictably reduce the polydispersity (PDI) of polymer solutions. The experimental investigation, carried out by the Barron group illustrated that a dilute polymer solution, when passed through a narrow constriction at high pressure can systematically reduce the PDI of the polymer solution. My contribution to this work was to develop a statistical model which calculates polymer molecular weight distributions and which can predict the resulting degraded polymer distribution. Two key things resulted from this investigation, the first is that polymers can break multiple times during a single scission event (i.e., one pass through the experimental system). Secondly we showed that it is possible to predictably reproduce polymer distributions after multiple scission events.