1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Proton transfers at the air-water interface

Proton transfer reactions at the interface of water with hydrophobic media, such as air or lipids, are ubiquitous on our planet. These reactions orchestrate a host of vital phenomena in the environment including, for example, acidification of clouds, enzymatic catalysis, chemistries of aerosol and atmospheric gases, and bioenergetic transduction. Despite their importance, however, quantitative details underlying these interactions have remained unclear. Deeper insight into these interfacial reactions is also required in addressing challenges in green chemistry, improved water quality, self-assembly of materials, the next generation of micro-nanofluidics, adhesives, coatings, catalysts, and electrodes. This thesis describes experimental and theoretical investigation of proton transfer reactions at the air-water interface as a function of hydration gradients, electrochemical potential, and electrostatics. Since emerging insights hold at the lipid-water interface as well, this work is also expected to aid understanding of complex biological phenomena associated with proton migration across membranes.

Based on our current understanding, it is known that the physicochemical properties of the gas-phase water are drastically different from those of bulk water. For example, the gas-phase hydronium ion, H₃O⁺(g), can protonate most (non-alkane) organic species, whereas H₃O⁺(aq) can neutralize only relatively strong bases. Thus, to be able to understand and engineer water-hydrophobe interfaces, it is imperative to investigate this fluctuating region of molecular thickness wherein the ‘function’ of chemical species transitions from one phase to another via steep gradients in hydration, dielectric constant, and density. Aqueous interfaces are difficult to approach by current experimental techniques because designing experiments to specifically sample interfacial layers (< 1 nm thick) is an arduous task. While recent advances in surface-specific spectroscopies have provided valuable information regarding the structure of aqueous interfaces, but structure alone is inadequate to decipher the function. By similar analogy, theoretical predictions based on classical molecular dynamics have remained limited in their scope.

Recently, we have adapted an analytical electrospray ionization mass spectrometer (ESIMS) for probing reactions at the gas-liquid interface in real time. This technique is direct, surface-specific,and provides unambiguous mass-to-charge ratios of interfacial species. With this innovation, we have been able to investigate the following:

1. How do anions mediate proton transfers at the air-water interface?

2. What is the basis for the negative surface potential at the air-water interface?

3. What is the mechanism for catalysis ‘on-water’?

In addition to our experiments with the ESIMS, we applied quantum mechanics and molecular dynamics to simulate our experiments toward gaining insight at the molecular scale. Our results unambiguously demonstrated the role of electrostatic-reorganization of interfacial water during proton transfer events. With our experimental and theoretical results on the ‘superacidity’ of the surface of mildly acidic water, we also explored implications on atmospheric chemistry and green chemistry. Our most recent results explained the basis for the negative charge of the air-water interface and showed that the water-hydrophobe interface could serve as a site for enhanced autodissociation of water compared to the condensed phase.

Oxidation of Volatile Organic Compounds in Aqueous Solution and at the Air-water Interface of Aqueous Microdroplets

Isoprene (ISO),the most abundant non-methane VOC, is the major contributor to secondary organic aerosols (SOA) formation. The mechanisms involved in such transformation, however, are not fully understood. Current mechanisms, which are based on the oxidation of ISO in the gas-phase, underestimate SOA yields. The heightened awareness that ISO is only partially processed in the gas-phase has turned attention to heterogeneous processes as alternative pathways toward SOA.

During my research project, I investigated the photochemical oxidation of isoprene in bulk water. Below, I will report on the λ > 305 nm photolysis of H₂O₂ in dilute ISO solutions. This process yields C₁₀H₁₅OH species as primary products, whose formation both requires and is inhibited by O₂. Several isomers of C₁₀H₁₅OH were resolved by reverse-phase high-performance liquid chromatography and detected as MH⁺ (m/z = 153) and MH⁺-18 (m/z = 135) signals by electrospray ionization mass spectrometry. This finding is consistent with the addition of ·OH to ISO, followed by HO-ISO· reactions with ISO (in competition with O₂) leading to second generation HO(ISO)₂· radicals that terminate as C₁₀H₁₅OH via β-H abstraction by O₂.

It is not generally realized that chemistry on the surface of water cannot be deduced, extrapolated or translated to those in bulk gas and liquid phases. The water density drops a thousand-fold within a few Angstroms through the gas-liquid interfacial region and therefore hydrophobic VOCs such as ISO will likely remain in these relatively 'dry' interfacial water layers rather than proceed into bulk water. In previous experiments from our laboratory, it was found that gas-phase olefins can be protonated on the surface of pH < 4 water. This phenomenon increases the residence time of gases at the interface, an event that makes them increasingly susceptible to interaction with gaseous atmospheric oxidants such as ozone and hydroxyl radicals.

In order to test this hypothesis, I carried out experiments in which ISO(g) collides with the surface of aqueous microdroplets of various compositions. Herein I report that ISO(g) is oxidized into soluble species via Fenton chemistry on the surface of aqueous Fe(II)Cl₂ solutions simultaneously exposed to H₂O₂(g). Monomer and oligomeric species (ISO)1-8H⁺ were detected via online electrospray ionization mass spectrometry (ESI-MS) on the surface of pH ~ 2 water, and were then oxidized into a suite of products whose combined yields exceed ~ 5% of (ISO)1-8H⁺. MS/MS analysis revealed that products mainly consisted of alcohols, ketones, epoxides and acids. Our experiments demonstrated that olefins in ambient air may be oxidized upon impact on the surface of Fe-containing aqueous acidic media, such as those of typical to tropospheric aerosols.

Related experiments involving the reaction of ISO(g) with ·OH radicals from the photolysis of dissolved H₂O₂ were also carried out to test the surface oxidation of ISO(g) by photolyzing H₂O₂(aq) at 266 nm at various pH. The products were analyzed via online electrospray ionization mass spectrometry. Similar to our Fenton experiments, we detected (ISO)1-7H⁺ at pH < 4, and new m/z⁺ = 271 and m/z^- = 76 products at pH > 5.

Equilibration of a liquid droplet-vapor-gas mixture downstream of a shock wave

The equations of motion for the flow of a mixture of liquid droplets, their vapor, and an inert gas through a normal shock wave are derived. A set of equations is obtained which is solved numerically for the equilibrium conditions far downstream of the shock. The equations describing the process of reaching equilibrium are also obtained. This is a set of first-order nonlinear differential equations and must also be solved numerically. The detailed equilibration process is obtained for several cases and the results are discussed.

The hydro-kinetic theory of liquid helium II

In Part I the kinetic theory of excitations in flowing liquid He II is developed to a higher order than that carried out previously, by Landau and Khalatnikov, in order to demonstrate the existence of non-equilibrium terms of a new nature in the hydrodynamic equations. It is then shown that these terms can lead to spontaneous destabilization in counter currents when the relative velocity of the normal and super fluids exceeds a critical value that depends on the temperature, but not on geometry. There are no adjustable parameters in the theory. The critical velocities are estimated to be in the 14-20 m/sec range for T ≤ 2.0° K, but tend to zero as T → T_λ. The possibility that these critical velocities may be related to the experimentally observed "intrinsic" critical velocities is discussed.

Part II consists of a semi-classical investigation of rotonquantized vortex line interactions. An essentially classical model is used for the collision and the behavior of the roton in the vortex field is investigated in detail. From this model it is possible to derive the HVBK mutual friction terms that appear in the phenomenalogical equations of motion for rotating liquid He II. Estimates of the Hall and Vinen B and B' coefficients are in good agreement with experiments. The claim is made that the theory does not contain any arbitrary adjustable parameters.

I. Spectroscopic observation of discrete sites in simple liquids. II. Infrared intensity perturbations of hydrogen halide fundamentals in liquid xenon. III. Rotation of HCl in solid rare gases.

Part I

The spectrum of dissolved mercury atoms in simple liquids has been shown to be capable of revealing information concerning local structures in these liquids.

Part II

Infrared intensity perturbations in simple solutions have been shown to involve more detailed interaction than just dielectric polarization. No correlation has been found between frequency shifts and intensity enhancements.

Part III

Evidence for perturbed rotation of HCl in rare gas matrices has been found. The magnitude of the barrier to rotation is concluded to be of order of 30 cm^(-1).

I. The attenuation and dispersion of sound in a condensing medium. II. The flow of a gas-particle mixture downstream of a normal shock in a nozzle

I. The attenuation of sound due to particles suspended in a gas was first calculated by Sewell and later by Epstein in their classical works on the propagation of sound in a two-phase medium. In their work, and in more recent works which include calculations of sound dispersion, the calculations were made for systems in which there was no mass transfer between the two phases. In the present work, mass transfer between phases is included in the calculations.

The attenuation and dispersion of sound in a two-phase condensing medium are calculated as functions of frequency. The medium in which the sound propagates consists of a gaseous phase, a mixture of inert gas and condensable vapor, which contains condensable liquid droplets. The droplets, which interact with the gaseous phase through the interchange of momentum, energy, and mass (through evaporation and condensation), are treated from the continuum viewpoint. Limiting cases, for flow either frozen or in equilibrium with respect to the various exchange processes, help demonstrate the effects of mass transfer between phases. Included in the calculation is the effect of thermal relaxation within droplets. Pressure relaxation between the two phases is examined, but is not included as a contributing factor because it is of interest only at much higher frequencies than the other relaxation processes. The results for a system typical of sodium droplets in sodium vapor are compared to calculations in which there is no mass exchange between phases. It is found that the maximum attenuation is about 25 per cent greater and occurs at about one-half the frequency for the case which includes mass transfer, and that the dispersion at low frequencies is about 35 per cent greater. Results for different values of latent heat are compared.

II. In the flow of a gas-particle mixture through a nozzle, a normal shock may exist in the diverging section of the nozzle. In Marble’s calculation for a shock in a constant area duct, the shock was described as a usual gas-dynamic shock followed by a relaxation zone in which the gas and particles return to equilibrium. The thickness of this zone, which is the total shock thickness in the gas-particle mixture, is of the order of the relaxation distance for a particle in the gas. In a nozzle, the area may change significantly over this relaxation zone so that the solution for a constant area duct is no longer adequate to describe the flow. In the present work, an asymptotic solution, which accounts for the area change, is obtained for the flow of a gas-particle mixture downstream of the shock in a nozzle, under the assumption of small slip between the particles and gas. This amounts to the assumption that the shock thickness is small compared with the length of the nozzle. The shock solution, valid in the region near the shock, is matched to the well known small-slip solution, which is valid in the flow downstream of the shock, to obtain a composite solution valid for the entire flow region. The solution is applied to a conical nozzle. A discussion of methods of finding the location of a shock in a nozzle is included.

Some properties of the coefficients of cyclotomic polynomials

An explicit formula is obtained for the coefficients of the cyclotomic polynomial F_n(x), where n is the product of two distinct odd primes. A recursion formula and a lower bound and an improvement of Bang’s upper bound for the coefficients of F_n(x) are also obtained, where n is the product of three distinct primes. The cyclotomic coefficients are also studied when n is the product of four distinct odd primes. A recursion formula and upper bounds for its coefficients are obtained. The last chapter includes a different approach to the cyclotomic coefficients. A connection is obtained between a certain partition function and the cyclotomic coefficients when n is the product of an arbitrary number of distinct odd primes. Finally, an upper bound for the coefficients is derived when n is the product of an arbitrary number of distinct and odd primes.

The structure of liquid argon as determined by x-ray diffraction

X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.

The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.

Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.

The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.

The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.

Chemical Reaction Dynamics of the Liquid/Vapor Interface Studied by Mass Spectrometry

This thesis presents investigations of chemical reactions occurring at the liquid/vapor interface studied using novel sampling methodologies coupled with detection by mass spectrometry. Chapters 2 and 3 utilize the recently developed technique of field-induced droplet ionization mass spectrometry (FIDI-MS), in which the application of a strong electric field to a pendant microliter droplet results in the ejection of highly charged progeny droplets from the liquid surface. In Chapter 2, this method is employed to study the base-catalyzed dissociation of a surfactant molecule at the liquid/vapor interface upon uptake of ammonia from the gas phase. This process is observed to occur without significant modulation of the bulk solution pH, suggesting a transient increase in surface pH following the uptake of gaseous ammonia. Chapter 3 presents real-time studies of the oxidation of the model tropospheric organic compound glycolaldehyde by photodissociation of iron (III) oxalate complexes. The oxidation products of glycolaldehyde formed in this process are identified, and experiments in a deoxygenated environment identify the role of oxygen in the oxidation pathway and in the regeneration of iron (III) following photo-initiated reduction. Chapter 4 explores alternative methods for the study of heterogeneous reaction processes by mass spectrometric sampling from liquid surfaces. Bursting bubble ionization (BBI) and interfacial sampling with an acoustic transducer (ISAT) generate nanoliter droplets from a liquid surface that can be sampled via the atmospheric pressure interface of a mass spectrometer. Experiments on the oxidation of oleic acid by ozone using ISAT are also presented. Chapters 5 and 6 detail mechanistic studies and applications of free-radical-initiated peptide sequencing (FRIPS), a technique employing gas-phase free radical chemistry to the sequencing of peptides and proteins by mass spectrometry. Chapter 5 presents experimental and theoretical studies on the anomalous mechanism of dissociation observed in the presence of serine and threonine residues in peptides. Chapter 6 demonstrates the combination of FRIPS with ion mobility-mass spectrometry (IM-MS) for the separation of isomeric peptides.