Showing papers in "The Journal of Physical Chemistry in 1977"

Exact Stochastic Simulation of Coupled Chemical Reactions

Abstract: There are two formalisms for mathematically describing the time behavior of a spatially homogeneous chemical system: The deterministic approach regards the time evolution as a continuous, wholly predictable process which is governed by a set of coupled, ordinary differential equations (the “reaction-rate equations”); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single differential-difference equation (the “master equation”). Fairly simple kinetic theory arguments show that the stochastic formulation of chemical kinetics has a firmer physical basis than the deterministic formulation, but unfortunately the stochastic master equation is often mathematically intractable. There is, however, a way to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. It is a relatively simple digital computer algorithm which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of the given chemical system. Like the master equation, this “stochastic simulation algorithm” correctly accounts for the inherent fluctuations and correlations that are necessarily ignored in the deterministic formulation. In addition, unlike most procedures for numerically solving the deterministic reaction-rate equations, this algorithm never approximates infinitesimal time increments df by finite time steps At. The feasibility and utility of the simulation algorithm are demonstrated by applying it to several well-known model chemical systems, including the Lotka model, the Brusselator, and the Oregonator.

Lipoid pH indicators as probes of electrical potential and polarity in micelles

Abstract: Two types of fluorescent pH indicators, a hydroxycoumarin and an aminocoumarin dye, are incorporated by means of long paraffinic chain substituents to neutral, anionic, and cationic micelles. The apparent pK values for the dyes in the micelles are compared to the pK values in aqueous solution. Shifts of the apparent pK are found for charged as well as for uncharged micelles, being different for the two indicators. A comparison of the pK shifts of the indicators in neutral micelles to pK shifts in a series of mixed solvents of different dielectric constant (e) leads us to attribute the shifts in the neutral system to a reduced polarity at the micelle surface for which a value of e 32 is estimated. With respect to charged micelles this polarity effect is responsible for part of the apparent pK shift. It may be revealed by comparing the results for the two indicator types. The value of the effective dielectric constant is found to be similar to that in the neutral micelle. The remaining part of the apparent pK shift may be taken as a measure of the electrical potential at the surface of the charged micelles. Some examples of potential measurements for various counterions are presented. A thermodynamical section attempts to present clear definitions of (and relations between) terms as “apparent pK”, “interfacial pK”, “interfacial pH”, and “acidity function”.

Heterogeneous photocatalytic oxidation of cyanide and sulfite in aqueous solutions at semiconductor powders

Abstract: Suggesting that there are at least two kinds of metal-C0 bonds involved which undoubtedly have different bond energies and that their approximate ratio is 5/1, the type of site greatest in quantity being that which bonds most strongly with CO. There may be other types of sites or these two kinds may actually include subtypes which have bond energies so close as to be indistinguishable by this experimental technique. Since the room temperature rate constant for displacement for process I is about 7 times greater than that for process 11, the activation energy for process I1 must be 1200 cal greater than that for process I. This suggests that the CO displaced in process I1 might be bonded to the metal 1200 cal more strongly than that which is displaced

Mechanism of the disproportionation of superoxide radicals

Abstract: New measurements are reported on the rate of the spontaneous uncatalyzed second-order decay of the superoxide radical in aqueous solution at 23/sup 0/C. By extreme purification of reagents, and addition of small amounts of EDTA to sequester traces of catalytic metal ions, purely second-order kinetics were found up to pH 13.2. The pH effects clearly show that the ionic form O/sub 2//sup -/ never reacts with itself but only with the HO/sub 2/ in equilibrium with it, even when the ratio HO/sub 2//O/sub 2//sup -/ is as small as 2 x 1/sup -8/; the rate constant for O/sub 2//sup -/ + O/sub 2//sup -/ is less than 0.3 M/sup -1/ s/sup -1/. The pK of HO/sub 2/ was determined as 4.75 +- 0.08, and the bimolecular rate constants were k/sub 1/ = (7.61 +- 0.55) x 10/sup 5/ M/sup -1/ s/sup -1/ for HO/sub 2/ + HO/sub 2/ and k/sub 2/ = (8.86 +- 0.43) x 10/sup 7/ M/sup -1/ s/sup -1/ for HO/sub 2/ + O/sub 2//sup -/, all in good agreement with published values. The change in the spontaneous decay of superoxide radicals with pH follows the equation k/sub obsd/ = (k/sub 1/ + k/sub 2/K/sub HO/sub 2///(H/supmore » +/))/(1 + K/sub HO/sub 2///(H/sup +/))/sup 2/. The optical extinction coefficients of hydrogen peroxide were determined over the pH range 6.1 to 13.8 at wavelengths from 280 to 230 nm.« less

Solvent-dependent fluorescence of pyrene-3-carboxaldehyde and its applications in the estimation of polarity at micelle-water interfaces

Abstract: The monomer fluorescence of pyrene-3-carboxaldehyde shows a strong dependence on solvent polarity. The fluorescence in nonpolar solvents such as n-hexane is very weak (quantum yield less than 0.001), but becomes quite intense in polar solvents (phi/sub F/ in methanol = 0.15). The fluorescence maximum shows a significant red shift with increased solvent polarity, which is linear with solvent dielectric constant at values greater than ten. This strong dependence of fluorescence on solvent polarity is used to obtain estimates of the polarity at the micelle--water interfaces for various ionic and nonionic detergent micelles. The measured values are in excellent agreement with zeta potential estimates for the micellar Stern layer, derived from double layer theory, and similar estimates using other fluorescence probes. The observed variations in the surface polarity at the micelle--water interfaces in the presence of external additives are also consistent with predictions from other data. The formation of Schiff's base by reaction of pyrenecarboxaldehyde with amines has also been investigated. Data on absorption and emission spectra of Schiff's bases are presented.

Thermodynamics of electrolytes. 8. High-temperature properties, including enthalpy and heat capacity, with application to sodium chloride

Abstract: The ion-interaction type of equation which has proven so successful for activity and osmotic coefficents of both pure and mixed electrolytes near room temperature is extended for wide temperature ranges and for the enthalpy and heat capacity. An improved equation is obtained for the dielectric constant of water over a wide range of temperature and density; it is used to calculate the Debye-Hueckel parameters to 350/sup 0/C for enthalpy and heat capacity as well as for osmotic and activity coefficients. These equations are applied to the extensive array of thermodynamic data for aqueous sodium chloride from 0 to 300/sup 0/C. Good agreement is obtained and the equations thus provide a convenient analytical representation of the thermodynamic properties of NaCl(aq). Also the results indicate that at 300/sup 0/C sodium chloride is still a strong electrolyte with little tendency toward the formation of ion pairs.

Nonlinear sensitivity analysis of multiparameter model systems

Abstract: Large sets of coupled, nonlinear equations arise in a number of disciplines in connection with computer-based models of physical, social, and economic processes. Solutions for such large systems of equations must be effected by means of digital computers using appropriately designed codes. This paper addresses itself to the critically important problem of how sensitive the solutions are to variations of, or inherent uncertainties in, the parameters of the equation set. We review here, and also present further developments of, our statistical method of sensitivity analysis. The sensitivity analysis presented here is nonlinear and thus permits one to study the effects of large deviations from the nominal parameter values. In addition, since all parameters are varied simultaneously, one can explore regions of parameter space where several parameters deviate simultaneously from their nominal values. We develop here the theory of our method of sensitivity analysis, then detail the method of implementation, and finally present examples of its use.

A numerical model of chemical kinetics of combustion in a turbulent flow reactor

Abstract: Calculations with a numerical model incorporating detailed chemical kinetics, hydrodynamic motion, and energy transport in a turbulent flow reactor have been compared with experimental results of Dryer and Glassman. A reaction mechanism, including 19 chemical species and 56 reactions, for the reaction of dilute moist carbon monoxide in air and of dilute methane in air was established for the temperature range 1000-1350 K. HO2 and H2O2 were found to be important in the mechanism for both carbon monoxide and methane oxidation, and CH2O, CH3O, C2H6, and C2H4 were found to be important in methane oxidation. Important steps in the reaction mechanisms have been identified, and optimal values for some key reaction rates have been determined. The branching ratio between reaction 3, H + O2 = OH + O, and reaction 17, H + O2 + M = HO2 + M, was found to be important in determining the length of the induction period in each experiment. At 1100 K the value determined for k17 was 2.6 X 10/sup 15/ cm/sup 6//(mol/sup 2/ s). Decomposition reaction 7 for HCO, HCO + M = H + CO + M, was found to play a key role in methane oxidation, providing the majormore » path for production of carbon monoxide. At 1100 K, k7 was found to be 2.4 X 10/sup 10/ cm/sup 3//(mol s). Even though the reaction studied was extremely oxygen rich, recombination of methyl radicals and subsequent oxidation of the ethane thus formed was found to provide a major route for methyl radical destruction. The assumption that plug flow conditions prevail in the turbulent flow reactor was examined and found to be valid under most practical conditions.« less

Utility of pulse nuclear magnetic resonance in studying protons in coals

Abstract: ESR, pulse NMR, and multiple pulse NMR were used to study free radical concentrations, and the extent to which protons in coals may be characterized by damping constants under specific radio-frequency pulse sequences in two Virginia vitrains, three Iowa vitrains, and selected model compounds. NMR pulse techniques were used to determine damping constants associated with proton spin--spin and spin--lattice relaxation. Multiple pulse line narrowing experiments were capable of narrowing the proton line width from roughly 30 kHz in all coals to roughly 700 Hz. Comparison of results on coals with pulse and multiple pulse measurements on the model compounds naphthalene, 2-methylnaphthalene, 4,4'-bismethylbenzophenone, m-tolylacetic acid, polystyrene, polyethylene, and polybutadiene indicated: (a) roughly 400 Hz of the residual proton line width in the coals under multiple pulse line narrowing experiments is due to free radical electron spin--nuclear spin dipolar coupling, (b) there is not a simple relation between spin--spin damping constants in coals, and aliphatic/aromatic proton ratios, and (c) resolution into aromatic and aliphatic protons will require removal of interproton dipolar interactions, proton chemical shift anisotropies, and electron--proton interactions by a combination of multiple pulse line narrowing experiments and magic angle rotation.

Rate constants for the reactions of hydrogen atoms with some silanes and germanes

Abstract: Rate constants for the reactions of H atoms, formed by mercury photosensitization of H/sub 2/-substrate mixtures at 32/sup 0/C, with (CH/sub 3//sub n/SiH/sub 4-n/ and (C/sub 2/H/sub 5/)/sub n/SiH/sub 4-n/ for n = 0, 1, 2, 3; with (CH/sub 3/)/sub n/SiD/sub 4-n/ for n = 0, 1; and with Si/sub 2/H/sub 6/, Si/sub 2/D/sub 6/, GeH/sub 4/, and Ge/sub 2/H/sub 6/ have been determined in experiments involving the competitive reaction of H atoms with C/sub 2/H/sub 4/ and i-C/sub 4/H/sub 8/. Activation energies, estimated from these rate constants, have been combined with thermochemical data by means of a bond-energy-bond-order (BEBO) method of calculation to yield a consistent set of dissociation energies for Si--H bonds in the R/sub n/SiH/sub 4-n/ series of silanes for n = 0, 1, 2, 3.

Radiolytic chain decomposition of peroxomonophosphoric and peroxomonosulfuric acids

Abstract: Radiolytic studies of peroxomonophosphoric acid, H/sub 3/PO/sub 5/, and peroxomonosulfuric acid, H/sub 2/SO/sub 5/, have been carried out over a wide pH range. Unlike the corresponding peroxodiacids, H/sub 4/P/sub 2/O/sub 8/ and H/sub 2/S/sub 2/O/sub 8/, the peroxomono acids undergo radiolytic chain decomposition, with G values increasing from about 6 to 60 in going from pH 1 to 12.6. Sharp rises in G values appear at pH values near the pK/sub a/ of the hydroperoxy proton (highest pK/sub a/). The mechanism suggested for these chain reactions involves successive oxidation and reduction of the parent compounds by radicals produced in the preceding step. Pulse radiolysis experiments showed that the reaction of e/sub eq//sup -/ with peroxomonophosphate (k = 4.4 x 10 M/sup -1/ s/sup -1/ at pH 7) produces OH radicals twice as frequently as HPO/sub 4//sup -/ radicals. Previous results with peroxomonosulfate showed a factor of 4 for similar reactions. The rate constant for reaction of OH radicals with peroxomonophosphate at pH 7 was found to be 4.3 x 10/sup 7/ M/sup -1/ s/sup -1/, and with peroxomonosulfate 1.7 x 10/sup 7/ M/sup -1/ s/sup -1/ at pH 7 and 2.1 x 10/sup 9/ M/sup -1/ s/sup -1/ at pHmore » 11. The reactions of OH are suggested to be the chain initiation step and possibly responsible for the main chain propagation as well.« less