Optical Factors Determined by the T-matrix Method in Turbidity Measurement of Absolute Coagulation Rate Constants

Turbidity measurement for the absolute coagulation rate constant of suspensions has been extensively adopted because of its simplicity and easy implementation. A key factor to derive the rate constant from experimental data is how to theoretically evaluate the so-called optical factor involved in calculating the extinction cross section of doublets formed in the aggregation. In a previous paper, we have shown that compared with other theoretical approaches, the T-matrix method provides a robust solution to this problem and is effective in extending the applicability range of the turbidity methodology as well as increasing measurement accuracy. This paper will provide a more comprehensive discussion about the physical insight of using the T-matrix method in turbidity measurement and associated technical details. In particular, the importance of ensuring the correct value for the refractive indices for colloidal particles and the surrounding medium used in the calculation is addressed because the indices generally vary with the wavelength of the incident light. The comparison of calculated results with experiments shows that the T-matrix method can correctly calculate optical factors even for large particles, whereas other existing theories cannot. In addition, the calculated data of the optical factor by the T-matrix method for a range of particle radii and incident light wavelengths are listed.

Toward an understanding of the turbidity measurement of fleterocoagulation rate constants of dispersions containing particles of different sizes

Our previous studies have shown that the determination of coagulation rate constants by turbidity measurement becomes impossible for a certain operating wavelength (that is, its blind point) because at this wavelength the change in the turbidity of a dispersion completely loses its response to the coagulation process. Therefore, performing the turbidity measurement in the wavelength range near the blind point should be avoided. In this article, we demonstrate that the turbidity measurement of the rate constant for coagulation of a binary dispersion containing particles of two different sizes (heterocoagulation) presents special difficulties because the blind point shifts with not only particle size but also with the component fraction. Some important aspects of the turbidity measurement for the heterocoagulation rate constant are discussed and experimentally tested. It is emphasized that the T-matrix method can be used to correctly evaluate extinction cross sections of doublets formed during the heterocoagulation process, which is the key data determining the rate constant from the turbidity measurement, and choosing the appropriate operating wavelength and component fraction are important to achieving a more accurate rate constant. Finally, a simple scheme in experimentally determining the sensitivity of the turbidity changes with coagulation over a wavelength range is proposed.

Microscopic theory of chemical-reaction rate

In this paper we deduce the formulae for rate-constant of microreaction with high resolving power of energy from the time-dependent Schrdinger equation for the general case when there is a depression on the reaetional potential surface (when the depression is zero in depth, the case is reduced to that of Eyring). Based on the assumption that Bolzmann distribution is appropriate to the description of reactants, the formula for the constant of macrorate in a form similar to Eyring's is deduced and the expression for the coefficient of transmission is given. When there is no depression on the reactional potential surface and the coefficient of transmission does not seriously depend upon temperature, it is reduced to Eyring's. Thus Eyring's is a special case of the present work.

I. The rate and mechanism of the vapor-phase reaction between water and parts-per-million concentrations of nitrogen dioxide. II. The rate and mechanism of the air oxidation of parts-per-million concentrations of nitric oxide in the presence of water vapor.

Part I

A study of the thermal reaction of water vapor and parts-per-million concentrations of nitrogen dioxide was carried out at ambient temperature and at atmospheric pressure. Nitric oxide and nitric acid vapor were the principal products. The initial rate of disappearance of nitrogen dioxide was first order with respect to water vapor and second order with respect to nitrogen dioxide. An initial third-order rate constant of 5.5 (± 0.29) x 10⁴ liter² mole^-2 sec^-1 was found at 25˚C. The rate of reaction decreased with increasing temperature. In the temperature range of 25˚C to 50˚C, an activation energy of -978 (± 20) calories was found.

The reaction did not go to completion. From measurements as the reaction approached equilibrium, the free energy of nitric acid vapor was calculated. This value was -18.58 (± 0.04) kilocalories at 25˚C.

The initial rate of reaction was unaffected by the presence of oxygen and was retarded by the presence of nitric oxide. There were no appreciable effects due to the surface of the reactor. Nitric oxide and nitrogen dioxide were monitored by gas chromatography during the reaction.

Part II

The air oxidation of nitric oxide, and the oxidation of nitric oxide in the presence of water vapor, were studied in a glass reactor at ambient temperatures and at atmospheric pressure. The concentration of nitric oxide was less than 100 parts-per-million. The concentration of nitrogen dioxide was monitored by gas chromatography during the reaction.

For the dry oxidation, the third-order rate constant was 1.46 (± 0.03) x 10⁴ liter² mole^-2 sec^-1 at 25˚C. The activation energy, obtained from measurements between 25˚C and 50˚C, was -1.197 (±0.02) kilocalories.

The presence of water vapor during the oxidation caused the formation of nitrous acid vapor when nitric oxide, nitrogen dioxide and water vapor combined. By measuring the difference between the concentrations of nitrogen dioxide during the wet and dry oxidations, the rate of formation of nitrous acid vapor was found. The third-order rate constant for the formation of nitrous acid vapor was equal to 1.5 (± 0.5) x 10⁵ liter² mole^-2 sec^-1 at 40˚C. The reaction rate did not change measurably when the temperature was increased to 50˚C. The formation of nitric acid vapor was prevented by keeping the concentration of nitrogen dioxide low.

Surface effects were appreciable for the wet tests. Below 35˚C, the rate of appearance of nitrogen dioxide increased with increasing surface. Above 40˚C, the effect of surface was small.

The rate and mechanism of the partial oxidation of acetaldehyde by PPM concentrations of nitrogen dioxide

The thermal reaction between nitrogen dioxide and acetaldehyde in the gas phase was investigated at room temperature and atmospheric pressure. The initial rate of disappearance of nitrogen dioxide was 1.00 ± 0.03 order with respect to nitrogen dioxide and 1.00 ± 0.07 order with respect to acetaldehyde. An initial second order rate constant of (8.596 ± 0.189) x 10^-3 1.mole^-1 sec^-1 was obtained at 22.0 ± 0.1 °C and a total pressure of one atmosphere. The activation energy of the reaction was 12,900 cal/mole in the temperature range between 22°C and 122°C.

The products of the reaction were nitric oxide, carbon dioxide, methyl nitrite, nitromethane and a trace amount of trans-dimeric nitrosomethane. The addition of nitric oxide increased the rate of formation of nitromethane and decreased the rate of formation of methyl nitrite. There were no measurable surface effects due to the addition of glass wool or glass beads to the reactor.

Reactants and products were analyzed by gas chromatography. A mechanism was proposed incorporating the principal features of the reaction.

Extraction kinetics of cerium(IV) from sulfuric acid medium by the primary amine N1923 using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamic studies on Ce(IV) extraction with primary amine N1923 demonstrate that primary amine N1923 is an excellent extractant for separation of Ce(IV) from Re(III). In order to clarify the mechanism of extraction and to optimize the parameters in practical extraction systems used in the rare earth industry, the extraction kinetics was investigated using a constant interfacial area cell with laminar flow in the present work.RESULTS: The data indicate that the rate constant (k(ao).) becomes constant when stirring speed exceeds 250 rpm. The apparent forward extraction rate is calculated to be 10(-1.70). The activation energy (E.) was calculated to be 20.5 kJ/mol from the slope of log kao against 1000/T. The minimum bulk concentration of the extractant necessary to saturate the interface (C-min) is lower than 10(-5) mol L-1.CONCLUSION: Studies of interfacial tension and the effects of stirring rate and specific interfacial area on the extraction rate show that the extraction rate is kinetically controlled, and a mass transfer model has been proposed. The rate equation has been obtained as: -d[Ce(IV)]/dt = 10(-1.70)[Ce(IV)] [(RNH3)(2)SO4](1.376). The rate-controlling step has been evaluated from analysis of the experimental results.

Mass transfer kinetics of yttrium(III) using a constant interfacial cell with laminar flow. Part II. Extraction with Cyanex 272

The yttrium(III) extraction kinetics and mechanism with bis-(2,4,4-trimethyl-pentyl) phosphinic acid (Cyanex 272, HA) dissolved in heptane have been investigated by constant interfacial cell with laminar flow. The data has been analyzed in terms of pseudo-first order constants. Studies on the effects of stirring rate, temperature, acidity in aqueous phase, and extractant concentration on the extraction rate show that the extraction regime is dependent on the extraction conditions. The plot of interfacial area on the rate has shown a linear relationship. This fact together with the strong surface activity of Cyanex 272 at heptane-water interfaces has made the interface the most probable location for the chemical reactions. The forward, reverse rate equations and extraction rate constant for the yttrium extraction with Cyanex 272 have been obtained under the experimental conditions. The rate-determining step has been also predicted from interfacial reaction models. The predictions have been found to be in good agreement with the rate equations obtained from experimental data, confirming the basic assumption that the chemical reaction is located at the liquid-liquid interface.

Kinetics of Y(III) stripping for the system Y/HCl/Cyanex 272-P507/heptane with constant interfacial area cell with laminar flow

Kinetics and mechanism of stripping of yttrium(III) previously extracted by mixtures of bis(2,4,4-trimethylpentyl)phosphinic acid (Cyanex 272, HA), and 2-ethylhexyl phosphonic acid mono-2-ethylhexl ester (P507, HB) dissolved in heptane have been investigated by constant interfacial-area cell by laminar flow. The corresponding equilibrium stripping equation and equilibrium constant were obtained. The studies of effects of the stirring rate and temperature on the stripping rate show that the stripping regime is dependent on the stripping conditions. The plot of interfacial area on the rate has shown a linear relationship. This fact together with the strong surface activity of mixtures of Cyanex 272 and P507 at heptane-water interfaces makes the interface the most probable locale for the chemical reactions. The stripping rate constant is obtained, and the value is compared with that of the system with Cyanex 272 and P507 alone. It is concluded that the stripping ability with the mixtures is easier than that of P507 due to lower the activation energy of the mixtures. The stripping rate equation has also been obtained, and the rate-determining steps are the two-step interfacial chemical reactions as predicted from interfacial reaction models.

An ultramicroelectrode study of ferrocene diffusion and heterogeneous electron transfer rate in polyelectrolyte

Steady-state voltammograms at a microdisk electrode are used to measure the diffusion coefficient (D) and standard heterogeneous rate constant (k(s)) of ferrocene in polyelectrolyte PEG.MClO(4). The diffusion coefficient and standard heterogeneous rate constant of ferrocene are both smaller in polymer solvents than in monomeric solvents. The D and k(s) of ferrocene have been estimated in PEG containing different concentrations and cations of supporting electrolytes, and the dependencies of D and k(s) on temperature have been observed. These results show that the D and k(s) of ferrocene increase with increasing temperature in polyelectrolyte, and with increasing cation radius of supporting electrolyte, eg D and k(s) increase in the order Bu(4)NClO(4) > NaClO4 > LiClO4. On the other hand, D and k(s) increase with decreasing concentration of supporting electrolyte. The dependence of the half-wave potential (E(1/2)) on the concentration of the supporting electrolyte is also observed. E(1/2) shifts in the negative direction as the concentration of supporting electrolyte increases. (C) 1997 Elsevier Science Ltd.

A temperature-dependent relative-rate study of the OH initiated oxidation of n-butane: the kinetics of the reactions of the 1-and 2-butoxy radicals

The kinetics of the reactions of 1-and 2-butoxy radicals have been studied using a slow-flow photochemical reactor with GC-FID detection of reactants and products. Branching ratios between decomposition, CH3CH(O-.)CH2CH3 CH3CHO + C2H5, reaction (7), and reaction with oxygen, CH3CH(O-.)CH2CH3 + O-2 -> CH3C(O)C2H5 + HO2, reaction (6), for the 2-butoxy radical and between isomerization, CH3CH2CH2CH2O. -> CH2CH2CH2CH2OH, reaction (9), and reaction with oxygen, CH3CH2CH2CH2O. + O-2 -> C3H7CHO + HO2, reaction (8), for the 1-butoxy radical were measured as a function of oxygen concentration at atmospheric pressure over the temperature range 250-318 K. Evidence for the formation of a small fraction of chemically activated alkoxy radicals generated from the photolysis of alkyl nitrite precursors and from the exothermic reaction of 2-butyl peroxy radicals with NO was observed. The temperature dependence of the rate constant ratios for a thermalized system is given by k(7)/k(6) = 5.4 x 1026 exp[(-47.4 +/- 2.8 kJ mol(-1))/RT] molecule cm(-3) and k(9)/k(8) = 1.98 x 10(23) exp[(-22.6 +/- 3.9 kJ mol(-1))/RT] molecule cm(-3). The results agree well with the available experimental literature data at ambient temperature but the temperature dependence of the rate constant ratios is weaker than in current recommendations.

Gas-phase kinetics of chlorosilylene reactions II. ClSiH + C2H4: absolute rate measurements and quantum chemical and RRKM calculations for the prototype pi addition reaction

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1-silacyclopent-3-ene, are carried out to obtain rate constants for its bimolecular reaction with ethene, C2H4, in the gas-phase. The reaction is studied over the pressure range 0.13-13.3 kPa (with added SF6) at five temperatures in the range 296-562 K. The second order rate constants, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1))=(-10.55 +/- 0.10) + (3.86 +/- 0.70) kJ mol(-1)/RT ln10. The Arrhenius parameters correspond to a loose transition state and the rate constant at room temperature is 43% of that for SiH2 + C2H4, showing that the deactivating effect of Cl-for-H substitution in the silylene is not large. Quantum chemical calculations of the potential energy surface for this reaction at the G3MP2//B3LYP level show that, as well as 1-chlorosilirane, ethylchlorosilylene is a viable product. The calculations reveal how the added effect of the Cl atom on the divalent state stabilisation of ClSiH influences the course of this reaction. RRKM calculations of the reaction pressure dependence suggest that ethylchlorosilylene should be the main product. The results are compared and contrasted with those of SiH2 and SiCl2 with C2H4.

A theoretical model for estimating the margination constant of leukocytes

Abstract Background Blood leukocytes constitute two interchangeable sub-populations, the marginated and circulating pools. These two sub-compartments are found in normal conditions and are potentially affected by non-normal situations, either pathological or physiological. The dynamics between the compartments is governed by rate constants of margination (M) and return to circulation (R). Therefore, estimates of M and R may prove of great importance to a deeper understanding of many conditions. However, there has been a lack of formalism in order to approach such estimates. The few attempts to furnish an estimation of M and R neither rely on clearly stated models that precisely say which rate constant is under estimation nor recognize which factors may influence the estimation. Results The returning of the blood pools to a steady-state value after a perturbation (e.g., epinephrine injection) was modeled by a second-order differential equation. This equation has two eigenvalues, related to a fast- and to a slow-component of the dynamics. The model makes it possible to identify that these components are partitioned into three constants: R, M and SB; where SB is a time-invariant exit to tissues rate constant. Three examples of the computations are worked and a tentative estimation of R for mouse monocytes is presented. Conclusions This study establishes a firm theoretical basis for the estimation of the rate constants of the dynamics between the blood sub-compartments of white cells. It shows, for the first time, that the estimation must also take into account the exit to tissues rate constant, SB.

Dissolution rate spectra data of calcite single crystal and micrite material

The large discrepancy between field and laboratory measurements of mineral reaction rates is a long-standing problem in earth sciences, often attributed to factors extrinsic to the mineral itself. Nevertheless, differences in reaction rate are also observed within laboratory measurements, raising the possibility of intrinsic variations as well. Critical insight is available from analysis of the relationship between the reaction rate and its distribution over the mineral surface. This analysis recognizes the fundamental variance of the rate. The resulting anisotropic rate distributions are completely obscured by the common practice of surface area normalization. In a simple experiment using a single crystal and its polycrystalline counterpart, we demonstrate the sensitivity of dissolution rate to grain size, results that undermine the use of "classical" rate constants. Comparison of selected published crystal surface step retreat velocities (Jordan and Rammensee, 1998) as well as large single crystal dissolution data (Busenberg and Plummer, 1986) provide further evidence of this fundamental variability. Our key finding highlights the unsubstantiated use of a single-valued "mean" rate or rate constant as a function of environmental conditions. Reactivity predictions and long-term reservoir stability calculations based on laboratory measurements are thus not directly applicable to natural settings without a probabilistic approach. Such a probabilistic approach must incorporate both the variation of surface energy as a general range (intrinsic variation) as well as constraints to this variation owing to the heterogeneity of complex material (e.g., density of domain borders). We suggest the introduction of surface energy spectra (or the resulting rate spectra) containing information about the probability of existing rate ranges and the critical modes of surface energy.

Accessing chain length dependent termination rate coefficients of methyl methacrylate (MMA) via the reversible addition fragmentation chain transfer (RAFT) process

The RAFT-CLD-T methodology is demonstrated to be not only applicable to 1-substituted monomers such as styrene and acrylates, but also to 1,1-disubstituted monomers such as MMA. The chain length of the terminating macromolecules is controlled by CPDB in MMA bulk free radical polymerization at 80 degrees C. The evolution of the chain length dependent termination rate coefficient, k(t)(i,i), was constructed in a step-wise fashion, since the MMA/CPDB system displays hybrid behavior (between conventional and living free radical polymerization) resulting in initial high molecular weight polymers formed at low RAFT agent concentrations. The obtained CLD of k(t) in MMA polymerizations is compatible with the composite model for chain length dependent termination. For the initial chain-length regime, up to a degree of polymerization of 100, k(t) decreases with alpha (in the expression k(t)(i,i) = k(t)(0) . i(-alpha)) being close to 0.65 at 80 degrees C. At chain lengths exceeding 100, the decrease is less pronounced (affording an alpha of 0.15 at 80 degrees C). However, the data are best represented by a continuously decreasing nonlinear functionality implying a chain length dependent alpha.

Electronic energy-transfer rate constants for geometrical isomers of a bichromophoric macrocyclic complex

The rate of electronic energy transfer (EET) between a naphthalene donor and an anthracene acceptor in [ZnL3]-(ClO4)(2) and [ZnL4](ClO4)(2) was determined by time-resolved fluorescence measurements, where L 3 and L 4 are the geometrical isomers of 6-[(anthracen-9-ylmethyl)amino]-trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-13-amine (L-2), substituted with either a naphthalen-1-ylmethyl or naphthalen-2-ylmethyl donor, respectively. The energy transfer rate constant, k(EET), was determined to be (0.92 +/- 0.02) x 10(9) s(-1) for the naphthalen-1-ylmethyl-substituted isomer, while that for the naphthalen-2-ylmethyl-substituted isomer is somewhat faster, with k(EET) = (1.31 +/- 0.01) x 10(9) s(-1). The solid-state structure of [(ZnLCl)-Cl-3]ClO4 has been determined, and using molecular modeling calculations, the likely distributions of solution conformations in CH3CN have been evaluated for both complexes. The calculated conformational distributions in the common trans-III N-based isomeric form gave Forster EET rate constants that account for the differences observed and are in excellent agreement with the experimental values. It is shown that the full range of conformers must be considered to accurately reproduce the observed EET kinetics.