Interfacial Reaction Kinetics

We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. We consider general dynamical exponent $z$, where $x_t\sim t^{1/z}$ is the rms diffusion distance after time $t$. At short times the number of reactions per unit area, $R_t$, is {\em 2nd order} in the far-field reactant densities $n_A^{\infty},n_B^{\infty}$. For spatial dimensions $d$ above a critical value $d_c=z-1$, simple mean field (MF) kinetics pertain, $R_t\sim Q_b t n_A^{\infty} n_B^{\infty}$ where $Q_b$ is the local reactivity. For low dimensions $d<d_c$, this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, $R_t \approx x_t^{d+1} n_A^{\infty} n_B^{\infty}$, provided $Q_b > Q_b^* \sim (n_B^{\infty})^{[z-(d+1)]/d}$. Logarithmic corrections arise in marginal cases. At long times, a cross-over to {\em 1st order} DC kinetics occurs: $R_t \approx x_t n_A^{\infty}$. A density depletion hole grows on the more dilute A side. In the symmetric case ($n_A^{\infty}=n_B^{\infty}$), when $d<d_c$ the long time decay of the interfacial reactant density, $n_A^s$, is determined by fluctuations in the initial reactant distribution, giving $n_A^s \sim t^{-d/(2z)}$. Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction $A+B\to\emptyset$. For $d>d_c$ fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and $n_A^s \sim t^{(1-z)/(2z)}$. We apply our results to simple molecules (Fickian diffusion, $z=2$) and to several models of short-time polymer diffusion ($z>2$).Comment: 39 pages, 7 figures, uses fund2.sty, submitted to Eur. Phys. J. B, 1 figure added, for short version see cond-mat/980409

Direct measurements of DOCO isomers in the kinetics of OD+CO

Quantitative and mechanistically-detailed kinetics of the reaction of hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal of contemporary chemical kinetics. This fundamental prototype reaction plays an important role in atmospheric and combustion chemistry, motivating studies for accurate determination of the reaction rate coefficient and its pressure and temperature dependence at thermal reaction conditions. This intricate dependence can be traced directly to details of the underlying dynamics (formation, isomerization, and dissociation) involving the reactive intermediates cis- and trans-HOCO, which can only be observed transiently. Using time-resolved frequency comb spectroscopy, comprehensive mechanistic elucidation of the kinetics of the isotopic analogue deuteroxyl radical (OD) with CO has been realized. By monitoring the concentrations of reactants, intermediates, and products in real-time, the branching and isomerization kinetics and absolute yields of all species in the OD+CO reaction are quantified as a function of pressure and collision partner.Comment: 19 pages, 4 figure

Enhanced reaction kinetics in biological cells

The cell cytoskeleton is a striking example of "active" medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown recently to have a spectacular impact on the mechanical and rheological properties of the cellular medium, as well as on its transport properties : a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose for the first time an analytical model of transport limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers like vesicles. We derive analytically the average interaction time with motor proteins which optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures like axons.Comment: 10 pages, 2 figure

Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations

We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution must coincide with this strong solution. Our assumptions on the reaction rates are just the entropy condition and local Lipschitz continuity; in particular, we do not impose any growth restrictions on the reaction rates. Therefore, our result applies to any single reversible reaction with mass-action kinetics as well as to systems of reversible reactions with mass-action kinetics satisfying the detailed balance condition. Renormalized solutions are known to exist globally in time for reaction-diffusion equations with entropy-dissipating reaction rates; in contrast, the global-in-time existence of weak solutions is in general still an open problem - even for smooth data - , thereby motivating the study of renormalized solutions. The key ingredient of our result is a careful adjustment of the usual relative entropy functional, whose evolution cannot be controlled properly for weak solutions or renormalized solutions.Comment: 32 page

On-line monitoring of the transesterification reaction between triglycerides and ethanol using near infrared spectroscopy combined with gas chromatography

Many analytical procedures have been developed to determine the composition of reaction mixtures during transesterification of vegetable oils with alcohols. However, despite their accuracy, these methods are time consuming and cannot be easily used for on-line monitoring. In this work, a fast analytical method was developed to on-line monitor the transesterification reaction of high oleic sunflower oil with ethanol using Near InfraRed spectroscopy and a multivariate approach. The reactions were monitored through sequential scans of the reaction medium with a probe in a one-liter batch reactor without collecting and preparing samples. To calibrate the NIR analytical method, gas chromatography-flame ionization detection was used as a reference method. The method was validated by studying the kinetics of the EtONa-catalyzed transesterification reaction. Activation energy (51.0 kJ/mol) was also determined by considering a pseudo second order kinetics model