Multiple rate-determining steps for nonideal and fractal kinetics

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.     

Crystallochemistry of some new niobium bromides with (Nb6Br18) units: Structures of CsErNb6Br18 and Cs2EuNb6Br18

Two new series of Nb₆ bromides, CsRENb₆Br₁₈ (RE = all the lanthanides excepted Eu and Yb, + Y) (type H ) and M₂RENb₆Br₁₈ (M = Cs, Rb, Tl; RE = Eu, Yb) (type R ) have been isolated. The crystal structures of CsErNb₆Br₁₈ and Cs₂EuNb₆Br₁₈, isotypic with the corresponding chlorides, have been determined by single crystal X-ray diffraction data. The (Nb₆Br₁₈) intra-unit strength is related to the nature and the charge of the counter cation. A comparison between the corresponding chlorides and bromides series, based on the chemical properties and the size of the halogen is discussed.     

UVB irradiation of normal human skin favors the development of type-2 T-cells in vivo and in primary dermal cell cultures

To determine the effect of UVB exposure on the balance of type-1 or type-2 T-cells in skin, we examined the expression of key markers interferon (IFN)-gamma and interleukin (IL)-4 in cryostat sections. IFN-gamma mRNA was clearly detectable in nonirradiated control skin, and IFN-gamma protein was found in 2% of the dermal CD3pos T-cells, whereas IL-4 mRNA was hardly detectable, and no IL-4 protein was found. In contrast, IL-4 mRNA expression increased upon irradiation, and IL-4 was found in 2% of the T-cells at day 2 after UVB-exposure. Concomitantly, IFN-gamma mRNA expression decreased, and IFN-gamma protein became absent. We also analyzed T-cells present in primary dermal cell cultures, which were used as an in vitro equivalent of the in vivo situation. As compared with T-cells from control skin, T-cells in dermal cell cultures from UVB-exposed skin displayed an increased IL-4 and decreased IFN-gamma expression. No such skewing occurred when the T-cells from irradiated skin were cloned in the absence of a dermal microenvironment. Except for an occasional positive T-cell, type-1-associated cell-surface markers (CCR5, CXCR3) or type-2 markers (CCR3, CD30, CRTH2) were undetectable in situ. But these markers were expressed on cultured dermal T-cells from UVB-exposed and control skin at a comparable level, but did not correlate with the IFN-gamma and IL-4 production. Altogether, UVB-induced changes of the dermal microenvironment favor the development of type-2 T-cells.     

Metal speciation dynamics in colloidal ligand dispersions

In this work we propose a dynamic metal speciation theory for colloidal systems in which the complexing ligands are localized on the surface of the particles; i.e., there is spatial heterogeneity of binding sites within the sample volume. The differences between the complex formation and dissociation rate constants of complexes in colloidal dispersions and those in homogeneous solutions originate from the differences in kinetic and mass transport conditions. In colloidal systems, when the effective rate of dissociation of the surface complexes becomes fully diffusion controlled, its value is defined via the geometrical parameters of the particle. We assess the extent to which the conventional approach of assuming a homogeneously smeared-out ligand distribution overestimates the lability of surface complexes in colloidal ligand dispersions. The validity of the theory is illustrated by application to binding of lead and cadmium by carboxyl modified latex particles: our approach correctly predicts the formation/dissociation rate constants, which differ by several orders of magnitude from their homogeneous solution counterparts.     

Selective hydrosilylation of styrene using an in situ formed platinum(1,3-dimesityl-dihydroimidazol-2-ylidene) catalyst

A highly active and selective in situ formed platinum(N-heterocyclic carbene) catalyst for the hydrosilylation of styrene with triethylsilane is described, which unlike all other known hydrosilylation catalysts, selectively yields hydrosilylation products, but (almost) no dehydrogenative silylation products.     

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows.     

Intermolecular Domino Reaction of Two Aryl Iodides Involving Two C?H Functionalizations

A palladium‐catalyzed intermolecular cross‐coupling of two aryl iodides is reported, giving polycyclic ring systems with a high level of convergence and efficiency.