Recent Developments in Dispersive Kinetics

On the Mechanism and Kinetics of Synthesizing Polymer Nanogels by Ionizing Radiation-Induced Intramolecular Crosslinking of Macromolecules

Nanogels-internally crosslinked macromolecules-have a growing palette of potential applications, including as drug, gene or radioisotope nanocarriers and as in vivo signaling molecules in modern diagnostics and therapy. This has triggered considerable interest in developing new methods for their synthesis. The procedure based on intramolecular crosslinking of polymer radicals generated by pulses of ionizing radiation has many advantages. The substrates needed are usually simple biocompatible polymers and water. This eliminates the use of monomers, chemical crosslinking agents, initiators, surfactants, etc., thus limiting potential problems with the biocompatibility of products. This review summarizes the basics of this method, providing background information on relevant aspects of polymer solution thermodynamics, radiolysis of aqueous solutions, generation and reactions of polymer radicals, and the non-trivial kinetics and mechanism of crosslinking, focusing on the main factors influencing the outcomes of the radiation synthesis of nanogels: molecular weight of the starting polymer, its concentration, irradiation mode, absorbed dose of ionizing radiation and temperature. The most important techniques used to perform the synthesis, to study the kinetics and mechanism of the involved reactions, and to assess the physicochemical properties of the formed nanogels are presented. Two select important cases, the synthesis of nanogels based on polyvinylpyrrolidone (PVP) and/or poly(acrylic acid) (PAA), are discussed in more detail. Examples of recent application studies on radiation-synthesized PVP and PAA nanogels in transporting drugs across the blood-brain barrier and as targeted radioisotope carriers in nanoradiotherapy are briefly described.

Kinetics of polymerization of a liquid with nanosize structural heterogeneities

We report the effects of chemically reacting, nanometer-size structural heterogeneity on a polymerization process. Heterogeneity is introduced by adding 2 nm size molecules of polyhedral oligomeric silsesquioxane with multiepoxide groups (POSS) while maintaining stoichiometry of a polymerizing triamine-diepoxide mixture. Calorimetric studies show that POSS addition first increases the polymerization rate and then decreases it progressively more. In the presence of nanometer-scale structural heterogeneity, diffusion-controlled kinetics begins sooner in time. The enthalpy of polymerization decreases with the amount of POSS heterogeneity according to the mixture rule; the glass-liquid transition endotherm of the partially polymerized state becomes broader, and the enthalpy of post polymerization decreases. The POSS-alone mixture polymerizes relatively slower, and the glass-liquid transition exotherm of the polymerized state is indistinguishably broad. Both are attributed to the distribution of diffusion rates or dispersive kinetics, and the development of dynamic heterogeneity more rapidly for the POSS-only mixture than for others. Increase in the polymerization rate on initial addition of nanometer-size POSS and then decrease on further addition is explained in terms of decoupling of diffusion from viscous flow, that is, when the diffusion rate decreases less rapidly with the polymerization time than the viscosity increases.

Permanganate oxidation of α-amino acids: kinetic correlations for the nonautocatalytic and autocatalytic reaction pathways

The reactions of permanganate ion with seven α-amino acids in aqueous KH(2)PO(4)/K(2)HPO(4) buffers have been followed spectrophotometrically at two different wavelengths: 526 nm (decay of MnO(4)(-)) and 418 nm (formation of colloidal MnO(2)). All of the reactions studied were autocatalyzed by colloidal MnO(2), with the contribution of the autocatalytic reaction pathway decreasing in the order glycine > l-threonine > l-alanine > l-glutamic acid > l-leucine > l-isoleucine > l-valine. The rate constants corresponding to the nonautocatalytic and autocatalytic pathways were obtained by means of either a differential rate law or an integrated one, the latter requiring the use of an iterative method for its implementation. The activation parameters for the two pathways were determined and analyzed to obtain statistically significant correlations for the series of reactions studied. The activation enthalpy of the nonautocatalytic pathway showed a strong, positive dependence on the standard Gibbs energy for the dissociation of the protonated amino group of the α-amino acid. Linear enthalpy-entropy correlations were found for both pathways, leading to isokinetic temperatures of 370 ± 21 K (nonautocatalytic) and 364 ± 28 K (autocatalytic). Mechanisms in agreement with the experimental data are proposed for the two reaction pathways.

Parallels between multiple population-period transient spectroscopy and multidimensional coherence spectroscopies

We have recently shown that homogeneous and heterogeneous kinetics can be distinguished by experiments that compare the evolution of the population of a state over two time intervals [E. van Veldhoven et al., ChemPhysChem 8, 1761 (2007)]. This paper elaborates on the analogy between these multiple population-period transient spectroscopy (MUPPETS) experiments and more familiar spectroscopies based on the evolution of coherences. Using a modified inverse-Laplace transform, a standard kinetics decay is re-expressed as a "rate spectrum." A nonexponential decay creates a linewidth in this spectrum. Mechanisms for line broadening in rate spectra are compared to those for line broadening in frequency-domain spectra. Homogeneous and heterogeneous kinetics are defined precisely and are shown to be the counterparts of homogeneous and inhomogeneous line broadenings in frequency-domain spectra. Homogeneous line broadening mechanisms are further divided into equilibrium and nonequilibrium mechanisms, with equilibrium mechanisms more prevalent in frequency spectra and nonequilibrium mechanisms more prevalent in rate spectra. Spectral representations of two-dimensional MUPPETS experiments are developed that are equivalent to two-dimensional coherence spectroscopies. In particular, spectra equivalent to hole-burning and to correlation spectra are defined. Frequency-domain spectra are often modeled as an inhomogeneous distribution of identical homogeneous line shapes. A parallel homogeneous-heterogeneous model for kinetics is defined. Within this model, MUPPETS has sufficient information to completely separate the homogeneous and heterogeneous contributions to a nonexponential decay, even when the homogeneous contribution is nonexponential.

Hydrates and solid-state reactivity: a survey of beta-lactam antibiotics

Crystalline hydrates of hydrolytically susceptible pharmaceuticals are commonly encountered, and are particularly prevalent in the beta-lactam class of antibiotics. In order to rationalize how the apparent chemical incompatibility between water and beta-lactams is reduced through crystallization, a review of the published literature and available structural information on the solid state stability was undertaken. A search in the CSD yielded a total of 32 crystal structures of water-containing beta-lactams which were examined and classified in terms of hydrogen-bonded networks. In most cases the waters of hydration in the single crystal structures were found to fulfill structural roles and were not sufficiently close in proximity to react with the beta-lactam ring. Published data for the solid-state of several hydrates were also considered. In general, the stability data indicate high thermal stability for the crystalline hydrates. Moreover, even when water molecules are in appropriate proximity and orientation with respect to the beta-lactam moiety for a reaction to occur, the crystalline solids remain stable. The use of the crystal structure information along with computational modeling suggests that a combination of proximal relationships, steric and mechanistic arguments can explain the observed solid-state stability of crystalline beta-lactam hydrates.

Influence of inorganic pyrophosphate on the kinetics of muscle pyruvate kinase: a simple nonallosteric feedback model

Potassium pyrophosphate was used instead of ATP as a model ligand for magnesium cation for the study of effector influence on the kinetics of pyruvate kinase muscle isozyme M(1). The pyruvate kinase activation by low concentration of pyrophosphate and inhibition by high concentration of pyrophosphate was considered to be the result of reversible reactions of magnesium cation with pyrophosphate, ADP, ATP, and PEP. The apparent K(m) and V(m) or in some cases the pseudo-first order reaction rate constant (instead of K(m) and V(m)) of pyruvate kinase at any given pyrophosphate concentration were analysed as a function of concentration of free magnesium cation and its complexes with all ligands present in an assay mixture. The functions of reaction parameters with respect to concentration of magnesium complexes indicate the coexistence in the reaction mixture of simple and mixed complexes of magnesium cation with substrates, pyrophosphate, and an enzyme-substrate complex. The parameters of the simulated reaction for the proposed interactions fit the measured experimental data. A simple model with nonallosteric feedback has been proposed. According to this model, mutual and simultaneous interactions of reaction products with substrates and with an enzyme result in the coexistence of simple and mixed, labile and inert complexes.