Thermodynamic analysis of chemically reacting mixtures – comparison of first and second order models

Recently, a method based on non-equilibrium continuum thermodynamics which derives thermodynamically consistent reaction rate models together with thermodynamic constraints on their parameters was analyzed using a triangular reaction scheme. The scheme was kinetically of the first order. Here, the analysis is further developed for several first and second order schemes to gain a deeper insight into the thermodynamic consistency of rate equations and relationships between chemical thermodynamic and kinetics. It is shown that the thermodynamic constraints on the so-called proper rate coefficient are usually simple sign restrictions consistent with the supposed reaction directions. Constraints on the so-called coupling rate coefficients are more complex and weaker. This means more freedom in kinetic coupling between reaction steps in a scheme, i.e., in the kinetic effects of other reactions on the rate of some reaction in a reacting system. When compared with traditional mass-action rate equations, the method allows a reduction in the number of traditional rate constants to be evaluated from data, i.e., a reduction in the dimensionality of the parameter estimation problem. This is due to identifying relationships between mass-action rate constants (relationships which also include thermodynamic equilibrium constants) which have so far been unknown

Thermodynamic Driving Forces and Chemical Reaction Fluxes; Reflections on the Steady State

Molar balances of continuous and batch reacting systems with a simple reaction are analyzed from the point of view of finding relationships between the thermodynamic driving force and the chemical reaction rate. Special attention is focused on the steady state, which has been the core subject of previous similar work. It is argued that such relationships should also contain, besides the thermodynamic driving force, a kinetic factor, and are of a specific form for a specific reacting system. More general analysis is provided by means of the non-equilibrium thermodynamics of linear fluid mixtures. Then, the driving force can be expressed either in the Gibbs energy (affinity) form or on the basis of chemical potentials. The relationships can be generally interpreted in terms of force, resistance and flux

Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions—Two Illustrative Examples

Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamicsbased theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with the entropic inequality (the second law of thermodynamics) are illustrated. The theory illustrated here can be viewed as a tool for verifying and generalizing traditional mass-action kinetics by means of modern non-equilibrium thermodynamics, which is able to deal also with such rather problematic cases

Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics

Linear algebra treatment of the permanence of atoms (mass conservation) naturally leads to the transformation of formation or destruction rates of components of a reaction mixture into rates of reaction steps, which are sufficient to describe the transformations mathematically. These steps form a scheme of independent reactions that can provide a rational basis for elucidating the reaction mechanism (network) while reducing both the component and parametric dimensionality of the description of kinetics. Several particular reaction examples are used to explain the method and show that rates of additional, dependent reactions cannot be unambiguously related to measured component rates. They also illustrate how the rates of dependent reactions can be correctly expressed in terms of the rates of independent reactions. The method starts only with a knowledge of the components of a reaction mixture. It is argued that the design of consistent reaction networks or mechanisms should take into account not only chemistry but also mathematics

Thermodynamic Analysis of the Landolt-Type Autocatalytic System

A recent work demonstrated on the example of the Landolt-type reaction system how the simplest autocatalytic loop is described by the kinetic mass action law and proper parametrization of direct and autocatalytic pathways. Using a methodology of non-equilibrium thermodynamics the thermodynamic consistency of that kinetic model is analyzed and the mass action description generalized including an alternative description by the empirical rate equation. Relationships between independent and dependent reactions and their rates are given. The mathematical modeling shows that following the time evolution of reaction rates provides additional insight into autocatalytic behavior. A brief note on thermodynamic driving forces and coupling with diffusion is added. In summary, this work extends and generalizes the kinetic description of the Landolt-type system placing it within the framework of non-equilibrium thermodynamics and demonstrating its thermodynamic consistency

Gradient hydrogels – overview of techniques demonstrating the existence of a gradient

Gradient hydrogels are promising future materials which could be usable in tissue engineering (scaffolds), pharmaceutical (drug delivery systems with controlled release) and many others re-lated disciplines. These hydrogels exhibit a more complex inner (gradient) structure (e.g. con-centration gradient) than simple isotropic hydrogel. Gradient structured hydrogels could be beneficial in, for example, understanding intercellular interactions. The fabrication of gradient hydrogels is relatively deeply explored, but a comprehensive description of the physi-co-chemical techniques demonstrating the existence of a gradient structure is still missing. Here, we summarize the state-of-the-art of available experimental techniques which could be applica-ble in proving and/or describing in physico-chemical terms the inner gradient structure of hy-drogels. The aim of this paper is to give the reader an overview of the existing database of suit-able techniques for characterizing gradient hydrogels

Fluorescence study of freeze-drying as a method for support the interactions between hyaluronan and hydrophobic species

A freeze-drying method enabling solubilization of hydrophobic species in aqueous solutions of native hyaluronan is described. The method is based on opening the access to supposed hydrophobic patches on hyaluronan by disturbing its massive hydration shell. Hydrophobic and/or polarity-sensitive fluorescence probes were used as hydrophobic models or indicators of interactions with hydrophobic patches. Fluorescence parameters specific to individual probes confirmed the efficiency of the freeze-drying method. This work is the first step in developing biocompatible and biodegradable carriers for hydrophobic drugs with targeted distribution of the active compound from native, chemically non-modified hyaluronan

Compositional and Temperature Effects on the Rheological Properties of Polyelectrolyte–Surfactant Hydrogels

The rheological properties of hydrogels prepared by physical interactions between oppositely charged polyelectrolyte and surfactant in micellar form were studied. Specifically, hyaluronan was employed as a negatively charged polyelectrolyte and Septonex (carbethopendecinium bromide) as a cationic surfactant. Amino-modified dextran was used as a positively charged polyelectrolyte interacting with sodium dodecylsulphate as an anionic surfactant. The effects of the preparation method, surfactant concentration, ionic strength (the concentration of NaCl background electrolyte), pH (buffers), multivalent cations, and elevated temperature on the properties were investigated. The formation of gels required an optimum ionic strength (set by the NaCl solution), ranging from 0.15–0.3 M regardless of the type of hydrogel system and surfactant concentration. The other compositional effects and the effect of temperature were dependent on the polyelectrolyte type or its molecular weight. General differences between the behaviour of hyaluronan-based and cationized dextran-based materials were attributed to differences in the chain conformations of the two biopolymers and in the accessibility of their charged groups