Showing papers on "Mass action law published in 1987"
TL;DR: In this article, the mass action law is applied to the concentration dependence of 13C nuclear magnetic resonance (NMR) shift data for sodium dodecylsulfate and it is shown that the extracted aggregation numbers are far too small.
Abstract: The assumptions underlying the extraction of micellar aggregation numbers by means of applying the mass action law to the concentration dependence of13C Nuclear Magnetic Resonance (NMR) shift data are discussed. Such data are presented for sodium dodecylsulfate and it is shown that the extracted aggregation numbers are far too small. It is argued that this is in part due to a failure of the mass action law to describe the micellization process but also due to covariance in the parameters of the mass action law. We also suggest a way to analyse13C shifts from surfactant systems that is void of artefacts due to changes in volume magnetic susceptibilities and other “unwanted” artefacts. Finally, we point out that by combining13C shifts with the fraction of micellized surfactant (as measured by for instance self diffusion coefficients) it should be possible to monitor changes in micellar shapes as the conditions are changed.
38 citations
TL;DR: A mathematical analysis of the Bjerrum function is carried out in this paper, where it is shown that there is only one positive root of the BFP, and thus that only a single equilibrium state can exist.
Abstract: A mathematical analysis of the Bjerrum function is carried out. This function arises from the Stepwise Equilibrium Model, which is used to describe successive complex formation in systems consisting of free metal ion, free ligand, and all theMLi complexes that can form in solution. The appropriate root of the Bjerrum polynomial allows the determination of the concentrations of all species present in solution, given the initial concentrations of metal and of ligand, and the equilibrium constants governing the system. It is proved that there is only one positive root of the Bjerrum polynomial, and thus that only a single equilibrium state can exist. It is also shown that the positive root of the Bjerrum polynomial can be reliably obtained by Newton's method, but only if the initialization point is properly chosen, and that the initial concentrationL of ligand is the optimum such point. Finding this root is a calculation that typically must be carried out at each iteration in nonlinear least squares procedures for determining equilibrium constants. Finally, the necessary mathematical analysis is carried out to determine the optimum initial concentrations of metal and lgand which maximize the resulting concentration of a particularMLi complex.
4 citations
TL;DR: In this article, the authors studied the kinetics of change carriers in an almost intrinsic semiconductor containing deep levels of one kind and subjected to exposure under photon energy greater than the forbidden bandwidth.
Abstract: Stationary states and the kinetics of change carriers are studied in an “almost intrinsic” semiconductor containing deep levels of one kind and subjected to exposure under photon energy greater than the forbidden bandwidth. The exposure intensity is assumed sufficiently large, such that the concentration of the photoexcited charge carriers would exceed equilibrium significantly. Taken into account are both the charge carrier heating by the light and the dependence of the forbidden bandwidth on the electron and hole concentration and temperature. The conditions are mentioned for which stochastic or periodic electron and hole temperature and concentration self-oscillations should occur in the specimen.