Kinetics of donor–acceptor complex polymerization. III. Assessment of some approximations in the kinetics

The mathematical solution of the equations derived from a kinetic scheme previously developed for donor–acceptor complex polymerization was based on steady-state conditions and the applicability of initial concentration conditions over a range of conversion. These assumptions are scrutinized and tested by computer simulation and by the exact differential equations utilizing Runge-Kutta method. The analysis shows that for case I conditions of low concentration of complexing-agent, the degree of conversion is not critical and that the previous approximate solutions are valid. The steady-state and non-steady-state conditions are compared, and the range of validity of the assumptions is established. The approximate solutions are found inapplicable in the instances of non-steady-state conditions coupled with a low concentration of either monomer.     

A general treatment for the conductivity of electrolytes in the whole concentration range in aqueous and nonaqueous solutions

Despite the great importance of ion transport, most of the widely accepted models and theories are valid only in the not very practical limit of low concentrations. Aiming to extend the range of applicability to moderate concentrations, a number of modified models and equations (some approximate, some fundamented on different assumptions, and some just empirical) have been reported. In this work, a general treatment for the electrical conductivity of ionic solutions has been developed, considering the electrical conductivity as a transport phenomenon governed by dissipation and feedback. A general expression for the dependence of the specific conductivity on the solution viscosity (and indirectly on concentration), from which the whole conductivity curve can be obtained, has been derived. The validity of this general approach is demonstrated with experimental results taken from the literature for aqueous and nonaqueous solutions of electrolytes.     

HMO correlations with the electronic spectra of a large non-homogeneous series

A basic set of electronic spectra for 46 compounds of widely divergent structures have been used to form a correlation with HMO transition energies for p-bands, and β-bands. Regression equations have been used to predict the location of these bands in a varied series of 88 additional compounds. The results serve to extend the applicability of the Hückel method as a simple tool for the qualitative and approximate quantitative prediction of the basic elements of singlet transitions.     

Application of He’s variational iteration method in nonlinear boundary value problems in enzyme– substrate reaction diffusion processes: part 1. The steady-state amperometric response

A mathematical model of amperometric biosensors has been developed. In this paper, He’s variational iteration method is implemented to give approximate and analytical solutions of non-linear reaction diffusion equations containing a non linear term related to Michaelis–Menten kinetic of the enzymatic reaction. The variational iteration method which produces the solutions in terms of convergent series, requiring no linearization or small perturbation. These analytical results are compared with available limiting case result and are found to be in good agreement.     

Functions defining capillary structure of microporous adsorbents

The applicability of earlier derived equations for adsorption isotherms for the determination of differential curves characterizing the approximate distribution of micropore volumes in relation to their radii is studied. It is concluded that besides the Gaussian distribution, the Rayleigh and exponential distributions also possess a physical sense.     

Diffusional release of a solute from a polymeric matrix — approximate analytical solutions

A refined integral method has been successfully applied to moving boundary problems encountered in the diffusional release of a solute from a polymeric matrix. The release kinetics has been analyzed for both erodible and non-erodible matrices with perfect sink and constant, finite external volume conditions. The range of applicability of these approximate analytical solutions has been established by comparison with available exact solutions. p]The approximate analytical solutions presented here are much more accurate than the pseudosteady-state results and much easier to use routinely than the exact solutions. For a dispersed solute, the results presented here are particularly useful for cases where the solute loading is not in great excess of the solute solubility in the matrix.     

Detection of heavy metals in water by fluorescence spectroscopy: on the way to a suitable sensor system

In order to develop a fiber optical heavy metal ion detection system, the applicability of selected complexing agents with fluorescent properties has been studied. Beginning with the application of known chelators, like BTC-5N, Newport Green, neocuproine, and chromotropic acid, a sensor configuration has been found, which allows the detection of Cd2+, Ni2+, and Cu2+ well below the chemical parameter threshold values of the new Water Quality Directive 98/83/EU. The sensor itself uses a membrane separation of the chelator flow from the sample volume. The diffusion across the membrane limits the response time to about 15 to 20 min. Applications are seen in monitoring networks.     

Thermodynamic issues associated with combined cyclic voltammetry and wafer curvature measurements in electrolytes

A thermodynamic framework has been provided for the interpretation of combined cyclic voltammetry and surface stress measurements, the latter being obtained from wafer curvature or beam deflection measurements of a solid electrode as a function of applied potential (so-called voltstressograms). Firstly, the derivation of electrocapillarity equations for solid electrodes has been critically reviewed by starting from the Gibbs adsorption equation appropriate for solid–electrolyte interfaces. This allowed us to demonstrate the critical importance of elastic surface strain in the thermodynamic boundary conditions of the partial derivatives intervening in the interpretation of voltstressograms. From these considerations, it was shown for the first time that the electrocapillarity equations for solid electrodes are not appropriate for describing the variation of surface stress with potential obtained from wafer curvature measurements, because such measurements are intrinsically incompatible with the constant strain condition implied in the electrocapillarity equations. An alternative explanation is provided for the experimentally observed proportionality between the current density, measured in cyclic voltammograms, and the first derivative of surface stress with respect to potential, obtained from voltstressograms.     

A method of incorporating quadruple correction in the scheme of multi-reference singly and doubly excited configuration interaction — a CSF based coupled pair approximation

Summary We develop an approximate size consistent method within a framework of the multi-reference configuration interaction scheme. The Rayleigh-Schrödinger perturbation theory is employed with a specific selection of the unperturbed part of the electronic Hamiltonian. The second order energy is obtained by a set of equations similar to the quasidegenerate variational perturbation theory of Cave and Davidson. The approximate fourth order energy is obtained by solving a set of equations similar to the coupled electron pair approximation (CEPA). The method has been tested for two simple systems, BeH₂ and N₂, and the results are quite encouraging.     

A unified cosolvency model for calculating solute solubility in mixed solvents

Organic solvents are amongst the most powerful solubilization agents for a large number of water-insoluble drugs. A number of equations has been reported for mathematical representation of solute solubility in mixed solvents. The question is then posed--is there a mathematical difference between these models? To address this point, it has been demonstrated that all cosolvency models could be made equivalent by using algebraic manipulations. In order to familiarize the readers with the available cosolvency models, they are briefly reviewed. The models can be divided into two mathematical categories, i.e. linear and non-linear models. The linear models include: the log-linear, extended Hildebrand solubility approach, excess free energy equations, combined nearly ideal binary solvent/Redlich-Kister equation and Margule equations which can be converted to a general single model which expresses the logarithm of mole fraction solubility of a solute as a power series of volume fraction of the cosolvent. The non-linear models include the mixture response surface methods, two step solvation model and modified Wilson model which can be converted to a non-linear general form. Also, it has been shown that both the general single model and a non-linear general model are mathematically identical. To show the applicability of the models on real experimental data, 35 data sets have been collected from the literature. Both linear and nonlinear models produced comparable accuracies when an equal number of constant terms was employed in numerical analyses.     

Two reliable wavelet methods to Fitzhugh–Nagumo (FN) and fractional FN equations

Fractional reaction–diffusion equations serve as more relevant models for studying complex patterns in several fields of nonlinear sciences. In this paper, we have developed the wavelet methods to find the approximate solutions for the Fitzhugh–Nagumo (FN) and fractional FN equations. The proposed method techniques provide the solutions in rapid convergence series with computable terms. To the best of our knowledge, until now there is no rigorous wavelet solutions have been reported for the FN and fractional FN equations arising in gene propagation and model. With the help of Laplace operator and Legendre wavelets operational matrices, the FN equation is converted into an algebraic system. Finally, we have given some numerical examples to demonstrate the validity and applicability of the wavelet methods. The power of the manageable method is confirmed. Moreover, the use of the wavelet methods is found to be accurate, efficient, simple, low computation costs and computationally attractive.     

Application of a sulphide-selective electrode in the absence of a pH-buffer

Calibration of a sulphide electrode in the pH-range 9-12 has been studied as an e.m.f. vs. (pH - p[HS(-)]) function by measuring e.m.f. and pH in parallel. Calibration can also be done in this pH range by using a differential amplifier with a three-electrode measuring cell (glass, sulphide-selective and reference electrodes). The effects of an antioxidant (ascorbic acid) and a complexing agent (DCTA) on the calibration of the glass-sulphide electrode cell at pH < 5 were studied. The applicability of this end-point indicator cell has been demonstrated for titrations of Ag(+), Pb(2+) and Bi(3+) with Na(2)S.     

Approximate treatment of higher excitations in coupled-cluster theory

The possibilities for the approximate treatment of higher excitations in coupled-cluster (CC) theory are discussed. Potential routes for the generalization of corresponding approximations to lower-level CC methods are analyzed for higher excitations. A general string-based algorithm is presented for the evaluation of the special contractions appearing in the equations specific to those approximate CC models. It is demonstrated that several iterative and noniterative approximations to higher excitations can be efficiently implemented with the aid of our algorithm and that the coding effort is mostly reduced to the generation of the corresponding formulas. The performance of the proposed and implemented methods for total energies is assessed with special regard to quadruple and pentuple excitations. The applicability of our approach is illustrated by benchmark calculations for the butadiene molecule. Our results demonstrate that the proposed algorithm enables us to consider the effect of quadruple excitations for molecular systems consisting of up to 10-12 atoms.     

Soliton solutions for time fractional coupled modified KdV equations using new coupled fractional reduced differential transform method

In this paper, new Coupled Fractional Reduced Differential Transform has been implemented to obtain the soliton solutions of coupled time fractional modified KdV equations. This new method has been revealed by the author. The fractional derivatives are described in the Caputo sense. By using the present method, we can solve many linear and nonlinear coupled fractional differential equations. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional coupled modified KdV equations. Numerical solutions are presented graphically to show the reliability and efficiency of the method. Solutions obtained by this new method have been also compared with Adomian decomposition method (ADM).     

Use of a digital computer in equilibrium calculations:the effects of dilution and ionic strength of the buffer index and sharpness index in the titration of a monoprotic acid with a strong base

The effects of dilution and ionic strength on weak acid-strong base titration curves and on the buffer index, β, and sharpness index, η, for these titrations have been calculated. It has been shown that the approximate equations generally used to calculate β and η are often misleading.     

Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique

Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree–Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F₂ and transition metal complexes such as NiO, Mn₂, and [Cu₂O₂]²⁺ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree–Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.     

Computer simulation of the steady state currents at enzyme doped carbon paste electrodes

The plate-gap model of porous enzyme doped electrode has been proposed and analyzed. It was suggested that reaction diffusion conditions in pores of bulk electrode resemble particular conditions in thin gap between parallel conducting plates. The model is based on the diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetic of the enzymatic reaction inside gap. Steady state current was calculated for the wide range of given parameters and substrate concentrations. All dependences of current on substrate concentration were approximated by hyperbolas in order to obtain “apparent” parameters (maximal currents and apparent Michaelis constants) of modelled biosensors. Simple approximate relationships between given and apparent parameters were derived. The applicability of theoretical plate-gap model was tested for the case of carbon paste electrodes which were doped with PQQ – dependent glucose dehydrogenase. It was found, that soluble glucose dehydrogenase based biosensors exhibit characteristic features of the theoretical plate-gap biosensors.