Comparison between theoretical values and simulation results of viscosity for the dissipative particle dynamics method

In order to investigate the validity of the dissipative particle dynamics method, which is a mesoscopic simulation technique, we have derived an expression for viscosity from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expressions of the viscosity due to momentum and dissipative forces have been obtained using the approximate solutions of the distribution functions. Also, we have conducted nonequilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method. The theoretical values of the viscosity due to dissipative forces in the Hoogerbrugge-Koelman theory are in good agreement with the simulation results obtained by the nonequilibrium dynamics method, except in the range of small number densities. There are restriction conditions for taking appropriate values of the number density, number of particles, time interval, shear rate, etc., to obtain physically reasonable results by means of dissipative particle dynamics simulations.     

Flow-alignment and rheology of polymer melts: Computation of the single-link orientational distribution function

The single-link orientational distribution function and the space-averaged stresses in the fluid are computed for the case of steady shear flow of polymer melts. The computation is achieved with Galerkin's method with spherical harmonics and Euler polynomials as trial functions. The stress components become power functions of shear rate when the latter is large. The single-link orientational distribution function f solves the Fokker-Planck equation subject to a boundary condition for f at the chain ends. A solution is obtained for every shear rate and ratio of the orientational and one-dimensional diffusion coefficient. It is demonstrated that the Fokker-Planck equation with appropriate boundary condition is useful in order to predict the flow-alignment and stresses in good agreement with experimental data as well as with recent results of a nonequilibrium molecular dynamics computer simulation on polymer melts.     

Spectral convergence of the quadrature discretization method in the solution of the Schrodinger and Fokker-Planck equations: comparison with sinc methods

Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I2 with a Morse potential is also considered.     

Solution of the Schrödinger equation for two different molecular potentials by the Nikiforov-Uvarov method

In this study, the solution of the Schr?dinger equation by a method developed by Nikiforov and Uvarov which is not based on the manipulation of formal power series has been schematically presented. The method gives elegant, easy and exact solutions of the Schr?dinger equation. In order to demonstrate the applications of the method, solutions of the Schr?dinger equation for the well-known pseudo-harmonic oscillator and a new symmetrical potential proposed by the authors are given. The concrete energy spectra and corresponding wave functions are obtained. The superiority and the limitations of the method compared to other methods have also been emphasized. Received: 20 November 1996 / Accepted: 1 October 1997     

Optimization of complex slater‐type functions with analytic derivative methods for describing photoionization differential cross sections

The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an method to solve the driven‐type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven‐type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater‐type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven‐type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc.     

Calculation of the viscosity dependence of the excited-state lifetime in pinacyanol solution

The viscosity dependence of the S₁ lifetime of pinacyanol in solutions is calculated by solving the appropriate Fokker-Planck equation considering     

Size Exclusion Chromatography (SEC) of Complex Polymers - Generalized Analytical Corrections for Imperfect Resolution

Abstract

Herein is reported generalized analytical solutions which permit correction for imperfect resolution when the molecular weight calibration curve is nonlinear and the variance of single-species chromatograms changes significantly with molecular size of the polymer solute. Two kinds of generalized analytical solutions have been obtained. One is a solution of Tung's integral equation for the corrected chromatogram or the molecular weight distribution and the other is a solution for the corrected molecular weight averages of the whole polymer. Also discussed is the use of local corrections for imperfect resolution across the chromatogram with detectors such as the low angle laser light scattering spectrophotometer (LALLS) when used with micro and macropackings.     

Effects of the bead-bead potential on the restricted rotational diffusion of nonrigid macromolecules

The influence of the bead-bead interaction on the rotational dynamics of macromolecules which are immersed into a solution has been investigated by starting from the microscopic theory of the macromolecular motion, i.e., from a Fokker-Planck equation for the phase-space distribution function. From this equation, we then derived an explicit expression for the configuration-space distribution function of a nonrigid molecule which is immobilized on a surface. This function contains all the information about the interaction among the beads as well as the effects from the surrounding solvent particles and from the surface. For the restricted rotational motion, the dynamics of the macromolecules can now be characterized in terms of a rotational diffusion coefficient as well as a radial distribution functions. Detailed computations for the rotational diffusion coefficient and the distribution functions have been carried out for HOOKEAN, finitely extensible nonlinear elastic, and a DNA type bead-bead interaction.     

A New Method for Identifying and Estimating the Parameters of the Instrumental Spreading Function in Size Exclusion Chromatography-Application to Particle Size Analysis

Abstract

Herein is reported a new method for identifying and estimating the instrumental spreading function in size exclusion chromatography. The method is based on the solution of the integral equation when the size distribution of the injected standards are known. A numerical method after Ishige et al. (1) to solve the integral equation for the corrected distribution is suitably modified to estimate instead the spreading function when the true and measured chromatograms are both known. The method is evaluated for synthesized chromatograms using the particle size distribution of Dow polystyrene latices. It is then applied to experimental chromatograms of the latices obtained by size exclusion chromatography. The resulting spreading functions were then analysed for variance, skewness and kurtosis.     

Nonequilibrium surface tension for mixed adsorption kinetics

Experimental nonequilibrium surface tension measurements of 1–9 nonanediol solutions obtained by the oscillating-jet method have been interpreted in terms of our theoretical predictions derived for a mixed-controlled adsorption kinetics of the surfactant. The surface tension values have been calculated from the Szyszkowski equation using the Langmuir model of surfactant adsorption. Our theoretical results, obtained by a numerical solution of the adsorption equations, agree well with experimental data giving a value of the kinetics Szyszkowski constant very similar to the thermodynamic equilibrium value determined from experimental measurements of the static surface tension of 1–9 nonanediol solutions of various concentration. The approximate kinetic equation derived by P. Joos, G. Bleys, and G. Petre (J. Chim. Phys.79, 387 (1982)) for purely barrier-controlled adsorption proved to be less accurate.     

The mechanism of activation and nonequilibrium distribution functions in unimolecular reactions

Nonequilibrium distribution functions for polyatomic molecules undergoing unimolecular reaction are considered. Two limiting cases of activation by collision are investigated: the mechanism of strong impacts, in which each collision with an activated molecule may be regarded as bringing about deactivation; and the diffusion mechanism in which the transition between states is described by the Fokker-Planck equation. An accurate solution of the diffusion equation for the thermal decomposition of a nonlinear triatomic molecule makes it possible to elucidate the kinetics of various reactions in relation to the activation mechansim.     

SYNTHESIS OF AMPHIPHILIC COIL-ROD-COIL BLOCK COPOLYMERS USING ATOM TRANSFER RADICAL POLYMERIZATION

ABSTRACT

Coil-rod-coil block copolymers composed from luminescent rigid units and acrylate flexible blocks have been synthesized using atom transfer radical polymerization. α,ω-Difunctionalized oligophenylenes properly modified to act as ATRP initiators have been used for the polymerization of the various acrylates. Copolymers with controlled shape and in some cases, relatively low polydispersities have been obtained as proved by size exclusion chromatography and NMR. In cases, where t-butyl acrylate blocks have been used as the flexible part, selective hydrolysis resulted in coil-rod-coil copolymers containing poly(acrylic acid) blocks. The solution behavior of the synthesized copolymers was explored in various solvents. The poly(acrylic acid) copolymers in aqueous solutions form large aggregates, while in organic selective solvents for the flexible block, monomolecular micelles seem to be formed.     

Study on Electric Double Layer of a Cylindrical Particle with Functional Theoretical Approach

A new method, i.e. the iterative method in functional theory, was introduced to solve analytically the nonlinear Poisson-Boltzmann （PB） equation under general potential ψ condition for the electric double layer of a charged cylindrical colloid particle in a symmetrical electrolyte solution. The iterative solutions of ψ are expressed as functions of the distance from the axis of the particle with solution parameters： the concentration of ions c, the aggregation number of ions in a unit length m, the dielectric constant e, the system temperature T and so on. The relative errors show that generally only the first and the second iterative solutions can give accuracy higher than 97%. From the second iterative solution the radius and the surface potential of a cylinder have been defined and the corresponding values have been estimated with the solution parameters, Furthermore, the charge density, the activity coefficient of ions and the osmotic coefficient of solvent were also discussed,     

The Effect of Simulation Cell Size on the Diffusion Coefficient of an Ionic Surfactant Aggregate

Results of all-atom molecular dynamics simulation have been presented for salt-free aqueous solutions of sodium dodecyl sulfate at its fixed total concentration in a simulation cell containing one to four preliminarily formed quasi-stable ionic aggregates with equal aggregation numbers n = 32. The obtained molecular dynamics trajectories have been used to study the structural and transport properties of the micellar solution. The value of the counterion diffusion coefficient obtained using the Green–Kubo relation has turned out to be somewhat higher than the corresponding value calculated by the Einstein equation. The diffusion coefficients of the aggregates in the systems containing from two to four aggregates have appeared to be higher than the diffusion coefficient of a single aggregate in a cell. The mean force potential obtained for the interaction between the aggregates having aggregation number n = 32 as a function the distance between the aggregate centers of mass has a local minimum in the system containing four such aggregates.     

Volumetric studies and thermodynamics of viscous flow of hydroxamic acids in acetone + water solvent at temperatures 303.15 and 313.15 K

Densities ρ and viscosities η of two hydroxamic acids, N-phenyl-2-chlorobenzo- and N-o-tolyl-4-chlorobenzo-, have been determined as a function of their concentration in aqueous acetone solution at temperatures 303.15 and 313.15 K. Apparent molar volumes, standard-state partial molar volumes and relative viscosities have been calculated. The viscosity data have been analyzed using Jones-Dole equation. The activation thermodynamic parameters of viscous flow have been evaluated using Feakins equation. These were obtained to throw light on the mechanism of viscous flow. Thermodynamic interactions in solutions have been studied in terms of a number of excess functions calculated from the experimental data. The effect of hydroxamic acid concentration and temperature on these parameters has been discussed. The results were interpreted in the light of solute-solvent interactions in aquo-organic media.     

Use of Inverse Multiple Linear Regression (ILS) for the Analytical Control of Pharmaceutical Preparations. UV-Visible Spectrophotometric Quantitation of an Active Principal in the Presence of Absorbing Excipients

ABSTRACT

The simplicity and robustness of inverse multiple linear regression (ILS) as a method for the analytical control of pharmaceutical preparations by UV–vis spectrophotometry is demonstrated. This calibration technique establishes a linear relation between the analyte concentration as dependent variable and absorbance values measured at a small number of wavelengths as independent variables. In this work, ILS was used to quantify the active principal in a pharmaceutical preparation commercially available as aqueous solution.

The preparation was diluted in 40:60 v/v methanol/aqueous 0.1 N NaOH and its UV spectrum recorded over the wavelength range 240–330 nm. The calibration equation was derived from laboratory-made solutions of the analyte and absorbing excipients in the preparation. The operating wavelengths used were those of the absorption maxima for the compounds of interest; the results are compared with those obtained by stepwise wavelength selection and high performance liquid chromatography (HPLC).