Application of significant structure theory of liquids to critical phenomena. Calculation of critical-point exponents

Three critical-point exponents β, δ, γ and the corresponding coefficients B, D and G are calculated using significant structure theory. The results are compared with those obtained from the van der Waals equation, Berthelot's equation and the Dieterici equation. The significant structure theory and the van der Waals equation behave similarly in the critical region. All these equations of state predict a finite C_ν at the critical point.     

A three-parameter cubic equation of state for asymmetric mixture density calculations

A new three-parameter cubic equation of state of the van der Waals type with one parameter temperature dependent, P = RT/(V − b) − a(T)/[V(V + c) + b(3V + c)], has been developed for representation of liquid volumes (or densities) for asymmetric mixtures such as CO₂C₁₉ and C₁C₁₀. The calculated results are better than those obtained from the two-parameter Peng—Robinson equation, the three parameter Schmidt—Wenzel equation, the volume-translated Soave—Redlich—Kwong equation proposed by Peneloux et al., and the volume-translated Peng—Robinson equation developed in this work. The parameters of the new equation have been generalized in terms of the acentric factor ω and reduced temperature T_r.     

Highly accurate and simple analytical approach to nonlinear Poisson–Boltzmann equation

A novel method is suggested to analytically solve a nonlinear Poisson–Boltzmann (NLPB) equation. The method consists chiefly of reducing the NLPB equation to linear PB equation in several segments by approximating a free term of the NLPB equation by piecewise linear functions, and then, solving analytically the linear PB equation in each segment. Superiority of the method is illustrated by applying the method to solve the NLPB equation describing a colloid sphere immersed in an arbitrary valence and mixed electrolyte solution; extensive test indicates that the resulting analytical expressions for both the electrical potential distribution Ψ (r) and surface charge density/surface potential relationship (σ/Ψ ₀) are characterized with two properties that mathematical structures are much simpler than those previously reported and application scope can be arbitrarily wide by adjusting the linear interpolation range. Finally, it is noted that the method is “universal” in that its applications are not limited to the NLPB equation.     

Quantum mechanical law of corresponding states from ISM equation of state: compressed liquids

In this paper, we explore the theory of the equation of state from the view point of Ihm–Song–Mason (ISM) equation of state, which has been derived on the basis of statistical mechanical perturbation theory, and is characterized by three temperature dependent parameters, α, b, B₂, and a free parameter Γ. This equation is applied well to non-polar fluids in subcritical and supercritical regions and to molten alkali metals. We present results that show Γ varies slightly with temperature. Among the nobles group, Γ values are quite the same and are correlated except He, which deviates so much even no moderate correlation is seen. In the alkali metals group, Γ values are roughly the same for K, Rb, and Cs but are different for Li and Na. We have previously shown that Γ conforms to B₂, the second virial coefficient, and thus to the nature of the particular fluid system. These observations plus the discussion on quantum mechanical law of corresponding states suggest that the ISM equation of state stands as an analytical equation of state which explicitly incorporates quantum effects by the parameter Γ. Then, we suggest a law of corresponding states as p*=p*(v*, T*, Γ) where, asterisks stand for reduced pressure, volume, and temperature, respectively.     

Stochastic theory of direct simulation Monte Carlo method

A treatment of direct simulation Monte Carlo method as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived from the master equation. An equation similar to the Boltzmann equation for single particle probability distribution is derived using assumption of molecular chaos. It is shown that starting from an uncorrelated state, the system remains uncorrelated always in the limit N→∞, where N is the number of particles. Simple applications of the formalism to direct simulation money games are given as examples to the formalism. The formalism is applied to the direct simulation of homogenous gases. It is shown that appropriately normalized single particle probability distribution satisfies the Boltzmann equation for simple gases and Wang Chang–Uhlenbeck equation for a mixture of molecular gases. As a consequence of this development we derive Birds no time counter algorithm. We extend the analysis to the inhomogeneous gases and define a new direct simulation algorithm for this case. We show that single particle probability distribution satisfies the Boltzmann equation in our algorithm in the limit N→∞, V _k →0, Δt→0 where V _k is the volume of kth cell. We also show that our algorithm and Bird’s algorithm approach each other in the limit N _k →∞ where N _k is the number of particles in the volume V _k .     

A model-free method for evaluating theoretical error of Kissinger equation

Kissinger equation is widely used to calculate the activation energy. However, since a number of assumptions and approximations are introduced in the derivation, the activation energy resolved by this method will have some errors. Here, we propose a model-free evaluation method to estimate the relative error of activation energy of Kissinger equation. Our work shows that the error in activation energy solved by Kissinger equation is not only related to the magnitude of x = E/RT, but also depended on the change of β and ?x = x ₁ ? x ₂. From the experimental and theoretical analysis on the degradation of polyamide-6, it can be found that the actual error and the theoretical error in the activation energy solved by Kissinger equation are almost same.     

Specific features of curing of oligodieneurethane isocyanate prepolymer with glycerol in the presence of an organotin catalyst at twofold excess of isocyanate groups

The results of rheokinetic studies of catalytic curing of oligo dieneurethane prepolymer with glycerol at double excess of isocyanate groups are presented. The curing is described in the initial step by the polymerization equation with varying number of active sites (up to conversion x ≈ 20%); then, by an equation of an autocatalytic reaction with adiabatic self-acceleration (up to x ≈ 40%); and in the final step (x > 40%), by a second-order equation with self-acceleration effect.     

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T ₀, characteristic density ρ₀, anisotropy factor α, and reduced quadrupolar moment Q*². The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.     

The analysis of the derivation principles of kinetic equations based on exactly solvable models of the bulk reaction A + B → Product

We have considered two many-particle models of the irreversible reaction A + B → Product for which closed kinetic equations for the mean concentration N_A(t) of A species can be exactly obtained. These equations are identically recast into a unified form of integro-differential equation of general kinetic theory. It is shown that the memory functions for both models under consideration can be represented as a sum of the Markovian and non-Markovian parts. It is essential that the Markovian part of the Laplace transform of any kernel can be obtained using the Laplace transform of the kernel itself, and is the root of the non-Markovian part of the Laplace transform of the kernel.The properties established allowed us to perform correct approximation of the memory functions at small concentrations [B] of B species and derive the binary non-Markovian integro-differential equation. Within the binary theory accuracy this equation has been rewritten in a regular frame of a familiar rate equation satisfying general principles of binary kinetic equations.Thus using particular exactly solvable many-particle models, we have reproduced the most essential steps of the known general way for the derivation of the binary kinetic equation avoiding the sophisticated many-particle technique and the corresponding approximations. Besides, the results obtained can serve as an additional evidence of the approximations made in a general many-particle approach to the derivation of the binary kinetic equation.     

A multiparameter thermal conductivity equation for R134a with an optimized functional form

A new multiparameter equation λ = λ(T, ρ) for the thermal conductivity of R134a has been developed from the available experimental data using a technique for the optimization of the functional form. The equation is valid in the temperature range from 200 to 540 K and for pressure up to 70 MPa, including also the near-critical region. The satisfactory performances of the equation are summarized by an average absolute deviation of 2.04% for the selected 5102 primary data points, with a significant improvement with respect to the present reference equation from the literature.The conversion of the independent variables of the experimental data into those of the equation, i.e. (T, P) into (T, ρ), is performed with a high accuracy equation of state for the fluid.     

On the random walk of energy to traps in disordered systems

Adams recently derived a theorem concerning solutions of the Schrödinger equation for an N-electron system. From this theorem he concludes that exact eigenvalues and (antisymmetric) eigenfunctions can be obtained by solving a different type of equation whose eigenfunctions are not antisymmetric. We critically discuss aspects of Adams' formalism.     

Evaluation of enzymatic kinetic parameters by thin-layer chromatography with radiometric detection

A radiochromatographic method is described for evaluating K_m and v_max based on a simple modification of the integrated Michaelis-Menten equation. Experimental points are ritted directly to this equation be an iterative technique, the validity of which is tested on simulated experimental data. Results for lysine, ornithine, and glutamic acid decarboxylases are reported.     

The equation of state for gas mixtures in the canonical form

The T ₀ and ρ variables, where ρ is the density and T ₀ the parametric temperature depending on T and ρ, were introduced to obtain the equation of state of a mixture for the Helmholtz energy. The equation explicitly includes an analogue of a pure substance as a component. Its properties are determined by the interactions of dissimilar molecules.     

Solution properties of copolyamides

Mark-Houwink-Sakurada relations for random copolymers from para-aminobenzoic acid and 6-aminohexanoic acid were determined in N,N-dimethylacetamide, dichloroacetic acid and trifluoroacetic acid. Unperturbed chain dimensions, solvent-polymer interaction parameters and conformational parameter, δ, were obtained by using the Stockmayer-Fixman equation. The unperturbed dimensions were also calculated by using a semi-empirical relation of Krigbaum; they compare favourably with values calculated through the use of (S-F) equation. The results show that the unperturbed dimensions are dependent on the solvent nature.     

Conductance of tetraethylammonium halides in ethylene glycol

Conductance measurements on tetraethylammonium halides in ethylene glycol at different temperatures and concentrations are reported. Experimental data are analysed on the basis of Onsager's equation and the Onsager—Fuoss—Skinner equation. The ion-size parameter a(Å) obtained from the Onsager—Fuoss—Skinner equation is reported at different temperatures. The temperature dependence of the Walden products of the salt solutions in ethyleneglycol is also discussed in terms of the structure-breaking/making characteristics of the salt.     

Solubility of Omeprazole Sulfide in Different Solvents at the Range of 280.35–319.65 K

Solubility data were measured for omeprazole sulfide in ethanol, 95 mass-% ethanol, ethyl acetate, isopropanol, methanol, acetone, n-butanol and n-propanol in the temperature range from 280.35 to 319.65 K by employing the gravimetric method. The solubilities increase with temperature and they are in good agreement with the calculated solubility of the modified Apelblat equation and the λh equation. The experimental solubility and correlation equation in this work can be used as essential data and model in the purification process of omeprazole sulfide. The thermodynamic properties of the solution process, including the Gibbs energy, enthalpy, and entropy were calculated using the van’t Hoff equation.     

The reduction of the multi-dimensional schrödinger equation to a one-dimensional integral equation

A method is proposed for reducing the multi-dimensional Schrödinger equation to a one-dimensional integral equation. The reduction is exact; and the resulting integral equation although complicated, may be treated by any of a number of numerical methods. Two 2-dimensional problems, the harmonic oscillator and the S-limit for helium and one 3-dimensional problem, the helium ground state are treated in this way.     

Modification of the Furter equation and correlation of the vapor–liquid equilibrium for mixed-solvent electrolyte systems

Isobaric vapor–liquid equilibrium values at 1 atm pressure were measured for the systems 1-propanol–water–potassium acetate and 2-propanol–water–potassium acetate under fixed salt mole fractions using a modified Othmer recirculation still. A modified Furter equation, ln(α_s/α)=k₁z+k₂z², was proposed for correlating the effect of dissolved salts on vapor–liquid equilibrium (VLE). The modified equation contains two parameters that are applicable to the entire salt/solvent composition range. Correlation of VLE for 15 mixed-solvent electrolyte systems was made by means of the proposed modified equation with better results than those obtained from the original equation.     

Quantitative thermal analysis,VI. Initial conditions of the mathematical description of thermal curves (gradient theory)

The fundamental concept of the theory of thermal analysis developed in this paper involves the movement of the transformation front in the mass of the sample. Equations are developed for the motion of the transformation front (in the case of invariant processes) for the simplest model of the thermoanalytical cell. For a cylindrical sample, the equation is $$t = \sqrt {\frac{{Hd}}{{\lambda B}}\left( {\frac{{R^2 - r^2 }}{2} - r^2 \ln \frac{R}{r}} \right)} $$ whereR is the external radius of the sample,H the thermal effect of the transformation,B the heating rate,D the density,λ the thermal conductivity,r the position of the transformation front, andt time. The equation is experimentally confirmed by the finding that, as concluded from the equation, the height of the peak is directly proportional to the square root of the rate of sample heating.     

The shape,size and flow behaviors of micelle forming various synthetic tannin materials in aqueous solutions

The results of viscometric and optical microscopic studies indicated that both Syntan 25 and Syntan PUR in aqueous concentrated solutions (above their c.m.c. values) at 25 °C are spherical in shape. The size and other physico-chemical parameters e. g. Volumes of the aggregated particleM _v, Radius of gyrationR _g, Hydrodynamic radius ¯R _h, Diffusion coefficient ¯D, and the Correlation times for aggregate rotationT _r Translational diffusionT _D and effective aggregation timeT _a have been derived on the basis of microscopic results. The viscosity data for both Syntan 25 and Syntan PUR were analysed in terms of Einstein equation, Moulik equation, Jones-Dole equation. It has been shown that Syntan PUR was more highly hydrated than that of Syntan 25 although the intrinsic viscosity [η], of Syntan PUR is nearly 1.5 times greater than that of Syntan 25. The Flory-Huggins equation and Thomas equation has been compared in both the Syntans and it has been concluded that the Thomas' constantk ₁ may be 12.50 for perfect spherical shape of the particle instead of 10.05 (which has originally been proposed by Thomas).