A modified copolymerization equation for three-component systems

A modified copolymerization equation substantiated by experimental evidence has been proposed for tricomponent systems.     

Novel generalized rate equation for free radical copolymerization

A generalized copolymerization rate equation is proposed. The North equation of copolymerization is a special case that can be derived from the generalized equation. According to the mass balance and charge-transfer complex (CTC) equilibrium equation, the free monomer concentration is differentiated from the feed monomer concentration. The effects on the copolymerization rate (the equilibrium constant, total monomer concentration, homopropagation constants, and reactivity ratios) are quantitatively calculated and discussed. The generalized equation may be applied to not only the systems with the participation of CTC, such as styrene/N-phenylmaleimide (PMI), but also those without the participation of CTC, such as methyl methacrylate/PMI. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2635–2639, 1999     

一种新的蒸气压方程

提出了一种新的2参数蒸气压方程,并用12种饱和蒸气压实验数据比较完整的典型物质对新方程的外推性与W agner方程、项方程和吴方程进行了比较。结果表明:新方程在三相点方向的外推性具有明显的优势,总体平均偏差为1.05%,而W agner方程、项方程和吴方程的总体平均偏差分别为41.4%,5.20%和5.60%;在临界点方向的外推性略差于W agner方程,与项方程和吴方程相当。尝试仅用4个实验数据点拟合各方程,结果表明:新方程在三相点和临界点方向同时外推的精度明显优于其他方程。     

A new procedure to solve the non-linearreaction-diffusion equation

1 INTRODUCTIONThe concentration distribution of reactant in porouscatalyst pellet not only is the basis of calculating theeffectiveness factor,but also has a great significancein investigating the reaction and mass transfer in thecatalyst pellet.In principle,the concentration distri-bution and the effectiveness factor of a catalyst pelletcan be obtained by solving the reaction-diffusion equation.However,most of the differential equations haveno analytical solution except for some simple cases.The previous investigators have made great efforts to calculate the effectiveness factors of catalysts.They first obtained asymptotic solutions of effective-ness factor in the cases of the Thiele modulus φ→Oand φ→oo by means of perturbation method,thensynthesized the information of the asymptotic solu-     

A new vapor pressure equation for pure substances

A new simple equation for prediction of vapor pressure of pure substances is proposed. The equation which has the Clausius-Clapeyron (C-C) equation form consists of three parameters: critical temperature, critical pressure and normal boiling point. Experimental data for organic and inorganic substances have been used to calculate equation parameters in the boiling point ranges from 169.45 to 457.55 K and critical temperature ranges from 282.75 to 699.15 K. Comparison of proposed equation estimation results with experimental data shows that the new equation has minor average error. The new equation is also 68 percent more accurate than the C-C equation     

A new technique for precedence-ordering chemical process equation sets

An algorithm that combines structural equation analysis with algebraic rearrangement and substitution has been developed to precedence-order algebraic chemical process equations. The SWS (Structural Analysis with Substitutions) algorithm selects an output variable for each equation, rearranges the equation to solve for that variable, and reduces the number of equations by substitution. The algorithm has been used for computer generation of Fortran programs to perform meterial and energy balances in the design of chemical processes.     

A new four-parameter cubic equation of state for fluids

A simple cubic equation of state of the van der Waals type has been developed and successfully applied to both nonpolar and polar fluids. It contains four parameters and only one parameter is temperature-dependent. The parameters have been determined by using reliable data of vapour pressure and saturated liquid volume, and correlated in terms of critical properties and acentric factor. The P-V-T relationships, vapour pressures, volumes, and enthalpies of vapourization were calculated for a variety of substances. Comparison of the calculated results with experimental data and with results obtained from other equations shows that the proposed equation is a superior one in overall performance.     

A new cubic equation of state for fluids and fluid mixtures

A new cubic equation of state for pure fluids is presented in this work. The new equation requires the critical temperature and pressure, as well as two additional parameters to characterize each particular fluid. These parameters have been evaluated by minimizing deviations in saturated liquid densities while simultaneously satisfying the equality of fugacities along the saturation curve. Thus, good predictions of volumetric properties in the liquid region are obtained, while accuracy in vapour—liquid equilibrium calculations is maintained. Parameters for polar as well as nonpolar fluids are presented in this paper. In the case of nonpolar fluids, the two parameters required can be correlated with the acentric factor. No such relationship with independently measured quantities could be found for polar fluids. It is shown that the new equation reproduces many of the good features of the Soave and Peng—Robinson equations of state for nonpolar fluids, whilst overcoming some of the limitations of these equations for polar fluids. Applications of the equation of state to the correlation of phase equilibria are demonstrated.     

A novel free radical interfacial copolymerization

Summary Free radical interfacial copolymerization which is carried out by means of an amphiphilic bifunctional initiator as a novel polymerization method was proposed for the first time. For utilizing the new polymerization method, an amphiphilic bifunctional initiator, palmitoyl (3-carboxy propionyl) sebacoyl diperoxide (PSD), was synthesized and further used to initiate the free radical interfacial copolymerization of acrylamide (AM) with n-butyl methacrylate (n-BMA) which gave the amphiphilic PAM/PnBMA block copolymers. The resulting PAM/PnBMA block copolymers were purified by solvent extraction and characterized by elemental analysis, solubility, IR and DSC.This work was supported by National Natural Science Foundation of China     

The copolymerization of vinyl chloride with 1-olefins. I. A new method of investigation of the kinetics of homopolymerization and copolymerization of vinyl chloride

The indirect volumetric method following the amount of monomers in the heterogeneous liquid reaction mixture in a constant volume of samples periodically withdrawn by means of gas chromatography. This new method utilizes periodic sampling of the heterogeneous reaction mixture from the reactor during the reaction and gas chromatographic determination of the unreacted monomers contained in the sample. Its suitability and reliability were verified for the suspension homopolymerization of vinyl chloride. The reproducibility of sampling and the accuracy of determination of the degree of conversion and of the initial reaction rate were investigated. The conversion curves obtained by this method are compared with those obtained by the classical gravimetric method.     

San bulk copolymerization: Some new insights in kinetics and microstructure

A comprehensive study of the kinetics of the industrially important system of free radical bulk copolymerization of styrene and acrylonitrile, both at low and high conversions, is presented. The influence of gel effect on the kinetics, molecular weight distribution, cumulative composition distribution and the sequence length distribution of the SAN copolymer is examined. The study provides a fresh insight into the polymer structure and the influence of gel effect on the reactor behaviour.     

Synthesis of new imidazole-based monomer and copolymerization studies with methyl methacrylate

In this study, copolymers were synthesized using methyl methacrylate (MMA) and 2-allyloxymethyl-1-methylimidazole (AOMMI) monomers at various ratios. For this purpose, hydroxyl end-functionalized imidazole was initially prepared with 1-methylimidazole and then it was used to prepare allyl-derived imidazole monomers. Finally, the synthesis of copolymers (poly(MMA-co-AOMMI)) was carried out using different proportions of commercial MMA and AOMMI monomers. Photopolymerization method was preferred as polymerization technique. The polymerization was carried out in solvent-free medium and benzophenone was used as the initiator. Fourier transform infrared spectroscopy (FTIR), nuclear magnetic resonance spectroscopy (1H NMR and 13C NMR) and elemental analysis were used for the structural characterization of the obtained copolymers. Molecular weights and the thermal behaviour of the synthesized copolymers were analysed with gel permeation chromatography (GPC) and thermogravimetry (TG) techniques, respectively. The surface of the products was tried to be illuminated using scanning electron microscopy (SEM). According to the obtained FTIR, NMR and elemental analysis results, the copolymers were successfully synthesized. A number average molecular weights of poly(MMA-co-AOMMI) samples were found 13,500 (MMA:2/AOMMI:1), 16,600 (MMA:1/AOMMI:2) and 17,300 (MMA:1/AOMMI:1) according to the mixing ratios. When the thermal stabilities of the synthesized copolymers were observed, it has been seen that those containing imidazole had higher stability than the neat PMMA.     

A new homotopy for seeking all real roots of a nonlinear equation

A new continuation method, which applies a new homotopy that is a combination of the fixed-point and Newton homotopies (FPN), is developed for seeking all real solutions to a nonlinear equation, written as f(x) = 0, without having to specify a bounded interval. First, the equation to be solved is multiplied by (x − x⁰), where x⁰ is the starting value, which is set to zero unless the function does not exist at x⁰, in which case x⁰ becomes a tracking initiation point that can be set arbitrarily to any value where the function does exist. Next, the new function, (x − x⁰)f(x) = 0, is incorporated into the FPN homotopy. The initial step establishes a single bifurcation point from which all real roots can be found. The second step ensures a relatively simple continuation path that consists of just two branches that stem from the bifurcation point and prevents the formation of any isola. By tracking the two branches of the homotopy path, all real roots are located. Path tracking is carried out with MATLAB, using the continuation toolbox of CL_MATCONT, developed by Dhooge et al. (2006), based on the work of Dhooge, Govaerts, and Kuznetsov (2003), which applies Moore-Penrose predictor-corrector continuation to track the path, using convergence-dependent step-size control to negotiate turning points and other sharp changes in path curvature. This new method has been applied, without failure, to numerous nonlinear equations, including those with transcendental functions. As with other continuation methods, f(x)must have twice-continuous derivatives.     

A new equation of state (hsft) based on fractal theory

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.     

A new rheological constitutive equation for the network model of polymer melts

A new network model is suggested and a constitutive equation is developed on the basis of the assumed validity of Boltzmann's superposition principle for the shear stress. The predictions of the model concerning the relaxation behavior of polymer melts after steady shear or instantaneous deformation are compared to Lodge's theoretical results and to experimental data from the literature.     

A new semiempirical equation of state for fluids—I: Derivation

A semiempirical equation of state has been developed for non-polar and weakly polar fluid substances from the square well model of the inter-molecular     

A new splitting wavelet method for solving the general aerosol dynamics equation

In this paper, a new and robust splitting wavelet method has been developed to solve the general aerosol dynamics equation. The considered models are the nonlinear integro-partial differential equations on time, size and space, which describe different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. The proposed method reduces the complex general aerosol dynamic equation to two one-dimensional splitting equations in each time interval, and further the wavelet method and the upstream finite difference method are proposed for solving the particle size directional and the spatial directional splitting equations. By the method, the aerosol size spectrum is represented by a combination of Daubechies’ wavelets and substituted into the size-directional splitting equation at each time step. The class of Daubechies’ wavelets in the wavelet-Galerkin scheme as trial and weight functions has the advantages of both compact support and orthonormality which can efficiently simulate the sharp shape distribution of aerosols along the particle size direction. Numerical experiments are given to show the efficient performance of the method.