RHEOLOGICAL BEHAVIOR OF POLYMER MELTS (I) UNIFIED MOLECULAR THEORY OF NON-LINEAR ISCOELASTICITY WITH CONSTRAINTS OF GAUSSIAN CHAIN ENTANGLEMENT FOR POLYMER MELTS

An approach with statistical mechanics and a unified molecular theory of non-linearviscoelasticity with constraints of Gaussian chain entanglement for polymer melts were proposed.Amultimode model structure for a single polymer chain with tail segments and N reversibleentanglement sites on the test polymer chain was developed.The probability distribution function ofthe end-to-end vector for a single polymer chain at entangled state and the viscoelastic free energyof deformation for polymer melts were calculated.Four types of stress-strain relationship and mem-ory function were derived from this theory.The above theoretical relationships were verified by experi-mental data of PS(polystyrene)and LDPE(low density polyethylene)melts.     

AN EXPERIMENTAL STUDY OF HOLE PRESSURES FOR POLYMER MELTS

A slit die apparatus is used to measure hole pressures for two polymer melts.Hole pressures up to 110kPa are determined and shear rates reach 200 s~(-1).Viscosity data obtained from the same apparatus agreewell with the values obtained from a cone-and-plate rheometer or a capillary rheometer.The hole pressuresobtained by direct measurements are all positive and increase with increasing shear stress.The values of the firstnormal stress difference obtained from hole pressures according to the Higashitani-Pritchard(HP)theory are ofthe right order of magnitude,but appear to be on the low side when compared with values obtained from a cone-and-plate rheometer or with values obtained via exit pressures.It is believed that the hole pressure is a measureof fluid elasticity,but cannot yield accurate values of the first normal stress difference according to the HP theory.     

RHEOLOGICAL BEHAVIOR OF POLYMER MELTS (Ⅱ) MULTIPLE ENTANGLEMENT MODEL FOR PREDICTING THE DEPENDENCE OF VISCOELASTIC BEHAVIOR ON DEFORMATION STATE AND PRIMARY MOLECULAR WEIGHTS AND THEIR DISTRIBUTION

In accordance with the memory function of Gaussian chain constraints in entangled polymermelts a set of material functions related to a certain"test flow"are formulated from the O-W-Ftype constitutive equation by the appropriate selection of the Cauchy-Green and Finger tensors.Thedependences of these material functions on the strain rate and the dependences of the linearviscoelastic functions on the primary molecular weight distribution and the entanglement sites sequencedistribution on polymer chain are derived from a multiple-entanglement model and a couple of mech-anisms of relaxation for the loop and terminal entanglement sites.When the primary polymer chainsare modelled with the Lansing-Kraemer molecular distribution function,a set of new relationshipsamong linear viscoelastic functions(η_0,ψ_(10)~0,η_(ext)~0 and τ_1)and the molecular weights and their distributionare formulated.These functions and relationships are verified with experimental data.     

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS I.CLOSE-PACKED LATTICE MODEL

using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of mixing is based on the revised Freed model developed previously.Asize parameter c_r and an energy parameter ε are used;the former can be temperature dependent,while the latter can depend on both temperature and chain-length of the polymer.The discretemulticomponent approach is adopted to derive expressions for chemical potentials,spinodals and criti-cal points.The continuous distribution function is then used in calculations of moments occurring inthose expressions.Computation programs are established for cloud-point-curve,shadow-curve,spinodal and critical-point calculations for polymer solutions with standard distribution or arbitrarydistribution of polymer.In the latter case,the derivative method developed previously is applied.lllustrations for phase-equilibrium calculations are shown     

用活度系数模型和PCOR状态方程预测聚合物溶液中的亨利常数（英文）

In this paper, the polymer chain of rotator (PCOR) equation of state (EOS) was used together with an EOS/GE mixing rule (MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers. The results of the proposed method compared with two equation of state (van der Waals and GC-Flory) and three activity coefficient models (UNIFAC, UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results. The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR, a and b, were fitted with experimental volume data (Tait equation). As a result, the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.     

EQUATIONS OF STATE FOR HARD-SPHERE CHAIN FLUIDS AND SQUARE-WELL CHAIN FLUIDS

Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of the corresponding reference system,where n is the chain lengthor the number of segments of a chain molecule.The reference system is a fluid composed of only cor-responding monomers.In this work,the n-particle CCF is approximated by a product of effectivetwo-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighboursegment pairs.The CCFs for SWCFs may be expressed by a product of the corresponding functionfor HSCFs and a perturbation term originated from the square-well attractive potential.All these ef-fective two-particle CCFs and perturbation terms are density dependent.The dependence is determinedmainly by using computer-simulation results.The obtained equations can excellently describecompressibility factors and second Virial coefficients for HSCFs     

VAPOR-LIQUID EQUILIBRIA OF POLYMER SOLUTION USING UNIQUAC

The UNIQUAC excess Gibbs energy model of Abrams and Prausnitz(1975)is extended to represent thevapor-liquid equilibria of polymer solution with only two adjustable parameters.Discussions on the application ofthe Staverman-Guggenheim and the Flory-Huggins combinatorial contribution in the UNIQUAC model are givenin this paper.The UNIQUAC model with either Staverman-Guggenheim or Flory-Huggins combinatorial expres-sion presents results with about the same accuracy for polymer solutions.Comparisons between the UNIQUAC model and the Flory equation show that theUNIQUAC model can give some better results than the Flory equa-tion in general.     

STUDIES ON SYNTHESIS OF SILICA SOL-ORGANIC POLYMER COMPOSITE EMULSION

An emulsion of polystyrene/poly (butylacrylate-methyl methacrylate acrylic acid) core/shell latex particles (PS/P (BA-MMA-AA)) has been prepared by use of three synthetic methods. The effects of synthetic methods on the distribution of carboxyl groups in latex particles were studied. The results show that the seed emulsion polymerization in which the pre-emulsified monomers were added by dropping method to the second stage is the best technique for obtaining the optimum distribution of carboxyl groups on the surface of the latex particles. Furthermore, by using PS/P (BA-MMA-AA), a type of novel composite emulsion of silica sol-PS/P (BA-MMA-AA) was synthesized with the above method. By observation through transmission EM, the morphology of the latex particles obtained shows that a composite structure has been formed between silica sol particles and organic polymer particles.     

RHEOLOGICAL BEHAVIOR OF POLYMER MELTS (II) MULTIPLE ENTANGLEMENT MODEL FOR PREDICTING THE DEPENDENCE OF VISCOELASTIC BEHAVIOR ON DEFORMATION STATE AND PRIMARY MOLECULAR WEIGHTS AND THEIR DISTRIBUTION

In accordance with the memory function of Gaussian chain constraints in entangled polymermelts a set of material functions related to a certain"test flow"are formulated from the O-W-Ftype constitutive equation by the appropriate selection of the Cauchy-Green and Finger tensors.Thedependences of these material functions on the strain rate and the dependences of the linearviscoelastic functions on the primary molecular weight distribution and the entanglement sites sequencedistribution on polymer chain are derived from a multiple-entanglement model and a couple of mech-anisms of relaxation for the loop and terminal entanglement sites.When the primary polymer chainsare modelled with the Lansing-Kraemer molecular distribution function,a set of new relationshipsamong linear viscoelastic functions(η_0,ψ_(10)~0,η_(ext)~0 and τ_1)and the molecular weights and their distributionare formulated.These functions and relationships are verified with experimental data.     

SRK状态方程用于聚合物体系的汽液和气液平衡

A simple extension of cubic equations of state （EOS） to polymer systems has been proposed. The Soave-Redlich-Kwong （SRK） EOS was taken as a prototype to be used to describe the PVT behavior of polymer melts in a wide temperature and pressure range. Combined with a modified Huron-Vidal gE-mixing rule it was applied for modeling vapor-liquid equilibria of polymer-solvent solutions and the solubility of supercritical gases in polymer melts. Satisfactory results are obtained.     

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS II.LATTICE-FLUID MODEL

Using lattice-fluid model,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.A two-stepprocess is deslgned to form a real polymer solution containing a solvent and a polydisperse polymersolute occupying a volume at fixed temperature and pressure.In the first step,close-packed purecomponents including solvent and polymers with different molar masses or different chain lengths aremixed to form a closed-packed polymer solution.In the second step,the close-packed mixture,con-sidered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a vol-ume dependent on temperature and pressure.Revised Freed's model developed previously is adoptedfor both steps.Besides pure-component parameters,a binary size parameter c_r and a binary energyparameter ε_(12) are used.They are all temperature dependent.The discrete-multicomponent approach isadopted to derive expressions for chemical potentials,spinoda     

EFFECTS OF ENTRAINERS ON THE PHASE EQUILIBRIUM OF SUPERCRITICAL FLUID EXTRACTION PROCESS

A flow apparatus was set up for measuring the solubility of a solid solute in a supercritical fluid withthe presence of a small amount of entrainer.The solubilities of biphenyl,diphenylamine and benzoic acid insupercritical carbon dioxide with one of the selected entrainers which were ethanol,acetone and n-hexanerespectively,were obtained in the pressure range of 10—32 MPa and the temperature range of 308—318K.Asolvolytic association theory has been proposed to explain the mechanism of entrainer effect,and theexperimental results were reasonably analysed.According to the solvolytic association theory,the association equa-tion of state was adopted to correlate the experimental data with good accuracy.     

Prediction of the phase behavior of gas condensates using Patel-Teja equation of state and gamma distribution function

The three-parameter Petal-Teja equation of state coupled with a characterization proceduref0r C_(7 )-fraction based on gamma distribution function was employed to predict the phase behaviorof eight gas condensates.The lumping of the subdivided single carbon number(SCN)hydrocarbons inthe plus-fraction and the choice of empirical correlations for calculating the critical properties andacentric factor of SCN hydrocarbons were discussed.     

动态平衡系统累积时间分布函数及其在聚合物分子量分布中的应用

The lumped time distribution functions were proposed,which can be used for describing the dynamic systems with two or more than two states of the end of growing polymer chain during chain addition polymerization.Numerical analysis of the lumped time distribution functions was carried out.The method for calculating molecular weight distribution of polymer in the stable free radical polymerization and more general cases was developed based on the lumped time distribution functions.     

Analogy between adsorption and sorption:An elementary mechanistic approach.I.Monolayer adsorption and sorption without solvent cluster formation

The elementary mechanistic model of adsorption and sorption is based on a simple hypothesis:the adsorption sites are uniformly distributed on the surface of the pore walls in the adsorbent,the sorption sites are uniformly distributed in the volume of the polymer.In this first paper we will analyze the simple case where one solute mol-ecule is only allowed to occupy a single adsorption or sorption site.A common elementary occupation law of the free sites is assumed:the differential increase of the number of the adsorbed/sorbed molecules is proportional to the differential increase of the activity of the solute and the concentration of the free(non-occupied)sites in the solid.The proportionality coefficient is called affinity coefficient depending on the solid/solute couple and on the temperature and independent of the concentration of the solute.In adsorption the concentration of the free sites is a surface concentration on the pore walls and in sorption it is expressed by the molarity.The simple mono-layer adsorption law of Jovanovi?is obtained:n=n0(1?e?KP)where n is the number of moles adsorbed when the pressure is P. n0is the total number of adsorption sites and K the affinity coefficient for adsorption.The sorption law writes:a= 1k? ?1??]+1?rk ln?1+1r?1??]where?,r and k hold respectively for the volume fraction of the solvent in the polymer,for the ratio of the molar volumes of the solvent to the elementary polymer chain containing one single adsorption site and for the sorption affinity coefficient.The confrontation of these equations to experimental isotherms is satisfactory in comparison with the classical Langmuir and Flory-Huggins equations:the best results are obtained for adsorption of vapors on a 5A zeolite and for all analyzed sorption results.     

数值模拟黏弹流体通过椭圆环模具的挤出胀大

The numerical simulation of extrudate swell is significant in extrusion processing.Precise prediction of extrudate swell is propitious to the control of melt flow and the quality of final products.A mathematical model of three-dimensional(3D)viscoelastic flow through elliptical ring die for polymer extrusion was investigated.The penalty function formulation of viscoelastic incompressible fluid was introduced to the finite element model to analyze 3D extrusion problem.The discrete elastic viscous split stress(DEVSS)and streamline-upwind PetrovGalerkin(SUPG)technology were used to obtain stable simulation results.Free surface was updated by updating the streamlines which needs less memory space.According to numerical simulation results,the effect of zero-shear viscosity and elongation parameter on extrudate swell was slight,but with the increase of volumetric flow rate and relax time the extrudate swell ratio increased markedly.Finally,the numerical simulation of extrudate swell flow for low-density polyethylene(LDPE)melts was investigated and the results agreed well with others’work.These conclusions provided quantitative basis for the forecasting extrudate swell ratio and the controlling of extrusion productivity shape.     

GRAVITY SETTLING OF DISPERSED PHASE DROP SWARMS IN EXTRACTION COLUMNS IN ABSENCE OF MASS TRANSFER

Taking into account the effect of velocity profiles of the continuous phase in interstices of drops,dragcoefficient and relative motion correlations for dispersed liquid-liquid two-phase flow in absence of mass transferwere developed in terms of the pseudo-fluid concept based on the simple similarity criteria and the mixtureviscosity model suggested by Ishii and Zuber.The present model was compared with the experimental data fromfive(different sources and also with seven other pertinent correlations available in literature.Fairly goodpredictions were obtained under wide ranges of the dispersed phase holdup and Reynolds number.The validity ofthe present model has also been checked against the experimental slip velocity data and holdup data obtained ina Karr reciprocating plate extraction column by the author of the present paper and satisfactory agreement isachieved、The results show that the equations of the motion of a multi-droplet system can be formulated in aform identical with those for a single dr     

铈盐引发高吸附量氨基化PGMA高分子微球合成及去除废水中Cr(VI)(英文)

A novel polyglycidylmethacrylate(PGMA) microspheres with high adsorption capacity of Cr(VI) was prepared by cerium(IV) initiated graft polymerization of tentacle-type polymer chains with amino group on polymer microspheres with hydroxyl groups.The micron-sized PGMA microspheres were prepared by a dispersion polym-erization method and subsequently modified by ring-opening reaction to introduce functional hydroxyl groups.The polymer microspheres were characterized by scanning electron microscopy(SEM) and Fourier transform infrared spectroscopy(FTIR).The results indicated that the polymer microspheres had an average diameter of 5 μm with uniform size distribution.The free amino group content was determined to be 5.13 mmol?g?1 for g-PGMA-NH2 mi-crospheres by potentiometric and conductometric titration methods.The Cr(VI) adsorption results indicated that the graft polymerization of tentacle-type polymer chains on the polymer microspheres could produce adsorbents with high adsorption capacity(500 mg?g?1).The polymer microspheres with grafted tentacle polymer chains have poten-tial application in large-scale removal of Cr(VI) in aqueous solution.     

2-萘磺酸/硫酸在弱碱性树脂上的吸附平衡研究

Experiments for single and bisolute competitive adsorption were carried out to investigate the adsorption behavior of β-naphthalenesulfonic acid(NSA and sulfuric acid from their solution at 25℃ onto weakly basic resin D301R,Adsorption affinity of sulfuric acid on D301R was found to be much higher than that of NSA.The data of single-solute adsorption were fitted to the Langmuir model and the Freundlich adsorption model.The ideal adsorbed solution theory(IAST) coupled with the single-solute adsorption models were used to predict the bisolute competitive adsorption equilibria.The IAST coupled with the Langmuir and the Freundlich model for sulfuric acid and NSA.Respectively,yields the favorable representation of the bisolute competitive adsorption behavior.