Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusion: Correlations of Total and Ultimate Extrudate Swell Effects to Growth Time,Shear Stress and Aspect Ratio Under the Free States

The dynamic theory of die swell deduced in a previous paper was extensively applied to study the xtrudate swelling behaviors of two entangled polymeric liquids (HDPE and PBD) in a simple shear flow at steady shear stress. The mechanism and dynamics for the recoils and the recoveries of viscoelastic strains in the extrudate were investigated under the free recovery and dynamic states. It was found that in the course of recovery the free recoil and the growth of die swell in the extrudate may be divided into two recovery regions (instantaneous and delayed regions) and three growth stages (instantaneous, delayed, and ultimate extrudate swelling stages). The free recoil and the extrudate swelling behaviors may be expressed as a function of shear stress. The correlations of instantaneous, delayed, total and ultimate extrudate swell effects to the molecular parameters and the operational variables in the simple shear flow at steady shear stress were derived from the dynamic theory of die swell. Also, two sets of new universal equations on the total extrudate swelling effect (TESE) and ultimate extrudate swelling effect (UESE) were deduced. The first is the universal equation of the logarithmic correlation between the TESE and the growth time under the free and dynamic states; the second is the universal equation of the logarithmic correlation between the UESE and the operational variables under the free and equilibrium states. The first equation was verified by experimental data of PBD with different molecular weights at different operational variables. The second equation was verified by experimental data of HDPE at two temperatures and different operational variables. An excellent agreement result was obtained. The excellent agreement shows that the two universal equations can be used directly to predict the correlations of the TESE and UESE to the growth time, the molecular parameters, and the operational variables under the dynamic and equilibrium states.     

高分子熔体和浓溶液流变性能的研究

基于多重缠结网络结构模型和高分子链上缠结点在流动中可进行动态解缠和再缠结的多重蠕动机理,用统计力学和动力学相结合的方法,分别计算出了缠结链组的末端距分布函数;处于缠结状态下高分子链构象统计分布函数;受力下聚合物熔体粘弹性形变自由能和解除外力下高分子挤出体可回复性粘弹性形变自由能,提出了高分子挤出体可回复形变的粘弹性分子理论。推导出的高分子熔体的回忆函数、简单剪切流下的本构方程和物料函数,并采用一种新的方法测定出物料的四种参数： η0、 GN0、 n′和 a。对于高分子挤出体,可回复性粘弹性形变由快速弹性形变和慢速粘弹性形变两者组成,当把两种形变量的复合结构参数－分子链的反式构象分数引入两种形变自由能表达式后,就从理论上得到了可回复形变量同挤出胀大比间的定量表达式,从而建立起一个具有分子链结构参数的新的挤出胀大比方程,可回复形变量同挤出条件（温度、挤出速率和量以及口模长径比不同的挤出机）和树脂结构特征（分子量及分布）的关系式以及在特殊情形下的简化表达式,并用几种高分子熔融体系的挤出胀大比和可回复性形变量的实验数据对理论进行验证,理论方程同实验数据较好的符合。     

Melt extrudate swell behavior of graphene nano-platelets filled-polypropylene composites

The extrudate swell ratios of polypropylene (PP) composite melts filled with graphene nano-platelets (GNPs) were measured using a capillary rheometer within a temperature range of 180–230 °C and apparent shear rate varying from 100 to 4000 s⁻¹ in order to identify the effects of the filler content and test conditions on the melt die-swell behavior. It was found that the values of the extrudate swell ratio of the composites increased with increasing apparent shear rate, with the correlation between them obeying a power law relationship, while the values of the extrudate swell ratio decreased almost linearly with rise in temperature. The values of the melt extrudate swell ratio increased approximately linearly with increasing shear stress, and decreased roughly linearly with an increase of the GNP weight fraction. In addition, the extrudate swell mechanisms are discussed from the observation of the fracture surface of the extrudate using scanning electronic microscopy. This study provides a basis for further development of graphene reinforced polymer composites with desirable mechanical performance and good damage resistance.     

Extrudate swell and flow analysis of polystyrene melt flowing in an electro‐magnetized die in a single screw extruder

An electro‐magnetized capillary die via a parallel co‐extrusion technique was used to study the changes in the overall and radial extrudate swell ratio of polystyrene (PS) melt flowing in a single screw extruder. The effects of magnetic flux density, wall shear rate (screw rotating speed) and die temperature were studied. The results suggested that, in the case of non‐magnetic die the average overall swell ratio of the melt ranged from 1.25 to 1.55. The swelling ratio increased with increasing wall shear rate up to 8.5 sec^?1 and then decreased at 17.1 sec^?1. Increasing die temperature caused a reduction of extrudate swell ratio. The changes in extrudate swell ratio can be explained using the simultaneously measured velocity profiles during the flow in the die, and the swell ratio decreased with increasing radial position. Melt contraction of the melt layer near the die wall was observed. The die temperature was found to have no effect on the change of the radial extrudate swell profiles. When an electro‐magnetized die was used, the average overall swell ratio was found to increase with increasing magnetic flux density to a maximum value and then decreased at higher flux densities. The magnetic flux density of the maximum swell was changed by the wall shear rate. It was associated with a balance of elastic and magnetic energies during the flow. The magnetic energy was thought to have a pronounced effect on the swell ratio at low shear rate and low die temperature. Considering the radial position, the highest swell ratio occurred at the duct center, in the range 2.4–3.3. There was no extrudate contraction of the melt layer near the die wall. Copyright © 2005 John Wiley & Sons, Ltd.     

Extrudate swell behavior of PS and LLDPE melts in a dual die with mixed circular/slit flow channels in an extrusion rheometer

Extrudate swell behaviors of polystyrene (PS) and linear low‐density polyethylene (LLDPE) melts in a dual channel die, having mixed circular/slit flow channels, in a constant shear rate rheometer were examined. The extrudate swell ratio for PS melt was observed to be higher than that for LLDPE melt for all cases, this being associated with the differences in molecular structures that could be described in terms of power law indexes and secondary flows near the die entrance. In single channel die, the extrudate swell of both PS and LLDPE melts in circular flow channel die was greater than that in slit flow channel, whereas, in dual channel die the slit channel exhibited a higher extrudate swell ratio, the results being explained by revealing the flow patterns of the melt in the barrel and die of the rheometer. It was found that the dimensionless size of the vortex flows near the entrance, and the extent of disentanglement of molecular chains on entering the die were the important factors for the differences in the extrudate swell ratios of the melts at the die exit influenced by the die designs used. Copyright © 2003 John Wiley & Sons, Ltd.     

聚合物熔体挤出胀大的三维数值模拟

采用粘弹性PTT模型对聚合物熔体的矩形口模挤出胀大进行了三维等温数值模拟,得出了不同条件下的口模外流动速度和挤出胀大率沿挤出方向的分布规律.模拟时利用罚函数有限元法和把动量方程转化成椭圆类方程的去耦算法以降低模拟对计算机内存的要求和增加计算收敛的稳定性,采用用路线法对挤出胀大自由表面进行更新迭代.模拟结果表明:We数越大,则挤出胀大率越大,而且对于矩形口模挤出而言,高度方向的挤出胀大率比宽度方向的挤出胀大率大.     

Flow behaviour of gas-containing LDPE/i-PP melts

An experimental study was conducted to investigate the rheological behaviour and extrudate swell of polyolefin blends based on two grades of low-density polyethylene (LDPE) and an isotactic polypropylene (i-PP). Blending was carried out on a twin-screw extruder “Brabender” at different composition ratios in the temperature range from 140 to 190°C. The LDPE/i-PP blends mixed with 0.5 wt.% blowing agent were extruded by means of “Brabender” extrusiograph at melt temperature of 200°C and different extrusion rates. The influence of composition content on the viscosity and extrudate swell was considered. The foam structure and morphology are discussed in terms of shear rate, molecular characteristics and composition content. The presence of layered structure was observed: an outer smectic layer and an inner partially crystalline layer. The thickness of smectic layer and size of spherulites were determined.     

Melt rheology and morphology of thermoplastic elastomers from polyethylene/nitrile‐rubber blends: The effect of blend ratio,reactive compatibilization,and dynamic vulcanization

A study of the melt‐rheological behavior of thermoplastic elastomers from high‐density polyethylene and acrylonitrile butadiene rubber (NBR) blends was carried out in a capillary rheometer. The effect of the blend ratio and shear rate on the melt viscosity reveals that the viscosity decreases with the shear rate but increases with NBR content. Compatibilization by maleic anhydride modified polyethylene has no significant effect on the blend viscosity, but a finer dispersion of the rubber is obtained, as is evident from scanning electron micrographs. The melt‐elasticity parameters, such as the die swell, principal normal stress difference, recoverable shear strain, and elastic shear modulus of the blends, were also evaluated. The effect of annealing on the morphology of the extrudate reveals that annealing in the extruder barrel results in the coalescence of rubber particles in the case of the incompatible blends, whereas the tendency toward agglomeration is somewhat suppressed in the compatibilized blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1104–1122, 2000     

经不同程度降解聚丙烯的熔体流变性质

<正> 聚丙烯(PP)的热降解和化学控制降解法七十年代开始应用于聚合物工业加工过程。聚丙烯在高温下热降解,一般认为服从无规断链机理。随降解过程进行,分子量变小,分子量分布变窄,由定向聚合反应产生的特征性高分子量尾端降解最为显著。该过程往往可显著改善PP熔体加工性,因此研究降解过程对PP熔体流变性质的影响殊属     

The ability to control swelling and degradation processes of hydrogels based on a mixture of PEGMA/PEGDA monomers

The ability of hydrogels based on acrylate derivatives of polyethylene glycol (PEG) with different ratios of monomers to swell and degrade, as well as their behavior during heating, have been explored. The possibility to control the swelling and degradation processes in the model medium by varying the ratio of PEG-methacrylate (PEGMA) and PEG-diacrylate (PEGDA) monomers was demonstrated.     

Evaluation of Calculating the Isotonic Swelling Ratio of Emulsion Liquid Membrane by Theoretical Viscosity Models

In this study, two viscous models, the Choi‐Schwalter and Phan‐Thien‐Pham models, are used to calculate the isotonic swelling ratio of emulsion liquid membrane. The purpose is to evaluate the usefulness of calculating isotonic swelling ratios of emulsion liquid membranes by viscous models through comparing theoretical isotonic swelling ratios with experimental swelling ratios of three kinds of emulsion liquid membranes. Comparison between theoretical swelling ratios and experimental swelling ratios indicates that experimental swelling ratios are close to those calculated by the Choi‐Schwalter model, but lower than those calculated by the Phan‐Thien‐Pham viscous model. But modified Phan‐Thien‐Pham viscous models predicts reasonable values. Therefore, the method of calculating the isotonic swelling ratio of emulsion liquid membrane by theoretical viscosity models is promising.     

Osmotic ensemble methods for predicting adsorption-induced structural transitions in nanoporous materials using molecular simulations

Osmotic framework adsorbed solution theory is a useful molecular simulation method to predict the evolution of structural transitions upon adsorption of guest molecules in flexible nanoporous solids. One challenge with previous uses of this approach has been the estimation of free energy differences between the solid phases of interest in the absence of adsorbed molecules. Here we demonstrate that these free energy differences can be calculated without reference to experimental data via the vibrational density of states of each phase, a quantity that can be obtained from molecular dynamics simulations. We show the applicability of this method through case studies of the swelling behaviors of two representative systems in which swelling upon adsorption of water is of importance: single-walled aluminosilicate nanotube bundles and cesium montmorillonite. The resulting predictions show that the aluminosilicate nanotube bundles swell significantly with increasing interstitial adsorption and that the layer spacing of cesium montmorillonite expands up to about 12.5 A?, giving good agreement with experiments. The method is applicable to a wide range of flexible nanoporous materials, such as zeolites, metal-organic frameworks, and layered oxide materials, when candidate structures can be defined and a force field to describe the material is available.     

Rheological characterization of the die swell phenomenon of rubber compounds

The die swell phenomenon of rubber compounds in capillary experiments with various ratios of length to diameter of capillaries is investigated. This knowledge is important for the design of injection heads for the extrusion of rubber profiles. The die swell of viscoelastic rubber compounds depends on the geometry of the capillary dies, on the melt temperature and on the shear strain rate. One empirical relationship will consider all these dependencies. Usage of this equation and identification of only one new material parameter enables the comparison and assessment of the die swell of different materials, independently of the corresponding geometry of the capillary die used. Furthermore, the influence of melt temperature, molecular structure and extrusion process on the die swell can be identified. The investigation was performed with various rubber compounds as well as rubber blends used in industry, mainly EPDM and carbon black in different compositions.     

粒径及加热速率对烟煤膨胀特性的影响

将不同粒径烟煤在实验室沉降炉中进行了不同加热速率下的热解实验，研究了煤粉粒径及其加热速率对煤粒膨胀特性的影响。实验结果表明，煤粒在热解过程中发生了明显的膨胀，形成了具有中空结构的煤胞型焦炭，这是煤中较高镜质组体积分数造成的。在相同加热速率下，随粒径减小煤粉颗粒膨胀越剧烈，随粒径增大煤粒膨胀程度之间的差异有减小的趋势。煤样不同膨胀特性是镜质组体积分数不同的结果。镜质组体积分数越高，在热解过程中更容易软化、变形，发生剧烈膨胀。当加热速率从0.5×104K/s升高到4×104K/s时，煤样膨胀程度先增加后减小，表明在0.5×104K/s～4×104K/s，存在一个最佳的加热速率，此时煤粒膨胀程度最高。     

Greffage radiochimique de l'acide methacrylique sur des films de polytetrafluoroethylene

Methacrylic acid was grafted into the bulk of PTFE films 50 μm thick by irradiating the films in aqueous solutions of monomer containing CuCl₂. The influences of radiation dose-rate and of temperature were investigated. The swelling of the grafted films was studied in the following solvents for the grafted branches: water, methanol, DMF and their mixtures. In each case the molar ratios corresponding to the limiting swelling were determined. It was further found that the grafted films swell in carboxylic acids such as methacrylic, acrylic and acetic acids, which are non-solvents for the grafted branches. This swelling is much slower than the swelling in good solvents. It is suggested that it results from a molecular association of the carboxyl groups of the solvent with those of the polymer.     

Comparison of the Aifrey-Price Q-e Scheme and a Simple Molecular Orbital Treatment of Copolymerization

A simple Huckel treatment of the transition states for the monomer-radical reactions in free radical copolymerization is developed. The resulting equations for the reactivity ratios are compared with those from the Q-e treatment of Alfrey and Price. It is concluded that the Q-e scheme can be regarded as a version of a molecular orbital approach.     

Shear thinning and shear dilatancy of liquid n-hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects

Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal (NVT) and isobaric-isothermal (NPT) ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid n-hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates (gamma) affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of gamma<1 x 10(11) s(-1), the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of gamma>1 x 10(11) s(-1), specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flow activation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.     

Phenomenological transient shear behavior of liquid crystalline polymers after the start-up of shear flow

Transient stresses of liquid crystalline polymers appear as damped oscillatory patterns after the start-up of shear flow. They are examined by using the constitutive equations which were modified to include the idea of an initial domain state in the Larson-Doi polydomain equation set. In order to be consistent with the phenomenological transient shear stress after the start-up in the region of low shear rates, the Hinch-Leal closure approximations were adopted for the domain-averaged (mesoscopic) fourth-order tensors of the director field. It is predicted as an important result that the amplitude of the first overshoot in the transient stress increases with an increase in the shear rate imposed at the start-up, which was found to be largely in agreement with phenomenology. In addition, the effects of parameters such as molecular concentration, initial domain size, and intensities of viscous and elastic contributions on the transient stress under the start-up process were also evaluated.     

Novel cationic pH-responsive poly(N,N-dimethylaminoethyl methacrylate) microcapsules prepared by a microfluidic technique

Novel monodisperse cationic pH-responsive microcapsules are successfully prepared using oil-in-water-in-oil double emulsions as templates by a microfluidic technique in this study. With the use of a double photo-initiation system and the adjustment of pH value of the monomer solution, cross-linked poly(N,N-dimethylaminoethyl methacrylate) (PDM) microcapsules with good sphericity and monodispersity can be effectively fabricated. The obtained microcapsule membranes swell at low pH due to the protonation of N(CH(3))(2) groups in the cross-linked PDM networks. The effects of various preparation parameters, such as pH of the aqueous monomer fluid, concentration of cross-linker, concentration of monomer N,N-dimethylaminoethyl methacrylate (DM) and addition of copolymeric monomer acrylamide (AAm), on the pH-responsive swelling characteristics of PDM microcapsules are systematically studied. The results show that, when the PDM microcapsules are prepared at high pH and with low cross-linking density and low DM monomer concentration, they exhibit high pH-responsive swelling ratios. The addition of AAm in the preparation decreases the swelling ratios of PDM microcapsules. The external temperature has hardly any influence on the swelling ratios of PDM microcapsules when the external pH is less than 7.4. The prepared PDM microcapsules with both biocompatibility and cationic pH-responsive properties are of great potential as drug delivery carriers for tumor therapy. Moreover, the fabrication methodology and results in this study provide valuable guidance for preparation of core-shell microcapsules via free radical polymerization based on synergistic effects of interfacial initiation and initiation in a confined space.     

Optical vs. direct sorption and swelling measurements for the study of stiff-chain polymer-penetrant interactions

This work involves interferometric ‘optical thickness’ and refractive index measurements performed in an optical thickness meter (OTM), on supported cellulose acetate (CA) films equilibrated with various activities of methylene chloride (MC) vapor. The relevant equilibrium sorption and volume swelling isotherms were determined by application of the Claussius-Mossotti equation on the assumption that these films swell unidimensionally along the thickness direction, and were compared with corresponding direct equilibrium sorption (weight gain), elongation and thickness dilation measurements on similar free films performed in a vacuum sorption/swelling apparatus (VSA) and complemented with refractive index data. Combined elongation and thickness dilation data from the VSA showed that free glass-cast CA films exhibit pronounced swelling anisotropy. The said anisotropy, although it cannot be completely eliminated, by conditioning at high degrees of swelling, does not appear to affect the extent of volume swelling significantly, thus permitting quantitative comparison of sorption and swelling isotherms determined by the VSA and the OTM. Such comparison showed satisfactory agreement between these two sets of results up to an MC uptake of ca. 0.4 gMC/cm³ of dry CA corresponding to a degree of swelling of ca. 0.2. Increasing discrepancies are observed at higher MC concentrations, which are attributable to breakdown of the assumption used that the supported films swell unidimensionally along the thickness direction. The present CA-MC volume swelling data exhibit the negative deviation from volume additivity on mixing typical glassy polymers.