Multiplex shear stress‐induced nucleation in dynamic microcellular foaming process

The effect of multiplex shear stress on the cell nucleation during microcellular foaming process was investigated using a dynamic foaming experimental apparatus. The multiplex oscillatory shear, which is different from previous one‐dimensional screw shear in a “stable” extrusion foaming process, is applied to the polymer melt through an axially vibrated rotor. The experimental results show that, by superimposing an axial vibration on the rotating rotor, the cell density increases and cell size decreases significantly when the shear rate is low. Both the uniformity of cell size and cell distribution are improved under vibration when compared with that without vibration regardless of how the shear rate changes. In addition, a simplified nucleation model based on shear energy has been carried out to qualitatively investigate the effect of both the simple steady shear and the multiplex oscillatory shear on the cell nucleation. Experiments and theoretical predictions all show that cell nucleation could be greatly improved by superimposing the oscillatory shear when the nucleation driving force induced by the steady shear is insufficient. Finally, the shear heat generated by excessive shear and strong vibration should be considered carefully although the isothermal condition was supposed in the present model. POLYM. ENG. SCI. 46:1728–1738, 2006. © 2006 Society of Plastics Engineers.     

The heterogeneous nucleation of microcellular foams assisted by the survival of microvoids in polymers containing low glass transition particles. Part I: Mathematical modeling and numerical simulation

The existing models based on classical nucleation theory are not able to explain satisfactorily the nucleation phenomenon of microcellular foams in thermoplastics. Here, we extend the analysis of Kweeder (24), who developed a new model that considers the presence of microvoids, resulting from the thermal processing history of the polymer, as potential nucleation sites. The nucleation model “concentrates” on the stresses and thus void formations in the rubber particles. Since these are pre-existing microvoids, bubble nucleation depends on the survival of these voids to grow rather than the formation of a new phase as modeled by classical nucleation theory. The population of viable microvoids with a sufficiently large radius to survive and overcome surface and elastic forces has been modeled to yield the cell density. A log-normal distribution, which relates to the rubber particle size, has been used to model the distribution of microvoids in the polymer composite material. The model depends on various process parameters such as saturation pressure, foaming temperature, concentration of nucleating agents, solubility of the blowing agent in the polymer, and the modulus. High impact polystyrene (HIPS) was added to polystyrene to obtain polymers with different concentrations of rubber gel particles, the nucleating agent, and used here for this study.     

剪切流场中微孔发泡的气泡成核理论研究现状

分析了经典成核理论对于动态聚合物熔体中气泡成核的局限性；概括了剪切流场中气泡成核的研究进展，并对剪切流场中泡核拉伸模型、空穴成核模型进行了详细的分析和讨论，指出了其对气泡成核过程解释的不足；介绍了最新的气泡成核中的剪切能成核理论，该理论较完善地解释了剪切流场中气泡成核过程；最后指出了气泡成核研究的发展方向。     

Interfacial stress in non-Newtonian flow through packed bed

This study investigates the pressure drop characteristics, shear stress in packed bed with shear thinning power law type non-Newtonian liquid. A mechanistic model has also been developed to analyze the pressure drop and interfacial stress in packed bed with non-Newtonian liquid by considering the loss of energy due to wettability. The Ergun's and Foscolo's equations were used for comparison with the experimental data. The Ergun equation was modified to account for the effect of flow behavior index of non-Newtonian fluid in the column. The intensity factor of shear stress and the friction factor were analyzed based on energy loss due to wettability effect of liquid on the solid surface.     

The heterogeneous nucleation of microcellular foams assisted by the survival of microvoids in polymers containing low glass transition particles. Part II: Experimental results and discussion

The experimental data obtained for the nucleation of microcellular foams are compared with the theoretical model developed in the first part of this paper. Polystyrene (PS) with rubber particles as nucleation sites is used as an exploratory system. Nitrogen is used as a physical blowing agent to nucleate the bubbles. The influence of process variables, such as saturation pressure, foaming temperature, and concentration and size of rubber particles, is discussed. Results indicate that all these variables play important roles during the nucleation process. A nucleation mechanism based on the survival of microvoids against the resisting surface and elastic forces has been modeled to obtain the cell nucleation density. Increase in saturation pressure increase the cell density to a critical pressure. Beyond this critical pressure, there is no increase in bubble number, indicating that all microvoids are activated. The effect of temperature is more complex than the effect of pressure. Increase in concentration of the rubber particles increase the nucleation cell density. In general, the experimental data are well described by the nucleation model presented in Part I.     

Numerical modeling of nonisothermal polymer crystallization kinetics: Flow and thermal effects

A numerical model able to simulate polymer crystallization under nonisothermal flows is developed. It is based on the assumption that the trace of the extra‐stress tensor, calculated according to a viscoelastic multimode Upper Convected Maxwell (UCM) model, is the driving force of the flow‐induced extra nucleation. Two distinct sets of Schneider equations are used to describe the growth of thermally and flow induced nuclei. The model is then coupled with the momentum equations and the energy equation. As an application, a shear flow configuration between two plates (Couette flow) is simulated. The relative influence of the mechanical and thermal phenomena on the crystallization development as well as the final morphology distribution is then analyzed as a function of the shearing intensity and the cooling kinetics, in terms of nucleation density and crystallite mean sizes. POLYM. ENG. SCI., 50:2044–2059, 2010. © 2010 Society of Plastics Engineers     

Crystal nucleation in sheared polymer melts

A semiquantitative procedure has been developed for analyzing crystal nucleation in undercooled polymer melts that are undergoing flow. This analysis was applied to the specific ease of molten high density polyethylene experiencing low levels of shearing flow. A custom-made concentric cylinder viscometer, which could be operated by the Rheometrics mechanical spectrometer instrument, was used to make simultaneous measurements of transmitted torque and optical anisotropy in isothermal melts, The result of the analytical procedure developed here was molecular Size-dependence of chain distensions caused by prevailing shear. This distribution function was verified by testing against experimentally obtained values of birefringence. Total entropy reduction resulting from this distorted state was then calculated, and the corresponding increase in free energy was found to be at least enough to account for comparable crystal nucleation rates in flowing melts at higher temperatures and in quiescent melts at lower temperatures.     

基于两相模型的聚合物流动诱导结晶数值模拟

基于两相流动诱导结晶模型,采用谱方法分别计算无定形相的构象张量分布函数和半晶相的取向张量分布函数,进而根据Avrami方程和晶核成核速率与第一法向应力差的关系计算成核速率和结晶度。预测剪切对体系结晶速度的影响,并模拟了活化晶核数目和晶体取向的演化。计算结果表明,剪切对聚合物的结晶动力学性能有显著的影响,但是剪切对聚合物结晶的加速作用不是无限制的,随着剪切强度的增加,对结晶加速作用会变得不再明显。     

泡沫塑料加工过程中的气泡成核理论(Ⅱ)——剪切能成核理论及其发展

介绍了剪切流场中泡沫塑料加工的气泡成核理论,分析评述了剪切流场中泡核拉伸模型、空穴成核模型对气泡成核机理的解释及存在的不足;对静态熔体中气泡成核过程进行了能量描述;介绍了最新的气泡成核中的剪切能成核理论,该理论较完善地解释了剪切流场中气泡成核过程;最后指出了气泡成核理论研究的发展方向。     

Influence of nanoparticle surface chemistry and size on supercritical carbon dioxide processed nanocomposite foam morphology

Creating polymer foams with controlled pore size and pore density is an important part of controlling foam properties. The addition of nanoparticles has been shown to cause heterogeneous nucleation and can be used to reduce pore size. In the current study, the effects of filler size and filler surface chemistry on pore nucleation in silica/PMMA nanocomposites are investigated. It was found that as the nanofiller size decreased, the pore density increased by a factor of 2-3 decades compared to that of unfilled PMMA (pore cell densities above 10¹² cells/cm³ were obtained). In addition, fluorination of the silica nanoparticle surface led to decreased pore size without changing the degree of silica aggregation and overall density. By monitoring the pore density as a function of pressure, a qualitative comparison was obtained that showed that fluorination of the nanoparticle reduced the critical free energy of nucleation.     

The nucleation of microcellular thermoplastic foam with additives: Part I: Theoretical considerations

Microcellular foam is a polymeric foam with bubble sizes of 10 microns or less that is produced by saturating a polymer with gas and then utilizing the thermodynamic instabilities that result when the polymer is heated and the pressure is reduced to nucleate the cells. A model for the nucleation of microcellular foam in amorphous polymers with additives has been developed. The nucleation process depends on the solubility, concentration, and interfacial energy of any additives present. At very low levels, additives in solution act to increase the free volume of the polymer, resulting in homogeneous nucleation within the free volume Well above the solubility limit, heterogeneous nucleation dominates, as it lowers the activation energy for nucleation to levels below that for homogeneous nucleation. In the vicinity of the solubility limit of the additive, these two nucleation mechanisms compete. The polystyrene-zinc stearate system has been chosen for experimental evaluation.     

Towards maximal cell density predictions for polymeric foams

Self-consistent field theory is used to make direct predictions for the maximum possible cell densities for model polymer foam systems without recourse to classical nucleation theory or activation barrier kinetic arguments. Maximum possible cell density predictions are also made subject to constraining the systems to have maximal possible internal interface and to have well formed bubbles (no deviation from bulk conditions on the interior of the bubble). This last condition is found to be the most restrictive on possible cell densities. Comparison is made with classical nucleation theory and it is found that the surface tension is not an important independent consideration for predicting conditions consistent with high cell density polymeric foams or achieving the smallest possible bubble sizes. Instead, the volume free energy density, often labelled as a pressure difference, is the dominant factor for both cell densities and cell sizes.     

Poly(ethylene terephthalate) nucleation as studied by shrinkage of film of low orientation level

Poly(ethylene terephthalate)s of weight average MW 74,000 and 30,000 have been uniaxially stretched, cooled under restraint, reheated, and shrunk unrestrained. Five stretch temperatures between 80 and 120°C and elongations up to 280 percent have been employed. Density and wide-angle X-ray diffraction results indicate conventional crystallization to have occurred only for the highly oriented samples, e.g., stretching above 200 percent at 90°C. The majority of stretching conditions studied produced only nucleated polymer. A sensitive, qualitative measure of nucleation is the degree of stretch imposed. Sufficiently high stretch temperature and low stretch rate lead to negligible nuclei formation. Nucleation in stretched, unshrunk films correlates with relatively high shrinkage, low orientation, low density and the absence of crystallinity until after the film has been shrunk. Crystallization on the other hand correlates with relatively high density, relatively low shrinkage and high orientation.     

A study of bubble nucleation in a mixture of molten polymer and volatile liquid in a shear flow field

Bubble nucleation in a mixture of volatile liquid and polymer melt under shear flow conditions was investigated, using a light scattering technique. In the study, a mixture of polystyrene and trichlorofluoromethane was extruded through a slit die having glass windows and bubble nucleation in the flow channel was observed optically. A He-Ne laser was used to illuminate the nucleating and growing bubbles. The light flux scattered by the growing bubbles at a fixed angle was detected by a photomultiplier with the aid of a high-voltage power supply. The bubble nucleating site in the flow channel was located using a computer controlled tracking system, which was designed to move the entire optical system automatically in the three dimensional space, and also had the ability to follow the software control command and cooperate with the data acquisition system. When the site of bubble nucleation was located, the coordinates of this site in the flow channel and the experimental conditions were automatically recorded on a floppy diskette by entering a software command. The pressure profile along the flow channel was measured by pressure transducers, with the aid of a microprocessor-based pressure reading system. It has been found that the site of bubble nucleation varies with the position in the direction perpendicular to the flow direction, which is attributed to the nonuniform velocity and stress distributions in the slit flow channel. The present investigation suggests that bubble nucleation can be induced either by flow and/or shear stress; specifically, flow-induced bubble nucleation is the dominant mechanism at positions near the center of the die opening, and shear-induced bubble nucleation is the dominant mechanism at positions near the die wall. It should be mentioned that the bubble near the die wall may also be generated by cavitation brought about by the surface roughness of the wall and also by thermal fluctuations due to the heat transfer between the metal (die wall) and the mixture of polymer and volatile component. The present study indicates that bubble nucleation in a shear flow field can occur at an unsaturated condition. This is in contrast to bubble nucleation under static conditions, where supersaturation is necessary.     

Nucleation of microcellular foam: Theory and practice

Microcellular polymer foams exhibit greatly improved mechanical properties as compared to standard foams due to the formers' small bubble size. Microcellular foams have bubbles with diameters on the order of 10 microns, volume reductions of 30 to 40 percent, and six or seven times the impact strength of solid parts. They are produced through the use of thermodynamic instabilities without the use of foaming agents. This method leads to a very uniform cell size throughout a part's cross section. A theoretical model for the nucleation of microcellular foams in thermoplastic polymers has been developed and experimentally confirmed. This model explains the effect of various additives and processing conditions on the number of bubbles nucleated. At levels of secondary constituents below their solubility limits, an increase in the concentration of the additive or the concentration of gas in solution with the polymer increases the number of bubbles nucleated. Nucleation in this region is homogeneous. Above the solubility limit of additives, nucleation is heterogeneous and takes place at the interface between second phase inclusions and the polymer. The number of bubbles nucleated is dependent on the concentration of heterogeneous nucleation sites and their relative effect on the activation energy barrier to nucleation. In the vicinity of the solubility limit, the two mechanisms compete.     

Studies of Micromechanical Deformation Processes in Particle-Filled Glassy Polymer

The deformation behavior of rubber-toughened polymer, which was prepared by incorporating soft, core-shell rubbery particles into a glassy polymer such as poly (methyl methacrylate) (PMMA), has been investigated by means of mechanical tests, optical monitoring (OM), and scanning electron microscopy (SEM). By mechanical testing, the neat PMMA reveals a 2% strain with high yield stress. After inclusion of 17.5 and 35 vol%rubber particles, the softened-PMMA samples exhibit corresponding strain of 20% and 38%, showing an increase of strain along with the relative decrease of yield stress, resulting in a toughening behavior of PMMA. Clear shear bands and stress whitening develop in the rubber-toughened PMMA after deformation, as observed by OM. Investigation by SEM shows crazes/cracks in the stretched, rubber-softened PMMA samples in which the core-shell particles are found to be cavitated. The mechanism of this deformation has been explained based on the void formation in the rubbery shell as well as the initiation and propagation of crazing.     

The effect of grafting density on the crystallization behavior of one-dimensional confined polymers

Grafting density and confinement scale of the nano-area are significant elements affecting the crystallization behavior of polymers. In this work, the crystallization processes of confined and unconfined polymer systems with different grafting density were systematically studied by MC simulation. The results show that when the grafting density of confined systems is low, the crystallization rate is faster and the final crystallinity is higher. However, the crystallization ability is reduced for higher grafting density. We found that for this confined system, the segmental density of interfacial region is larger, and the movement of chain segment is lower. Due to the higher grafting density, the crowding effect of polymer chains is strong, which leads to the intermolecular nucleation. The critical nucleation free energy barrier is higher. Moreover, only homogeneous nucleation occurs in confined polymer systems. With the increasing grafting density, the crystals change from lying on the substrate surface to being perpendicular to the substrate surface in unconfined polymer systems. The crystals are mainly lying on the substrate surface in confined polymer systems. These simulation results are helpful to understand the microscopic mechanism of crystallization behaviors of polymer nanocomposites and provide a theoretical basis for the design of nanocomposites with excellent physical properties.     

An atomic force microscopy study of the effect of surface roughness on the fracture energy of adhesively bonded aluminium

The effect of roughening an initially polished aluminium surface using the Forest Products Laboratory chemical etch on the adhesive joint strength has been determined. It was found that while the lap shear strength increased rapidly with etching for short times, the fracture energy did not increase significantly until etching had occurred for at least 15 min. An atomic force microscope (AFM) was used to study the surface/interface morphology and to quantify the surface roughness. The AFM images showed that etching occurs heterogeneously across the aluminium surface and a correlation was found between the fracture energy and the fraction of etched surface. A model based on Griffith's fracture energy approach has been proposed to explain this observation. The lap shear strength was found to be more sensitive to a finer scale roughness which is generated at shorter etching times. Other observations regarding the mode of fracture and the variability in joint strength as a function of the surface roughness are explained on the basis of varying stress concentrations at the crack tip.     

BOILING HEAT TRANSFER ON SURFACES WITH ARTIFICIAL NUCLEATION SITES (Ⅰ) EFFECT OF CAVITY SIZE, CAVITY DENSITY ON BUBBLE DEPARTURE DIAMETER AND FREQUENCY

By means of high-speed photography and optical-fiber probe, the effect of nucleation cavity size and cavity density on the bubble departure diameter and frequency has been investigated. The enhanced heating surface employed has artificial nucleation sites arranged regularly.Based on the analysis of the various forces exerted on the vapor bubble, a mathmatical model has been developed for correlating bubble departure diameter and frequency with the surface geometry and the degree of superheat.Experimental data has confirmed the availability of the model presented.     

Development of freeze flow apparatus to study filled polymer melts

A novel method to study the distribution of filler particles and polymer orientation of a polymer melt within a capillary die has been developed. Material within the die is quench‐cooled and then removed to provide information about the flow regime at the instant it was frozen. The equipment has been used to examine calcium carbonate‐filled high density polyethylene under high shear. The samples were examined using Energy Dispersive X‐ray Spectrometry (EDS) as well as being studied using X‐ray Diffraction (XRD). The distribution of filler particles across the radius of the capillary has been studied at high and low wall shear rates using EDS. A constant particle distribution across the radius of the die was observed for both flow regimes. The arrangement of crystalline structures within the specimens was examined by XRD. An increase in crystalline order was noticed with increasing wall shear rate. POLYM. ENG. SCI., 47:1937–1942, 2007. © 2007 Society of Plastics Engineers