Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process

A simulation of simultaneous bubble nucleation and growth was performed for a batch physical foaming process of polypropylene (PP)/CO₂ system under finite pressure release rate. In the batch physical foaming process, CO₂ gas is dissolved in a polymer matrix under pressure. Then, the dissolved CO₂ in the polymer matrix becomes supersaturated when the pressure is released. A certain degree of supersaturation produces CO₂ bubbles in the polymer matrix. Bubbles are expanded by diffusion of the dissolved CO₂ into the bubbles. The pressure release rate is one of the control factors determining number density of bubbles and bubble growth rate.To study the effect of pressure release rate on foaming, this paper developed a simple kinetic model for the creation and expansion of bubbles based on the model of Flumerfelt's group, established in 1996 [Shafi, M.A., Lee, J.G., Flumerfelt, R.W., 1996. Prediction of cellular structure in free expansion polymer foam processing. Polymer Engineering and Science 36, 1950-1959]. It was revised according to the kinetic experimental data on the creation and expansion of bubbles under a finite pressure release rate. The model involved a bubble nucleation rate equation for bubble creation and a set of bubble growth rate equations for bubble expansion. The calculated results of the number density of bubbles and bubble growth rate agreed well with experimental results. The number density of bubbles increased with an increase in the pressure release rate. Simulation results indicated that the maximum bubble nucleation rate is determined by the balance between the pressure release rate and the consumption rate of the physical foaming agent by the growing bubbles. The bubble growth rate also increased with an increase in the pressure release rate. Viscosity-controlled and diffusion-controlled periods exist between the bubble nucleation and coalescence periods.     

Visual observation and numerical studies of N2 vs. CO2 foaming behavior in core‐back foam injection molding

We investigated , by visual observation and numerical calculations , the foaming behavior of polypropylene within a foam injection mold cavity with the environmentally benign physical blowing agents nitrogen (N₂) and carbon dioxide (CO₂) . An 85‐ton core‐back injection‐molding machine with temperature and pressure monitoring systems as well as a high‐pressure view cell was used for the investigation . The experiments showed a prominent difference in bubble nucleation and growth between N₂ and CO₂ injection foaming . Even when the weight concentration of N₂ dissolved in polymer was one‐third that of CO₂ , N₂ injection foaming provided a bubble number density that was 30 times larger and a bubble size that was one‐third smaller compared to CO₂ injection foaming . Classical bubble nucleation and growth models developed for batch foaming were employed to analyze these experimental results . The models reasonably explained the differences in injection foaming behavior between N₂ and CO₂ . It was clearly demonstrated by both experiments and numerical calculations that N₂ provides a higher number of bubbles with a smaller bubble size in foam injection molding compared to CO₂ as a result of the lower solubility of N₂ in the polymer and the larger degree of super‐saturation . POLYM. ENG. SCI., 2011. ©2011 Society of Plastics Engineers     

Plasticization effects on bubble growth during polymer foaming

During polymer foaming with physical blowing agents, plasticization affects the melt viscosity, gas diffusivity in the melt, and the gas–melt interfacial tension. In this paper, we propose a model for plasticization during bubble growth, and estimate its effects under typical foaming conditions. The theoretical model incorporates well‐established mixture theories into a recent model for diffusion‐induced bubble growth. These include the free‐volume theories for the viscosity and diffusivity in polymer‐blowing agent mixtures and the density gradient theory for the interfacial tension. The viscoelasticity of the melt is represented by an Oldroyd‐B constitutive equation. We study the radial growth of a single bubble in an infinite expanse of melt, using parameter values based on experiments on polystyrene–CO₂ systems. Our results show that even at relatively low gas concentrations, plasticization increases the blowing‐agent diffusivity markedly and thus boosts the rate of bubble growth. In contrast, the reduction in melt viscosity and interfacial tension has little effect on bubble growth. Though not intended as quantitative guidelines for process design, these results are expected to apply qualitatively to typical foaming conditions and common polymer‐blowing agent combinations. POLYM. ENG. SCI., 46:97–107, 2006. © 2005 Society of Plastics Engineers     

Modeling nanoporosity development in polymer films for low‐k applications

The bubble growth dynamics of a polymer supersaturated with CO₂ have been modeled for micron‐size films after nucleation. The model equations are based on the shell model of Arefmanesh, Advani, and Michaelides in which a nucleated bubble is surrounded by a finite concentric shell of polymer supersaturated with gas. Bubbles grow by mass transfer of dissolved gas from this shell. The model is extended to allow for diffusion of dissolved gas out of the shell in addition to diffusion into the bubble. A parametric analysis is performed to examine the effects of film thickness, temperature, diffusivity at the T_g and Henry's law constant. POLYM. ENG. SCI., 45:640–651, 2005. © 2005 Society of Plastics Engineers     

Polymer foaming with chemical blowing agents: Experiment and modeling

An experimental and theoretical analysis of the polypropylene foaming process using three different chemical blowing agents (CBA) was performed. A simple experiment was designed to analyze the foaming process of polypropylene (PP)/CO₂ system under two different pressure conditions. The expansion ratio and final foam structure was measured both by direct observation and from optical measurements and image analysis, showing a good agreement. A single bubble simulation based on relevant differential scanning calorimetry and thermo‐gravimetrical analysis experiments, assuming each CBA particles as a nucleation site and accounting for gas diffusion in the surrounding polymer matrix has been built. The sensitivity of the model to physical and processing parameters has been tested. The calculation results are compared to the experiments and open the route to a simplified method for evaluating the efficiency of CBA. POLYM. ENG. SCI., 55:2018–2029, 2015. © 2014 Society of Plastics Engineers     

Experimental and numerical studies on bubble dynamics in nonpressurized foaming systems

This work explores the influence of rheological properties on polymer foam development in nonpressurized systems. To understand the complex contributions of rheology on the mechanism of bubble growth during different stages of foam processing, visualization studies were conducted by using a polymer‐foaming microscopy setup. The evolving cellular structure during foaming was analyzed for its bubble surface density, bubble size, total bubble projected area, and bubble size distribution. Morphological analysis was used to determine the rheological processing window in terms of shear viscosity, elastic modulus, melt strength and strain‐hardening, intended for the production of foams with greater foam expansion, increased bubble density and reduced bubble size. A bubble growth model and simulation scheme was also developed to describe the bubble growth phenomena that occurred in nonpressurized foaming systems. Using thermophysical and rheological properties of polymer/gas mixtures, the growth profiles for bubbles were predicted and compared to experimentally observed data. It was verified that the viscous bubble growth model was capable of depicting the growth behaviors of bubbles under various processing conditions. Furthermore, the effects of thermophysical and rheological parameters on the bubble growth dynamics were demonstrated by a series of sensitivity studies. POLYM. ENG. SCI., 54:1947–1959, 2014. © 2013 Society of Plastics Engineers     

Numerical simulation of polymer foaming process in extrusion flow

Computer simulations of polymer foaming processes in extrusion flow have been carried out in order to improve current understanding of viscoelasticity and bubble growth effects on die-swelling in the production of polymer foam. The linear and non-linear viscoelastic materials functions of a commercial low density polyethylene (LDPE) melt have been extracted by fitting its rheometric data with constitutive models including a simple viscoelastic model (SVM), the exponential Phan-Thien–Tanner (EPTT) model and the double convected pom–pom (DCPP) model. Simulations of LDPE melt under extrusion flow without foaming show that the predictions of the die-swell by the SVM are in reasonably good agreement with the results obtained from the EPTT and DCPP models. By comparison of the simulation results of LDPE foaming in extrusion flow using the Bird–Carreau model and the SVM, a cooperative effect of polymer viscoelasticity and bubble growth on the die-swell has been quantified. The numerical results also show that the density of polymeric foam decreases significantly with the increasing concentration of foaming agent, and that the combination of the SVM and bubble growth model can account for some essential physics of polymer foaming process in extrusion flow.     

Polypropylene‐dispersed domain as potential nucleating agent in PS and PMMA solid‐state foaming

The potential of using dispersive domains in a polymer blend as a bubble nucleating agent was investigated by exploiting its high dispersibility in a matrix polymer in the molten state and its immiscibility in the solid state. In this experiments, polypropylene (PP) was used as the nucleating agent in polystyrene (PS) and poly(methyl methacrylate) (PMMA) foams at the weight fraction of 10, 20, and 30 wt %. PP creates highly dispersed domains in PS and PMMA matrices during the extrusion processing. The high diffusivity of the physical foaming agent, i.e., CO₂ in PP, and the high interfacial tension of PP with PS and PMMA could be beneficial for providing preferential bubble nucleation sites. The experimental results of the pressure quench solid‐state foaming of PS/PP and PMMA/PP blends verified that the dispersed PP could successfully increase the cell density over 10⁶ cells/cm³ for PS/PP and 10⁷ cells/cm³ for PMMA/PP blend and reduce the cell size to 24 μm for PS/PP and 9 μm for PMMA/PP blends foams. The higher interfacial tension between PP and the matrix polymer created a unique cell morphology where dispersed PP particles were trapped inside cells in the foam. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

On‐line NIR sensing of CO2 concentration for polymer extrusion foaming processes

An on‐line sensor using near infrared (NIR) spectroscopy is developed for monitoring CO₂ concentration in polymeric extrusion foaming processes. NIR absorption spectra are acquired by a probe installed at the foaming extruder die. The calibration curve relating the absorbance spectrum at 2019 nm to the dissolved gas concentration is derived so as to infer dissolved CO₂ gas concentration on‐line from measured NIR spectra. Experimental results show the developed on‐line NIR sensor can successfully estimate dissolved CO₂ concentration in the molten polymer and illustrate that the developed NIR sensing technique is among the more promising methods for quality control of polymeric extrusion foaming processes.     

Foaming behavior of high‐melt strength polypropylene/clay nanocomposites

The foaming behavior of high‐melt strength polypropylene (HMS‐PP) and HMS‐PP/Cloisite 20A nanocomposites (PPNC) was studied in a batch process. PPNCs with 2, 4, 8, and 10 wt% clay were prepared in a twin screw extruder. The morphology of the nanocomposites was studied using XRD and TEM. Subsequently, foaming experiments were conducted using supercritical CO₂ as the blowing agent in a batch process, and foams with cell sizes varying from the sub micrometer to the micro meter range were prepared. The effect of variation in saturation pressure and temperature, foaming temperature, foaming time, and quench temperature was determined experimentally. Dynamic rheological measurements were conducted to relate the influence of nanocomposites morphology with foam cell growth and nucleation. Extensional rheological measurements were also conducted to detect the presence of strain hardening effect at the foaming temperatures used in the experiment. It was found that the nucleation efficiency of clay reduces with increase in clay loading. Also, the optimum amount of filler for generation of fine celled foams was found to be around the percolation threshold of the polymer. The extended strain hardening effect shown by the polymer in presence of clay plays an important role in stabilizing foam cell sizes. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

CO2 foaming of poly(ethylene glycol)/polystyrene blends: Relationship of the blend morphology,CO2 mass transfer,and cellular structure

When polymer blends are foamed by physical foaming agents, such as CO₂ or N₂, not only the morphology and viscosity of the blend polymers but also the solubility and diffusivity of the physical foaming agents in the polymers determine the cellular structure: closed cell or open cell and monomodal or bimodal. The foam of poly(ethylene glycol) (PEG)/polystyrene (PS) blends shows a unique bimodal (large and small) cellular structure, in which the large‐size cells embrace a PEG particle. Depending on the foaming condition, the average size of the large cells ranges from 40 to 500 μm, whereas that of small cells becomes less than 20 μm, which is smaller than that of neat PS foams. The formation mechanism of the cellular structure has been investigated from the viewpoint of the morphology and viscosity of the blend polymer and the mass‐transfer rate of the physical foaming agent in each polymer phase. The solubility and diffusivity of CO₂, which determine the mass‐transfer rate of CO₂ from the matrix to the bubbles, were measured by a gravimetric measurement, that is, a magnetic suspension balance. The solubility and diffusivity of CO₂ in PS differed from those in PEG: the diffusion coefficient of CO₂ in PEG at 110°C was 3.36 × 10^?9 m²/s, and that in PS was 2.38 × 10^?10 m²/s. Henry's constant in PEG was 5600 cm³ (STP)/(kg MPa) at 110°C, and that in PS was 3100 cm³ (STP)/(kg MPa). These differences in the transport properties, morphology of the blend, and CO₂‐induced viscosity depression are the control factors for creating the unique cellular structure in PEG/PS blends. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1899–1906, 2005     

Numerical and experimental studies of bubble growth during the microcellular foaming process

A new experimental technique for studying the dynamics of bubble growth in thermoplastics using scanning electron microscopy is developed. The influence of temperature, saturation pressure, molecular weight, and the nature of physical blowing agent are investigated. The experimental results show that, the above, process variables control the growth of foams during processing. The existing Newtonian model for the growth of a single bubble in an infinite amount of polymer has been modified to account for the non-Newtonian effects by modeling the polymer as a power law fluid. The experimental data has been compared with the appropriate viscoelastic cell model which considers the growth of closely spaced spherical bubbles during the foaming process. The simulation results indicate that the predictions of the cell model are in qualitative agreement with the trends of the experimental data and the quantitative agreement is reasonable. The cell model also gives an equilibrium radius which agrees with the experimental data. Other viscous models do not predict the equilibrium radius of the bubble and underpredict the experimental data.     

Bubble growth model and its influencing factors in a polymer melt under nonisothermal conditions

Traditionally, in order to simplify the bubble growth process in a polymer melt, an isothermal model is typically used. In fact, the temperature of the polymer melt is changing during the foaming process. In order to accurately study the growth mechanism of bubbles in polymer melts, we build a physical and mathematical model of bubble growth in a polymer melt under nonisothermal conditions. The parameters of pressure, zero-shear viscosity, relaxation time, Henry's constant, diffusion coefficient, and surface tension were determined. The fourth-order Runge–Kutta method was used to solve the nonisothermal bubble model in the polymer melt. A computational program is developed to find the dimensional change during the bubble growth process, and the correctness of the model is verified. The nonisothermal growth mechanism of and factors influencing bubbles in the polymer melt are analyzed. Combined with the design of experiment (DOE) analysis method, the transfer function of the bubble radius and the maximum growth rate of bubbles with the process parameters were obtained, such as cooling rate, system pressure, and gas concentration. The results show that system pressure has the most significant effect on bubble growth. At the same time, a bubble growth prediction model is built, which can be used to predict the growth of bubbles. Through optimization analysis, it can be used to control the growth of bubbles. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47210.     

Bubble nucleation and growth in polymer solutions

The molecular cluster model for homogeneous bubble nucleation was extended to predict the bubble nucleation events in elastomers, polymers and polymer solutions. For nucleation in elastomers and polymers, the strain energy overcome by a critical bubble during growth period was also considered. The calculation results for the number of bubbles nucleated are in good agreement with observed results. Further, the growing of the critical bubble by the diffusion process in a viscoelastic medium was treated by an integral method for the concentration boundary layer. The calculated cell sizes depending on the initial saturation pressure are in close agreement with the observed sizes. The governing equations developed in this study may be used in polymer processing of microcellular foams. Polym. Eng. Sci. 44:1890–1899, 2004. © 2004 Society of Plastics Engineers.     

Numerical simulation of polypropylene foaming process assisted by carbon dioxide: Bubble growth dynamics and stability

A mathematical model was established to simulate the bubble growth process during foaming of polypropylene (PP) by carbon dioxide, taking into account of a wide range of physical and rheological properties (solubility, diffusivity, surface tension, long-chain branching, zero shear viscosity, relaxation time, strain hardening), as well as processing conditions. By employing the Considère construction the possibility of growth instability and bubble rupture at later stage of bubble growth was predicted. The simulation revealed that the improvement of foamability of polypropylene by introducing long-chain branching was due to the well-defined viscoelastic characteristics of the melt. Rheological factors that impede bubble growth are beneficial in stabilizing the bubble growth. Stability during bubble growth is further facilitated by moderate strain hardening characteristics and elastics properties of the polymers. The diffusivity and solubility characteristics also have profound impact on the bubble growth stability, while the influence of the surface tension is negligible.     

Visualization of bubble dynamics in foam injection molding

This article presents a visualization study on nonisothermal bubble growth and collapse in the foam injection molding process (FIM). Observation study can give more insight to the bubble growth in foaming process, especially in the challenging injection foaming process. In this study, besides the growth of bubbles, collapse of the bubbles was also observed which could provide knowledge to the final foam morphology. Cell growth vs. time was recorded and analyzed using a software‐equipped high speed camera. To investigate the cell collapse, various holding pressure was exerted on the gas‐charged molten polymer. The amount of holding pressure had noticeable effect on the rate of bubble collapse. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Extrusion foaming behavior of a polypropylene/nanoclay microcellular foam

With maleic anhydride grafted polypropylene (PP‐g‐MAH) as a compatibilizer, composites of block‐copolymerized polypropylene (B‐PP)/nanoclay were prepared. The effects of the PP‐g‐MAH and nanoclay content on the crystallization and rheological properties of B‐PP were investigated. The microcellular foaming behavior of the B‐PP/nanoclay composite material was studied with a single‐screw extruder foaming system with supercritical (SC) carbon dioxide (CO₂) as the foaming agent. The experimental results show that the addition of nanoclay and PP‐g‐MAH decreased the melt strength and complex viscosity of B‐PP. When 3 wt % SC CO₂ was injected as the foaming agent for the extrusion foaming process, the introduction of nanoclay and PP‐g‐MAH significantly increased the expansion ratio of the obtained foamed samples as compared with that of the pure B‐PP matrix, lowered the die pressure, and increased the cell population density of the foamed samples to some extent. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44094.     

Extruded foams from microbial poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) and its blends with cellulose acetate butyrate

Extrusion foaming of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) (PHBV) and two blends of PHBV with cellulose acetate butyrate (CAB) were studied using an azodicarbonamide (AZ) blowing agent and a single‐screw extruder. The concentration of the blowing agent was systematically varied from 0 to 4.0 phr to achieve maximum density reduction reaching 41%, as well as to obtain information on the dependence of cell growth on blowing agent concentration. Extruded foams were characterized in terms of their bulk densities and cellular morphologies. Stereological and statistical methods permitted full characterization of the three‐dimensional cell size distributions, assessing the average cell diameters (ranging from 58 to 290 μm) and cell densities (ranging from 650 to 180,000 cm^?3). The variation in cellular morphology among foams consisting of different polymer matrix or blowing agent concentration was compared. The results were analyzed by considering the influence of viscoelastic properties of the polymer matrix on the bubble growth during foaming. Significantly higher melt viscosity and elasticity and reduced gas solubility of the PHBV/CAB blends are believed to retard cell coalescence and collapse during foam expansion, resulting in more uniform cell size distribution and better homogeneity of cellular morphology. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Numerical simulation for bubble growth during supercritical CO2 foaming epoxy resin process based on chemorheology

The bubble growth process of epoxy resin foams has been evaluated through a combination of numerical simulation and chemorheology. It was discovered that rheological properties play an essential role in forecasting bubble growth during supercritical CO₂ epoxy resin foaming. Time–cure superposition was conducted revealing that shear storage modulus increased from 10⁻³ to 10⁶ Pa during the curing reaction process. The complex viscosity increased up to 10⁵ Pa s and the characteristic relaxation time increased up to 53.1 s with the curing degree. The epoxy resin with high rigid modulus could effectively inhibit bubble growth. Furthermore, the simulation results indicated that the bubble growth process for epoxy resin foams was influenced by both the CO₂ content and CO₂ plasticization on rheology properties.     

Effect of grafted polymeric foaming agent on the structure and properties of nano-silica/polypropylene composites

To promote dispersion of nano-silica in polypropylene (PP), a polymerizable foaming agent p-vinylphenylsulfonylhydrazide was synthesized and grafted onto the nanoparticles via free-radical polymerization. It was found that the grafted poly(p-vinylphenylsulfonylhydrazide) played dual role when being melt mixed with PP. The side sulfonylhydrazide groups were gasified to form polymer bubbles, leading to rapid inflation of the surrounding matrix that pulled apart the agglomerated nanoparticles, while the remaining backbone of the grafted polymer helped to improve the filler/matrix interaction through chain entanglement and interdiffusion at the interface. Mechanical tests indicated that the grafted nano-SiO₂/PP composites prepared according to the above strategy were simultaneously toughened, strengthened and stiffened. Compared with conventional graft polymerization treatment where no blowing function is associated, the technique proposed in this work could significantly enhance notch impact strength of PP.