Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers

Bubble growth processes are highly complex processes, which are not only dependent on the foaming process parameters (temperature, pressure and blowing agent concentration) but also on the type and structure of the polymer used. Since the elongational viscosity at the bubble wall during bubble growth also depends on these influencing factors, the so-called transient elongational viscosity plays a key role in describing the gas bubble growth behavior in polymer melts. The model-based description of the transient elongational viscosity function is difficult due to its dependence on time, Hencky strain and strain rate. Therefore, representative viscosities or shear viscosity models are usually used in the literature to predict the bubble growth behavior. In this work, the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth is described holistically for the first time. This is achieved by extending the so-called molecular stress function (MSF) model by superposition principles (temperature, pressure and blowing agent concentration) and by using the elongational deformation behavior (Hencky strain and strain rate) at the bubble wall during the initial, and thus viscosity-driven, bubble growth process. Therefore, transient uniaxial elongational viscosity measurements are performed and the non-linear MSF model parameters of the two investigated polymers PS (linear polymer chains) and PLA (long-chain branched polymer chains) are determined. By applying the superposition principles and by changing the strain mode parameter to the equibiaxial case in the MSF model, the transient equibiaxial viscosity master curve is obtained and used to describe the bubble growth process. The results show that the extended MSF model can fully predict the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth processes. The bubble growth behavior over time can then be realistically described using the defined transient equibiaxial elongational viscosity function at the bubble wall. This is not possible, for example, with a representative viscosity and therefore clearly demonstrates the influence and importance of knowing the transient deformation behavior that prevails at the bubble wall during bubble growth processes.

Study on the Flow, Foaming Characteristics and Structural Strength of Polypropylene Structural Foam Injection Molding by Innovative Nitrogen and Molten Plastic Mixing Mechanism

Plastic foam molding methods include thermoforming, extrusion and injection molding. Injection foam molding is a one-time molding method with high production efficiency and good product quality. It is suitable for foamed plastic products with complex shapes and strict size requirements. It is also the main method for producing structural bubbles. In this investigation, we developed a structural foam injection molding technology using the gas supply equipment connected to the unique plasticizing mechanism of the injection machine and studied its influence on the specimens' melt rheology quality and foam structures. In the experiment, the forming material was polypropylene (PP), and the gas for mixing/forming foaming characteristics was nitrogen (N₂). Additionally, in order to observe the rheological properties of N₂/melt mixing, a melt flow specimen mold cavity was designed and the change in the melt viscosity index was observed using a melt pressure sensing element installed at the nozzle position. With the nitrogen supply equipment connected to a unique plasticizing mechanism, the mixing of gas and molten plastic can be achieved at the screw plasticizing stage, where the foaming effect is realized during the melt-filling process due to the thermodynamic instability of the gas. It was also found that an increase in N₂ fill content increased melt fluidity, and the trend of melt pressure and melt viscosity index showed that the higher the gas content, the lower the trend. The foaming characteristic depends on the gas thermodynamic instability and the pressure release, so it can be seen from the melt fill path that, the greater the pressure near the gate, the lower the foaming amount and the internal structure (SEM) after molding; the farther from the gate, the greater the relative increase in the foaming growth/amount. This phenomenon will be more obvious when the N₂ fill content is increased.

Development of a Rheology Die and Flow Characterization of Gas-Containing Polymer Melts

We present a novel measurement die for characterizing the flow behavior of gas-containing polymer melts. The die is mounted directly on the injection-molding cylinder in place of the mold cavity and thus enables near-process measurement of viscosity (i.e., under the conditions that would be present were a mold attached). This integration also resolves the issue of keeping gas-containing polymer melts under pressure during measurement to prevent desorption. After thermal characterization of the die, various correction approaches were compared against each other to identify the most suitable one for our case. We conducted measurements using polypropylene in combination with two different chemical blowing agents. Increasing the blowing-agent content to up to 6% revealed an interestingly low influence of gases on melt viscosity, which was confirmed by elongational viscosity measurements. For verification, we compared our results to corresponding measurements taken on a high-pressure capillary rheometer and found that they were in excellent agreement. Our die cannot only be used for rheological characterization. Combined with ultrasound sensors, it provides an innovative way of measuring the volumetric flow rate. This development represents an important step in improving the sustainability of gas-containing polymer processing.

Evaluating the gas-laden ability of polymer melt under atmospheric conditions using a modified torque rheometer

To investigate the effects of incorporating gas and the associated influencing factors on polymer melt, a method of evaluating the gas-laden ability using modified rheometric measurements was proposed. In this study, common and widely used thermoplastic materials—polypropylene (PP) and high-density polyethylene (HDPE), and their blends with different weight ratios—were selected, and the rheological properties of neat melt and gas-laden melts were tested using a modified torque rheometer. The foamed samples were also produced using a regular injection-molding machine, and the foamed morphology was examined by scanning electron microscope (SEM). The comparison of rheological curves of neat melt and gas-laden melt indicated that the incorporation of gas influenced the rheological properties of the gas-laden polymer melts as evidenced by a decrease of zero-rotational torque and an increase in the melt flow index. The results also suggested that the gas-laden ability of polymer melt could be evaluated quantitatively by the decay (due to desorption) of gas using the modified rheological measurement method. This study also demonstrated that the gas-laden ability can be used to predict the foaming behavior of polymer melts.

Solubility and diffusion coefficient of supercritical CO2 in polystyrene dynamic melt

The solubility and diffusion coefficient of supercritical CO2 in polystyrene (PS) dynamic melt were studied by using a new constant pressure experimental device. By comparing the experimental results with those of other researchers, the validity of the experimental device and the reliability of the calculated results are verified. The solubility and diffusion coefficient of supercritical CO2 in polystyrene dynamic melts at different temperatures and pressures were obtained. The numerical calculation method, dissolution process, and experimental results are analyzed and compared with that of the static melt. Finally, the effects of stirring speed, pressure, and temperature fluctuation on the solubility and diffusion coefficient are also analyzed.

Viscosity measurement of polypropylene loaded with blowing agents (propane and carbon dioxide) by a novel inline method

Decreased viscosity due to the influence of blowing agent in thermoplastic polymer melts is a key issue for understanding the process of foam extrusion. In a process for direct foam extrusion, a novel approach for inline viscosity measurement of single-phase systems in single screw extruders is used to experimentally evaluate a viscosity decrease. Two blowing agents (propane and carbon dioxide) are tested for their effect on the viscosity of a polypropylene melt. While mass fractions of blowing agent below [Formula: see text] show little to no effect in regard to viscosity reduction compared to a pure polymer melt, a mass fraction of [Formula: see text] already results in significantly decreased viscosity values. While melt temperature influences the viscosity of the polymer melt, measurements show no significant additional effect in regard to a lowered viscosity of a single-phase system of polymer and fully dissolved blowing agent.

Insight into bubble nucleation at high-pressure drop rate

This paper presents insight in bubble nucleation in polymer foaming with physical blowing agent using a batch foaming technique. In our experiments the bubble nucleation is triggered by a sudden pressure drop that causes the supersaturation in the polymer gas solution. In fact, the pressure drop rate is an important process variable since it plays a role in both bubble nucleation and growth. Herein, we investigated very high pressure drop rates, and confirmed the great importance of the pressure drop rate as foaming process variable. The results show that the number of nucleated bubbles increases of one order of magnitude and the foam density is reduced if the pressure drop rate is increased from 50 to 500 MPa/s. Interestingly, the number of nucleated bubble increases linearly in a bi-logarithmic scale as function of pressure drop rate at all the investigated temperatures. Moreover, in the current paper, it is discussed how talc used as nucleating agent plays a role in cooperation with pressure drop rate on bubble nucleation at different foaming temperatures.

Study of Shear and Extensional Viscosities of Biodegradable PBS/CO2 Solutions

The purpose of this research is to study the pressure drop profiles of biodegradable polybutylene succinate (PBS)/CO2 solutions in a slit die and to measure the rheological properties of the solutions as a function of the blowing agent concentration. A slit die with four pressure transducers has been designed to describe the effects of shear rate, temperature, pressure, and gas content on the shear viscosity and extensional viscosity of the flowing PBS/CO2 solutions. The low shear rate viscosity of the pure polymer was measured using a cone and plate rheometer. Extensive experiments were conducted to investigate the polymer/gas solution viscosities at five different shear rates, three temperatures and five gas contents. Cross-Carreau model and generalized Arrhenius equation were used to describe the shear-viscosity behaviors of PBS/CO2 solutions. The extensional viscosity of solution was modeled based on Cogswell’s equation.

Complex cellular structure evolution of polystyrene/poly (ethylene terephthalate glycol-modified) foam using a two-step depressurization batch foaming process

In order to decrease the cell size and maintain very high volume expansion ratio simultaneously, a methodology for the preparation of complex cellular structure (CCS) in polystyrene/poly(ethylene terephthalate glycol-modified) (PS/PETG) blend using two-step depressurization pressure batch foaming process was proposed. First, the optimum foaming temperature for PS and PS/PETG blend, respectively, were confirmed by one-step depressurization foaming process. Then, the CCS in PS and PS/PETG blending foam were fabricated by two-step depressurization foaming process at the optimum foaming temperature. The rheological properties of PS and PS/PETG blend were tested by dynamic rotational rheometer. The dispersion morphologies and foam morphologies were observed by scanning electron microscope. The lowest densities of PS and PS/PETG blending foams were obtained at the temperature of 136℃. The interfaces between PS and PETG could act as nucleation sites for the cell nucleation, which were helpful to fabricate the CCS. The CCS could be controlled by tuning the degree of the first-step depressurization and the holding time. The results showed that the large cells could be beneficial to decrease the foam density and the presence of small cells was beneficial to increase the cell number.

Effect of Physical Foaming Agents on the Viscosity of Various Polyolefin Resins

The effect of temperature and type of physical foaming agent (HCFC-142b, n-pentane, and carbon dioxide) on the shear viscosity have been investigated for various types of polyolefin resins (PP, LLDPE, and HDPE). The viscosity changes have been monitored using a commercial on-line process control rheometer mounted on a twin-screw extruder.

A plasticization index, based on the respective molecular weights of the foaming agent and the repeat unit of the polymer, is proposed. Comparison with an amorphous polymer, namely polystyrene, is also made for mixtures using the same physical foaming agents.

Supercritical CO2 Processed Polystyrene Nanocomposite Foams

Polystyerene (PS) nanocomposite foams were prepared using CO2 supercritical fluid (SCF) as a solvent and blowing agent. PS was first in situ polymerized with 0, 1, and 3% Montmorillonite-Layered Silicate (MLS) mixtures, which were then compression-molded into thin laminates. The laminates were foamed in a batch process at temperatures and pressures within the range of 60–85 C and 7.6–12 MPa. Characterization was accomplished with scanning electron microscopy (SEM), Differential Scanning Calorimetry (DSC), and X-ray Diffraction (XRD). SEM images revealed the effects of different processing parameters on the foam’s cellular morphology, and also showed that the MLS layers were arranged in alignment with the foam cell walls. DSC data indicated that different concentrations of MLS have a notable effect on the glass transition temperature (Tg) of the composite, and that the foaming process itself alters the endothermic behavior of the material. XRD spectra suggested that the PS–MLS composite had an intercalated structure at both the 1 and 3% mixtures, and that the intercalation may be enhanced by the foaming process.

Relationship of Fractional Free Volumes Derived from the Equations of State (EOS) and the Doolittle Equation

This research investigates the relationships of the pressure–volume–temperature (PVT) and the zero-shear viscosity of polymer melts through their correlations with the fractional free volume. Polystyrene (PS) has been used as a case example in this study. First, the fractional free volume is determined from the Simha–Somcynsky (SS) equation of state (EOS) or the Sanchez–Lacombe (SL) EOS using the PVT data of a polymer melt. Then the fractional free volume is also determined from the Doolittle equation (with respect to the occupied volume) using the zero-shear viscosity and PVT data. These two fractional free volumes are compared to check if the EOS and the Doolittle equation consistently describe the PVT behaviors and the zero-shear viscosity through the fractional free volume. Before comparison, the fractional free volume based on the Doolittle equation is recalculated with respect to the total volume to be consistent with other fractional free volumes defined with respect to the total volume.

Finite Element Analysis of Cell Coarsening in Plastic Foaming

In this study, cell coarsening in plastic foaming is investigated through numerical simulation. Cell coarsening occurring in two adjacent bubbles of different sizes in a finite volume of polymer melt is considered to be representative of the whole foaming system. A quadratic triangle-based finite element analysis with an implicit scheme for time evolution is utilized to solve the governing diffusion equation in the axisymmetric coordinate system. The effects of the bulk gas concentration, the intercellular distance, and the initial bubble sizes on cell coarsening are estimated. Efforts are made to improve a fundamental understanding of cell coarsening in plastic foaming.

Numerical Modeling of Bubble Growth in Microcellular Polypropylene Produced in a Core-Back Injection Process Using Chemical Blowing Agents

A core-back polypropylene foaming injection process using chemical blowing agents (CBA) has been studied. First, injection tests were carried out with two different CBAs and the different morphologies of the obtained samples have been analyzed. Structural parameters such as cell density and average radius size were calculated. Then, a bubble growth model was developed to predict the foaming development during the process, controlled by the depressurization of the mold cavity during the short core-back opening coupled with the evolution of the temperature during core-back and subsequent cooling. A good agreement is found between theoretical predictions and experimental results.

A new approach designed for improving flame retardancy of intumescent polypropylene via continuous extrusion with supercritical CO2

scCO₂-aided IFR dispersion of PP/IFR composites and their improved flame retardancy.

Application of supercritical CO2 as the processing medium to tune impact fracture behavior of polypropylene/poly(ethylene-co-octene) blends

The new approach of applying scCO₂ as a processing medium was proven effective in tuning the fracture behavior of PP/POE blends.

Study of volume swelling and interfacial tension of the polystyrene-carbon dioxide-dimethyl ether system

We investigated the interaction of blended carbon dioxide (CO2) and dimethyl ether (DME) with polystyrene (PS) through volume swelling and interfacial tension. The experiments were carried out over a temperature range of 423-483 K, and the pressure was varied from 6.89 MPa to 20.68 MPa. With an incremental concentration of DME in the blend, the volume swelling increased while the interfacial tension between the PS/blend gas mixture and the blend gas decreased. The validity of the Simha-Somcynsky (SS) equation of state (EOS) for the ternary system was established by comparing experimentally measured volume swelling to that obtained via SS-EOS.

Bubble morphological evolution and surface defect formation mechanism in the microcellular foam injection molding process

A multiphase model was established to simulate the bubble morphological evolution in MFIM, and a new phenomenon of surface collapse and pits with the gradient depth was discovered.

The effects of viscoelastic properties on the cellular morphology of silicone rubber foams generated by supercritical carbon dioxide

Silica content, saturation temperature and pressure all have an effect on silicone rubbers' viscoelastic properties, which further has a close connection with the cellular structure.

Effect of Chain Extension on the Rheological Property and Thermal Behaviour of Poly(lactic acid) Foams

Epoxy-based chain extended high-melt-strength poly (lactic acid) (PLA) was prepared. Rheological properties and the thermal behaviours of the chain extended PLA were studied. The rheological properties indicated that the melt elasticity and melt strength of the chain extended PLA samples were gradually improved by increasing the content of chain extender (CE). Moreover, the thermal results showed that the crystallinity and the spheruilite morphology of PLA were greatly influenced due to the introduction of CE. The effect of CE contents on foam morphology was also studied. Adding CE resulted in higher expansion ratio and smaller cell size of PLA foams.

Development of a Hybrid Solid-Microcellular Co-injection Molding Process

This paper presents the development of a hybrid solid-microcellular co-injection molding process that combines aesthetic and processing advantages of injection molding with benefits and property attributes of microcellular plastics (MCPs). A two-color injection molding machine has been modified and equipped with an interfacial platen and a supercritical fluid (SCF) unit for co-injection molding with regular resins and MCPs. Co-injection molded polystyrene (PS) parts with a microcellular core encapsulated by the solid skin layer have been successfully produced. Systematic experiments were carried out with solid-microcellular co-injection molding, conventional solid-solid co-injection molding, and regular microcellular injection molding processes to study the effects of process conditions and core/skin volume ratios on the penetration and morphology of the microcellular core. Light microscopy and scanning electron microscopy (SEM) of the solid-microcellular co-injection molded specimens reveal a microcellular core with fairly fine and uniform cell size of 8 to 12 microns and a cell density of up to 3 × 10 cells/cm. Under similar process conditions, microcellular cores were found to penetrate longer and generate a more uniform and thicker skin layer than do solid cores. While improving the surface finish with solid skin layers, this process is capable of producing parts with reduced sink marks, lighter part weights, and shorter cycle times.

Effects of Pressure and Supercritical Fluid on Melt Viscosity of LDPE in Conventional and Microcellular Injection Molding

In this study, the flow and rheological behaviors of low density polyethylene (LDPE) and single-phase LDPE/N2 polymer/gas solutions at various gas contents were measured using a high-pressure slit-die rheometer. The resulting rheology data of LDPE and LDPE/N2 were curve fit using the Cross–WLF model to obtain the seven material model constants, which were then used in the simulation of conventional and microcellular injection molding processes. The pressure effect on the shear viscosity of LDPE was also studied. The pressure dependency coefficient, D3, in the Cross–WLF model was determined by the use of simulation to best fit the experimental results. In addition, a three-dimensional plot of shear viscosity as a function of shear rate and pressure at various temperatures was constructed. Based on this three-dimensional viscosity–shear rate–temperature–pressure plot, the increase in viscosity due to the pressure effect was found to be more profound at high pressures, low temperatures, and low shear rates.

Visualization Analysis of a Multilayer Foam Development Process in Microcellular Injection Molding

In this study, cross-sectional analyses were performed on microcellular injection-molded high-impact polystyrene products. The results confirm that the following five types of layers were formed: Skin layers I (the silver streak layer) and II (a nonfoamed layer), Core layers I (cell diameter, d > 150 μm), II (d < 50 μm), and III (d > 100 μm). As the maximum in-mold pressure (Pmax) was increased from 5 to 30 MPa, the thickness of Skin layer II remained nearly constant. However, the foam types in the core layers changed from I and II to II and III or III only, resulting in an increase in cell diameter and a decrease in cell density. The process of cellular structure formation was observed using a glass-inserted mold, which revealed that this process consists of a flow (with a burst of cells at the melt front and the subsequent flow of the melt containing the cells), an end of the filling (involving elastic compression or the dissolution and disappearance of cells formed in the flow stage), and a cooling (new cell generation and growth and cooling solidification). Based on these cross-sectional observations, in concert with melt-pressure measurements and visualizations, we developed a model describing the formation process of Skin layer II and the core layers including a new concept that considers the melt pressure inside the cavity. The following layers are incorporated into the model: Skin layer II: A nonfoamed layer is formed in the area of the melt front where gases diffuse out from within the melt during the filling stage, and this nonfoamed layer moves to from melt front to the surface of the product due to fountain flow. Core layers I and II: A multilayer is formed containing a distribution of cells preserved from the flow stage due to the low compression forces, Core layer III: cells are dissolved in the melt due to strong compression forces at the end of the filling stage and then reform and grow in the cooling stage.

The Effect of CO2 Pressure on Viscoelasticity of LDPE

The effect of impregnated carbon dioxide (CO2) and pressure on dynamic viscoelastic responce of a commercial LDPE was investigated by a magnetic driven rotational rheometer equipped with a high-pressure chamber. It was found that i) the mode distribution of the viscoelastic relaxation is not sensitive to CO2 pressure realizing the superposition among moduli obtained at different pressures, that ii) the horizontal shift factor for the superposition reflecting the monomeric friction exponentially decreases with increase of the pressure, and that iii) the vertical shift factor relating to the entanglement number density is not sensitive to the pressure. From the observation it is suggested that CO2 and pressure mainly affect the monomeric friction and the effect on the entanglement dilation is not significant. The results are consistent with the dielectric measurement on polyisoprene (Matsumiya et al., Nihon Reoroji Gakkaishi, 35, 155–161, 2007).

Challenges to the Formation of Nano-cells in Foaming Processes

This paper uses a finite element analysis to investigate the morphological changes of nano-cells in a polystyrene (PS) – CO2 foaming system. The system was composed of a finite polymer melt with a central cell and eight surrounding cells. The computational domain was discretized using linear triangular elements. The growth and shrinkage of nano-sized cells were tracked using the moving mesh method. The effects of the initial bulk gas concentration, cell size, intercellular distance, and system temperature on cell ripening were examined. The results show that smaller nano-sized cell(s) are doomed to collapse very quickly once they have interacted with larger cell(s), making it difficult to survive. Efforts were made to improve the general understanding of the challenges posed to the formation of nano-cells in foaming processes.