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.     

超临界CO2/PS微孔塑料挤出成型中成核数对气泡核自由长大的影响

以超临界CO2为发泡剂,研究了PS微孔塑料挤出成型中气泡核自由长大的机理,选用球形模型为表征气泡长大的物理模型,利用Dewitt本构方程、守恒定律和理想气体状态方程导出了气泡核自由长大阶段的数学模型。通过此数学模型着重对气泡成核数与气泡核自由长大平均半径之间的关系进行了数值模拟预测,并以实验验证了其正确性,结果表明：当其他加工条件不变时,增加气泡的成核数,气泡长大的平均半径将变小。因此,在制备微孔塑料时,我们可以通过增加气泡的成核数来改善制品的泡孔结构。     

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 polymer foaming behavior of polypropylene/carbon dioxide system in a core‐back injection molding process

Thermoplastic foaming within a mold cavity was visualized as it was conducted in an 85‐ton core‐back injection‐molding machine. The core‐back molding process moved a section of the mold just after injecting a molten polymer into the cavity, quickly reducing the pressure to enhance the bubble nucleation. The foaming behavior during core‐back was observed directly through the glass windows of the mold. In the experiments, impact copolymer polypropylene was foamed with carbon dioxide. The effects of the gas concentration and the core‐back rate on bubble nucleation and growth were investigated. It was experimentally confirmed that the bubbles disappeared when the cavity was fully packed and that bubble nucleation occurred when the mold plate was moved and the cavity pressure dropped. Faster core‐back rates and higher gas concentrations increased the number of bubbles while decreasing their size. To analyze the experimental results, a bubble nucleation and growth model was employed that was based on batch foaming. The numerical results were a reasonable representation of the experiments, and this study demonstrated the applicability of the conventional free foaming model to the industrial core‐back molding process. Many aspects of the foaming in the core‐back molding aresimilar to the behaviors observed by batch foaming. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

Filamentary extrusion of microcellular polymers using a rapid decompressive element

An extrusion process for manufacturing microcellular plastics is presented. In the past, microcellular structures have been produced in batch processes by using a thermodynamic instability of a polymer/gas system. In order to utilize such a thermodynamic instability in a continuous extrusion process, a large amount of gas must be dissolved quickly in a molten plastic flowing in the machine, and a rapid drop in the gas solubility must be induced in the flowing polymer/gas solution. Since the solubility of a gas in a polymer is a sensitive function of pressure, a thermodynamic instability for producing a microcellular structure can be induced by rapidly lowering the pressure. This paper presents a means for continuously forming the polymer/gas solution at an industrial processing rate and a means of nucleating microcells in the polymer/gas solution using a nozzle. Finally, a process model for controlling the cell morphology is presented by identifying the key parameters that control microcellular foaming in a continuous process. The experimental results agree with theoretical analyses, confirming the fact that the processing pressure strongly affects the microcellular foaming process through its effects on the amount of gas dissolved in the polymer and the magnitude of the pressure drop in the nucleation device.     

微孔塑料挤出成型中气泡成核的聚合物刷子模型

气泡成核是微孔塑料连续挤出成型中的关键步骤之一，临界气泡核直径是影响制品中泡孔直径的主要因素，成核密度则是影响制品泡孔密度的主要因素，但现有的成核理论大都是以经典成核理论为基础的，而经典成核理论虽然人出了临界气泡核及成核速率的计算公式，但并没有考虑到聚合物的物性参数，并且不能计算临界气泡核半径的具体数值，所以其应用有很大的局限性，从聚合物刷子模型出发建立气泡成核的刷子模型，从而得出临界气泡核半径的计算公式，并分析温度，压力，聚合物相对分子质量等对临界气泡核半径的影响。     

Ultrasonic processing of thermoplastic foam

Ultrasonically induced bubble formation for the production of thermoplastic foam was investigated experimentally and theoretically as a basic study. A general purpose polystyrene and blends of low density polyethylene and polyethylene wax were saturated with nitrogen gas under various pressures and the ultrasonic excitation was applied to the polymer system upon release of gas pressure. The ultrasonic nucleation of bubbles in the polymer matrix was modeled by utilizing the classical nucleation theory. The negative pressure generated by the ultrasonic excitation was considered as the environmental pressure at the moment of nucleation. The experimental results showed that the heterogeneous nucleation must be used for ultrasonic foaming of the viscous fluid and the homogeneous nucleation for the low viscosity fluid. The theoretical analysis also indicated that the ultrasonic nucleation can be applied to the production of thermoplastic foam if the ultrasonic excitation generates large enough negative pressure.     

Solid‐state microcellular polycarbonate foams. I. The steady‐state process space using subcritical carbon dioxide

The process parameters for production of solid‐state microcellular polycarbonate using subcritical CO₂ were explored. Sufficiently long foaming times were used to produce foams, where cell growth had completed, resulting in steady‐state structures. A wide range of foaming temperatures and saturation pressures below the critical pressure of CO₂ were investigated, establishing the steady state process space for this polymer–gas system. Processing conditions are presented that produce polycarbonate foams where both the foam density and the average cell size can be controlled. The process space showed that we could produce foams at a constant density, while varying the cell size by and order of magnitude. At a relative density of 0.5, the average cell size could be varied from 4 to 40 μm. The ability to produce such a family of foams opens the possibility to explore the effect of microstructure, like cell size on the properties of cellular materials. It was found that the minimum foaming temperature for a given concentration of CO₂, determined from the process space, agrees well with the predicted glass transition temperature of the gas–polymer solution. A characterization of the average cell size, cell size distribution, and cell nucleation density for this system is also reported. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

An extrusion system for the processing of microcellular polymer sheets: Shaping and cell growth control

A new processing system for the extrusion of microcellular polymer sheets is presented. Specifically, the detailed design of a shaping and cell growth control system is discussed in the context of an overall extrusion system design with particular emphasis on the system level functional requirements of cell nucleation, cell growth, and shaping. The principle of the basic extrusion system design is to shape a nucleated polymer/gas solution flow under pressure and accurate temperature control. In this way, the initial cell growth is controlled so as to prevent degradation of the nucleated cell density during shaping. Two foaming die designs for satisfying the initial shaping and cell growth requirements are presented. Critical experiments are then presented which verified the concept of shaping a nucleated polymer/gas solution. Moreover, these experiments demonstrated the feasibility of the overall microcellular polymer sheet extrusion system design.     

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.     

超临界二氧化碳制备热塑性聚氨酯弹性体发泡材料的发泡机理和性能研究

用超临界二氧化碳制备热塑性聚氨酯弹性体发泡材料(E-TPU),分析发泡机理并研究发泡性能。结果表明:泄压速率和发泡温度是影响E-TPU发泡性能的两个重要因素;增大泄压速率有利于提高气泡成核速率和成核数量;升高发泡温度使气泡易膨胀长大,E-TPU密度减小;但发泡温度过高会导致气泡破裂和塌陷,E-TPU密度增大;当发泡温度为130℃左右时,E-TPU密度最小,发泡性能最好。     

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.     

Research on formation mechanisms and control of external and inner bubble morphology in microcellular injection molding

This study investigates the formation mechanisms and control of external and inner bubble morphology in MIM. First, the related theories about foaming and filling flow are analyzed. Second, the assumptions for the formation of inner bubble morphology, external bubble morphology, and the compact skin layer in MIM process are proposed based on theoretical analysis. Finally, experiments of MIM process are conducted to verify the theoretical assumptions. In addition, gas counter pressure (GCP) and rapid mold heating and cooling (RMHC) technology are used for control of bubble morphology. It is found that foaming process in MIM can be divided into foaming during filling and foaming during cooling. Foaming during filling produce oriented and deformed bubbles while foaming during cooling produce spherical or polygonal bubbles. As the bubbles formed by foaming during filling can reach melt flow front, they will be pushed to the cavity surface where they are stretched further and frozen to generate the silver or swirl marks. The compact skin layer is formed due to the redissolution of the gases within bubbles into polymer melt and also restraint of foaming by high cavity pressure. GCP and RMHC are two effective methods for controlling external and inner bubble morphology. POLYM. ENG. SCI., 55:807–835, 2015. © 2014 Society of Plastics Engineers     

Effect of the pressure drop rate on cell nucleation in continuous processing of microcellular polymers

Microllular plastics are cellular polymers characterized by cell densities greater than 10⁹ cells/cm³ and cells smaller than 10 μm. One of the critical steps in the continuous production of microcellular plastics is the promotion of high cell nucleation rates in a flowing polymer matrix. These high nucleation rates can be achieved by first forming a polymer/gas solution followed by rapidly decreasing the solubility of gas in the polymer. Since, in the processing range of interest, the gas solubility in the polymer decreases as the pressure decreases, a rapid pressure drop element, consisting of a nozzle, has been employed as a continuous microcellular nucleation device. In this paper, the effects of the pressure drop rate on the nucleation of cells and the cell density are discussed. The experimental results indicate that both the magnitude and the cell density are discussed. The experimental results indicate that both the magnitude and the rate of pressure drop play a strong role in microcellular processing. The pressure phenomenon affects the thermodynamic instability induced in the polymer/gas solution and the competition between cell nucleation and growth.     

微孔塑料成型技术及关键步骤

微孔塑料的成型方法主要包括间歇成型法、连续挤出成型法、注射成型法和相分离法等,并且各有优缺点.其中,连续挤出成型法及注射成型法适合工业化生产.微孔塑料的成型过程包括聚合物 /气体均相体系的形成、气泡成核和气泡长大及定型高的三个步骤,与常规泡沫塑料相比较,其加工过程的要求非常高,必须有高的气体浓度、高的成核速率、成核密度和短的长大定型时间.     

Nanocellular Polymers with a Gradient Cellular Structure Based on Poly(methyl methacrylate)/Thermoplastic Polyurethane Blends Produced by Gas Dissolution Foaming

Graded structures and nanocellular polymers are two examples of advanced cellular morphologies. In this work, a methodology to obtain low‐density graded nanocellular polymers based on poly(methyl methacrylate) (PMMA)/thermoplastic polyurethane (TPU) blends produced by gas dissolution foaming is reported. A systematic study of the effect of the processing condition is presented. Results show that the melt‐blending results in a solid nanostructured material formed by nanometric TPU domains. The PMMA/TPU foamed samples show a gradient cellular structure, with a homogeneous nanocellular core. In the core, the TPU domains act as nucleating sites, enhancing nucleation compared to pure PMMA and allowing the change from a microcellular to a nanocellular structure. Nonetheless, the outer region shows a gradient of cell sizes from nano‐ to micron‐sized cells. This gradient structure is attributed to a non‐constant pressure profile in the samples due to gas desorption before foaming. The nucleation in the PMMA/TPU increases as the saturation pressure increases. Regarding the effect of the foaming conditions, it is proved that it is necessary to have a fine control to avoid degeneration of the cellular materials. Graded nanocellular polymers with relative densities of 0.16–0.30 and cell sizes ranging 310–480 nm (in the nanocellular core) are obtained.     

A study of the dynamics of foam growth: Analysis of the growth of closely spaced spherical bubbles

A mathematical analysis of bubble growth in an expanding foam is presented. The analysis is based on a cell model whereby the foam is divided into spherical microscopic unit cells of equal and constant mass, each consisting of a liquid envelope (or shell) and a concentric spherical gas bubble. Expansion occurs by diffusion of a dissolved gas from the supersaturated envelope into the bubble. This cell model is capable of describing important qualitative features of a real system of numerous bubbles growing in close proximity to one another, and is intended as the building block of a global analysis of macroscopic foam expansion. The coupled algebraic and differential equations governing the growth of a cell are derived and solved numerically. Five dimensionless parameters are identified for the case of constant temperature and pressure outside the cell, and their effects are demonstrated through computer simulations of the system. Of these parameters, surface tension and initial radius prove to be of relatively little importance in the practical cases considered. The other parameters are the thermodynamic driving force, the cell mass (inversely proportional to the number density of bubbles), and the ratio of characteristic times for mass and momentum transport.     

Effect of surface curvature and wettability on nucleation of methane hydrate

Natural gas hydrate nucleation is a complex physical and chemical process that is not well understood presently. In this article, an improved thermodynamic model is proposed to analyze the effects of surface curvature and wettability on methane hydrate nucleation for the first time. The results indicate that methane hydrate nucleation is more difficult on hydrophilic curvature surfaces under the same conditions, with a larger critical nucleation radius and required energy barrier than on hydrophobic surfaces. Furthermore, a convex surface is more favorable for forming methane hydrate under the same conditions than a concave surface. The model's results are critical in elucidating the microscopic mechanism of methane hydrate nucleation and providing a theoretical foundation for developing technologies for strengthening and inhibiting hydrate formation.     

Bubble growth in thermoplastic structural foams

The inflation and growth kinetics of bubbles in thermoplastic structural foams are discussed in some detail using a model which assumes the initial existence of very small voids in the pressurized polymer melt. The effects of a drop in external pressure, the presence of a distribution of bubble sizes, and the diffusion of gas between neighboring bubbles are considered. It is shown that at a given pressure the number of growing bubbles present in the melt at any onetime depends on the ratio of the critical radius to the average radius of the microvoids assumed to be present in the melt It is also demonstrated that gas diffusion between neighboring bubbles reduces the growth rate appreciably only when the interbubble distance is reduced to a micron or less.     

Microcellular sheet extrusion system process design models for shaping and cell growth control

The feasibility of shaping a nucleated polymer/gas solution represents a significant advancement for microcellular plastics process technology. Through proper design of the foaming die, nucleated solution flows can be shaped to arbitary dimensions while maintaining the functional independence of cell nucleation, cell growth and shaping. To maintain funcational independence, stringent pressure and temperature design specifications, which supersede those of conventional foam processing, must be met by the foaming die design. As a means of aiding the design process, a model is developed for predicting pressure losses and flow rates of nucleated polymer/gas solutions. A comparison of the model predictions and the actual foaming die design performance shows good agreement for limited data. These relatively simple models capture the major physics of the complicated two-phase flow field and provide a sound base from which scale-up of the foaming die concept can be achieved. The nucleated polymer/gas solution flow models predict highly nonlinear volumetric flow rates contrasting constant flow rates predicted for the neat polymer flow. In addition, a convenient method for classifying nucleated polymer/gas solution flow is presented based on a dimensionless ratio of the characteristic flow rate to the characteristic gas diffusion rate.