Impact of approximating the initial bubble pressure on cell nucleation in polymeric foaming processes

According to the classical nucleation theory, the free energy barrier for bubble nucleation, and thereby the nucleation rate, are functions of the initial bubble pressure, P_bubble,0. In almost all of the previous studies that have used computer simulations to investigate polymeric foaming processes, the value of P_bubble,0 has been approximated using the saturation pressure, P_sat. This article employs the thermodynamic equilibrium condition and the Sanchez–Lacombe (SL) equation of state (EOS) to determine the value of P_bubble,0. It is shown that using P_sat to approximate P_bubble,0 may lead to significant overestimations of the nucleation rate and the final cell density. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 902–908, 2007     

Prediction of foam growth and its nucleation in free and limited expansion

The influence volume approach (IVA) is often utilized for modeling the mass transfer process dictating bubble growth dynamics in physical foaming. However, the assumed concentration profile in the IVA method is only valid when the changes in dissolved gas concentration are small (less than 5%). In addition, the validity of the IVA method is difficult to justify in chemical foaming applications because of the difficulties involved in defining the dissolved gas concentration profile.In the present work, we define two distinct stages of bubble growth for physical foaming. These two stages are termed as free and limited expansion and are controlled by the bubble nucleation rate. Bubble nucleation is assumed to occur only in the free expansion stage. In this stage, the bubble pressure drops substantially from an initially high pressure in the supersaturated state while the dissolved gas concentration changes very little. The second stage of our two-stage mass transfer model is termed the limited expansion stage and accounts for bubble growth in the late stages of foam evolution, when the pressure changes become small. However, in the limited stage of bubble growth the dissolved gas concentration drops significantly, as the available dissolved gas is depleted. To summarize our two-stage mass transfer model of foam expansion, the pressure difference between the bubble phase and the liquid phase is the primary mechanism for driving mass transfer in the early (free) stages of foam growth and the concentration difference is the driver for bubble growth in the late (limited) stages of growth. The first stage can be regarded as the nucleation stage and it is relatively short; while the second stage can be regarded as the bubble growth stage and is much longer. Most of the bubble volume expansion takes place in the second stage.The concentration gradient at the bubble edge, which is often ignored in other models, is analyzed in detail in this paper. The details of our novel mass transfer model are also presented.     

受限纳米通道内气泡核化的分子动力学模拟

采用分子动力学方法模拟研究受限纳米通道内液体在固体壁面上的核化生长过程,本文主要研究固体壁面润湿性对液体核化生长的影响并分析了气泡成核机理。结果表明：不同壁面润湿性对气泡核化生长产生较大影响。壁面润湿性强时,近壁面处会形成一层液膜,出现与池沸腾不同的现象,流体在液膜层发生均质核化,气泡核化生长速度较快;壁面润湿性较弱时,液体在近壁面处发生异质核化,气泡核化生长速度相对较慢;壁面润湿性最弱时,在近壁面处会形成一层气膜,热量通过气膜传递给流体,传热效果不佳,液体很难发生核化现象。形成这种现象的原因是壁面润湿性强,近壁面处会形成“类固体”层,热量由壁面经“类固体”层传给通道内流体,传热效果好,此外,“类固体”层越厚传热效果越好。壁面润湿性弱时,近壁面处没有“类固体”层,会形成一层气膜,降低传热效果,影响通道内流体核化生长。     

泡沫塑料加工过程中的气泡成核理论(Ⅰ)——经典成核理论及述评

介绍了泡沫塑料加工过程中气泡成核的经典理论,给出了几种成核方式的临界成核半径、所需克服的吉布斯(Gibbs)自由能及成核速率的计算公式;评述了经典成核理论的发展,包括自由体积和气体过饱和度对气泡成核的影响,并分析指出了经典成核理论对动态聚合物熔体气泡成核解释存在的不足。     

Ideal surface geometries of nucleating agents to enhance cell nucleation in polymeric foaming processes

Ideal nucleating agents are expected to improve the cell morphology of plastics foams (i.e., increasing the cell density, reducing the cell size, and narrowing cell-size distribution) by providing heterogeneous nucleation sites. A nucleating agent's surface geometry is one factor that governs its nucleating power. This paper discusses the surface geometry of an ideal nucleating agent. On the basis of computer simulations of a batch foaming process using polystyrene and carbon dioxide, we found that nucleating agents having numerous crevices with small semiconical angles are the most desirable for polymeric foaming processes. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Multiple percolation in a carbon‐filled polymer composites via foaming

This article describes an investigation into the effects of foaming on the electrical conductivity for a carbon‐filled cyclic olefin copolymer (COC) composite incorporating both chopped carbon fibers (cCF) and carbon black (CB). Foamed and solid samples were injection molded and then analyzed for cell size, fiber length, fiber orientation, and electrical conductivity. Foamed samples exhibited higher electrical conductivity in the through‐plane direction for materials containing only CB or composites containing both filler types, and reduced electrical conductivity in the cCF‐filled composites. The increased electrical property gained by foaming was attributed to multiple percolation with CB aggregates forming more effective conductive clusters and networks in the continuous polymer phase during growth of the gas domains. A mechanism for the phenomenon was proposed based on these experimental observations. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Prediction of cellular structure in free expansion of viscoelastic media

A systematic model is presented for a free expansion polymer foaming process that includes simultaneous nucleation and bubble growth. An influence volume approach, which couples nucleation and bubble growth, is used to account for the limited supply of dissolved gas. The melt rheology is described using the Larson viscoelastic model. The initial conditions are obtained at the upper bound of critical cluster size under conditions of elastic deformation. The resulting set of equations are solved using a combination of numerical techniques. A parametric study is conducted to examine the effects of key process variables on bubble growth, nucleation, and final bubble size distribution. It shows that the factors influencing nucleation and growth affect the ultimate bubble sizes and their distribution. The Gibbs number, a dimensionless measure of the barrier to overcome for nucleation, has the strongest impact on the cellular structure of the foam. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1353–1368, 1998     

A nucleation mechanism leading to stacking of lamellar crystals in polymer thin films

Systematic studies based on well‐controllable model systems aim at understanding how crystallization from a melt or solution of randomly coiled polymers leads to the formation of mono‐lamellar crystals. However, besides mono‐lamellar crystals also various other morphologically simple but yet not well understood structures are found. In particular, stacks of correlated lamellar crystals have been observed since the early days of the study of polymer crystallization. Here, we demonstrate that a recently proposed mechanism of self‐induced nucleation within lamellar crystals provides a possibility to explain how in such stacks lamellar crystals can be correlated. Examining various polymer systems, we show that the probability for generating self‐induced nuclei depends on the morphology of an initiating dendritic basal lamellar crystal. In addition, we provide evidence that this self‐induced nucleation mechanism, together with a high rate of transport of molten polymer to the fold surface, may allow the formation of polymer crystals with similar size in all three dimensions, containing a large number of superposed correlated lamellae. © 2019 The Authors. Polymer International published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.     

Further evidence against the alleged failure of the classical nucleation theory below the glass transition range

We collected a plethora of new data to test the hypothesis that the failure of the Classical Nucleation Theory (CNT) below the glass transition range is just an experimental artifact. Since reaching the steady-state nucleation regime takes a significant time for treatments below the glass transition temperature, data collected in this temperature range tend not to have reached a steady state. Because of this potential problem, we examined the CNT using new experimental data for three stoichiometric silicate glasses: Li₂Si₂O₅, BaSi₂O₅, and Na₄CaSi₃O₉. We also measured the equilibrium viscosity for the studied glass batches and used it as a proxy for the effective diffusion coefficient. The analysis was conducted by applying a steady-state criterion and evaluating the error propagation throughout all calculations. Using this rigorous procedure, we have not observed the alleged CNT failure. Our comprehensive results support recent studies questioning this possible CNT failure helping solve a longstanding problem in glass science.     

Study of microcellular foaming of polystyrene aided with 45 kHz of ultrasound waves energy

ABSTRACT

In the microcellular foam plastic processing, cellular formation stage was being an essential stage since the nucleation and growth of the cell take place within. Based on classical nucleation theory, diminution of the free energy for nucleation, exponentially lead to an increase in the nucleation rate. This can be done by increasing the super-saturation level which achieved by heating the gas-saturated polymer. Hence, the advance is taken out by utilizing the ultrasound wave simultaneously with heating for foaming Polystyrene-scCO₂, which, not only to keep the super-saturation degree but also reduce the nucleation barrier. In this work, foaming was conducted under 45 kHz of ultrasound and varying the foaming temperature after saturating polystyrene with scCO₂. The results demonstrate, that foaming under ultrasound, the expansion ratio attained up to 1.5 fold, increase along with the heating temperature. Higher cell densities obtained with ultrasound applied at 50°C, however only slight difference can be seen, which about 10¹⁰–10¹¹ cell/cm³. From the cell size distribution results, cell distributed around 0.5–3.5 µm, with or without ultrasound applied for 60 and 70°C, Meanwhile at 50°C of foaming, the lowest cell size obtained with the aid of ultrasound in the range of 0.3–2.4 µm.     

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     

超临界发泡法制备高性能热塑性高分子微/纳孔泡沫材料研究进展

国民经济和高科技领域的飞速发展,对高分子泡沫材料的高强度及耐高低温性能、无毒无烟及本征阻燃、易加工成型等方面的要求进一步提高,通用高分子泡沫材料,如聚乙烯（PE）、聚丙烯（PP）、聚苯乙烯（PS）等难以满足使用要求。因此,聚醚酰亚胺（PEI）、聚酰亚胺（PI）、聚醚砜（PES）、聚芳砜（PPSU）、聚苯硫醚（PPS）、聚醚醚酮（PEEK）等高性能热塑性高分子泡沫材料和制品的研究成为新的热点。本文对超临界流体发泡原理和超临界流体发泡技术进行了系统介绍,重点综述了超临界流体（supercritical fluid）,如scCO₂或scN₂作物理发泡剂,结合各种发泡技术,如釜压发泡、注塑发泡、挤出发泡和珠粒发泡,在高性能热塑性高分子发泡领域中的应用及取得的研究成果,以期为高性能高分子材料的研究及应用提供借鉴。最后,对开发操作简单、所得泡沫制品尺寸精确的发泡技术作了展望。     

石墨烯/聚合物泡沫压阻式应变传感器研究进展

基于石墨烯和聚合物的三维多孔结构的导电聚合物基复合材料（CPCs）具有轻量化、高灵敏度、宽应变检测范围、低成本和可扩展性等优点，已成为可穿戴柔性应变传感器的理想选择。首先，总结了柔性压阻式泡沫应变传感器的裂纹扩展机制、重叠-断开机制和隧穿效应机制；其次，介绍了3种具有多孔结构的石墨烯/聚合物柔性应变传感器的构筑工艺，包括基于聚合物泡沫、基于石墨烯/聚合物混合分散液、基于石墨烯泡沫的方法；然后，综述了通过上述3种工艺制备的柔性多孔应变传感器的传感性能，并列举了其在人体运动监测领域中的应用实例；最后，对基于石墨烯和聚合物的柔性多孔应变传感器面临的挑战和发展前景进行了展望。     

CO2 bubble nucleation in polystyrene: Experimental and modeling studies

Polymer foams are used extensively in a variety of applications. A firm understanding of bubble nucleation is vital to predict foam properties based on process conditions. However, a number of theoretical and experimental challenges have thus far limited progress in this area. We propose the use of a scaling theory to connect nucleation behavior to well understood bulk phase behavior of polystyrene-CO₂ systems, which can be predicted by equations of state, such as the Sanchez–Lacombe equation of state. Scaling theory of nucleation asserts that when the reversible work of critical nucleus formation is properly normalized and plotted against the normalized degree of supersaturation, the resulting scaling curve is insensitive to temperature and the materials being used. Once the form of the scaling function is known, it can be used to predict the nucleation barrier knowing only the initial foaming conditions and calculating only bulk thermodynamic values. Using an extension of diffuse interface theory, we determined the slope of the scaling curve near saturation. This initial slope allows us to constrain the scaling function for better predictions of the reversible work. We also performed a series of experiments to help verify the accuracy of the scaling theory. The scaled free energy barriers determined from our experiments are consistent with the scaling function so constructed, and our theoretical results qualitatively agree with those found previously. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Effect of polymer additives on hydrodynamics and oxygen transfer in a bubble column bioreactor

The influence of polymer additives (polyethylene oxide and polyacrylamide) on the hydrodynamics and oxygen transfer in a bubble column bioreactor was examined. The addition of small amounts of these polymers has been known to cause significant drag reduction in turbulent flow circumstances. The gas hold-up was slightly decreased and the liquid-phase mixing was somewhat enhanced due to the addition of the polymers. The addition of polymer additives brought about a reduction of the volumetric oxygen transfer coefficient by about 40%. In dilute polymer solutions, large bubbles formed by bubble coalescence moved with high rise velocities in the presence of many small bubbles and the bubble size distributions were less uniform compared with those in water. The complicated changes in bubble hydrodynamic characteristics were examined to give possible explanations for oxygen transfer reduction.     

Supercritical CO2-assisted extrusion foaming: A suitable process to produce very lightweight acrylic polymer micro foams

A strategy of CO₂-assisted extrusion foaming of PMMA-based materials was established to minimize both foam density and porosities dimension. First a highly CO₂-philic block copolymer (MAM: PMMA-PBA-PMMA) was added in PMMA in order to improve CO₂ saturation before foaming. Then the extruding conditions were optimized to maximize CO₂ uptake and prevent coalescence. The extruding temperature reduction led to an increase of pressure in the barrel, favorable to cell size reduction. With the combination of material formulation and extruding strategy, very lightweight homogeneous foams with small porosities have been produced. Lightest PMMA micro foams (ρ = 0.06 g cm⁻³) are demonstrated with 7 wt% CO₂ at 130°C and lightest blend micro foams (ρ = 0.04 g cm⁻³) are obtained at lower temperature (110°C, 7.7 wt% CO₂). If MAM allows a reduction of T^foaming, it also allows a much better cell homogeneity, an increase in cell density (e.g., from 3.6 10⁷ cells cm⁻³ to 2 to 6 10⁸ cells cm⁻³) and an overall decrease in cell size (from 100 to 40 μm). These acrylic foams produced through scCO₂-assisted extrusion has a much lower density than those ever produced in batch (ρ ≥ 0.2 g cm⁻³).     

挤出发泡片材褶皱分析及模拟计算

结合气泡成核和生长理论模拟分析挤出发泡片材的褶皱生成过程,采用制品出机头口模后单位宽度的增长速率来反映制品褶皱数量,并通过聚苯乙烯挤出发泡实验验证其准确性。结果表明,实验中制品褶皱数量随口模间隙的减小呈先增多后减少的趋势,与模拟计算结果一致;随零切黏度和松弛时间的增大,制品的褶皱数量减少。     

Analysis of bubble coalescence and determination of the bubble radius for long-chain branched poly(ethylene terephthalate) melt foaming with a pressure balanced bubble-growth model

A pressure balanced bubble-growth (PBB) model was proposed to analyze bubble coalescence and determine the bubble radius for the melt foaming of long-chain branched poly(ethylene terephthalate) (LCB-PET). The key for the PBB model calculation was to determine the bubble inner pressure composed of additional pressure induced by interface tension, and molecular stress, that is, the biaxial tensile stress of the polymer cell wall calculated with the molecular stress function model. LCB-PET was generated by reactive extrusion, and the molecular structure and viscoelasticity were well characterized. Batch melt-foaming experiments with CO₂ were conducted for the LCB-PET. The critical coalescence radius curve was calculated with the PBB model to dynamically describe the bubble coalescence and evaluate the melt foamability. The PBB model was also used to determine the bubble size of LCB-PET foam. Both the evaluation of the melt-foamability and the determination of the bubble radius agreed well the experimental results.     

Microcellular extrusion of PLA utilizing solid‐state nucleation in the gas‐saturated pellet extrusion process

In this study, we explore the use of solid‐state nucleation in polymer pellets as a means to create microcellular PLA foams in extrusion. This is achieved by using gas‐saturated PLA pellets as input to the extruder. Foam density, bubble size, and bubble density is reported and compared with microcellular foams created in the gas‐injection extrusion process. PLA pellet gas concentrations between 17 and 29 mg CO₂/g PLA was found to produce quality microcellular foams in this process. Gas concentrations within this range were achieved by varying methods that included partial saturation, desorption from full saturation, and blending saturated with unsaturated pellets. This gas concentration window that produced microcellular foams was found to be independent of the saturation and desorption process used to achieve the desired concentration. We further compare the pressure drop and pressure drop rate of the gas‐saturated pellet extrusion process showing that similar foams can be produced at pressures orders of magnitude lower than the alternative gas‐injection extrusion processes. Investigations into extrusion pressures support the hypothesis that the gas‐saturated pellet extrusion process utilizes solid‐state nucleation in the feed section of the extruder to achieve high bubble density foams. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Investigation on the cell nucleation and cell growth in microcellular foaming by means of temperature quenching

The cell nucleation and real‐time cell growth with increasing cell growth time in microcellular foaming were investigated by means of temperature quenching in a supercritical CO₂ pressure‐quench process. Samples of uniform size and shape were saturated in a vessel under conditions of 100–180°C and 30 MPa, and then depressurized to the atmosphere in 10 s. After depressurization, these samples were removed from the vessel at prescribed intervals, and immediately immersed in an ice‐water slurry to obtain foamed samples with various cell growth times. It was found that the nucleation density is closely correlated to the gas absorption capacity of the polymer matrix, so that the final cell density should not be adopted as the nucleation density, as done commonly. The change of cell structure and mass density with increasing cell growth time was dominated by gas diffusion behavior, which was strongly influenced by the temperature. The final cell structure was mainly determined by the cell growth step, where gas diffusion played a key role. The final cell density was in direct proportion to the gas remaining in the substrate, which ranged from 6.0 × 10⁹ to 4.7 × 10⁶ cells/cm³. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 163–171, 2004