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The effect of expansion conditions on the batch foaming dynamics of St–MMA copolymer
Abstract
In this study, we synthesized styrene–methyl methacrylate copolymer particles by suspension polymerization process to study the foaming dynamics via visual batch foaming apparatus. The weight ratio of styrene–methyl methacrylate was 53–47. The foaming system consisted of a self-sealing observation cell equipped with two glass windows and a stereo microscope attached with a high-speed digital camera as well as a pressure and temperature controller. The required pentane pressure was supplied by heating a small pentane flask. The synthesized copolymer particles impregnated by pentane and then the foaming dynamics were recorded after a rapid pressure release. The effect of different foaming conditions, such as temperature, impregnation time, and impregnation pressure on the expansion ratio of styrene–methyl methacrylate copolymer was investigated. It was concluded that impregnation pressure, time, and temperature have different effects on the foaming ratio at impregnation pressures lower and higher than 4 bar.
... 25,26 However, there are no appreciable studies about the foaming dynamics of this copolymer, thus we investigated the foaming condition in one composition of St-MMA copolymer in our previous work. 27 In this study, we synthesized St-MMA copolymer particles in three different compositions by suspension polymerization process. As well as the solubility and diffusivity of n-pentane in copolymers was measured via our designed batch foaming apparatus to examine the effect of copolymer composition on the dissolved gas content of n-pentane in different samples. ...
... More details of the copolymerization procedure have been published in our previous works. 1,27,28 Copolymer characterization Particles composition was determined by 1 H-NMR in our previous works. [27][28][29] The particles were dissolved in deuterated chloroform, CDCl 3 ; the spectra of the samples were obtained using a Bru¨ker (Adavance DPX) NMR spectrometer working at 500 MHz. ...
... 1,27,28 Copolymer characterization Particles composition was determined by 1 H-NMR in our previous works. [27][28][29] The particles were dissolved in deuterated chloroform, CDCl 3 ; the spectra of the samples were obtained using a Bru¨ker (Adavance DPX) NMR spectrometer working at 500 MHz. The molar percentage of monomers incorporated to the particles was determined from the peak of OCH 3 group (at 3.6 ppm), and the peaks correlated to the aromatic ring (between 6.5 and 7.5 ppm). ...
In this work, styrene–methyl methacrylate copolymer particles were synthesized by suspension polymerization process with different copolymer compositions. A system was designed to measure the solubility and diffusivity of n-pentane in the synthesized copolymers. The designed system consisted of the self-sealing cell equipped to the pressure and temperature controllers. The synthesized copolymer particles were impregnated by n-pentane and their expansion were recorded visually. Furthermore, the solubility and diffusivity of n-pentane in copolymer particles were measured by the same apparatus. The effect of different foaming conditions on the solubility and diffusivity of n-pentane in the samples were examined. It was concluded that the sorption pressure and temperature have contradictory effects on the solubility and diffusivity of n-pentane in styrene–methyl methacrylate copolymers at different sorption pressures. It was concluded that with methyl methacrylate content increment in copolymer, the diffusivity and dissolved n-pentane content in copolymer were reduced.
... At the following, dissolved gas in the polymer matrix diffuse into the bubbles and bubbles grow. Generally speaking, the bubble nucleation and growth of the bubble play an important role in the polymeric foaming dynamics and has dramatic impact on the final product properties [4][5][6][7][8][9][10]. ...
... In situ observation of the batch foaming dynamics has been developed by Taki et al. [13] and Guo et al. [14] which a polymeric film was placed into the chamber with high pressure and temperature and after rapid pressure drop, foaming process was recorded by high speed camera. More researchers have focused on the in situ observation of the foaming process using supercritical CO 2 and N 2 as physical foaming agent [15][16][17][18][19][20][21] but a few, researchers such Salejova and Kosek [22] and Azimi et al. [4,5] studied the foaming dynamics using pentane as blowing agent. They investigated the effect of some foaming parameters such as impregnation time, temperature and sorption pressure on the foaming dynamics of polystyrene and styrene-methyl methacrylate copolymer, respectively. ...
... To convert the complex modulus, G * (Ω), or linear relaxation modulus, G(t), to w(M), the relaxation spectrum, H(λ), was computed. The basic equation based on the double reptation rule was used to effect the transformation of H(λ) into w(M) [4,31,32]: ...
At the present work, foaming process (bubbles nucleation and growth) of Polystyrene (PS)/n-pentane batch foaming system was studied experimentally and theoretically. Synthesized PS was characterized by rheological measurements and the foaming dynamics was studied using a designed in-situ observation apparatus. The saturation time at the lowest mass diffusivity conditions was determined to ensure that all experiments would be performed at saturation state. Dissolved content and Henry’s constant of n-pentane in PS at foaming conditions were also determined. The effects of temperature and sorption pressure as operation parameters on the foaming dynamics of PS/n-pentane system were investigated and it was found that temperature had a dramatic effect on the foaming dynamics and other parameters such solubility, diffusivity and melt strength were affected by temperature. Moreover, the bubble growth behavior of PS/n-pentane system was simulated and it was compared to the experimental results. To calculate concentration profile in the shell, mass diffusion equations were solved by implicit method with considering gas escape from the outer layer of the viscoelastic shell around the bubble. Furthermore the effect of mass diffusivity and viscosity on the bubble growth behavior was examined simultaneously and it was emphasized that the bubble growth behavior was a mass diffusion controlled phenomenon.
... 25,26 But there were no appreciable studies about the foaming dynamics of this copolymer, thus we investigated the foaming condition in one composition of St/MMA copolymer in our previous work. 27 In this study, we synthesized St/MMA copolymer particles in three compositions by suspension polymerization process to investigate the foaming dynamics via visual batch foaming apparatus and examine the effect of different foaming conditions, like temperature, sorption pressure, and MMA content in copolymer on the foaming ratio of the synthesized copolymer. The rheological behavior of neat copolymers was also investigated to compare the effect of copolymer viscoelastic properties with different compositions on the foaming dynamics of the sample. ...
... More details of the copolymerization procedure have been published in our previous works. 1,27,28 Copolymer characterization Particles composition was determined by proton nuclear magnetic resonance ( 1 H NMR) spectroscopy. The particles were dissolved in deuterated chloroform, the spectra of the samples were obtained using a Bruker Avance DPX NMR spectrometer (Billerica, Massachusetts, USA) working at 500 MHz. ...
... The peaks correlated to the CH 2 and CH groups were used to verify the integration error. 27 Differential scanning calorimetry (DSC) endotherms were recorded using a Netzsch-DSC200 F3 Maia (Germany) for T g determination and was calibrated with indium standard at a heating rate of 1 C min À1 under nitrogen purge. All the experiments were carried out under nitrogen purge at a flow rate of 50 ml min À1 . ...
In this work, styrene/methyl methacrylate (St/MMA) copolymer particles were synthesized
by suspension polymerization process with different copolymer compositions
to study the visual batch foaming dynamics. The visualization system consisted of the
self-sealing observation cell equipped to the pressure and temperature controller. The
synthesized copolymer particles were impregnated by n-pentane, followed by
recording of particle expansion. The cell structure of foams was studied by scanning
electron microscopy. The effect of different foaming conditions on the expansion
behavior of copolymers was examined. It was concluded that sorption pressure and
temperature have contradictory effects on the foaming ratio of the synthesized
copolymers at lower and higher sorption pressures, and the results were confirmed
with the foams’ cell structure. Furthermore, it was shown that, at different temperatures
and pressures, the expansion behavior change dramatically with increasing of
MMA content in the copolymer.
... St-MMA copolymer, PS and PMMA homopolymer particles were synthesized by suspension polymerization method in our research group and many articles were published about synthesis and characterization of these polymers [22][23][24][25][26][27]. In our previous works, suspension copolymerization of styrene-methyl metacrylate (St-MMA) copolymer particles was conducted and the effects of different synthesis parameters were investigated [22,23], subsequently the non-isothermal degradation kinetics of synthesized St-MMA copolymer foams was investigated under nitrogen and oxygen atmospheres [24,25], as well as the foaming condition in one composition of St-MMA copolymer was examined [26]. ...
... St-MMA copolymer, PS and PMMA homopolymer particles were synthesized by suspension polymerization method in our research group and many articles were published about synthesis and characterization of these polymers [22][23][24][25][26][27]. In our previous works, suspension copolymerization of styrene-methyl metacrylate (St-MMA) copolymer particles was conducted and the effects of different synthesis parameters were investigated [22,23], subsequently the non-isothermal degradation kinetics of synthesized St-MMA copolymer foams was investigated under nitrogen and oxygen atmospheres [24,25], as well as the foaming condition in one composition of St-MMA copolymer was examined [26]. ...
The present study focuses on synthesizing styrene-methylmethacrylate (St-MMA) copolymer particles in a batch reactor using suspension polymerization process at different copolymer compositions. Also for further comparisons, the neat polystyrene (PS) and polymethyl methacrylate (PMMA) were synthesized by the same method. The solubility and diffusivity of supercritical carbon dioxide (scCO2) into the synthesized copolymers at two temperatures (393K and 423K) and pressures in the range from 5 to 12 MPa were measured by a magnetic suspension balance. The Sanchez-Lacombe (SL) equation of state was used to estimate the swelling effect of CO2 on copolymers. The results showed that the solubility and diffusivity of CO2 increased with increasing of CO2 pressure and slightly improved with methyl methacrylate (MMA) content in copolymer. As well as the solubility of CO2 in samples decreased with temperature increment and contrary behavior was observed for diffusivity. Fujita, Maeda and Paul’s diffusion models were combined to estimate the diffusion coefficients for the copolymers and neat polymers.
... In the work of Tuladhar and Mackley [36], pentane is impregnated in the polymer melt and then allowed to nucleate and evaporate through a rapid pressure drop to induce phase separation. Effect of foaming parameters such as impregnation time, temperature and sorption pressure on the foaming dynamics of PS and styrene-methyl methacrylate copolymer were studied using pentane as the blowing agent by Salejova and Kosek [37] and Azimi et al. [38,39]. On the same note, Mostafa et al. [40] studied experimentally and theoretically PS/n-pentane batch foaming. ...
This work investigates the peculiarities of using a liquid blowing agent, namely dimethoxymethane (Methylal) to foam a thermoplastic polyurethane (TPU) in the laboratory practice of batch foaming equipment. We preliminarily measured thermodynamic properties of the polymer/gas system relevant to foaming, namely the vapor-liquid pressures at the TPU foaming temperatures. Three different paths were then explored for foaming. First, we used Methylal under its liquid-vapor equilibrium condition, in which both liquid and vapor are present. Secondly, we used Methylal in the liquid state to experiment with liquid foaming strategies. We have observed specific aspects, details, and issues related to the use of liquid blowing agents and devised strategies to deal with them. Finally, we used Methylal as a co-blowing agent together with CO2. In all cases, we examined the impact of pressure, pressure drop rate, and temperature on foam density and morphology.
Overall, liquid foaming has proven to be a viable technique and Methylal an effective blowing agent, especially in cooperation with other gaseous blowing agents, where it significantly improves the expansion ratio of the final product.
... Besides, the TEMs have other advantages, such as the particle sizes, the expansion temperature and the expansion ratio of the TEMs are easily to be controlled [9][10][11][12][13]. However, most of the TEMs are fabricated using acrylonitrile (AN) or methylacrylonitrile (MAN) as the monomers via suspension polymerization [14,15]. These nitrilemonomers are toxic and not friendly to the environment. ...
In this study, we developed a new type of thermo-expandable microcapsules (TEMs) with the anionic/nonionic waterborne polyurethane as the shell and low boiling point agent, n-hexane, as the blowing agent. Thermo-gravimetric analyzer (TGA), laser particle size analyzer, thermo-mechanical analyzer (TMA) and scanning electron microscope (SEM) were used to investigate the blowing agent encapsulation, particle sizes and expansion performances of the TEMs, respectively. Results showed that the nonionic hydrophilic monomer, polyethylene glycol monomethyl ether (MPEG), improved the amount of encapsulation and encapsulation efficiency of n-hexane in TEMs and affected the expansion performance of the TEMs. When the amount of MPEG was 13.4 wt%, the amount of encapsulation and encapsulation efficiency of n-hexane in TEMs could reach 13.2 wt% and 66%, respectively, with the particle size of about 80 nm. 1,4-Butanediol (BDO) enhanced the encapsulation of n-hexane in TEMs. When the amount of BDO was 33.2 mol %, DMPA was 6.7 wt % and MPEG was 13.4 wt %, respectively, the TEMs showed good thermo-expansion performance. The TEMs showed the onset expansion temperature of 206 °C, the peak expansion temperature of 220 °C, and the expansion ratio of 4.1 times, respectively. The successful foaming of the TEMs in epoxy resin indicates that the prepared TEMs have great potentials in foam material applications.
... Expansion ratio was calculated by dividing average diameter of 20 expanded particles at 160°C with a specific heat exposure time to the average diameter of 20 particles before expansion. The expansion rate was calculated by dividing the expansion ratio by time [34]. Thermogravimetric analysis (TGA) was done by means of a thermo-gravimetric analyzer (Polymer Laboratories, TGA 1500, UK). ...
Graphene oxide (GO) was prepared via Hummers' method and reduced by hydrazine monohydrate. GO was modified with (3-methacryloxypropyl)triethoxysilane (MPS) and the obtained GO-MPS nanosheets were reduced by hydrazine monohydrate. The different modified nanosheets were utilized to fabricate microballoons based on methyl methacrylate-triethylene glycol dimethacrylate (TEGDMA) copolymer having a core/shell structure which contained pentane as a blowing agent. To investigate the effect of the presence of nanosheets on the properties of microballoons, gel point occurrence, initial pentane content and the remained pentane during expansion, the expansion properties, and the particle morphology were studied. Kinetic studies showed that GO and GO-MPS accelerated polymerization, whereas the reduced nanosheets exhibited a retardation effect on kinetics. The microballoons containing GO and GO-MPS encapsulated more pentane and effectively retained it during the expansion process. Also, higher pentane content led to lower density of synthesized nanocomposites whereas improved expansion properties were achieved. According to the scanning electron microscopy images, due to retardation effect of reduced graphene oxide (rGO) and rGO-MPS nanosheets, the shell surrounding the hydrocarbon in the microballoons contained more defects which could accelerate penetration of pentane through the shell. This resulted in a less expansion for the microballoons having poly(methyl methacrylate) (PMMA)/rGO or PMMA/rGO-MPS shells compared to those having PMMA/GO or PMMA/GO-MPS shells.
... Expansion ratio was calculated by dividing average diameter of 20 expanded particles at 160°C with a specific heat exposure time to the average diameter of 20 particles before expansion. The expansion rate was calculated by dividing the expansion ratio by time [34]. Thermogravimetric analysis (TGA) was done by means of a thermo-gravimetric analyzer (Polymer Laboratories, TGA 1500, UK). ...
Triethylene glycol dimethacrylate (TEGDMA) crosslinked poly(methyl methacrylate) (PMMA) hollow particles with a core/shell structure containing an inert hydrocarbon (pentane) as a blowing agent were prepared by a suspension polymerization. From the synthesized microspheres, the sieved particles having sizes in the range of 44–149 μm were selected for further investigations and the effect of TEGDMA (as a cross-linker) content on the properties of synthesized particles was studied. In addition, the gel point, shell composition, particle size and its distribution, pentane content, thermal expansion properties, and particle morphology were studied. The results showed that a small change in TEGDMA concentration had a significant influence on the properties of synthesized microballoons. Kinetic studies showed that decreasing in the TEGDMA content shifted the gel point to higher reaction times. According to scanning electron microscopy (SEM) images, the shell thickness increased and particle size decreased with a decreased cross-linker concentration. The results of SEM analysis also proved the decrement of average particle size for lower TEGDMA contents. The expansion behavior of the prepared samples was investigated by means of SEM analysis. The density measurements were performed to study how the density of the particles was affected by cross-linker concentration. All samples were able to be expanded at 160 °C but the particles synthesized with lower cross-linker concentrations exhibited better expansion.
Computational methods for the optimization of synthetic as well as processing parameters for the fabrication of polymeric foams based on styrene and methyl methacrylate are introduced in the current study....
In this work, we investigated the effect of Gelatin on the solubility and diffusivity of normal pentane in poly (vinyl alcohol) (PVA)/Gelatin (Gel) blends. The processibility of PVA was enhanced after adding the gelatin as plasticizer to PVA which gelatin could extend the process widow of PVA with destroying the hydrogen bonding of the polymer matrix. Therefore, the PVA/Gel blends with different concentrations were prepared by simple solution-casting method. The intermolecular suitable interactions in PVA/Gel blends were confirmed using the FTIR, XRD and SEM/EDX analyzes. In the following, the effect of various factors like temperature, pressure and gelatin content on the thermodynamic parameters like specific free volume, solubility and diffusivity was investigated. It was shown that there was a relationship between the specific free volume of the blends with the solubility and diffusivity of normal pentane in blends. The specific free volume of blends was determined by applying the PVT data and the Sanchez-Lacombe (SL) equation of state, in which it was enhanced with increasing of the temperature and gelatin in blends, respectively. Also, the solubility and diffusivity of normal pentane in samples were determined by the magnetic suspension balance (MSB) system. The results presented that the solubility and diffusivity of n-pentane improved with increasing of gelatin content in blend, pressure and temperature decrement, respectively.
In this work, we used three gases (CO 2 , N 2 and normal hexane) for diffusivity measurements in Acrylonitrile butadiene styrene (ABS). We proposed a diffusion model that the diffusion coefficients of each gas in ABS could be estimated from the specific volume of ABS/gas mixture and chemical potential of gas in ABS. The solubility and diffusivity of three gases into ABS were determined by a magnetic suspension balance. The results showed that the solubility and diffusivity of three gases increased with increasing of pressure. Also it was determined that N 2 has a lowest solubility and the highest diffusivity in ABS in all temperature and pressure ranges. It was shown that there was a suitable overlapping between the experimental and predicted values from the proposed model, in which the proposed model could successfully estimate the diffusion coefficient of mentioned gases in ABS in all temperature and pressure ranges.
Thermo-expandable microcapsules (TEMs) with polyurethane as the shell and n-hexane as the blowing agent were synthesized by interfacial reaction between isocyanate-terminated polyurethane prepolymer aqueous dispersion and polyamine chain extender. The synthetic process for the thermo-expandable PU-shelled microcapsules was established. The factors which affected the efficiency for blowing agent encapsulation were investigated by fourier transform infrared spectroscopy (FT-IR), laser particle size analyzer and thermo-gravimetric analysis (TGA). The foaming performances of the microcapsules were characterized by polarizing optical microscope with hot platform (POM) and thermo-mechanical analyzer (TMA). The results showed that PU-shelled thermo-expandable microcapsules were successfully synthesized and had good foaming performance. The NCO/OH ratio was found to have a significant effect on the encapsulation of n-hexane and the appropriate ratio was found to be 3:1. Diethylenetriamine (DETA), which is a polyamine chain extender, was found to be a more suitable chain-extender than other polyamine chain extenders in encapsulation the hexane. PU-shelled thermo-expandable microcapsules containing 25.8% blowing agent was fabricated. The onset expand temperature of TEMs was found to be 206 °C, and the maximum foaming temperature was at 235 °C, according to thermo-mechanical analysis. The volume expansion ratio of TEMs reached 27 times according to the measurement by polarizing optical microscope. The PU shelled TEMs showed good foaming performance in vinyl acetate-ethylene copolymer matrix.
In the present study, two-step foaming procedure with a designed in-situ foaming observation apparatus was used to study the foaming dynamics of styrene-methyl methacrylate (St-MMA) copolymer/nanosilica composites. For this purpose, the St-MMA copolymer was synthesized using suspension copolymerization and its nanocomposites were prepared using solution method. The foaming dynamics was studied through temperature-induced (two-step batch foaming) method. Furthermore, the effects of content, size and surface chemistry of silica nanoparticles on the impregnation process, the foaming dynamics and the final morphology of prepared foams were investigated. The impregnation data showed that the presence of silica nanoparticles in matrix prolonged the impregnation and decreased diffusion coefficient. This effect would be clearer where nanoparticle contents are high and the temperature is quite above Tg. The foaming dynamics results illustrated that the nucleation and foaming rate were enhanced with the nanoparticle addition and its size reduction. At the St-MMA copolymer foaming system, the silica nanoparticles with hydrophilic surface chemistry are more efficient in comparison to hydrophobic nanoparticles where all foaming dynamics and the final microstructure parameters were improved.
In this work, the solubility and diffusivity of supercritical carbon dioxide (scCO2) in Polystyrene (PS) at different temperatures and pressures were studied using a magnetic suspension balance (MSB). Bubble nucleation and growth in PS/CO2 mixture were investigated via visual observation in a batch foaming system at different temperatures and pressures. A firm relationship between bubble nucleation and growth with solubility and diffusivity was observed. The results show that bubble density during the process can be controlled by changing the temperature and the pressure release rate. Furthermore, bubble growth was simulated considering mass diffusion equations and implicit method. The simulation results were in a good agreement with the experimental data. Finally, the effects of diffusivity and zero shear viscosity on the bubble growth were investigated and it was found that the bubble growth is a diffusion controlled phenomenon.
The foaming process involves three important steps: nucleation, bubble growth, and stability. In the present work, the foaming dynamics of styrene–methyl methacrylate (St-MMA) copolymer/n-pentane batch foaming system was studied at nonpressurized condition using rapid temperature increasing method. Synthesized copolymers with different compositions were characterized by proton nuclear magnetic resonance analysis and rheological measurements. An in situ foaming observation apparatus was designed, and the foaming dynamics (nucleation and bubble growth behavior) was studied. Dissolved n-pentane contents in all synthesized copolymer compositions at saturation temperatures, near their glass transition temperatures, were determined. The effects of foaming temperature, copolymer composition, and n-pentane content on the foaming dynamics of St-MMA copolymer/n-pentane system were investigated. The foaming results revealed that the nucleation rate was increased with the increasing foaming temperature, while two other aforementioned parameters were kept constant. The nucleation and bubble growth rate were decreased with increasing MMA units in copolymer composition and increased with dissolved n-pentane content increment in copolymer matrix.
Structured micrometric polystyrene/poly(methyl methacrylate) particles were obtained by suspension polymerization and their expansion behavior was investigated using n‐pentane as blowing agent. The expanded particles presented two distinct microstructures with an outer region (PMMA‐rich shell) composed by cells of about 10 µm while the center of the particle (PS‐rich core) had much larger cells (50–100 μm). The core–shell particles did not expand at 100°C meaning that the PMMA shell hindered the expansion of the particles. Maximum expansion was dependent on the PMMA concentration and also on the heating temperature and the increase in the PMMA molar mass led to a delay in the onset of the process. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 4521–4527, 2013
The molecular weight distribution (MWD) affects characteristic properties of polymers. Especially, rheological data depend on the MWD of the investigated polymer. Models combining rheological data with the MWD are described by
(1)
Numerical and analytical methods are developed to invert the double reptation mixing rule to determine the molecular weight distribution (MWD). An analytic method involving Mellin transforms is developed for the case of a single exponential monodisperse relaxation function. A general analytic solution for the MWD is generated for a step‐function monodisperse relaxation function. Numerical methods are developed for more general multiple time constant monodisperse relaxation functions. Both analytical and numerical methods are simple, robust, and capable of appropriately handling error‐infected experimental data. The power‐law relaxation modulus associated with broad MWD commercial polymer is analytically inverted to generate the corresponding molecular weight distribution. MWDs calculated from rheological data for polybutadiene and polypropylene are in close agreement with the corresponding GPC data and are very sensitive to small amounts of high molecular weight material present. The fundamental origins of this sensitivity lie in the intrinsically nonlinear nature of the dependence of rheological properties on molecular weight. The quality of the results suggest that the ‘‘double reptation’’ mixing rule captures an essential feature of the physics of entangled polydisperse polymeric systems.
Using UV light as the energy source and polystyrene- (PS-) or polymethyl methacrylate- (PMMA-) macroinitiators with active aromatic or aliphatic thiyl end groups, PS-PMMA and PMMA-PEA (poly-ethyl acrylate) block copolymers were synthesized. The molecular weights of both block copolymers increased with increasing reaction time. The reactivity of macroinitiators depended on the type of thiyl groups and monomer and not on the length of the polymer chain. The most reactive were macroinitiators containing resonance stabilized non-substituted or substituted aromatic end groups. The decomposition of the macroinitiators took place over the formation of the thiyl radical and macroradical. The bond length, the bond dissociation energy, and the bond order of macroradical end groups were calculated. The most reactive monomer was ethyl acrylate; the less reactive was styrene. The structure, the molecular weight, and the Tg of the styrene-acrylate block copolymers were determined. The PMMA/PEA block copolymer had two of block's Tgs, the first at 105°C, the second at −24°C, and a third at 16°C which probably represents contacting segments.
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.
A review of the literature was conducted in search of an appropriate kinetic model applicable to the polystyrene foam decomposition phenomena encountered in the lost foam casting process. A brief review of the models describing the physical process of foam degradation is also presented. During this investigation, various kinetic models describing polystyrene thermal decomposition in the plastics recycling process have been reviewed. The review indicates that the process conditions in which these models were developed were very different from the casting process conditions, and hence no one model could be suitably employed for the latter. The authors suggest that a more rigorous and intrinsic kinetic experiment depicting the actual foundry conditions is necessary to develop a model that describes the foam degradation kinetics.
Free radical suspension copolymerization of styrene (St) with methyl methacrylate (MMA) in the presence of n-pentane was investigated. The batch polymerization was performed in a stirred reactor via a two-stage process. First, free radical suspension polymerization of St and MMA in aqueous media was carried out at about 80—90°C with the aid of a monofunctional initiator to the monomer conversions up to about 70%. Second process, called impregnation stage, consisted of a high temperature—high pressure cycle (110—120°C and 10 bars) in which the blowing agent was charged in the reactor and polymerization was carried out with the aid of a high temperature initiator. Fine particles of micron sizes of St/MMA copolymer were synthesized by manipulation of some experimental parameters governing the copolymerization system. Polymerization was carried out at different agitation rates, suspending agent and aqueous phase initiator concentrations as well as emulsifier amounts, while keeping constant the MMA/St ratio. To reach a desired bead size, the above parameters were optimized using the Taguchi method for experimental design and the relative importance of the mentioned parameters was analyzed. Particles with a spherical shape of 250—350 μm were formed. The obtained copolymers were also characterized in terms of molecular weight, polydispersity index, copolymer composition, morphology of the polymer beads, thermal behavior, and particle size and particle size distribution.
The pressure–volume–temperature (PVT) data for polymer/gas solutions is an important fundamental property of which accurate measurement has not been reported until recently. The diffusivity, solubility and surface tension are critical physical properties of polymer/gas systems for understanding and controlling polymer processing such as foaming, blending, extraction reaction and so on. However, the determination of these properties relies on accurate PVT data as a prerequisite. In this study, we have developed a new methodology for measuring the PVT properties of polymer melts saturated with high-pressure gas at elevated temperatures. This paper presents a description of the methodology, including the experimental apparatus design and data analysis. A case study on neat polypropylene (PP) density measurement and determination of PP/CO2 solution volume swelling was presented to elucidate and verify the methodology at high-pressure and high-temperature conditions.
Copolymerization of styrene (St) and methyl methacrylate (MMA) was carried out using 1,1,2,2-tetraphenyl-1,2-bis (trimethylsilyloxy) ethane (TPSE) as initiator; the copolymerization proceeded via a “living” radical mechanism and the polymer molecular weight (Mw) increased with the conversion and polymerization time. The reactivity ratios for TPSE and azobisisobutyronitrile (AIBN) systems calculated by Finemann–Ross method were rSt = 0.216 ± 0.003, rMMA= 0.403 ± 0.01 for the former and rSt= 0.52 ± 0.01, rMMA= 0.46 ± 0.01 for the latter, respectively, and the difference between them and the effect of polymerization conditions on copolymerization are discussed. Thermal analysis proved that the copolymers obtained by TPSE system showed higher sequence regularity than that obtained by the AIBN system, and the sequence regularity increased with the content of styrene in copolymer chain segment. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1474–1482, 2001
September 24, 2006
Summary: In this work, we address the industrially relevant problem of the foaming of expandable polystyrene (PS) impregnated by pentane as a traditional down-stream processing in the suspension polymerization of styrene. Once the polystyrene foam is formed by means of a proper foaming agent, e.g., pentane or fluoro- or chloro-hydrocarbons, the blowing agent diffuses out from the cellular structure. Environmental efforts call for the reduced consumption of blowing agents. The dynamics of foaming of polystyrene particles was recorded video-microscopically in our laboratory as the sequence of images of expanding particle located in the small pressure cell placed under the microscope with sufficient depth of focus. The amount of pentane sorbed in PS was controlled by the length of the impregnation period and was determined independently by gravimetric measurements. Strong dependence of the structure of the produced foam and of the foaming dynamics on the amount of sorbed pentane, temperature and particle size is reported and explanations for some observed foaming phenomena are provided.
The thermal degradation of MMA–St random copolymer and EPS lost foams was studied by thermal gravimetric analysis (TGA) oxygen atmospheres and the results were compared with nitrogen one. The stabilizing effect of oxygen on thermal degradation of both foams and consequently possible mechanism was investigated. The activation energy was calculated under nitrogen and oxygen atmospheres by the Flynn–Wall–Ozawa method as a reliable way of determining the kinetic parameters. In this study the correlation method and isokinetic relationship (IKR) were used to estimate a model-independent pre-exponential factor (lnA) corresponding to a given degree of conversion under both atmospheres.
Methylmethacrylate-styrene (MMA-St) random copolymer was synthesized by suspension copolymerization. The thermal degradation of MMA-St copolymer and EPS lost foams was studied by non-isothermal thermal gravimetric analysis under nitrogen purge. Thermal decomposition behavior of MMA-St copolymer lost foam was examined and compared with EPS. It was found that EPS foam starts to decompose at higher temperatures than MMA-St copolymer foam in all heating rates. The apparent activation energy was calculated by the Flynn-Wall-Ozawa method. It has been concluded that the model fitting methods unable to reveal the complexity of the pyrolysis process and the model-free methods can be suggested as a reliable way of determining the kinetic parameters.
Time-dependent, purely radial, incompressible, irrotational, extensional flow around a spherical bubble growing or collapsing in viscolastic liquid is analyzed by means of a new integral constitutive equation of BKZ type designed for any mixture of extensional and shear flow. It requires the history of the relative deformation Finger tensor, which is readily evaluated in the spherosymmetric flow with its straight pathlines. The continuity equation relates radial velocity simply to bubble wall speed, and the momentum equation reduces to a nonlinear integrodifferential equation for the evolution of the bubble radius. This equation is discretized by means of linear basis functions on finite elements of time and Galerkin's weighted residual method; the set of nonlinear algebraic equations is solved by Newton iteration, which converges quadratically up to a Deborah number (extension rate at bubble wall times average relaxation time) of 60. Beyond that value the convergence rate slows. Given as initial condition, a sharp change in the difference between pressure in the bubble and ambient pressure, can excite an oscillatory solution. With the constitutive equation fitted to independent measurements of stress in small amplitude sinusoidal oscillations and in steady shear, computed time courses agree with Pearson and Middleman's [1977] experiments on bubble collapse in hydroxypro-pylcellulose and polyacrylamide solutions (which provide only a limited test of the constitutive equation, however).
In this paper, we undertook an experimental and theoretical analysis of the pressure-drop behaviors of a batch foaming system with a visualization window that was designed for microcellular foaming simulation. A polystyrene (PS)-CO2 system was used in the experiment and analysis. The maximum pressure-drop rate achievable was 2.5 GPa/s from the designed system. Some experimental simulation results at high pressure-drop rates and at low pressure-drop rates are also discussed. We observed that the application of a higher pressure-drop rate results in a higher cell density (and, thereby, a smaller cell size) for plastic foams. This confirms that the pressure-drop rate is one of the most important parameters to control the cell density of plastic foams. In addition, the results show that the content of the blowing agent (CO2) dissolved into a given polymer has a significant effect on bubble nucleation and growth.
Effects of polydispersity on Theological properties of entangled polymers are analyzed. A number of models of tube renewal are discussed and compared with each other and with experiments. A theory incorporating reptation, tube renewal, and fluctuations in the tube length into a general description of stress relaxation is developed. Dynamical moduli were calculated for monodispersed and bidispersed systems and compared with experiments. The product of viscosity and recoverable shear compliance is predicted to be of the order of the longest relaxation time of the higher molecular weight component with a weak dependence on the relative volume fraction of the binary mixture for a large enough concentration of longer molecules.
This paper discusses the research conducted to achieve an accurate bubble-growth model and simulation scheme to describe precisely the bubble-growth phenomena that occur in polymeric foaming. Using the accurately measured thermophysical and rheological properties of polymer/gas mixtures (i.e., the solubility, the diffusivity, the surface tension, the viscosity, and the relaxation time) as the inputs for computer simulation, the growth profiles for bubbles nucleated at different times were predicted and carefully compared to experimentally observed data obtained from batch foaming simulation with online visualization. A polystyrene/carbon dioxide (PS/CO2) system is used herein as a case example. It was verified that the cell-growth model is capable of thoroughly depicting the growth behaviors of bubble nuclei nucleated under varying processing conditions without using any fitting parameter. These results indicate that the established model accounts for most of the physics behind the bubble-growth phenomena. Furthermore, the effects of the aforementioned thermophysical and rheological parameters on the cell-growth dynamics were demonstrated by a series of sensitivity studies.
Living radical polymerization of methyl methacrylate (MMA) through the use of benzyl diethyl dithiocarbamate (BDC) was studied. The aim was to investigate the role of the concentration, BDC-to-MMA mol ratio, and reaction time upon the molecular weight, polydispersity, and conversion of the product. It was found that the molecular weight and the conversion increase with increase of the concentration at the expense of low polydispersity. The reaction time also played a significant role, especially at a relatively long reaction time where molecular weight, polydispersity, and conversion increased with increasing reaction time. In terms of the mol ratio effect, it was found that there was a critical mol ratio for maximum conversion. The results indicate that the kinetics of polymerization of MMA through the use of a BDC inifeter is different from that in the presence of a conventional initiator. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 938–944, 2000
A new thermally expandable microcapsule was developed for use with foaming polypropylene (PP) by injection molding and extrusion processes at operating temperatures above 200°C. The microcapsule consists of a blowing agent as the core and a shell polymer. The rheological properties of the shell polymer were controlled by a crosslinking agent to design the expandability and shrinkage. The effects of rheological properties on the expandability and the surface appearance of foam products were thoroughly investigated. It was found that storage modulus G′ and tan δ significantly affected the expandability and shrinkage and were controllable through crosslinking polymerization. Visual observation of batch foaming, rheological measurement, and experiments of foam injection molding and extrusion elucidated the existence of the optimal degree of crosslinking that could realize more than 30% density reduction while maintaining a smoothsurface at PP foam injection molding and extrusion. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers
Transport models of diffusion-induced bubble growth in viscous liquids of finite and infinite extent are developed and evaluated. Results from the present study are compared with results from the often-cited papers by Amon and Denson (1984) and Arefmanesh et al (1992) and found to be in good agreement. Predictions for the bubble radius and pressure from the finite- and infinite-liquid models are compared over a range of conditions. As anticipated, predictions from the two models coincide at early stages of the growth process, and differ at late stages of the growth process when the equilibrium bubble radius Is approached for the finite-liquid model. Agreement between the two models at intermediate stages is observed only for relatively low growth rates.
An experimental and theoretical study was carried out to achieve a better understanding of bubble dynamics in foam extrusion through a converging die. For the experimental study, a number of converging channels were constructed of aluminum, with glass windows on both sides. Bubble dynamics in the flow channel were recorded on movie film as a gas-charged molten polymer was extruded. The dies had various converging angles (30, 45, 60, 90, and 150 degrees), and the polymer was polystyrene. As blowing agent, sodium bicarbonate (generating CO2) was used. It was found that the gas bubbles moving along the centerline of the channel grow initially at the upstream end of the die, and then start to collapse as the gas-charged molten polymer approaches the exit plane of the die. In order to help interpret the experimental results, a theoretical analysis was made of bubble dynamics in a converging channel, in which a thread-like bubble was assumed to flow along the centerline of the converging channel and the Coleman-Noll second-order fluid model was assumed to describe the rheological behavior of the polymer melt. Some mathematically convenient simplifying assumptions not-withstanding, the theoretical analysis corroborates the experimental observations. The practical significance of the present investigation is discussed in connection with controlling the cell structure in extruded foam products.
Nuclear magnetic resonance (NMR) spin–lattice relaxation times (T1) in various polyethylene and polypropylene resins were measured at 20 MHz and at temperatures of 130–490 K. At each temperature and for all resins, only a single value of T1 was found, which was consistent with the occurrence of rapid spin diffusion throughout the protons attached to the polymer chains. The data were analyzed for the estimation of activation energies corresponding to molecular motion causing spin–lattice relaxation. Two well-defined minima were found for loge(T1) plotted as a function of temperature for all of the polypropylene resins. Single very broad minima were found for all of the polyethylene samples. In contrast, the free induction decay signals from all of the resins following single radio-frequency pulses were observed to contain a rapidly decaying component followed by a much more slowly decaying signal. These components were used to estimate the amount of rigid component present in the solid resins at room temperature. Samples of one high-density polyethylene and one low-density polyethylene were irradiated with radiation up to a 500-kGy dose to examine the effects of crosslinking on the NMR relaxation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 572–584, 2002; DOI 10.1002/polb.10116
In this article, the foaming processes of polyimide foams and its reinforced foams were observed by a self-made visualization device at different heating rates ranging from 10°C/min to 120°C/min. Contributing factors such as chemical structure of polyimide, fillers, and heating rate were investigated to determine the effects on the inflation onset temperature and morphological change of polyimide foam precursor powders. The results showed that the powder might grow into a single bubble mesostructure at a lower heating rate or a multibubble mesostructure at a higher heating rate. Because of the filling of reinforcing fillers, the inflation morphology of reinforced polyimide foam precursor powders show a different change trend with the increase of temperature compared to the pure polyimide foam precursor powders. For all kinds of polyimide foam precursor powders investigated in this article, the inflation morphologies showed a similar variation trend with different heating rates, and the final inflation degrees were slightly different. The inflation onset temperatures of all polyimide foam precursor powders studied decreased with increasing heating rate. POLYM. COMPOS., 2010. © 2008 Society of Plastics Engineers
An experimental study was carried out to investigate the flow behavior of gas-charged molten polymers in foam extrusion. For the study, a rectangular slit die with glass windows was constructed to permit visual observations, from the direction perpendicular to flow, of the dynamic behavior of gas bubbles when a gas-charged molten polymer flows between two parallel planes. Pictures were taken of gas bubbles in the flow channel with the aid of a camera attached to a microscope, and these were later used to determine the position at which gas bubbles start to grow. Using three melt pressure transducers mounted on the short side of the rectangular slot, pressure distributions were measured along the longitudinal centerline of the die. The polymeric materials used were high-density polyethylene and polystyrene, and the chemical blowing agents used were a proprietary hydrazide which generates nitrogen, and sodium bicarbonate which generates carbon dioxide. It was observed that the gas-charged molten polymer shows a curved pressure profile as the melt approaches the die exit, whereas the polymer without a blowing agent shows a linear pressure profile. The visual observations of the bubble growth in the flow channel, together with the pressure measurements, permitted us to determine the bubble inflation pressure, often referred to as the critical pressure for bubble inflation. It was found that the critical pressure decreases with increasing melt extrusion temperature, and increases with increasing blowing agent concentration. It was also found that the bulk viscosity of gas-charged molten polymers decreases with increasing blowing agent concentration and with increasing melt temperature. A general remark is made concerning the precaution one should take when an Instron rheometer is used for determining the bulk viscosity of gas-charged molten polymers.
An experimental study was carried out to gain a better understanding of the dynamic behavior of gas bubbles during the structural foam injection molding operation. For the study, a rectangular mold cavity with glass windows on both sides was constructed, which permitted authors to record on a movie film the dynamic behavior of gas bubbles in the mold cavity as a molten polymer containing inert gas was injected into it. Injection pressure, injection melt temperature, and mold temperature were varied to investigate the kinetics of bubble growth (and collapse) during the foam injection molding operation. It was found that the processing variables (e. g. , the mold temperature, the injection pressure, the concentration of blowing agent) have a profound influence on the nucleation and growth rates of gas bubbles during mold filling. Whereas almost all the theoretical studies published in the literature deal with the growth (or collapse) of a stationary single spherical gas bubble under isothermal conditions, in structural foam injection molding the shape of the bubble is not spherical because the fluid is in motion during mold filling. It is suggested that theoretical study be carried out on bubble growth in an imposed shear field under nonisothermal conditions.
A method for determining the molecular weight distribution (MWD) of a polymer melt has been developed using the dynamic elastic modulus (G'), plateau modulus (G), and zero shear complex viscosity (η). The cumulative MWD was found to be proportional to a plot of (G'/G)0.5vs. measurement frequency (ω). Frequency (ω) was found to be inversely proportional to (MW)3.4, as expected. Results were scaled to absolute values using the empirical relationship η ∝ (M̄w)3.4, where M̄w is the weight-average MW. M̄w, M̄n (number-average MW) and M̄w/M̄n calculated from melt measurements were found to agree with size exclusion chromatography usually well within 10 percent for broad and bimodal distribution samples. M̄w/M̄n tended to be approximately 20 percent higher for narrow distribution samples (M̄w/M̄n < 1.2) because we did not account for a finite distribution of relaxation times from a collection of monodisperse polymer chains. We also did not account for the plasticizing effect of short chains mixed with long ones which caused peak positions to be closer together for Theological vs, size exclusive chromatography (SEC) determinations of MW for bimodal distribution blends.
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.
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.
Modern theories of the dynamics of concentrated polymeric liquids have not yet accounted for the effects of polydispersity to a sufficient extent. In order to approach quantitatively the problem of polydispersity, a model is proposed here which is based on the concept that the “tube” of constraints around a chain enlarges as the relaxation proceeds. Predictions of linear viscoelasticity obtained with this model compare favorably with experimental results on homopolymeric blends reported in the literature. However, the theory is limited to the case of very long chains and it embodies an arbitrary, if plausible, closure assumption in the self-consistency scheme. Thus, quantitative agreement remains incomplete.
An experimental study is described of the formation and growth of gas bubbles in crosslinked elastomers. A critical condition for bubble formation is found to hold in most cases: The gas supersaturation pressure must exceed 5G/2, where G is the shear modulus of the elastomer. The kinetics of bubble growth are shown to be in good accord with a simple diffusion‐controlled growth relation for a variety of gases, elastomers, temperatures, and pressures. The number of bubbles depends strongly upon the degree of supersaturation above the critical level. This effect is attributed partly to kinetic factors and partly to the presence initially of internal holes of a range of sizes.
Transport models of diffusion-induced bubble growth in viscoelastic liquids are developed and evaluated. A rigorous model is formulated that can be used to describe bubble growth or collapse in a non-linear viscoelastic fluid, and takes into account convective and diffusive mass transport as well as surface tension and inertial effects. Predictions for bubble growth dynamics demonstrating the importance of fluid elasticity are presented. These predictions indicate that for diffusion-induced bubble growth in viscoelastic liquids, the lower bound for growth rate is given by growth in a Newtonian fluid and the upper bound by diffusion-controlled growth. The influence of non-linear fluid rheology on bubble growth dynamics is examined and found to be relatively minor in comparison to fluid elasticity. It is shown how previously published models employing various approximations can be derived from the rigorous model. Comparisons of predicted bubble growth dynamics from the rigorous and approximate models are used to establish the ranges of applicability for two commonly-used approximations. These comparisons indicate that models using a thin boundary layer approximation have a rather limited range of applicability. An analysis of published experimental bubble growth data is also carried out using appropriate transport models.
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.
The visual observations of batch and continuous foaming processes were conducted to understand the bubble nucleation and bubble growth behaviors in polymers. The batch foaming was performed using a newly developed high-pressure cell, where two sapphire windows were equipped on the walls so as to observe the early stage of bubble nucleation and growth behaviors with the help of a high-speed digital camera and microscope. In the batch process, homo polypropylene was foamed at different pressure release rates using CO2 as a physical blowing agent to see the effects of operating condition on the bubble nucleation and growth rates. The in situ observation could identify that (1) the bubble nucleation and growth occur simultaneously, (2) the influence region, where the nucleation was suppressed, exists around bubbles, and (3) the nucleation rate and the growth rate increase as the pressure release rate increases. The continuous foaming was performed using a different visualization unit, which consists of an autoclave and an extrusion slit-die with quartz windows. It was found that the nucleation mechanism in the continuous foaming, i.e., extrusion foaming, was different from that of batch foaming. In the continuous extrusion foaming, the nucleation could be induced by flow and/or shear stress, and by cavitations brought by the surface roughness of the wall.
A numerical simulation for polymeric foaming extrusion processes was conducted. Combining classical nucleation rate and bubble growth models with a non-Newtonian fluid model of a flow, a simultaneous bubble nucleation and growth behavior in a flow field was simulated. Simulation results were compared with the experimental data obtained by visual observations at a foaming extruder, where a polypropylene resin was physically foamed. The effects of physical parameters in foaming model on bubble size and number density calculation were intensively examined by sensitivity analysis.
A review of physical and kinetic models of thermal degradation of expanded polystyrene foam and their application to the lost foam casting process journal of analytical applied pyrolysis
- P Kannan
- J J Birnacki
- D P Visco
Kannan P, Birnacki JJ and Visco DP. A review of physical and kinetic models of
thermal degradation of expanded polystyrene foam and their application to the lost
foam casting process journal of analytical applied pyrolysis. J Anal Appl Pyrolysis
2007; 78: 162-171.
Microcellular sheet extrusion system process design models for shaping and cell growth control
- D F Baldwin
- Cbp Nam
- P Suh
Baldwin DF, Nam CBP and Suh P. Microcellular sheet extrusion system process design
models for shaping and cell growth control. Polym Eng Sci 1998; 38: 535-705.
Nuclear magnetic relaxation in polyolefin resins
- P N Songkhla
- J Wootthikanokkhan
Songkhla PN and Wootthikanokkhan J. Nuclear magnetic relaxation in polyolefin
resins. J Polym Sci, Part B: Polym Phys 2002; 40: 572-584.