The effect of copolymer composition,gas content,and temperature on the bubbles nucleation and growth of styrene–methyl methacrylate copolymer/ n -pentane foaming process

Abstract

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.

Keywords

Foaming dynamics St-MMA copolymer visualization cell density bubble growth

Introduction

Polymeric foams have a porous structure composed of gaseous cells surrounded by a polymeric matrix. The low density and high cell density of these materials are more effective compared to the other properties.^1
–3 Generating foams using a physical blowing agent consists of saturating the polymer matrix with a blowing agent at a certain sorption temperature and pressure. The saturated polymer matrix is then subjected to a sudden thermodynamic instability (temperature increase or pressure drop), which causes the saturated gas to escape. Then, dissolved gas molecules in the polymer matrix diffuse into the nucleated bubbles and take them to grow up. In general, the foaming process involves three important steps: bubbles nucleation, growth, and stability.^4
–6 It is well-known that the cell density, cell size, cell size distribution, and foam density have important effects on the final property of prepared foam. Subsequently, a basic understanding of the relationships between the processing conditions and microstructure during foaming process (the number of nucleated bubbles and bubble size distribution) remains important to control the final microstructure of foams and consequently producing foams with high useful properties.^7

–10

Rapid pressure drop method is mostly used to study the foaming process,^11

–14 but some researchers such Iliev et al.¹⁵ and Emami et al.¹⁶ used temperature increasing method at nonpressurized conditions to examine the foaming dynamics. Generally, the rapid pressure drop method has been used more than temperature increasing method to study the foaming dynamics. Among processing parameters, sorption pressure and pressure drop rate have defined effect in each foaming system process, in which the nucleation and bubble growth rate increase with increasing sorption pressure and suddenly pressure drop, but temperature has no similar effect on the foaming dynamics in different foaming systems.¹⁷

Some researchers have used supercritical CO₂ (ScCo₂) and ScN₂ as physical blowing agents to study the in situ observation of the foaming dynamics (nucleation and bubble growth),^18

–22 but a few researchers such as Salejova and Kosek,²³ Azimi et al.,⁶ and Kasiri et al.⁷ have studied the foaming dynamics of impregnated particles using pentane as a blowing agent. It is noted that nucleation phenomenon and bubble growth behavior have not been investigated deeply in the foaming system using pentane as the blowing agent compared to ScCO₂ and ScN₂. Since sorption pressure in batch foaming system using n-pentane as the blowing agent is not too high compared to ScCO₂ and ScN₂, pressure drop rate will not be too high. So, according to classical nucleation theory, nucleation rate is low, and the prepared foams by this foaming system have lower cell density compared to the high-pressure foaming systems.^6,7,23

To increase the cell density of prepared foams by n-pentane, temperature increment method at nonpressurized condition was used in this work. So, styrene–methyl methacrylate (St-MMA) copolymers were synthesized by suspension copolymerization process to investigate their foaming dynamics (bubbles nucleation and growth behavior) with n-pentane as the blowing agent via a batch foaming visualization apparatus. The effect of foaming temperature, n-pentane gas content, and copolymer composition on the foaming dynamics was also examined, which has not been investigated before.

Experimental

Materials

MMA and St monomers (Dae-Jung Chemicals & Metals Co., Ltd., Gyeonggi-do, South Korea) were used to synthesize St-MMA copolymer. Benzoyl peroxide (BPO) as a radical initiator; polyvinyl alcohol (PVA) with a molecular weight of 72,000 g mol⁻¹, hydroxyethyl cellulose (HEC), and polyvinylpyrolidone (PVP) with a molecular weight of 360,000 g mol⁻¹ as drop stabilizers; and potassium persulfate (K2S2O8) as an aqueous phase initiator were supplied by Merck (Darmstadt, Germany). Tricalcium phosphate (TCP) and sodium dodecylbenzene sulfonate (DBSNa) as suspending agents were supplied by Sigma-Aldrich (Sigma-Aldrich Chemie Gmbh, Munich, Germany). Physical blowing agent in foaming experiments was n-pentane with 99% purity (CARLO ERBA Reagents, Italy).

Suspension copolymerization

The St–MMA particles were synthesized in three copolymer compositions using a batch suspension polymerization according to our previous works.^1,5

–8,24 To identify the synthesized copolymers with different compositions, Co1, Co2, and Co3 abbreviations were used for St–MMA with 70/30, 53/47, and 30/70 feed ratios (wt%), respectively. First, the mixture of PVA, TCP, PVP, HEC, DBSNa, and K₂S₂O₈ with distilled deionized water in a certain amount was prepared in the reactor under stirring rate of 280 r min⁻¹ for at least a few hours to produce a homogeneous mixture.^1,5

–8,24 Then, the mixture of monomers which involved St and MMA monomers and BPO at a required amount^6,24 was stirred for 30 min and transferred to the reactor. Then, the reactor was heated to the reaction temperature (80°C) and held for 7 h. After completion of the reaction, the reactor was cooled to 35°C, and the reaction mixture was brought out, washed with water, dried, and sieved.

Copolymer characterization

Composition of the synthesized copolymers was determined using the proton nuclear magnetic resonance (H-NMR) analysis of the samples obtained with a Bruker (Avance DPX) NMR spectrometer working at 500 MHz according to our previous studies. The molar percentage of monomer incorporated to the particles was determined using equation (1):^6,8,24

\frac{m_{1}}{m_{2}} = \frac{\frac{A_{1}}{5}}{\frac{(A_{2} - A_{1} \times \frac{8}{5})}{8}}

where m ₁ and m ₂ are the mole fractions of St and MMA units in copolymer, respectively. A ₁ is the integrated area of the phenyl protons of St unit at 6.5–7.5 ppm, and A ₂ is the integrated area of all the protons of the copolymer.^8,24

In this work, the viscoelastic and rheological measurements were used to provide information on molecular weight (M _w) and molecular weight distribution of synthesized copolymers according to our previous works.^5,6,24 The rheological measurements of synthesized copolymers were conducted at T = 200°C, angular frequencies (0.04–625 s⁻¹), and strain of 1% under nitrogen atmosphere using a Physica MCR 301 dynamic rheometer (Anton Paar, Graz, Austria) with parallel-plate geometry.

Foaming procedure

A batch foaming observation system which was designed and explained clearly in our previous work was used to conduct foaming experiments.^5
–7 Copolymer sheets with a thickness of 200 μm were prepared by Brabender Polystat 200 T hot press (Brabender Co., Germany) and were placed into the designed chamber (Figure 1(a)). The samples were heated up to the required temperature, and subsequently, n-pentane blowing agent was inserted into sealed chamber from pentane flask. The copolymer sheet was impregnated by n-pentane in certain saturation pressure, temperature, and time. After impregnation period, the temperature of system was decreased quickly. When the temperature reached below the boiling temperature of n-pentane, the sample was taken out from the chamber.

Figure 1.

The schematic view of the designed (a) batch impregnation system and (b) foaming visualization system.

At the next step, the prepared disk with a diameter of 5 mm through impregnated and cooled sheets was placed into hot stage with a certain temperature, and the foaming process was started and recorded by a digital camera attached to the stereo microscope (Figure 1(b)). Each foaming experiment was carried out more than three times to examine the repeatability of the results. The resulting in situ visualization data of such enumeration of nucleated bubbles and their radius were analyzed using Bell View software (Bell, Italy) to obtain the bubble density and bubble growth profiles at each experimental condition.

Dissolved gas content measurement

The designed chamber according to Figure 1(a) was also used to measure dissolved n-pentane content in copolymers. The copolymer sheets with a thickness of 200 μm were prepared and weighted (m ₁). After certain time (more than 3 h), they were impregnated by n-pentane at the specified temperature and sorption pressure. Then, the chamber was cooled quickly, and as soon as the temperature decreased below the boiling temperature of n-pentane, the sheets were brought out from the chamber and weighted (m ₂). The dissolved content of n-pentane in sample was calculated using equation (2).^1,5

% n -pentane = \frac{(m_{2} - m_{1})}{m 1} \times 100

Results and discussion

Characterization of synthesized copolymers

Figure 2(a) to (c) shows typical H-NMR spectra of St-MMA copolymers at different feeding ratios for Co1, Co2, and Co3 samples. Peaks between 6.5–7.3 ppm and 3.6 ppm corresponds to C₆H₅ and OCH₃ groups, respectively. The peak occurring at 2.8 ppm was assigned to the OCH₃ group of poly(methyl methacrylate) bonded to the polystyrene segment, which was absent in the H-NMR spectra of both relevant homopolymers.^8,24 Compositions of the copolymers were evaluated using H-NMR spectroscopy and are presented in Table 1. As it can be seen, the calculated copolymer compositions are close to the monomer feed ratios.

Figure 2.

H-NMR spectra of the synthesized St-MMA copolymer which St-MMA weight ratio in feed is (a) 70/30, (b) 53/47, and (c) 30/70.

Table 1.

Compositions of synthesized copolymers calculated from H-NMR spectra.

Monomer feed ratio (St/MMA)	70/30	53/47	30/70
Copolymer composition (St/MMA)	68.05/31.95	50.67/49.33	28.82/71.18

H-NMR: proton nuclear magnetic resonance; St-MMA: styrene–methyl methacrylate.

Complex viscosity (η*) and storage modulus (G′) of synthesized copolymers versus angular frequency are shown in Figures 3 and 4, respectively. Corresponding molecular weight and its distribution determined by rheological experiment are presented in Table 2. As it is clear, the complex viscosity and storage modulus of copolymer are increased with increasing MMA content, which could be attributed to the higher molecular weight of copolymers containing higher amount of MMA (Table 2). The zero-shear rate viscosity (η ₀) for all copolymer compositions was calculated through rheological experiments using Carreau–Yasuda model and Cox–Merz rule,^25,26 which was 8.6 × 10³, 8 × 10⁴, and 7.8 × 10⁵ for Co1, Co2, and Co3, respectively.

Figure 3.

Complex viscosity (η*) of synthesized St-MMA copolymers versus angular frequency at 200°C. The lines represent nonlinear regression using the Carreau–Yasuda model.

Figure 4.

Storage modulus (G′) of synthesized St-MMA copolymers versus angular frequency at 200°C. The lines are drawn to guide the eyes.

Table 2.

Molecular weights and polydispersity index of St-MMA copolymers.

Sample	M _n (g mol⁻¹)	M _w (g mol⁻¹)	PDI
Co1	279,200	664,800	2.381
Co2	416,600	841,300	2.019
Co3	629,900	1,189,000	1.888

PDI: polydispersity index; St-MMA: styrene–methyl methacrylate.

Solubility measurements of n-pentane in St-MMA copolymers

Figure 5 shows the amount of impregnated n-pentane into copolymer sheets versus impregnation time at 100°C and sorption pressure of 4 bar. Since all samples were almost saturated after approximately 180 min, the impregnation time at the present study was taken more than 180 min for all samples and experiments. Moreover, it was found that the samples with higher St content were saturated more quickly than the other copolymers with lower St content. This finding depicts that the mass diffusivity of n-pentane increases with increasing St content in St–MMA copolymer.

Figure 5.

Sorption of n-pentane in copolymers versus impregnation time at T = 100°C and sorption pressure of 4 bar.

The dissolved amounts of n-pentane in St-MMA copolymers at different copolymer compositions, temperatures, and sorption pressures are shown in Figure 6(a) to (c). As it can be seen, the dissolved amount of n-pentane in all samples was increased with increasing sorption pressure and decreased with increasing temperature. As the gas concentration in the impregnation chamber (surrounding the sample) was increased with sorption pressure, the diffusion driving force was increased, which led to the higher solubility of n-pentane in St-MMA copolymer. Furthermore, the mobility of gas molecules was increased at elevated temperatures suppressing diffusion of gas into the polymer matrix. Comparison among Figure 6(a) to (c) shows that the amount of dissolved gas decreased with increasing MMA units in copolymer composition, which could be attributed to the polarity of MMA units compared with n-pentane and St units in copolymers.

Figure 6.

Dissolved contents of n-pentane in (a) Co1, (b) Co2, and (c) Co3 at different temperatures versus sorption pressure. Symbols indicate the average value of the solubility of four repeated experiments, the asymmetric error bars signify the minimum and maximum of data, and the solid lines represent linear regression.

Foaming dynamics of St-MMA/n-pentane system

The main purpose of the present study is to focus on the investigation of the effect of copolymer composition, foaming temperature, and gas content on the foaming dynamics. Therefore, the investigated parameters in the foaming dynamics are listed according to Table 3, and all copolymer samples were impregnated by n-pentane based on conditions in Table 4. These conditions were justified using Figure 6 to reach the solubility of 4% n-pentane in St–MMA copolymers.

Table 3.

Investigated parameters in the foaming dynamics.

Sample	105°C	120°C	140°C	160°C	180°C
Co1 with 4% gas content	√	√	√	√	—
Co2 with 4% gas content	—	√	√	√	—
Co3 with 4% gas content	—	—	√	√	√
Co2 with 8% gas content	√	√	√	√	—

Table 4.

Saturation conditions to receive 4% dissolved content of n-pentane in copolymer sheets.

Sample	Temperature (°C)	Sorption pressure (bar)	Impregnation time (min)
Co1	100	3 ± 0.1	180
Co2	100	3.4 ± 0.1	180
Co3	100	4.5 ± 0.1	240

Figures 7 to 9 represent a sequence of optical micrographs of the foaming process of Co1, Co2, and Co3 samples, respectively, saturated with 4% gas content at different foaming temperatures. No bubbles were observed in the foaming temperature below 105°C for Co1, 120°C for Co2, and 140°C for Co3. Since melt strength (Figures 3 and 4) and glass transition temperature (T _g) are increased with increasing MMA content in copolymers, minimum foaming temperature would increase as well.^1,6 Moreover, it can be observed that foaming process occurred earlier at higher foaming temperatures because of the reduction of copolymer matrix melt strength.

Figure 7.

Visualization of Co1/n-pentane foaming process versus foaming time at nonpressurized condition with 4% dissolved n-pentane content and foaming temperature of (a) 105°C, (b) 120°C, (c) 140°C, and (d) 160°C. All images are 1336 µm in height and 1670 µm in width.

Figure 8.

Visualization of Co2/n-pentane foaming process versus foaming time at nonpressurized condition with 4% dissolved n-pentane content and foaming temperature of (a) 120°C, (b) 140°C, and (c) 160°C. All images are 1336 µm in height and 1670 µm in width.

Figure 9.

Visualization of Co3/n-pentane foaming process versus foaming time at nonpressurized condition with 4% dissolved n-pentane content and foaming temperature of (a) 140°C, (b) 160°C, and (c) 180°C. All images are 1336 µm in height and 1670 µm in width.

The number density of the observed bubbles versus foaming time for Co1, Co2, and Co3 samples with 4% n-pentane content is depicted in Figure 10(a) to (c). In this figure, each point represents the average bubble density of three experiments, and asymmetric error bars signify the minimum and maximum values of bubble density. Figures 10 and 11 also represent the effect of foaming temperature on the observed bubble density during the foaming process (nucleation rate) and the final bubble density at constant gas content and copolymer composition. The results reveal that increasing foaming temperature increase the nucleation rate and final bubble density. These figures also show that nucleation rate and final bubble density are decreased, and the foaming time is increased with increasing MMA content in copolymer composition. As the melt strength of the matrix is high and diffusivity of n-pentane is low in copolymers with high MMA content, both the nucleation and bubble growth rate are decreased.

Figure 10.

Number density of observed bubbles versus unfoamed volume respect to time in St-MMA copolymer/n-pentane foaming process at nonpressurized condition and different foaming temperatures with 4% dissolved n-pentane content: (a) Co1, (b) Co2, and (c) Co3.

Figure 11.

Maximum bubble density versus foaming temperature for different copolymer samples with 4% dissolved n-pentane content.

The average diameters of observed bubbles are presented in Figure 12(a) to (c) for Co1, Co2, and Co3 copolymers with 4% n-pentane content, respectively. The bubble expansion is a mass transfer-controlled process; therefore, increasing the mass diffusion coefficient accelerates the bubble growth rate.^5,27 As it can be seen, in all copolymer compositions, the higher expansion rate is attributed to higher foaming temperature because of the higher gas diffusivity and lower melt strength in those samples. Comparing the bubble growth behavior (Figure 12) shows that bubbles grow more slowly with MMA content increment in copolymers. This finding could be attributed to the reduction of n-pentane diffusivity and an increase in the melt strength of the copolymer matrix. Figure 12 also depicts that the final average size of bubbles in all copolymers is decreased as foaming temperature increases. Since the observed bubble density is increased at higher foaming temperatures, shell thickness around the bubbles becomes thinner, indicating that the available n-pentane for each growing bubble is decreased. Although the average bubble sizes are small, they grow up faster due to higher gas diffusivity at higher foaming temperature. It should be noted that while Co3 sample had lower nucleation rate (i.e. higher available n-pentane for each growing bubble), bigger bubbles are not observed for this sample, especially when compared to Co2 sample. In the case of Co3 sample, it can be concluded that the effect of lower diffusivity of n-pentane and higher melt strength of this copolymer matrix overcomes the effect of higher available gas content, which consequently led to smaller bubble size.

Figure 12.

Average bubble diameter respect to time in St-MMA copolymer/n-pentane foaming process at nonpressurized condition and different foaming temperatures with 4% dissolved n-pentane content: (a) Co1, (b) Co2, and (c) Co3.

To investigate the effect of the available gas content on the foaming process, Co2 sample impregnated with n-pentane at 100°C and 4.7 bar for 4 h to attain the solubility of about 8% (Figure 6(b)). Then, the impregnated samples are foamed at different temperatures (100–160°C). The optical microscopy images of the foaming process are presented in Figure 13. As it can be noted, Co2 sample with 4% n-pentane is not foamed at a foaming temperature of 100°C; however, the sample with 8% n-pentane is expanded at 100°C. Higher amount of n-pentane in this copolymer matrix reduces the T _g of the matrix, which makes it possible to be softer and expandable.

Figure 13.

Visualization of Co2/n-pentane foaming process versus foaming time at nonpressurized condition and different foaming temperatures with 8% dissolved n-pentane content and foaming temperature of (a) 105°C, (b) 120°C, (c) 140°C, and (d) 160°C. All images are 1336 µm in height and 1670 µm in width.

The number density of observed bubbles during foaming process and final bubble density are presented in Figures 14 and 15, respectively. Figure 15 and comparison of Figure 10(b) with Figure 14 reveal that the nucleation rate and the final number density of observed bubbles are increased as the dissolved n-pentane content increases. It can be related to increasing saturation pressure with increasing available gas content, which decreases the critical bubble radius according to classical nucleation theory. Therefore, more bubbles have been passed from the nucleation barrier energy with increasing gas content. Figure 16 represents the average diameter of the observed bubble, and comparison of Figure 16 with Figure 12(b) demonstrate that the average bubbles diameter is decreased with increasing n-pentane content, which could be related to the increased bubble density, whereas the shell thickness around the bubbles would decrease.

Figure 14.

Number density of observed bubbles versus unfoamed volume respect to time in Co2/n-pentane foaming process at nonpressurized condition and different foaming temperatures with 8% dissolved n-pentane content.

Figure 15.

Maximum bubble density versus foaming temperature for Co2 (St53-MMA47) sample with 4% and 8% dissolved n-pentane content.

Figure 16.

Average bubble diameter respect to time Co2/n-pentane foaming process at nonpressurized condition and different foaming temperatures with 8% dissolved n-pentane content.

Conclusion

In the present study, the foaming dynamics of the synthesized St-MMA copolymer/n-pentane foaming system was studied at nonpressurized condition. Synthesized copolymers were characterized using H-NMR spectroscopy and rheological measurements. It was found that the compositions of synthesized copolymers were close to the monomer feed ratios, and the copolymer matrix melt strength and average molecular weight were increased with increasing MMA content in copolymer compositions. The dissolved content of n-pentane in copolymers was determined at 100°C and 120° at different sorption pressures using designed batch foaming system. The dissolved content of n-pentane increased with increasing sorption pressure and declined with increasing temperature and MMA content. The effects of foaming temperature, copolymer composition, and n-pentane content on the foaming dynamics (observed bubble density and average bubble diameter) were investigated using obtained micrograph images through the foaming process. It was found that bubble nucleation and growth rate increased with increasing the foaming temperature and n-pentane content but decreased as MMA content increased.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Mostafa Rezaei

References

Azimi

Rezaei

. Solubility and diffusivity of carbon dioxide in St-MMA copolymers. J Chem Thermodyn 2013; 58: 279–287.

Lee

. Foam extrusion: principles and practice. 1st ed. Boca Raton, FL: CRC Press, 2000.

Lee

Ramesh

. Polymeric foams: mechanisms and materials. Boca Raton, FL: CRC Press, 2004.

Salehi

Rezaei

Salami Hosseini

. Experimental and theoretical investigation on polystyrene/n-pentane foaming process. Int J Mater Form 2017; 10(3): 421–434.

Sauceau

Fages

Common

. New challenges in polymer foaming: a review of extrusion processes assisted by supercritical carbon dioxide. Prog Polym Sci 2011; 36: 749–766.

Azimi

Rezaei

Salehi

. The effect of copolymer composition on the batch foaming dynamics of styrene/methylmethacrylate copolymers. J Thermoplast Compos Mater.2015; 30(1): 47–66.

Kasiri

Rezaei

Zandi

. The effect of polyethylene graft maleic anhydride compatibilizer on the physical, mechanical, and thermal properties of extruded noncross-linked low-density polyethylene nanocomposite foams. J Thermoplast Compos Mater 2015; 28: 1537–1549.

Azimi

Rezaei

Abbasi

. The effect of expansion conditions on the batch foaming dynamics of St-MMA copolymer. J Cell Plast 2011; 48(2): 125–140.

Jalili

Abbasi

Nasiri

. Preparation and characterization of expandable St/MMA copolymers produced by suspension polymerization. J Cell Plast 2009; 45(3): 197–224.

10.

Mohammadian

Rezaei

Azdast

. Microstructure, physical, and mechanical properties of LDPE/UHMWPE blend foams: an experimental design methodology. J Thermoplast Compos Mater 2016; 29(9): 1229–1260.

11.

Taki

Nakayama

Yatsuzuka

. Visual observations of batch and continuous foaming processes. J Cell Plast 2003; 39: 155–169.

12.

Guo

Wang

Park

. A microcellular foaming simulation system with a high pressure-drop rate. Ind Eng Chem Res 2006; 45(18): 6153–6161.

13.

Wong

Park

. A visualization system for observing plastic foaming processes under shear stress. Polym Test 2012; 31(3): 417–424.

14.

Wong

Wijnands

SFL

Kuboki

. Mechanisms of nanoclay-enhanced plastic foaming processes: effects of nanoclay intercalation and exfoliation. J Nanopart Res 2013; 15(8): 1815–1829.

15.

Ilieve

Dong

. Visualization of the foaming mechanism of polyethylene blown by chemical blowing agents under ambient pressure. Adv Polym Tech 2007; 26(4): 213–222.

16.

Emami

Thompson

Vlachopoulos

. Experimental and numerical studies on bubble dynamics in nonpressurized foaming systems. Polym Eng Sci 2014; 54: 1947–1959.

17.

Wong

Leung

GYG

. Role of processing temperature in polystyrene and polycarbonate foaming with carbon dioxide. Ind Eng Chem Res 2007; 46: 7107–7116.

18.

Wong

Mark

Hasan

. The synergy of supercritical CO₂ and supercritical N₂ in foaming of polystyrene for cell nucleation. J Supercrit Fluids 2014; 90: 35–43.

19.

Wong

Park

. The effects of extensional stresses on the foamability of polystyrene–talc composites blown with carbon dioxide. Chem Eng Sci 2012; 75: 49–62.

20.

Kim

Leung

Park

. The effect of dispersed elastomer particle size on heterogeneous nucleation of TPO with N₂ foaming. Chem Eng Sci 2011; 66(16): 3675–3686.

21.

Kim

Lee

JWS

Park

. Enhancing cell nucleation of thermoplastic polyolefin foam blown with nitrogen. J Appl Polym Sci 2010; 118: 1691–1703.

22.

Leung

Wong

Wang

. Mechanism of extensional stress-induced cell formation in polymeric foaming processes with the presence of nucleating agents. J Supercrit Fluids 2012; 63: 187–198.

23.

Salejova

Kosek

. Dynamics of foaming of polystyrene particles. Macromol Symp 2006; 243: 233–246.

24.

Mehravar

Abbasi

Jalili

. Synthesis and expansion characteristics of expandable styrene/methyl methacrylate copolymer beads: the effects of monomer composition and cell structure modifying aid. J Cell Plast 2012; 48(2): 161–190.

25.

Rezaei

Golshan Ebrahimi

Kontopoulou

. Thermal properties, rheology and sintering of ultra high molecular weight polyethylene and its composites with polyethylene terephthalate. Polym Eng Sci 2005; 45: 678–686.

26.

Eberle

APR

Baird

Wapperom

. Using transient shear rheology to determine material parameters in fiber suspension theory. J Rheol 2009; 53(3): 685–705.

27.

Taki

. Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process. Chem Eng Sci 2008; 63: 3643–3653.