1 Introduction

Polymer foam is a kind of solid/gas composite material characterized by a polymer matrix replete with numerous tiny foam holes, commonly referred to as porous polymer material. In contrast to unfoamed polymers, polymer foam exhibits many advantages, including low density, lower thermal conductivity, high impact strength, and lower dielectric constant, etc. [1,2,3,4]. Owing to their outstanding functional characteristics and low material cost, polymer foam can be widely used in some fields such as aircraft, automobiles, food packaging, sports equipment, insulation materials, and filter materials [5,6,7,8,9,10,11,12,13,14]. In recent years, the increased demand for polymer foam, coupled with its extensive applications, has driven the rapid development of the polymer foam industry.

The conventional approach for preparing polymer foams employs chemical foaming technology [15,16,17,18,19,20]. Chemical foaming agents, such as azodicarbonamide, p-toluenesulfonyl hydrazine, sodium bicarbonate, and zinc carbonate, have often been employed in polymer foaming, releasing gases such as carbon dioxide (CO2) and nitrogen (N2) upon decomposition by heating. The released gas dissolves within the polymer matrix and initiates bubble nucleation, thereby facilitating the creation of a cellular structure. In addition to adding a chemical blowing agent into the polymer matrix, the inert gases also would be generated by chemical reactions between the two polymers, which can initiate the nucleation and growth of cells. The chemical foaming method has attracted much attention due to its advantages, including cost-effectiveness, simplicity, shortened molding cycles, and the capacity to fabricate large and intricate structural components. However, there are some drawbacks in chemical foaming: firstly, incomplete decomposition of the foaming agent leads to the existence of residues in the resulting foam, restricting its applications, especially in the medical industry. Secondly, the gas generated by chemical foaming is not easy to diffuse uniformly within the polymer, posing challenges in controlling the ultimate cellular structure [21]. The prepared foam material presented inferior cell morphology and non-uniform cell size, which is not conducive to improving the performance of the foam product. Furthermore, chemical foaming agents are detrimental to the human body, resulting in skin, respiratory irritation and allergic reactions [22,23,24], thus failing to meet green environmental protection standards.

To meet the green, healthy, and pollution-free development, supercritical fluids are being considered as sustainable alternatives for the replacement of the traditional chemical blowing agents during polymer foaming. Supercritical fluids combine the properties of both liquids and gases. They exhibit densities and solvating properties akin to liquids while concurrently possessing diffusivity and viscosity levels on par with gases. The plasticizing effect of supercritical fluid on polymers can drastically reduce the melt viscosity, melting point, and glass transition temperature (Tg) of the polymer, which is conducive to obtaining moderate processing conditions and easy to control over the processing procedure. Polymer foaming with supercritical fluids offers several advantages over chemical foaming, including the absence of organic solvents, non-toxicity, better control of foaming conditions (e.g., temperature and pressure), and the ability to achieve microcellular foam with higher cell density, uniform cell size distribution, and smaller cell size. Consequently, the preparation of polymer foam using the supercritical fluid has emerged as a central research focus. Several articles have been published, covering various topics such as the formation of nanocellular foam [25,26,27], polymer blend foaming [28, 29], semi-crystalline polymers foaming [30, 31], the foaming of elastomer materials [32,33,34], engineering plastics and composites foaming [35, 36], and biological materials foaming [37, 38]. Polymer foaming assisted by supercritical fluid constitutes a multifaceted dynamic process necessitating an in-depth grasp of polymer science, physics and chemistry of solutions and interfaces, thermodynamics, and interacting substances, in addition to basic knowledge of process engineering and polymer materials. In this letter, we initially present fundamental insights into supercritical fluids and subsequently delve into a comprehensive analysis of their applications in polymer foaming processes. Lastly, we discussed the research and development of supercritical fluids in foam technology.

2 Supercritical fluids

2.1 Supercritical fluids: definition and properties

The growth of the economy has led to a heightened prominence of environmental concerns. Green chemistry stands out as a vital approach for addressing contemporary environmental challenges. Simultaneously, there is a growing emphasis on adopting a green and health-oriented lifestyle. Consequently, physical foaming agents, particularly supercritical fluids, are progressively supplanting chemical foaming agents [39].

Pure substances undergo state changes, transitioning between gas, liquid, and solid phases as dictated by temperature and pressure. At a specific combination of temperature and pressure, the liquid–gas interface disappears, marking the critical point. Supercritical fluid is characterized as a dense-phase fluid with both pressure and temperature exceeding their respective critical values (see Fig. 1). Under these conditions, the substance presents a behavior between gases and liquids. Specifically, it can permeate solids akin to a gas and dissolve materials in a manner reminiscent of a liquid (see Table 1) [40]. Furthermore, in proximity to the critical point, it is possible to finely adjust the density of supercritical fluids through minor alterations in pressure or temperature within the critical region [41]. Table 2 lists the parameters of supercritical fluids of several common substances [40]. Supercritical fluids exhibit low viscosity and nearly zero surface tension. Consequently, they facilitate rapid mass transfer into swollen polymers [42]. Moreover, Supercritical fluids are characterized by their chemical inertness, non-toxicity, and non-flammability [43]. The unique amalgamation of gas-like viscosity and liquid-like density found in the supercritical fluids renders them the outstanding solvents or plasticizers in polymer processing, such as polymer blending, polymer modification, particle production, polymer composites, polymer synthesis, and especially in microcellular foaming [2, 44,45,46,47].

Fig. 1
figure 1

Typical phase diagram for a pure substance

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Table 1 Value Ranges of Density, Viscosity, and Diffusivity for Gas, Supercritical Fluid, and Liquid
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Table 2 Critical Conditions of Representative Supercritical Fluids
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2.2 Supercritical carbon dioxide

Currently, supercritical CO2 represents the predominant foaming agent in supercritical foaming technology, offering the greatest practical potential for development. It serves as the primary compressible fluid capable of facilitating the formation of polymer foam with microcells in both batch and continuous processes [48]. The plasticizing effect of Supercritical CO2 on polymers can enhance the mobility of polymer chains and reduce the viscosity of polymer melt [49,50,51,52] by lowering the Tg or melting temperature (Tm) [53].

Furthermore, CO2 possesses numerous advantages: (a) Being a component of the atmosphere, CO2 is cost-effective to obtain and readily available, as it can be directly extracted from the air without causing environmental pollution. (b) It exhibits favorable physical properties, including non-toxicity, chemical stability, and non-flammability. (c) CO2 stands as the most commonly employed substance, primarily owing to the low critical temperature (31.1 °C) and moderate critical pressure (7.38 MPa), rendering it well-suited for polymer foaming applications.

Supercritical CO2 foaming technology offers several notable advantages. (a) It does not emit harmful gas, avoiding damage to the environment. (b) Controlling the foaming parameters is straightforward, allowing for precise adjustment of cell size. (c) Supercritical CO2 exhibits high solubility, robust diffusion capabilities, making it advantageous for producing porous polymer materials with a high nucleation density. (d) CO2 removal is straightforward and leaves no residual traces [54,55,56,57,58].

Supercritical foaming technology employing supercritical CO2 as the foaming agent finds extensive application. Firstly, it aids in the extrusion foaming for various applications, including food production and the manufacture of composite materials. Nevertheless, this integrated approach is a recent development and necessitates additional investigation [59]. Secondly, it amalgamates the benefits of processing materials from solvent solutions and supercritical CO2 batch foaming to create foams with controllable cells while minimizing solvent residues [48]. Thirdly, supercritical CO2 foaming yields porous silicone rubber foam materials suitable for mechanical energy harvesting. For example, supercritical CO2 is used in extrusion foaming to produce samples for energy harvesting from tires, while supercritical CO2 injection foaming is employed to fabricate shoe-shaped samples for capturing energy produced by human motion [57]. Fourthly, supercritical CO2 is integrated with the elimination of solid porogens to produce drug-loaded scaffolds, addressing the challenge of cell size adjustment druing foaming [56].

2.3 Supercritical nitrogen

Supercritical fluid technology utilizing N2 as the foaming agent encompasses the following characteristics. (a) The resulting polymer foam exhibits a significantly small cell size and a high cell density. (b) This foaming process is environmentally friendly and does not emit toxic gases. (c) N2 diffuses slowly, reducing the probability of foam collapse after formation. The utilization of supercritical N2 proves advantageous for foaming elastic materials. Compared to supercritical CO2, the more uniform cell structure in ethylene-propylene diene monomer (EPDM) rubber profile extrudates was observed when supercritical N2 was employed as the foaming agent [60]. The foaming behavior of polypropylene (PP) injection molds with N2 and CO2 as physical foaming agents was studied using a visual observation device equipped with temperature and pressure monitoring systems [61]. The results showed that polymer foams with smaller cell size, uniform cell structure and higher cell density employing N2 as the foaming agent could be obtained, which can ascribed to the lower solubility and higher supersaturation of N2 within the polymer. In supercritical foaming technology, compared to CO2, the effectiveness of N2 as a foaming agent is notably lower, resulting in a relatively higher consumption of N2. As a result, in practical applications, the cost of using N2 as the foaming agent surpasses that of utilizing CO2.

2.4 Co‑foamer

Supercritical CO2 and supercritical N2 are the predominant foaming agents employed in contemporary supercritical foaming technology, with infrequent utilization of other supercritical fluids. Furthermore, co-foaming agents involving the admixture of supplementary reagents, including ethanol, water, and acetone, with supercritical CO2 or supercritical N2 are introduced during the supercritical foaming technology to enhance the foaming ability of plastic materials.

In batch foaming, the effects of ethanol content, temperature, and pressure on the cell structure of polycaprolactone (PCL) were studied by using CO2 and CO2-ethanol mixtures, respectively [62]. Compared to supercritical CO2, a more uniform cell structure was produced with CO2-ethanol mixtures as the blowing agent. Furthermore, the cell size increases and the cell density decreases with increasing ethanol concentration. The foaming behavior of thermoplastic polyurethane (TPU) was studied by employing CO2-water as co-foaming agents, and the uniform cell size of the foamed sample was obtained [63]. Salerno et al. utilized a CO2-ethyl lactate mixture to facilitate the foaming of both PCL and polylactic acid (PLA). The results revealed that incorporating ethyl lactate resulted in a decrease in the operational temperature and enhanced the morphological uniformity of the resulting foam [64]. The foaming behavior of polystyrene (PS) with supercritical CO2-N2 as co-foaming agents was explored under elevated temperature and pressure through a visualization system [65]. A synergistic effect was achieved when CO2 and N2 were combined at 3:1, which expanded the processing temperature range to achieve a foamed material with the highest cell density. Furthermore, supercritical CO2 enhances the solubility of supercritical N2 within PS, leading to an augmented nucleation rate of cells. Consequently, co-foaming agents have the potential to enhance foam properties and hold great promise in the production of high-performance polymer foams [66].

3 Principle of foaming process

The process of polymer foaming typically encompasses the fundamental stages of the formation of a polymer/gas homogeneous system, cell nucleation, and cell growth and stabilization, as shown in Fig. 2.

Fig. 2
figure 2

Schematic diagram of supercritical fluid foaming

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Under specific temperature and pressure conditions, gas diffuses into the polymer matrix, eventually reaching a state of dissolution equilibrium to create a polymer/gas homogeneously saturated system. The plasticizing effect of gas on polymer can enhance the mobility of the polymer molecular chain, thereby reducing the free energy barrier for cell nucleation. The cell nucleation is driven by thermodynamic instability within the system [67,68,69]. This instability can be induced by adjusting pressure and temperature during foaming, effectively altering gas solubility in the solution [70, 71]. Once thermodynamic instability occurs, the polymer and gas undergo phase separation, fostering cell nucleation. However, only nuclei that reach a critical size can persist stably. Subsequently, the gas dissolved within the polymer matrix diffuses into the cell nucleus, causing an increase in its diameter. The process of cell growth involves continuous gas consumption and reduction. After a certain period, insufficient gas remains in the system to sustain further cell expansion, leading to a decrease in the driving force for bubble growth. Meanwhile, with decreasing temperature, the viscoelasticity of the polymer melt increases, leading to an increase in resistance to cell growth. Eventually, cell growth stopped and the cell structure and density remained stable. A comprehensive exploration of the foaming mechanism can optimize the processes of polymer foaming, thereby enhancing the performance of polymer foam.

3.1 Formation of a polymer/gas homogeneous system

The inert gas (such as CO2 or N2) is diffused and dissolved within the polymer under specific temperature and pressure, resulting in the formation of a uniform polymer/gas saturation system. During the saturation phase, the pressure gradient at the polymer matrix surface causes two phenomena: gas dissolution and diffusion within the polymer matrix. The primary foaming agent employed in supercritical foaming technology is supercritical CO2. Therefore, the discussion was only focused on the dissolution and diffusion of CO2 within polymer matrix.

3.1.1 Dissolution and diffusion of CO2 in polymer matrix

Achieving a homogeneous polymer/gas system is pivotal in the foaming process, and it represents a significant challenge in the development of microcellular foaming. Insufficient uniformity results in low cell density and a broader cell size distribution in the final product. To ensure the formation of a homogeneous system, an appropriate quantity of foaming agent should be added to ensure complete dissolution within the polymer melt. Hence, determining gas solubility in polymer melts holds paramount importance.

Solubility measures the quantity of gas absorbed by a material. The concentration of dissolved gas (C) at a given temperature is determined by the pressure (P), as expressed in Eq. (1) [72]:

$$C=S\left(C\right)P$$
(1)

where S represents the gas solubility. The effect of pressure on the absorption of CO2 was investigated in polyetherimide (PEl) plaques with a thickness of 1.5 mm [73]. An increase in pressure could potentially raise the maximum solubility of CO2. Yu et al. studied the dissolution behaviors of CO2 in PLA melt with the framework of dynamic density functional theory and found that the solubility increases with increasing pressure (see Fig. 3).

Fig. 3
figure 3

Solubilities of CO2 in PLA at various temperatures and pressures. x1 is the mass fraction (wt%) of CO2 in PLA melt. The scatter dots at different temperatures (463 k [74], 333 k [75], 308 k [76]) are the experimental data

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The solubility of gas (S) is also temperature-dependent, as outlined by previous studies [77, 78]:

$$S={{S}_{0}e}^{\frac{{-{\Delta H}}_\mathrm{s}}{RT}}$$
(2)

where S0 is the pre-exponential factor, ΔHs is activation energy for sorption(negative), T is temperature and R is gas constant. Since ΔHs is negative, the gas solubility decreases with increasing the temperature [79]. Raising the temperature from 40 °C to 150 °C led to a 50% reduction in CO2 absorption within poly(ethylene glycol), covering saturation pressures ranging from 5 to 15 MPa [80]. Sato [81,82,83] investigated the solubility of CO2 in a range of polymers (such as PP, polystyrene (PS), high-density polyethylene (HDPE), etc.) under elevated temperature and pressure conditions. The study revealed that as the temperature increased, the solubility of CO2 in polymers decreased.

In most cases, achieving fully saturated polymer/gas systems is imperative for the nano-cell formation process, making the absorption of CO2 to be a pivotal parameter. Therefore, the adsorption time must be adequate to attain equilibrium between the polymer and gas, which depends on gas diffusion. The temporal progression of the gas concentration distribution is also elucidated using Fick’s classical law, as outlined below:

$$\frac{\partial C}{\partial t}=\nabla \cdot {D}_{12}\nabla C$$
(3)

where D12 represents the mutual binary diffusion coefficient, reliant not only on the volume fraction of dissolved CO2 but also on the average hole free volume within the polymer/CO2 system [84, 85]. According to the free volume theory, temperature and local thermal expansions lead to fluctuations in solvent diffusion within the polymer [86, 87]. The impact of pressure on gas diffusion within polymer materials was emphasized by the free volume theory [88]. Polymer chains have a tendency to constrict under high pressure, restraining free volume. Simultaneously, the gas concentration rises, resulting in an expansion of free volume. For a given temperature, it considers both of these effects, the following relation was proposed:

$$D\left(P,C\right)={{D}_{0}e}^{\beta P+\alpha C}$$
(4)

where D0 represents a pre-exponential factor, β signifies a negative term associated with the density increase of the polymer matrix, and α is a positive term linked to the increase of the gas concentration within the polymer matrix. The increasing of free volume in the polymer/CO2 system enhances solvent diffusion [49]. Similarly, when a solvent is introduced, increasing the system's free volume, the glass transition occurs at a temperature below that of the polymer Tg [87].

3.1.2 Determination of solubility of carbon dioxide in polymers

Researchers have employed various methods to assess the solubility of gas in polymers. The pressure decay method is commonly employed to ascertain gas solubility in polymers due to its simplicity and cost-effective equipment setup. However, the pressure decay method presents challenges when measuring gas solubility in molten polymers, as it necessitates a high-resolution pressure sensor capable of functioning at elevated temperatures. Moreover, this approach demands a sample with a larger size, inevitably extending the measurement duration.

An alternative approach involves employing an electronic balance to directly measure mass increments in adsorption experiments [89, 90]. This method offers rapid measurements and high accuracy. Nonetheless, it is primarily applicable for assessing gas solubility in polymers at lower temperatures due to electronic balance operational constraints. In response, researchers have developed systems to independently control the temperature of the gas absorption chamber and electronic balance [91, 92]. A drawback of this approach is that the change in gas density caused by convection can affect measurement accuracy. Kleinrahm and Wanger introduced a magnetically suspended balance (MSB) to address this issue effectively [93]. In this device, the sample is positioned within a compartment separate from the gas adsorption chamber, allowing to avoid effectively the influence of convection on the mass determination. Consequently, this apparatus can assess gas solubility and diffusivity in polymers under elevated temperature and pressure. Some researchers have embraced this technique to ascertain gas solubility in polymers [83, 94, 95]. Nevertheless, the buoyancy effect of the swollen polymer causes the measured dissolved gas mass (referred to as apparent solubility) by the magnetic levitation balance to be lower than the true solubility.

When precise pressure–volume-temperature data for polymer-gas mixtures is unavailable, researchers commonly employ different equations of state (EOS) to estimate expansion levels to reduce the effects of buoyancy [96, 97]. The Sanchez Lacombe equation of state [98] and Simha Samcynsky equation of state [99] are two widely used equations of state.

3.1.3 Theory on polymer/CO2 interactions

In solute/solvent systems, solubility is contingent upon the interactions among the constituent components. The Flory–Huggins interaction parameter χ is commonly employed to assess the affinity between solute and solvent [100]. χ is directly proportional to (δ1 – δ2)2, where δ1 and δ2 represent the solubility parameters of components 1 and 2, respectively. When δ1 and δ2 exhibit proximity, there is a commensurate increase in the solubility between the constituent components. Therefore, the miscibility can be evaluated through the calculation of solubility parameters δ. Hildebrand and Scott [101] introduced a model grounded in the calculation of cohesive energy density for solute/solvent systems, as indicated by the following equation:

$$\delta ={\left(\frac{\Delta E}{V}\right)}_{T}^{0.5}\approx {\left(\frac{\partial E}{\partial V}\right)}_{T}^{0.5}={\left(T{\left(\frac{\partial P}{\partial T}\right)}_{V}-P\right)}^{0.5}$$
(5)

where ΔE/V represents cohesive energy density, P is internal pressure and T signifies temperature. Williams and Colle [102] elucidated this principle in greater detail, demonstrating that supercritical CO2 exhibits a higher solution parameter than gaseous CO2, approaching that of hydrocarbon chains (approximately ~ 10 MPa1/2). Strauss [103] demonstrated that in the context of a PS/CO2 system, achieving good gas solubility necessitates the fulfillment of the condition δ1 − δ2 < 1, which mandates the pressure of 90 MPa at 80 °C. However, some studies have evidenced that CO2 molecules exhibit partial solubility within PS matrices, with solubilities exceeding 13 wt% at pressures below 20 MPa [104, 105]. The phenomenon arises due to the failure of the model to consider the specific chemical interactions.

Another model is grounded in the distribution of interactions among three distinct contributions [106]. By this framework, δ can be deconstructed as follows:

$${\delta }^{2}={\delta }_{d}^{2}+{\delta }_{p}^{2}+{\delta }_{h}^{2}$$
(6)

where δd represents the dispersion component, δp denotes the polar component, and δh is the hydrogen-bonding component. They can be calculated theoretically based on the consideration of their chemical group contributions, as documented in the available literature [107]. Despite CO2 lacking a permanent dipole, the substantial influence of its quadrupole moment on interaction is noteworthy, resulting in positive values for δp and δh within the Hansen model [102]. The finding illustrates the model's constraints. Similar to the Hildebrand and Scott model, the model fails to consider chemical interactions that increase the solubility of gas in polymers [108]. Hence, the gas adsorption behavior varies among different polymers (such as PMMA and PS), contingent upon their intrinsic properties, even when they share the same Tg. This suggests that distinct molecular compositions of polymers result in varying interactions with CO2. Extensive research has been conducted on the solubility of block copolymers and fluorinated polymers in CO2 due to the noteworthy chemical interactions between fluoropolymers and CO2 [109, 110]. These chemical interactions may exhibit characteristics of Lewis acid–base interactions. Specifically, the fluorine atom serves as a Lewis base alongside the electron-deficient carbon in CO2. Simultaneously, the hydrogen atoms adjacent to the fluorine atom acquire an induced positive charge and engage with the gaseous oxygen atoms, forming a Lewis acid [111]. Cooper [45] postulated that fluoropolymers create weak complexes with CO2, resulting in heightened gas solubility within fluoropolymers. Certain silicon-based polymers may be regarded as CO2-philics polymers. This phenomenon appears to be attributed to the flexibility of the polymer chains [112, 113]. According to Kirby [114] and Nalawade [44], it has been observed that the solubility of CO2 in poly(dimethyl-) and poly(phenylmethyl-) siloxane exceeds that observed in other polymers, primarily attributable to their notably greater free volume fraction.

Despite being less CO2-philic than fluoro- or silicon-based polymers, acetate and acrylate polymers are noteworthy due to the significant interaction between their carbonyl groups and CO2. Especially, PMMA has been extensively investigated for its affinity toward CO2 in contrast to polyolefins or PS. This affinity can be attributed to carbonyl/gas interactions, similar to the Lewis acid/base interactions observed in fluoro-based polymers, which increase gas solubility [103]. Fourier transform infrared spectroscopy (FT-IR) has been utilized for analyzing these interactions in PMMA, cellulose acetate, and vinyl acetate [115, 116]. Kazarian and colleagues [105] analyze the PMMA/CO2 interaction by studying the normal vibrational mode v2 (bending) of CO2 around 660 cm−1. The spectral band splits into two peaks at 662 and 654 cm−1 in PMMA, a phenomenon attributed to interactions between carbonyl groups and gas [44], which is not observed in PS/CO2 systems [103, 116]. Reglero-Ruiz and colleagues conducted a comparative analysis of CO2 affinity between PMMA and PS [117]. Their findings demonstrated that PMMA exhibits over a 6 wt% higher gas uptake than PS at 40 °C and 30 MPa.

The affinity between the polymer and CO2 is a critical factor to consider in the foaming process. Indeed, CO2-philic polymers enable the attainment of substantial CO2 absorption at lower saturation pressures and/or shorter durations. Moreover, it is worth noting that the CO2 solubility can exert an influence on the processes of cell nucleation and growth during polymer foaming.

3.2 Cell nucleation

Nucleation is the phenomenon where molecules from a second phase, previously dissolved in the initial phase, aggregate to establish a stable second phase, driven by thermodynamic instability. Once the supercritical fluid dissolves into the polymer, resulting in the formation of a homogeneous system, the system enters a supersaturated state due to either increased temperature or decreased pressure. The subsequent generation of the bubbles facilitates the attainment of a low-energy stable state. The formation of bubbles in the foaming process can be described by the classical nucleation theory. Colton and Suh et al. [118,119,120] developed the classical nucleation theory of polymer foaming, widely regarded as the predominant empirical theory for describing the mechanism of cell nucleation.

The assumptions and approximations in classical nucleation theory are as follows [121, 122]: (a) It postulates the nucleus to be a spherical droplet characterized by clearly defined boundaries. (b) All nuclei possess identical physical properties to the bulk material. (c) The theory considers the influence of pressure drop on cell nucleation while disregarding the pressure drop rate. (d) It further postulates that nucleation occurs instantaneously alongside an instantaneous pressure drop, which is unrealistic as pressure drop occurs gradually over time. (e) The bubble interface is similarly described as an infinite, flat planar surface.

Classical nucleation theory has faced challenges due to its underlying assumptions and approximations, leading to significant deviations from experimental observations in some cases, and raising questions about its accuracy and validity [123]. Nonetheless, despite these limitations, classical nucleation theory offers valuable conceptual insights into the nucleation process. Therefore, it is utilized in this paper to elucidate the mechanisms governing bubble nucleation in polymer foams. Classical nucleation theory categorizes cell nucleation into two types: homogeneous nucleation and heterogeneous nucleation.

3.2.1 Homogeneous nucleation

Homogeneous nucleation refers to the spontaneous and stochastic creation of cells within a homogeneous system during the embryo formation stage, without the presence of foreign substances or two-phase incompatible media. It typically arises in reaction to random fluctuations or variations in temperature or pressure. Theoretically, every molecule can potentially serve as a nucleation site, resulting in the most ideal nucleation density and cell radius in homogeneous nucleation. However, due to the absence of induction by nucleating agents, the free energy required for nucleation is high, which requires the system to have a large degree of supersaturation. During the foaming process, the supersaturated polymer-gas homogeneous system exhibits thermodynamically unstable due to fluctuations in the temperature or pressure, leading to the aggregation of gas molecules. The critical radius (rc) denotes the minimum size for an embryo to become a stable bubble. A maximum of free energy barrier reaches when the radius of the bubble (R) equals rc. When the embryo's size falls below rc, it collapses into the melt. Conversely, when it surpasses rc, a stable nucleus emerges, persistently growing and causing a decrease in the free energy of the system (see Fig. 4a).

Fig. 4
figure 4

(a) Bubble nucleation and growth as a function of free energy, (b) contact angle and semi-conical angle for heterogeneous bubble nucleation

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Additionally, bubble stability hinges on the pressure difference ΔP (the disparity between internal bubble pressure and the surrounding pressure) and the interfacial energy, both of which are considered when deriving an expression for Gibbs free energy, as illustrated [124]:

$$\Delta G\left(R\right)=-\frac{4}{3}\pi {R}^{3}\Delta P+\pi {R}^{3}\gamma -{\Delta V}_{\mathrm{free}-\mathrm{vol}}$$
(7)

where R represents the bubble radius, ΔP is the pressure difference, γ denotes the interfacial tension. ΔVfree-vol is the change of free volume caused by the additives, which is disregarded in the homogeneous nucleation.

The critical radius rc depends on the ratio of the interfacial tension γ to the pressure difference ΔP, as shown in the Eq. (8). Therefore, Gibb’s free energy barrier ΔGHom for homogeneous nucleation is expressed by Eq. (9).

$${r}_{c}=\frac{2\gamma }{\Delta P}$$
(8)
$${\Delta G}_{hom}=\frac{16\pi {\gamma }^{3}}{{3\Delta P}^{2}}$$
(9)

The rate of homogeneous nucleation can be determined by Eq. (10).

$${N}_{\mathrm{hom}}={f}_{0}{C}_{0}\mathrm{exp}\left(\frac{-{\Delta G}_{hom}}{{K}_{B}T}\right)$$
(10)

where f0 represents the frequency factor of the gas molecules attaching to the nucleus and varying with its surface area, C0 is the concentration of gas molecules, KB shows the Boltzmann constant; T donates the temperature, ΔGhom stands for the energy barrier associated with homogeneous nucleation.

3.2.2 Heterogeneous nucleation

Heterogeneous nucleation arises when a nucleus forms at the interface between the continuous polymer-gas phase and a third phase, initiated by nucleating agents acting as nucleation centers, rather than spontaneously (see Fig. 4b). Nucleating particles, including fillers [124,125,126,127,128,129,130,131,132,133,134] and crystals [135,136,137,138,139,140], are frequently employed in both conventional and microcellular foaming processes. They serve to increase nucleation density by offering heterogeneous surfaces that reduce the energy barrier for nucleation [141]. Yu et al. explored the foaming characteristics of the pure poly(L-lactic acid) (PLLA) and PLLA/poly(D-lactic acid) (PDLA) using an environmentally friendly supercritical CO2 [142]. The result indicates that the stereocomplex crystals can serve as nucleation sites, effectively lowering the energy barrier for nucleation, resulting in a remarkable augmentation in cell density and a reduction in cell diameter in PLLA/PDLA foam samples (see Figs. 5, 6, and 7).

Fig. 5
figure 5

Cellular morphology of PLLA foams prepared under different foaming temperatures: (a1, a2) 90 °C; (b1, b2) 100 °C; (c1, c2) 105 °C; (d1, d2) 110 °C; (e1, e2) 115 °C; (f1, f2) 120 °C

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Fig. 6
figure 6

Cellular morphology of D2.5 foams prepared under different foaming temperatures: (a1, a2) 90 °C; (b1, b2) 100 °C; (c1, c2) 105 °C; (d1, d2) 110 °C; (e1, e2) 115 °C; (f1, f2) 120 °C

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Fig. 7
figure 7

(a) Cell density; (b) average diameter of PLLA and D2.5 foams under different foaming temperatures; (c) cell size distribution of PLLA foams prepared at 115 °C; (d) cell size distribution of D2.5 foams prepared at 115 °C (the insert figure shows the cell size distribution of mesh-like holes)

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Furthermore, the Gibbs free energy maximum is influenced by the surface topography of the nucleating agent, quantified as the shape factor (S). Considering these factors, the expressions of the shape factor were presented in Eqs. (11) and (12).

$${\Delta G}_{het}={\Delta G}_{hom}S\left(\theta \right)$$
(11)
$$S\left(\theta \right)=\frac{1}{4}\left(2+3\mathrm{cos}\left(\theta \right)-{\mathrm{cos}}^{2}\left(\theta \right)\right)$$
(12)

Moreover, the determination of the shape factor (S) relies upon the contact angle (θ) established between the bubble radius (R) and the additive surface. As θ increases, S decreases, resulting in further reduction of ΔGhet. Notably, some nucleating agents, like talc, do not have a plate-like structure but a particle-like one. For these agents, nucleation occurs within a conically shaped pit, characterized by the semi-conical angle (β) (see Eq. (13)) [143], as illustrated in Fig. 4b.

$$S\left(\theta ,\beta \right)=\frac{1}{4}\left[-2\mathrm{sin}\left(\theta -\beta \right)+\frac{\mathrm{cos}\theta {\mathrm{cos}}^{2}\left(\theta -\beta \right)}{\mathrm{sin}\beta }\right]$$
(13)

Polymer-nucleating agent interactions are of paramount importance in assessing nucleation efficiency. Notably, smaller nucleating agents exhibit a propensity for higher nucleation densities [144, 145]. Besides nucleating agent size, the topography of their surfaces significantly impact nucleation. Compared to tubular nucleating agents, those with flat surfaces demonstrate improved nucleation rates owing to their curved edges [146]. In a study by Leung et al. [147], an exploration was conducted into the impact of both the wetting angle (θ) and the conical cavity angle (β) of nucleating agents. The findings indicated that the difference between these angles (θ − β) plays a pivotal role in dictating the growth state of the bubble. ΔGhet decreases with increasing θ. Additionally, it has been demonstrated that when θ = 90°, a smaller value of β promotes heterogeneous nucleation. Conversely, when θ and β are small, heterogeneous nucleation becomes unfavorable. Hence, an ideal nucleating agent should exhibit uniform size and shape, a large wetting angle, and facile dispersal within a polymer matrix.

3.2.3 Limitations of the classical nucleation theory

While classical nucleation theory delineates the primary parameters governing nucleation, its application to assess nucleation rate in polymer/gas systems frequently diverges from experimental outcomes. Surface tension, dependent on the critical nucleus size, remains inaccessible through experiments. In classical theory, γ is approximated by the surface tension γ∞ of a planar interface, but this approximation frequently leads to substantial errors. For instance, if the actual surface tension is merely 80% of the planar surface tension, the classical theory may underestimate the nucleation rate by an astonishing 20 orders of magnitude, given a typical free energy barrier of 50 kBT. In addition, the physical meaning of ΔP is often misunderstood in the literature. While it has been characterized as the pressure difference between the interior and exterior of a bubble, the definition holds only for sufficiently large bubbles [118,119,120]. Equally critical, internal pressure remains beyond direct measurement. Some researchers have characterized ΔP as the pressure drop required to initiate nucleation, resulting in potential overestimations of ΔP by as much as 30–40%. Such errors could inflate the nucleation rate by several orders of magnitude, reaching levels on the order of 109–1010.

In response to this error, new theories have been proposed to improve the accuracy of prediction. One particularly promising theory is self-consistent field theory. An effective Hamiltonian is introduced in self-consistent field theory, formulated as a straightforward function of a spatially varying field, such as the number density of polymer chain segments, and it incorporates adjustable parameters. By evaluating the associated partition function for this Hamiltonian, it becomes possible to calculate a range of thermodynamic properties. The self-consistent field theory has been effectively employed to model bubble nucleation in the hexadecane-CO2 system with reasonable accuracy [148]. For the hexadecane-CO2 model system, Binder and his colleagues observed that classical nucleation theory closely matched self-consistent field theory results in the vicinity of the bimodal region. However, the accuracy of classical nucleation theory diminished for smaller nucleation barriers, which are more representative of experimental conditions.

Statistical-mechanical density functional theory, as described in references [149,150,151,152,153,154], initiates by constructing a detailed molecular-level model of the system. The associated free energy of this model system is expressed as a function of the spatially varying density distribution of the particles. To minimize the free energy, an equilibrium density distribution was determined. Once the equilibrium distribution is established, the thermodynamic properties of the system can be derived from the function. The statistical-mechanical density functional theory offers a more comprehensive system description compared to self-consistent field theory but demands significantly greater computational resources. Consequently, statistical-mechanical density functional theory and self-consistent field theory complement each other in the study of nucleation and serve as potent tools for addressing the limitations of classical nucleation theory. However, it's important to note that both theories still rely on approximations to facilitate tractable calculations. As such, further experimental investigations are essential to validate and refine these theories.

3.3 Cell growth

The process of bubble growth is highly intricate, encompassing mass, momentum, and heat transfer phenomena. This complexity is further compounded by the intricate rheological behavior of the fluid, making an accurate description of bubble growth challenging. To elucidate the mechanisms governing bubble growth, prior researchers have conducted comprehensive experimental and theoretical investigations, yielding valuable insights.

3.3.1 The bubble radius calculated by the empirical formula

Epstein and Plesset [155] established the correlation between bubble growth and time through an investigation of bubble growth within polymer melts.

$$\frac{dR}{dt}=\alpha \left[\frac{1}{R}+\frac{1}{\left(\pi Dt\right)\frac{1}{2}}\right]$$
(14)

where R represents the bubble radius; D represents the gas diffusion coefficient; α is a coefficient related to the gas concentration and pressure.

Subsequently, Hobbs [156] investigated the inflation and growth kinetics of bubbles in thermoplastic structural foams. Their model assumes the initial existence of minuscule voids within polymer melt. It takes into account factors such as changes in external pressure, the presence of a range of bubble sizes, and gas diffusion between adjacent bubbles. The research reveals that, under specific pressure conditions, the quantity of expanding bubbles in the molten material relies on the ratio between the critical radius and the average radius of the hypothetical microvoids within the melt. Additionally, it illustrates that the growth rate experiences a notable reduction due to gas diffusion between adjacent bubbles when the inter-bubble separation decreases to a micron or less.

Based on the theory of Epstein [155], an approximate equation for calculating the bubble radius is proposed as follows:

$$R\left(t\right)={R}_{0}+{ABt}^\frac{1}{2}+\frac{\left(1-A\right){B}^{2}t}{{2R}_{0}+{Bt}^\frac{1}{2}}$$
(15)

where R(t) is the radius of the bubble at time t, R0 is of the bubble initial radius, A and B are constants associated with the system. The equation takes into account bubble coalescence, providing a more accurate representation of how the bubble radius changes over time. Nevertheless, it is also derived from empirical data and experimental observations, making it challenging to establish a clear relationship between the bubble radius and the parameters influencing bubble expansion. As a result, its application is subject to certain limitations.

3.3.2 “Sea-island” model

The process of bubble growth encompasses both thermodynamics and kinetics, often necessitating computer-based numerical simulations to elucidate the influence of various parameters on bubble expansion [157]. To delve deeper into the mechanism of cell growth, Han and Yoo [158] introduced the sea-island model. This model delineates the expansion of a single bubble within a rectangular cavity immersed in an infinite volume of polymer melt, as depicted in Fig. 8. The model operates under the following assumptions: (a) The bubble remains small during expansion, assuming a spherical shape; (b) Due to the ample width of the cavity, bubble expansion is unrestricted by cavity walls; (c) Polymer melts exhibit incompressibility; (d) The polymer melt viscosity is exceptionally large, rendering the buoyancy effects during bubble expansion negligible. This model elucidates the growth patterns of bubbles across the entire system by scrutinizing the growth dynamics of individual bubbles. Building upon this concept, Papanstasiou and Scriven [159] employed numerical methods to investigate the growth and rupture of individual spherical bubbles within an infinite volume of polymer melt, grounded in the island model.

Fig. 8
figure 8

Island model [158]

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In fact, in the real nucleation process, when thermodynamic instability occurs, a large number of bubbles will be generated instantaneously. Given their close proximity, these bubbles experience hindered growth. Therefore, the cell growth process based on the island model will deviate from the actual growth situation, resulting in limited applicability.

3.3.3 Cell model

The growth process of the single bubble in the infinite melt represents the expansion law of bubbles in the entire system, which deviates from reality. Therefore, employing the sea-island model for calculations inevitably introduces errors. To address this, Amon et al. [160] proposed a cell model, where a polymer melt containing numerous bubbles is divided into an equivalent number of blister units. Each cell comprises a spherical bubble core surrounded by a concentric melt shell. In this model, gas in a supersaturated state within the melt shell continuously diffuses into the bubbles, driving their growth, as depicted in Fig. 9. They conducted a study on the diffusion-controlled growth of bubbles enveloped by a Newtonian fluid film using the cell model, simulating the growth of a multitude of bubbles during the foaming process [161]. The cell model accurately reflects the conditions of cell growth and addresses interactions among adjacent bubbles during the growth process, making it widely accepted among researchers.

Fig. 9
figure 9

Schematic of cell model

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According to the cell model, the bubble growth kinetics under isothermal conditions can be described by coupled mass and momentum conservation equations. The gas mass conservation in the bubble is expressed as:

$$\frac{d}{dt}\left(\frac{4\pi }{3}\frac{{R}^{3}{P}_{D}}{{R}_{g}T}\right)=4\pi {R}^{2}D\frac{\partial \mathrm{c}}{\partial \mathrm{r}}\left|r=R\right.$$
(16)

The gas mass conservation in the melt can be expressed as:

$$\frac{\partial \mathrm{c}}{\partial \mathrm{t}}+\frac{{RR}^{2}}{{\mathrm{r}}^{2}}\frac{\partial \mathrm{c}}{\partial \mathrm{r}}=\frac{\mathrm{D}}{{\mathrm{r}}^{2}}\frac{\partial }{\partial \mathrm{r}}\left({r}^{2}\frac{\partial \mathrm{c}}{\partial \mathrm{r}}\right)$$
(17)

The momentum conservation equation is given by:

$${P}_{D}-{P}_{C}-\frac{2\gamma }{R}+2{\int }_{R}^{\infty }\frac{{\sigma }_{rr}-{\sigma }_{\theta \theta }}{r}dr=\frac{4\eta }{R}\left(\frac{dR}{dt}\right)$$
(18)

where R is the bubble radius, \(R=dR/dt\) is the bubble growth rate, PD is the pressure inside the bubble, PC is the pressure of ambient, D is the diffusion coefficient, γ is the interfacial tension, c is the gas concentration, Rg is the gas constant, η is the melt viscosity, and σ is the viscoelastic stress tensor. The viscoelasticity of a polymer is determined by the difference in normal stress σrr − σθθ.

The constitutive equation can choose the Oldroyd-B model [49, 162], Larson model [163], Phan-Thien/Tanner (PTT) model [164, 165], and Pom-Pom model [166]. These governing equations for bubble growth dynamics are complex, involving highly coupled nonlinear equations with both partial differential and integral components. The associated boundary conditions are as follows:

$$c\left(R,0\right)=k_HP_D\left(0\right)=\overline c\left({t}^{'}\right)$$
(19)

Through simulating the bubble growth process, it becomes possible to identify the crucial factors that govern bubble expansion. By adjusting these parameters, the objective of controlling the bubble pore structure can be achieved. While these simulations offer valuable insights into bubble growth kinetics, it's important to note that factors like cell density and cell size distribution may require a comprehensive examination that considers both cell growth kinetics and nucleation processes for accurate determination [167,168,169,170,171].

4 Foam manufacturing techniques

Currently, the production of polymer foam materials can be categorized based on the level of continuous operation into batch foaming, extrusion foaming, and injection molding foaming [172].

4.1 Batch foaming

Batch foaming typically occurs within a high-pressure reactor, creating a controlled, sealed environment with elevated temperature and pressure (see Fig. 10). In this setting, CO2 or N2 gradually permeates and dissolves into the polymer matrix. Over time, the gas within the polymer saturates. Subsequently, altering either temperature or pressure induces the gas within the polymer to enter a supersaturated state, resulting in overflow. A large number of bubble nuclei are produced during the overflow process, and the bubble nuclei gradually grow to form cells. Finally, the polymer is cooled, preserving the resulting cell structure within. Batch foaming is typically classified into two categories: temperature-induced and pressure-induced methods.

Fig. 10
figure 10

Schematic representation of batch foaming

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For the temperature-induced approach [173,174,175,176], the initial step involves placing the sample in a low-temperature environment (below Tg) saturated with gas. In this setting, the mobility of the polymer chain is constrained, preventing nucleation. Once saturation is achieved, the sample is removed from the autoclave. Subsequently, the saturated sample is immersed in a high-temperature oil bath for a specified duration, initiating cell nucleation and growth. Elevated temperature (ΔT) serves as the driving force for bubble nucleation. This approach segregates the creation of the polymer/gas-saturated system from the subsequent cell nucleation and growth stages, allowing for independent adjustment of process parameters like pressure, temperature, and time. However, this method entails increased complexity and a longer production cycle.

In the temperature-induced process, Miller et al. [73] investigated the foaming behavior of polyetherimide (PEl) sheets saturated for 280 h at 21 °C and 5 MPa. These samples absorbed absorbing 40 wt% CO2 and underwent foaming in a heated silicone oil bath, resulting in foams with a cell size of 30 nm. Polycarbonate (PC) absorbs approximately 20.4 wt% of CO2 after saturation at -30 °C for 72 h. Subsequently, it is heated to 70 °C to initiate foaming, resulting in foam with cell size of 21 nm and cell density of 4.1 × 1014 cells/cm3 [177].

The pressure-induced approach was initially introduced by Goel and Backman [68, 178]. The sample is placed under high-temperature and high-pressure conditions to achieve saturation of CO2 or N2 absorption within the polymer sample. Subsequently, the pressure is rapidly reduced, rendering the system thermodynamically unstable and prompting cell nucleation and growth. Costeux [179] utilized the pressure-induced approach to foam PMMA-CO-EMA (a random copolymer of MMA with 50 wt% ethyl methacrylate) copolymers at 30 MPa and 40 °C, resulting in nano-foams with the cell size of 95 nm and the cell density of 8.6 × 1015 cells/cm3. Yang et al. [180] investigated the foaming behavior of PS-OMS (PS filled with 5 wt% of spherical ordered mesoporous silica) samples through a pressure-induced process. The results revealed that the sample achieved saturation under high pressure at 120 °C for 18 h, and then, the high pressure was swiftly released for 0.5 s, resulting in foam with the average cell size of 7.8 μm and the cell density of 3.55 × 109 cells/cm3.

Batch foaming techniques provide precise control and are extensively employed for the investigation of diverse process variables. Moreover, the equipment necessary for batch foaming is relatively uncomplicated, and the investment requirement is modest. Nevertheless, its commercial application is constrained due to the incapacity of continuous production.

4.2 Extrusion foaming

Extrusion foaming shares the same operational principles as plastic extrusion, with the primary distinction being the introduction of a physical blowing agent at a specific point along the extrusion line (see Fig. 11). The majority of industrial foam extrusion lines operate in tandem, but single lines are also utilized. Extrusion foaming offers advantages in terms of continuous operation and high output efficiency, making it widely prevalent in industrial production. Initially, polymer pellets or powders are loaded into the temperature-controlled first barrel of the extruder through the hopper. These pellets undergo melt-plasticization at elevated temperatures and pressures. Subsequently, a physical blowing agent, such as supercritical CO2, is injected into the melt using an injection unit situated on the barrel. The shearing of the screw accelerates CO2 diffusion into the polymer melt [181], leading to complete CO2 dissolution within the polymer melt, resulting in the formation of a homogeneous polymer/CO2 system.

Fig. 11
figure 11

Schematic representation of foam extrusion on a tandem-line

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The homogeneous system is transported to the second barrel via the movement of the screw. The molten material gradually undergoes cooling to a temperature below that of the extruder's first barrel. However, even at this lower temperature, sufficient mixing is still ensured. Cell nucleation is prevented as a result of the high pressure experienced in the barrel. Polymer melt flow rates are regulated by melt pumps, allowing for independent control of flow regardless of temperature and pressure fluctuations. Furthermore, a heat exchanger is employed to provide additional cooling for the homogeneous system. Ultimately, the homogeneous system is conveyed to the extruder head, where pressure is rapidly decreased via a dedicated nozzle. Within this process, CO2 within the system attains a supersaturated state, escapes from the melt, and initiates nucleation and growth of bubbles. These bubbles continue to expand until vitrification is achieved. Larson and Neldin [182] utilized a 2% epoxy-functional chain extender in masterbatch form to foam PLA, achieving foams with a cell size of 22 μm. Zhang et al. [183] investigated the extrusion foaming of PS using CO2-water as co-blowing agents. Their experiments employed a throughput of 4 kg/h, a 0.4 mm slot die, and a die temperature of 120 °C, resulting in foams with an average cell diameter of approximately 75 μm when 0.5% graphite (GR) was added as a nucleating agent. Okolieocha et al. [184] conducted a similar study on a tandem foam extrusion line, employing a mixture of carbon dioxide and ethanol as a physical blowing agent (PBA). Their experiments used a 0.5 mm slot die at 126 °C and a throughput of 4.5 kg/h, which yielded foams with a cell size of 25 μm with just 1 wt% TRGO (thermally reduced graphite oxide). Jing Wang et al. [185] investigated the extrusion foaming behavior of PLA with varying molecular weights and branched topologies. They observed that cell density and expansion rate all increased with molecular weight and branching density. For the branched PLA, crystallization enabled stable production of high expansion ratio microcellular foams across a broad temperature range. By controlling crystallinity, it became feasible to produce foams with consistent cell morphology while achieving variations in mechanical properties and surface gloss.

4.3 Injection foaming

Foam injection molding essentially extends the conventional injection molding procedure by incorporating an additional gas injection unit (see Fig. 12). Initially, raw material is introduced into the barrel and directed to the front section of the extruder, where it undergoes melting facilitated by high temperature and screw-driven shearing. Subsequently, gas is introduced into the extruder through a gas injection device, diffusing and dissolving within the melt to establish a homogeneous system. This homogeneous system is then transported to a diffusion chamber. Due to the sudden increase in temperature, the solubility of gas in the melt rapidly decreases, inducing a state of supersaturation and initiating nucleation. During this process, the system maintains high pressure to deter premature cell expansion during mold filling. Bubbles commence growth during the depressurization process following mold filling.

Fig. 12
figure 12

Schematic representation of foam injection

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Microcellular injection foaming technology stands as one of the prevalent techniques for producing microcellular foam materials, characterized by product cell sizes smaller than those found in traditional foam plastics. These microcells serve to passivate the pre-existing material defects and microcracks, subsequently enhancing plastic strength and, consequently, material mechanical properties. As a result, microcellular injection foaming technology has emerged as a prominent research focus within the field of polymer foam molding.

Li et al. [186] utilized supercritical N2 to foam polyetherimide with 1 wt% of multiwalled carbon nanotubes, achieving foams characterized by an average cell size of 16.7 μm through the uniform dispersion of multiwalled carbon nanotubes within the polymer matrix. Ming-Cheng Guo et al. [187] investigated the cell structure and mechanical properties of PP foamed samples. They observed that smaller, uniformly distributed cells were attainable with higher injection speeds and lower injection pressures. Tong Lisheng [188,189,190,191,192,193] employed microcellular injection foaming to prepare PA6-Clay nanocomposites, noting that uniform cell formation was favored by lower melting temperatures, higher gas content, and increased injection speed. Pilla. S and Hwang. S et al. [194,195,196] delved into the impact of nanoparticle additives on PLA foaming behavior in microcellular injection molding. They reported that the inclusion of nanoparticles enabled the production of foaming materials featuring an average cell diameter ranging from 3 to 40 μm.

5 Conclusions

In the context of growing energy shortages, polymer foam products have garnered significant attention due to their material-saving and cost-effective attributes, coupled with their commendable mechanical and thermal stability, low thermal conductivity, and exceptional dielectric properties. As environmental concerns become increasingly pronounced, green chemistry emerges as a pivotal approach to address environmental and energy challenges. Supercritical foaming technology, as a green technique, aligns more closely with contemporary demands, and consequently, it has found extensive utility in the fabrication of microcellular polymer foam products. Supercritical foaming technology, in comparison to chemical foaming, yields microcellular plastic foam with higher cell densities, smaller cell sizes, and superior comprehensive properties.

Common foaming agents employed in supercritical foaming technology include supercritical CO2 and supercritical N2. Supercritical CO2 exhibits superior solubility and diffusion rates in polymers when compared to supercritical N2, making it the predominant foaming agent in supercritical foaming technology. When supercritical N2 is used as a blowing agent, it leads to foams characterized by smaller cell diameters, greater cell densities, and uniform cell sizes. However, in the context of supercritical foaming technology, utilizing N2 as a foaming agent presents limited success rates, leading to relatively high N2 consumption. Incorporating co-foaming agents (additional reagents mixed with supercritical CO2 or supercritical N2) in supercritical foaming technology can enhance both foaming capacity of sample and the performance of foamed products.

Polymer foaming constitutes a complex dynamic process. To attain foams with high cell density and small cell size, comprehending the gas dissolution and diffusion within the polymer, the mechanisms of cell nucleation and growth, and the requisite foaming conditions is essential. Gas dissolution and diffusion in polymers yield a plasticizing effect, enhancing the fluidity of the polymer matrix, consequently reducing the free energy barrier for cell nucleation and affecting nucleation and growth. The preferred nucleation rates are driven by high thermodynamic instability, stemming from pronounced temperature and pressure gradients, as well as substantial CO2 absorption. An alternative strategy for controlling nucleation rates and cell growth is to combine various nucleating agents to manipulate the heterogeneous nucleation phenomenon. Additionally, cell growth mechanisms can be elucidated through prior experiments and theoretical investigations.

Batch foaming technology affords precise control and is widely employed for studying the influence of various process parameters (e.g., time, temperature, pressure, and depressurization rate) on polymer foaming behavior. Batch foaming yields uniform cell sizes, enables controlled cell shapes, and results in relatively superior foam performance. However, its limited suitability for continuous production hinders its commercial application. Extrusion foaming offers advantages such as continuous production, high output, and minimal investment, with the additional advantage of unrestricted product length. Injection foam is well-suited for fabricating small, intricate parts in the industrial sector. Notably, there are fewer studies on injection foaming compared to batch and extrusion foaming, possibly attributed to the higher mechanical costs associated with injection foaming.

Researchers have extensively investigated supercritical foaming technology and its mechanisms, achieving significant advancements. Yet, certain topics remain underexplored, including (a) the industrial-scale production of polymer foams; (b) the influence of thermal history on foaming behavior; (c) the effect of rheological properties such as viscoelasticity and melt strength on foaming behavior; (d) the development of novel foaming agents; (e) the innovation of new foaming techniques. As polymer supercritical foaming technology advances continuously, the overarching trend is to produce highly integrated, precise, and top-quality foam products. By regulating the aggregated structure and morphology of polymer products, foam performance can be elevated to meet evolving product requirements. Diverse, high-quality foam products are poised for broad applications and promising prospects.