Gas dissolution 22

The first stage of microcellular injection molding is creating the polymer/gas solution. As aforementioned above, every foaming technology differs from the other in the way of introducing the gas into the polymer. MuCell® places its gas injector unit in the dosing zone of the barrel, while IQ Foam® incorporates the gas at the feeding area of the plasticizing unit together with the polymer in pellets form. Thus, in both cases the polymer/gas solution is formed once the polymer is melt inside the barrel. As the gas flows into the molten polymer, big gas droplets are generated, whose size depends on the gas pressure, gas flow rate, viscosity of the plastic and wiping frequency of the flights [58].

Figure 2.7. Stages of microcellular polymer foaming process.

Then, the screw rotation induces elongation of the gas droplets by shear deformation, until they break up into many small gas droplets. These gas droplet are stabilized in the screw channels to form bubbles which diffuses quickly into the polymer due to shear deformation increasing area-to-volume ratio. As a result, a polymer/gas solution with excellent tiny bubbles distribution is created, which could be ideally considered as a single-phase solution, that is, without separation between gas and polymer phases.

The main difficulty when making a nice single-phase solution is the limited mixing time and short recovery time in the plasticizing unit within the conventional injection molding cycle. For this reason, MuCell® developers leaned towards injecting the gas into the molten polymer at supercritical conditions. In this state, that is, at pressure and temperature above the critical point (Figure 2.8) the blowing agent exhibit some properties that maximize the solubility and dissolution in the polymer [70]. On one hand, the supercritical fluid (SCF) has liquid-like properties, like the density. On the other hand, it keeps some gas-like properties, such as low viscosity and surface tension. Both liquid-like and gas-like properties are essential to precisely meter the SCF and mix with the molten polymer. In case of IQ Foam®, gas does not require to be injected at supercritical conditions, due to the fact that polymer and gas move forward along the barrel from the feeding zone to nozzle, having longer time and space to increase pressure and temperature and form the proper polymer/gas solution. In the view of the above, it may be concluded that solubility and diffusivity are the key factors for achieving foams with the desired fine cell structure. Solubility is the capability of the gas to be dissolved in the molten polymer. Usual techniques for measuring solubility is the increase in mass due to the gas sorption [71]. Thus, the higher the solubility, the more amount of gas is absorbed by the polymer. According to experiments conducted by Sato et al. [72] solubility increases almost linearly with pressure and decreases with increasing temperature. Nevertheless, if energy is absorbed from dissolution process (case of organic solvents like polymers), a “reverse solubility” phenomena occurs and solubility raises with temperature.

Figure 2.8. Diagram of material phases. Modified from [58].

Either way, solubility changes more quickly with the pressure than with the temperature, so an increase in solubility with the pressure is expected in most cases, being the effect of temperature secondary [58]. At this point, within the plasticizing stage of the injection molding machine, under high pressure and temperature, the solubility of the gas is also high and the polymer becomes saturated with the blowing agent.

The gas concentration (C) can be estimated by the Henry’s law [73], as a function of the molten polymer pressure (Pm) and temperature (Tpoly) in thermodynamic equilibrium:

𝐶 = 𝐻(𝑃𝑚, 𝑇𝑝𝑜𝑙𝑦)𝑃𝑚 (2.2)

Where H is the Henry’s law constant. It is constant at low temperatures, but it becomes time-dependent as temperature raises:

𝐻 = 𝐻₀𝑒−𝐸𝑠/𝑅𝑔𝑇𝑝𝑜𝑙𝑦 _(2.3)

In Equation (2.3), H0 is a preexponential constant for Henry’s law, Es is the activation

energy and Rg is the gas constant.

Some Henry’s law constants have been determined experimentally, and an experimental relationship for amorphous polymers has been also found [74]:

Here, Tcr is the critical temperature of the gas. The gas concentration in semicrystalline

plastics depends on the extent of crystallinity (Xc) and the solubility of the gas in an

amorphous region of the semicrystalline polymer (Xa):

𝐶 = (1 − 𝑋_𝑐)𝑋𝑎 (2.5)

On the other hand, diffusivity refers to the rate at which gas molecules move through the molten polymer matrix [58]. It determines the time needed to dissolve the blowing aging in the polymer as well as the kinetics of cell nucleation and growth. The diffusion coefficient D can be determined by sorption/desorption experiments and through the Fick’s second law [75]: 𝑀𝑡 𝑀₀ = 4 · (𝐷/𝜋) 1/2_(𝑡 𝑎 1/2 /ℎ) (2.6)

Where M0 is the equilibrium concentration of gas without desorption, Mt is the amount

of gas absorbed by the polymer at time ta and h is the sample thickness. A theoretical

diffusion coefficient can be also estimated following an Arrhenius-type temperature- dependence law [56] with a maximum diffusion coefficient D0 (at infinite temperature), the

activation energy for diffusion Ed, the molar gas constant Rg, and the absolute temperature T:

𝐷 = 𝐷0𝑒−𝐸𝑑/𝑅𝑔𝑇 (2.7)

Diffusivity of gases is low at room temperature, and increases considerably with the temperature. Diffusivity is also dependent on the blowing agent. Gases with lower molecular weight, such as carbon dioxide (CO2) and nitrogen (N2), present higher diffusivity under same

pressure and temperature conditions, resulting in higher cell nucleation and growth. Solubility and diffusivity also varies with the polymer matrix. Lin et al. [76] concluded that amorphous polymers absorbed much more gas and at higher rate than semicrystalline ones. Even in semicrystalline plastics, crystalline regions prevent from gas concentration and the blowing agent is absorbed by amorphous regions [77], giving rise to non-uniform cell distribution in the foam. In reinforced polymers, gas solubility is improved because of gas concentration in the interphase between polymer and fillers [58].

Carbon dioxide (CO2) and nitrogen (N2) are commonly employed as physical blowing

agents because they are chemically inert, inexpensive, non-flammable and non-toxic permanent gases. Additionally, they can be easily processed at supercritical conditions, due to

their low critical pressure and temperature points. Table 2.1 displays the physical properties of both gases. They have similar diffusion rates, but lower solubility of N2 than that of CO2

has been reported [78, 79]. However, N2 has been found to be more effective to produce

foams with larger cell densities and reduced cell sizes in Polypropylene (PP) and Polyethylene (PE) [80, 81].

Table 2.1. Physical properties of CO2 and N2 blowing agents [58].

Property CO2 N2

Molecular weight 44 28

Gas density at 21 ºC (g/cm3) 0.00183 0.00116

Thermal conductivity (W/m·K) / ºC 0.0166 / 30 0.0261 / 27

Boiling point (ºC) -78.5 -

Vapor specific heat (cal/g·K)/ºC 0.204 / 25 0.243 / 25

Heat of vaporization (cal/g) 137 -

Global warming potential (GWP) 0.00025 -

Triple point, temperature (ºC) / pressure (MPa) -57 / 0.52 -

Critical temperature (ºC) 31.1 -147.0

Critical pressure (MPa) 7.22 3.4

Density at 25 ºC (g/cm3) 1.811 1.146