Abstract
The foaming behaviors of high-density polypropylene–nanoclay composites with intercalated and exfoliated nanoclay particles blown with carbon dioxide were examined via in situ observation of the foaming processes in a high-temperature/high-pressure view-cell. The intercalated nanoclay particles were 300–600 nm in length and 50–200 nm in thickness, while the exfoliated nanoclay particles were 100–200 nm in length and 1 nm in thickness. Contrary to common belief, it was discovered that intercalated nanoclay yielded higher cell density than exfoliated nanoclay despite its lower particle density. This was attributed to the higher tensile stresses generated around the larger and stiffer intercalated nanoclay particles, which led to increase in supersaturation level for cell nucleation. Also, the coupling agent used to exfoliate nanoclay would increase the affinity between polymer and surface of nanoclay particles. Consequently, the critical work needed for cell nucleation would be increased; pre-existing microvoids, which could act as seeds for cell nucleation, were also less likely to exist. Meanwhile, exfoliated nanoclay had better cell stabilization ability to prevent cell coalescence and cell coarsening. This investigation clarifies the roles of nanoclay in plastic foaming processes and provides guidance for the advancement of polymer nanocomposite foaming technology.
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The authors of this paper are grateful to the Consortium of Cellular and Micro-Cellular Plastics (CCMCP) and Natural Sciences and Engineering Council of Canada (NSERC) for their financial support of this study.
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Appendix: classical nucleation theory
Appendix: classical nucleation theory
The CNT and the concept of R cr was first developed by Gibbs (1961). Over the years, various researchers have built on this theory to examine the necessary conditions and free energy barrier for homogeneous nucleation (Blander and Katz 1975; Ward et al. 1970; Forest and Ward 1976, 1978; Tucker and Ward 1975; Katz and Blander 1973) as well as heterogeneous nucleation with different surface geometries (Ward et al. 1983; Ward and Levart 1984; Cole 1974; Wilt 1986; Fisher 1948; Fletcher 1958; Apfel 1971; Jarvis et al. 1975).
Homogeneous nucleation
According to the CNT, the free energy change (ΔF hom) from a metastable liquid–gas solution to the homogeneous formation of a gas bubble within the liquid can be given as (Tucker and Ward 1975; Ward et al. 1970):
where P bub is the pressure inside the bubble; P local is the system pressure surrounding the bubble; V g is the bubble volume; γ lg is the surface tension of the bubble–liquid interface; and A lg is the bubble surface area. The first term on the left hand side (i.e., −(P bub − P local)V g) is the work done by the expansion of gas volume inside the bubble, and the second term (i.e., γ lg A lg) is the work required to create the liquid–gas interface that constitutes the bubble. Assuming that the bubble is spherical in shape, Eq. A1 can be rearranged as:
where R bub is the radius of the bubble. Based on Eq. A2, a ΔF hom versus R bub plot can be generated (see Fig. 1), which exhibits a maximum ΔF hom value. The maximum ΔF hom represents the free energy barrier for homogeneous nucleation (W hom), and the R bub at which ΔF hom is at the maximum is the R cr. Since a system tends to seek a low energy configuration, a bubble smaller than R cr tends to collapse, and a bubble larger than R cr tends to grow spontaneously. By taking the derivative of ΔF hom with respect to R bub and equating it to zero, the R cr could be determined as (Tucker and Ward 1975; Ward et al. 1970):
where P bub,cr is the pressure inside a critical bubble. By substituting Eq. A3 into A2, the free energy barrier for homogeneous nucleation (W hom) can be determined to be (Tucker and Ward 1975; Ward et al. 1970):
Equation A4 indicates that W hom is strongly dependent on γ lg and the degree of supersaturation, which is defined to be (P bub,cr − P local). A lower γ lg and a higher degree of supersaturation would cause R cr and W hom to decrease, which lead to a higher tendency for bubble nucleation.
Heterogeneous nucleation
The derivation of R cr and the free energy barrier for heterogeneous nucleation (W het) could be formulated in a similar fashion. To be specific, the free energy change (ΔF het) from a metastable liquid–gas solution to the heterogeneous formation of a gas bubble within the liquid on a liquid/solid interface can be given as (Ward et al. 1983; Ward and Levart 1984; Cole 1974; Wilt 1986; Fisher 1948; Fletcher 1958; Apfel 1971; Jarvis et al. 1975):
where γ sg and γ sl are the surface tension along the solid–gas interface and solid–liquid interface; and A sg and A lg is the surface area along the solid–gas and liquid–gas interface. Similar to the case of homogeneous nucleation, the first term on the left hand side (i.e., −(P bub − P local)V g) is the work done by the expansion of gas volume inside the bubble. The second term is the energy required to replace the solid–liquid interface (e.g., nucleating agent–polymer interface) with a solid–gas interface (e.g., nucleating agent–bubble interface). The third term (i.e., γ lg A lg) is the work required to create the liquid–gas interface that constitutes the bubble. Using the Young’s equation, which relates the interfacial energies and the contact angle (θ c) between the liquid and gas phase (measured in the liquid phase) (Ward and Tucker 1975):
and the expressions for V g, A sg, and A lg (which is specific to the surface geometry of the nucleating site), Eq. 11 can be simplified to:
where F is a geometric factor that equals to the ratio of the volume of a heterogeneously nucleated bubble to that of a spherical bubble having the same radius of curvature. By taking the derivative of ΔF het with respect to R bub and equating the resulting equation to zero, it can be shown that the expression for R cr is the same as the homogeneous nucleation case (Eq. A3). The expression for W het can then be determined by substituting Eq. A3 into A7; which, after simplification, differs slightly from W hom, as follows (Fisher 1948):
Since F ≤ 1 in most scenarios, W het is lower than W hom in most cases. Therefore, nucleation is more likely to occur heterogeneously on nucleating agents or impurities as supposed to homogeneously within the bulk phase of a polymer–gas solution.
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Wong, A., Wijnands, S.F.L., Kuboki, T. et al. Mechanisms of nanoclay-enhanced plastic foaming processes: effects of nanoclay intercalation and exfoliation. J Nanopart Res 15, 1815 (2013). https://doi.org/10.1007/s11051-013-1815-y
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DOI: https://doi.org/10.1007/s11051-013-1815-y