The mechanics of solid-state nanofoaming

Abstract

Solid-state nanofoaming experiments are conducted on two polymethyl methacrylate (PMMA) grades of markedly different molecular weight using CO2 as the blowing agent. The sensitivity of porosity to foaming time and foaming temperature is measured. Also, the microstructure of the PMMA nanofoams is characterized in terms of cell size and cell nucleation density. A one-dimensional numerical model is developed to predict the growth of spherical, gas-filled voids during the solid-state foaming process. Diffusion of CO2 within the PMMA matrix is sufficiently rapid for the concentration of CO2 to remain almost uniform spatially. The foaming model makes use of experimentally calibrated constitutive laws for the uniaxial stress versus strain response of the PMMA grades as a function of strain rate and temperature, and the effect of dissolved CO2 is accounted for by a shift in the glass transition temperature of the PMMA. The maximum achievable porosity is interpreted in terms of cell wall tearing and comparisons are made between the predictions of the model and nanofoaming measurements; it is deduced that the failure strain of the cell walls is sensitive to cell wall thickness.

Molecular dynamics simulations of ultrathin PMMA films

“…Note that the elastic rubbery regime above the glass transition is absent for the current linear (N-s-b: 1000-0-0) PMMA films. This is consistent with the experimentally observed response of the linear (N-s-b: 924-0-0) PMMA in bulk form [35].…”

“…The practical usefulness of the results is then illustrated by a nanofoaming case study: we make use of the thickness−dependent tensile ductility to provide molecular−level insight into the rupture of cell walls during solid−state nanofoaming of PMMA. The results support the hypothesis that cell wall tearing accounts for the observed limit in maximum attainable porosity [35].…”

“…for the case of uniaxial tension at a nominal strain rate of 5.9 × 10 −2 s −1 [35]. Both the MDpredicted and the measured [35] values of yield stress decrease with increasing temperature.…”

“…3a. MD-predicted T g value of the overall film is 379 K. For reference, the MD-predicted and the measured T g values of PMMA in bulk form are 417 K (for N-s-b: 1000-0-0) and 388 K (for N-s-b: 924-0-0 by differential scanning calorimetry at a heating rate of 10 K/min [35]), respectively. At each value of T /T g , the mass density of the free surface layers (1 and 7) is markedly less than that of the inner layers (2 to 6), implying that the molecular free volume and the molecular mobility of the free surface layers are greater than the interior to the film.…”

“…In the glassy and glass transition regimes, the MD-predicted failure strain f for the film exceeds that measured experimentally for the bulk; this is attributed to the fact that preexisting defects are present in macro-scale specimens [16] but are absent in the current MD systems. For example, for the linear (N-s-b: 924-0-0) PMMA in bulk form, the measured true tensile failure strain f decreases almost linearly from f = 2.82 at T /T g = 1.04 to f = 0.6 at T /T g = 0.97 in uniaxial tension at a nominal strain rate of 5.9 × 10 −2 s −1 [35]. In contrast, for a linear (N-s-b: 1000-0-0) PMMA film, of thickness h = 48.3 nm (h/d ee = 1.05), subjected to uniaxial tension, the MD-predicted true failure strain f decreases almost linearly from f = 2.58 at T /T g = 1.49 to f = 2.45 at T /T g = 0.75.…”