Stress in aerogel during depressurization of autoclave: I. theory

Aerogels are made by heating a wet gel in an autoclave to a temperature and pressure exceeding the critical point of the solvent, then releasing the pressure. This avoids the capillary stresses that usually cause cracking during drying (since there is no liquid/vapor meniscus above the critical point). However, if the pressure is released too quickly, the fluid inside the gel does not have time to flow out of the network, so it expands within the gel and can cause cracking. The pressure in the pores of the network has been analyzed, so that the stress in the gel can be calculated as a function of the rate of pressure release. Quantitative comparisons of the measured strength of the gel with the calculated stresses (for depressurization rates known to cause cracking) are presented in a companion paper.