VIII. Why Does Aerogel Shrink During Drying?
1. Core Physics: Capillary Pressure (Laplace Pressure)
· During drying, liquid–gas interfaces form menisci inside nanopores, exerting negative capillary pressure on the fragile skeleton:
P=2γcosθrP = \frac{2 \gamma \cos \theta}{r}
· γ\gamma: surface tension of solvent
· θ\theta: contact angle (for hydrophilic surfaces, θ≈0∘\theta \approx 0^\circ, cosθ≈1\cos \theta \approx 1)
· rr: pore radius (smaller pore → higher stress)
· Magnitude example (hydrophilic case):
o Ethanol: γ≈0.022 N/m,r=10 nm⇒P≈4.4 MPa\gamma \approx 0.022\ \text{N/m}, r=10\ \text{nm} \Rightarrow P \approx 4.4\ \text{MPa}
o Water: γ≈0.072 N/m,r=10 nm⇒P≈14.4 MPa\gamma \approx 0.072\ \text{N/m}, r=10\ \text{nm} \Rightarrow P \approx 14.4\ \text{MPa}
Such stress is far above the yield strength of the “wet” silica skeleton, leading to elastic–plastic deformation, pore collapse, shrinkage, densification, or even cracking.
2. Structural & Chemical Factors
· Smaller pores / narrow distribution → stronger capillary stress.
· Insufficient neck growth (weak skeleton) due to poor aging → prone to irreversible plastic shrinkage.
· Surface state: hydrophilic Si–OH surfaces (low θ\theta) → high stress; hydrophobic surfaces (high θ\theta) reduce stress.
· Solvent: high γ\gamma (e.g., water) increases stress.
· Sample geometry: thick monoliths develop drying gradients → cracks; thin films/felts are less prone.
· Pre-shrinkage (syneresis) during gelation/aging can set the stage for further collapse.
Summary: Shrinkage mainly comes from capillary pressure; small pores, hydrophilic surfaces, high-γ\gamma solvents, weak skeletons, and thick parts all worsen it.