Cracking in Drying Colloidal Films

It has long been known that thick films of colloidal dispersions such as wet clays, paints, and coatings crack under drying. Although capillary stresses generated during drying have been recently identified as the cause for cracking, the existence of a maximum crack-free film thickness that depends on particle size, rigidity, and packing has not been understood. Here, we identify two distinct regimes for crack-free films based on the magnitude of compressive strain at the maximum attainable capillary pressure and show remarkable agreement of measurements with our theory. We anticipate our results to not only form the basis for design of coating formulations for the paints, coatings, and ceramics industry but also assist in the production of crack-free photonic band gap crystals.

Figure 1

Thickness profile of a dried film. (a) Thickness profile measured along the diameter of a dry styrene-butadiene film. (b) SEM of the film surface in the crack-free region. (c) SEM of the film interior in the crack-free region. The region between $S$ and $T$ was crack-free.

Figure 2

Critical thickness variations as a function of the shear modulus. At random close packing, the menisci at the top particle layer exert a compressive force on the particle network. For very soft particles, the particles deform completely to close the voids for capillary pressure less than the maximum so that the uniaxial compressive strain is $\epsilon \equiv \frac{(h_{\mathrm{rcp}}-h)}{h_{\mathrm{rcp}}}=1-{\varphi }_{\mathrm{rcp}}$. In case of hard particles, the menisci adjust their curvature till the maximum capillary pressure ($P_{\max }$) is reached, beyond which they recede into the network resulting in partial deformation.

Figure 3

The measured critical thickness vs the characteristic scale, $\frac{GM{\varphi }_{\mathrm{rcp}}{R}^3}{2\gamma }$. The data points are for films of acrylic [■, $G=0.8\mathrm{GPa}$, $2R=82$, 133, 206, and 353 nm, and ${\varphi }_{\mathrm{rcp}}(M)=0.65(6.7)$, 0.66(6.8), 0.68(7.0), and 0.67(6.9), respectively], styrene-butadiene [○, $G=1\mathrm{GPa}$, $2R=250\mathrm{nm}$, and ${\varphi }_{\mathrm{rcp}}(M)=0.64(6.6)$], silica [▴, $G=31\mathrm{GPa}$, $2R=330$, and 22 nm, and ${\varphi }_{\mathrm{rcp}}(M)=0.60(6.1)$ for both], alumina [8] [●, $G=156\mathrm{GPa}$, $2R=230$, 379, 458, and 489 nm, and ${\varphi }_{\mathrm{rcp}}(M)=0.60(6.1)$ for all], polystyrene [8] [★, $G=1.6\mathrm{GPa}$, $2R=300\mathrm{nm}$, and ${\varphi }_{\mathrm{rcp}}(M)=0.60(6.1)$], and zirconia [8] [$*$, $G=81\mathrm{GPa}$, $2R=200\mathrm{nm}$, and ${\varphi }_{\mathrm{rcp}}(M)=0.60(6.1)$]. Here the value of surface tension, $\gamma$, is taken as $0.072\mathrm{N}/\mathrm{m}$ for all the cases. The solid line is a power law with an exponent $1/2$ and the multiplying coefficient is obtained via regression. The inset plots the same data in the nondimensional form.