Plasticity and Fracture in Drying Colloidal Films

Lucas Goehring, William J. Clegg, and Alexander F. Routh

Phys. Rev. Lett. 110, 024301 – Published 7 January 2013

Abstract

Cracks in drying colloidal dispersions are typically modeled by elastic fracture mechanics, which assumes that all strains are linear, elastic, and reversible. We tested this assumption in films of a hard latex, by intermittently blocking evaporation over a drying film, thereby relieving the film stress. Here we show that although the deformation around a crack tip has some features of brittle fracture, only 20%–30% of the crack opening is relieved when it is unloaded. Atomic force micrographs of crack tips also show evidence of plastic deformation, such as microcracks and particle rearrangement. Finally, we present a simple scaling argument showing that the yield stress of a drying colloidal film is generally comparable to its maximum capillary pressure, and thus that the plastic strain around a crack will normally be significant. This also suggests that a film’s fracture toughness may be increased by decreasing the interparticle adhesion.

Received 8 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.024301

Authors & Affiliations

Lucas Goehring^1,*, William J. Clegg^2,†, and Alexander F. Routh^3,4,‡

¹Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany
²Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, United Kingdom
³Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom
⁴BP Institute for Multiphase Flow, University of Cambridge, Madingley Rise, Madingley Road, Cambridge CB3 0EZ, United Kingdom

^*lucas.goehring@ds.mpg.de
^†wjc1000@cam.ac.uk
^‡afr10@cam.ac.uk

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Vol. 110, Iss. 2 — 11 January 2013

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Images

Figure 1
Directional drying occurs when a thin colloidal film dries from its edges inward (e.g., Refs. 1, 16, 17, 38). A series of drying fronts form and travel toward (1) the still-liquid region of the film. As the material dries it first (2) orders, then (3) solidifies into an aggregated, porous particle network. Evaporation continues from the saturated film, balanced by the flow of dispersant toward the drying fronts from the liquid region. This flow is driven by a gradient in capillary pressure that also leads to (4) fracture. When the capillary pressure is large enough (5) the pores open and the film dries. Understanding the mechanical properties relevant to film fracture has proved challenging, as these properties are transitory, changing when the film dries into region (5).Reuse & Permissions
Figure 2
The crack opening width $δ$ varies as $\sqrt{r}$ , near its tip. Shown are averages of at least ten crack widths with $a = 72 nm$ in films with dried thicknesses of $5 μ m$ (green triangles), $26 μ m$ (red crosses), and $95 μ m$ (blue dots), and a best-fit square-root line to the thick-film data. Arrows indicate film thickness, after which deviations from this line are expected, as $δ$ saturates. The inferred ratio (inset) of fracture toughness to Young’s modulus, $K_{C} / E$ , has no strong dependence on particle radius, over the range 50–100 nm.Reuse & Permissions
Figure 3
Approximately 20%–30% of the crack opening $δ$ is reversible. (a) When evaporation over a film of colloidal polystyrene ( $a = 58 nm$ ) is blocked by a glass slide, $δ$ decreases from its stressed value $δ_{0}$ . (b) By repeatedly covering and uncovering the film, the crack repeatedly closes and opens. (c) A similar degree of closure can be achieved by flooding part of a film ( $a = 72 nm$ ), eliminating evaporation locally. The inset shows the same crack before and after flooding, with the crack tip and extent of flooding indicated by arrows.Reuse & Permissions
Figure 4
Topographic atomic force micrographs of drying latex ( $a = 99 nm$ ). (a) A crack shows damage and microcracks ahead of the crack tip. Out-of-plane deformation is also noticed: the height profile across the overlain line segment (inset) shows a step in height of one stacking plane ( $λ = 2 a \sqrt{6} / 3$ ). (b) Another crack shows a damage zone that develops into a bridge when (c) the crack advances. The particles (d) immediately adjacent to a crack face (the black region partly seen at the bottom of the image) rearrange when (e) the crack advances. Here the dashed boxes highlight two particular areas where a large particle submerges and where many particles rearrange.Reuse & Permissions

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