Environmental Nanoparticle-Induced Toughening and Pinning of a Growing Crack in a Biopolymer Hydrogel

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Environmental Nanoparticle-Induced Toughening and Pinning of a Growing Crack in a Biopolymer Hydrogel

O. Ronsin, I. Naassaoui, A. Marcellan, and T. Baumberger

Phys. Rev. Lett. 123, 158002 – Published 8 October 2019

Abstract

We study the interplay between a crack tip slowly propagating through a hydrogel and nanoparticles suspended in its liquid environment. Using a proteinic gel enables us to tune the electrostatic interaction between the network and silica colloids. Thereby, we unveil two distinct, local toughening mechanisms. The primary one is charge independent and involves the convective building of a thin particulate clog, hindering polymer hydration in the crack process zone. When particles and network bear opposite charges, transient adhesive bonding superimposes, permitting the remarkable pinning of a crack by a liquid drop.

Received 19 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.158002

Physics Subject Headings (PhySH)

Biomechanics Biomimetic & bio-inspired materials Cracking Fracture Tissue engineering

Biological materials Nanoparticles Polymer gels

Condensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

O. Ronsin¹, I. Naassaoui^1,2, A. Marcellan³, and T. Baumberger¹

¹Institut des NanoSciences de Paris, Sorbonne University, CNRS, F-75005 Paris, France
²Laboratoire de Physique de la Matière Molle et de la Modélisation Électromagnétique, Université de Tunis, El Manar, 2092 Tunis, Tunisia
³Laboratoire Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL University, Sorbonne University, CNRS, F-75005 Paris, France

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Vol. 123, Iss. 15 — 11 October 2019

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Images

Figure 1
Left: Schematic representation of a crack propagating a velocity $V$ in the midplane of a stretched gel slab. A drop of NP solution moves along with the crack tip. The amount of elastic energy $G$ released by opening a unit area of crack surface is imposed by the fixed grip displacement (vertical arrows). The crack opening $Δ h$ is typically a few millimeters. Right: Enlargement of the tip, showing the PZ of depth $d$ and height $Λ$ , made of polymer chains (red online) pulled out taut from the gel matrix. Triple-helix cross-links, distant of $ξ$ (mesh size) on average, are unzipped at the frontier between the fibrillar zone and the bulk. Because of the nonlinear elastic response of the surrounding matrix, the PZ is quasi-2D (aspect ratio $d / Λ ≪ 1$ ), perpendicular to the crack plane. Nanoparticles (blue online) have diameters $2 R ≳ ξ$ .
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Figure 2
Time-dependent position of an initially dry, steady crack in a gelatin $A$ hydrogel. Upon wetting (at $t = 0$ ) its tip by a drop of AM Ludox solution (see the inset) at a fixed grip, a new steady state is reached. Depending on the silica volume fraction $ϕ$ , the crack speeds up ( $ϕ = 0$ ), slows down ( $ϕ_{1} = 5 %$ ), or even gets pinned ( $ϕ_{2} = 16 %$ ). (See Supplemental Movies [30].)
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Figure 3
(a) Rate-dependent fracture energies $Γ (V)$ of cracks in a weakly negatively charged gelatin $B$ gel with different tip environments: wet (lower curve), dry (upper curve), and $NP ϕ$ (intermediate curves) with negatively charged TM-grade silica nanoparticles of volume fraction increasing from right to left: $ϕ = 4.8 %$ , 10%, 16%, 23%, 31%. Curves are guides for the eyes. (b) Fracture energy shifts with respect to the wet case. The poroelastic velocity $V_{poro} ≃ 2 mm s^{- 1}$ and the associated drained and undrained crack propagation regimes are defined in the text. In the undrained limit, the energy shift reaches a plateau $Δ Γ^{dry}$ for a dry crack and $Δ Γ^{NP} (ϕ)$ for a $NP ϕ$ crack.
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Figure 4
Reduced toughening parameter in the undrained regime for gelatin $B$ gels (repulsive case) plotted with respect to the dimensionless parameter $ϕ d / R$ with $d = 100 nm$ the depth of the process zone (as estimated in Ref. [12]) and nanoparticle radii: $R = 6 nm$ for AM particles (small bullets) and $R = 11 nm$ for TM particles (big circles). Bars indicate the standard deviation over 3–4 different samples. The linear fit corresponds to the clog model $Δ Γ_{clog} = C ϕ d / R$ with $C ≃ 0.2$ .
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Figure 5
(a) Relative fracture energy shift for gelatin $A$ gels and TM nanoparticles (adhesive case). The data for $NP ϕ$ cracks are ordered from bottom to top with increasing silica volume fraction. Curves are guides for the eyes. The values of $ϕ$ and colors (online) are the same as in Fig. 3. Note that the dry crack curve stands in an intermediate position. (b) Adhesive contribution to crack toughening $Δ Γ_{adh}$ (see the text) with respect to the silica volume fraction $ϕ$ , for AM (small bullets) and TM (big circles) particles. (c) Schematic representation of the fracture energy of a crack in its three tip states (dry, wet, and $NP ϕ$ in the adhesive regime) showing the geometric construct of the crack velocity at constant energy release rate $G$ . A dry crack running at velocity $V_{0}$ speeds up to $V_{1}$ upon wetting by pure solvent but gets pinned upon wetting by a suitably concentrated NP solution (see Fig. 2 and Supplemental Movies [30]).
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