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, 8 (1), 16817

Apparent Strength Versus Universality in Glasses of Soft Compressible Colloids

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Apparent Strength Versus Universality in Glasses of Soft Compressible Colloids

Ruben Higler et al. Sci Rep.

Abstract

Microgel colloids, solvent swollen hydrogel particles of microscopic size, are in osmotic equilibrium with their surroundings. This has a profound effect on the behaviour of dense solutions of these polymeric colloids, most notably their ability to swell and deswell depending on the osmotic pressure of the system as a whole. Here we develop a minimal simulation model to treat this intrinsic volume regulation in order to explore the effects this has on the properties of dense solutions close to a liquid-solid transition. We demonstrate how the softness dependent volume regulation of particles gives rise to an apparent change in the fragility of the colloidal glass transition, which can be scaled out through the use of an adjusted volume fraction that accounts for changes in particle size. Moreover, we show how the same model can be used to explain the selective deswelling of soft microgels in a crystalline matrix of harder particles leading to robust crystals free of defects. Our results not only highlight the non-trivial effects of osmotic regulation in governing the apparent physics of microgel suspensions, but also provides a platform to efficiently account for particle deswelling in simulations.

Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
(AC) Visual representation of two-dimensional glasses of compressible particles where the particles are colour-coded according to their relative deswelling ratio a/a0 as indicated by the colour bar, for κ = 50000 and ζ/ζg = 0.59 (A), κ = 500 and ζ/ζg = 0.58 (B) and κ = 50 and ζ/ζg = 0.59 (C). (DL) Distribution of relative particle sizes, illustrating the extent of osmotic deswelling as a function of compressibility scale κ for κ = 50000 and ζ/ζg = 0.59 (D), 0.23 (G), 0.10 (J), κ = 500 and ζ/ζg = 0.58 (E), 0.23 (H), 0.06 (K) and κ = 50 and ζ/ζg = 0.59 (F), 0.23 (I), 0.10 (L).
Figure 2
Figure 2
(A) Radial distribution function, g(r), calculated for simulation snapshots at ζ = 1.15 for κ = 5, 50, 500, 5000, & 50000 (left triangles, down triangles, circles, up triangles, squares). (B) Fs(q, t) from triplicate repeats and the original simulation for ζ = (from left to right) 0.646, 0.769 & 0.86. (C) Self-intermediate scattering functions Fs(q, t) from simulations (symbols) and fitted as described in the text (lines) for q = 5.2 μm−1, κ = 50000 and ζ = (from left to right) 0.0581, 0.103, 0.149, 0.192, 0.232, 0.258, 0.287, 0.322, 0.363, 0.413, 0.474, 0.534, 0.568, 0.605, 0.646, 0.769, 0.860, 0.930 & 1.010. (D) Terminal structural relaxation time τ as a function of the effective packing fraction ζ and (E) the same data in an Angell representation, where ζg is defined as the condition where log(τ/τ0) = 5. Inset: Kinetic fragility index m as a function of osmotic deswelling energy κ, dotted line at m = 5 gives the limiting fragility for a purely strong glass, dotted line at m = 38 that for the most fragile glass in these simulations. (F) The same data plotted as a function of ϕ, as calculated according to equation 4. Inset: Stretched-exponential exponent γ as a function of ϕ for all κ as in (A).
Figure 3
Figure 3
(A) Overlap area per particle, averaged over the last 100 simulation snapshots, as a function of ϕ. The dashed line indicated the maximum overlap found at 0.34 σ2. Inset: Same data plotted as a function of ζ. (B) Average change in area of the particles as a function of ϕ. As in panel A this is averaged over the last 100 simulation snapshots. Dashed line again indicates a value of 0.34 σ2.
Figure 4
Figure 4
Displacement probability distribution Px) from our simulations. For soft particles, κ = 50, (A) and incompressible particles, κ = 50000, (B) Both have displacements recorded at dt* ≈ 6 and dt* ≈ 1100. Note the difference in true volume fraction, ϕ, between the two samples. (C) Non-Gaussian parameter β2 for soft particles, κ = 50 and (D) for incompressible particles, κ = 50000. As a function of lag time t for a wide variety of packing fractions (red = low, blue = high), (E) Maximum value of the non-Gaussian parameter β2max as a function of the extrapolated packing fraction ζ and (F) as a function of the true volume fraction ϕ.
Figure 5
Figure 5
Left: Osmotically-induced particle size fluctuations as a function of time, for κ = 50 (red triangles), κ = 500 (blue circles), and κ = 50000 (green squares). Right: corresponding probability distributions P(a) of the size of a single particle over time, which reveal a Gaussian shape. All samples are at ζ = 0.93.
Figure 6
Figure 6
Snapshot from the simulations with the particles color coded according to their a/a0, with their displacements δr over a time interval equal to the lag-time of β2max projected as a scaled red line, for (A) κ = 50, ζ = 0.93 (ϕ = 0.46), and dt* = 71 at 1.5x original displacements (B) κ = 500, ζ = 0.93 (ϕ = 0.71), and dt* = 529 at 1.5x original displacements (C) κ = 50000, ζ = 0.93 (ϕ = 0.92), and dt* = 4180 at 2.5x original displacements. (D) Probability distribution of cluster size for cluster made up of the 10% most mobile particles. Calculated for three samples at the same ζ and κ = 50, 500 & 50000 corresponding to panels (A–C). Dashed lines are guides to the eye (E) Probability distribution of cluster size for cluster made up of the 10% most mobile particles. Calculated for three samples at similar volume fractions, ϕ = 0.63, 0.63 & 0.64, and κ = 50, 500 & 50000. Dashed lines are guides to the eye.
Figure 7
Figure 7
Left: Probability distributions P(a) of the size of a single particle over time for a particle in the crystalline matrix far away from the intruder (red circles) and for the intruder (blue triangles). Calculated from simulations with κi = 5000 ((A) equal to the matrix) and κi = 500 ((B) weaker than the matrix). Right: corresponding ψ6 maps, calculated over the average of 1000 consecutive simulation snapshots. The maps show a small fraction of the simulation box (N = 2025) centred around the intruder particle depicted in red. All samples are hexagonal close-packed at initiation of the simulation.

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