Origin and detection of microstructural clustering in fluids with spatial-range competitive interactions

Ryan B. Jadrich, Jonathan A. Bollinger, Keith P. Johnston, and Thomas M. Truskett

Phys. Rev. E 91, 042312 – Published 23 April 2015

Abstract

Fluids with competing short-range attractions and long-range repulsions mimic dispersions of charge-stabilized colloids that can display equilibrium structures with intermediate-range order (IRO), including particle clusters. Using simulations and analytical theory, we demonstrate how to detect cluster formation in such systems from the static structure factor and elucidate links to macrophase separation in purely attractive reference fluids. We find that clusters emerge when the thermal correlation length encoded in the IRO peak of the structure factor exceeds the characteristic length scale of interparticle repulsions. We also identify qualitative differences between the dynamics of systems that form amorphous versus microcrystalline clusters.

Received 12 December 2014
Revised 3 April 2015

DOI:https://doi.org/10.1103/PhysRevE.91.042312

Authors & Affiliations

Ryan B. Jadrich^*, Jonathan A. Bollinger^*, Keith P. Johnston, and Thomas M. Truskett^†

McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA

^*Contributed equally to the work.
^†truskett@che.utexas.edu

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Vol. 91, Iss. 4 — April 2015

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Figure 1
(a) Structure factors $S (k)$ for reference attractive (RA, red dashed curve) and short-range attractive long-range repulsive (SL, blue solid curve) fluids at packing fraction $ϕ = 0.125$ for repulsions with ranges $ξ_{R}$ and strengths $β A$ . Curves are derived from integral equation theory, where the $ξ_{R} = 10$ curves are shown for attraction $β ε = 4.35$ and the $ξ_{R} = 2$ curves (shifted vertically) are shown for $β ε = 4.75$ . (b),(c) $S (k)$ curves from (a) replotted to highlight $k \to 0$ behaviors. (d) Fourier transforms $β ω (k)$ of the potentials from (a) with $ξ_{R} = 2$ curves shifted vertically. (e) RA and SL potentials $β φ (r)$ for the $ξ_{R} = 2$ case.
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Figure 2
(a) Symbols show thermal correlation lengths $ξ_{T}$ for SL simulations of polydisperse (filled) and monodisperse (unfilled) systems with attractive strengths $β ε$ and packing fractions $ϕ = 0.050$ , 0.125, and 0.250. Symbol shapes indicate whether the state point is dispersed fluid (triangles), clustered (circle), or percolated (diamond), and the horizontal dashed line indicates $ξ_{T} = ξ_{R}$ . Solid lines show $ξ_{T}$ calculated via theory. (b) Phase behavior calculated via theory for potentials from (a), including RA macrophase spinodal (red unfilled squares); SL curves (blue filled squares) corresponding to $ξ_{T} = 2$ and $ξ_{T} = 5$ ; and $S (k_{SL}^{*}) = 2.7$ curve (black x). “L+G” indicates liquid-gas coexistence, “C” indicates clustered phase, and “F” indicates fluid phase. (c) Cluster-size distributions indicating probability $p (n)$ of $n$ -particle cluster formation and (d) $S (k)$ profiles from polydisperse simulations at $ϕ = 0.125$ .
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Figure 3
(a) Phase diagrams calculated via theory, comprising RA macrophase spinodals (unfilled red symbols) and SL $ξ_{T} = ξ_{R}$ curves (filled blue symbols) for $ξ_{R} = 10$ and two repulsive strengths $β A$ . (b) RA spinodals and curves along which $S (k_{SL}^{*}) = 2.7$ (filled black symbols) for the same systems as in (a). (c) Phase diagram calculated via theory comprising RA macrophase spinodal (unfilled red triangles); SL curves corresponding to macrophase spinodal at low $ϕ$ (right-pointing blue triangles) and $ξ_{T} = ξ_{R} = 2$ at high $ϕ$ (left-pointing blue triangles); and disorder line (purple squares) in the fluid region (see text). “L+G” indicates liquid-gas coexistence, “C” indicates clustered phase, and “F” indicates fluid phase.
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Figure 4
Cluster phase simulation snapshots of (a) polydisperse and (b) monodisperse systems at $ϕ = 0.125$ with attractive strength $β ε = 5.2$ and repulsions defined by $ξ_{R} = 2$ and $β A = 0.20$ . Particles comprising a single cluster (determined at time $t$ ) are rendered opaque in their positions at times $t$ (left) and $t^{'} = t + Δ t$ (right). The lag time is $Δ t = 25 τ_{d}$ , where $τ_{d} = d^{2} / D$ is the characteristic time for $d = 1$ particles to diffuse and $D$ is the long-time bulk diffusion coefficient determined via mean-squared displacements. Colors correspond to small, medium $(d = 1)$ , and large particles, which are shaded yellow, red, and blue, respectively. Visualizations created with vmd [23].
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Figure 5
Cluster phase simulation snapshots of polydisperse systems at $ϕ = 0.125$ with various attractive strengths $β ε$ and repulsions defined by $ξ_{R} = 2$ and $β A = 0.20$ . In all snapshots, particles comprising a single cluster (determined at time $t$ ) are rendered opaque in their positions at time $t$ . For cases (a) and (b) that are not gelled, the same particles are also shown in their positions at $t^{'} = t + Δ t$ . The lag time in (a) and (b) is $Δ t = 25 τ_{d}$ , where $τ_{d} = d^{2} / D$ is the characteristic time for $d = 1$ particles to diffuse and $D$ is the long-time bulk diffusion coefficient determined via mean-squared displacements. For cases (c) and (d), the configurations are dynamically arrested and $τ_{d}$ cannot be practically measured within the time scale of simulations. Colors correspond to small, medium $(d = 1)$ , and large particles, which are shaded yellow, red, and blue, respectively. Visualizations created with vmd [23].
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