Reentrant network formation in patchy colloidal mixtures under gravity

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Reentrant network formation in patchy colloidal mixtures under gravity

Daniel de las Heras, Lucas L. Treffenstädt, and Matthias Schmidt

Phys. Rev. E 93, 030601(R) – Published 1 March 2016

Abstract

We study a two-dimensional binary mixture of patchy colloids in sedimentation-diffusion equilibrium using Monte Carlo simulation and Wertheim's theory. By tuning the buoyant masses of the colloids we can control the gravity-induced sequence of fluid stacks of differing density and percolation properties. We find complex stacking sequences with up to four layers and reentrant network formation, consistently in simulations and theoretically using only the bulk phase diagram as input. Our theory applies to general patchy colloidal mixtures and is relevant to understanding experiments under gravity.

Received 7 December 2015

DOI:https://doi.org/10.1103/PhysRevE.93.030601

Physics Subject Headings (PhySH)

Granular flows

Colloids Patchy particles

Polymers & Soft Matter

Authors & Affiliations

Daniel de las Heras^*, Lucas L. Treffenstädt, and Matthias Schmidt

Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany

^*Corresponding author: delasheras.daniel@gmail.com

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Issue

Vol. 93, Iss. 3 — March 2016

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Images

Figure 1
(a) Illustration of the two types of patchy particles showing the inner hard core (diameter $σ$ ) and the patches (diameter $δ$ ). (b) Bulk phase diagram of the mixture at $k_{B} T / ε = 0.10$ (left) and $0.15$ (right) in the $μ_{1} - μ_{2}$ plane of chemical potentials according to Wertheim's theory. The black solid line is the binodal. The dashed line is the percolation line. The empty circle is the critical point. The binodal and the percolation line divide the phase diagram into percolated and nonpercolated regions as indicated. The straight line is an example of a sedimentation path. The arrow indicates the direction of the path from bottom to top. (c) Geometry of the simulation box to study sedimentation: a rectangular vessel (width $100 σ$ and height $h = 200 σ$ ) made of hard walls.
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Figure 2
Binary mixture of patchy colloids under gravity, $g = 0.005 ε / (m_{1} σ)$ . First column: Phase diagram in the plane of chemical potentials $μ_{1} - μ_{2}$ showing the sedimentation path (straight line). The arrows indicate the direction of the path from the bottom to the top of the sample. The path is colored in orange (cyan) in the percolated (nonpercolated) region. The height of the sample is $h = 200 σ$ . Second and third columns: Density profiles $ρ_{i}$ of species $i = 1$ (solid violet line) and species $i = 2$ (dashed green line), percolation threshold $p$ (dotted blue line), and probability that a patch is bonded $f_{b}$ (dot-dashed black line). The orange (cyan) rectangle on the right of each panel indicates the percolated (nonpercolated) region, i.e., the region where $f_{b} > p (f_{b} \leq p)$ . Results are according to theory (second column) and simulations (third column). The fourth column shows characteristic snapshots of the simulation. Each row corresponds to a different ratio of buoyant masses: $m_{2} / m_{1} = 1$ (first row), $m_{2} / m_{1} = 5$ (second row), and $m_{2} / m_{1} = - 3$ (third row). The inset in (c4) is a close view of a small region. In all cases the temperature is $k_{B} T / ε = 0.15$ , the composition of the mixture is $x = 0.6$ , and in simulation $N = 7500$ .
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Figure 3
(a) Bulk phase diagram according to Wertheim's theory in the plane of chemical potentials at $k_{B} T / ε = 0.1$ together with a sedimentation path (straight line). The path corresponds to the case $g = 0.002 ε / (m_{1} σ), m_{2} = - 5 m_{1}, h = 200 σ$ and average densities ${\bar{ρ}}_{1} σ^{2} = 0.288, \bar{} ρ_{2} σ^{2} = 0.313$ . (b) Density profile $ρ_{i}$ of species $i = 1$ (solid violet line) and species $i = 2$ (dashed green line), percolation threshold $p$ (dotted blue line), and bonding probability $f_{b}$ (dot-dashed black line) corresponding to the sedimentation path shown in (a). The orange (cyan) rectangle on the right of panel (b) indicates the percolated (nonpercolated) region, i.e., the region where $f_{b} > p (f_{b} \leq p)$ . The sedimentation path (a) has the same color code.
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