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Dynamic heterogeneities and non-Gaussian behavior in two-dimensional randomly confined colloidal fluids

Simon K. Schnyder, Thomas O. E. Skinner, Alice L. Thorneywork, Dirk G. A. L. Aarts, Jürgen Horbach, and Roel P. A. Dullens
Phys. Rev. E 95, 032602 – Published 6 March 2017
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  • INTRODUCTION
  • COLLOIDAL MODEL SYSTEM
  • SIMULATION
  • RESULTS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    A binary mixture of superparamagnetic colloidal particles is confined between glass plates such that the large particles become fixed and provide a two-dimensional disordered matrix for the still mobile small particles, which form a fluid. By varying fluid and matrix area fractions and tuning the interactions between the superparamagnetic particles via an external magnetic field, different regions of the state diagram are explored. The mobile particles exhibit delocalized dynamics at small matrix area fractions and localized motion at high matrix area fractions, and the localization transition is rounded by the soft interactions [T. O. E. Skinner et al., Phys. Rev. Lett. 111, 128301 (2013)]. Expanding on previous work, we find the dynamics of the tracers to be strongly heterogeneous and show that molecular dynamics simulations of an ideal gas confined in a fixed matrix exhibit similar behavior. The simulations show how these soft interactions make the dynamics more heterogeneous compared to the disordered Lorentz gas and lead to strong non-Gaussian fluctuations.

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    • Received 17 August 2016
    • Revised 10 February 2017

    DOI:https://doi.org/10.1103/PhysRevE.95.032602

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Anomalous diffusionConfinementCritical phenomenaDiffusionPercolationTransport phenomena
    1. Physical Systems
    Colloids
    1. Techniques
    Molecular dynamics
    Polymers & Soft MatterStatistical Physics & Thermodynamics

    Authors & Affiliations

    Simon K. Schnyder1,2,*, Thomas O. E. Skinner3, Alice L. Thorneywork3, Dirk G. A. L. Aarts3, Jürgen Horbach1,†, and Roel P. A. Dullens3,‡

    • 1Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
    • 2Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
    • 3Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom

    • *skschnyder@gmail.com
    • †horbach@thphy.uni-duesseldorf.de
    • ‡roel.dullens@chem.ox.ac.uk

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    Issue

    Vol. 95, Iss. 3 — March 2017

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    Images

    • Figure 1
      Figure 1

      (a) Schematic of the experiment, a binary system of small and large particles confined between two glass slides (particle diameters to scale). The large particles support the top slide. The magnetic field B tunes the effective interaction between the particles. (b) Mean-squared displacement for the fluid particles in a very dilute 2D cell. A dashed line indicating diffusive behavior, δr2(t)∼t, is shown as a guide to the eye. (c) State diagram for the effective area fractions of the fluid (ΦF) vs the matrix particles (ΦM). (d) Snapshot of the system at state point L1P6 in a quadrant of size 214×171μm.

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    • Figure 2
      Figure 2

      Experiment: single-particle probability distributions from 2D histograms of all particle positions in a quadrant measured for state points (a) L1P1, (b) L1P6, (c) L2P1, and (d) L2P6. The distributions are normalized such that the total probability of the whole quadrant is unity. The size of the particles is indicated by the red circles under the scale bars in each plot, and the size of the hard-core excluded area for centers of mobile particles is indicated in (a) by the blue circle under the scale bar.

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    • Figure 3
      Figure 3

      Simulation: single-particle probability distributions from 2D histograms in the confined ideal gas case. Shown are square sections of length 20σM and the histograms are normalized such that the total probability integrated over the shown section is unity.

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    • Figure 4
      Figure 4

      Experiment: partial radial distribution functions, for the (a) matrix-matrix interaction gMM(r), (b) fluid-fluid interaction gFF(r), and (c) fluid-matrix interaction gMF(r) for each state point along line 1 and line 2. Line 2 is shifted by 2 in each plot.

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    • Figure 5
      Figure 5

      Simulation: partial radial distribution functions, for the (a) matrix-matrix interaction gMM(r), (b) fluid-fluid interaction gFF(r), and the fluid-matrix interaction gMF(r) for the single-energy and confined-ideal-gas cases [the latter data is shifted upwards by 5 in (b) and by 1 in (c)].

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    • Figure 6
      Figure 6

      Experiment: self-part of the intermediate scattering function Fs(q,t) for the fluid particles for a range of wave numbers q relating to state points (a) L1P1, (b) L1P6, (c) L2P1, and (d) L2P6 (in colors), as well as the corresponding Gaussian approximations (in gray). A measure of the nonergodicity parameter is obtained with fs(q)≈Fs(q,t≈3300s), indicated by the dotted line, and shown in Fig. 8.

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    • Figure 7
      Figure 7

      Simulation: self-part of the intermediate scattering function Fs(q,t) in the simulation for the single-energy case (colored dashed lines) and the confined ideal gas case (colored solid lines) for particle diameters (a) σF=0.2, (b) 0.45, and (c) 0.7, as well as the corresponding Gaussian approximations (in gray).

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    • Figure 8
      Figure 8

      (a) Long-time limit of the SISF fs(q) of the experiment along lines 1 and 2 in semilogarithmic presentation. (b) Long-time limit of the SISF fs(q) in the simulation for the single-energy (dashed) and ideal-gas case (solid).

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    • Figure 9
      Figure 9

      Mean-quartic displacement δr4(t) for experiment (a) and simulation (b) as a function of time. In the simulation, single-energy case (dashed lines) and confined-ideal-gas case (solid lines) are shown. The straight gray lines ∼t2 and ∼t4/ẑ with ẑ≈2.955 serve as a guide to the eye.

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    • Figure 10
      Figure 10

      Non-Gaussian parameter α2(t) for the experiment (a), and for the simulation in the (b) single-energy and (c) confined-ideal-gas cases.

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    • Figure 11
      Figure 11

      Experiment: mean-squared displacement δr2(t) for the matrix particles at all state points (color), the center of mass of the matrix particles (red), and the fluid particles at the lowest and highest state points (gray) along line 0 (a), line 1 (b), and line 2 (c).

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    • Figure 12
      Figure 12

      Experiment: histograms of the maximum distance r* that each particle travels away from its initial position at t=0 over the whole duration of the experiment for both the matrix and fluid particles along line 0 (a) and (b), line 1 (c) and (d), and line 2 (e) and (f). The reclassification cutoff distance rrc* is marked by vertical line in the histograms of the fluid particles.

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    • Figure 13
      Figure 13

      Experiment: single-particle probability distributions from all small particle positions in a quadrant measured for state points (a) L0P1 and (b) L0P5. Normalized so that the total probability is unity. The size of the colloidal particles is indicated as red circles and the size of the hard-core excluded area for centers of mobile particles is indicated in (a) as blue circle.

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    • Figure 14
      Figure 14

      Experiment: partial radial distribution functions: (a) for the matrix-matrix interaction gMM(r), (b) fluid-fluid interaction gFF(r), and (c) fluid-matrix interaction gMF(r) for each state point along line 0.

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    • Figure 15
      Figure 15

      Experiment: self-part of the intermediate scattering function Fs(q,t) for the fluid particles for a range of wave numbers q relating to state points (a) L0P1 and (b) L0P5 (in colors), as well as the corresponding Gaussian approximations (in gray). A measure of the nonergodicity parameter is obtained with fs(q)≈Fs(q,t≈3300s), indicated by the dotted line, and shown in (c).

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    • Figure 16
      Figure 16

      Experiment: (a) mean-squared displacement δr2(t) for the state point along line 0. The straight gray lines indicate ∼t and ∼t2/z with z≈3.036 and serve as a guide to the eye. (b) Mean-quartic displacement δr4(t) for the state points along line 0. The straight gray lines indicate ∼t2 and ∼t4/ẑ with ẑ≈2.955 and serve as guide to the eye. (c) The corresponding non-Gaussian parameter α2(t) for the state point along line 0.

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