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Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

O. Henrich, A. M. Puertas, M. Sperl, J. Baschnagel, and M. Fuchs
Phys. Rev. E 76, 031404 – Published 27 September 2007
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  • INTRODUCTION
  • MODE COUPLING THEORY
  • SIMULATION SETUP
  • ASPECTS OF THE NUMERICAL MCT SOLUTIONS
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semiquantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

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    • Received 7 May 2007

    DOI:https://doi.org/10.1103/PhysRevE.76.031404

    ©2007 American Physical Society

    Authors & Affiliations

    O. Henrich1, A. M. Puertas2, M. Sperl1, J. Baschnagel3, and M. Fuchs1

    • 1Department of Physics, University of Konstanz, 78457 Konstanz, Germany
    • 2Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, 04120 Almeria, Andalucía, Spain
    • 3Institut Charles Sadron, 6, rue Boussingault, BP 40016, 67083 Strasbourg Cedex, France

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    Vol. 76, Iss. 3 — September 2007

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    Images

    • Figure 1
      Figure 1
      Interaction potential for two particles with the average radius. The polymer fractions are ϕp=0.42 and ϕp=0.25 for the (lower) thin and (upper) thick curves, respectively (values close to the glass transition in the simulation and MCT, respectively). Note that in our units, the thermal energy is kBT=4∕3.Reuse & Permissions
    • Figure 2
      Figure 2
      (Color online) Sq from MD simulations at a colloid packing fraction of ϕc=0.40 and a polymer concentration of ϕp=0.25, which is in the gel close to the critical point in MCT. The repulsive barrier affects Sq in the region below qD≤13; system (A) without barrier (dashed-dotted, black) shows neither a prepeak nor a primary peak, which is as high as in systems (B) and (C) with barrier (full red, dashed black). The inset demonstrates that polydispersity causes the q-tail oscillations in Sq to be suppressed for large wave vectors. The Sq for the polydisperse model (C) falls below the noise level for qD≥45, whereas the monodisperse systems (A) and (B) virtually coincide there.Reuse & Permissions
    • Figure 3
      Figure 3
      (Color online) Critical Sq at the boundaries of the gel phase: Black dashed-dotted, red full, and black dashed lines mark results from (A), (B), and (C). The red diamonds indicate Sq at ϕp=0.42, which is close to the arrested state in the simulation (D). In the simulation, the prepeak at qD≃2.5 rises and shifts to smaller q values with increasing polymer concentration. The inset gives an enlarged view of the q tail where systems (A) and (B) show pronounced oscillations driven by the short-ranged attraction.Reuse & Permissions
    • Figure 4
      Figure 4
      (Color online) Critical nonergodicity parameters fqc at the transition in the simulation (D) (red diamonds), from MCT with monodisperse [(A),(B)] Sq (black dashed-dotted and red full line) and polydisperse (C) Sq (black dashed line). Serious differences occur, when the average Sq of a polydisperse system is used as input to a monodisperse theory; the shape of fq for (C) resembles more one of a repulsive glass.Reuse & Permissions
    • Figure 5
      Figure 5
      (Color online) Enlarged view of the nonergodicity parameters of Fig. 4 and structure factors in the low-q region: Minor differences in fqc show up in the region qD≤10 only, where also the input Sq differs considerably. Simulation data [(D) red symbols] agree qualitatively with the model calculation (B) including the barrier.Reuse & Permissions
    • Figure 6
      Figure 6
      (Color online) Critical amplitudes in simulation (D) (red diamonds) and MCT [(A),(B),(C)] (black dashed-dotted, red full, black dashed) close to dynamic arrest. Because of the different α times in simulation and theory the MCT results for (A), (B) were scaled on the simulation results.Reuse & Permissions
    • Figure 7
      Figure 7
      (Color online) α-relaxation times τq in MCT for the systems (A), (B), (C) (black dashed-dotted, red full, black dashed line) and in the polydisperse simulation [(D) red diamonds]. The curves are normalized to the value of τq at qD=22.7. In the inset, the results for models (A) and (B) and simulation (D) are shown in a log-log plot. The straight line gives the asymptotic behavior τq=q−1∕b valid for large q with the corresponding von Schweidler b=0.37 obtained previously.Reuse & Permissions
    • Figure 8
      Figure 8
      (Color online) Density correlation functions in simulation [(D) red solid lines] and MCT calculations in model (B) (black dashed lines): The horizontal black bars indicate the critical plateau values of fqc in MCT. The wave vectors from bottom to top are qD=57.1,45.9,33.9,22.7,12.5. The short-time diffusion coefficient was set to Ds∕D2=0.133. The theoretical curves correspond to a polymer concentration of ϕp=0.2461, which means a separation parameter of about εMCT=−0.001. The simulation results were obtained for a polymer concentration ϕp=0.42, which corresponds to a separation parameter of εsimu=−0.015.Reuse & Permissions
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