Activated dynamics in dense fluids of attractive nonspherical particles. I. Kinetic crossover, dynamic free energies, and the physical nature of glasses and gels

We apply the center-of-mass versions of naïve mode coupling theory and nonlinear Langevin equation theory to study how short-range attractive interactions modify the onset of localization, activated single-particle dynamics, and the physical nature of the transiently arrested state of a variety of dense nonspherical particle fluids (and the spherical analog) as a function of volume fraction and attraction strength. The form of the dynamic crossover boundary depends on particle shape, but the reentrant glass-fluid-gel phenomenon and the repulsive glass-to-attractive glass crossover always occur. Diverse functional forms of the dynamic free energy are found for all shapes including glasslike, gel-like, a glass-gel form defined by the coexistence of two localization minima and two activation barriers, and a “mixed” attractive glass characterized by a single, very short localization length but an activation barrier located at a large displacement as in repulsive-force caged glasses. For the latter state, particle trajectories are expected to be of a two-step activated form and can be accessed at high attraction strength by increasing volume fraction, or by increasing attraction strength at fixed high enough volume fraction. A new classification scheme for slow dynamics of fluids of dense attractive particles is proposed based on specification of both the nature of the localized state and the particle displacements required to restore ergodicity via activated barrier hopping. The proposed physical picture appears to be in qualitative agreement with recent computer simulations and colloid experiments.

Figure 1

The shape anisotropic particles studied. (a) rod, (b) rings, (c) disk, and (d) three-dimensional polyhedral particles.

Figure 2

The fluid-fluid spinodal (dashed) and ideal NMCT nonergodicity transition (solid) curves in the representation of contact attraction strength (in thermal energy units) versus volume fraction for spheres (light blue circles) and snub disphenoids (green diamonds) with attraction ranges of $a=0.02\hspace{0.5em}\sigma$ (filled circles and diamonds), and $a=0.10\hspace{0.5em}\sigma$ (open circles and diamonds).

Figure 3

Ideal NMCT kinetic arrest diagrams for fluid-nonergodic state transitions (solid lines and filled symbols) and the repulsive glass-to-attractive glass transition (dashed lines and open symbols) at an attraction range of $a=0.02\sigma$ for many different shapes: spherical particles (black circles), rods of six sites (dark blue diamonds), rods of eight sites (dark blue triangles), hexagonal particles (pink circles), disks of eight sites (red diamonds), cubes (green squares), and octahedra (green triangles).

Figure 4

Center-of-mass static structure factor as a function of dimensionless wavevector for fluids of hexagonal particles at $\varphi =0.33$ and different attraction strengths. Note the nonmonotonic behavior of the primary peak in the reentrant region. Inset: corresponding site-site radial distribution functions near contact. Note the contact value monotonically increases with attraction strength.

Figure 5

Ideal NMCT kinetic arrest diagram for the eight-site disk. The six trajectories for which calculations are shown in Figs. 6 and 7 are indicated.

Figure 6

Dynamic free-energy curves as a function of dimensionless particle CM displacement for eight-site disks at (a) $\varphi =0.35$ and increasing attraction strength corresponding to trajectory 1 in Fig. 5, (b) $\varphi =0.39$ and increasing attraction strength corresponding to trajectory 2 in Fig. 5, (c) $\varphi =0.43$ and increasing attraction strength corresponding to trajectory 3 on Fig. 5, and (d) $\varphi =0.45$ as the attraction strength increases corresponding to trajectory 4 on Fig. 5.

Figure 7

The main panel displays the dynamic free-energy curves as a function of dimensionless particle CM displacement for eight-site disks at $\varepsilon =2.5$ and increasing volume fraction corresponding to trajectory 5 in Fig. 5. The inset demonstrates the sudden (but continuous) change in barrier location as a function of volume fraction at fixed $\varepsilon =3.8$, along trajectory 6 in Fig. 5.

Figure 8

Qualitatively accurate schematic generic kinetic arrest diagram based on the dynamic free energy. The solid lines correspond to ideal NMCT transitions, where the narrow region bounded by the A3 point and nose indicates the gel-glass coexistence region. The two dashed lines represent soft crossover boundaries between the gel and attractive glass (where the barrier location undergoes a sharp, but continuous, transition from gel-like to glasslike values), as well as the repulsive glass and attractive glass regions where the localization length undergoes a sharp, but continuous, transition from glasslike to gel-like values.