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Microscopic theory of the glassy dynamics of passive and active network materials
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10.1063/1.4773349
/content/aip/journal/jcp/138/12/10.1063/1.4773349
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4773349
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic of model interactions. Blue line: βU(r) for passive networks. Elastic stretching initiates at r = L e . Purple (s > 0) and magenta (s < 0) lines: βeff U eff(r) for active networks. Motor action induces effective attraction even in the buckling regime (shaded area). Susceptible motors (s > 0) enhance the long range attraction whereas load-resisting motors (s < 0) may lead to long-range repulsion at high motor activity.

Image of FIG. 2.
FIG. 2.

Monitoring the generation of fiducial structures. (a) Mean square displacement (MSD) versus number of simulation steps. (b) Evolution of the potential energy. E a and E r denote for attractive and repulsive interactions, respectively, and E tot for their sum. (c) Radial distribution function g(r). Red: Initial binary system; blue: final monodisperse structure. Model parameters are L e = 1.2, βγ = 2.5, P c = 0.5, η = 1. Here η represents the volume fraction of the nodes.

Image of FIG. 3.
FIG. 3.

Illustration of interface formation. A quenched typical fiducial particle configuration with color-coded α values is shown. Color scale is given on the right hand side. Green frames indicate the creation of an initial sharp contact between two bulk stable phases. With the α values in the boundary layers being pinned (indicated by blue and red anchored arrows), the final α configuration develops a smooth interface, showing a gradual progression of phases.

Image of FIG. 4.
FIG. 4.

Highly connected networks descend deeper into the glassy regime and exhibit strong-liquid behavior. (a) The configurational entropy density s c vs connectivity P c . (b) The fluctuations of configurational entropy density vs connectivity P c . Model parameters are L e = 1.2, βγ = 2.5, η = 1.

Image of FIG. 5.
FIG. 5.

Quasi-universality of the surface energy and the interface width with respect to network connectivity. (a) Distribution of the calculated local interactions {J i } of the analogous magnets. Left to right: P c = 0.5, 0.8 and 1. (b) J vs P c . Typical surface tension J (≡ (1/N)∑ i J i ) is close to the RFOT estimate J RFOT ≃ 0.58. (c) Initial and final α profiles at various P c . A broad interface forms between localized and mobile bulk states. Model parameters are L e = 1.2, βγ = 2.5, η = 1. A large value of packing fraction η implies the system is located in a deeply glassy regime.

Image of FIG. 6.
FIG. 6.

Locating analogous magnets on the RG phase diagram for a random field Ising model at zero average field (adapted from Fig. 3 in Ref. 17 ). The colored symbols correspond to model networks with L e = 1.8, P c = 0.5 at βγ = 5 (green) and 20 (purple), and to those with L e = 1.2, βγ = 2.5 at Pc = 0.5 (blue), 0.8 (yellow), and 1 (red). The analogous magnets are located close to the strong glass forming liquid (square mark).

Image of FIG. 7.
FIG. 7.

The variation of interface energetics and structure with reducing packing fraction η. (a) Initial and final α profiles along x axis at various packing fractions. Homogeneous high α and low α solutions get closer as η decreases. (b) Corresponding color-coded α configurations. Same color scheme as in Fig. 3 . (c) Surface tension versus iteration round number. Final surface tension almost vanishes as η approaches η A ≃ 0.85. (d) Surface tension versus packing fraction. The model parameters are L e = 1.2, βγ = 2.5, P c = 0.5.

Image of FIG. 8.
FIG. 8.

The variation of interface width (ξ) with reducing packing fraction η. (a) Quantification of the interface width at η = 1 (upper) and η = 0.87 (lower). x in indicates the location of interface where most significant variation in α occurs. The black dotted line represents a linear fit to the log (α/α H ) versus x curve at x in . (b) The interface width ξ in units of inter-particle spacing r 0 versus packing fraction. The interface broadens as η decreases toward η A . Model parameters are L e = 1.2, βγ = 2.5, P c = 0.5.

Image of FIG. 9.
FIG. 9.

The variation of configurational entropy s c (a) and surface tension J (b) with reducing packing fraction η. The model parameters are L e = 1.2, βγ = 2.5, P c = 0.5.

Image of FIG. 10.
FIG. 10.

Glassy characteristics for active networks. The dependence of configurational entropy density s c (a) and (c) and surface tension J (b) and (d) on motor activity Δ, susceptibility s and effective temperature T eff is shown. We also indicate by black crosses the corresponding quantities for passive networks with the same underlying architecture (at Δ = 0 and thus T eff = T) for comparison. Model parameters are L e = 1.2, βγ = 2.5, P c = 0.5, η = 1.

Image of FIG. 11.
FIG. 11.

The RFOT estimate of the magnitude of activation barrier. We plot barrier height log (τ/τ0) versus (a) motor activity Δ and (b) configurational entropy s c , for a series of motor susceptibility s. “Control” gives the passive value at Δ = 0 for comparison. Model parameters are L e = 1.2, βγ = 2.5, P c = 0.5, η = 1.

Image of FIG. 12.
FIG. 12.

Dependence of reconfiguration barrier on motor susceptibility and network connectivity. We plot barrier height log (τ/τ0) versus packing fraction η for susceptible motors (s = 1, triangle) and load-resisting motors (s = −0.25, square) at different network connectivity P c . Passive curve (with black circles) corresponds to ATP-depletion in experiments. Model parameters are L e = 1.2, βγ = 2.5, Δ = 1.

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/content/aip/journal/jcp/138/12/10.1063/1.4773349
2013-01-07
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Microscopic theory of the glassy dynamics of passive and active network materials
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4773349
10.1063/1.4773349
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