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Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition
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10.1063/1.4769422
/content/aip/journal/jcp/138/12/10.1063/1.4769422
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4769422
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Figures

Image of FIG. 1.
FIG. 1.

Strictly anharmonic portion of the total average energy (kinetic and potential) per particle u − 3k B T of the system in term of the thermostat temperature T. This is obtained by averaging over 10 cooling simulations of supercooled Z2 Dzugutov systems using τ10 = 400. 3k B T has been subtracted from the energy to help identify the glass transition. The glass transition temperature k B T g ∼ 0.88 is estimated by finding the temperature at which the function slope changes most rapidly. The vertical dashed line is located at T = T g . The energy scale is normalized through our choice of potential parameters (see Sec. III ).

Image of FIG. 2.
FIG. 2.

Structure factors S(k) for Z2 Dzugutov systems supercooled using τ10 = 500 for various temperatures. The curves have been averaged over 10 realizations. (a) Cubic fits of the small-wavenumber (k < 2) structure factors. The type of fits and their cutoff are chosen such that they accurately reproduce the features of the structure factors, in particular the positive linear dependence near k = 0. (b) Larger wavenumber structure factors.

Image of FIG. 3.
FIG. 3.

Growing length scales for Z2 Dzugutov systems generated using various cooling schedules. For each cooling schedule, the results have been averaged over 10 realizations and fitted to the sum of an exponential and a linear function to smooth out the numerical noise. (a) Limit of for k → 0, calculated using linear fits of S(k). (b) The static length scale ξ c , defined by relation (38) , associated with these systems. Note that the nearest neighbor distance between particles at T = 0 is 1.0539.

Image of FIG. 4.
FIG. 4.

Nonequilibrium index X for Z2 Dzugutov systems supercooled using various cooling schedules defined in Eq. (40) .

Image of FIG. 5.
FIG. 5.

Timescale τ of the early relaxation process of the system versus the nonequilibrium index X. Both quantities have been averaged over 10 configurations. The circles are centered on the averages of X and τ, while the horizontal and vertical lines represent their respective uncertainties, with their half-length set equal to the average standard deviations. The initial configurations which are allowed to relax at constant temperature are generated from the liquid phase through a cooling schedule employing τ10 = 50. Each datum represents a single temperature. Observe that τ and X are positively correlated. Therefore, since X is a monotonically decreasing function of the temperature T (see Fig. 4 ), τ also increases with decreasing T. The values of T/T g associated with each datum are, in order of smallest to largest τ are as follows: 1.80, 1.61, 1.43, 1.28, 1.14, 1.01, and 0.90.

Image of FIG. 6.
FIG. 6.

Example of a decorated Kob-Andersen glass configuration (a small subregion of the configuration only). The larger disks represent the A particles, while the smaller disks represent B particles. The radii of the disks are chosen such that the two closest A particles of the whole configuration are in contact and the closest AB pair of particles are in contact. The configuration shown has been generated using τ10 = 100, and is at a temperature of T/T g = 6.7 × 10−5. The particle radii are R A = 0.513720 and R B = 0.329883 (R A /R B = 1.55728).

Image of FIG. 7.
FIG. 7.

Strictly anharmonic portion of the total average energy (kinetic and potential) per particle u − 2k B T of the system in terms of the thermostat temperature T. This is obtained by averaging 10 cooling simulations of supercooled Kob-Andersen systems using τ10 = 400. 2k B T has been subtracted from the energy to help identify the glass transition. The glass transition temperature T g ∼ 0.31 is estimated by finding the temperature at which the function slope changes the most rapidly. The vertical dashed line is located at T = T g . The energy scale is normalized through our choice of potential parameters (see Sec. III ).

Image of FIG. 8.
FIG. 8.

Spectral density versus wavenumber k for Kob-Andersen A 65 B 35 systems supercooled using τ10 = 400. The curves have been averaged over 10 realizations and fitted using fourth degree polynomials. The types of fits have been chosen for their ability to reproduce accurately the features of the structure factors for the range presented (0 < k < 3). The disk radii for the decorations are calculated independently for each configuration.

Image of FIG. 9.
FIG. 9.

Growing length scales for two-dimensional Kob-Andersen systems. For each cooling schedule, the results have been averaged over 10 realizations and fitted to the sum of an exponential and a quadratic functions to smooth out the numerical noise. (a) Limit of for k → 0, calculated using the linear fits of . (b) The static length scale ξ C , defined by relation (42) , associated with these systems.

Image of FIG. 10.
FIG. 10.

Smallest eigenvalue of lim k → 0 C(k), calculated using a linear fit of the matrix structure factor S(k). While the qualitative behavior of this eigenvalue can be compared to (see Fig. 9(a) ), their quantitative values cannot directly be compared because they have different units: has units of volume, while is dimensionless.

Image of FIG. 11.
FIG. 11.

Nonequilibrium index X for Kob-Andersen systems supercooled using various cooling schedules defined in Eq. (45) .

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/content/aip/journal/jcp/138/12/10.1063/1.4769422
2013-01-02
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4769422
10.1063/1.4769422
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