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Affinity and its derivatives in the glass transition process
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10.1063/1.4733333
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Affiliations:
1 Institut Néel, CNRS et UJF, 25 Avenue des Martyrs, 38042 Grenoble Cedex 09, France
2 LIMMS/CNRS-IIS, Institute of Industrial Sciences, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
3 Departement of Materials Science, Chair of Glass and Ceramics, University of Erlangen-Nuernberg, 91058 Erlangen, Germany
a) Electronic mail: jean-luc.garden@grenoble.cnrs.fr.
b) Permanent address: Institut Néel, CNRS et UJF, 25 Avenue des Martyrs, 38042 Grenoble Cedex 09, France.
J. Chem. Phys. 137, 024505 (2012)
/content/aip/journal/jcp/137/2/10.1063/1.4733333
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## Figures

FIG. 1.

Evolution of the order parameter as a function of temperature at constant pressure p = 0.1 MPa. The arrows and colors indicate the sense of variation of the temperature: down and blue correspond to cool down and vitrification, whereas up and red correspond to reheating. The temperatures variation rates are γ T = ±0.3 K/min (thick lines) and γ T = ±6 K/min (dashed lines).Insets: (a) Equilibrium order parameter as a function of temperature on the whole temperature range. (b) Evolution of log (τ) as a function of temperature.

FIG. 2.

Evolution of the order parameter as a function of pressure at constant temperature T = 271.6 K. The arrows and colors indicate the sense of variation of the pressure : down and blue correspond to pressure increase and vitrification, whereas up and red correspond to pressure decrease. The pressure variation rates are γ p = ±1.25 MPa/min (thick lines) and γ T = ±25 MPa/min (dashed lines). Inset: (a) Equilibrium order parameter as a function of pressure on the whole pressure range. (b) Evolution of log (τ) as a function of pressure.

FIG. 3.

The affinity A divided by RT as function of temperature. The pressure is p = 0.1 MPa. The arrows and colors indicate the sense of variation of the temperature: down and blue correspond to cool down and vitrification, whereas up and red correspond to reheating. The temperatures variation rates are γ T = ±0.3 K/min (thick lines) and γ T = ±6 K/min (dashed lines).

FIG. 4.

The affinity A divided by RT as a function of applied pressure. The temperature is T = 271.6 K. The arrows and colors indicate the sense of variation of the pressure: down and blue correspond to pressure increase and vitrification, whereas up and red correspond to pressure decrease. The pressure variation rates are γ p = ±1.25 MPa/min (thick lines) and γ T = ±25 MPa/min (dashed lines).

FIG. 5.

Comparison between the affinity A, its derivative with respect to temperature , and .∂ΔH conf /∂ξ) p, T in a glass transition simulated for cooling and heating protocol of γ T = ±6 K/min. The pressure is kept constant and equal to 0.1 MPa. The dashed line shows the affinity. Because of the scale, the cooling and heating curves are superimposed. The thick lines show TdA/dT and the arrows and colors indicate the sense of variation of the temperature: up and blue correspond to temperature decrease and vitrification, whereas down and red correspond to subsequent reheating and structural recovery. Finally, the constant black line corresponds to the term .∂ΔH conf /∂ξ) p, T .

FIG. 6.

Computations of the configurational specific heat according to formula (17) of Ref. 18 (dashed lines) and Eq. (16) of this work (thick lines). The temperature variation rate is γ T = ±0.3 K/min. The pressure is kept constant and equal to 0.1 MPa. The arrows and colors indicate the sense of variation of the temperature: the blue color corresponds to temperature decrease and vitrification, whereas the red color corresponds to subsequent reheating and structural recovery. The equilibrium configurational specific heat is plotted as a thick black line (cooling or warming).

FIG. 7.

The normalized heat capacity at constant pressure (p = 0.1 MPa) as a function of temperature. The arrows and colors indicate the sense of variation of the temperature: down and blue correspond to temperature decrease and vitrification, whereas up and red correspond to subsequent reheating. The temperature variation rates are γ T = −0.3 K/min (thick blue), γ T = +0.3 K/min (thick red), γ T = −0.5 K/min (dashed blue), γ T = +20 K/min (dashed red).

FIG. 8.

Computation of the normalized configurational coefficient of thermal expansion. The temperature variation rate is γ T = ±0.3 K/min. The pressure is kept constant and equal to 0.1 MPa. The arrows and colors indicate the sense of variation of the temperature: the blue color corresponds to temperature decrease and vitrification, whereas the red color corresponds to subsequent reheating and structural recovery.

FIG. 9.

Comparison of (red lines) and (black lines) for two pressure rates. The arrows indicate the sense of pressure variation. The pressure variation rates are γ P = 1.5 MPa/min (thick line) and γ P = 25 MPa/min (dashed line).

FIG. 10.

Normalized configurational compressibility at constant temperature of 271.6 K. The data for a pressure variation rate of γ p = 1.5 MPa/min (thick line) and of γ p = 25 MPa/min (dashed line) are represented. Inset: absolute values of the configurational compressibility over the full pressure range for γ p = 1.5 MPa/min (thick line) and γ p = 25 MPa/min (dashed line).

FIG. 11.

Fictive temperatures as a function of temperature during cooling at a temperature rate of −0.5 K/min at constant pressure of 0.1 MPa. The read one, which comes from the classical definition of the fictive temperature, is issued from integration of the corresponding normalized heat capacity data. The blue one is issued from the Eq. (28). The black one is inferred from calculation of Tropin and co-workers with an approximate value of the affinity (see Eq. (50) of Ref. 22).

## Tables

Table I.

Characteristic of o-terphenyl melting and corresponding parameters used in the lattice-hole model.

Table II.

Table of the parameters used for the numerical computations used in this work.

/content/aip/journal/jcp/137/2/10.1063/1.4733333
2012-07-12
2014-04-18

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