glasspy.viscosity package
Submodules
glasspy.viscosity.diffusion module
Equations for computing the effective diffusion coefficient from viscosity.
- glasspy.viscosity.diffusion.diff_coeff_eyring(T, viscosity, diameter)
Computes the viscosity diffusion coefficient using Eyring equation
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
viscosity – float or array_like with same lenght as T Viscosity at temperature T.
diameter – float or array_like with same lenght as T The diameter of the structural unit that is moving due to viscous flow.
- Returns:
Returns the effective diffusion coefficient computed using the Eyring equation. This equation is similar to the Stokes-Einstein equation, but they were obtained by different routes.
References
- [1] Eyring, H. (1936). Viscosity, plasticity, and diffusion as examples of
absolute reaction rates. The Journal of Chemical Physics 4, 283–291.
- glasspy.viscosity.diffusion.diff_coeff_stokeseinstein(T, viscosity, diameter)
Computes the viscosity diffusion coefficient using Stokes-Einstein equation
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
viscosity – float or array_like with same lenght as T Viscosity at temperature T.
diameter – float or array_like with same lenght as T The diameter of the structural unit that is moving due to viscous flow.
- Returns:
Returns the effective diffusion coefficient computed using the Stokes-Einstein equation. This equation is similar to the Eyring equation, but they were obtained by different routes.
References
- [1] Einstein, A. (1905). On the movement of small particles suspended in
stationary liquids required by the molecular-kinetic theory of heat. Annalen Der Physik 17, 549–560.
- [2] Einstein, A. (1905). Über die von der molekularkinetischen Theorie der
Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen Der Physik 322, 549–560.
- [3] Stokes, G.G. (1851). On the effect of the internal friction of fluids
on the motion of pendulums. Transactions of the Cambridge Philosophical Society 9, 8–106.
glasspy.viscosity.equilibrium module
Equations for equilibrium viscosity.
- glasspy.viscosity.equilibrium.ag(T, eta_inf, B, S_conf_fun)
Computes the viscosity using the Adam & Gibbs equation.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
B – float Adjustable parameter related to the potential energy hindering the cooperative rearrangement per monomer segment.
S_conf_fun – callable Function that computes the configurational entropy. This function accepts one argument, which is the absolute temperature.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
References
- [1] Adam, G., and Gibbs, J.H. (1965). On the temperature dependence of
cooperative relaxation properties in glass-forming liquids. The Journal of Chemical Physics 43, 139–146.
- glasspy.viscosity.equilibrium.am(T, eta_inf, alpha, beta)
Computes the viscosity using the Avramov & Milchev equation.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
alpha – float Adjustable parameter, see original reference. Unitless.
beta – float Adjustable parameter with unit of Kelvin.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
References
- [1] Avramov, I., and Milchev, A. (1988). Effect of disorder on diffusion
and viscosity in condensed systems. Journal of Non-Crystalline Solids 104, 253–260.
- [2] Cornelissen, J., and Waterman, H.I. (1955). The viscosity temperature
relationship of liquids. Chemical Engineering Science 4, 238–246.
- glasspy.viscosity.equilibrium.am_alt(T, eta_inf, T12, m)
Computes the viscosity using the Avramov & Milchev equation.
This is the rewriten AM equation found in ref. [3].
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
T12 – float Temperature were the viscosity is 10**12 Pa.s. Unit: Kelvin.
m – float Fragility index as defined by Angell, see ref. [4]. Unitless.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
References
- [1] Avramov, I., and Milchev, A. (1988). Effect of disorder on diffusion
and viscosity in condensed systems. Journal of Non-Crystalline Solids 104, 253–260.
- [2] Cornelissen, J., and Waterman, H.I. (1955). The viscosity temperature
relationship of liquids. Chemical Engineering Science 4, 238–246.
- [3] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [4] Angell, C.A. (1985). Strong and fragile liquids. In Relaxation in
Complex Systems, K.L. Ngai, and G.B. Wright, eds. (Springfield: Naval Research Laboratory), pp. 3–12.
- glasspy.viscosity.equilibrium.myega(T, eta_inf, K, C)
Computes the viscosity using the MYEGA equation.
Mathematicaly, this equation is the same as that proposed in ref. [2] (see page 250), however the physical considerations are different.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
K – float See the original reference for the meaning. Unit: Kelvin.
C – float See the original reference for the meaning. Unit: Kelvin.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
Notes
In the original reference the equation is in base-10 logarithm, see Eq. (6) in [1].
References
- [1] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [2] Waterton, S.C. (1932). The viscosity-temperature relationship and some
inferences on the nature of molten and of plastic glass. J Soc Glass Technol 16, 244–249.
- glasspy.viscosity.equilibrium.myega_alt(T, eta_inf, T12, m)
Computes the viscosity using the MYEGA equation.
This is an alternate form of the MYEGA equation found in [1]
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
T12 – float Temperature were the viscosity is 10**12 Pa.s. Unit: Kelvin.
m – float Fragility index as defined by Angell, see ref. [2]. Unitless.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
References
- [1] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [2] Angell, C.A. (1985). Strong and fragile liquids. In Relaxation in
Complex Systems, K.L. Ngai, and G.B. Wright, eds. (Springfield: Naval Research Laboratory), pp. 3–12.
- glasspy.viscosity.equilibrium.vft(T, eta_inf, A, T0)
Computes the viscosity using the empirical Vogel-Fulcher-Tammann eq.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
A – float Adjustable parameter inside the exponential. Unit: Kelvin.
T0 – float Divergence temperature. Unit: Kelvin.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
References
- [1] Vogel, H. (1921). Das Temperatureabhängigketsgesetz der Viskosität von
Flüssigkeiten. Physikalische Zeitschrift 22, 645–646.
- [2] Fulcher, G.S. (1925). Analysis of recent measurements of the viscosity
of glasses. Journal of the American Ceramic Society 8, 339–355.
- [3] Tammann, G., and Hesse, W. (1926). Die Abhängigkeit der Viscosität von
der Temperatur bie unterkühlten Flüssigkeiten. Z. Anorg. Allg. Chem. 156, 245–257.
- glasspy.viscosity.equilibrium.vft_alt(T, eta_inf, T12, m)
Computes the viscosity using the Vogel-Fulcher-Tammann eq.
This is the rewriten VFT equation found in ref. [4].
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
T12 – float Temperature were the viscosity is 10**12 Pa.s. Unit: Kelvin.
m – float Fragility index as defined by Angell, see ref. [5]. Unitless.
- Returns:
it is not the logarithm of viscosity.
- Return type:
Returns the viscosity in the units of eta_inf. Note
References
- [1] Vogel, H. (1921). Das Temperatureabhängigketsgesetz der Viskosität von
Flüssigkeiten. Physikalische Zeitschrift 22, 645–646.
- [2] Fulcher, G.S. (1925). Analysis of recent measurements of the viscosity
of glasses. Journal of the American Ceramic Society 8, 339–355.
- [3] Tammann, G., and Hesse, W. (1926). Die Abhängigkeit der Viscosität von
der Temperatur bie unterkühlten Flüssigkeiten. Z. Anorg. Allg. Chem. 156, 245–257.
- [4] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [5] Angell, C.A. (1985). Strong and fragile liquids. In Relaxation in
Complex Systems, K.L. Ngai, and G.B. Wright, eds. (Springfield: Naval Research Laboratory), pp. 3–12.
glasspy.viscosity.equilibrium_log module
Equations for the base-10 logarithm of equilibrium viscosity.
- glasspy.viscosity.equilibrium_log.ag(T, eta_inf, B, S_conf_fun)
Computes the viscosity using the Adam & Gibbs equation.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
B – float Adjustable parameter related to the potential energy hindering the cooperative rearrangement per monomer segment.
S_conf_fun – callable Function that computes the configurational entropy. This function accepts one argument, which is the absolute temperature.
- Returns:
Returns the base-10 logarithm of viscosity.
References
- [1] Adam, G., and Gibbs, J.H. (1965). On the temperature dependence of
cooperative relaxation properties in glass-forming liquids. The Journal of Chemical Physics 43, 139–146.
- glasspy.viscosity.equilibrium_log.am(T, log_eta_inf, alpha, beta)
Computes the viscosity using the Avramov & Milchev equation.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
alpha – float Adjustable parameter, see original reference. Unitless.
beta – float Adjustable parameter with unit of Kelvin.
- Returns:
Returns the base-10 logarithm of viscosity.
References
- [1] Avramov, I., and Milchev, A. (1988). Effect of disorder on diffusion
and viscosity in condensed systems. Journal of Non-Crystalline Solids 104, 253–260.
- [2] Cornelissen, J., and Waterman, H.I. (1955). The viscosity temperature
relationship of liquids. Chemical Engineering Science 4, 238–246.
- glasspy.viscosity.equilibrium_log.am_alt(T, log_eta_inf, T12, m)
Computes the viscosity using the Avramov & Milchev equation.
This is the rewriten AM equation found in ref. [3].
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
T12 – float Temperature were the viscosity is 10**12 Pa.s. Unit: Kelvin.
m – float Fragility index as defined by Angell, see ref. [4]. Unitless.
- Returns:
Returns the base-10 logarithm of viscosity.
References
- [1] Avramov, I., and Milchev, A. (1988). Effect of disorder on diffusion
and viscosity in condensed systems. Journal of Non-Crystalline Solids 104, 253–260.
- [2] Cornelissen, J., and Waterman, H.I. (1955). The viscosity temperature
relationship of liquids. Chemical Engineering Science 4, 238–246.
- [3] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [4] Angell, C.A. (1985). Strong and fragile liquids. In Relaxation in
Complex Systems, K.L. Ngai, and G.B. Wright, eds. (Springfield: Naval Research Laboratory), pp. 3–12.
- glasspy.viscosity.equilibrium_log.myega(T, log_eta_inf, K, C)
Computes the viscosity using the MYEGA equation.
Mathematicaly, this equation is the same as that proposed in ref. [2] (see page 250), however the physical considerations are different.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
K – float See the original reference for the meaning. Unit: Kelvin.
C – float See the original reference for the meaning. Unit: Kelvin.
- Returns:
Returns the base-10 logarithm of viscosity.
Notes
In the original reference the equation is in base-10 logarithm, see Eq. (6) in [1].
References
- [1] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [2] Waterton, S.C. (1932). The viscosity-temperature relationship and some
inferences on the nature of molten and of plastic glass. J Soc Glass Technol 16, 244–249.
- glasspy.viscosity.equilibrium_log.myega_alt(T, log_eta_inf, T12, m)
Computes the viscosity using the MYEGA equation.
This is an alternate form of the MYEGA equation found in [1]
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
T12 – float Temperature were the viscosity is 10**12 Pa.s. Unit: Kelvin.
m – float Fragility index as defined by Angell, see ref. [2]. Unitless.
- Returns:
Returns the base-10 logarithm of viscosity.
References
- [1] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [2] Angell, C.A. (1985). Strong and fragile liquids. In Relaxation in
Complex Systems, K.L. Ngai, and G.B. Wright, eds. (Springfield: Naval Research Laboratory), pp. 3–12.
- glasspy.viscosity.equilibrium_log.vft(T, log_eta_inf, A, T0)
Computes the viscosity using the empirical Vogel-Fulcher-Tammann eq.
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
A – float Adjustable parameter inside the exponential. Unit: Kelvin.
T0 – float Divergence temperature. Unit: Kelvin.
- Returns:
Returns the base-10 logarithm of viscosity.
References
- [1] Vogel, H. (1921). Das Temperatureabhängigketsgesetz der Viskosität von
Flüssigkeiten. Physikalische Zeitschrift 22, 645–646.
- [2] Fulcher, G.S. (1925). Analysis of recent measurements of the viscosity
of glasses. Journal of the American Ceramic Society 8, 339–355.
- [3] Tammann, G., and Hesse, W. (1926). Die Abhängigkeit der Viscosität von
der Temperatur bie unterkühlten Flüssigkeiten. Z. Anorg. Allg. Chem. 156, 245–257.
- glasspy.viscosity.equilibrium_log.vft_alt(T, log_eta_inf, T12, m)
Computes the viscosity using the Vogel-Fulcher-Tammann eq.
This is the rewriten VFT equation found in ref. [4].
- Parameters:
T – float or array_like Temperature. Unit: Kelvin.
eta_inf – float Asymptotic viscosity at the limit of infinite temperature.
T12 – float Temperature were the viscosity is 10**12 Pa.s. Unit: Kelvin.
m – float Fragility index as defined by Angell, see ref. [5]. Unitless.
- Returns:
Returns the base-10 logarithm of viscosity.
References
- [1] Vogel, H. (1921). Das Temperatureabhängigketsgesetz der Viskosität von
Flüssigkeiten. Physikalische Zeitschrift 22, 645–646.
- [2] Fulcher, G.S. (1925). Analysis of recent measurements of the viscosity
of glasses. Journal of the American Ceramic Society 8, 339–355.
- [3] Tammann, G., and Hesse, W. (1926). Die Abhängigkeit der Viscosität von
der Temperatur bie unterkühlten Flüssigkeiten. Z. Anorg. Allg. Chem. 156, 245–257.
- [4] Mauro, J.C., Yue, Y., Ellison, A.J., Gupta, P.K., and Allan, D.C.
(2009). Viscosity of glass-forming liquids. Proceedings of the National Academy of Sciences of the United States of America 106, 19780–19784.
- [5] Angell, C.A. (1985). Strong and fragile liquids. In Relaxation in
Complex Systems, K.L. Ngai, and G.B. Wright, eds. (Springfield: Naval Research Laboratory), pp. 3–12.