Lennard-Jones Models (chemicals.lennard_jones)¶
This module contains lookup functions and estimation methods for the parameters molecular diameter sigma and the Stockmayer parameter epsilon. These are used for diffusivity calculations. It also contains several methods for computing the collision integral, another parameter used in the Lennard-Jones model.
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Stockmayer Parameter¶
- chemicals.lennard_jones.Stockmayer(CASRN='', Tm=None, Tb=None, Tc=None, Zc=None, omega=None, method=None)[source]¶
This function handles the retrieval or calculation a chemical’s Stockmayer parameter. Values are available from one source with lookup based on CASRNs, or can be estimated from 7 CSP methods. Will automatically select a data source to use if no method is provided; returns None if the data is not available.
Preferred sources are ‘Magalhães, Lito, Da Silva, and Silva (2013)’ for common chemicals which had valies listed in that source, and the CSP method Tee, Gotoh, and Stewart CSP with Tc, omega (1966) for chemicals which don’t.
- Parameters
- CASRN
str
,optional
CASRN [-]
- Tm
float
,optional
Melting temperature of compound [K]
- Tb
float
,optional
Boiling temperature of compound [K]
- Tc
float
,optional
Critical temperature of compound, [K]
- Zc
float
,optional
Critical compressibility of compound, [-]
- omega
float
,optional
Acentric factor of compound, [-]
- CASRN
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
- Other Parameters
- method
str
,optional
A string for the method name to use, as defined by constants in Stockmayer_all_methods
- method
Notes
These values are somewhat rough, as they attempt to pigeonhole a chemical into L-J behavior.
The tabulated data is from [2], for 322 chemicals.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
- 2
Magalhães, Ana L., Patrícia F. Lito, Francisco A. Da Silva, and Carlos M. Silva. “Simple and Accurate Correlations for Diffusion Coefficients of Solutes in Liquids and Supercritical Fluids over Wide Ranges of Temperature and Density.” The Journal of Supercritical Fluids 76 (April 2013): 94-114. doi:10.1016/j.supflu.2013.02.002.
Examples
>>> Stockmayer(CASRN='64-17-5') 1291.41 >>> Stockmayer('7727-37-9') 71.4
- chemicals.lennard_jones.Stockmayer_methods(CASRN=None, Tm=None, Tb=None, Tc=None, Zc=None, omega=None)[source]¶
Return all methods available to obtain the Stockmayer parameter for the desired chemical.
- Parameters
- CASRN
str
,optional
CASRN [-]
- Tm
float
,optional
Melting temperature of compound [K]
- Tb
float
,optional
Boiling temperature of compound [K]
- Tc
float
,optional
Critical temperature of compound, [K]
- Zc
float
,optional
Critical compressibility of compound, [-]
- omega
float
,optional
Acentric factor of compound, [-]
- CASRN
- Returns
See also
- chemicals.lennard_jones.Stockmayer_all_methods = ('Magalhães, Lito, Da Silva, and Silva (2013)', 'Poling et al. (2001)', 'Tee, Gotoh, and Stewart CSP with Tc, omega (1966)', 'Stiel and Thodos Tc, Zc (1962)', 'Flynn (1960)', 'Bird, Stewart, and Light (2002) critical relation', 'Tee, Gotoh, and Stewart CSP with Tc (1966)', 'Bird, Stewart, and Light (2002) boiling relation', 'Bird, Stewart, and Light (2002) melting relation')¶
Tuple of method name keys. See the Stockmayer for the actual references
Stockmayer Parameter Correlations¶
- chemicals.lennard_jones.epsilon_Flynn(Tc)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses critical temperature. CSP method by [1] as reported in [2].
- Parameters
- Tc
float
Critical temperature of fluid [K]
- Tc
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
References
- 1
Flynn, L.W., M.S. thesis, Northwestern Univ., Evanston, Ill. (1960).
- 2
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
Examples
>>> epsilon_Flynn(560.1) 345.2984087011443
- chemicals.lennard_jones.epsilon_Bird_Stewart_Lightfoot_critical(Tc)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses critical temperature. CSP method by [1].
- Parameters
- Tc
float
Critical temperature of fluid [K]
- Tc
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> epsilon_Bird_Stewart_Lightfoot_critical(560.1) 431.27700000000004
- chemicals.lennard_jones.epsilon_Bird_Stewart_Lightfoot_boiling(Tb)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses boiling temperature. CSP method by [1].
- Parameters
- Tb
float
Boiling temperature [K]
- Tb
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> epsilon_Bird_Stewart_Lightfoot_boiling(357.85) 411.5275
- chemicals.lennard_jones.epsilon_Bird_Stewart_Lightfoot_melting(Tm)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses melting temperature. CSP method by [1].
- Parameters
- Tm
float
Melting temperature [K]
- Tm
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> epsilon_Bird_Stewart_Lightfoot_melting(231.15) 443.808
- chemicals.lennard_jones.epsilon_Stiel_Thodos(Tc, Zc)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses Critical temperature and critical compressibility. CSP method by [1].
- Parameters
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
References
- 1
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
Examples
Fluorobenzene
>>> epsilon_Stiel_Thodos(358.5, 0.265) 196.3755830305783
- chemicals.lennard_jones.epsilon_Tee_Gotoh_Steward_1(Tc)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses Critical temperature. CSP method by [1].
- Parameters
- Tc
float
Critical temperature of fluid [K]
- Tc
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
Notes
Further regressions with other parameters were performed in [1] but are not included here, except for epsilon_Tee_Gotoh_Steward_2.
References
- 1(1,2)
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
Examples
>>> epsilon_Tee_Gotoh_Steward_1(560.1) 433.5174
- chemicals.lennard_jones.epsilon_Tee_Gotoh_Steward_2(Tc, omega)[source]¶
Calculates Lennard-Jones depth of potential-energy minimum. Uses critical temperature and acentric factor. CSP method by [1].
- Parameters
- Returns
- epsilon_k
float
Lennard-Jones depth of potential-energy minimum over k, [K]
- epsilon_k
Notes
Further regressions with other parameters were performed in [1] but are not included here, except for epsilon_Tee_Gotoh_Steward_1.
References
- 1(1,2)
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
Examples
>>> epsilon_Tee_Gotoh_Steward_2(560.1, 0.245) 466.55125785
Molecular Diameter¶
- chemicals.lennard_jones.molecular_diameter(CASRN=None, Tc=None, Pc=None, Vc=None, Zc=None, omega=None, Vm=None, Vb=None, method=None)[source]¶
This function handles the retrieval or calculation a chemical’s L-J molecular diameter. Values are available from one source with lookup based on CASRNs, or can be estimated from 9 CSP methods. Will automatically select a data source to use if no method is provided; returns None if the data is not available.
Preferred sources are ‘Magalhães, Lito, Da Silva, and Silva (2013)’ for common chemicals which had valies listed in that source, and the CSP method Tee, Gotoh, and Stewart CSP with Tc, Pc, omega (1966) for chemicals which don’t.
- Parameters
- CASRN
str
,optional
CASRN [-]
- Tc
float
,optional
Critical temperature, [K]
- Pc
float
,optional
Critical pressure, [Pa]
- Vc
float
,optional
Critical volume, [m^3/mol]
- Zc
float
,optional
Critical compressibility, [-]
- omega
float
,optional
Acentric factor of compound, [-]
- Vm
float
,optional
Molar volume of liquid at the melting point of the fluid [K]
- Vb
float
,optional
Molar volume of liquid at the boiling point of the fluid [K]
- CASRN
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
- Other Parameters
- method
str
,optional
A string for the method name to use, as defined by constants in molecular_diameter_all_methods
- method
Notes
These values are somewhat rough, as they attempt to pigeonhole a chemical into L-J behavior.
The tabulated data is from [2], for 322 chemicals.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
- 2
Magalhães, Ana L., Patrícia F. Lito, Francisco A. Da Silva, and Carlos M. Silva. “Simple and Accurate Correlations for Diffusion Coefficients of Solutes in Liquids and Supercritical Fluids over Wide Ranges of Temperature and Density.” The Journal of Supercritical Fluids 76 (April 2013): 94-114. doi:10.1016/j.supflu.2013.02.002.
Examples
>>> molecular_diameter(CASRN='64-17-5') 4.23738 >>> molecular_diameter('7727-37-9') 3.798
- chemicals.lennard_jones.molecular_diameter_methods(CASRN=None, Tc=None, Pc=None, Vc=None, Zc=None, omega=None, Vm=None, Vb=None)[source]¶
Return all methods available to obtain the molecular diameter for the desired chemical.
- Parameters
- CASRN
str
,optional
CASRN [-]
- Tc
float
,optional
Critical temperature, [K]
- Pc
float
,optional
Critical pressure, [Pa]
- Vc
float
,optional
Critical volume, [m^3/mol]
- Zc
float
,optional
Critical compressibility, [-]
- omega
float
,optional
Acentric factor of compound, [-]
- Vm
float
,optional
Molar volume of liquid at the melting point of the fluid [K]
- Vb
float
,optional
Molar volume of liquid at the boiling point of the fluid [K]
- CASRN
- Returns
See also
- chemicals.lennard_jones.molecular_diameter_all_methods = ('Magalhães, Lito, Da Silva, and Silva (2013)', 'Poling et al. (2001)', 'Tee, Gotoh, and Stewart CSP with Tc, Pc, omega (1966)', 'Silva, Liu, and Macedo (1998) critical relation with Tc, Pc', 'Bird, Stewart, and Light (2002) critical relation with Tc, Pc', 'Tee, Gotoh, and Stewart CSP with Tc, Pc (1966)', 'Stiel and Thodos Vc, Zc (1962)', 'Flynn (1960)', 'Bird, Stewart, and Light (2002) critical relation with Vc', 'Bird, Stewart, and Light (2002) boiling relation', 'Bird, Stewart, and Light (2002) melting relation')¶
Tuple of method name keys. See the molecular_diameter for the actual references
Molecular Diameter Correlations¶
- chemicals.lennard_jones.sigma_Flynn(Vc)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical volume. CSP method by [1] as reported in [2].
- Parameters
- Vc
float
Critical volume of fluid [m^3/mol]
- Vc
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Vc is originally in units of mL/mol.
References
- 1
Flynn, L.W., M.S. thesis, Northwestern Univ., Evanston, Ill. (1960).
- 2
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
Examples
>>> sigma_Flynn(0.000268) 5.2506948422196285
- chemicals.lennard_jones.sigma_Bird_Stewart_Lightfoot_critical_2(Tc, Pc)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical temperature and pressure. CSP method by [1].
- Parameters
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Original units of critical pressure are atmospheres.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> sigma_Bird_Stewart_Lightfoot_critical_2(560.1, 4550000) 5.658657684653222
- chemicals.lennard_jones.sigma_Bird_Stewart_Lightfoot_critical_1(Vc)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical volume. CSP method by [1].
- Parameters
- Vc
float
Critical volume of fluid [m^3/mol]
- Vc
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Original units of Vc are mL/mol.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> sigma_Bird_Stewart_Lightfoot_critical_1(0.000268) 5.422184116631474
- chemicals.lennard_jones.sigma_Bird_Stewart_Lightfoot_boiling(Vb)[source]¶
Calculates Lennard-Jones molecular diameter. Uses molar volume of liquid at boiling. CSP method by [1].
- Parameters
- Vb
float
Boiling molar volume of liquid [m^3/mol]
- Vb
- Returns
- sigma
float
Lennard-Jones collision integral, [Angstrom]
- sigma
Notes
Original units of Vb are mL/mol.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> sigma_Bird_Stewart_Lightfoot_boiling(0.0001015) 5.439018856944655
- chemicals.lennard_jones.sigma_Bird_Stewart_Lightfoot_melting(Vm)[source]¶
Calculates Lennard-Jones molecular diameter. Uses molar volume of a liquid at its melting point. CSP method by [1].
- Parameters
- Vm
float
Melting molar volume of a liquid at its melting point [m^3/mol]
- Vm
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Original units of Vm are mL/mol.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> sigma_Bird_Stewart_Lightfoot_melting(8.8e-05) 5.435407341351406
- chemicals.lennard_jones.sigma_Stiel_Thodos(Vc, Zc)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical volume and compressibility. CSP method by [1].
- Parameters
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Vc is originally in units of mL/mol.
References
- 1
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
Examples
Monofluorobenzene
>>> sigma_Stiel_Thodos(0.000271, 0.265) 5.94300853971033
- chemicals.lennard_jones.sigma_Tee_Gotoh_Steward_1(Tc, Pc)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical temperature and pressure. CSP method by [1].
- Parameters
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Original units of Pc are atm. Further regressions with other parameters were performed in [1] but are not included here, except for sigma_Tee_Gotoh_Steward_2.
References
- 1(1,2)
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
Examples
>>> sigma_Tee_Gotoh_Steward_1(560.1, 4550000) 5.48402779790962
- chemicals.lennard_jones.sigma_Tee_Gotoh_Steward_2(Tc, Pc, omega)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical temperature, pressure, and acentric factor. CSP method by [1].
- Parameters
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Original units of Pc are atm. Further regressions with other parameters were performed in [1] but are not included here, except for sigma_Tee_Gotoh_Steward_1.
References
- 1(1,2)
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
Examples
>>> sigma_Tee_Gotoh_Steward_2(560.1, 4550000, 0.245) 5.412104867264477
- chemicals.lennard_jones.sigma_Silva_Liu_Macedo(Tc, Pc)[source]¶
Calculates Lennard-Jones molecular diameter. Uses critical temperature and pressure. CSP method by [1].
- Parameters
- Returns
- sigma
float
Lennard-Jones molecular diameter, [Angstrom]
- sigma
Notes
Pc is originally in bar. An excellent paper. None is returned if the polynomial returns a negative number, as in the case of 1029.13 K and 3.83 bar.
References
- 1
Silva, Carlos M., Hongqin Liu, and Eugenia A. Macedo. “Models for Self-Diffusion Coefficients of Dense Fluids, Including Hydrogen-Bonding Substances.” Chemical Engineering Science 53, no. 13 (July 1, 1998): 2423-29. doi:10.1016/S0009-2509(98)00037-2
Examples
>>> sigma_Silva_Liu_Macedo(560.1, 4550000) 5.164483998730177
Utility Functions¶
- chemicals.lennard_jones.T_star(T, epsilon_k=None, epsilon=None)[source]¶
This function calculates the parameter T_star as needed in performing collision integral calculations.
- Parameters
- Returns
- T_star
float
Dimentionless temperature for calculating collision integral, [-]
- T_star
Notes
Tabulated values are normally listed as epsilon/k. k is the Boltzman constant, with units of J/K.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
Examples
>>> T_star(T=318.2, epsilon_k=308.43) 1.0316765554582887