Relative Permittivity/Dielectric Constant (chemicals.permittivity)

This module contains various permittivity calculation routines and dataframes of coefficients for correlations.

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Correlations for Specific Substances

chemicals.permittivity.permittivity_IAPWS(T, rho)

Calculate the relative permittivity of pure water as a function of. temperature and density. Assumes the 1997 IAPWS [1] formulation.

$$\epsilon(\rho, T) =\frac{1 + A + 5B + (9 + 2A + 18B + A^2 + 10AB + 9B^2)^{0.5}}{4(1-B)}$$

$$A(\rho, T) = \frac{N_A\mu^2\rho g}{M\epsilon_0 kT}$$

$$B(\rho) = \frac{N_A\alpha\rho}{3M\epsilon_0}$$

$$g(\delta,\tau) = 1 + \sum_{i=1}^{11}n_i\delta^{I_i}\tau^{J_i} + n_{12}\delta\left(\frac{647.096}{228}\tau^{-1} - 1\right)^{-1.2}$$

$$\delta = \rho/(322 \text{ kg/m}^3)$$

$$\tau = T/647.096\text{K}$$

Parameters

Tfloat

Temperature of water [K]

rhofloat

Mass density of water at T and P [kg/m^3]

Returns

epsilonfloat

Relative permittivity of water at T and rho, [-]

Notes

Validity:

273.15 < T < 323.15 K for 0 < P < iceVI melting pressure at T or 1000 MPa, whichever is smaller.

323.15 < T < 873.15 K 0 < p < 600 MPa.

Coefficients and constants (they are optimized away in the function itself):

ih = [1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 10]

jh = [0.25, 1, 2.5, 1.5, 1.5, 2.5, 2, 2, 5, 0.5, 10]

Nh = [0.978224486826, -0.957771379375, 0.237511794148, 0.714692244396,

-0.298217036956, -0.108863472196, 0.949327488264E-1, -.980469816509E-2, 0.165167634970E-4, 0.937359795772E-4, -0.12317921872E-9]

polarizability = 1.636E-40

dipole = 6.138E-30

References

1

IAPWS. 1997. Release on the Static Dielectric Constant of Ordinary Water Substance for Temperatures from 238 K to 873 K and Pressures up to 1000 MPa.

Examples

>>> permittivity_IAPWS(373., 958.46)
55.565841872697234

>>> permittivity_IAPWS(650., 40.31090)
1.2659205723606064

chemicals.permittivity.permittivity_CRC(T, a, b, c, d)

Return the relative permittivity (epsilon) of a chemical using a polynomical equation as in [1].

Parameters

Tfloat

Temperature of fluid, [K]

afloat

Constant coefficient, [-]

bfloat

Constant coefficient, [1/K]

cfloat

Constant coefficient, [1/K^2]

dfloat

Constant coefficient, [1/K^3]

Returns

epsilonfloat

Relative permittivity of fluid at T, [-]

Notes

The permittivity is given by $\epsilon_r = A + BT + CT^2 + DT^3$

References

1

Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014.

Examples

Calculate the permittivity of 4-Nitroaniline:

>>> permittivity_CRC(450., 487, -1.5, 0.00129, 0.)
73.225

Fit Coefficients

All of these coefficients are lazy-loaded, so they must be accessed as an attribute of this module.

chemicals.permittivity.permittivity_data_CRC

Data from [1] with coefficients fit to a polynomial in terms of temperature in K. $\epsilon_r = A + BT + CT^2 + DT^3$ is the equation, although some chemcials only have a constant value.

1

Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014.

In [1]: import chemicals

In [2]: chemicals.permittivity.permittivity_data_CRC
Out[2]: 
                                                   Chemical  ...   Tmax
CAS                                                          ...       
50-70-4                                          D-Glucitol  ...    NaN
50-78-2                           2-(Acetyloxy)benzoic acid  ...  416.0
51-79-6                                     Ethyl carbamate  ...  368.0
54-11-5                                          L-Nicotine  ...  363.0
55-63-0                                    Trinitroglycerol  ...    NaN
...                                                     ...  ...    ...
100295-85-0                        6-Methyl-3-heptanol, ()-  ...  383.0
100296-26-2                        2-Methyl-3-heptanol, ()-  ...  403.0
111675-77-5                        2-Methyl-1-heptanol, ()-  ...  328.0
111767-95-4                        5-Methyl-1-heptanol, ()-  ...  328.0
123434-07-1  2,4,6-Trimethyl-3-heptene (unspecified isomer)  ...    NaN

[1303 rows x 9 columns]