# -*- coding: utf-8 -*-
import warnings
try:
from numpy import any as _any
except ImportError:
def _any(arg):
if arg is True:
return True
if arg is False:
return False
return any(arg)
# Parameters from paper (SI-units):
gamma = 2.063
dgamma = 0.051
D0 = 1.635e-8
TS = 215.05
dD0 = 2.242e-11
dTS = 1.2
low_t_bound = 273.15 # 0 deg C, (m.p. at ambient pressure)
high_t_bound = 373.15 # 100 deg C, (b.p. at ambient pressure)
[docs]def water_self_diffusion_coefficient(T=None, units=None, warn=True,
err_mult=None):
"""
Temperature-dependent self-diffusion coefficient of water.
Parameters
----------
T: float
Temperature (default: in Kelvin)
units: object (optional)
object with attributes: Kelvin, meter, kilogram
warn: bool (default: True)
Emit UserWarning when outside temperature range.
err_mult: length 2 array_like (default: None)
Perturb paramaters D0 and TS with err_mult[0]*dD0 and
err_mult[1]*dTS respectively, where dD0 and dTS are the
reported uncertainties in the fitted paramters. Useful
for estimating error in diffusion coefficient.
References
----------
Temperature-dependent self-diffusion coefficients of water and six selected
molecular liquids for calibration in accurate 1H NMR PFG measurements
Manfred Holz, Stefan R. Heila, Antonio Saccob;
Phys. Chem. Chem. Phys., 2000,2, 4740-4742
http://pubs.rsc.org/en/Content/ArticleLanding/2000/CP/b005319h
DOI: 10.1039/B005319H
"""
if units is None:
K = 1
m = 1
s = 1
else:
K = units.Kelvin
m = units.meter
s = units.second
if T is None:
T = 298.15*K
_D0 = D0 * m**2 * s**-1
_TS = TS * K
if err_mult is not None:
_dD0 = dD0 * m**2 * s**-1
_dTS = dTS * K
_D0 += err_mult[0]*_dD0
_TS += err_mult[1]*_dTS
if warn and (_any(T < low_t_bound*K) or _any(T > high_t_bound*K)):
warnings.warn("Temperature is outside range (0-100 degC)")
return _D0*((T/_TS) - 1)**gamma
# generated at doi2bib.org:
bibtex = """
@article{Holz2000,
doi = {10.1039/b005319h},
url = {http://dx.doi.org/10.1039/B005319H},
year = {2000},
publisher = {Royal Society of Chemistry ({RSC})},
volume = {2},
number = {20},
pages = {4740--4742},
author = {Manfred Holz and Stefan R. Heil and Antonio Sacco},
title = {Temperature-dependent self-diffusion coefficients of water and six
selected molecular liquids for calibration in accurate 1H {NMR}
{PFG} measurements},
journal = {Phys. Chem. Chem. Phys.}
}
"""