To provide exact values of self-diffusion coefficients of water (H_{2}^{16}O)
over a broad range of temperatures as reference values for testing and calibrating
diffusion measurements, e. g., in diffusion-weighted magnetic resonance imaging (MRI).

Several publications provide values of self-diffusion coefficients of water
at different temperatures [1–9].
These data points (listed below in the Data section)
can be interpolated
and extrapolated using the dependence between log *D* and 1/*T*
(Arrhenius plot).

Here, an interactive interface is provided to calculate self-diffusion coefficients of water at different temperatures (or, alternatively, to calculate the temperature corresponding to a given diffusion coefficient). The (default) list of measured data points, i. e., of pairs (temperature, diffusion coefficient), used for these calculations consists of the results summarized in Tables 1–5 below. The list of data points can be extended or shortened (e. g, it may be advisable to remove data of low (≤ 5 °C) and high (≥ 50 °C) temperatures if interested in the intermediate range between 15 and 40 °C).

Diffusion coefficients of water do not follow an exact linear relationship in the Arrhenius plot. This is accounted for by the quadratic fit option that results in a very good agreement of measured data points and fit function. It is strongly recommended to use the quadratic fit when calculating diffusion coefficients. (In an earlier version of this document, only the linear fit was available; calculated diffusion coefficients based on this linear interpolation must be expected to be systematically too low by about 0.4 % in the range between 15 and 30 °C.)

All diffusion coefficients are given in μm^{2}/ms =
10^{–3} mm^{2}/s = 10^{–9} m^{2}/s.

quadratic fit linear fit | |

Add to list (e. g., “20.5, 2.05”): | |

Temperature (°C): | Diff. coefficient (10^{–3} mm^{2}/s): |

Table 1 shows data measured with a diaphragm-cell
technique; the estimated error is “a few tenths of a per cent” [1].
Newer results measured with a diaphragm cell are presented in
Table 2;
the listed values are calculated from the published results for H_{2}^{18}O
using the relation *D*(H_{2}^{16}O) =
1.0105 *D*(H_{2}^{18}O);
the estimated error is ±0.2 % [2].
Table 3 shows data from NMR measurements on a
19.8-MHz (0.47 T) spectrometer
with an estimated experimental error of ±1 % [3].
Data from NMR measurements on a Bruker MSL200 (4.7 T) spectrometer
with a total uncertainty (95 % confidence limit) of 1.5 % are
shown in Table 4 [4].
Diffusion coefficients of water measured with a Bruker AM 300 instrument
(300 MHz,
i. e., 7 T) with error limits ≤ 1 % are shown in
Table 5 [5].
Diffusion coefficients of supercooled liquid water
down to –31 °C are presented in
Table 6; the measurements were
performed with an NMR spectrometer and the errors were estimated to be
±5 % (95 % confidence limits) [6].
Data from various publications are summarized in
Table 7 [7–9].

Temperature | D/(μm^{2}/ms) | |
---|---|---|

1 °C | 274.15 K | 1.149 |

4 °C | 277.15 K | 1.276 |

5 °C | 278.15 K | 1.313 |

15 °C | 288.15 K | 1.777 |

25 °C | 298.15 K | 2.299 |

35 °C | 308.15 K | 2.919 |

45 °C | 318.15 K | 3.575 |

Temperature | D/(μm^{2}/ms) | |
---|---|---|

0 °C | 273.15 K | 1.130 |

10 °C | 283.15 K | 1.536 |

20 °C | 293.15 K | 2.022 |

25 °C | 298.15 K | 2.296 |

30 °C | 303.15 K | 2.590 |

40 °C | 313.15 K | 3.240 |

50 °C | 323.15 K | 3.968 |

60 °C | 333.15 K | 4.772 |

70 °C | 343.15 K | 5.646 |

80 °C | 353.15 K | 6.582 |

90 °C | 363.15 K | 7.578 |

100 °C | 373.15 K | 8.623 |

Temperature | D/(μm^{2}/ms) | |
---|---|---|

4 °C | 277.15 K | 1.27 |

10 °C | 283.15 K | 1.55 |

25 °C | 298.15 K | 2.30 |

45 °C | 318.15 K | 3.55 |

60 °C | 333.15 K | 4.70 |

Temperature | D/(μm^{2}/ms) | |
---|---|---|

15 °C | 288.15 K | 1.756 |

20 °C | 293.15 K | 2.023 |

25 °C | 298.15 K | 2.317 |

30 °C | 303.15 K | 2.616 |

Temperature | D/(μm^{2}/ms) | |
---|---|---|

15 °C | 288.15 K | 1.766 |

20 °C | 293.15 K | 2.025 |

25 °C | 298.15 K | 2.299 |

30 °C | 303.15 K | 2.597 |

35 °C | 308.15 K | 2.895 |

40 °C | 313.15 K | 3.222 |

45 °C | 318.15 K | 3.601 |

50 °C | 323.15 K | 3.983 |

56 °C | 329.15 K | 4.444 |

Temperature | D/(μm^{2}/ms) | |
---|---|---|

–30.65 °C | 242.5 K | 0.187 |

–28.75 °C | 244.4 K | 0.219 |

–26.85 °C | 246.3 K | 0.263 |

–24.95 °C | 248.2 K | 0.321 |

–23.15 °C | 250.0 K | 0.341 |

–21.35 °C | 251.8 K | 0.395 |

–19.15 °C | 254.0 K | 0.438 |

–17.35 °C | 255.8 K | 0.477 |

–14.45 °C | 258.7 K | 0.553 |

–11.65 °C | 261.5 K | 0.633 |

–9.45 °C | 263.7 K | 0.700 |

0.35 °C | 273.5 K | 1.05 |

12.15 °C | 285.3 K | 1.58 |

25.05 °C | 298.2 K | 2.23 |

Temperature | D/(μm^{2}/ms) | Ref. | |
---|---|---|---|

18.4 °C | 291.55 K | 1.98 ± 0.14 | [7] |

18.5 °C | 291.65 K | 1.95 ± 0.02 | [8] |

18.5 °C | 291.65 K | 2.03 ± 0.01 | [8] |

25.0 °C | 298.15 K | 2.36 ± 0.04 | [8] |

25.0 °C | 298.15 K | 2.23 ± 0.06 | [9] |

A simple application based on these data is the calibration of an MRI system with
an ice-water phantom [10]. For water at 0 °C, a
diffusion coefficient of 1.12 μm^{2}/ms is estimated using the default
data from Tables 1–5, but after removal of all measurements performed at
temperatures > 30 °C.

[1] R. Mills. Self-diffusion in normal and heavy water in the range 1–45°. The Journal of Physical Chemistry, Vol. 77, No. 5, 685–688 (1973). DOI: 10.1021/j100624a025

[2] A.J. Easteal, W.E. Price, L.A. Woolf. Diaphragm cell for high-temperature diffusion measurements. Journal of the Chemical Society: Faraday Transactions 1, Vol. 85, No. 5, 1091–1097 (1989). DOI: 10.1039/F19898501091

[3] K.R. Harris, L.A. Woolf. Pressure and temperature dependence of the self diffusion coefficient of water and oxygen-18 water. Journal of the Chemical Society: Faraday Transactions 1, Vol. 76, 377–385 (1980). DOI: 10.1039/F19807600377

[4] P.S. Tofts, D. Lloyd, C.A. Clark, G.J. Barker, G.J.M. Parker, P. McConville, C. Baldock, J.M. Pope. Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo. Magnetic Resonance in Medicine, Vol. 43, No. 3, 368–374 (2000). DOI: 10.1002/(SICI)1522-2594(200003)43:3<368::AID-MRM8>3.0.CO;2-B

[5] M. Holz, S.R. Heil, A. Sacco. Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1H NMR PFG measurements. Physical Chemistry Chemical Physics, Vol. 2, 4740–4742 (2000). DOI: 10.1039/B005319H

[6] K.T. Gillen, D.C. Douglass, M.J.R. Hoch. Self-diffusion in liquid water to –31°C. The Journal of Chemical Physics, Vol. 57, No. 12, 5117–5119 (1972). DOI: 10.1063/1.1678198

[7] J.S. Murday, R.M. Cotts. Self-diffusion in liquids:
H_{2}O, D_{2}O, and Na. The Journal of Chemical Physics,
Vol. 53, 4724–4725 (1970).
DOI: 10.1063/1.1674011

[8] C.R. Becker, L.R. Schad, W.J. Lorenz. Measurement of diffusion coefficients using a quick echo split NMR imaging technique. Magnetic Resonance Imaging, Vol. 12, No. 8, 1167–1174 (1994). DOI: 10.1016/0730-725X(94)90082-3

[9] D.E. O'Reilly, E.M. Peterson. Self-diffusion coefficients and rotational correlation times in polar liquids. II. The Journal of Chemical Physics, Vol. 55, No. 5, 2155–2163 (1971). DOI: 10.1063/1.1676386

[10] T.L. Chenevert, C.J. Galbán, M.K. Ivancevic, S.E. Rohrer, F.J. Londy, T.C. Kwee, C.R. Meyer, T.D. Johnson, A. Rehemtulla, B.D. Ross. Diffusion coefficient measurement using a temperature-controlled fluid for quality control in multicenter studies. Journal of Magnetic Resonance Imaging, Vol. 34, No. 4, 983–987 (2011). DOI: 10.1002/jmri.22363