Calculating the self-diffusion coefficient


DiffAtOnce software calculates in a very simple and intuitive way the self-diffusion coefficientes at once. It provides an unique D-value for every slope defined previously by just clicking no more than three buttons.

DiffAtOnce features
DiffAtOnce features

The user has to select among the sequences available: PGSE (Pulse Gradient Spin Echo), PGSTE (Pulse Gradient Stimulated Echo), and PGSTE-BPP (Pulse Gradiebnt Stimulated Echo with Bipolar Pulse Pairs). Double Stimulated sequences (DSTE and DSTE-BPP) are not implemented in the standard version, and will be provided on demand. A very important parameter that might be selected in order to obtain quantitative selfdiffusion coefficientes is the shape of the gradient.

DiffAtOnce features

The user can choose between sine or rectangular shapes. The mathematics and therefore the D-value is different depending on this feature.

In this step, the user has to introduce the standard employed for radii calculation. Usually, experimental D values are all referenced to HDO. However, in this software any other substance can be used in the mathematics. For instance, one may like to use the D-value of a monomer for the calculation of its dimer.


The temperature is an important parameter since it modifies the solvent viscosity employed for the molecular size estimation. The whole screen is automatically refreshed as soon as the temperature is modified.

DiffAtOnce features

The standard version of the DIFFATONCE program (1.0.0.0) does not afford error theory, but could be implemented on demand via www.diffatonce.com. T As an added value, the software allows the user to introduce the parameters (A to D) that regulate the viscosity in the whole temperature range, so by just changing the temperature in the upper-right part of the screen, the program calculates the correct viscosity number that will be used for the calculation.
The program identifies through this code Recta X@X.XX the chemical shift monitored along the experiments. At the same time the user can find the regression coefficient, the slope, the nucleus and the most important diffusion parameters such as small delta (d) and big delta (D). Depending on the nucleus chosen the program employs automatically its corresponding gyromagnetic constant.
The software calculates the size of the diffusing species using a cylinder or an ellipsoid as models, and provides the semi-axis values for both of them. The Ro parameter is usually interpreted as the average hydrodynamic radius of a solid sphere with the same volume of the calculated cylinder or ellipsoid. As soon as the user defines the solvent, the program automatically calculates the hydrodynamic radius by the internal use of the Stokes-Einstein equation.

The user defines the desired points in the loaded spectrum, and clicking in the right botton all the regresion lines appear in the work area. In the standard version of the program 1.0.0.0, a maximum of 20 points are allowed, which permits to screen a fair amount of components in your mixture.


Estimating molecular shapes

It calculates the hydrodynamic size of the diffusing species using three models: sphere, cylinder or ellipsoid, providing Ro or the semi-axis dimensions for a given P (a/b) or Q (b/a) geometry. The Ro parameter is usually interpreted as the average hydrodynamic radius of a solid sphere having the same volume of the calculated cylinder or ellipsoid.


Non-ideal shape, advanced diffusion equation


$$ D = \frac{k·T}{c(r_s,R_H)· f_s(a,b) · \pi · \nu · R_H} $$

$$c(r_s,R_H) = 6 · f(r_{sl},R_H) $$

$$ \frac{\partial \psi(t,z)}{\partial t} = -i · \gamma · G(t,z) · \psi(t,z) + D · \nabla^2 \psi(t,z) - v_z · \nabla \psi(t,z) $$

A non-ideal shape and size of a real molecule can be accounted for with the diffusion equation modified, which include some constraints due to the relation between the solvent and the molecule. The factor form is used as well for calculating the real diffusion coefficient, nevertheless it is only recommend for advanced users in diffusion experiments.