Diffusion NMR or Diffusion Ordered SpectroscopY (DOSY) is measured by combining radiofrequency (RF) pulses with pulsed field gradients. 

The simplest sequence to measure diffusion NMR is called the pulsed field gradient spin-echo (PGSE). The magnetization is excited with a 90-degree RF pulse then dispersed using a magnetic field gradient pulse. After a period of D/2 (D is the diffusion time) a 180-degree RF pulse inverts the dispersed magnetization, and a second gradient pulse is applied to refocus the signal. Refocusing is only achieved for spins that did not change their location during the time between the 2 gradients (i.e., the diffusion time D). Diffusion causes the spins to move away from where their signals can be refocused thereby reducing the intensity of the resulting signal. 

The attenuation of the NMR signal is a factor of the strength and duration of the magnetic field gradient pulse and the time between the two gradients.  

In the diffusion experiment the gradient strength is incremented, and the signal intensity is measured for each gradient with all the other experimental parameters kept constant. By plotting ln of the normalized signal as a function of [g2d2G2(D-d/3)], known as b values, where g is the gyromagnetic ratio (4257 s-1 Gauss-1 for 1H), G is the gradient strength and d is its duration, and D is the time between the gradients, a linear curve is obtained. The slope of this plot is –D (D is the diffusion coefficient).  

The diffusion coefficient of a molecule is related to its radius through the Stokes-Einstein equation, where D is the diffusion coefficient, k is the Boltzmann constant, T is the temperature, η is the viscosity and r is the radius of the diffusing molecule (assuming a spherical shape). 

Large molecules diffuse much slower than small molecules. 

The diffusion coefficient is also affected by the viscosity of the solution. The diffusion coefficient of the same molecule is much faster in acetonitrile than in DMSO, which is a more viscous solvent.

Diffusion NMR can be used for many applications: 

To follow molecular interactions and exchange, calculate association constants, study encapsulation and molecular cages and capsules, extract information regarding molecular size and shape for small molecules and for complexes, dendrimers, and polymers and to study ion pairing and organometallic systems. 

There are some practical aspects that must be considered while performing a diffusion experiment:  

1. Choosing the appropriate pulse sequence:  
   There are four main pulse sequences to measure diffusion: Pulsed Gradient Spin Echo (PGSE), Pulsed Gradient Stimulated Echo (PGSTE), Longitudinal Eddy current Delay (LED) and Bipolar Pulse Longitudinal Eddy current Delay (BPLED). For singlets with a relatively long T2 – PGSE is better. For large molecules with short T2 and long T1 BPLED is much better. 
2. Minimize the effect of convections: The temperature must be stable and by using high gas flow, a coaxial NMR tube and a solvent with high viscosity, convections can be avoided. 
3. The pulsed gradients must be calibrated in advance either by a 1D image of a ‘phantom’ in an NMR tube from which the applied gradient strength is calculated or by performing the diffusion experiment with a calibration sample of a known diffusion coefficient. 
4. Choose the optimized parameters for the experiment: Experimental parameters that need to be defined are the diffusion time, D, the gradient pulse duration, d, and the range of gradient strengths, Gmin to Gmax. The aim is to obtain a well-characterized decay profile to allow reliable data fitting (a decrease of 90% in the signal intensity).   

Diffusion spectra can be presented as a 2D plot with chemical shift on the horizontal axis and the diffusion coefficient on the vertical axis. This representation is called Diffusion Ordered SpectroscopY (DOSY). The chemical shift dimension is analyzed by a Fourier transform and the diffusion coefficient dimension is obtained by an inverse Laplace transform (ILT). The DOSY presentation can separate spectroscopically different species based on their diffusion coefficient/molecular weight.