2-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective area k(1) and k(2) separated by a time interva l can formally be expressed as a means to probe k space in a two-dimensiona l way. While for most applications, a Full coverage of the [k(1), k(2)] spa ce is not necessary, an experiment with k(1) = -k(2) can be regarded as a s ampling of the secondary diagonal in [k(1), k(2)] space. Likewise, the main diagonal is represented by the condition k(1) = k(2) and encodes position. Thus, the [r(1), r(2)] space conjugate to [k(1), k(2)], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45 degrees. While displacement R = r(2) - r(1) corresponds to an average v elocity (v) over bar = R/, an extension towards higher-order derivations su ch as acceleration is straightforward by modification of the pulse sequence . We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capi llary systems in the light of the suggested interpretation.