Chemistry Reference
In-Depth Information
The category of diffusion imaging can be subdivided into a number of different
techniques including diffusion-weighted imaging (DWI), apparent diffusion co-
efficient (ADC) mapping, diffusion tensor imaging (DTI), q-space imaging, and
diffusion spectroscopy.
A.
Brownian Motion
Diffusion is a manifestation of the random translational motion of molecules due to
their thermal energy. The random walk [12, 13] executed by the diffusing molecules
is called Brownian motion. Following the account of the phenomenon first recorded
in a systematic way by the botanist Robert Brown in 1827 [12], the characteristics
of Brownian motion as observed from detailed experiments were described by
Gouy [12, 14]. The motion of a Brownian particle is very irregular; its trajectory
comprises translations and rotations and appears to have no tangent (Fig. 1). The
composition and density of the particles do not influence the motion, however, the
smaller their size, the more active the motion. In a less viscous fluid, or at higher
temperatures, the motion is also more vigorous. The motion of the particles never
ceases.
In order to provide a background to the phase diffusion in NMR, we must first
outline the theory of the translational Brownian motion as formulated by Einstein
in 1905 [15] (here we follow in outline the exposition of Coffey [16]). We do this
by using the probability density diffusion equation for the displacements of the
Brownian particles and by Langevin in 1908 [15] by using the equation of motion
Figure 1.
An example of particles performing a random walk. The dots indicate either the start
or end of an observation time interval.
