Diffusion Manual Outline

3
Chapter 1
Section 1.1
Introduction to Diffusion
Introduction
Self-diffusion is a measure of the translational motion of a molecule. Diffusion is
closely related to molecular size as illustrated by the Stokes-Einstein equation seen
below:
D = k T
f
where k is the Boltzman constant, T is the temperature and f is the friction coefficient.
For the simple case of a spherical particle of a hydrodynamic radius r s in a solvent of
viscosity η, the friction factor is given by f = 6 π η r s
Translational diffusion can be used to determine the size and shape of individual
molecules as well as molecular aggregates. This provides an excellent way of analyzing
complex mixtures without having to physically separate out each individual component.
Pulsed-field gradient (PFG) NMR can be used to measure translational diffusion
by applying externally controlled magnetic field gradients. These gradients spatially
encode the position of each nuclear spin. This spatial distribution can be decoded after
waiting a short time by applying a second gradient. If the waiting time is very short
between the encoding and decoding gradients the spins will not have had a chance to
change position and in turn the magnetization will refocus without a net phase change.
However the spins that have moved during the waiting time between the encoding and
decoding steps will acquire a net phase change. The summation of the accumulated
phases over the entire sample will lead to partial cancellation of the observable
magnetization and hence an attenuation of the NMR signal. This signal attenuation is
dependent on the strength of the applied gradients, the time between the gradients
(diffusion time) and the diffusion coefficient of the molecules under study.
Section 1.2
Some Theory
Nuclear spins within a homogeneous magnetic field precess at the Larmor
frequency according to the equation
ω o = γB o
where ω o is the Larmor frequency
γ is the gyromagnetic ratio and
B o is the strength of the magnetic field