The influence of dipolar interactions on the longitudianl relaxation o
f deuteron spin systems is investigated. Spin diffusion rates are eval
uated, including approximate rates due to double quantum spin diffusio
n and three-spin flip-flop transitions. It is shown that slow molecula
r rotations in supercooled liquids do not affect the spin diffusion ra
tes significantly provided that the motional correlation times are bel
ow the average spin lattice relaxation time T-l which becomes on the o
rder of one second close to the glass transition temperature T-g. Howe
ver, the broad distribution of deuteron T-l values at T < T-g results
in a large effect of spin diffusion upon the long time decay of the lo
ngitudinal magnetization in T-l experiments. These effects are estimat
ed in terms of a simple model in agreement with recent experiments. It
is also shown that the initial decay determining the average rate [T-
l(-l)] remains unaffected by spin diffusion. Finally, we show that sma
ll amplitude motions on a time scale of 10(-6)-10(-3) s may cause temp
erature dependent spin diffusion effects. (C) 1995 American Institute
of Physics.