For elastomer networks above the glass transition temperature T-g, a u
nified approach is presented to relate the residual dipolar couplings
in various independent NMR experiments to the cross-link density. This
is demonstrated on a series of cross-linked polylstyrene-co-butadiene
) elastomers. The presence of dynamic physical and permanent chemical
cross-links leads to a nonzero average of the homonuclear and heteronu
clear dipolar couplings, which results in a solid-like MMR relaxation
behavior. The residual dipolar couplings are expressed as a function o
f the effective number of statistical segments N-e between the physica
l and N-e(X) between the chemical cross-link points, using a simplifie
d network model with Gaussian statistics. These effective numbers are
extracted for each sample of the series from the C-13-edited transvers
e H-1 magnetization relaxation of the CH group. It is shown that the r
espective N-e values can be used to scale the time domain of various N
MR experiments such as (a) the free induction decay, (b) the C-13-edit
ed H-1 transverse magnetization relaxation, (c) the cross-polarization
curves, and (d) the H-1 magnetization exchange between the CH and CH2
groups. This proves the validity of the unified view on the dipolar i
nteractions in elastomer networks and provides a way to estimate the c
ross-link density.