A simplified approach to the interpretation of nuclear spin correlations in entangled polymeric liquids

We derive closed-form expressions for a sine correlation function β(2τ,τ) which is particularly sensitive to modulations of nuclear dipolar (and quadrupolar) interactions caused by slow molecular reorientations. This function is placed in the context of traditional nuclear magnetic resonance (NMR) experiments—the Free Induction Decay $\mathrm{R(t)}$ and the solid echo amplitude $\mathrm{E(\tau )}$ and families of expressions are evaluated for (i) motion governed by an exponential correlation function and (ii) macromolecular motion dominated by reptation. We introduce a simple correlation function for reptation that depends on only two parameters, $\overline{M_2},$ the preaveraged dipolar interaction strength and ${\tau }_d,$ the tube disengagement time. From proton NMR measurements of β in poly(dimethyl siloxane) melts we estimate $\overline{M_2}{\text{=1.3×10}}^6\hspace{0.17em}{\mathrm{s}}^{\text{−2}}$ and ${\tau }_d\text{=0.019\hspace{0.17em}}\mathrm{s}$ at 300 K, in reasonable agreement with a calculated value for $\overline{M_2}$ and an independent NMR estimate of the terminal relaxation time.