Atomistic molecular dynamics simulations are used to investigate $^1$H NMR $T_1$ relaxation of water from paramagnetic Gd$^{3+}$ ions in solution at 25$^{circ}$C. Simulations of the $T_1$ relaxivity dispersion function $r_1$ computed from the Gd$^{3+
}$--$^1$H dipole--dipole autocorrelation function agree within $simeq 8$% of measurements in the range $f_0 simeq $ 5 $leftrightarrow$ 500 MHz, without any adjustable parameters in the interpretation of the simulations, and without any relaxation models. The simulation results are discussed in the context of the Solomon-Bloembergen-Morgan inner-sphere relaxation model, and the Hwang-Freed outer-sphere relaxation model. Below $f_0 lesssim $ 5 MHz, the simulation overestimates $r_1$ compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting $r_1$ at high frequencies in chelated Gd$^{3+}$ contrast-agents used for clinical MRI.
The mechanism behind the $^1$H NMR frequency dependence of $T_1$ and the viscosity dependence of $T_2$ for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an
extended range of frequencies ($f_0 = 0.01 leftrightarrow$ 400 MHz) and viscosities ($eta = 385 leftrightarrow 102,000$ cP) using $T_{1}$ and $T_2$ in static fields, $T_{1}$ field-cycling relaxometry, and $T_{1rho}$ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times $T_{1LM} propto f_0$ and $T_{2LM} propto (eta/T)^{-1/2}$ with a phenomenological model of $^1$H-$^1$H dipole-dipole relaxation which includes a distribution in molecular correlation times and internal motions of the non-rigid polymer branches. We show that the model also accounts for the anomalous $T_{1LM}$ and $T_{2LM}$ in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the $T_{1} propto f_0$ dispersion and $T_2$ of similar polymers simulated over a range of viscosities ($eta = 1 leftrightarrow 1,000$ cP) are in good agreement with measurements and the model. The $T_{1} propto f_0$ dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under confinement, without the need to invoke paramagnetism.
