Water Dynamics at the Solid–Liquid Interface to Unveil the Textural Features of Synthetic Nanosponges

A fast-field-cycling NMR investigation was carried out on a set of polyurethane cyclodextrin nanosponges, in order to gain information on their textural properties, which have been proven to be quite difficult to assess by means of ordinary porosimetric techniques. Experiments were performed on both dry and wet samples, in order to evaluate the behavior of the “nonexchangeable” C-bound 1H nuclei, as well as the one of the mobile protons belonging to the skeletal hydroxyl groups and the water molecules. The results acquired for the wet samples accounted for the molecular mobility of water molecules within the channels of the nanosponge network, leading back to the possible pore size distribution. Owing to the intrinsic difficulties involved in a quantitative assessment of the textural properties, in the present study we alternatively propose an extension to nanosponges of the concept of “connectivity”, which has been already employed to discuss the properties of soils.


Supporting Information
i) Short outline of FFC-NMR theory. 1 Fast field cycling (FFC) NMR relaxometry is the major technique to be applied in studying the behavior of a liquid system on the surface of a porous medium. In particular, as a solid material is added with liquid water, water molecules are subjected to two different types of motions. From the one hand, water molecules stay in the proximity of the solid surface for a short time during which they are subjected to a horizontal diffusion.
From the other hand, molecules laying on the surface can leave it and reenters the bulk, while they are replaced by bulk water molecules. The distribution of water motional frequencies depends upon the homogeneity of the surface of the porous medium. Water confined in small-sized pores is more tightly constrained than that freely moving in larger spaces. The distributions of magnetic fields (DMF) due to the motional fluctuations are responsible for the dispersion of the longitudinal (or spin-lattice) relaxation times (T1) occurring when each frequency in DMF matches the Larmor frequencies (ωL) of the observed nuclei. In the case of water containing systems, the observed nuclei are the protons in water molecules. Water near the surface can also interact with surficial paramagnetic systems. The resultant modulation of the local dipolar magnetic field generated by paramagnetism additionally contributes to spin-lattice relaxation. The direct relationship between the frequency of the water motion and the 1 H Larmor frequency is related to the water dynamics in porous media through the modulation of the intensity of the applied magnetic field. Fast field cycling NMR relaxometry is based on the fast change of the intensity of an applied magnetic field in order to monitor the variations of 1 H T1 values of a dynamic system. Figure S1 shows the basic FFC NMR experimental design where the typical preparation-evolution-acquisition steps of the basic NMR experiment are replaced by polarization-relaxation-acquisition intervals. As outlined below, a pre-polarized (PP) and a non-polarized (NP) sequence can be recognized. During the first step of the PP sequence, a longitudinal magnetization is generated through the application of a polarization field (BPOL) for a limited and fixed period of time (referred to as polarization time, TPOL). Afterwards, the magnetic field S2 is switched to a new one (indicated as relaxation field, BRLX), applied for a period τ during which the magnetization intensity relaxes to reach a new equilibrium condition. Finally, the application of a 1H 90° pulse into an acquisition magnetic field (BACQ) held for a fixed time makes the magnetization observable and the free induction decay (FID) acquirable. In the NP sequence, BPOL is null. The PP sequence is applied when the relaxation field becomes very low in intensity and enhancement of sensitivity is needed for FID achievement.
The crossover field between the NP and PP sequences is approximately retrieved when the relaxation field intensity is half of that of the polarization field. The longitudinal relaxation time (T1) values of the observed nuclei are obtained for every given BRLX through a progressive variation of the τ values. Figure S1. Scheme of the typical sequence used in FFC NMR relaxometry. The non-polarized sequence is obtained when BPol is null. Conversely, as BPol is non-null, the pre-polarized sequence is achieved.
The relationship between signal intensity and τ can be modeled as in equation (S1) for the PP sequence and as in equation (S2) for the NP sequence: In both equations (S1) and (S2), M(τ) is the magnetization intensity at the selected τ value; a is the offset; bi Here, Const is a constant parameter, ωL is the proton Larmor frequency (i.e., the BRLX value), and τC is the correlation time (i.e., the time taken for a molecule to rotate one radian or to move a distance of the order of its dimension). The longer the τC value, the slower the molecular motions are, thereby revealing restrictions in the motional freedom-degrees of spatially restrained molecular systems. Conversely, as a molecule encompasses faster motions due to higher degrees of freedom in larger spaces, shorter correlation time values are expected.
Equation (S5) is only valid when a non-stretched NMRD curve is obtained. When the NMR dispersion profiles are stretched as a consequence of the complexity of the re-orientational dynamics within the molecular system, the mathematical model developed by Halle and co-workers 2 must be accounted for. It is also referred to as "model-free analysis" and is described as in equation (S6).
In equation (S6), ωL is the proton Larmor frequency, ci is a fitting parameter, and τCi is the ith correlation time of the i-th component of the molecular system. The ci and τCi values are used as in equation (S7) to obtain an average correlation time of the whole system: ii) Table S1. R1 vs ωL data.   S11 v) Table S3. Log-normal regression parameters for normalized Inverse-Laplace (UPEN) T1 distribution curves.