Spin diffusion transfer difference (SDTD) NMR: an advanced method for the characterisation of water structuration within particle networks

HYPOTHESIS
The classical STD NMR protocol to monitor solvent interactions in gels is strongly dependent on gelator and solvent concentrations and does not report on the degree of structuration of the solvent at the particle/solvent interface. We hypothesised that, for suspensions of large gelator particles, solvent structuration could be characterised by STD NMR when taking into account the particle-to-solvent 1H-1H spin diffusion transfer using the 1D diffusion equation.


EXPERIMENTS
We have carried out a systematic study on effect of gelator and solvent concentrations, and gelator surface charge, affecting the behaviour of the classical STD NMR build-up curves. To do so, we have characterised solvent interactions in dispersions of starch and cellulose-like particles prepared in deuterated water and alcohol/D2O mixtures.


FINDINGS
The Spin Diffusion Transfer Difference (SDTD) NMR protocol is independent of the gelator and solvent concentrations, hence allowing the estimation of the degree of solvent structuration within different particle networks. In addition, the simulation of SDTD build-up curves using the general one-dimensional diffusion equation allows the determination of minimum distances (r) and spin diffusion rates (D) at the particle/solvent interface. This novel NMR protocol can be readily extended to characterise the solvent(s) organisation in any type of colloidal systems constituted by large particles.

. Energy levels for a two-spin system. (a) When the two spins are equivalent, the αβ and βα states are degenerate. The dipolar coupling between the two nuclei induces an energy-conserving "flip-flop" transitions between these two states, and cross-correlation occurs. (b) When the two spins are not equivalent, the transition is not energy conserving and its probability is low. (c) When the two inequivalent spins are coupled to (many) other spins, the energy levels of the two-spin system are broadened and an overlap occurs between some of the αβ and βα levels. Cross-correlation has high probability and spin diffusion occurs (Adapted from Emsley 2009) 1 .

SDTD NMR as a tool for quantifying the spin diffusion coefficient at the interface (Dinterface)
The phenomenon of spin diffusion can be described as the diffusion in space of nuclear magnetisation. It is mainly mediated by dipolar couplings and has been extensively used to retrieve a wealth of information about distances between atomic or molecular entities and for the characterisation of soft and solid materials. However, to obtain molecular spatial information it is of fundamental importance to experimentally determine the spin diffusion coefficient (D). A straightforward way to achieve this is to create a nonequilibrium spatial distribution of magnetisation along the protons of a molecular entity. Then, magnetisation is allowed to evolve freely for a specific time, and subsequently detected. During the evolution time, the spatial distribution differences of proton magnetisation will equilibrate via spin diffusion (i.e. dipolar couplings). The time to achieve the spatial equilibration of magnetisation will depend on the morphology of the molecular entity. In other words, the velocity of the equilibration step will depend on proton-proton distances and proton density.
The diffusion process of spin diffusion can be mathematically described by the Fick's law of diffusion 3

M(r, t) = ∇[D(r)∇M(r, t)]
Eq. S1 Where ∇ is the Laplace operator, D is the diffusion gradient, r is the space vector, t is the diffusion time and M (r,t) is defined as the ratio between the z-magnetisation m(r, t) and the mass fraction of protons mH(r) Where QH is the proton density and Vtot is the total volume of the molecular entity.
The solution of the diffusion equation for a point source is the Gaussian function While for an infinite solid the error function of the Gaussian function can be a solution for the diffusion equation In a two-phase system A and B where the magnetisation non-equilibrium spatial distribution is achieved by saturating selected protons on phase A and detecting it in phase B, the diffusion can still be described for each phase by the error function.
For two phases A and B.
Eq. S6 Where EA and EB are the magnetisations at the interface.
At t=0 Using the interface condition EA = EB and the flux equilibrium at the interface jA(r0, t) = jB (r0, t) it can be shown that Eq. S10 Notably, to detect the magnetisation in phase B we can use the 1 H NMR STD technique. The 1 H STD NMR pulse program has been used successfully in the biomolecular field in the last 20 years. The main advantage of STD NMR is being a ligand-observed NMR technique, hence using small molecules as reporters of the macromolecular environment in an easy, inexpensive and robust way. In this paper, we explore the use of 1 H STD NMR to access the interfacial spin diffusion phenomenon rationalised using Fick's 2 nd law of diffusion.
Importantly, to relate the 1 H STD NMR experiment to Eq. S10 the following considerations apply: 1. The small molecule is constantly in fast exchange between free and bound species in the phase B. Indeed, the overall exchange constant (k ex =k on +k off ) between the free and bound states is expected to be high due to a kon that can be considered at the diffusion limit and a koff that is expected to be relatively high so that kex >> Dinterface 2. The half-life time of the instantaneous small molecule/macromolecule interaction is expected to be short compared to the interfacial diffusion time. In order to achieve the interface condition, several cycles of association dissociation for the small molecule will take place before the magnetisation can be efficiently transported through phase A (macromolecule) and subsequently to phase B (small molecule) in a continuous fashion, and detected in phase B.
3. In phase B, the spin diffusion of the small molecule in the free state is the same as the molecular diffusion and approaches the diffusion limit so there is virtually no difference between spin diffusion coefficient Dsp, (no matter transport is involved) and molecular diffusion coefficient D (matter transport is involved). However, the relaxation of small molecules via spin diffusion is highly inefficient. Indeed, the small molecules that received the magnetisation through interacting with the macromolecule will maintain that magnetisation for a long time before relaxing. This will create again a new non-equilibrium spatial distribution of magnetisation through the protons of phase B that can be described by the error function and can be related to Eq. S10. As the interfacial spin diffusion is the slowest process it will be rate limiting for the entire process. Indeed, it is safe to substitute DB = DInterface in Eq. S10.
4. Finally, Dinterface can be obtained experimentally by varying the saturation time in the 1 H NMR STD pulse sequence, selecting specific protons of phase A and detecting the diffusion of magnetisation in the phase B through the proportionality MB (r, t) ∝ to I/I0 .

Sample preparation
Gels prepared in D 2 O Dispersions of TEMPO-oxidised cellulose nanofibrils (OCNF), corn starch (CS) and enzymatically produced cellulose (EpC) at different concentrations were prepared in D2O.
OCNF of a degree of oxidation of ~ 25%, produced from purified softwood fibre and processed via high pressure homogenization, was kindly provided by Croda. These were further purified by dialysis against ultra-pure water (DI water, 18.2 MO cm) and stirred at room temperature for 30 min. Then the dispersion was acidified to pH 3 using HCl solution and dialysed against ultra-pure water (cellulose dialysis tubing MWCO 12400) for 3 days with the DI water replaced twice daily. The dialysed OCNF suspension was processed via mechanical shear (ULTRA TURRAX, IKA T25 digital, 30 minutes at 6500 rpm) and the pH was adjusted to 7 using NaOH solution. This dispersion was further dialysed to remove any remaining salts and dispersed using a sonication probe (Ultrasonic Processor, FB-505, Fisher), via a series of 1 s on 1 s off pulses for a net time of 60 min at 30% amplitude in an ice bath, and subsequently freeze-dried.
To prepare the OCNF dispersions for NMR investigation, OCNF powder and water were weighted to provide the desired weight concentrations of OCNF, and then probe sonicated for 30 min at 20% amplitude using pulses of 1 s on and 2 s off, using an ultrasonic processor The STD spectra (ISTD) were obtained by subtracting the on-(Isat) to the off-resonance (I0) spectra. To determine the STD response or STD factor (ηSTD), the peak intensities in the difference spectrum (ISTD) were integrated relative to the peak intensities in the off-resonance spectrum (I0). The SDTD build-up curves were obtained by normalising all the STD factors against the highest value (usually corresponding to the longest saturation time).

Simulation of the SDTD build-up curves
To obtain a good fit of the SDTD build-up curve, it is essential to achieve a good sampling of both the lag phase and the plateau of the curve. To do so, using saturation times ranging from tens of milliseconds to 6-8 seconds is advised. The SDTD build-up curves were represented as a function of the square root of the saturation time and simulated in Matlab (Script 1) using Eq. 2. Here, the dependent variable is the normalized intensity of the NMR observable and the independent variable is the square root of the saturation time (in ms), r is the minimum distance of the grid (in nm), D is the spin diffusion rate (in nm 2 /ms) at the particle-solvent interface, erfc is the complementary error function, C is the proportionally constant of the fit, and b is a parameter to centre the function around x. Notably, the growth rate of the SDTD curve presents a proportional and inversely proportional relationship to the spin diffusion rate D and the minimum distance r, respectively, both related to the degree of solvent structuration within the gel network. Hence, faster spin diffusion rates D and shorter distances r reflect increased solvent structuration.  D2O/2PrOD (c) cosolvent mixtures of 10 wt% (black symbols), 30 wt% (red symbols), 50 wt% (green symbols) and 60 wt% (blue symbols) alcohol content. Note the faster growth of the SDTD build-up curves for HDO compared to the alcohols in all the gels. OCNF 1 wt% CS 15 wt% C 1.14 (± 0.13) 1.12 (± 0.14) D (nm 2 /ms) 9.80E-05 (± 1.13E-05) 1.28E-04 (± 1.70E-05) R 2 0.9951 0.9952