FUNPOLYMER (PID2021-126445OB-I00) tackles a central question in polymer physics: how to predict molecular weight from diffusion NMR experiments without being limited by solvent choice or sample concentration. Until now, reliable diffusion-based Mw prediction required extremely dilute samples and solvent-specific calibration curves, restricting the practical impact of diffusion NMR outside academic laboratories.
Previous work had shown that the product Dη (diffusion coefficient times viscosity) follows universal scaling laws with molecular weight, but only under very dilute conditions. FUNPOLYMER goes one step further: it shows that the concentration dependence can also be described by a universal scaling law and that, by combining it with the infinite-dilution calibration, it is possible to recover the true molecular weight at any concentration and in any solvent.
The key result is the relation Dη|c = Dη|1/∞ · exp(− κ Cν), where Dη|c is the diffusion–viscosity product at a given concentration, Dη|1/∞ is its value at infinite dilution, C is polymer concentration, κ is a molecular-weight-dependent parameter and ν ≈ 1 for polymers. Together with the scaling laws Dη|1/∞ = a·Mw−b and κ = m·Mw + n, this provides a universal expression that allows Mw to be computed iteratively from any diffusion experiment.
The methodology has been validated for polystyrene (PS) and polypropylene glycol (PPG) in several deuterated solvents (CDCl3, C6D6, toluene-d8 and THF-d8) over a broad concentration range (1.7–150 mg/mL), with Mw errors always below 4 %, covering from a few hundred up to hundreds of thousands of daltons.
In addition, an extensive database of universal calibration curves has been developed, treating viscosity as an independent parameter so that the curves can be applied to a wide variety of polymer systems regardless of the solvent used. Calibration curves are currently available for:
A key achievement of the project is that this database is combined with the innovative methodology for Mw prediction at any concentration and in any solvent, validated through the κ(Mw) and infinite-dilution Dη|1/∞(Mw) curves. In this way, the same infrastructure extends the universal approach well beyond PS and PPG.
DiffAtOnce is the software platform where this physics and mathematical formalism are implemented and made usable in practice.
The diffusion coefficient measured by NMR is not only controlled by molecular weight: solvent type, viscosity and polymer concentration also play a major role. In practice this forced measurements close to 1 mg/mL, solvent-specific calibrations and frequent recalibration, limiting the routine use of diffusion NMR for Mw determination.
FUNPOLYMER shows that both viscosity and concentration dependences can be captured in a single universal scaling law. The equation Dη|c = Dη|1/∞·exp(−κCν) disentangles concentration effects from intrinsic polymer physics, provided κ(Mw) and Dη|1/∞(Mw) curves are available.
From a measured D value at concentration C and the solvent viscosity, DiffAtOnce computes Dη|c, applies the new scaling law iteratively and returns the Mw that makes the universal κ and infinite-dilution curves consistent with the experiment, with computation times on the order of milliseconds.
All methodological lines in the project converge towards concentration-independent molecular weight prediction:
Optimisation of PGSE, DOSY and extended diffusion sequences to obtain accurate diffusion coefficients over concentrations from 1.7 to 150 mg/mL, avoiding the need to always work in extreme dilution.
Combined use of ILT methods (LMS/DiffAtOnce, TRAIn, dART, SILT-DOSY) to recover diffusion coefficients with typical errors below 3 %, even for complex gradient matrices and noisy data.
Construction of the universal Kappa curve and the infinite-dilution curve from systematic datasets, which form the backbone of the iterative Mw solver.
Algorithm that, starting from an initial Mw guess, repeatedly updates Dη|1/∞ and κ until the difference between measured and calculated Dη|c is minimized, with computation times on the order of 200 ms per sample.
Integration of machine-learning models and GPU-accelerated computation to explore extensions of the method to more complex distributions and to fast acquisition schemes (UF and time-resolved diffusion NMR).
Systematic comparison of diffusion-based Mw values with SEC references, with typical deviations between 1 and 4 %, showing that the new methodology is competitive while offering superior flexibility in solvent and concentration.
