(144g) Quantitative Scaling Analyses for Estimating Domain Sizes and Compositions at Particle Surfaces By Surface-Enhanced NMR

Quantitative scaling analyses for estimating
domain sizes and compositions at particle surfaces by surface-enhanced NMR

Nathan A. Prisco,¹ Arthur
Pinon,^2,3 Brennan Walder,² Lyndon Emsley,²
Bradley F. Chmelka¹

¹ Department of Chemical Engineering, University
of California, Santa Barbara, California, 93106  U.S.A.

² Institut des Sciences et
Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, Switzerland CH-1015.

³ Department of
Electrical Engineering, Center for Hyperpolarization in Magnetic
Resonance, Technical University of Denmark, Building 349, DK-2800 Kgs
Lyngby, Denmark

Surface compositions, interactions,
and domain sizes are often central to the diverse physiochemical properties of
solid particulate systems, including heterogeneous catalysts, semiconductors,
structural materials, and in batteries. Identifying compositions and domain
sizes at particle surfaces is exceedingly challenging especially for
disordered, non-porous, and/or low-surface-area (<1 m²/g) inorganic
oxides. At early hydration times (ca. hours), cementitious silicate particles are
believed to form thin layers (<50 nm) of monomeric or partially condensed
calcium silicate hydrates upon contact with water. The ability to characterize surface
compositions, mean thicknesses of hydrated domains and the kinetics associated
with their growth is crucial to understanding and controlling hydration,
silicate dissolution, and subsequent strength development in cements.¹
Here, low temperature (100 K) dynamic nuclear polarization surface enhanced NMR
spectroscopy (DNP-SENS) is used in combination with ¹H-¹H
spin-diffusion modelling analyses to determine the dimensions and compositions
of hydrated surface-layers formed on tricalcium silicate particles (ca. 20 µm
diameter). Importantly, the quantitative DNP-SENS analyses used here depend on
quantum-mechanical² or rate-law models³ to calculate approximate
domain sizes from transient signal intensity build-up curves. By application of
Chemical Engineering principles, we develop
an energy-conserving constitutive model that quantitatively describes the transfer
and dissipation of non-Boltzmann spin polarization across dissimilar material
interfaces, as manifested by experimental observations in large heterogeneous
spin systems (>10⁵ spins).

DNP-SENS using stable bisnitroxide radicals can achieve sensitivity improvements ranging
from 10² to 10⁵ over traditional solid-state NMR and enable
preferential detection of surface species (e.g.,
dilute adsorbates or surface hydrates). In this technique, microwave-driven
polarization transfer from electron to nuclear spins is used to generate
spin-polarization gradients via free-radical polarizing agent suspended within
a frozen organic solvent. Polarization is generated near the radical species
and subsequently relayed, typically by ¹H-¹H spin
diffusion, to particle surfaces and may penetrate into
the interior of ¹H-containing solids. Depending on the relative rates
of generation, propagation and relaxation of spin polarization in a given
medium, non-Boltzmann polarization may be relayed by ¹H-¹H
dipole-dipole couplings over distances ranging from <1 nm to tens of µm.⁴
Importantly, a scaling analysis leads to dimensionless parameters that have
analogies to those in mass- or heat-transfer processes, but which combine
aspects of both. Specifically, spin-polarization analogs of the Thiele modulus,
Biot, and Damköhler numbers
are determined that depend solely on known material properties or separately
measurable properties or parameters. Our combined experimental and theoretical
analyses on hydrated Ca₃SiO₅ indicates that over the
course of the induction period (<4 h hydration), the particle surfaces
primarily consist of disordered monomeric and dimeric calcium silicate hydrates
which are tens of nanometers thick.         

References

¹ Pustovgar,
E.; Sangodkar, R.P.; Andrew, A.S.; Palacius, M.; Chmelka, B.F.; Flatt, R.J.; Lacaillerie, J.B. Nat.
Commun. (7), 10952 (2016).

² Mentink-Vigier, F.;
Vega, S.; De Paëpe, G. Phys. Chem. Chem. Phys., 19 (5), pp 3506 (2017).

³ Smith, A.A.; Corzilius,
B.; Barnes, A.B.; Maly, T.; Griffin, R.G. J. Chem. Phys. 136, 015101 (2012).

⁴ Pinon, A.C.; Schlagnitweit, J.; Berruyer, P.;
Rossini, A.J.; Lelli, M.; Socie,
E.; Tang, M.; Pham, T.; Lesage, A.; Schantz, S.;        Emsley, L. J. Phys. Chem. C. 121 (29), 15993 (2017).