Molecular Weights of Cyclic and Hollow Clusters Measured by DOSY NMR Spectroscopy

Abstract

The Stokes-Einstein expression of the diffusion coefficient as a function of the hydrodynamic radius of the diffusing object does not explicitly carry the mass dependency of the object. It is possible to correlate the translational self-diffusion coefficients D with the molecular weight M for an ensemble of cyclic or hollow clusters ranging from about 200 to 30,000 g x mol(-1). From this correlation, the mass of a cluster can be deduced from its diffusion coefficient. Consistency of diffusion as a power law of mass and Stokes-Einstein formulation is completely fulfilled with the selected compounds of this contribution.

Forced assembly by multilayer coextrusion to create oriented graphene reinforced polymer nanocomposites

“…Such an assumption is reasonable because of the short residence time of the melt streams and slow diffusion of the graphene nanoplatelets in the mixing elements (w2 min). Using the StokeseEinstein equation [35] and an equivalent spherical diameter [36] for the graphene nanoplatelets. For example, for diameters of 28.8 nm (for a 5 nm  50 nm  50 nm platelet) and 72.6 nm (for a 5 nm  200 nm  200 nm platelet), the mean-square diffusion displacement in 2 min is estimated to be 1130 nm 2 (d z 34 nm) and 449 nm 2 (d z 21 nm), respectively, for a melt viscosity of 5367 Pa.s at a temperature of 225 C. Considering the concentration of graphene, the system is not a dilute dispersion, and we would, therefore, expect that the particle diffusion should be slower than the StokeseEinstein estimate because of the particle interactions [37].…”

Pre-organisation or a hydrogen bonding mismatch: silver(I) diamide ligand coordination polymers versus discrete metallo-macrocyclic assemblies

“…Reaction of AgPF 6 with L1 in a mixture of acetonitrile and methanol, followed by slow environment have been shown to be inversely proportional to the ratio of their radii, [63][64][65][66][67] this indicates that the species formed from AgNO 3 and L1 is larger than the original ligand. Such analysis has been utilised to estimate the relative size of a molecule from a comparison of the diffusion rates and is more readily applied than establishing a Stokes-Einstein relation for this type of system.…”

Tetrapropylammonium Occlusion in Nanoaggregates of Precursor of Silicalite-1 Zeolite Studied by 1H and 13C NMR

“…For instance, pulsed-field gradient (PFG) NMR enables self-diffusion measurements [34]. Careful PFG NMR enabling in the pulse sequence to measure accurately diffusion, known under the acronym DOSY NMR, has been proven to be a valuable tool to study diffusion of a variety of molecules, especially chemical objects with different dimensionality [35,36]. Application of 29 Si DOSY NMR has been performed successfully on some aqueous silicate solutions for studying silicate speciation and spectral assignment [37][38][39].…”