It is evident based upon both this work and previous literature studies of MAO and the ion-pairs derived from it that a reliable estimate of molar mass from Dt (or VH) values is needed to relate PGSE NMR experiments to the limited ESI-MS (or MS) data that are available. The linear correlation reported in ref. 25 is not appropriate in the sense that the density of the compounds used to construct it were all ≤1 g mL -1 while MAO and the ionpairs derived from it are expected to have higher densities. For example, the crystalline density of 26,9 is 1.26 g mL -1 though toluene is incorporated into the lattice. We decided to pursue the approach reported in ref. 26 but recognized that we would need a suitable standard of similar MW and shape to the substances in MAO but with known Dt and molar mass. Of the compounds studied by Zaccaria et al.25 the polyhedral octasilsesquioxane (POSS) compound (i-BuSi)8O11(OH)2 or the Ti complex derived from it seemed appropriate as being roughly spherical with an appropriate molar mass. Ghiotto et al. had used (i-OctSi)8O12 as an internal standard in their PGSE NMR experiments.20 The Dt vs. molar mass data for this compound also lies on the correlation line established by Zaccaria et al. 25 It should be noted that in the Supporting Information in ref. 20 that the (i-C8H17Si)8O12 standard in use was actually a mixture of (i-C8H17Si)8O12 (58 mol%), (i-C8H17Si)10O15 (34 mol%) and (i-C8H17Si)12O16 (8 mol%) as determined by GPC. Thus, the average mass and van der Waals volume were calculated as 1493.6 g mol -1 and 1980 Å 3 , respectively in this work. To construct the calibration, we selected some representative structures for MAO comprised of reasonably stable sheets,13 cages13 and nanotubes12 varying in molar mass between 750 -2000 g mol , including two unreported, sheet and cage structures corresponding to the neutral compound 23,7 and some 16,4 tube structures located at M06-2X/TZVP level of theory. We also included the structure of the 26,9 sheet recently reported. 14 The properties of the aluminoxane models, along with those of the POSS standards are summarized in Table and the structures of any unreported aluminoxane models depicted in Figure . Their van der Waals volumes (VvdW) and those of the reference compounds were estimated using the Connolly method 57 with a probe radius of 1.4 Å as implemented in Chem3D. We chose this convenient approach as the Connolly solvent excluded volumes of the compounds, cholesterol, camphor, neopentane and methane were in very good agreement with the van der Waals volumes previously estimated by the method of Bondi. Ideally the standard and unknowns should have similar densities, though this was not true of the original correlation reported for low MW compounds. 26 The experimental liquid densities reported for (i-BuSi)8O12 and (i-OctSi)8O12 are 1.13 and 1.01 g mol -1 . Our calculated densities (Table , entries 14 and 15) are significantly higher as VvdW volumes are smaller than molar volumes as they do not include free volume. 59 The complex Ti[O2(i-Bu8Si8O11)]2 has higher density and does not lie on the correlation line that was established by Zaccaria et al. 25 Note that use of the molar mass and volume data reported in ref. 20 for (i-C8H17Si)8O12 results in a somewhat higher calculated density for this compound (Table , entry 18). In any event the calculated densities of all the POSS derivatives are comparable to those of the MAO models suggesting any of them could be used to construct suitable correlations. VvdW (Å 3 ) ρcalc (g mL ) The best correlation was obtained using the Ti[O2(i-Bu8Si8O11)]2 standard (R 2 = 0.9985, Figure ) though good correlations with R 2 = 0.9979 or 0.9876 were also obtained using our calculated mass and volume data for (i-C8H17Si)8O12 or Zaccaria's data for (i-BuSi)8O11(OH)2, respectively. Only the Ti POSS complex actually lies close to the correlation line for the MAO models (Figure ). It is instructive to consider prior literature reports as well as the data reported here with reference to this correlation. The original data for 30 wt% Chemtura MAO had Dt = 3.1×10 -10 m 2 s - 1 giving MW = 2860 g mol -1 (limiting [Al] = 328 mM20) which is lower but in reasonable agreement with the earlier estimate based on VH (ca. 3380 g mol -1 ). This Dt value is marginally lower from that reported for diluted 10 wt% MAO from Sigma Aldrich or W. R. Grace at similar concentrations (Table ). Material from Sigma Aldrich has a limiting Dt = 4.02×10 -10 m 2 s -1 which corresponds to lower MW material (1850 g mol -1 ), with material from W. R. Grace somewhat higher in molar mass (2050 g mol ). These limiting values are higher than 𝑀 ̅ 𝑤 from SANS data (1803 g mol but with a range between 1400 -2800 g mol indicate that they have VvdW of 1660 and 1740 Å and have comparable densities of ρcalc = 1.70 and 1.62 g mL -1 with models for MAO itself (Table ). The Sigma Aldrich results with a limiting value of Dt = 3.22×10 -10 m 2 s -1 suggest 𝑀 ̅ 𝐷 = 2670 g mol for OSIP 1 derived from DMAO while the more recent result (𝑀 ̅ 𝐷 = 2590 g mol -1 ) is not much different using the 10 wt% W. R. Grace formulation. Both are significantly larger than the calculated mass of the ion-pair 1 (1695.4 g mol -1 ), corresponding to the most intense anion [16,6] -detected by ESI-MS. We note that the average m/z ratio of the anion distribution is sensitive to the Al:Zr ratio. For ratios of 100:1 vs. 1000:1 the values are 1395 and 1484 Da, respectively (Supporting Information, Figure ). This means the nominal mass of the ion-pair 1 should vary between 1702 and 1791 Da. Better agreement is seen when it comes to ISIP 2 where PGSE NMR indicates 𝑀 ̅ 𝐷 = 2130-2320 g mol -1 while the estimates from ESI-MS would be between 1630-1719 g mol -1 .