Here, we investigated whether the average distances among phosphonic acid groups in the ZrHEDP samples were concentrated to facilitate the packed-acid mechanism by comparing them with the theoretical suggestion in our previous report. Based on the results discussed in Section 4.1, the ZrHEDP samples include not only the structure in Fig. (c) but also Fig. ). The distance between -PO3H2s is 9~11 Å in the structure of Fig. (d), along with the zirconium phosphonate layer. The distance is estimated by -PO3H2 concentrations based on ICP-AES results and the volume and weight of the pellets for proton conductivity measurement (See Section 3.2 and Section III in Supplementary Information for more detailed methods). The average distances are 7.4, 9.0, and 10.7 Å for P/Zr = 3.0, 2.8, and 2.5, respectively. Our theoretical material design proposed that the hydrocarbon-based phosphonic acid moieties are better to exist at a close distance (~13 Å) to facilitate the packed-acid mechanism. The estimated average lengths of -C(OH)CH3-PO3H2 in ZrHEDP samples are within the suggested range. In addition, the theoretical results indicated that the frequency of the mechanism increases gradually as the distance between acids becomes close. Thus, the gradual change of the RH dependence associated with the P/Zr is also explained by the theoretical insights. The ZrHEDP samples with P/Zr = 2.5 and 1.8 show higher dependence on RH as P/Zr decreases. In these samples with low P/Zr, other mechanisms, such as structural diffusion or vehicle mechanism, seem to be dominant, and the packed-acid mechanism is not (these mechanisms can occur in parallel).