As shown in Table in Supplementary Infomation, we could not obtain ZrHEDP with P/Zr > 3. HEDP, where both phosphonic acid groups are immobilized as -PO3 in ZrHEDP with P/Zr = 2, can bridge two ZrHEDP layers. Therefore, ZrHEDP with P/Zr > 3 will have fewer "bridging-HEDPs," resulting in more open space for water adsorption and less packed-PO3H2s. Therefore, if the appropriate synthesis (or washing) condition leads to the P/Zr > 3, that sample might have strong RH dependence. In addition, an excessive amount of -PO3H2 in ZrHEDP with P/Zr > 3 might induce overly hydrophilic properties, which can be the reason to be washed out and not exceed P/Zr = 3 (see Section I in Supplementary information).