Thermodynamic Evidence for Type II Porous Liquids

Porous liquids are an emerging class of microporous materials where intrinsic, stable porosity is imbued in a liquid material. Many porous liquids are prepared by dispersing porous solids in bulky solvents; these can be contrasted by the method of dissolving microporous molecules. We highlight the latter “Type II” porous liquids—which are stable thermodynamic solutions with demonstrable colligative properties. This feature significantly impacts the ultimate utility of the liquid for various end-use applications. We also describe a facile method for determining if a Type II porous liquid candidate is “porous” based on assessing the partial molar volume of the porous host molecule dissolved in the solvent by measuring the densities of candidate solutions. Conventional CO2 isotherms confirm the porosity of the porous liquids and corroborate the facile density method.


Partial Molar Volume from Density Derivation
By starting with the partial molar volume of the solution in equation S1, we can derive a connection between the total solution volume and the constituent materials volume.
First, divide the entire expression in equation S1 by the total number of moles in the system, where represents the mole fraction of species 1 or 2.
Then divide equation S2 by the molar volume of the entire solution.
The mole fraction of a species in solution can be related to the mass fraction via equation S4. The relation in equation S4 can be substituted into equation S3 to obtain equation S5. In equation S4, represents the weight fraction of species 1 or 2, shows the density of the solution, and is the molar mass of a species.
Lastly, the relation between the weight fraction, density, and concentration, , shown in equation S6 can be substituted into equation S5 and rearranged to get equation 2, which relates density to the concentration of the cage in the solvent through a linear relationship.

Critical deposition velocity (CDV) calculations
Type III porous liquids differ from Type II porous liquids in that they are dispersions instead of solutions. Type III porous liquids can potentially deposit microporous frameworks throughout operating units, which can lead to safety and economic concerns. The critical deposition velocity of potential and developed Type III porous liquids or porous dispersions on separations processes were calculated to understand the impact of Type III porous liquids or porous dispersions. The critical deposition velocity is the speed at which a slurry or dispersion must be maintained to prevent particles from depositing while flowing in a horizontal pipe. 1 The Thomson velocity has been applied to particles under 100 µm diameter particles and was used to calculate the CDV of MOF slurries in different solvents (Equation S7). 2 The densities of the MOFs were calculated using the Mercury software. 3-10 In equation 3, represents the acceleration due to gravity, is the viscosity of the carrier fluid (for this correlation, it is assumed to be the viscosity of water, methanol, 2'-hydroxyacetophenone, or sesame oil), is the ratio of the density of the solid to the density of the carrier fluid, represents the diameter of the pipe, and lastly represents the density of the carrier fluid. The Thomson critical deposition velocity is typically used as a lower bound value. Figure S1: Schematic outlining design of pressure decay cell used to obtain gas isotherms for porous liquids and neat solvents (top), drawing of sample holder used to hold the liquids (bottom)

Critical Deposition Velocity of Type III Porous Liquids
The critical deposition velocity is defined as the speed at which a slurry or dispersion must be maintained to prevent particles from depositing while flowing in a horizontal pipe. In industrial gas absorption separations using solvents, it is preferred to have fluid velocities around 1-4 m/s, depending on the pipe diameter. 11,12 Above these flow velocities, there can be safety concerns, including erosion and critical failure of the pipes. If Type III porous liquids are to be useful in the context of gas separations, then the deposition velocities of the particles must be below that range to avoid particle accumulation in the process units. However, upon analysis of the critical deposition velocities for various porous liquids, the critical deposition velocities for the Type III porous liquids are potentially much higher than 1-4 m/s, posing process complications. The trends in critical deposition velocity for dispersions as a function of various parameters are shown in Figure S3. According to the Thomson equation, the critical deposition velocities increase when using high viscosity fluids and high density particles. Figure S3 highlights that for porous dispersions, it could be difficult to find a stable dispersion with a critical deposition velocity that allows for safe operation. It is important to note that various factors can impact the actual critical deposition velocity of Type III porous liquids. Specifically, the attractive forces between the solvent and host material could lead to a more stable dispersion or direct surface engineering of the porous solid, which could also enhance these interactions.
The critical deposition velocities of various MOFs in several fluids are shown in Figure S4 to represent several dispersions (some of which are Type III porous liquids). When interpreting the following results, it is critical to understand that these calculations are only valid for qualitative comparisons between different slurries. The critical deposition velocity results shown in Figure   Figure S3: Qualitative plot of critical deposition velocity trends for slurry transport as a function of pipe diameter, viscosity ( ), and particle density ( ). Dashed line represents the maximum fluid velocity that can be used safely in an industrial system. Green shaded region shows safe operating conditions for porous liquid 1. Red shaded region shows inoperable velocities for liquid 1 due to particle accumulation and/or unsafe velocities.
S4 are not necessarily representative of the actual critical deposition velocity of the mentioned slurries because of a lack of information on interactions between the solvent and the porous solids, especially for nanoscopic particles such as those typically used in Type III porous liquids. Type III porous liquids have potential in gas separations and various other applications. Still, researchers must consider the impact of the critical deposition velocity on those materials in industrial use. The MOFs were chosen to get a range of densities for the critical deposition velocity analysis. More information on the chosen MOFs can be found in the supplemental information (Table S2).
Water and methanol do not create porous liquids with any of the MOFs used because they are small enough to penetrate the pores of the MOFs, but they serve as good lower-bound solvents for this analysis because of their low viscosity. 2'-hydroxyacetophenone, as explained previously, has been used to create Type II porous liquids and has a moderate viscosity of 3.9 cP at ambient conditions. Sesame oil was chosen as an upper bound solvent since it has the highest viscosity and has been referenced as an effective and inexpensive solvent for creating Type III porous liquids. The viscosities of methanol, water, 2HAP, and sesame oil employed were 0.7, 1.0, 3.9, and 31 cP, respectively.
For each carrier fluid and MOF combination, the deposition velocity follows similar trends when plotted against the pipe diameter. For the low viscosity carrier fluids, water and methanol, the deposition velocities range from 4-12 m/s at a pipe diameter of 0.05 m and 5-21 m/s at a pipe diameter of 0.3 m. 2'-hydroxyacetophenone has a viscosity of about 4 times that of water and leads to a critical deposition velocity increase of about 10-15% compared to the water/MOF combinations. Lastly, sesame oil is an order of magnitude more viscous than 2'hydroxyacetophenone. This large increase in viscosity leads to a much larger set of critical deposition velocities that can exceed 45 m/s for the densest MOFs (Zn MOF-74). Cu(Qc) 2 dispersed in sesame oil creates a Type III porous liquid that shows promise for ethane/ethylene separations; however, that dispersion has an estimated critical deposition velocity ranging from 25-38 m/s. Although sesame oil is a cheap and effective material for making a porous liquid, it could lead to porous liquids with quite high deposition velocities, which may limit its use in gas separation applications. As stated in the main text these calculations are not representative of actual critical deposition velocities of these slurries due to lack of experimental information. But they are relevant for qualitative comparison.