3.3 Dissolution activation energy
To intuitively characterize the
tendency of molecules dissolving into pore entrances on membrane
surface, dissolution activation energy (E S) is
proposed here, which reflects the origin and energy variation of
dissolution behaviors. For molecule transport through a membrane, the
total activation energy
(E P) includesE S and diffusion activation energy
(E μ).[48,49] TheE P is extracted from
Arrhenius plot by measuring molecule
permeance through membrane over a temperature range of 10 to 45 °C
(Figure 3a), and the corresponding equation
is:[19,50]
\begin{equation}
P=P_{0}\times e^{\frac{-E_{P}}{\text{RT}}}\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }(3)\nonumber \\
\end{equation}In equation 3, P andP 0 (L m-2 h-1bar-1) represent the permeance of a solvent and the
pre-exponential factor, respectively, R (kJ
mol-1 K-1) is the gas constant, andT (K) is the temperature. Accordingly, E Pvalues of various solvents for these membranes are obtained (Tables S1
and S2). Then theE μ is
calculated by the following equations:[51]
\begin{equation}
\mu=\mu_{0}\times e^{\frac{E_{\mu}}{\text{RT}}}\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }(4)\nonumber \\
\end{equation}In equation 4, μ and μ 0 (Pa s) are the
viscosity of solvent and pre-exponential factor, respectively. By
combining equations 3 and 4, the obtained expression is
below:[52]
\begin{equation}
P\ \sim\ \mu\times e^{\frac{-E_{P}}{E_{\mu}}}\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }(5)\nonumber \\
\end{equation}Therefore, E μ is obtained from the slope value in
the correlation plot between solvent permeance and viscosity (Figure
3b). As an example, the E μ of water for
MOF-CH3@CH3 membrane is calculated to be
16.64 kJ mol-1. To vouch for the accuracy of
calculated E μ values, another method based on
Darcy’s law is adopted (Figure S18).[45,53] And
the result is 16.96 kJ mol-1, close to that calculated
by equation 5. Next,E S values of
solvents for hierarchical lamellar
membranes are acquired.
Note that molecules would spread on the membrane surface firstly before
dissolving into membrane, where the spreading activation energy should
be considered. Here, the spreading activation energy of water on
MOF-CH3@CH3 and
MOF-CH3@NH2 membrane surface was
calculated as an example (Figures S19-22). Results show that the
spreading activation energy values are comparable for
MOF-CH3@CH3 (107.6 kJ
mol-1) and MOF-CH3@NH2(113.2 kJ mol-1) membranes, which should be resulted
from the uniform MOF skeleton structure on membrane
surface.[54] To eliminate the impact of spreading
activation energy value on the calculation of E Sfor molecules drilling into pore entrance, membranes are immersed into
corresponding solvents to reach a saturation condition, under which the
following E S values are
acquired.[55]
For molecules drilling into pore entrances, theE S is mainly controlled by molecule-molecule and
molecule-pore interactions. Specifically,
molecules in bulk state need to
adjust the configuration to drill into confined pores
(from
larger aggregates to smaller ones), during which the bindings between
molecules should be broken, thus inevitably consuming energy. Meanwhile,
molecules that contact the pore entrances would exert interactions with
the groups on pore rims, which releases energy to compensate the energy
consumed.[56] Therefore, these two energies should
determine molecular dissolution efficiency collectively. Figure 3c
displays that for
MOF-CH3@CH3membrane with hydrophobic pores on surface layer, theE S values of both polar and nonpolar solvents are
above 0. This indicates that the energy released by the formation of
molecule-pore interactions is smaller than the energy consumed by
molecule rearrangement. Thus extra energy is needed to push the
molecules to drill into pore entrances. In contrast, for
MOF-CH3@NH2 membrane with hydrophilic
pores on surface layer, the E S values for
nonpolar solvents are above 0, while that for polar solvents are below
0. This finding implies that hydrophilic groups on pore entrance tend to
exert stronger interactions with polar solvent (e.g. hydrogen
bond interaction), thus producing more positive energy that compensates
the energy consumed by molecule rearrangement. Therefore, polar solvents
tend to spontaneously drill into hydrophilic pores. As shown in Figure
3d, taking water as an example, water molecules in bulk state are bonded
with each other through hydrogen bonds. Upon contacting pore entrances,
new hydrogen bonds are formed between water molecules and
–NH2 groups on pore
rims. Meanwhile, the configuration of bulk water is adjusted to drill
into confined pores, accompanied by the breakage of intermolecular
hydrogen bonds. In this manner, water molecules dissolve into the
hierarchical MOF lamellar membrane.