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\begin{document}

\title{Molecular dissolution behaviors on porous membrane surface using
hierarchical metal-organic framework lamellar membrane}



\author[1]{Yihao Chen}%
\author[2]{Jingjing Chen}%
\author[2]{Chongchong Chen}%
\author[1]{Xiaoli Wu}%
\author[2]{Yifan Li}%
\author[2]{Jie Zhang}%
\author[2]{jingtao wang}%
\affil[1]{Affiliation not available}%
\affil[2]{Zhengzhou University}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\selectlanguage{english}
\begin{abstract}
Lamellar membranes, especially assembled by microporous framework
nanosheets, have excited interest for fast molecular permeation.
However, the underlying molecular dissolution behaviors on membrane
surface, especially at pore entrances, remain unclear. Here,
hierarchical metal-organic framework (MOF) lamellar membranes with 7
nm-thick surface layer and 553 nm-thick support layer are prepared.
Hydrophilic (--NH2) or hydrophobic (--CH3) groups are decorated at pore
entrances on surface layer to manipulate wettability, while --CH3 groups
on support layer provide comparable, low-resistance paths. We
demonstrate that molecular dissolution behaviors are determined by
molecule-molecule and molecule-pore interactions, derived from intrinsic
parameters of molecule and membrane. Importantly, two dissolution model
equations are established: for hydrophobic membrane surface, dissolution
activation energy (ES) obeys ES=Kmln{[}(\selectlanguage{greek}γ\selectlanguage{english}L-\selectlanguage{greek}γ\selectlanguage{english}C)\selectlanguage{greek}μ\selectlanguage{english}d2{]}, while turns to
ES=Kaln{[}(\selectlanguage{greek}γ\selectlanguage{english}L-\selectlanguage{greek}γ\selectlanguage{english}C)\selectlanguage{greek}δ\selectlanguage{english}e\selectlanguage{greek}μ\selectlanguage{english}d2{]} for hydrophilic one. Particularly, hydrophilic
pore entrances exert strong interaction with polar molecules, thus
compensating the energy consumed by molecule rearrangement, giving fast
permeation (\textgreater{} 270 L m-2 h-1 bar-1).%
\end{abstract}%



\sloppy


\textbf{Molecular dissolution behaviors on porous membrane surface using
hierarchical metal-organic framework lamellar membrane}

Yihao Chen\textsuperscript{+}, Jingjing Chen\textsuperscript{+},
Chongchong Chen\textsuperscript{+}, Xiaoli Wu*\textsuperscript{,++},
Yifan Li\textsuperscript{+}, Jie Zhang\textsuperscript{+}, Jingtao
Wang*\textsuperscript{,+,++}

\textsuperscript{+}School of Chemical Engineering, Zhengzhou University,
Zhengzhou 450001, P. R. China.

\textsuperscript{++}Henan Institute of Advanced Technology, Zhengzhou
University, Zhengzhou 450003, P. R. China.

E-mails:\emph{jingtaowang@zzu.edu.cn}(J.
Wang);\emph{xiaoliwu@zzu.edu.cn}(X. Wu)

\textbf{Abstract}

Lamellar membranes, especially assembled by microporous framework
nanosheets, have excited interest for fast molecular permeation.
However, the underlying molecular dissolution behaviors on membrane
surface, especially at pore entrances, remain unclear. Here,
hierarchical metal-organic framework (MOF) lamellar membranes with 7
nm-thick surface layer and 553 nm-thick support layer are prepared.
Hydrophilic (--NH\textsubscript{2}) or hydrophobic
(--CH\textsubscript{3}) groups are decorated at pore entrances on
surface layer to manipulate wettability, while
--CH\textsubscript{3}groups on support layer provide comparable,
low-resistance paths. We demonstrate that molecular dissolution
behaviors are determined by molecule-molecule and molecule-pore
interactions, derived from intrinsic parameters of molecule and
membrane. Importantly, two dissolution model equations are established:
for hydrophobic membrane surface, dissolution activation energy
(\emph{E} \textsubscript{S}) obeys\emph{E} \textsubscript{S}=\emph{K}
\textsubscript{m}ln{[}(\selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{L}-\selectlanguage{greek}\emph{γ}
\selectlanguage{english}\textsubscript{C})\selectlanguage{greek}\emph{μd}\selectlanguage{english} \textsuperscript{2}{]}, while turns
to\emph{E} \textsubscript{S}=\emph{K} \textsubscript{a}ln{[}(\selectlanguage{greek}\emph{γ}
\selectlanguage{english}\textsubscript{L}-\selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{C})\selectlanguage{greek}\emph{δ}
\selectlanguage{english}\textsubscript{e}\selectlanguage{greek}\emph{μd}\selectlanguage{english} \textsuperscript{2}{]} for hydrophilic one.
Particularly, hydrophilic pore entrances exert strong interaction with
polar molecules, thus compensating the energy consumed by molecule
rearrangement, giving fast permeation (\textgreater{} 270 L
m\textsuperscript{-2} h\textsuperscript{-1}bar\textsuperscript{-1}).

\textbf{KEYWORDS}

metal-organic framework, hierarchical lamellar membrane, pore entrance,
dissolution activation energy, dissolution model equation

\textbf{1 INTRODUCTION}

Membrane separation technology with high energy efficiency and low
carbon footprints has drawn increasing attention in a wide range of
applications including petroleum refining, water purification and carbon
capture, \emph{etc} .\textsuperscript{{[}1-5{]}} Two-dimensional (2D)
lamellar membranes with controllable microstructure and well-aligned
nanochannels make excellent candidates for devising fast molecule
permeation and precise sieving.\textsuperscript{{[}6-8{]}} Typically,
membranes assembled by porous nanosheets offer continuous transfer
highways in vertical direction, which further shortens mass transfer
distance and permits fast transport.\textsuperscript{{[}9-11{]}}Molecule
transport through porous lamellar membranes should firstly dissolve into
pore entrances on membrane surface and then diffuse through inner pores.
It has been demonstrated that the resistance of molecular dissolution
process accounts for 20\% \textasciitilde{} 40\% of the total transport
resistance, and even 70\% for membranes with sub-10 nm
thickness.\textsuperscript{{[}12-14{]}}Therefore, molecular dissolution
process exerts huge and even decisive impact on molecular transport
efficiency, which deserves the investigation of underlying molecular
dissolution behaviors on membrane surface.

In general, experimental researches have confirmed that enhancing the
affinity of membrane surface to molecules by grafting active sites or
attaching compatible films could obviously improve molecular dissolution
rate and hence permeation ability.\textsuperscript{{[}15-17{]}} As a
noteworthy example, water-capture capacity of over 300\% was achieved
for graphene oxide (GO) lamellar membrane by modifying tannic acid on
membrane surface, which highly improve water permeance from 175 to 320 L
m\textsuperscript{-2}
h\textsuperscript{-1}.\textsuperscript{{[}18{]}}These observations are
generally attributed to the strong molecule-membrane interactions that
enrich molecules on membrane surface and promote them to enter into
inner channels. In contrast, recent studies discovered that due to the
strong interactions between water molecules and
--COO\textsuperscript{--} groups on the pore rim of aquaporins, water
permeance was 6 times lower than in carbon nanotube porins (CNTPs) which
possessed similar channel size but hydrophobic pore
rim.\textsuperscript{{[}19{]}} This phenomenon parallels findings by
simulation where the addition of four --COO\textsuperscript{--} groups
to the rims of a 1.1-nm-diameter CNTPs reduced the water flux by 3 folds
due to the enhanced water-rim interactions. These controversial
viewpoints suggest that molecular dissolution behaviors need deep
investigation, espeically for porous materials. On the other hand,
expect for molecule-membrane interaction, other factors such as
molecule-molecule interaction should also count much due to the
confinement effect of molecules on pore entrances. However, the pores in
current porous lamellar membrane are usually artificially created with
random distribution and wide pore size
distribution.\textsuperscript{{[}20-22{]}}And the chemical groups on
pore entrances are heterogeneous, which hampers the control of
molecule-pore interactions on molecule level. More importantly, lamellar
membranes generally possess homogeneous structure, and the high
resistance of molecular diffusion in inner pores exerts huge impact on
molecule permeance. This conceals the contribution of dissolution
process on molecule permeance, hence impeding the exploration of
underlying molecular dissolution
behaviors.\textsuperscript{{[}20,23,24{]}}Therefore, constructing
hierarchical porous lamellar membranes with independently manipulated
surface and support layers, and especially regular and controllable pore
entrances on surface layer, should provide desired platform.

Metal-organic frameworks (MOFs) show great expectations as
next-generation materials for porous membranes because of intrinsic
characteristics including large porosity, well-defined pore structures,
and tunable molecule-/ion- specific functional
groups.\textsuperscript{{[}25-29{]}} Significantly, the intrinsic pores
(usually \textless{} 2 nm) in MOF nanosheets can be subtly tailored by
controlling metallic node and organic
linkers.\textsuperscript{{[}30-32{]}} And the topology and chemical
composition of pores are periodically distributed within the frameworks,
which permits subtle manipulation of molecule-pore interaction on
molecule level. Additionally, some MOFs can be synthesized in the form
of ultrathin nanosheets with large lateral size (\textgreater{} 2 \selectlanguage{greek}μ\selectlanguage{english}m),
holding promise for constructing porous lamellar
membranes.\textsuperscript{{[}9,33,34{]}} On the other hand,
electrostatic atomization technology provides a novel strategy to evenly
spray atomized nanodrops that carry desired nanosheets onto receiver to
assemble ultrathin lamellar
architectures.\textsuperscript{{[}35,36{]}}In this way, hierarchical
lamellar membranes with independently controlled surface and support
layer can be facilely constructed.

Herein, hierarchical MOF lamellar membranes with ultrathin
(\textasciitilde{} 7 nm) surface layer and identical support layer
(\textasciitilde{} 553 nm) were prepared\emph{via} double-needled
electrostatic atomization technology. Specifically, MOF nanosheets with
hydrophobic (--CH\textsubscript{3}) pores were sprayed on Nylon
substrate to construct support layers. And MOF nanosheets with
hydrophilic (--NH\textsubscript{2}) or hydrophobic
(--CH\textsubscript{3}) groups on pores were assembled to create surface
layers, respectively. Based on these platforms, molecular dissolution
behaviors on porous membrane surface was investigated in detail.
Dissolution performances demonstrate that molecular dissolution
behaviors are highly affected by molecule-molecule and molecule-pore
interactions. Furthermore, the corresponding dissolution model equations
were established in term of dissolution activation energy (\emph{E}
\textsubscript{S}) on membrane surface with hydrophilic and hydrophobic
pore entrances. Importantly, membrane with hydrophilic pores on surface
exerts strong interactions with polar solvents, contributing to
low\emph{E} \textsubscript{S} and high permeance of over 270 L
m\textsuperscript{-2} h\textsuperscript{-1} bar\textsuperscript{-1} for
polar solvents. In addition, the regular pores within MOF lamellar
membranes bring precise sieving with rejection of 99\% for reactive red
(1.6 \selectlanguage{ngerman}× 1.4 nm). The elucidation of molecular dissolution behaviors on
membrane surface is paramount to develop highly permeable and selective
membranes for separation applications.

2 MATERIALS AND METHODS

2.1 Materials

NiCl\textsubscript{2}·6H\textsubscript{2}O (99.9\%) and
CoCl\textsubscript{2}·6H\textsubscript{2}O (99.9\%) were purchased from
Aladdin Reagent. Triethylamine (TEA), benzenedicarboxylic acid (BDC),
2-aminoterephthalic acid (NH\textsubscript{2}-BDC),
2-methylterephathalic acid (CH\textsubscript{3}-BDC) and diiodomethane
were bought from Macklin Reagent. Organic solvents (methanol, ethanol,
dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), acetonitrile,
acetone, n-octane, cyclohexane, n-hexane, n-pentane and toluene) were
obtained from Tianjin Kemiou Chemistry Reagent Co., Ltd. Nylon
microfiltration substrates (0.2 \selectlanguage{greek}μ\selectlanguage{english}m pore size, 50 mm diameter) were
bought from Tianjin Jinteng Experimental Equipment Co., Ltd.
Polyethylene glycol (PEG, 200, 300, 400, 600, 800, 1000), Brilliant blue
(BB), reactive red (RR), rhodamine B (RB), crystal violet (CV), and
methylene blue (MB) were supplied by Aladdin Chemical Co., Ltd. These
were used as received without further treatment, and deionized water was
used throughout the experiment.

\textbf{2.2 Synthesis of MOF nanosheets}

The MOF nanosheets were solvothermally synthesized under continuous
ultrasonication as reported in
literature.\textsuperscript{{[}37{]}}Primarily, 0.375 mmol
CoCl\textsubscript{2}\selectlanguage{ngerman}·6H\textsubscript{2}O and 0.375 mmol
NiCl\textsubscript{2}·6H\textsubscript{2}O were fully dissolved in 32 mL
DMF. Then, ethanol (2 mL), water (2 mL), and TEA (0.8 mL) were added
into the solution under constant stirring, followed by adding 0.375 mmol
organic ligands (BDC, NH\textsubscript{2}-BDC, or
CH\textsubscript{3}-BDC). The organic ligands were completely dissolved
in solution and it was further stirred for 2 h to obtain a uniform
colloidal suspension. Whereafter, the colloidal suspension was
continuously ultrasonicated for 20 h under airtight condition and the
precipitates were collected \emph{via} centrifugation. The obtained MOF
nanosheets were then washed with ethanol by 4 times to remove the
residual reactants, and vacuum dried at room temperature. Finally, MOF
nanosheets were dispersed in ethanol for further utilization.

\textbf{2.3 Preparation of hierarchical MOF lamellar membranes}

Hierarchical MOF lamellar membranes were prepared by double-needled
electrostatic atomization technology as shown in Scheme 1. Primarily,
Nylon substrates were smoothly adhered on the receiver roller.
MOF-CH\textsubscript{3}nanosheet dispersion (0.1 g
L\textsuperscript{-1}) was injected into one syringe (A), and
MOF-CH\textsubscript{3}, MOF-BDC or MOF-NH\textsubscript{2}nanosheet
dispersion (0.1 g L\textsuperscript{-1}) was injected into another
syringe (B). The two syringes both connected with a high voltage of 18
kV, and the tip-to-collector distance was 15 cm. Subsequently, 240 mL
MOF-CH\textsubscript{3} nanosheet dispersion in A syringe was pumped out
at a speed of 0.005 mm s\textsuperscript{-1} along with scanning
cyclically along roller surface at a speed of 160 rpm to prepare support
layer. After that, 3 mL solution in B syringe was sprayed on the support
layer under the same conditions, to construct ultrathin membrane surface
layer.

\textbf{Hosted file}

\verb`image1.emf`  available at \url{https://authorea.com/users/510119/articles/587306-molecular-dissolution-behaviors-on-porous-membrane-surface-using-hierarchical-metal-organic-framework-lamellar-membrane}

\textbf{Scheme 1.} Schematic illustration of the hierarchical MOF
lamellar membrane preparation.

\textbf{2.4 Characterization of nanosheets and lamellar membranes}

The structure and morphology of MOF nanosheets and hierarchical MOF
lamellar membranes were characterized by X-ray diffraction (XRD,
RigakuD/max2500 v/Pc), N\textsubscript{2} absorption and desorption
(Quantachrome Ltd., America), atomic force microscopy (AFM, Bruker
Dimension FastScan), scanning electron microscope (SEM, Auriga FIB SEM,
Zeiss, Germany), and high-resolution transmission electron microscopy
(HRTEM, Tecnai G2 F20, FEI, U.S.). The chemical properties were analyzed
by X-ray photoelectron spectroscopy (XPS, AXIS Supra, Kratos, UK) and
fourier transform infrared spectroscopy (FTIR, Nicolet MANGNA-IR560).
The wettability and dynamic contact angle were probed by FACE (model OCA
25, Germany).

\textbf{2.5 Nanofiltration performance of hierarchical MOF lamellar
membranes}

Nanofiltration performance was evaluated after immersing hierarchical
MOF lamellar membrane in corresponding solution for 3 h to reach a fully
equilibrium state. Based on the home-made device, solvent permeance and
dye rejection were tested. Dyes dissolved in methanol (10 mg
L\textsuperscript{-1}) were used for rejection measurement and analyzed
by UV-vis spectrophotometer. The solvent permeance \emph{P} (L
m\textsuperscript{-2} h\textsuperscript{-1} bar\textsuperscript{-1}) was
calculated by using the following equation:

\(P=\frac{V}{P\times A\times t}\) (1)

where \emph{V} , \selectlanguage{greek}\emph{ΔP}\selectlanguage{english} , \emph{A} and \emph{t} , represent the
permeate volume (L), operating pressure (bar), effective membrane area
(m\textsuperscript{2}), and testing time (h), respectively. The
following expression was obtained for the calculation of dye rejection
(\emph{R} , \%):

\(R=\left(1-\frac{C_{p}}{C_{f}}\right)\times 100\) (2)

where \emph{C} \textsubscript{f} and \emph{C} \textsubscript{p} are the
concentration of feed solution and permeate solution, respectively. The
obtained data were average of three parallel tests.

3 RESULTS AND DISCUSSION

3.1 Preparation and characterization of hierarchical MOF lamellar
membranes

MOF nanosheets were solvothermally synthesized from a mixed solution of
metal ions (Ni\textsuperscript{2+}, Co\textsuperscript{2+}) and organic
linkers under continuous ultrasonication.\textsuperscript{{[}37{]}}Here,
three kinds of organic linkers with distinct functional groups
(--CH\textsubscript{3}, --NH\textsubscript{2}, and no extra groups) were
selected (Figure S1), which are designed to construct MOF nanosheets
bearing intrinsic pores with close size but different groups. These
nanosheets were denoted as MOF-CH\textsubscript{3},
MOF-NH\textsubscript{2}, and MOF-BDC, corresponding to the constructed
organic ligands, respectively. AFM and SEM images in Figure 1a and
Figures S2, S3 show that the synthesized MOF samples display typical
sheet morphology, with uniform transverse size of \textasciitilde{} 1.5
\selectlanguage{greek}μ\selectlanguage{english}m and thickness of \textasciitilde{} 3.7 nm. And the XRD spectra
(Figure 1b) show that three MOF nanosheets possess the same lattice
structure, where the typical (200) peak at 2\selectlanguage{greek}\emph{θ} \selectlanguage{english}= 8.7\selectlanguage{ngerman}° reflects the
intrinsic pores.\textsuperscript{{[}37{]}} This agrees with the HRTEM
images in Figure S4, which visually show the lattice spacing of
\textasciitilde{} 1.05 nm for these
nanosheets.\textsuperscript{{[}38,39{]}} Furthermore,
N\textsubscript{2}sorption/desorption spectra, Figures 1c and S5, reveal
that the average pore sizes for MOF-CH\textsubscript{3},
MOF-NH\textsubscript{2} and MOF-BDC nanosheets are 1.12 nm, 1.05 nm, and
1.29 nm, respectively. It should be noted that the pore size of
MOF-CH\textsubscript{3} and MOF-NH\textsubscript{2} nanosheets is
smaller than that of MOF-BDC nanosheet, which is originated from the
steric effect of --CH\textsubscript{3} and --NH\textsubscript{2} groups
on the pores.\textsuperscript{{[}40,41{]}}

FTIR result (Figure S6) shows that, compared with MOF-BDC nanosheet, the
typical C=O peak gives a blue shift for MOF-CH\textsubscript{3} and
MOF-NH\textsubscript{2} nanosheets at 1360 \textasciitilde{} 1380
cm\textsuperscript{-1}, owing to the presence of
--CH\textsubscript{3}/--NH\textsubscript{2} groups adjacent to C=O
group. Meanwhile, the grafting of --NH\textsubscript{2} groups bring a
new strong peak at 1253 cm\textsuperscript{-1}, which assigned to Ar--N
on FTIR and a typical characteristic peak of N element at 400 eV in XPS
spectra of MOF-NH\textsubscript{2} (Figure
S7).\textsuperscript{{[}42{]}} While the decorating of
--CH\textsubscript{3}groups is supported by the higher C element content
for MOF-CH\textsubscript{3} relative to MOF-BDC. Specifically, the
content of N element on MOF-NH\textsubscript{2} nanosheet is tested to
be 2.95\%, matching well with the theoretical value calculated from
lattice structure. This also implies that there is one
--NH\textsubscript{2} group in a unit cell,\textsuperscript{{[}41{]}}and
the condition is identical for MOF-CH\textsubscript{3} nanosheet
(Figures 1g and i), this implies the topological structure of MOF is
explicitly constructed during synthetic process. Note that there is no
extra group in the pore of MOF-BDC nanosheet, which is designed as a
comparison.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 1.} Characterization of MOF nanosheets and membranes. (a)
AFM image of MOF-CH\textsubscript{3} nanosheets. (b) XRD patterns and
(c) pore size distributions of MOF-BDC, MOF-CH\textsubscript{3} and
MOF-NH\textsubscript{2} nanosheets. Cross-sectional (d) SEM and (e)
HRTEM images of MOF-CH\textsubscript{3}@NH\textsubscript{2} membrane.
(f) XPS depth profiles of
MOF-CH\textsubscript{3}@NH\textsubscript{2}membrane. Models of the pore
structure (left) and the stacking configuration of nanosheets (right)
for (g) MOF-CH\textsubscript{3}@NH\textsubscript{2} and (i)
MOF-CH\textsubscript{3}@CH\textsubscript{3} membrane surfaces,
corresponding to XRD data. (h) XRD patterns of hierarchical MOF lamellar
membranes.

Next, hierarchical MOF lamellar membranes were prepared by
double-needled electrostatic atomization technology. Concretely,
MOF-CH\textsubscript{3} nanosheets were sprayed on Nylon substrate to
construct a smooth support layer, and the hydrophobic micropores of
which would provide low-resistance diffusion paths for molecules that
dissolve through the surface
layer.\textsuperscript{{[}19{]}}Subsequently, MOF nanosheets
(MOF-CH\textsubscript{3}, MOF-BDC or MOF-NH\textsubscript{2}) were
sprayed on support layer to assemble surface layer. The strong
electrostatic repulsion among nanosheets under high-voltage field,
coupled with the shear force from rotational receiver, contribute to
flat deposition of MOF nanosheets on substrate (Scheme
1).\textsuperscript{{[}43{]}} The obtained hierarchical lamellar
membranes were marked as MOF-CH\textsubscript{3}@CH\textsubscript{3},
MOF-CH\textsubscript{3}@BDC and
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes, respectively.

AFM and SEM images in Figures S8 and S9 show that membrane surface is
defect-free and smooth, indicating the ordered stacking of MOF
nanosheets. This can be directly confirmed by the cross-sectional SEM
and HRTEM images in Figures 1d, e and Figures S10, S11, which also
deliver the information that the interlayer space is \textasciitilde{}
0.8 nm and the membrane thickness is around 560 nm. Here, it should be
noted that, considering the nanofiltration performance and mechanical
stability, membrane thickness of 560 nm is selected. Additionally, the
ordered stacking of MOF nanosheets is further identified by the sharp
peaks at 2\selectlanguage{greek}\emph{θ} \selectlanguage{english}= 11.4\selectlanguage{ngerman}° on XRD spectra of membranes, which also
suggests the interlayer space of 0.76 nm (Figure 1h). And the
corresponding structural models are presented in Figures 1g and
i.\textsuperscript{{[}38{]}} It should be noted that the typical (200)
peak for MOF powder is not observed in the spectra of MOF membrane, it
is ascribed to the strong diffraction peaks corresponding to nanosheet
stacking could mask the weak peaks of MOF powder. This phenomenon is
also reported in other literature.\textsuperscript{{[}44{]}} Here,
MOF-CH\textsubscript{3}@CH\textsubscript{3}, MOF-CH\textsubscript{3}@BDC
and MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes are prepared
with similar thickness (\textasciitilde{} 560 nm) for the following
performance testing. Next,
MOF-CH\textsubscript{3}@NH\textsubscript{2}membranes are employed to XPS
compositional depth analysis (Figures 1f and S13b), which shows that the
peak of N element (400 eV) disappears abruptly and that of C element
(285 eV) enhances at \textasciitilde{} 7 nm. This observation validates
that the MOF lamellar membrane contains hierarchical structure, and the
thickness of surface layer is around 7 nm. The results are similar for
MOF-CH\textsubscript{3}@BDC membranes as shown in Figures S12 and S13.
Furthermore, the manipulated surface layer endows MOF lamellar membranes
with distinct wettability. As shown in Figure S14, water contact angles
are 38.1°, 71.3°, and 100.6° for
MOF-CH\textsubscript{3}@NH\textsubscript{2},
MOF-CH\textsubscript{3}@BDC, and
MOF-CH\textsubscript{3}@CH\textsubscript{3} membranes, respectively,
indicating the hydrophilicity of
MOF-CH\textsubscript{3}@NH\textsubscript{2} and hydrophobicity of
MOF-CH\textsubscript{3}@CH\textsubscript{3} membrane surfaces. Such
ultrathin and adjustable surface layers with regular pores should
provide suitable platform for the investigation of molecular dissolution
behaviors.

\textbf{3.2 Solvent permeance of hierarchical MOF lamellar membranes}

The solvent permeance of hierarchical MOF lamellar membranes was
evaluated by a home-made dead-end cell under pressure of 1.0 bar using
seven polar solvents and five nonpolar solvents (Figure S15). Results in
Figure 2 reveal that hierarchical MOF lamellar membranes permit fast
molecule transport: 275.4 and 266.8 L m\textsuperscript{-2}
h\textsuperscript{-1}bar\textsuperscript{-1} for acetone and n-pentane,
respectively. The permeance is almost one order of magnitude higher than
that of nonporous graphene-based membranes (Figure S16). This is
contributed by the vertical channels throughout the membrane
architecture, which greatly shorten mass transfer distance and reduce
transfer resistance.\textsuperscript{{[}21,22{]}} Furthermore, Figure 2a
shows that the permeance displays a good linear relationship with
reciprocal of solvent viscosity for MOF-CH\textsubscript{3}@BDC
membrane, that is, obeying Hagen--Poiseuille
equation.\textsuperscript{{[}45{]}} While for
MOF-CH\textsubscript{3}@CH\textsubscript{3} and
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes (Figures 2b and
c), molecule transport deviates obviously from Hagen\selectlanguage{english}-Poiseuille law,
implying that it is also affected by other factors expect for
viscosity,\emph{e.g.} molecular diameter and solubility
parameter.\textsuperscript{{[}46{]}} In general, the permeance of polar
solvents is higher than that of nonpolar solvents for
MOF-CH\textsubscript{3}@NH\textsubscript{2} membrane, while the
condition is inverse for
MOF-CH\textsubscript{3}@CH\textsubscript{3}membrane. Taking acetone and
n-hexane with similar viscosity as examples,
MOF-CH\textsubscript{3}@NH\textsubscript{2} membrane gives a permeance
of 275.4 L m\textsuperscript{-2}
h\textsuperscript{-1}bar\textsuperscript{-1} for acetone, which is about
2 times higher than that of n-hexane. While for
MOF-CH\textsubscript{3}@CH\textsubscript{3}membrane, acetone permeance
is 119.1 L m\textsuperscript{-2} h\textsuperscript{-1}
bar\textsuperscript{-1}, about half of that of n-hexane permeance (214.8
L m\textsuperscript{-2}h\textsuperscript{-1} bar\textsuperscript{-1}).
Since these hierarchical lamellar membranes bear identical support
layer, the variation of molecule permeance should derive from distinct
dissolution efficiency on surface layer. Water and diiodomethane contact
angles on the membrane surfaces (Figure S17) show that water contact
angle on hydrophilic surface of
MOF-CH\textsubscript{3}@NH\textsubscript{2}membrane decreases quickly in
the first 1 s. And then it continues to drop moderately, confirming the
positive tendency for water molecules drilling into the subcutaneous
tissue of membrane surface. In contrast, hydrophobic
MOF-CH\textsubscript{3}@CH\textsubscript{3} membrane surface permits
diiodomethane to spread more smoothly than water, proving the strong
affinity toward nonpolar molecules. However, the contact angles keep
almost constant after initial spreading, which implies that hydrophobic
pores give inert dissolution to both polar and nonpolar
solvents.\textsuperscript{{[}47{]}} These observations deliver the fact
that molecular dissolution behavior is affected by the characteristics
of both molecule and membrane surface.

\textbf{Hosted file}

\verb`image3.emf`  available at \url{https://authorea.com/users/510119/articles/587306-molecular-dissolution-behaviors-on-porous-membrane-surface-using-hierarchical-metal-organic-framework-lamellar-membrane}

\textbf{Figure 2.} The solvent permeance of (a)
MOF-CH\textsubscript{3}@BDC, (b)
MOF-CH\textsubscript{3}@CH\textsubscript{3} and (c)
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes.

\textbf{3.3 Dissolution activation energy}

To intuitively characterize the tendency of molecules dissolving into
pore entrances on membrane surface, dissolution activation energy
(\emph{E} \textsubscript{S}) is proposed here, which reflects the origin
and energy variation of dissolution behaviors. For molecule transport
through a membrane, the total activation energy (\emph{E}
\textsubscript{P}) includes\emph{E} \textsubscript{S} and diffusion
activation energy (\emph{E}
\selectlanguage{greek}\textsubscript{μ}\selectlanguage{english}).\textsuperscript{{[}48,49{]}} The\emph{E}
\textsubscript{P} is extracted from Arrhenius plot by measuring molecule
permeance through membrane over a temperature range of 10 to 45 \selectlanguage{ngerman}°C
(Figure 3a), and the corresponding equation
is:\textsuperscript{{[}19,50{]}}

\begin{equation}
P=P_{0}\times e^{\frac{-E_{P}}{\text{RT}}}\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }(3)\nonumber \\
 \end{equation}

In equation 3, \emph{P} and\emph{P} \textsubscript{0} (L
m\textsuperscript{-2} h\textsuperscript{-1}bar\textsuperscript{-1})
represent the permeance of a solvent and the pre-exponential factor,
respectively, \emph{R} (kJ mol\textsuperscript{-1}
K\textsuperscript{-1}) is the gas constant, and\emph{T} (K) is the
temperature. Accordingly, \emph{E} \textsubscript{P}values of various
solvents for these membranes are obtained (Tables S1 and S2). Then
the\emph{E} \selectlanguage{greek}\textsubscript{μ} \selectlanguage{english}is calculated by the following
equations:\textsuperscript{{[}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, \selectlanguage{greek}\emph{μ} \selectlanguage{english}and \selectlanguage{greek}\emph{μ} \selectlanguage{english}\textsubscript{0} (Pa s) are the
viscosity of solvent and pre-exponential factor, respectively. By
combining equations 3 and 4, the obtained expression is
below:\textsuperscript{{[}52{]}}

\begin{equation}
P\ \sim\ \mu\times e^{\frac{-E_{P}}{E_{\mu}}}\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ }(5)\nonumber \\
 \end{equation}

Therefore, \emph{E} \selectlanguage{greek}\textsubscript{μ} \selectlanguage{english}is obtained from the slope value
in the correlation plot between solvent permeance and viscosity (Figure
3b). As an example, the \emph{E} \selectlanguage{greek}\textsubscript{μ} \selectlanguage{english}of water for
MOF-CH\textsubscript{3}@CH\textsubscript{3} membrane is calculated to be
16.64 kJ mol\textsuperscript{-1}. To vouch for the accuracy of
calculated \emph{E} \selectlanguage{greek}\textsubscript{μ} \selectlanguage{english}values, another method based on
Darcy's law is adopted (Figure S18).\textsuperscript{{[}45,53{]}} And
the result is 16.96 kJ mol\textsuperscript{-1}, close to that calculated
by equation 5. Next,\emph{E} \textsubscript{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-CH\textsubscript{3}@CH\textsubscript{3} and
MOF-CH\textsubscript{3}@NH\textsubscript{2} membrane surface was
calculated as an example (Figures S19-22). Results show that the
spreading activation energy values are comparable for
MOF-CH\textsubscript{3}@CH\textsubscript{3} (107.6 kJ
mol\textsuperscript{-1}) and
MOF-CH\textsubscript{3}@NH\textsubscript{2}(113.2 kJ
mol\textsuperscript{-1}) membranes, which should be resulted from the
uniform MOF skeleton structure on membrane
surface.\textsuperscript{{[}54{]}} To eliminate the impact of spreading
activation energy value on the calculation of \emph{E}
\textsubscript{S}for molecules drilling into pore entrance, membranes
are immersed into corresponding solvents to reach a saturation
condition, under which the following \emph{E} \textsubscript{S} values
are acquired.\textsuperscript{{[}55{]}}

For molecules drilling into pore entrances, the\emph{E}
\textsubscript{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.\textsuperscript{{[}56{]}} Therefore, these two energies should
determine molecular dissolution efficiency collectively. Figure 3c
displays that for MOF-CH\textsubscript{3}@CH\textsubscript{3}membrane
with hydrophobic pores on surface layer, the\emph{E} \textsubscript{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-CH\textsubscript{3}@NH\textsubscript{2}
membrane with hydrophilic pores on surface layer, the \emph{E}
\textsubscript{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 (\emph{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 --NH\textsubscript{2}
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.

\textbf{Hosted file}

\verb`image4.emf`  available at \url{https://authorea.com/users/510119/articles/587306-molecular-dissolution-behaviors-on-porous-membrane-surface-using-hierarchical-metal-organic-framework-lamellar-membrane}

\textbf{Figure 3.} Correlations between water permeance and (a)
temperature, (b) viscosity for
MOF-CH\textsubscript{3}@NH\textsubscript{2} and
MOF-CH\textsubscript{3}@CH\textsubscript{3} membranes. (c) The
dissolution activation energy of various solvents for
MOF-CH\textsubscript{3}@NH\textsubscript{2} and
MOF-CH\textsubscript{3}@CH\textsubscript{3} membranes. (d) Schematic
illustration of water molecules dissolution behavior through pores on
MOF-CH\textsubscript{3}@NH\textsubscript{2} membrane surface.

To support above findings, molecular dynamics (MD) simulations were
performed to probe the interaction energy of molecule-molecule and
molecule-pore on molecule level. Specifically, they are calculated by
Lennard-Jones interaction simulation (Figures 4d, e and Table S3).
Results in Figures 4a and b show that the experimentally calculated
\emph{E} \textsubscript{S} values exhibit a linear relationship with
that of simulated theoretical values (\emph{E} \textsubscript{T}, kJ
mol\textsuperscript{-1}). Here, the\emph{E} \textsubscript{T} value is
acquired by subtracting molecule-molecule interaction energy from
molecule-pore interaction energy, which represents the theoretical
dissolution activation energy.\emph{E} \textsubscript{S} and \emph{E}
\textsubscript{T} obey the equation of \emph{E} \textsubscript{S} =
\emph{KE} \textsubscript{T} +\emph{C} , where \emph{K} is a
proportionality constant. \emph{K} value should vary with properties of
membrane surface property and temperature, while \emph{C} is determined
by the physical factors of pore, \emph{e.g.} , steric
hindrance.\textsuperscript{{[}12{]}} This equation further underpins
that molecular dissolution behaviors are controlled by both
molecule-molecule and molecule-pore interactions. It should be noted
that some researchers calculated the interfacial resistance of molecule
transporting through membrane to analysis molecule dissolution, while
the resistance equation can not reveal the molecular dissolution
capacity on molecule level.\textsuperscript{{[}57,58{]}}

\textbf{Hosted file}

\verb`image5.emf`  available at \url{https://authorea.com/users/510119/articles/587306-molecular-dissolution-behaviors-on-porous-membrane-surface-using-hierarchical-metal-organic-framework-lamellar-membrane}

\par\null

\textbf{Figure 4.} Correlation between experimental and theoretical
dissolution activation energy values of (a)
MOF-CH\textsubscript{3}@CH\textsubscript{3} and (b)
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes. (c)\emph{E}
\textsubscript{S} of glucose solution, water and urea solution for
MOF-CH\textsubscript{3}@CH\textsubscript{3} and
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes. (d) Interaction
energy between toluene and NH\textsubscript{2}-BDC, toluene,
CH\textsubscript{3}-BDC. (e) Interaction energy between water and
NH\textsubscript{2}-BDC, water, CH\textsubscript{3}-BDC. Grey for C,
blue for N, red for O, white for H.

To further verify this hypothesis, molecule-molecule and molecule-pore
interactions were respectively adjusted. Taking water as an example,
glucose and urea solution (150 mmol L\textsuperscript{-1}) were mixed
with water to strengthen and weak the interactions between water
molecules, respectively.\textsuperscript{{[}19,59{]}} Figure 4c shows
that \emph{E} \textsubscript{S} of glucose solution (24.23 kJ
mol\textsuperscript{-1}) is higher than that of pure water (18.74 kJ
mol\textsuperscript{-1}), suggesting that the enhancement of water-water
interactions elevates the energy for breaking hydrogen bonds from bulk
state, thus lifting the \emph{Es} of water. In contrast, urea solution
displays weaker water-water interactions than pure water, thus the
energy for molecule arrangement is reduced and brings lower\emph{E}
\textsubscript{S} (15.99 kJ mol\textsuperscript{-1}). For another,
molecule-pore interactions were also adjusted. For instance, Figure 3c
reveals that MOF-CH\textsubscript{3}@NH\textsubscript{2}membrane surface
with --NH\textsubscript{2} groups on pore entrances gives much lower
\emph{E} \textsubscript{S} (-4.16 kJ mol\textsuperscript{-1}) for water
than that of MOF-CH\textsubscript{3}@CH\textsubscript{3} membrane
surface with --CH\textsubscript{3} groups (13.70 kJ
mol\textsuperscript{-1}). Moreover, compared with other nonpolar
solvents, toluene and cyclohexane display much lower \emph{E}
\textsubscript{S} for MOF-CH\textsubscript{3}@NH\textsubscript{2}
membrane than that of MOF-CH\textsubscript{3}@CH\textsubscript{3}
membrane. This is due to the weak hydrogen bonds between
--NH\textsubscript{2} with active --H on cyclic
hydrocarbon,\textsuperscript{{[}60,61{]}} which compensates for the
consumed energy considerably. This again delivers the fact that
molecule-pore interactions exert paramount impact on molecular
dissolution behaviors.

\textbf{3.4 Dissolution model equation}

To further quantize the key parameters that affect molecular dissolution
behaviors, the critical surface tension (\selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{C}) of
membrane is extracted by Zisman Plot.\textsuperscript{{[}57,62,63{]}}
Here, contact angles for polar (water, methanol, ethanol, acetone,
acetonitrile and DMF) and nonpolar solvents (cyclohexane, n-octane,
toluene, n-hexane) were measured to determine the \selectlanguage{greek}\emph{γ}
\selectlanguage{english}\textsubscript{C} of membranes. Zisman Plots in Figures 5a and b show
that \selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{C} values of
MOF-CH\textsubscript{3}@NH\textsubscript{2} and
MOF-CH\textsubscript{3}@CH\textsubscript{3} membranes are 19.7 and 17.6
mN m\textsuperscript{-1}, respectively. This defines the wetting
threshold for these two membranes, which means that solvents with
surface tensions less than the \selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{C} are predicted
to wet the membrane surface completely. Here, two phenomenological model
equations that well correlate to \emph{E} \textsubscript{S} and
intrinsic parameters of membrane surface and molecule are proposed for
MOF-CH\textsubscript{3}@CH\textsubscript{3} (equation 6) and
MOF-CH\textsubscript{3}@NH\textsubscript{2} (equation 7), respectively:

\(E_{S}=K_{m}\ln\left[\left(\gamma_{L}-\gamma_{C}\right)\mu d^{2}\right]\)(6)

\(E_{S}=K_{a}\ln\left[\left(\gamma_{L}-\gamma_{C}\right)\delta_{e}\mu d^{2}\right]\)(7)

where \selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{L} and \selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{C} (mN
m\textsuperscript{-1}) are the surface tension of solvent and the
critical surface tension of membrane surface, respectively, \emph{d} (m)
is the kinetic diameter and \selectlanguage{greek}\emph{δ}
\selectlanguage{english}\textsubscript{e}(Pa\textsuperscript{0.5}) is the Hansen solubility
parameter of solvent,\emph{K} \textsubscript{m} and \emph{K}
\textsubscript{a} are the coefficient constant of
MOF-CH\textsubscript{3}@CH\textsubscript{3} and
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes, respectively.

These two equations indicate that molecular dissolution capacity is
positively correlated with the difference between solvent surface
tension and membrane critical surface tension. Therefore, the
interfacial properties (\selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{L}-\selectlanguage{greek}\emph{γ}
\selectlanguage{english}\textsubscript{C}) of membrane surface and molecule both count
significantly in the equation. Besides, the parameters that correlate
with molecule transport in pores (\selectlanguage{greek}\emph{μd}\selectlanguage{english} \textsuperscript{2}) also
affect molecular dissolution efficiency (Figure 5c). Interestingly,
molecular dissolution behaviors on
MOF-CH\textsubscript{3}@NH\textsubscript{2} membrane do not obey this
dissolution model equation, but adding another parameter of\selectlanguage{greek}\emph{δ}
\selectlanguage{english}\textsubscript{e}, which represents the cohesive energy density of
molecules (Figures 5d and S23). This should be ascribed to the formation
of strong molecule-pore interactions, which promote the breakage of
molecule-molecule interactions and then the thorough rearrangement of
molecules, thus doubling the effect of molecule-molecule interaction on
dissolution efficiency. According to the dissolution equations,
molecular dissolution process should include two main steps: wetting the
membrane surface and then entering into pores. Concretely, the wetting
step is controlled by the difference of surface tension between molecule
and membrane surface (\selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{L}-\selectlanguage{greek}\emph{γ}
\selectlanguage{english}\textsubscript{C}), which reflects the wettability of membrane surface
for molecules. Subsequently, the step of molecules entering into pores
should relate to the \selectlanguage{greek}\emph{μ} \selectlanguage{english}and \emph{d} for hydrophobic pore
entrances, while relating to \selectlanguage{greek}\emph{δ} \selectlanguage{english}\textsubscript{e},\selectlanguage{greek}\emph{μ} \selectlanguage{english}and
\emph{d} for hydrophilic pore entrances (Table S4). Different from the
strategy of calculating interfacial resistance, this viewpoint of
dissolution activation energy systematically reveals the influence of
molecule-molecule and molecule-pore interactions on dissolution
behaviors on molecule-level.\textsuperscript{{[}12,57,58{]}}

\textbf{Hosted file}

\verb`image6.emf`  available at \url{https://authorea.com/users/510119/articles/587306-molecular-dissolution-behaviors-on-porous-membrane-surface-using-hierarchical-metal-organic-framework-lamellar-membrane}

\textbf{Figure 5.} Zisman plots with identified critical surface tension
for (a) MOF-CH\textsubscript{3}@CH\textsubscript{3} and (b)
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes. The molecular
dissolution equations of (c)
MOF-CH\textsubscript{3}@CH\textsubscript{3}and (d)
MOF-CH\textsubscript{3}@NH\textsubscript{2} membranes.

\textbf{3.5 Dye rejection and stability of hierarchical MOF lamellar
membranes}

Then, the structural stability and long-term operational stability of
as-prepared hierarchical MOF lamellar membranes were conducted. Figure 6
shows that these membranes display favorable anti-fouling and
anti-pressure performance. Preliminarily, five dyes with a series of
sizes were filtered through the membranes to detect rejection ability
(Figures 6a and S24). Before testing, membranes were compacted under 1
bar for 20 min to reach a complete equilibrium state.
MOF-CH\textsubscript{3}@NH\textsubscript{2} and
MOF-CH\textsubscript{3}@CH\textsubscript{3} membranes exhibit comparable
dye rejection, because of their similar pore sizes. Specifically, for MB
with small size of 1.4 \selectlanguage{ngerman}× 0.58 nm, membranes show an invalid rejection
(22\%). Upon increasing the size of dyes to 1.6 × 1.4 nm (RR) and 2.2 ×
1.7 nm (BB), membrane rejection experiences a sharp rise to almost
100\%, verifying the precise sieving of membranes by intrinsic pores
(1.02 nm). Meanwhile, to detect the dye adsorption on membrane
rejection, PEGs with different molecular weight were filtered through
the MOF membranes, and these membranes exhibited a\emph{MWCO} of
\textasciitilde{}600 Da (Figure S25). According to Stokes
equation,\textsuperscript{{[}64{]}} the diameter is calculated to be 1.1
nm, which is well consistent with the pore size of membranes. This
confirms that the dyes should be slightly adsorbed on membrane, which
contribute to a higher rejection, while the size sieving effect is the
main separation mechanism for these MOF membranes. In addition, cyclic
operation (24 h) test displays that methanol permeance begins reducing
at 16 h, and after washing, the permeance returns by 99\% (Figure 6b and
S26). This is ascribed to the dye molecules retained on the membrane
surface block the transport of solvents to a certain extent, and after
washing, the clean membrane regain its excellent performance. Moreover,
pressure cyclic measurement results (Figure 6c) reveal that the lamellar
structure of MOF membrane is able to bear transmembrane pressure as high
as 6 bar without obvious collapse. This is supported by the negligible
permeance fluctuation (below 5\%) for methanol when elevating the
pressure from 1 bar to 6 bar and adjusting back to 1 bar. Furthermore,
long-term operation stability test (Figure 6d) displays that methanol
permeance of MOF lamellar membranes experiences a moderate decline
(below 5\%) in the initial 2 h, and then maintains steady during the
following 98 h. The slight decrease should be stemmed from the moderate
compaction of adjacent nanosheets within lamellar structure, and similar
observations are also reported for other lamellar
membranes.\textsuperscript{{[}9,43{]}} In general, the as-prepared MOF
lamellar membranes exhibit satisfactory structural and operational
stability, which is mainly contributed by the strong \selectlanguage{greek}π-π \selectlanguage{english}stacking
interactions within membrane
structure,\textsuperscript{{[}65,66{]}}holding promise for practical
applications (Figure S27).

\textbf{Hosted file}

\verb`image7.emf`  available at \url{https://authorea.com/users/510119/articles/587306-molecular-dissolution-behaviors-on-porous-membrane-surface-using-hierarchical-metal-organic-framework-lamellar-membrane}

\textbf{Figure 6.} (a) Dye rejection, (b) cyclic operation measurement,
(c) pressure cyclic measurement, and (d) methanol permeance and RR
rejection against operation time for
MOF-CH\textsubscript{3}@NH\textsubscript{2} and
MOF-CH\textsubscript{3}@CH\textsubscript{3} membranes.

\textbf{4 CONCLUSIONS}

In summary, hierarchical MOF lamellar membranes with ultrathin surface
layer (\textasciitilde{} 7 nm) and low-resistance support layer (553 nm)
were prepared by double-needled electrostatic atomization technology.
The wettability of pore entrances on surface layer is subtly adjusted by
hydrophilic (--NH\textsubscript{2}) and hydrophobic
(--CH\textsubscript{3}) groups. While the inner pores with
--CH\textsubscript{3} groups provide identical and low-resistance
diffusion paths in support layer. Based on this novel platform, the
underlying molecule dissolution behaviors are systematically
investigated from the viewpoint of dissolution activation energy
(\emph{E} \textsubscript{S}). we demonstrate that molecule-pore and
molecule-molecule interactions play crucial roles for dissolution
process. For hydrophobic membrane surface, \emph{E} \textsubscript{S} is
above 0 for both polar and nonpolar solvents, confirming the negative
tendency for molecules to dissolve into pore entrances. In contrast, for
hydrophilic membrane surface,\emph{E} \textsubscript{S} is above 0 for
nonpolar solvents but below 0 for polar solvents, suggesting that polar
solvents can actively dissolve into pore entrances. This is ascribed to
the hydrophilic groups exert strong interactions with polar solvents,
thus compensating the energy consumed by molecule rearrangement, thus
permitting fast permeation (over 270 L m\textsuperscript{-2}
h\textsuperscript{-1} bar\textsuperscript{-1} for acetone).
Significantly, dissolution model equations on hydrophilic and
hydrophobic membrane surface are established, respectively, which are
stemmed from the intrinsic parameters of molecules (\selectlanguage{greek}\emph{μ} ,\selectlanguage{english}\selectlanguage{greek}\emph{δ}
\selectlanguage{english}\textsubscript{e} \selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{L}, \emph{d} ) and membrane
surface (\selectlanguage{greek}\emph{γ} \selectlanguage{english}\textsubscript{C}). This elucidating molecular
dissolution behaviors on porous membrane surface would provide new
guidelines for the design of advanced membranes.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the financial support from
National Natural Science Foundation of China (U2004199), Excellent Youth
Foundation of Henan Province (202300410373) and China Postdoctoral
Science Foundation (2022TQ0292). Center for advanced analysis and
computational science, Zhengzhou University is also highly acknowledged.

\textbf{DATA AVAILABILITY STATEMENT}

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

\textbf{AUTHOR CONTRIBUTIONS}

\textbf{Yihao Chen:} Data curation; investigation; writing-original
draft; writing-review \& editing. \textbf{Jingjing Chen:} Software;
writing-original draft. \textbf{Chongchong Chen:} Data curation;
investigation; software; writing-original draft. \textbf{Xiaoli
Wu:}Funding acquisition; Software; writing-review \& editing;
investigation; Project administration; supervision. \textbf{Yifan Li:}
Writing-original draft; supervision. \textbf{Jie Zhang:} Data curation;
investigation.\textbf{Jingtao Wang:} Funding acquisition; project
administration; supervision; writing-original draft; writing-review \&
editing.

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