Formation and properties of a terpyridine-based 2D MOF on the surface of water

As a first step to understand the 2D network we examine its structure and properties.

The 2D MOF is interlinked with terpyridine-Zn bridges, where six pyridyl groups coordinate each ion as shown in figure 1(b). This gives rise to three inequivalent Zn–N distances: to the axial pyridyls (${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{ax}}}$), to the pyridyls in direct contact with the substrate (${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{supp}}}$) and to those exposed to vacuum (${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{vac}}}$). The coordination environment is furthermore characterized by the relative orientation of the two terpy groups. The planes of the two ligands (approximated as best-fit planes through the central pyridyl hexagon and the two adjacent carbon atoms on the outer pyridyls) intersect at an angle, ${{\rm{\Phi }}}_{{\mathsf{T}},{\mathsf{T}}}$, which describes this orientation. Figure 2(a) illustrates these quantities with a schematic representation of the Zn coordination environment.

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We plot time-averaged histograms of ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ for (TTPB_w-Zn₃)_n and (TTPB_g-Zn₃)_n in figure 2(b). All N–Zn distances are characterized by rather smooth distributions around an average, typically showing a slight skew towards larger values. Estimates of the full width at half maximum (FWHM) of the distributions are indicated in the figures. They vary between 0.16 and 0.30, depending on the local environment.

In both systems, the axial pyridyl groups form the shortest bonds to Zn (≈ 2.1 Å). They appear largely unaffected by the presence or absence of the water substrate. These distributions are also the narrowest, with an FWHM around 0.16 Å in both cases. ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{vac}}}$ and ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{supp}}}$ are equivalent (≈ 2.25 Å) in (TTPB_g-Zn₃)_n, as all participating ligands are exposed to the same environment. The distributions are superimposed and have the same FWHM. In contrast, as seen in the top panel, ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ are different on the water-exposed and vacuum-exposed sides of the MOF. ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{supp}}}$ is markedly shortened (compared to (TTPB_g-Zn₃)_n) to an average of 2.17 Å in the presence of the liquid substrate and the FWHM is slightly reduced. On the other hand, ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{vac}}}$ increases to an average value of 2.36 Å, almost 5% longer than in (TTPB_g-Zn₃)_n, and the distribution substantially widens, indicating that the vacuum-exposed groups have an increased flexibility. Remarkably, the overall average ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ is the same, 2.21 Å, for both (TTPB_g-Zn₃)_n and (TTPB_w-Zn₃)_n. The corresponding ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ distribution in TTPB_2w-Zn is essentially identical to the one of (TTPB_w-Zn₃)_n (figure S2 in the supporting information), indicating that each TTPB-Zn-TTPB environment is decoupled from the others in the network. We can thus conclude that the pyridyl groups in TTPB are independent from one another when forming the network.

These data show that the presence of the liquid substrate influences the structural properties of the adsorbed sheet. The water-exposed pyridyl groups are restricted in their fluctuations and pushed closer to the Zn ions. In turn, this appears to destabilize the vacuum-exposed N–Zn bonds, shifting ${d}_{{\mathsf{N}},{\mathsf{Zn}}}^{{\mathsf{vac}}}$ to larger values compared to the free-standing sheet. We have noted this mild confining effect of the liquid also for the TTPB monomer [8], and confirm it with the observations here.

Beyond intra-sheet bond distances, the 'flatness' of the network as characterized by ${{\rm{\Phi }}}_{{\mathsf{T}},{\mathsf{T}}}$ is another relevant property of the 2D MOF. Figure 2(c) shows the distribution of ${{\rm{\Phi }}}_{{\mathsf{T}},{\mathsf{T}}}$ for (TTPB_w-Zn₃)_n and (TTPB_g-Zn₃)_n. Both curves have approximately the same shape and FWHM, but are centered around average values of 69° and 102°, respectively. The coordination environment around Zn is quite strongly flattened in the adsorbed sheet compared to the ideal octahedral geometry. On the other hand, in (TTPB_g-Zn₃)_n ${{\rm{\Phi }}}_{{\mathsf{T}},{\mathsf{T}}}$ is somewhat increased, making the pyridyl arms stand out further from that plane. The four equatorial pyridyl groups remain close to the plane of the 2D sheet and consequently (TTPB_w-Zn₃)_n is thinner than (TTPB_g-Zn₃)_n. Specifically, the thickness of (TTPB_g-Zn₃)_n is approximately 13.0 Å, in good agreement with both experimental (15 Å) and computed (12 Å) data for a comparable molecule [4]. The water-confined network has a significantly lower thickness of approximately 9.1 Å. We attribute this to the presence of the water surface, which exerts an attraction towards the adsorbate and flattens it.

In conclusion, it becomes clear that the dynamic flexibility of the network has a crucial influence on its structural properties. The presence of the liquid layer significantly influences this flexibility on the level of individual ligand groups and their relative orientation. We now explore the implications of this on the binding strength of the 2D network.

In order to quantify the binding strength of the 2D MOF assembled on water, we rely on the binding free energy of the dimer TTPB_2w-Zn as a model. For this purpose, we use the metadynamics method to facilitate the exploration of the potential energy space and reconstruct the FES of the dissociation reaction

$$\begin{eqnarray*}&&{\mathrm{TTPB}}_{2}-\mathrm{Zn}\ \rightleftharpoons \mathrm{TTPB}\ +\mathrm{TTPB}-\mathrm{Zn}.\end{eqnarray*}$$

We define the following CVs to map the FES:

• ${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$, the Zn–N coordination number, expected to change from 6 to 3 in as the dimer dissociates.
• ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$, the distance between the two axial N of the binding site, expected to sharply increase from the average value of 4.15 Å for the bound dimer.
• ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$, the Zn–O coordination number, which may increase as some pyridyl groups coordinating Zn are replaced by water.

Starting from a bound configuration, the adaptive bias potential allows the system to quickly explore the configurational space, oscillating between bound and unbound states.

The series of images in figure 3 shows snapshots extracted from the MTD trajectory, depicting the breaking and reassembly of TTPB_2w-Zn.

• (a)  
  Fully bound TTPB_2w-Zn(${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ = 5.84, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ = 4.21 Å, ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$ = 0.09).
• (b)  
  Partial breaking of the binding site, with 1 pyridyl group transiently rotating into a trans conformation (${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ = 4.63, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ = 4.68 Å, ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$ = 1.94).
• (c)  
  Further bond breaking, leaving the dimer bridged by a single Zn–N bond (${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ = 4.00, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ = 5.99 Å, ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$ = 1.20).
• (d)  
  Transient rotation of one pyridyl group into the trans conformation, yielding an undercoordinated Zn ion (${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ = 2.03, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ = 8.04 Å, ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$ = 2.98).
• (e)  
  Re-formation of a Zn–N bond with the second TTPB (${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ = 3.75, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ = 4.82 Å, ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$ = 1.21).
• (f)  
  Fully re-assembled dimer (${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ = 5.75, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ = 3.95 Å, ${n}_{{\mathsf{O}},{\mathsf{Zn}}}^{}$ = 0.56).

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As can be seen from the snapshots, the breaking of the dimer follows a similar stepwise mechanism as the uptake of the Zn²⁺ from solution [8]. The bias potential causes individual TTPB-Zn bonds to break and the monomers to separate until the dimer has fully broken. This is accompanied by the rotation of individual pyridyl groups, that intermittently reduce the Zn–N coordination (we observed a similar behavior also when TTPB binds metal ions from the liquid phase [8]). The successful re-formation of the full dimer indicates that the available configurational space has been explored sufficiently and the trajectory has visited all relevant minima.

Evidently, the (rotational) flexibility of the ligand arms is a crucial aspect of the binding process. Moreover, the intermittent breaking of Zn-coordination and turning away of the pyridyl ligands competes with a complete and stable binding and thus indirectly weakens the network.

In the process of forming a full 2D network, additional molecules need to be incorporated. The dimer can be considered a first nucleus from which the layer can subsequently grow. As the TTPB monomers are expected to be more mobile on the liquid surface than larger assemblies, we envision that network growth proceeds by stepwise binding of free TTPB. For this to occur in two-dimensions, several terpy-metal-terpy bonds have to be formed at the same time. While our results show that the defect-free network is stable, the kinetics of this growth process make it likely that point defects occur in places where not all three binding sites of the monomer can be occupied. However, the flexiblity of the ligands should make it possible to remove many such defects by mild annealing. Additionally, the formation of 'grain boundaries' can be expected in places where larger network fragments coalesce.

The reconstructed FES of the TTPB_2w-Zn breaking process is shown in figure 4 (left panel) as a function of ${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ and ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$. The system is characterized by two minima, one for the bound state (top left, ${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ $\approx$ 5.8, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ $\approx$ 4.0 Å) and one for the unbound state (bottom right, ${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ $\approx$ 3.0, ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ $\approx$ 8.0 Å), where the dimer is dissociated into a TTPB and a TTPB-Zn fragment. The topography of the FES also reveals some intermediate states at higher energy. One corresponds to a bound dimer with undercoordinated Zn²⁺ at reduced ${n}_{{\mathsf{N}},{\mathsf{Zn}}}^{}$ and small ${d}_{{\mathsf{N}},{\mathsf{N}}}^{{\mathsf{ax}}}$ (see figure 3(b)). Furthermore, Zn can also be undercoordinated in the dissociated state, missing one bond to a pyridyl group (see figure 3(d)).

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The free energy difference between the bound and unbound dimer amounts to 143.1 kJ mol⁻¹. Taking into account the higher entropy of TTPB + TTPB-Zn relative to TTPB_2w-Zn, due to the higher number of particles and larger conformational flexibility, the binding enthalpy of the dimer should be appreciably larger than this. For comparison, the experimental binding enthalpy of Zn(terpy)₂²⁺ is −60.7 kJ mol⁻¹ [17], considerably smaller.

The right panel in figure 4 shows the free energy profile along the MEP. The breaking of the dimer is rather steeply uphill in energy, with a shallow local minimum of the undercoordinated dimer. A barrier of 185 kJ mol⁻¹ is crossed before reaching the shallow minimum of TTPB + TTPB-Zn. As this MEP describes the breaking of the dimer, its reverse corresponds to the formation. Thus, only a small barrier of 42.1 kJ mol⁻¹ has to be overcome by the system in order to form a dimer with a binding free energy of −143.1 kJ mol⁻¹.