Seok J Lee

Celine Doussot

Anthony Baux

Lujia Liu

Geoffrey B Jameson

Christopher Richardson

Joshua J Pak

Fabien Trousselet

Francois-Xavier Coudert

Shane G Telfer

Multicomponent Metal-Organic Frameworks as Defect-Tolerant Materials

Multicomponent metal-organic frameworks (MOFs) comprise multiple, structurally-diverse linkers fixed into an ordered lattice by metal ions or clusters as secondary building units (SBUs). Here, we show how multicomponent MOFs are ideal platforms for engineering materials with high levels of vacancy defects. First, a new type of quaternary MOF that is built up from two neutral, linear ditopic linkers, a threefold-symmetric carboxylate ligand, and a dinuclear paddlewheel SBU was synthesized. This MOF, named MUF-32 (MUF = Massey University Framework), is constructed from dabco, 4,4'-bipyridyl (bipy), 4,4',4''-nitrilotrisbenzoate (ntb) and zinc(II), and it adopts an ith-d topology. The zinc(III) ions and ntb ligand define an underlying [Zn 2 (ntb) 4/3 ] sublattice (with pto topology) that is 'load bearing' and maintains the structural integrity of the framework. On the other hand, the dabco and bipy ligands are 'decorative' and high levels of vacancy defects can be introduced by their omission. These defects can be generated by direct synthesis or by postsynthetic modification. The framework structure, crystallinity and porosity are maintained even when vacancy levels of 80% are reached. Defect healing is possible by introducing free ligands in a solvent-assisted process to restore pristine MUF-32. Computational analysis reveals that the mechanical instability of the [Zn 2 (ntb) 4/3 ] sublattice sets an upper limit on defect levels in this material.

Introduction

Building metal-organic frameworks (MOFs) from multiple organic linkers has emerged as a fruitful strategy for obtaining materials with remarkable properties. [START_REF] Burrows | Mixed-Component Metal-Organic Frameworks (Mc-Mofs): Enhancing Functionality through Solid Solution Formation and Surface Modifications[END_REF][START_REF] Bunck | Mixed Linker Strategies for Organic Framework Functionalization[END_REF] There are two categories of such MOFs: (1) multivariate MOFs in which the linkers have identical backbones, and (2) multicomponent MOFs in which the linkers are structurally distinct. While exceptional functional behavior has been observed for some MOFs in category 1, [START_REF] Deng | Multiple Functional Groups of Varying Ratios in Metal-Organic Frameworks[END_REF][START_REF] Park | Nonlinear Properties in Coordination Copolymers Derived from Randomly Mixed Ligands[END_REF] the linkers are imperfectly ordered, which leads to pore heterogeneity. We [START_REF] Liu | Programmed Pore Architectures in Modular Quaternary Metal-Organic Frameworks[END_REF][START_REF] Liu | Systematic Ligand Modulation Enhances the Moisture Stability and Gas Sorption Characteristics of Quaternary Metal-Organic Frameworks[END_REF] and others [START_REF] Bunck | Mixed Linker Strategies for Organic Framework Functionalization[END_REF][START_REF] Dutta | Coordination Copolymerization of Three Carboxylate Linkers into a Pillared Layer Framework[END_REF][START_REF] Koh | Exceptional Surface Area from Coordination Copolymers Derived from Two Linear Linkers of Differing Lengths[END_REF][START_REF] Koh | Coordination Copolymerization Mediated by Zn 4 o(Co 2 r) 6 Metal Clusters: A Balancing Act between Statistics and Geometry[END_REF][START_REF] Grunker | A New Metal-Organic Framework with Ultra-High Surface Area[END_REF][START_REF] Helten | Copolymerisation at Work: The First Example of a Highly Porous Mof Comprising a Triarylborane-Based Linker[END_REF][START_REF] Klein | Route to a Family of Robust, Non-Interpenetrated Metal-Organic Frameworks with Pto-Like Topology[END_REF][START_REF] Müller | Postsynthetic Paddle-Wheel Cross-Linking and Functionalization of 1,3-Phenylenebis(Azanetriyl)Tetrabenzoate-Based Mofs[END_REF][START_REF] Furukawa | Ultrahigh Porosity in Metal-Organic Frameworks[END_REF][START_REF] Dutta | A Non-Regular Layer Arrangement of a Pillared-Layer Coordination Polymer: Avoiding Interpenetration Via Symmetry Breaking at Nodes[END_REF] have focused on frameworks in the second category. Since the ligands are distinct they can be discriminated during crystallization of the MOF and occupy specific positions in the lattice. For example, UMCM-1 comprises btb (benzene-1,3,5tribenzoate) and bdc (benzene-1,4-dicarboxylate) linkers riveted in place by Zn 4 O secondary building units (SBUs). [START_REF] Koh | A Crystalline Mesoporous Coordination Copolymer with High Microporosity[END_REF] The MUF-7 and MUF-77 families are quaternary MOFs constructed from Zn 4 O clusters, bdc, and bpdc (biphenyl-4,4'-dicarboxylate) and threefold symmetric carboxylate ligands. [START_REF] Liu | Programmed Pore Architectures in Modular Quaternary Metal-Organic Frameworks[END_REF][START_REF] Liu | Systematic Ligand Modulation Enhances the Moisture Stability and Gas Sorption Characteristics of Quaternary Metal-Organic Frameworks[END_REF] Here, the distinct lengths of the bdc and bpdc linkers allow them to be differentiated during framework assembly and located in specific lattice positions. Owing to their structural regularity, insights into the relationship between ligand structure, pore topography, and guest uptake can be drawn from these multicomponent MOFs.

A number of MOFs with defects have emerged in the recent literature, and beneficial impacts of defects on framework properties have been established. [START_REF] Fang | Defect-Engineered Metal-Organic Frameworks[END_REF] Notable examples include the report from Li et al. on the creation of ordered vacancies in a cubic MOF based on Zn(II) and pyrazole-carboxylic acid by removing a quarter of the metal ions and half of the linkers. [START_REF] Tu | Ordered Vacancies and Their Chemistry in Metal-Organic Frameworks[END_REF] This provides access to a host of materials with intricate, ordered structures that cannot be synthesized directly. Partial replacement of the terephthalate linkers by capping trifluoroacetate ligands introduces large pores and open metal sites in UiO-66, which render this MOF catalytically-active for Meerwein reduction reactions. [START_REF] Vermoortele | Synthesis Modulation as a Tool to Increase the Catalytic Activity of Metal-Organic Frameworks: The Unique Case of Uio-66(Zr)[END_REF] Advances in the characterization of defective frameworks have also propelled our understanding of the distribution and properties of defects in MOF crystals. [START_REF] Cliffe | Correlated Defect Nanoregions in a Metal-Organic Framework[END_REF][START_REF] Katzenmeyer | Assessing Chemical Heterogeneity at the Nanoscale in Mixed-Ligand Metal-Organic Frameworks with the Ptir Technique[END_REF] We propose that multicomponent MOFs can serve as platforms for generating materials with high levels of vacancy defects. This concept has parallels with architectural principles where buildings are designed with both 'load-bearing' and 'decorative' walls. Our strategy, as detailed herein, involves the design of multicomponent MOFs in which certain components are essential for maintaining structural integrity (load-bearing), while other components are nonessential (decorative). Since absence of these decorative components can be tolerated by the framework, vacancy defects are easily generated.

MOFs with an ith-d topology well-suited to this strategy. Such frameworks can be deconstructed into two subcomponents: an underlying pto sublattice (Fig. 1a) and linear struts (Fig. 1b). [START_REF] Han | A Non-Interpenetrated Porous Metal-Organic Framework with High Gas-Uptake Capacity[END_REF][START_REF] Klein | Route to a Family of Robust, Non-Interpenetrated Metal-Organic Frameworks with Pto-Like Topology[END_REF] These struts link adjacent square planar four-connected nodes of the pto net to produce the ith-d net. [START_REF] Ko | Connection of Zinc Paddle-Wheels in a Pto-Type Metal-Organic Framework with 2-Methylimidazolate and Subsequent Incorporation of Charged Organic Guests[END_REF] Translating this to feasible chemical building blocks, [M 2 (L) 4/3 ] nets with the pto topology are readily generated by combining triangular tris(carboxylate) ligands paddlewheel metal nodes into lattices. [START_REF] O'keeffe | The Reticular Chemistry Structure Resource (Rcsr) Database of, and Symbols for, Crystal Nets[END_REF][START_REF] Li | Topological Analysis of Metal-Organic Frameworks with Polytopic Linkers and/or Multiple Building Units and the Minimal Transitivity Principle[END_REF][START_REF] He | Metastable Interwoven Mesoporous Metal-Organic Frameworks[END_REF][START_REF] Furukawa | Isoreticular Expansion of Metal-Organic Frameworks with Triangular and Square Building Units and the Lowest Calculated Density for Porous Crystals[END_REF][START_REF] Zhu | Polymorphism of Metal-Organic Frameworks: Direct Comparison of Structures and Theoretical N 2 -Uptake of Topological Pto-and Tbo-Isomers[END_REF][START_REF] Johnson | Direct X-Ray Observation of Trapped Co2 in a Predesigned Porphyrinic Metal-Organic Framework[END_REF][START_REF] Zhao | Assembly of Two 3d Porous Metal-Organic Frameworks Based on 1,2,3-Triazole-4,5-Dicarboxylate Exhibiting Novel Coordination Modes[END_REF] For the linear struts there are several requirements: (i) they must coordinate via one donor atom to the axial sites of the paddlewheel nodes, (ii) they must be neutral so that charge balance is maintained in their absence, (iii) they must be of a suitable length to bridge the gap between adjacent nodes.

On the basis of the foregoing considerations we identified dabco and bipy (4,4'-bipyridine) as potentially useful linear struts. With respect to point (iii) above, the two ligands have an average length of 9.0 Å (Table 1). When combined with ntb, the length ratios given by the equation [twofold linker length]/[threefold linker length] is 1.11. This is close to the ratio of 1.18 found in [Zn 2 (btb) 4/3 (bipy)], [START_REF] Han | A Non-Interpenetrated Porous Metal-Organic Framework with High Gas-Uptake Capacity[END_REF][START_REF] Klein | Route to a Family of Robust, Non-Interpenetrated Metal-Organic Frameworks with Pto-Like Topology[END_REF] which implies that a linker set of ntb, bipy and dabco is geometrically comptible for coassembly into a quaternary MOF. The utility of linker length ratios in formulating viable multicomponent MOF ligand sets is highlighted in Table 1 by the examples of [Zn 4 O(btb) 4/3 (ndc)] [START_REF] Furukawa | Ultrahigh Porosity in Metal-Organic Frameworks[END_REF][START_REF] Klein | A Mesoporous Metal-Organic Framework[END_REF] (ndc = naphthalene-2,6-dicarboxylate) and MUF-7. Since their linker length ratios are very similar (1.33 and 1.30, respectively), in conjunction with Zn 4 O nodes both btb/ndc and btb/bpdc/bdc linker sets readily assembly into MOFs with the same ith-d topology.

We herein report the successful demonstration that multicomponent MOFs are excellent platforms for creating materials with vacancy defects. We showing how Zn(II) paddlewheel nodes and ntb linkers combine to generate a load-bearing pto sublattice, which can be cross-linked into an ith-d net by bipy and dabco ligands. Since these latter linkers are not required for structural integrity, high levels of vacancy defects can be tolerated (Fig. 1c). 1.18 [e] dabco/bipy 9.0 [b] 1.11 [c] 0.94 bdc 10.1 1.25 [d] 1.05 [f] ndc 12.8 1.58 1.33 [g] bpdc 14.9 1.84 1.55 bdc/bpdc 12.5 [b] 1.54 1.30 [h] [a] In Å.

[b] Average length of bdc and bpdc.

[c] This work. [d] UMCM-4. [START_REF] Koh | Coordination Copolymerization Mediated by Zn 4 o(Co 2 r) 6 Metal Clusters: A Balancing Act between Statistics and Geometry[END_REF] [e] FJI-1/DUT-23. [START_REF] Han | A Non-Interpenetrated Porous Metal-Organic Framework with High Gas-Uptake Capacity[END_REF][START_REF] Klein | Route to a Family of Robust, Non-Interpenetrated Metal-Organic Frameworks with Pto-Like Topology[END_REF] [f] UMCM-1. [START_REF] Koh | A Crystalline Mesoporous Coordination Copolymer with High Microporosity[END_REF] [g] MOF-205/DUT-6. [START_REF] Furukawa | Ultrahigh Porosity in Metal-Organic Frameworks[END_REF][START_REF] Klein | A Mesoporous Metal-Organic Framework[END_REF] [h] MUF-7. [START_REF] Liu | Programmed Pore Architectures in Modular Quaternary Metal-Organic Frameworks[END_REF] ] is a known compound. [33] Results and discussion

Synthesis of MUF-32

We were delighted to find that the reaction of H 3 ntb, bipy and dabco (Fig. 2) with Zn(NO 3 ) 2 in DMF produces a framework with the formula [Zn 2 (ntb) 4/3 (bipy) 1/2 (dabco) 1/2 ], henceforth referred to as MUF-32 (MUF = Massey University Framework). This MOF can be produced in the form of both a microcrystalline powder (MUF-32mc), and, if benzoic acid is added as a modulator to the reaction mixture, as high-quality single crystals (MUF-32sc). Xray crystallography on MUF-32sc reveals that all three organic components are incorporated into unique positions in the lattice to produce a well-ordered MOF. Each ntb ligand coordinates to three dinuclear zinc(II) paddlewheels via its carboxyl groups to generate the underlying pto sublattice (Fig. 1a and purple net in Fig. 3b). The paddlewheels additionally coordinate to the nitrogen donor atoms of one bipy and one dabco ligand in their axial sites (Fig. 3a). These linear ligands link the metal clusters to generate a network with ith-d topology. Three different cavities exist in MUF-32: two dodecahedral cavities with interatomic diameters of 25.8 Å and 24.3 Å (Figs. 3c-d), and a smaller tetrahedral cavity (Fig. 3e). MUF-32 joins a small group of known quaternary frameworks and is the first to feature neutral N-donor ligands. Due to the large number of components in the reaction mixture, a number of phases that are derived from just one or two ligands can compete with MUF-32 during synthesis (Fig. 2). Known compounds built up from Zn(NO 3 ) 2 , ntb, dabco and/or bipy include [Zn 4 O(ntb) 2 ] (MOF-150), [33] [Zn(bipy)](NO 3 ) 2 , [START_REF] Ahuja | Preparation and Characterization of Divalent Cobalt, Nickel, Zinc, Cadmium and Monovalent Silver Nitrate Complexes with 4.4′-Bipyridine[END_REF] and a variety of discrete Zn(II)-dabco complexes. [35] In spite of the existence of these competing phases, we were able to prepare phase-pure MUF-32 by optimization of the synthesis conditions. Yields were maximized by maintaining a high ratio of glass surface area to solvent volume in the reaction vessel. Bulk phase purity was established by 1 H NMR spectroscopy on dissolved samples (Fig. S1), which confirms that the ligands are present in the expected ratios, and a match between the PXRD pattern of a bulk sample with the pattern calculated from the single-crystal structure (Fig. S8). PXRD patterns recorded after exposure of MUF-32 to the atmosphere indicate that it has good stability under these conditions (Fig. S8).

Following activation by solvent exchange with CH 2 Cl 2 , the permanent porosity of MUF-32 was established by gas adsorption. Its N 2 adsorption isotherm measured at 77K displays a steep rise in the low pressure region followed by a plateau beyond P/P o ~0.08 (Figs. S9,S11). This is consistent with the microporosity expected on the basis of its single-crystal structure. An apparent BET surface area of 2810 m 2 /g can be calculated from the isotherm for MUF-32mc, and 3260 m 2 /g for MUF-32sc. The capacity of both forms of MUF-32 to adsorb CO 2 , CH 4 , and N 2 at 273 and 298 K was also assessed (Figs. S10,S12). Linear isotherms are observed in all cases. Relative uptake capacities follow the expected trend CO 2 > CH 4 > N 2 , and are higher for MUF-32sc as compared to MUF-32mc owing to the higher accessible pore volume of the former (as evidenced by the N 2 uptake at 77 K)..

Synthesis of MUF-21 and MUF-22

We subsequently sought to deliberately synthesize ternary MOFs from combinations of (i) ntb and bipy, and (ii) ntb and dabco. This expands this family of multicomponent MOFs and enables confirmation (by PXRD) that these phases do not contaminate MUF-32.

Using synthetic conditions similar to those employed for MUF-32, the combination of zinc(II), H 3 ntb and bipy produces the ternary framework [Zn 3 (ntb) 2 (bipy) 3/2 (DMF)] (MUF-21). Using a linker set comprising H 3 ntb and dabco, we observed formation of the ternary framework [Zn 3 (ntb) 2 (dabco)] (MUF-22). MUF-21 and MUF-22 were characterized by single-crystal X-ray diffraction, thermogravimetric analysis (TGA) and gas adsorption isotherms. In MUF-21, three crystallographically-independent zinc(II) SBUs -a paddlewheel and two mononuclear nodes -link the ntb and bipy linkers into a 3D network (Fig. S5). This network comprises 2D sheets that are formed by the fusion of tubes that run along the crystallographic b direction. Adjacent sheets are interpenetrated. MUF-22 features an uncommon [START_REF] Tranchemontagne | Secondary Building Units, Nets and Bonding in the Chemistry of Metal-Organic Frameworks[END_REF][START_REF] Vs | Racemic Metalloligands: Impact on Metal-Organic Framework Structure and Synthesis[END_REF] type of eight-connected trinuclear zinc(II) SBU that links the ntb and dabco ligands into a 3D network (Fig. S6). Channels with a crosssection of ~22 × 27 Å (interatomic distances) propagate along the c axis. [START_REF]While this work was in progress the structure of MUF[END_REF] N 2 adsorption isotherms measured at 77K established the porosity of MUF-21 and MUF-22 following activation (Figs. S13-14). For MUF-21, a steep rise in N 2 uptake up to P/P o ~0.01 is followed by a near-plateau region between P/P o ~0.01 -0.1. This is consistent with the microporosity anticipated from the X-ray crystal structure. An upward inflection of the isotherm beyond P/P o = 0.02 and hysteresis in the desorption curve in this region are consistent with a gradual gate-opening process. From a structural viewpoint, this is likely to be associated with movement of the interpenetrated sublattices relative to one another. [START_REF] Furukawa | Control over Flexibility of Entangled Porous Coordination Frameworks by Molecular and Mesoscopic Chemistries[END_REF][START_REF] Horike | Soft Porous Crystals[END_REF] The Type I profile of the isotherm recorded for MUF-22, with a slight inflection at P/P o ~0.05, is in keeping with the mesoporous nature of this framework. Its apparent BET surface area is 1810 m 2 /g.

Defect engineering in MUF-32

Several observations during the synthesis and handling of MUF-32 indicated that it was indeed amenable to high levels of bipy and dabco vacancy defects: (i) when adjusting the feed ratio of the three linkers to optimize the synthetic route to MUF-32 we noticed that frameworks with substoichiometric quantities of bipy were frequently produced; (ii) when pristine MUF-32 was washed with DMF some of the bipy dissociated from the framework into solution; (iii) TGA traces exhibited gradual weight loss at moderate temperatures, which could be traced to the expulsion of dabco from the framework (Fig. S4).

We conducted a systematic investigation on the deliberate engineering of defects in MUF-32. Both vacancy defects, specifically the absence of bipy or dabco ligands, and substitution defects, bipy or dabco being partially replaced by another ligand, are possible. As summarized in Table 2, defects were introduced to MUF-32 by three different routes. The deliganded frameworks are formulated as [Zn 2 (ntb) 4/3 (bipy) x (dabco) y ], where x and y deviate from the value of ½ observed in pristine MUF-32. Defects were quantified by 1 H NMR spectroscopy on digested frameworks on the assumption that, for reasons of charge balance, the ntb ligand sites are always fully occupied and only the bipy and dabco ligands assume substoichiometric ratios. Form [a] Route [b] x [c] with substoichiometric levels of bipy were directly synthesized by systematically reducing the amount of bipy in the synthesis mixture. Although SCXRD on MUF-32G-J was not possible due to the presence of multiple crystal domains (Fig. S19), PXRD indicated that the overall architecture of MUF-32 was retained in all cases (Figs. S18,S23). The amount of bipy ligand incorporated into these materials was determined by [START_REF] Burrows | Mixed-Component Metal-Organic Frameworks (Mc-Mofs): Enhancing Functionality through Solid Solution Formation and Surface Modifications[END_REF] H NMR spectroscopy on digested samples. The creation of bipy absence defects correlates with an uptick in the amount of incorporated dabco linker, particularly for the single-crystalline materials (Table 2). In all cases, the total quantity of bipy and dabco per paddlewheel (x + y) does not exceed unity, which suggests that the dabco occupies some of the bipy sites in the lattice. Since major variations are not seen in the PXRD patterns of these materials, it is unlikely that the dabco ligand bridges two paddlewheels, since this would necessitate a significant structural reorganization, but rather that it coordinates to the framework by just one of its nitrogen donors (Fig. S7). It is likely that solvent molecules, e.g. H 2 O, DMF, fill the remaining coordination site on the paddlewheel cluster vacated by the bipy ligand.

Route 2: Postsynthetic introduction of defects by soaking in DMF.

Bipy is expelled from MUF-32mc and MUF-32sc simply by soaking in fresh DMF. When this method was employed for preparative purposes, the numerical superscript at the end of the sample code indicates the soaking period in minutes (Table 2). The release of bipy was confirmed by 1 H NMR spectroscopy of DMF-d 7 solvent in contact with solid samples of these materials (Figs. S17, S24, S25). Replacing DMF by CH 3 NO 2 or CH 2 Cl 2 in the soaking experiments led to no loss of the bipy ligand, which suggests that the ability of DMF to coordinate to the coordination site made vacant on the zinc SBU is important. The exchange of MOF ligands by solvent molecules has precedence in the literature. [START_REF] Tan | Stability and Hydrolyzation of Metal Organic Frameworks with Paddle-Wheel Sbus Upon Hydration[END_REF][START_REF] Chen | Reversible Two-Dimensional-Three Dimensional Framework Transformation within a Prototype Metal-Organic Framework[END_REF] Interestingly, many known examples involve the displacement of dabco linkers, rather than bipy as seen here. We posit that in this case bipy is expelled in preference to dabco owing to its weaker basicity. Steric effects may play a role, as well as entropic effects since bipy gains torsional degrees of freedom that dabco does no upon release into solvent.

Due to its smaller particle size, defect creation is much more rapid in MUF-32mc than in MUF-32sc, however in both cases the amount of bipy ligands released from the lattice, as quantified by 1 H NMR spectroscopy on digested samples, plateaus at ~20% (Figs. S16,S22). The overall network of MUF-32 is sustained upon displacement of the bipy linkers, as evidenced by PXRD patterns (Figs. S18,S23).

Route 3: Postsynthetic introduction of defects by heating.

The third route to generating defects in MUF-32 is by heating to moderate temperatures. Deliganded MUF-32 frameworks, MUF-32F from MUF-32mc and MUF-32L from MUF-32sc, which are deficient in dabco are produced by this method (Table 2). The loss of dabco by heating is consistent with it being the most volatile of the framework components. Chun et al. have previously reported on the thermal expulsion of dabco from a MOF. [START_REF] Chun | A Simple and Rational Approach for Binodal Metal-Organic Frameworks with Tetrahedral Nodes and Unexpected Multimodal Porosities from Nonstoichiometric Defects[END_REF] The release of the dabco ligands could be monitored by TGA experiments where samples were heated to 150 °C and held at that temperature for three hours (Fig. S20). Since TGA cannot be used as a quantitative tool due to the unavoidable presence of volatile guest molecules that also contribute to the observed weight loss, we employed 1 H NMR spectroscopy on digested samples to assess the extent of dabco vacancy formation (Figs. S15,S21). Owing to its larger particle size, MUF-32sc releases dabco much less readily than MUF-32mc: only 16% of the dabco ligands are absent from MUF-32L, whereas ~50% of the dabco linkers are expelled in producing MUF-32F. If the sample is placed in a vacuum chamber during heating, the reduced pressure results in significant loss of both the dabco and bipy ligands (MUF-32M). In all cases, PXRD clearly indicates that the overall structure of the parent MUF-32 framework is maintained following thermal defect generation (Figs. S18,S23).

Gas adsorption properties of defect MUF-32 materials

To assess the textural characteristics of deliganded MUF-32 materials, gas adsorption isotherms were measured. Crucially, MUF-32 maintains high levels of porosity -and thus its structural integrity -even when significant defects are introduced (Fig. 5). This can be ascribed to its multicomponent nature: the underlying [Zn 2 (ntb) 4/3 ] sublattice provides a sound structural foundation that resists collapse when a significant fraction of the bipy and dabco ligands are absent.

CO 2 adsorption isotherms measured on the microcrystalline materials at 273 K reveal several interesting trends (Fig. 5). MUF-32A and MUF-32E [START_REF] Deng | Multiple Functional Groups of Varying Ratios in Metal-Organic Frameworks[END_REF] , in which ~20% of the bipy sites are vacant, adsorb fractionally less CO 2 than pristine MUF-32mc. On the other hand, despite taking up less N 2 at 77 K, MUF-32B and MUF-32D take up more CO 2 . A greater number of bipy linkers are absent from these frameworks and some of these sites are occupied by dabco. Since in this situation the dabco coordinates in a monotopic fashion, this leaves one of its nitrogen atoms free to interact with guest molecules (Fig. S7). Favorable electrostatic interactions between CO 2 molecules and the dabco nitrogen thus underlie the affinity of MUF-32B and MUF-32D for this gas. [START_REF] Sumida | Carbon Dioxide Capture in Metal-Organic Frameworks[END_REF] The CO 2 capacity of MUF-32mc is increased by 15% in going to its deliganded analogue MUF-32D. At 273 K, the CO 2 uptake capacities of the deliganded singlecrystalline materials ranges from 79 to 92 cm 3 (STP)/g (Fig. 5). CO 2 uptake increases for the directly-synthesized defect frameworks as progressively more of the bipy ligands are replaced by monotopic dabco ligands (MUF-32G-J). As outlined above, this can be ascribed to interactions between the CO 2 and the free dabco nitrogen atom. MUF-32H-J outperform MUF-32sc in terms of CO 2 adsorption despite having lower N 2 uptake at 77 K. The postsynthetic removal of bipy ligands from MUF-32sc to give MUF-32K 1440 has little impact on the CO 2 uptake capacity.

Defect healing

MUF-32E [START_REF] Deng | Multiple Functional Groups of Varying Ratios in Metal-Organic Frameworks[END_REF] and MUF-32K 1440 can be healed by soaking in a solution of bipy to regenerate pristine MUF-32 (Table 2). The success of the healing process was judged by 1 H NMR spectroscopy. For MUF-32K 1440 , defect healing significantly improves its structural order, as evidenced by single-crystal X-ray diffraction patterns. Upon soaking MUF-32 single crystals in DMF for various periods to produce the MUF-32K x materials, the diffraction quality is reduced. The diffraction spots become more diffuse and often split into multiple spots (Fig. S28). This indicates that the long-range order in the lattice of MUF-32K is reduced with respect to MUF-32sc and that multiple domains develop upon defect formation. Upon healing the bipy vacancies in MUF-32K 1440 to generate MUF-32K 1440 h, sharp and single spots are restored to the diffraction pattern (Fig. S28). Optical microscopy shows that the external form and transparency of the MUF-32 crystals are maintained through the defect production and healing steps. Gas adsorption measurements conducted on the healed single-crystalline materials MUF-32Gh, MUF-32Ih and MUF-32K 1440 h indicate that high levels of porosity are maintained during the healing process (Fig. 5).

For MUF-32Bh, MUF-32Dh, MUF-32Gh and MUF-32Ih, healing of the defect frameworks produces materials other than pristine MUF-32. For example, MUF-32G has the formula [Zn 2 (ntb) 4/3 (bipy) 0.35 (dabco) 0.62 ], indicating that dabco occupies some of the bipy sites. Soaking MUF-32G in a solution of bipy in CH 2 Cl 2 produces MUF-32Gh, [Zn 2 (ntb) 4/3 (bipy) 0.42 (dabco) 0.56 ]. The reduction in the dabco content vis-a-vis MUF-32G indicates some of the dabco ligands residing in the bipy sites are displaced by incoming bipy ligands. However, the extent to which these 'imposter' dabco ligands can be displaced has an upper limit, even after extensive exposure to a solution of bipy (Table 2). It is noteworthy that the sum of the bipy and dabco stoichiometries nears the maximum value of unity, implying that almost all bipy sites are occupied by either a bipy or a dabco linker.

Computational analysis

To further understand the ability of MUF-32 to tolerate defects we performed a quantum-chemistry calculations at the Density Functional Theory (DFT) level for eight crystalline structures of formula [Zn 2 (ntb) 4/3 (bipy) x (dabco) y ], with 0 ≤ x, y ≤ ½. We focused on the relative energies of these materials and their mechanical stability. Ordered models with various compositions were generated from the MUF-32 crystallographic structure by removal of bipy or dabco ligands (Table S3). Energy minimization was then performed for each model, giving both a relaxed structure and its energy. The structures calculated in this way are in good agreement with the crystallographic coordinates (Fig. S47). On the basis of the relaxed structures, second-order elastic constants were calculated and the elastic properties analyzed following a procedure established in earlier literature. [START_REF] Ortiz | Anisotropic Elastic Properties of Flexible Metal-Organic Frameworks: How Soft Are Soft Porous Crystals?[END_REF][START_REF] Ortiz | Metal-Organic Frameworks with Wine-Rack Motif: What Determines Their Flexibility and Elastic Properties[END_REF] The computational results underscore the utility of multicomponent MOFs creating materials with high levels of defects:

(i) The calculated unit cell volume and cell parameters of the defective frameworks were found to vary only slightly (±1.7%) from MUF-32 (Table 3), which shows that the creation of defect does not involve a substantial structural reorganization. This is consistent with the experimental PXRD patterns. One geometric parameter that does change between calculated structures of MUF-32 and [Zn 2 (ntb) 4/3 ] is the distance between the paddlewheels. In the latter it adopts a uniform value and does not alternate between short (dabco sites) and long (bipy sites) values as it does in MUF-32. The insertion of both bipy and dabco linkers to link the axial sites of the paddlewheel SBUs therefore does involve a local deformation, however it results in minimal strain on the [Zn 2 (ntb) 4/3 ] sublattice.

(ii) Although not experimentally observed, [Zn 2 (ntb) 4/3 ] was found to be energetically feasible since it corresponds to a local energy minimum. The same holds for the structures with (x, y) = (1/2, 0) and (0, 1/2). Rather than compare absolute energies, which is fraught with difficulty for these kinds of materials, we calculated the binding energies of the bipy and dabco ligands to these structures. The binding energies to the [Zn 2 (ntb) 4/3 ] sublattice are 238 kJ/mol (bipy) and 329 kJ/mol (dabco) per ligand. The stronger binding of dabco is in agreement with experimental observations that this ligand is more difficult to remove from MUF-32 when generating vacancy defects.

We found that these binding energies do not depend strongly on the composition of the rest of the framework. For bipy, where compositions of x = 0, 1/6, 2/6 and 1/2 were tested, we observe that the binding energy has only a slight (and almost linear) dependency on the number of vacancies, varying between 233 and 242 kJ/mol. Likewise, the binding energy of dabco to [Zn 2 (ntb) 4/3 (bipy) 1/2 ] is only marginally smaller (303 kJ/mol) than that to [Zn 2 (ntb) 4/3 ] (329 kJ/mol). Thus, from an energetic perspective, there is no barrier to creating [Zn 2 (ntb) 4/3 (bipy) x (dabco) y ] materials with any values of x and y between 0 and ½.

(iii) Geometric pore space analysis was performed on the relaxed structures. Porosity (φ) decreases monotonously with both x and y, ranging from φ = 0.45 (MUF-32) to φ = 0.55 ([Zn 2 (ntb) 4/3 ]). The surface area S (in cm 2 /g) is found to increase slightly upon ligand removal owing to the decrease in mass. It is interesting to note that the variation of S observed upon varying x is smaller than the variations in BET surfaces as extracted from N 2 adsorption experiments. There are thus additional aspects than pure geometric considerations that drive the adsorption in the deliganded MUF-32, such as presence of guest molecules inside the pores or flexibility of the framework. Additional theoretical work on adsorption properties will be needed to settle this question.

(iv) Bulk modulus, which quantifies the volumetric response to isotropic compression) is almost unaffected by ligand removal (Table S4), meaning that the global stiffness of all MUF-32 materials is mostly determined by the underlying [Zn 2 (ntb) 4/3 ] sublattice. However, large changes are seen in the Young's and shear moduli, i.e. responses to uniaxial compression and shearing. In particular, the spatially-averaged shear modulus, equal to 1.84 GPa in pristine MUF-32, is decreased to 0.99 GPa upon total removal of dabco [to Zn 2 (ntb) 4/3 (bipy) 1/2 ], and further to 0.54 GPa in [Zn 2 (ntb) 4/3 ]. The Young's moduli follow the same trend: the lower connectivity of the metal clusters in deliganded MOFs renders the substoichiometric lattices more susceptible to both shear forces and compression along the directions of missing linkers.

The small value of shear modulus in [Zn 2 (ntb) 4/3 ] reveals why compounds with high proportions of both bipy and dabco vacancies, including [Zn 2 (ntb) 4/3 ] itself, are not observed. Although energetically feasible, it is the mechanical properties of MUF-32 that set an upper limit on the extent to which it can sustain vacancy defects. This situation is similar to that of hypothetical ZIF frameworks which, although of relatively low formation enthalpy, [START_REF] Lewis | Zeolitic Imidazole Frameworks: Structural and Energetics Trends Compared with Their Zeolite Analogues[END_REF] are not mechanically stable enough to be able to be synthesized. [START_REF] Bouëssel Du Bourg | Thermal and Mechanical Stability of Zeolitic Imidazolate Frameworks Polymorphs[END_REF] This theoretical study is a first to demonstrate the relationship between ligand vacancies and mechanical properties in MOFs, and parallels some recent work by Cliffe et al. showing the dependence of thermal properties on the concentration of defects in UiO-66(Hf). [START_REF] Cliffe | Defect-Dependent Colossal Negative Thermal Expansion in Uio-66(Hf) Metal-Organic Framework[END_REF]

Conclusion and outlook

We have established a new strategy for deliberately introducing vacancy defects in MOFs. This strategy relies on coassembling both load-bearing and decorative components into the same framework. An underlying three-dimensional sublattice is maintained by the metal cluster and one of the linkers. Since the two other linkers are neutral and not essential for the structural integrity of the network, the network can be sustained when they are present at substoichiometric levels. Defects can be introduced in multiple ways, involving both de novo synthesis and postsynthetic modification, and defect levels can be used to tune the adsorption properties. In addition, we have shown how defect healing can restore the pristine parent MOF or produce a range of new materials. More broadly, our strategy can be viewed as an example of the recently introduced principle of 'using weakness as a synthetic tool,' [START_REF] Morris | Exploiting Chemically Selective Weakness in Solids as a Route to New Porous Materials[END_REF] and contributes a new angle to the current surge of interest in MOFs with defects. [START_REF] Fang | Defect-Engineered Metal-Organic Frameworks[END_REF] Taking advantage of multicomponent ligand sets to rationally engineer 'defectogenic' frameworks promises to be a widely-applicable methodology for fabricating materials with novel structural features and properties.

Table of Contents artwork

Figure 1 .

 1 Figure 1. (a) A load-bearing sublattice with a pto topology is readily constructed from triangular tris(carboxylate) ligands and metal paddlewheel SBUs. (b) Adding two different linear struts to the pto lattice generates a quaternary MOF with an ith-d topology. (c) Since the linear struts are not essential to the structural integrity of the MOF vacancy defects can be sustained.

Figure 3 .

 3 Figure 3. (a) The six-connected dinuclear zinc(II) SBU of MUF-32, highlighting the coordination of three different ligands, (b) the network structure of MUF-32 with the pto sublattice shown in purple, (c) the larger dodecahedral cavities of MUF-32 that are

  [a] MC = microcrystalline powder, SC = large single crystals. [b] Route 1 = direct synthesis; Route 2 = washing with DMF, the superscripts on the sample codes indicate the lengths of time, in minutes, the sample was exposed to DMF; Route 3 = direct heating of solid sample; Route 4 = defect healing by soaking in a solution of bipy in CH2Cl2. [c] The stoichiometry of bipy and dabco was determined by 1 H NMR spectroscopy using the ntb peak integrals as a reference. [d] Heated to 150 °C in a TGA instrument. [e] Heated to 150 °C in a vacuum oven for three hours. [f] By X-ray diffraction on a single crystal, x = 0.474(6).

Figure 4 .Route 1 :

 41 Figure 4. Three routes that were developed to create defects in MUF-32. The network structures of the MOFs are presented. Purple = ntb; green = bipy, red = dabco. Route 1: Introduction of defects by de novo synthesis. MUF-32A-D (microcrystalline) and MUF-32G-J (single crystalline)with substoichiometric levels of bipy were directly synthesized by systematically reducing the amount of bipy in the synthesis mixture. Although SCXRD on MUF-32G-J was not possible due to the presence of multiple crystal domains (Fig.S19), PXRD indicated that the overall architecture of MUF-32 was retained in all cases (Figs.S18, S23). The amount of bipy ligand incorporated into these materials was determined by[START_REF] Burrows | Mixed-Component Metal-Organic Frameworks (Mc-Mofs): Enhancing Functionality through Solid Solution Formation and Surface Modifications[END_REF] H NMR spectroscopy on digested samples. The creation of bipy absence defects correlates with an uptick in the amount of incorporated dabco linker, particularly for the single-crystalline materials (Table2). In all cases, the total quantity of bipy and dabco per paddlewheel (x + y) does not exceed unity, which suggests that the dabco occupies some of the bipy sites in the lattice. Since major variations are not seen in the PXRD patterns of these materials, it is unlikely that the dabco ligand bridges two paddlewheels, since this would necessitate a significant structural reorganization, but rather that it coordinates to the framework by just one of its nitrogen donors (Fig.S7). It is likely that solvent molecules, e.g. H 2 O, DMF, fill the remaining coordination site on the paddlewheel cluster vacated by the bipy ligand.

Figure 5 .

 5 Figure 5. Plot showing N 2 (650 Torr, 77 K) and CO 2 (760 Torr, 273 K) capacities of MUF-32mc, MUF-32sc and related defect and healed materials.

Table 1 .

 1 Ligand length ratios, given by the formula [twofold linker length]/[threefold linker length], for ligand sets of known and putative ternary and quaternary metal-organic frameworks. The length ratios of known frameworks with an ith-d topology are bolded.

	Zn	Zn	Zn			Zn	Zn
	O	O	N			O	O	linker length
	linker length
	O	O	N	Zn	O	O		O	O	Zn
	ditopic linkers Zn Zn	Zn	Zn		tritopic linkers	Zn
	tritopic				ntb			btb
			length [a]			8.1			9.6
	ditopic
	dabco		6.7			0.83 [c]			0.70
	bipy		11.3			1.40 [c]

Table 2 .

 2 Summary of MUF-32 materials with vacancy defects, which are formulated as [Zn 2 (ntb) 4/3 (bipy) x (dabco) y ].

  y

	Defect creation
	MUF-32mc	MC	pristine 0.50	0.50
	MUF-32A	MC		0.40	0.50
	MUF-32B	MC		0.33	0.54
	MUF-32C	MC		0.20	0.62
	MUF-32D	MC		0.10	0.68
	MUF-32E 3	MC		0.40	0.50
	MUF-32E 10	MC		0.39	0.50
	MUF-32E 30	MC		0.39	0.50
	MUF-32F	MC	[d]	0.47	0.26
	MUF-32sc	SC	pristine 0.50	0.50
	MUF-32G	SC		0.35	0.62
	MUF-32H	SC		0.27	0.70
	MUF-32I	SC		0.20	0.76
	MUF-32J	SC		0.14	0.78
	MUF-32K 10	SC		0.48	0.50
	MUF-32K 30	SC		0.47	0.50
	MUF-32K 180	SC		0.44	0.50
	MUF-32K 1440	SC		0.40	0.50
	MUF-32L	SC	[d]	0.49	0.42
	MUF-32M	SC	[e]	0.37	0.32
	Defect healing
	MUF-32Bh	MC		0.44	0.53
	MUF-32Dh	MC		0.21	0.68
	MUF-32E 3 h	MC		0.51	0.51
	MUF-32Gh	SC		0.42	0.56
	MUF-32Ih	SC		0.23	0.74
	MUF-32K 1440 h [f]	SC		0.50	0.50

Table 3 .

 3 Structural and mechanical properties of eight frameworks with formulae [Zn 2 (ntb) 4/3 (bipy) x (dabco) y ] as calculated by Density Functional Theory.Quantities listed: volume variation, (V)with respect to MUF-32 (in percent), porosity φ, accessible surface area S (in cm 2 /g), spatially-averaged Young's (E) and shear (G) moduli, both in GPa.

	(x, y)	MOF	∆V	φ	S	E	G
			(%)
	(1/2, 1/2)	MUF-32	0	0.45 3920 5.24 1.84
	(1/3, 1/2)	defect	-0.47 0.46 3980
	(1/6, 1/2)	defect	-1.21 0.48 4040
	(0, 1/2)	defect	-1.74 0.50 4120 2.89 0.99
	(1/2, 0)	defect	-0.24 0.47 4460
	(1/3, 0)	defect	0.13	0.50 4520
	(1/6, 0)	defect	0.66	0.52 4590
	(0, 0)	[Zn 2 (ntb) 4/3 ] 1.68	0.55 4670 1.60 0.54

ACKNOWLEDGMENT

We thank Dr. Hui Yang for valuable experimental assistance and advice. SGT is grateful to the RSNZ Marsden Fund for supporting this research, and FT and FXC acknowledge access to HPC resources provided by GENCI (grant i2015087069).

ASSOCIATED CONTENT Supporting Information

Experimental and computational details, additional characterization data, and crystallographic information (CIF) files.

AUTHOR INFORMATION Corresponding Author

Email: s.telfer@massey.ac.nz

Notes

The authors declare no competing financial interests.


Daniel Knorreck

Ludovic Apvrille

Renaud Pacalet

An Interactive System Level Simulation Environment for Systemson-Chip

Keywords: System-on-Chip, Design Space Exploration, UML, Simulation, Interactive, HW/SW partitioning, DIPLODOCUS

This article presents an interactive simulation environment for high level models intended for Design Space Exploration of Systems-On-Chip. The existing open source development environment TTool supports the MARTE compliant UML profile DIPLODOCUS and enables the designer to create, simulate and formally verify models. The goal is to obtain first performance estimations of the system intended for design while minimizing the modeling effort. The contribution outlined in this paper is an additional module providing means for controlling the simulation in real time by performing step wise execution, saving and restoring simulation states as well as animating UML models of the system. Moreover the paper elaborates on the integration of these new features into the existing framework consisting of a simulation engine on the one hand and a graphical user interface on the other hand.

Introduction

A System-on-Chip can be defined as a set of communicating electronic components integrated into one single chip. The latter components are highly heterogeneous in nature: digital, analog and mixed signal components may be interconnected to make up complex systems ranging from mobile hand sets and set top boxes to automotive controllers and feedback control systems for rail cars. Due to recent advances in the field of semiconductor physics, higher and higher integration densities are achieved so that a given piece of silicon accommodates more and more transistors.

In order to make use of the available resources, the complexity of embedded systems and Systems-on-Chip has been increasing rapidly. On the one hand, users are demanding products exhibiting sophisticated features which are reliable, easy to use and affordable. On the other hand, the gap increases between integration and designer efficiency due to inadequate tools and methodologies. In addition to the increased demand of functionality, time-to market is an issue of great concern. Hence, developers are facing significant difficulties due to an exponentially raising complexity.

It becomes more and more unlikely that an optimal design represents an intuitive solution, thus the experience of the designer may not lead him/her to optimal designs with respect to functional and nonfunctional requirements such as performance, size, energy consumption, reliability.

Thus, given a particular functionality and associated requirements, the design space is considered as representing all functionally equivalent implementation alternatives. Being almost infinitely large at the very beginning of the design flow, the design space should be gradually reduced during the design process by refining the model of the system. The analysis of systems at low abstraction levels exhibits a high degree of accuracy but comes with the downside of being demanding and slow. Traditional simulation techniques operating at register transfer level (RTL), instruction or transaction level are not appropriate for system level Design Space Exploration (DSE) for two reasons: • Only a very limited number of implementation alternatives can be examined due to the high modeling effort and extensive simulation runtime.

•

The lack of specification at early design stages may prohibit the construction of detailed models -even if the effort was acceptable.

Thus, abstractions are the key to success in performing System Level Design. In this context, we have previously introduced a UML-based environment named DIPLODOCUS. The strength of our approach relies on formal verification capabilities and fast simulation techniques ( [START_REF] Waseem | Abstract application modeling for system design space exploration[END_REF] [START_REF] Apvrille | A UML-based environment for system design space exploration[END_REF]). DIPLODOCUS design approach is based on the following fundamental principles:

•

Use of a high level language (UML)

Related Work

Some of the current state of the art UML modeling tools ( [START_REF]Topcased. Topcased[END_REF], [START_REF] Tau | [END_REF], [START_REF]Rhapsody[END_REF], [START_REF] Artisan | Artisan studio[END_REF] amongst others) exhibit simulation capabilities. Simulations can only be performed based on purely functional models in an untimed fashion. Our interactive simulator however also accounts for architecture semantics like arbitration of shared resources, speed or data throughput of devices, etc. Furthermore, the execution behavior of models is tool dependent as the UML standard lacks an execution semantics.

The DIPLODOCUS profile however fills that semantic gap and thus also paves the way for formal verification. Related work in the field of system level modeling and simulation often suffers from one of the following problems: Off the shelves solutions like [10] and [START_REF]Coware Virtual Platforms[END_REF] mostly do not permit an orthogonalization of functionality and architecture. Detailed RTL models of HW components and the final software code must be at hand to perform co-simulation. For instance, Instruction Set Simulators are often used to estimate the impact on performance of software execution on a specific processor. Thus, only little abstraction may be applied to communication (SystemC TLM [START_REF]Members of the SystemC Verification Working Group[END_REF], etc) and computations. Some academic approaches enable the design of distinct models for architecture and application ( [START_REF] Ristau | A mapping framework for guided design space exploration of heterogeneous mp-socs. Design, Automation and Test in Europe[END_REF], [START_REF] Vidal | A codesign approach for embedded system modeling and code generation with uml and marte[END_REF], [START_REF] Pimentel | Towards efficient design space exploration of heterogeneous embedded media systems[END_REF], [START_REF] Pimentel | A systematic approach to exploring embedded system architectures at multiple abstraction levels[END_REF], [START_REF] Vidal | A codesign approach for embedded system modeling and code generation with uml and marte[END_REF]). In this case, the level of abstraction is often not pushed high enough to explore a representative subset of the HW/SW design space in a reasonable time. Sometimes application models do not exhibit data/functional abstractions. In other cases, the simulation strategy does not leverage abstractions and models have to be refined before being executable. For instance, [START_REF] Tero Arpinen | Performance evaluationof uml2-modeled embedded streaming applications with system-level simulation[END_REF] bears resemblance with our approach with respect to the modeling methodology where UML is applied for architecture, application and mapping models. As opposed to our framework, the focus is put on streaming applications exhibiting only occasional control messaging and branching. For this reason, the semantics of Kahn Process Networks has been adopted for application models. Simulation is carried out on SystemC TLM level, thus it does not leverage all abstraction applied at the modeling stage. Analytical approaches like [START_REF] Chakraborty | A general framework for analysing system properties in platform-based embedded system designs[END_REF] and [START_REF] Henia | System level performance analysis -the symta/s approach[END_REF], [START_REF] Hamann | A framework for modular analysis and exploration of heterogeneous embedded systems[END_REF]

The DIPLODOCUS UML Profile and Tooling

DIPLODOCUS is a UML profile targeting the design of Systems-on-Chip at a high level of abstraction. A UML profile customizes UML [START_REF]UML 2.0 Superstructure Specification[END_REF] for a given domain, using UML extension capabilities. Furthermore, a UML profile commonly provides a methodology and is supported by a specific toolkit.

Methodology

DIPLODOCUS follows the Y-Chart methodology [START_REF] Lieverse | A methodology for architecture exploration of heterogeneous signal processing systems[END_REF] and is therefore characterized by the following threestep design flow (see Figure 1): • Applications are first described as a network of abstract communicating tasks using a UML class diagram. The latter represents the static view of the application. Each task behavior is described with a UML activity diagram. • Targeted architectures are modeled independently from applications as a set of interconnected generic hardware nodes. The latter may be parametrized to exhibit a more specific behavior. UML nodes were defined to model HW elements (e.g. CPUs, buses, memories, hardware accelerators, bridges).

• A mapping process defines how application tasks can be bound to execution entities and also how abstract communications between tasks are assigned to communication and storage devices.

Figure 1: Global view of the Design Space Exploration methodology

Within a SoC design flow, Design Space Exploration is supposed to be carried out at a very early stage. Hence, the main DIPLODOCUS objective is to help designers to spot a suitable hardware architecture even if algorithmic details have not yet been stipulated thoroughly.

To achieve this, DIPLODOCUS relies (i) on fast simulation and formal proof techniques, both at application and mapping level, and (ii) on application models clearly separated from architecture models (also referred to as Y-Chart approach [START_REF] Lieverse | A methodology for architecture explorationof heterogeneous signal processing systems[END_REF]). Due to the high abstraction level of both application and architecture models, simulation speed can be increased significantly with regards to simulations usually performed at lower abstraction level (e.g. TLM level, RTL level, etc.). Additionally, efficient formal static analysis techniques may be applied before and after mapping [START_REF] Knorreck | Pacalet Formal Systemlevel Design Space Exploration[END_REF].

Application Modeling

An application model is the description of functions to be performed by the targeted SoC. As it merely stipulates a partial ordering of actions, a refined execution semantics is introduced at the mapping stage. One has to bear in mind that, at application modeling level, computations and communication are accounted for by abstract cost operators. The time it takes to process the latter can only be resolved with the aid of parameters which are annotated to the architecture model. Abstract cost operators entail two kinds of abstractions which reflect the degree of uncertainty inherent to early design stages:

• Data abstraction: Only the amount of transferred data is taken into account, not the data itself.

•

Functional abstraction: Algorithmic details are abstracted by means of their complexity operators. As mentioned before, functions are modeled as a set of abstract tasks described within UML class diagrams. Task behavior is modeled using UML activity diagrams which are built upon the following operators: control flow and variable manipulation operators (loops, tests, assignments, etc.), communication operators (reading/writing abstract data samples in channels, sending/receiving events and requests), computational cost operators and delay operators. This section briefly describes a subset of the aforementioned operators as well as their semantics and provides definitions for Channels, Events and Requests: Channels are characterized by a point-to-point unidirectional communication between two tasks. The following Channel types exist: be finite or infinite. In case of an infinite FIFO, incoming events are never lost. When adding an event to a finite FIFO, the incoming event may be discarded or the oldest event may be dropped if the FIFO is full. Thus, a single element FIFO may be used to model hardware interrupts. In tasks, events can be sent (NOTIFY), received (WAIT) and tested for their presence (NOTIFIED).

Requests are characterized by a multi-point to one point unidirectional asynchronous communication between tasks. A unique infinite FIFO between senders and the receiver is used to store all incoming requests. Consequently, a request cannot be lost. ). As a consequence, mapping models have less possible execution traces than application models

Toolkit

The DIPLODOCUS UML profile -including its methodology -has been implemented in TTool [START_REF] Ttool | the Turtle Toolkit[END_REF].

TTool is an open-source toolkit that supports several UML2/SysML profiles, including TURTLE [START_REF] Apvrille | TURTLE: A Real-Time UML Profile Supported by a Formal Validation Toolkit[END_REF] and DIPLODOCUS [START_REF] Apvrille | TTool for DIPLODOCUS: An Environment for Design Space Exploration[END_REF]. The main idea behind TTool is that all models may be formally verified or simulated.

In practice, UML diagrams are first automatically translated into an intermediate specification expressed in a formal language, which serves as starting point for deriving formal specifications and simulation code (compare Figure 2). Based on the three building blocks (mapping, application, architecture), TTool automatically generates simulation code (C++) or formal specifications at the push of a button. The module which allows the designer to control the simulation in real time by performing step wise execution, saving and restoring simulation states as well as providing live feedback to UML diagrams will be elaborated in section 5.

The Simulation Strategy

Before going into details, it should be clearly emphasized what we understand by fast simulation. Our fast simulation approach is centered around two basic principles: • A modeling methodology which allows for conceiving abstract application models by applying both data and functional abstractions.

•

A simulation strategy which efficiently exploits these characteristics of the high level model. The granularity of the simulation thereby matches the granularity of the application model. This implies that the gain in terms of simulation speed can hardly be expressed in cycles per second as it highly depends on the application model. Indeed, in theory the simulator could attain any ratio of cycles/second if transactions were sufficiently large. But in this case the respective model would be far from reflecting key characteristics of the real system for lack of detailedness. The trade-off between detailedness and simulation speed is still subject to our research and can be varied smoothly thanks to the simulation environment. When experimenting with models such the one of an MPEG2 decoder, simulation speed increased by factor 30 as compared to a cycle-based SystemC simulator [START_REF] Knorreck | Fast simulation techniques for design space exploration[END_REF]. A car communication application where we experienced a simulation speed up to 30 times faster than real time may be also considered as a rough guide. The simulator detailed in this paper is transactionbased. A transaction refers to a computation internal to a task, or a communication between tasks. Those transactions may obviously span up to hundreds of clock cycles. The duration of transactions is initially defined according to the application model, that is to say the maximum duration is given by the length of the corresponding operator within the task model. At simulation runtime, a transaction may have to be broken down into several chunks of smaller size, just because for example, a bus is not accessible and so the task is put on I/O wait on its CPU. Transaction cutting is more likely to happen if the amount of inter task communication is high and hence the need for synchronization arises. The aggregation of cycles may slightly impact simulation semantics when incorrect branch predictions arise on CPUs. The exact point in time of their occurrence cannot be resolved and thus the resulting delay is determined on a per-transaction base. The transaction based simulation embraces mainly three layers (compare Figure 3) representing the semantics of the application model, the semantics of the underlying execution platform and finally a layer dedicated to the discrete event simulation itself. The topmost layer is subdivided into two parts: the first one accounting for the computational part of abstract tasks, the second one for the communication semantics of abstract channels. Based on the knowledge of their internal behavior, tasks are able to determine the next operation which has to be executed within their scope. The abstract cost of this command (in terms of computation or communication units) is subsequently encapsulated in a transaction data structure. The latter is tagged with the earliest possible start time (which corresponds to the finish time of previous transaction of the task). In case the system is dealing with communication or synchronization commands, transactions are forwarded to the dedicated layer for abstract channels. This layer takes into account constraints imposed by the channel semantics like the maximum number of samples to b4e stored, the blocking behavior, etc.

The hardware layer can be decomposed in the same manner as the model layer (as depicted in Figure 3): execution hardware elements (CPUs and hardware accelerators) and communication elements (bridges, buses, memories) alter the time stamp of transactions initially defined at the task layer. The basic idea is that this timing information is used to update the internal clock of hardware elements. Time stamps thus serve as means of synchronization among the local clocks of hardware elements. More precisely, on time management, CPUs have to recalculate the start time of transactions based on their internal schedule and they are able to convert the abstract length to time units. Moreover, a hardware component may delay transactions and modify their duration according to the execution time needed by that specific component. In so doing, the simulation algorithm accounts for the speed of CPUs, the data rate of buses, bus contention and other parameters characterizing the hardware configuration. If several devices are involved in the execution process, transactions are simply passed from one device to another while being modified accordingly. This procedure is for instance applied if an abstract channel at application level is mapped onto several buses and bridges. The final values for start time and duration are hence determined incrementally by forwarding transactions to dedicated hardware nodes. Finally, the main scheduler acts as a discrete event simulator and assures the causality of the simulation. This is achieved by simply querying all CPUs for their next transaction and selecting for execution the transaction with the earliest finish time.

Interactive Simulation Environment

Usage and features

The above mentioned simulation environment has been enhanced and it henceforth allows for an interactive exploration of the application which is mapped onto a particular architecture. After having developed the static view of the application in terms of classes, the behavioral view, the architecture and the mapping, the developer first checks the syntax of the models. If the models comply to the constraints of the meta-model, the next stage is to generate the C++ counterpart of the graphical model. Once the sources have been compiled, the interactive simulation module is launched. All of the aforementioned stages are accomplished at the push of a button. No expertise in C++ programming, simulation or formal verification (in case the model should be verified) is required. The starting point for an interactive exploration is hence the window depicted in Figure 4.

The interface provides the following simulation commands:

• Different flavors of run commands: a given amount of transactions, commands or time units can be simulated... • …likewise the simulation may be interrupted when a particular hardware element (CPU, bus, bridge, memory) or an application entity (channel) processes a transaction. • Reset the simulation to the initial state.

• Save and restore the simulation state, especially useful when several branches of control flow are to be looked into. The user is not aware of the existence of these commands as they merely serve as a vehicle to convey information to the graphical user interface.

• Commands may also be supplied directly in text format, without using the graphical interface at all. Thus, scripts can be written to automate the simulation procedure.

TTool encompasses a graphical interface to direct the simulation (shown in Figure 4) and thus unburdens the user from familiarizing with a lowlevel simulation language. The feedback from the simulation engine is exploited by the graphical user interface and used to animate UML application diagrams. For instance, the current command of a task is highlighted so that the user is able to closely follow the simulation progress.

In addition to traces, simulation results comprise performance figures like the utilization of hardware elements, the contention delay for bus masters, the execution time of tasks, the average time a task gets blocked due to CPU contention, etc (compare Figure 8).

Technical Issues

As illustrated in figure 5, the simulator and the graphical user interface embedded in TTool are hosted in different processes communicating via a TCP connection. Therefore, the simulator and the graphical user interface can be run on different machines for the sake of performance. To get a better understanding of this interaction, let us now follow a user request which aims at defining a breakpoint. The user selects the option by clicking on the respective command within the UML activity diagram. In turn, the logic of the graphical user interface identifies the concerned command and signals a modification to the TTool client. The latter may perform additional checks and wraps information about the command (its ID,…) and the request into a message in text format. The message is sent over the network and received by the server thread of the simulator. The latter distinguishes so called synchronous and asynchronous requests. Asynchronous requests may be issued at any time and normally request information about the simulation without altering the simulation state. Asynchronous requests are handled in the scope of the server thread. Synchronous requests however directly impact the simulation state and must therefore be processed in order. Our breakpoint request is considered as such. Synchronous commands are carried out by the simulator thread which reads the FIFO entries one after another. In case of the breakpoint request, the simulator updates internal data structures accordingly and notifies the successful breakpoint insertion to the server. The server in turn encapsulates the reply into an XML message and sends it over the network. The TTool client subsequently interprets the message and informs the graphical user interface. The latter provides a feedback to the user indicating that the breakpoint has been set successfully. As stated previously, conditional breakpoints are intended to stop the simulation as soon as a condition (a function of task variables) evaluates to true. To deal with this kind of breakpoints, the simulator has to generate a C++ routine first which is subsequently compiled and attached to the process in the form of a dynamic library. This procedure prevents the cumbersome and costly interpretation of conditions at simulation runtime.

Usage Scenario

As a simple example, let us consider an algorithm having two main branches which significantly differ in terms of execution time and resource usage in general. For the performance evaluation of a specific architecture, it would be crucial to try out both alternatives. Hence, the coverage of the simulation should be enhanced. As a first step, the designer could benefit from the various conditional run commands so as to get a more intuitive view of the behavior of the application and the interaction of hardware components. The next step could be to reset the simulation and to set a breakpoint on the branch command which is crucial for the continuation of the simulation. The simulation will stop at the previously defined choice command therefore allowing the user to specify which branch he means to explore. In combination with the feature of capturing simulation states, complex scenarios can be evaluated and meaningful traces be recorded. In our example, the user would certainly save the simulation state when reaching the choice command so that it can be restored to study other alternative executions.

Conclusions and perspectives

In conclusion it can be said that the contribution of this paper is on the one hand the extension of our simulation environment with a module providing an interactive control of the simulation procedure. On the other hand, the new simulation features have been tightly coupled to our integrated development environment TTool so that simulation progress is directly visualized within the UML diagrams representing the application model. Thus, a powerful toolbox is provided to the designer which is helpful when performing Design Space Exploration. It may alleviate considerably the process of

• Debugging applications

• Accessing intermediate simulation results

• Returning to previous system states

• Enhancing the coverage of the simulation by exploring several control flow branches.

Trading off accuracy against model complexity of hardware components will remain subject to our research. For example, instruction cache-misses and data cache-misses have been accounted for by static probabilities so far. Indeed, as algorithmic details are represented by symbolic instructions, the real code of the application is not available thus making state of the art cache models unsuited. Furthermore, the accuracy of bus and memory models shall be validated against a real embedded system. A fair comparison with a real implementation shall therefore reveal whether a set of parameters can be found to limit the inaccuracy to a reasonable percentage. To simplify the modeling of systems making extensive use of DMA engines, a specific UML stereotype could be introduced. This way, the designer would not have to model DMA transfers explicitly using a dedicated execution unit.

In addition to technical improvements of the simulator, future work will also include the automatic exploration of several alternative executions in order to enhance the simulation coverage. The exploration of some control flow branches could be privileged or abandoned based on certain criteria (CPU usage, resource contention, etc). When taking into account different executions, recurring system states should be tracked so as to be able to merge similar simulation runs.

Regarding formal verification, our environment will be enhanced with a refinement process from the application modeling step to the after-mapping step. The objective is to preserve properties proved at application level.

Figure 2 :

 2 Figure 2: Modeling and verification capabilities of TTool

3. 3 Figure 3 :

 33 Figure 3: Layered Architecture of the Simulation Environment

Figure 4 :

 4 Figure 4: Graphical Interface of the Simulation Environment

Figure 5 :

 5 Figure 5: Interaction of the Frontend and the Simulator within the TTool Framework

Figure 6 :Figure 7 :Figure 8 :

 678 Figure 6: Traces in VCD Format

states may be saved and restored

	•	Use of fast simulation and formal static analysis
		techniques, both at application and mapping
		levels
	The designer is supposed to model in an orthogonal
	fashion the application and the architecture of the
	targeted system. Thereafter, a mapping stage
	associates application and architectural components.
	The strength of our approach relies in simulation and
	formal proofs techniques that can be applied to
	modeled systems at all methodological stages. UML
	application models can be simulated with
	respect to the underlying hardware, as opposed
	to state of the art UML model simulators which
	operate on a purely functional level. Feedback from
	the simulation is directly visualized within the
	application model by for instance highlighting the
	currently executed operators. This feature paves the
	way for getting an intuitive insight into the behavior
	of application models on different hardware
	architectures. Simulation The paper is organized in 6 sections. Section 2
	surveys related work in the field of System Level
	Modeling and UML model simulation. Section 3
	elaborates on the DIPLODOCUS methodology and
	its tooling. Section 4 details the simulation strategy
	which is embedded into the development
	environment TTool. Section 5 gives insights into the
	features and the technical realization of the
	interactive simulation environment. Section 6 finally
	concludes the paper and draws perspectives of
	future work.
		•	Clear separation between application and
			architectural matters
		•	Data abstraction

so as to explore several possible executions and branches of non-deterministic decision operators can be explicitly selected by the user. Also, our environment totally hides knowledge of simulation or formal proofs techniques: knowledge of our UML profile is the only asset for engineers. Today, this methodology is supported by an open-source toolkit named TTool

[START_REF] Ttool | the Turtle Toolkit[END_REF]

.

DIPLODOCUS Application _______ _______ _______ TML DIPLODOCUS Architecture _______ _______ _______ TARCHI DIPLODOCUS Mapping

					_______
					_______
					_______
					TMAP	Modeling
	TML Intermediate Format	• •	Blocking Read/Blocking Write (BR-BW) Blocking Read/Non Blocking Write (BR-NBW) TMAP Intermediate Format
				•	Non Blocking Read/Non Blocking Write (NBR-
	_______ _______	_______ _______	_______ _______		_______ NBW) _______	_______ _______
	_______ Simulation code (SystemC, C++)	_______ UPPAAL	_______ LOTOS	_______ Events are characterized by a point-to-point _______ unidirectional asynchronous communication between Simulation code LOTOS (SystemC,
				two tasks. Events are stored in an intermediate FIFO
				between the sender and the receiver. This FIFO may

C++) Verification Bisimulation Static Simulation Library Static Simulation Library