Isabelle Chaduc

Julien Parvole

Tristan Doussineau

Rodolphe Antoine

Anthony Désert

Pierre-Yves Dugas

Serge Ravaine

Etienne Duguet

Elodie Bourgeat-Lami

Muriel Lansalot

Towards a one-step method for preparing silica/polymer heterodimers and dimpled polymer particles

Silica/PS and silica/PMMA heterodimers were obtained in very good yields using 80 nm silica particles first functionalized with a polymerizable alkoxysilane and then used as seeds for the emulsion polymerization of either styrene or methyl methacrylate. Aiming at a one-pot and scalable process, a commercial silica sol was used and the grafting reaction of silica with the functional silane was directly performed in the mixture of surfactants subsequently used for the polymerization. The effect of silica content, nature and concentration of the surfactant, of the reactive alkoxysilane or of the monomer, on the formation of the silica/PS heterodimers was investigated. Either dumbbell-or snowman-like dimers were obtained depending on monomer conversion. The typical morphological yield reached 60% with respect to all morphologies. The synthesis of silica/PMMA dumbbell-like dimers was also successful. In addition to TEM and DLS, the emerging technique of charge detection mass spectrometry (CD-MS) was used to provide the true mass distribution and the sample composition in terms of morphologies. Finally, this system also proved to be efficient for the synthesis of dimpled polymer particles.

Introduction

In recent years many efforts have been devoted to the synthesis of colloidal clusters of spherical particles for both fundamental studies and preparation of new materials. [1][2][3][4] In particular, anisotropic clusters constituted of both organic and inorganic particles have been the topic of many studies and different processes both physicochemical and chemical have been developed and a vast range of morphologies obtained. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] A few years ago we reported a one-pot seeded-growth emulsion polymerization process allowing the nucleation and growth of a controlled number of polystyrene (PS) latex nodules onto the surface of silica seed particles. 20 To promote the affinity between both phases, the surface of the silica seed was previously treated by an alkoxysilane bearing a polymerizable group.

The idea was to promote the capture of the growing chains initiated in water by copolymerizable species located at the surface of the silica seed, and thus favour the nucleation/growth of the polymer nodules onto the seed. According to this strategy various morphologies have been observed such as dumbbell-or snowman-like dimers, 21 and multipod-like clusters. 20,22 Various parameters such as the concentration and nature of the compatibilizing agent, the nature and concentration of the surfactant, the size and concentration of the silica seed or the grafting density of the silane molecules proved to strongly impact the final morphology.

To date, the synthesis of heterodimers (either snowman-or dumbbell-like) has been limited to low monomer conversions and the influence of the experimental conditions on the control of the morphology has not been studied in details. Aiming at a scalable and robust process allowing the formation of a large quantity of dissymmetrical particles in one step, the original process 21 has been modified and improved in many ways. Within this work, a commercial silica sol was used instead of home-made silica seeds. In place of common hydroalcoholic protocols, the grafting reaction was performed directly in water in the presence of the surfactants subsequently used for the emulsion polymerization, providing the opportunity to skip time-consuming steps of separation /redispersion of the silica in water. To improve both the polymerization kinetics and the colloidal features of the polymer nodules (stability and dispersity), an anionic surfactant was added to the non-ionic one used in the initial recipe. Using this new protocol, the effect of various experimental parameters (silica content, nature and concentration of the surfactants, alkoxysilane and monomer) on the formation of silica/PS dimers was investigated. The formation of silica/poly(methyl methacrylate) (PMMA) dimers is also reported for the first time using alkoxysilane-modified seeds. The final silica/polymer dimers were characterized by using conventional transmission electron microscopy (TEM) and dynamic light scattering (DLS) techniques. A very innovative aspect of this work is that the emerging technique of charge detection mass spectrometry (CD-MS) 23 was used as a complementary tool for the characterization of the silica/polymer dimers 24 to clear any doubt about the sample composition in terms of cluster morphology. Finally, this system also revealed to be an efficient strategy for the synthesis of dimpled polymer particles.

Experimental

Materials. Styrene (Sty, 99% from Acros) was purified by passing over a column of basic aluminum oxide. Methyl methacrylate (MMA, 99% from Acros), sodium dodecyl sulfate (SDS, 99% from Aldrich), Synperonic® NP30 (NP30, from Fluka), sodium persulfate (NaPS, 98% from Acros), methacryloxy methyl triethoxysilane (MMS) and methacryloxy propyl dimethyl methoxysilane (MPDMS, 92% from ABCR) were used without further purification. Commercial silica particles (Klebosol 30R50, AZ Electronic Materials, 32 wt%) were first centrifugated at 15 000 rpm for 15 minutes to remove the very small particles (diameter ≤ 50 nm) present in the sample. The number-and mass average particle diameter (D n and D w , respectively) as well as the particle-diameter dispersity (D w /D n ) of the silica seeds after centrifugation were determined from TEM observations (D n,Silica = 80 nm, D w /D n = 1.02). Water was deionized before use (Purelab Classic UV, Elga LabWater). All chemical structures are shown in the Supporting Information (Scheme S1).

Surface modification of the silica seed. The surface of the silica seeds was treated by grafting MMS or MPDMS directly in water. The silane (0.1 function nm -2 ) was added to the silica suspension containing NP30 and/or SDS and the mixture (pH = 8.5) was stirred at room temperature overnight.

Emulsion polymerization.

Styrene or MMA was added to the silane-modified silica suspension. The mixture was introduced in a 250 mL glass thermostated reactor fitted with a condenser and purged with nitrogen under stirring (275 rpm) for 30 min. It was then heated to 70 °C and NaPS (0.5 wt.% relative to the monomers) dissolved in 1 mL of deionized water was added to start the emulsion polymerization. The regular withdrawal of samples allowed us to follow the monomer conversion with time by gravimetric analysis. The various polymerizations performed for this study are presented in Table 1.

Formation of dimpled PS particles.

A polymerization experiment was carried out following a D8-type recipe (run D11, see Table 1), stopped after 35 min (corresponding to 34% styrene conversion). The sample was then gently stirred for one week under nitrogen bubbling. ; Silane: 0.1 function nm -2 ; T = 70 °C. b M stands for monomer. c Global concentration of surfactant (i.e. NP30 + SDS). d For PS, the size of the nodules was determined by TEM, except for run D10

where cryo-TEM images were used. For PMMA, the size of the nodules was determined by cryo-TEM exclusively. Note that the swelling of the PS particles by styrene (run D10) or the swelling of the PMMA particles by MMA (runs D12-D15) likely led to overestimated D n values. e Calculated from the average diameter of the PS nodules obtained by TEM and using equation 1, except for run D10 and runs D12 to D15, where N Latex /N Silica was determined from the manual counting of the number of latex particles and the number of silica particles in the cryo-TEM images, and making the ratio.

Analytical techniques. The latexes (diluted solution deposited on a carbon/formvar-coated copper grid and allowed to evaporate) were observed by transmission electron microscopy (TEM) with a Philips CM120 microscope operating at an accelerating voltage of 80 kV (Centre Technologique des Microstructures (CTµ), plate-forme de l'Université Claude Bernard Lyon 1, Villeurbanne, France). In order to provide a more reliable analysis of particle size and morphology, some selected samples of silica/PS dimers and all silica/PMMA samples were observed in their natural hydrated environment using cryogenic TEM (cryo-TEM). Thin liquid films of the suspensions were deposited onto on 300 Mesh holey carbon films (AgarScientific, UK) and quench-frozen in liquid ethane using a cryo-plunge workstation (made at LPS Orsay). The specimens were then mounted on a precooled Gatan 626 specimen holder, transferred in the microscope and observed as described previously (at an accelerating voltage of 120 kV). The number-and mass-average particle diameter (D n and D w , respectively) as well as the particle-diameter dispersity (D w /D n ) were determined using AnalySIS software (Soft Imaging System).

The number ratio of polymer (PMMA or PS) latex particles to silica particles, N Latex /N Silica , was determined through statistical analysis of the TEM images. Silica and polymer particles show significantly different contrast and can be thus unambiguously identified on the micrographs. However, the procedure for PS was different from that used for PMMA. For the silica/PS dimers, the average diameter of the PS nodules, D n,PS , was determined by TEM and the ratio N Latex /N Silica calculated using equation 1:

N Latex /N Silica = C C ilica d ilica d n, ilica n, (1)
with C Silica and C PS (g L -1 ) the silica and PS concentrations, respectively, d Silica and d PS (g cm -3 ) the silica and PS densities (2.0 and 1.05, respectively), and D n,Silica and D n,PS (nm) are the diameters of the silica and PS particles determined by TEM, respectively. For the silica/PMMA dimers, due to the likely swelling of PMMA particles by residual MMA, the N Latex /N Silica ratio was directly determined from the cryo-TEM images by manually counting the number of latex particles and the number of silica particles in the cryo-TEM images, and making the ratio. The morphological yield was calculated with respect to the total number of morphologies present in the sample (i.e. organic/inorganic particles, free polymer particles and free silica seeds).

Charge detection mass spectrometry (CD-MS) experiments were performed on a custom-built charge detection-mass spectrometer coupled with an electrospray source (ESI). This instrument was described in details in previous works. 25 CD-MS simultaneously and independently measures m/z and z (m is the molar mass and z the number of charges) for individual ions. Highly charged ions, produced by ESI, pass one at a time through a small metal flight tube attached to a charge-sensitive preamplifier that captures their image current. Once frequency-filtered, amplified and shaped, the primary image current signal is characterized by a double-pulse readout signal. The time between the two pulses corresponds to the flight time required for the ion to traverse the length of the pick-up tube and is a function of the m/z ratio of the ion. The amplitude of the signal is proportional to z. A primary advantage of the CD-MS measurement approach is the rate of highly charged individual ions that are analyzed. In such conditions, several thousands of ions can be analyzed individually in less than one minute. Calibration in charge was performed using a test capacitor that allowed a known amount of charge to be pulsed onto the pick-up tube. The test pulses were generated with a shaping-pulse generator so that the time dependent signal response could be determined as well. The charge of a particle was then directly deduced from this calibration and from the average value of the voltage intensity of the two pulses generated by the particle on the detector. Calibration in mass was performed externally using NIST

Results and discussion

The original recipe used for several years for the synthesis of various silica/PS clusters was based on a nonionic surfactant (i.e. (poly(ethylene glycol) nonylphenyl ether, with 30 PEG units -referred to as Synperonic® NP30) used in relatively high concentration (ca. 3 g L -1 ). However, it is well known that nonionic surfactants usually show poor efficiency in terms of nucleation. As a result, complete conversion was rarely observed. 20 In addition, even if well-defined clusters could be obtained at low conversion (typically lower than 30% for 2 h of reaction), the system was contaminated by a secondary nucleation of pure PS particles finding its origin in NP30 molecules originally present in the monomer droplets and progressively released in the medium as the polymerization proceeds. 26 On the other hand, using a pure anionic surfactant such as sodium dodecylsulfate (SDS) led, as expected, to higher monomer conversion but the particle morphology appeared less easy to control. 27 The presence of the non-ionic surfactant indeed seemed to be mandatory and this is likely related to the well-known affinity of poly(ethylene oxide)-based macromolecules for silica surfaces. 28,29 This adsorption probably favors both the localization of monomer molecules owing to the phenyl group of NP30 and the growth of the polymer chains at the surface.

For the synthesis of pure polymer particles, one way to improve the nucleation in non-ionic surfactantbased systems consists in the addition of a few percent of an anionic surfactant such as SDS to the nonionic one. [30][31][32][33] This strategy is widely used in the industry to take advantage of the complementary roles of both types of surfactants. The anionic surfactant will provide efficient nucleation, while the non-ionic one will ensure the stabilization of the latex over a broad range of conditions (stability against freezethaw, shear or in the presence of polyelectrolytes).

We recently showed that the polymerization recipe could be optimized for the synthesis of multipods/silica clusters by the substitution of 5 wt% of NP30 for SDS. 22 In this case, large amounts of either tetrapods or hexapods (i.e. four, respectively six, PS nodules surrounding one silica core) were prepared with yields over 80%. In the present paper, the use of the mixed surfactant system was extended to the synthesis of silica/polymer (either PS or PMMA) dimers with the aim of producing large amounts of materials (at the gram scale). In the original studies, 21 silica/PS dimers were obtained using NP30 as a surfactant and 80 nm silica seeds (10 g L -1 ) obtained by the Stöber process and surfacemodified with MMS with a nominal surface density of 0.1 function nm -2 . MMS grafting was performed in hydroalcoholic media. In the present work, we put a special focus on simplifying the process to allow broad use of this strategy and an easy access to gram-scale products. A commercial aqueous silica dispersion was thus used instead of home-made silica seeds, and MMS grafting was performed directly in water in the presence of NP30 and/or SDS instead of using a water/ethanol mixture requiring further separation/redispersion steps. Therefore, the second role of the surfactant(s) was to help the dispersion of MMS molecules in water. 27

Synthesis of silica/PS heterodimers

A first series of experiments was carried out with various surfactant systems using the 80 nm silica seeds (10 g L -1 ) surface-modified with MMS (0.1 function nm -2 ). Sodium persulfate was used as initiator and various mixtures of NP30/SDS as surfactants (runs D1-D3, Table 1 and Figure 1). As expected, the rate of styrene consumption was greatly increased when SDS was used together with NP30 (run D3), the polymerization being complete in 5 h, while for the same polymerization time only ca. 25% of styrene was converted in the absence of SDS (run D1). In the latter case, secondary nucleation occurred (evidenced by the increase of the polymerization rate at ca. 4.5 h corresponding to the formation of a new crop of particles, and by TEM observations) and the latex was not stable after 2 hours of polymerization. As expected, using pure SDS (run D2) led to even faster polymerization but to the detriment of the morphology control as in this case the nucleation was too efficient (even if the initial SDS concentration was lowered to 2 g L -1 ). An accurate statistical analysis of particle morphologies using TEM images remained quite difficult, the particles being prone to aggregate on the TEM grids. This was actually the case for most of the TEM observations performed throughout this work. The value of the ratio N Latex /N Silica was consequently chosen to discuss the outcomes of an experiment. In the case of run D2 (pure SDS), a few dimers were observed together with a large amount of free PS particles leading to N Latex /N Silica = 3.6 (Figure 2b). The N Latex /N Silica ratio decreased to 2.8 for NP30/SDS 99/1 (wt/wt) with mainly tetrapods and tripods present (Figure 2c). The influence of the NP30/SDS weight ratio (99/1; 98/2; 95/5; 90/10) was also studied (data not shown). A 99/1 ratio appeared as the best compromise between a high polymerization rate and a reduced number of free polymer particles (the proportion of which increased with the SDS fraction). 1 for detailed experimental conditions.

To decrease the N Latex /N Silica ratio, one experiment was then carried out with a higher silica concentration (run D4, [Silica] = 22 g L -1 , Table 1). Indeed, increasing the number of silica seeds while keeping the same amount of styrene was expected to lead to the formation of less PS nodules per silica particle. N Latex /N Silica was effectively decreased to 2.1 with the formation of some dissymmetrical particles, together with a majority of dipods and a few tripods. In addition, the conversion was limited to ca. 30% conversion, the latex becoming quickly unstable, preventing any reliable statistical analysis.

As an increase in silica concentration led to a loss of colloidal stability, another strategy was then envisioned to reduce the number of PS nodules per silica seed (i.e. the amount of tri-and/or tetrapods), consisting in the use of a monofunctional silane, MPDMS, instead of MMS (run D5, see Table 1 and Figure 3). Indeed, for the same initial nominal amount (i.e. 0.1 function nm -2 ), the grafting density was expected to be easier to control with MPDMS as a trifunctional silane such as MMS may react with the silica surface (as expected) but also with other silane molecules. 34 The use of MPDMS effectively led to the formation of fewer particles and the kinetics was consequently slower (data not shown). At the end of the polymerization (i.e. after 4 h corresponding to 87% conversion), the ratio N Latex /N Silica was a) b) c)

effectively reduced to 1.5 and snowman-like dissymmetrical particles with a PS lobe close to 180 nm were observed on TEM pictures with a yield of ca. 60% (red arrows, Figure 3d). However, other morphologies such as dipods or very low amounts of free silica or PS particles were also observed. Note that in both cases dimpled particles corresponding to detached PS nodules could be seen at low monomer-to-polymer conversions (see black arrows in Figure 3a or 3c). These peculiar morphologies are discussed later. Besides the production of these snowman-like silica/PS particles, the production of dumbbells, i.e. with a PS lobe of the same size than the silica one (80 nm), was also envisioned. We thus played with the concentration of both styrene and the surfactants to reduce the size of the PS nodules. First, styrene concentration was divided by 4 (i.e. 25 g L -1 ) keeping the same concentration of surfactants (3 g L -1 ) (run D6, Table 1). The size of the PS nodule was effectively decreased (D n,PS = 57 nm) but the surfactant concentration was too high for this amount of styrene and many free PS particles were formed (N Latex /N Silica = 10) together with multipods-like structures with very small PS lobes (D n,PS = 34 nm). analysis based on 100 particles gave 53% dimers, 8% dipods, less than 1 % tetrapods, and 38% isolated silica spheres. This recipe actually offers the possibility to vary the morphology from mainly snowmanlike (at low and high conversions, silica being initially the largest lobe, and finally the smallest one) to dumbbell-like dimers at an intermediate conversion. With the goal of obtaining the clearest picture of the dispersed state of the system and thus clearing any doubt about the sample composition in terms of cluster morphology, further analyses were undertaken using the emerging technique of charge detection mass spectrometry (CD-MS). 23,24 The CD-MS-based analyses, thanks to the single-ion measuring approach, provide a direct measurement of molar mass distributions along with the charge distributions of nanoparticles. For heterogeneous samples (as in the current case), this technique appears to be efficient to fathom the relative composition of the mixture. 24,35 CD-MS measurements analyze up to several thousand particles and could thus provide a picture of the whole sample complementary to the information brought by TEM. A comparison of both techniques was performed on the sample obtained at medium (20%) and high (77%) conversion for a D8-type recipe (run D10, Table 2). The ion population corresponding to the resulting colloidal clusters was deconvoluted in a sum of several sub-population contributions as described in Experimental Section and illustrated in Figure 6 for the low conversion sample. Both techniques provide a similar analysis of the sample composition at a given styrene conversion time. For instance, at 20 % styrene conversion, proportion of dimers of 52.3 % and 55 % are found in TEM and CD-MS, respectively, thus demonstrating the majority proportion reached for the targeted cluster type.

In addition, both analyses exhibited the same trend while extending the styrene conversion time. The proportion of free silica significantly decreased (from 20 % to 8.5 % in TEM and from 12 % to 2 % in CD-MS) and the proportion of dipods and tripods increased slightly relatively to that of dimers.

a) 8% conversion b) 25% conversion c) 82%conversion

Synthesis of silica/PMMA heterodimers

To show the versatility of our synthetic strategy, the formation of silica/PMMA dimers was also undertaken. Such heterodimers were recently obtained in our group using a new and different strategy which relies on the adsorption of a bicationic initiator on the silica surface, 36 and both snowman-and dumbbell-like silica/polymer clusters were obtained through emulsion polymerization of MMA or styrene. The first experiment was carried out using experimental conditions similar to those adopted for styrene, targeting low conversion to reach dumbbell-like morphologies (run D12, Table 1). Due to the higher water solubility and reactivity of MMA leading to a more efficient nucleation, the number of free PMMA particles was higher than expected (N Latex /N Silica = 1.9). The concentration of silica was thus increased to 20 g L -1 (run D13) and then to 30 g L -1 (run D14). In both cases the N Latex /N Silica ratio was effectively lowered, reaching 1.3 in the latter case (Table 1). This ratio could not be decreased further, higher silica concentration leading to colloidal stability issues. Many dimers could be clearly observed by cryo-TEM in run D14 (Figure 7), statistical analyses indicating 47% of dimers, 35% of dipods, 2% of tripods, 2% of free PMMA particles and 14% of free silica particles. Both statistical analyses of TEM images and CD-MS measurements were performed on a D14-type recipe (run D15). The data shown in Table 2 again indicate a relatively good agreement between the two techniques, with however significant differences in the case of tripods (Figure S3). Table 1 for detailed experimental conditions. Arrows point at some of the dimers.

Formation of dimpled polymer particles

One very interesting phenomenon was observed with the samples containing residual styrene. As evidenced by the TEM images of run D8 at low conversion (Figure 3a and3c), the link between the silica and PS lobes seems to be quite weak as free dimpled PS particles could be observed. In order to manipulate these objects, we tried to remove styrene by gentle stirring under nitrogen bubbling of the dispersion containing dumbbell-like morphologies (run D11, 25% conversion). The latex became unstable and a phase separation occurred after 4 days. Whereas the bottom layer was essentially constituted of silica particles, TEM observation of the top layer (Figure 8) showed the presence of free dimpled PS particles, which took off from the silica surface. This separation of the PS nodule from the silica seed is very likely related to weak adhesion forces, essentially secured by a few PS chains covalently bonded to the silica surface and directly dependent on the low grafting density of the copolymerizable silane. Besides, these polymer chains should be quite mobile in the context of a polymer nodule swollen with unreacted monomer (25% conversion), promoting their disentanglement from the PS nodule ones. This makes the assembly silica seed/PS nodule quite fragile with regard to shear stress as potentially occurring during mechanical stirring or centrifugation stage. On the other hand, the presence of a notch on the PS particles is objective evidence that particle growth occurred at the silica surface. Occasionally, PS particles with two dimples, originating from dipods silica/PS clusters could be observed. Dimpled particles are a very interesting class of colloidal objects which can be used as building block in various architectures such as new colloidal molecules or low-symmetry photonic crystals. [37][38][39][40][41] In comparison with the strategies depicted in the literature, our synthetic approach is very simple and already efficient at the gram scale; nevertheless it is restricted to the fabrication of polymer particles mainly bearing a single circular notch.

Conclusions

Silica/PS heterodimers have been successfully obtained by emulsion polymerization using silica seeds pre-functionalized by a reactive silane. Aiming at a scalable and robust process allowing the formation of large amounts of dimers, a commercial silica sol was used, and the silane grafting reaction was successfully performed directly in the mixture of surfactants subsequently used for the polymerization instead of in alcoholic media, thus avoiding time-consuming purification steps. The influence of various experimental parameters (silica content, nature and concentration of both the surfactant and the alkoxysilane) on the formation of silica/PS dimers was investigated. A fine tuning of the silica, styrene and surfactants concentrations using the monofunctional silane MDPMS led to the formation of either dumbbell-or snowman-like dimers, depending on monomer conversion. The typical morphological yield reached 60% with respect to all the morphologies present in the sample. The synthesis of silica/PMMA dumbbell-like dimers was also successful. For both types of heterodimers, CD-MS revealed to be a powerful technique for the characterization of the silica/polymer clusters, complementary to and in good agreement with TEM analyses. This emerging technique provided the true mass distribution and consequently the cluster composition in terms of morphologies, thus clearing any doubt about the clusters' structure. Finally, this system also proved to be an efficient way to access to dimpled polymer particles.

  traceable size standards (70, 100, 150, 200, 250, 300, 350, 400, 450 and 500 nm PS nanospheres supplied by Polysciences Europe GmbH). Aqueous mother solutions of dimer samples were diluted in H 2 O/MeOH = 1:1 solvent mixture at concentration around 10 14 objects L -1 before injection to the ESI source. Mass histograms are built from the collection of a statistically relevant number N of single mass measurement for each sample (N > 5000 typically). Samples are a mixture of free polymer particles (PS or PMMA), free silica particles, dimers, bipods, and tripods. The experimental mass histograms are thus fitted with multiple LogNormal distribution fit functions, each corresponding to the individual contribution of free polymer particles, free silica particles, dimers, bipods, and tripods to the overall mass distribution. First, the mass distribution of primary free silica seed particles were measured by CD-MS, from which we extracted parameters xc(silica) and w(silica) of LogNormal function (FigureS1).Mean masses of polymer nodules (xc(pol)) were calculated on the basis of the diameter of the objects as determined by TEM and assuming perfectly spherical geometry and densities of 1.05 and 1.19 for PS and PMMA, respectively. These measured and calculated parameters were then combined as a basis for fixing the xc fit parameters for dimers, bipods, and tripods contributions (xc(dim), xc(bipods), and xc(tripods)). Finally the weight of each contribution was modulated to best fit the experimental distribution (Figures6, S2 and S3).

Figure 2 :

 2 Figure 2: TEM images of the silica/PS latexes obtained for different surfactant systems in the synthesis of silica/PS heterodimers: a) NP30 (run D1, time = 1 h, before destabilization), b) SDS (run D2, time = 3 h) and c) NP30/SDS (99/1 wt/wt, run D3, time = 2 h). SeeTable 1 for detailed experimental conditions.

Figure 3 :

 3 Figure 3: TEM images of the silica/PS latexes obtained using different silanes. MMS (run D3): (a) 20 min, 12% conversion, (b) 2h, 83% conversion; and MPDMS (run D5): (c) 20 min, 6% conversion, (d) 4h, 87% conversion. See Table1for detailed experimental conditions. In images a) and c), arrows point to the PS dimpled particles. In image d), red arrows point to the silica/PS snowman-like particles.

Figure 5 :

 5 Figure 5: Cryo-TEM images showing the evolution of particle morphology with conversion for the synthesis of silica/PS dimers using a D8-type recipe (run D9, see Table 1 for detailed experimental conditions): a) 8% conversion: D n,PS = 64 nm, D w /D n = 1.04, b) 25% conversion, D n,PS = 90 nm, D w /D n = 1.05, c) 82% conversion, D n,PS = 127 nm, D w /D n = 1.05.

Figure 7 :

 7 Figure 7: Cryo-TEM image of the silica/PMMA latex obtained using 30 g L -1 of silica (run D14, 13% conversion). See

Figure 8 :

 8 Figure 8: TEM images of the PS particles obtained after one week of gentle stirring (run D11, seeTable 1 for detailed experimental conditions). Only the supernatant was analyzed.

Table 1 :

 1 One-pot seeded-growth emulsion polymerization of styrene or MMA using silane-functionalized silica seeds a

Run a [M] g L -1 b NP30/SDS (w/w) [Surf] g L -1 c Silane [Silica] g L -1 Time (h) Conv (%) D n,PS or PMMA (nm) d D w /D n N Latex / N Silica e Styrene emulsion polymerization

	D1	100	100/0	3	MMS	10	2	18	103	1.12	1.8
	D2	100	0/100	2	MMS	10	3	93	65	1.10	3.6
	D3	100	99/1	3	MMS	10	5	94	144	1.02	2.8
	D4	100	99/1	3	MMS	22	5	32	94	1.03	2.1
	D5	100	99/1	3	MPDMS	10	4	87	179	1.04	1.5
	D6	25	99/1	3	MPDMS	10	3	90	57	1.22	10
	D7	25	99/1	1.5 MPDMS	10	3	91	103	1.02	2.3
	D8	25	99/1	0.75 MPDMS	10	3	79	121	1.02	1.1
								0.1	8	64	1.04	0.8
	D9	25	99/1	0.75 MPDMS	10	0.5	25	90	1.05	1.0
								3.0	82	127	1.05	1.0
	D10	25	99/1	0.75 MPDMS	10	0.5 3.0	20 77	82 115	1.05 1.08	1.0 1.2
	D11	25	99/1	0.75 MPDMS	10	0.6	34	91	1.01	0.9
					MMA emulsion polymerization
	D12	100	99/1	3	MPDMS	10	10	15	101	1.02	1.9
	D13	100	99/1	3	MPDMS	20	10	20	108	1.02	1.5
	D14	100	99/1	3	MPDMS	30	10	13	73	1.02	1.3
	D15	100	99/1	3	MPDMS	30	10	20	84	1.06	1.1
	a All experiments were carried out with [NaPS] = 0.5 g L	-1

Table 2 :

 2 Proportion of the different morphologies encountered in the silica/PS heterodimers batch (run D10) and in the silica/PMMA heterodimers batch (run D15) as determined by TEM and CD-MS Mass distribution of silica/PS dimers sample measured by CDMS (black edged circles) at 20% monomer conversion (t = 30 min). The blue line corresponds to the possible contribution of free silica particles to the overall distribution, green lines are contributions of free PS particle, dimers, dipods, and tripods, respectively, while the red line is the sum of all the contributions.

	a

Table 1

 1

for detailed experimental conditions). Only the supernatant was analyzed.

nm

Acknowledgements

The support of the Agence Nationale pour la Recherche is gratefully acknowledged (ToCoMo projectcontract # ANR-07-BLAN-0271; PONAME project -contract # ANR-11-PDOC-032-01).

Consequently, the surfactant concentration was reduced to 1.5 g L -1 (run D7, Table 1) and finally to 0.75 g L -1 (run D8, Table 1) which effectively induced in both cases a lower number of particles nucleated (N Latex /N Silica = 2.3 and 1.1, respectively) and consequently a higher diameter for the PS lobe (D n,PS = 103 nm and 121 nm, respectively, Table 1 and Figure 4). Again, an accurate statistical analysis of the TEM pictures remained quite difficult, the particles being prone to aggregation on the TEM grids. The size of the PS lobe in run D8 (N Latex /N Silica = 1.1) was higher than targeted but it is worth mentioning that the monomer conversion remained quite high (79%). (run D8). See Table 1 for detailed experimental conditions. Arrows point to the silica/PS dissymmetrical particles.

In all the recipes presented so far the obtained dimers showed a snowman-like morphology at high conversion, the PS lobe being systematically bigger than the silica seed. To obtain dumbbell-like dimers one strategy consists in quenching the polymerization when the PS lobe is close to 80 nm. To determine the moment when this size was reached, the evolution of particle morphology was monitored as a function of conversion for a D8-type recipe (run D9, Figure 5). To provide a more reliable analysis of particle morphology, the hybrid particles were observed by cryo-TEM in their hydrated environment. As expected, the size of the PS lobe increased with conversion, and dumbbell-like particles were obtained after 30 min corresponding to 25% conversion (D n,PS = 90 nm, D w /D n = 1.05). In this case, a statistical


Dr Benjamin H Wilson
email: ben.wilson@ul.ie

Macdiarmid

Dr J.-L Liu

Prof C Mathonière

Dr R Clérac
email: clerac@crpp-bordeaux.cnrs.fr

Single-Molecule Magnetism Self-Assembly Synthesis of a [2]Catenane Co II Single-Molecule Magnet

Keywords: Catenane, Coordination Chemistry, Mechanically Interlocked Molecules, Single Molecule Magnetism, Supramolecular Chemistry

We describe herein the self-assembly synthesis of an octanuclear Co II [2]catenane {[Co 4 (H 2 L) 6 ] 2 16 + } formed by the mechanical interlocking of two {[Co 4 (H 2 L) 6 ] 8 + } rectangles of unprecedented topology. Subtle manipulation of the synthetic conditions allows the isolation of a mixed-valence [Co 2 III / Co 2 II ] 10 + non-catenated rectangle. The Co II centers in the [2]catenane exhibit slow relaxation of their magnetic moment, i. e. single-molecule magnet properties, dominated by quantum tunneling and Raman relaxation processes. This work shows that metallo-supramolecular chemistry can precisely control the organization of single-molecule magnets in topologically complex arrangements.

The synthesis of mechanically interlocked molecules has long been the pique of supramolecular chemists. Since Sauvage and co-workers pioneered the template-assisted synthesis of aesthetically appealing interlocked molecules, [1] many variations of catenanes, rotaxanes, and knots have been reported. [2] A driving force behind this research centers upon the application of these interlocked assemblies as nano-scale molecular machines. [3,4] Innovative work by Fujita and co-workers established the use of metal-ligand self-assembly to produce so-called "magic ring" catenanes: two metallocycles which spontaneously catenate under specific conditions. This approach allows for the one-pot synthesis of metallo-catenanes [START_REF]Co3 Atoms Distance (Å) Atoms Angle (°) Atoms Angle[END_REF] and more recently catenanes based on interlocking 2 × 2 grids [6] among other types of metallo-supramolecular structures. [START_REF]Co4 Atoms Distance (Å) Atoms Angle (°) Atoms Angle[END_REF] Further, Leigh and co-workers have adapted the approach to form metallosupramolecular grids which act as templates [8] for the synthesis of topologically complex molecular knots. [9] The incorporation of transition-metal ions into mechanically interlocked assemblies enables the introduction of additional properties into the super-structure such as redox, luminescence and magnetism. The latter is of particular interest as some transition-metal ions in metallosupramolecular assemblies can display slow paramagnetic relaxation to yield single-molecule magnets (SMMs). [10,11] Research in the field of SMMs is prolific and stimulated by the potential application of these molecules in nanoscale data storage and spintronic devices. [12][13][14] A sub-class of these materials is known as mononuclear SMMs, for which the slow relaxation of magnetization is intrinsic to a single metal ion in a complex and not due to magnetically coupled spin systems. Co II has emerged as one of the key 3d metal ions for generating SMM assemblies as it possesses high magnetic anisotropy, which favors thermally activated relaxation of the magnetization. [15] Interestingly, Winpenny and co-workers exploited the ring architecture of a polymetallic inorganic macrocycle to synthesize mechanically interlocked molecules to form rotaxane structures, which behaved as molecular electron spin qubits. [16] More recently they extended these to more complex mechanically interlocked arrays such as daisy-chains, [17] interlocked double chains [18] and [2]rotaxanes as ligands. [19] By using mechanically interlocked systems with intricate topologies, many SMM active centers can be specifically arranged in complex arrays. Herein, we report the use of a rigid ditopic ligand bearing 3-(2-pyridyl)-1,2,4-triazole coordinating motifs which, upon complexation with Co II ions, generates a catenated metallosupramolecular assembly. This catenated structure exhibits slow magnetization dynamics intrinsic to the individual Co II sites and is the first catenane to exhibit SMM behavior.

The 1,2-bis(5-(2-pyridyl)-4H-1,2,4-triazol-3-yl)-benzene ligand, H 2 L, (Figure 1) was synthesized following literature procedures [20] (see the Supporting Information) and is relatively insoluble in all common laboratory solvents. However, a solution could be obtained in the presence of a metal salt. The addition of two equivalents of cobalt(II) perchlorate to a stirred suspension of three equivalents of H 2 L in nitromethane resulted in an orange solution after gentle heating (50 °C) for several hours. Addition of an aqueous solution of lithium bromide, followed by vapor diffusion of chloroform to the nitromethane solution over a period of two days, yielded orange lozenge-shaped crystals of {[Co 4 (H 2 L) 6 ] 2 16 + }, 1, suitable for a single-crystal X-ray diffraction study (Figure 2).

The diffraction data collected at 120 K was solved and refined in the tetragonal space group I4 1 /a (Table S1). The asymmetric unit is comprised of two octahedral Co II centers and three H 2 L ligands (Figure S3). Two ligands coordinate to the Co II centers in a bidentate fashion via the pyridine nitrogen atom and the N-2 nitrogen atom of the triazole ring. The third ligand coordinates via the pyridine nitrogen atom and the N-4 nitrogen atom of the triazole ring (Figure S2). The Co N bond lengths and corresponding N Co N bond angles are indicative of high-spin Co II centers, which are noticeably distorted from idealized octahedral symmetry as evidenced by the octahedral distortion parameters (Table S2). [21] The action of a 2-fold rotation generates a {[Co 4 (H 2 L) 6 ] 8 + } molecular rectangle of unique topology. [22] Two sides of the rectangle are made up of two ligands with twisted conformation which π-π stack to form a "double pillar" and bridge two Co II centers (Figures 2 andS4). The remaining two sides of the rectangle are made up of a single ligand strand bridging two Co II centers. These ligands adopt a trans-conformation where the two bidentate binding sites are oriented in opposite directions (Figures 2, S2 and S3). The Co…Co separations on the double pillared sides of the rectangle are shorter (ca. 10.9 Å) than those on the sides with the single ligand strand (ca. 14.0 Å). A symmetrically equivalent rectangle is generated by the action of a 4-fold roto-inversion parallel to the crystallographic c axis. The two symmetry-equivalent rectangles mechanically interlink to form a [2] andS6). The overall + 16 charge of the [2]catenane is compensated by nine bromide and seven perchlorate anions, many of which exhibit significant disorder and are modelled as partial occupancy. A cavity is formed inside the [2]catenane and is occupied by a bromide anion which is disordered equally over four positions. The triazole N H moieties of H 2 L orient into the cavity of the catenane and interact with the bromide anions via (N)H•••Br hydrogen bonds (Figure S6). Crystals of 1 did not form in the absence of bromide potentially indicating its templating role in the formation of the [2]catenane. Further hydrogen-bonding interactions are evident about the periphery of 1 and throughout the crystal lattice (Figures S7, S8 and Table S3).

The electrospray mass spectrum of crystals of 1 redissolved in acetonitrile showed a peak corresponding to a non-catenated structure {(Co 4 (H 2 L) 6 )-5H} 3 + , 2. The occurrence of smaller peaks evenly spaced between the main peaks corresponding to this non-catenated structure indicates the occurrence of a minor species with a + 6 charge. This can be attributed to the catenated structure {(Co 4 -(H 2 L) 6 ) 2 -10H} 6 + , (Figure S1). This result indicates that in solution, under the conditions of the mass-spectrometry experiment, a non-catenated structure is present. Indeed, the coordination of the triazole rings results in the N H hydrogen atoms being sufficiently acidic that they are lost during the ionization process to minimize the charge density of the complex. Much effort was made to isolate this noncatenated species and success was finally achieved when the nitromethane solution of 1 was spiked with 50 μL of mxylene and subsequent vapor diffusion of chloroform. After several days, orange lozenge-shaped crystals of 1 formed, and after several weeks, orange plate crystals grew on top of the previously formed crystals. Single-crystal X-ray diffraction revealed that the orange plate crystals were a noncatenated complex, {[Co 4 (H 2 L) 6 ] n + }, 2 (Figure S9). Crystals of 2 only ever formed as a minor product in the presence of 1, so bulk phase analysis on 2 was not possible.

Complex 2 crystallized in the monoclinic space group P2 1 /c (Table S1). The asymmetric unit contains a complete tetranuclear cobalt complex, which now forms a square motif, along with a multitude of disordered bromide, perchlorate anions and solvents of crystallization (Figure S9). As with the structure of 1, two pyridyl-1,2,4-triazole motifs coordinate via the N-2 nitrogen atom of the triazole, while the third coordinates via the N-4 nitrogen atom. From consideration of the bond lengths and angles about each cobalt center, it is best concluded that Co(1) and Co(3) are Co III , whereas Co(2) and Co( 4) are Co II (Table S4), with oxidation most likely occurring during the prolonged crystallization time. Unlike 1, the single ligand stranded sides of 2 feature the ligands now coordinating in synfashion, with the bidentate binding sites orientated in the same direction (Figures S2 andS9). The ligands of the double pillared sides in 2 are arranged similarly to those of 1 and are stabilized by π-π stacking interactions. Ligand coordination in 2 results in a more compacted structure with the four Co centers arranged in a distorted square topology (Figure S10). The Co…Co separations on the double pillared sides of the square are comparable to those in 1 (ca. 10.7 Å), whereas those on the sides with the single ligand stranded sides are considerably shorter (ca. 10.3 Å). This ca. 4 Å shortening reduces the size of the cavity and its aperture, and does not permit the formation of a [2] catenane. The cavity contains disordered partial occupancy bromide and perchlorate anions. Two bromide anions hydrogen bond to triazole N H moieties, on the ligands that make up the inner strands of the rectangle, in a bridging manner (Figure S12). Three of the peripheral triazole protons hydrogen bond to bromide and perchlorate anions with (N)H•••A (Figure S12, Table S5). The squares pack closely together, stabilized by π-π stacking interactions between the pyridine ring of one ligand and the central phenyl spacer of another (Figure S13).

Isolated Co II centers have shown promise as candidates for SMM properties. Therefore, an in-depth analysis of the magnetic behavior was carried out. Magnetic measurements were performed on polycrystalline samples of 1, first frozen in its mother liquor and then subsequently dried (see Supporting Information for specific experimental details; Figures 3 andS14). As both sets of measurements were virtually identical, the magnetic data shown herein are those collected on the dried sample. The χT product at 250 K is slightly higher (15.5 cm 3 K mol 1 ) than what is expected for eight magnetically isolated S = 3/2 spin centers (15 cm 3 K mol 1 ), indicating a small orbital contribution to the magnetic moment of the Co II centers. The gradual decrease of the χT product from 200 K suggests the depopulation of low-lying excited states. This could be attributed to either the magnetic anisotropy of the spin carriers or antiferromagnetic interactions between the Co II centers. When considering the large separations between the Co II centers in the catenane, the magnetic coupling is expected to be negligible. The decrease in the χT product can therefore be attributed to the intrinsic magnetic anisotropy of the Co II sites. The isothermal dc field (H) dependence of the magnetization (M) up to 7 T was measured below 8 K (inset Figure 3 and Figure S14). Saturation is not reached at 1.85 K, even with an applied field of 7 T, with a measured magnetization of 12.7 μ B . This is approximately half of the theoretical saturation of magnetization of 24 μ B for eight isolated S = 3/2 spin-only centers (g = 2.0).

This result in conjunction with the non-superposition of the M vs. HT 1 curves (Figure S14) confirms the presence of a large magnetic anisotropy as expected for Co II 4) cm 1 ( 86.6(6) K; Figure 3). The magnetization dynamics and the possible presence of SMM behavior in 1 was probed by ac magnetic susceptibility measurements. At 1.9 K and in the absence of a dc field, the in-phase ac susceptibility (χ') is frequency independent up to 10 kHz in agreement with the absence of an out-of-phase component (χ''). Upon application of a dc field, an out-ofphase signal is detected, and both components exhibit frequency and temperature dependent behavior. This verifies that 1 displays a slow relaxation of its magnetic moment and can therefore be regarded as a SMM (Figures S15-S18).

The field dependence at 1.9 K (Figure S15) and the temperature dependence at 1000 Oe (Figure S17) of the ac susceptibility were thoroughly studied. The corresponding χ' vs. ν and χ'' vs. ν data were fit to a generalized Debye model [23] in order to extract the field dependence (at 1.9 K) and the temperature dependence (at 1000 Oe) of the relaxation time, τ (Figure 4; as well as all the other parameters of the generalized Debye model: [23] α, ν, χ 0 ', χ 1 ' and χ 0 ' χ 1 '; Figures S16 andS18). The estimated standard deviations (ESD) of the relaxation time (vertical solid bars in Figure 4) calculated from the α parameter (which quantify the broadness of the relaxation time distribution) [23,24] are immediately informative on the necessary caution that should be taken when analyzing these variations.

Four main mechanisms, which include quantum tunneling of the magnetization (QTM), [11a,c] thermally activated (i.e. Arrhenius), [11c, 12a, 25] Raman [25,26] and direct [26] relaxation processes, are usually involved in the paramagnetic relaxation. The relaxation rate (τ 1 ) can be then summarized by Equations ( 1) and ( 2), which contain four corresponding terms, which have their own temperature and dc-field dependence:

t 1 à t 1 Raman á t 1 Direct á t 1 Arrhenius á t 1 QTM (1) t 1 à C 1 á C 1 H 2 1 á C 2 H 2 T n á ATH 4 át 1 0 exp D k B T ✓ ◆ á B 1 1 á B 2 H 2 (2)
The field dependence of the relaxation time (left part of Figure 4) exhibits an increase between 0 and 1000 Oe, compatible with either QTM or Raman (with C 2 > C 1 ) mechanisms. At higher fields, a decrease is observed with an H 3 variation above 5000 Oe, which is not perfectly compatible with either a direct relaxation (H 4 ) or a Raman mechanism (H 2 with C 2 ! C 1 ). Thus, the τ vs. H and τ vs. T data shown in Figures 4 andS20 have been fitted by two simple models including i) Raman and direct and ii) QTM and Raman processes. Considering the ESD of the relaxation time, additional processes were not necessary to provide a satisfactory agreement between the theory and experimental data. It is worth mentioning that above 4 K, the ln(τ) vs. T 1 plot (Figure S19) experiences a linear variation, which could be compatible with a thermally activated Orbach relaxation process (with a pre-exponential factor, τ 0 , of 1.6(5) × 10 6 s and an energy gap of 12(2) K). However, the energy gap between ⌃ 1/2 and ⌃ 3/2 states estimated by fitting of dc magnetic data should be 2D/k B ⇡ 173 K, which is an order of magnitude higher than the above estimated energy gap. This suggests that the observed relaxation cannot be influenced by an Orbach process in the explored temperature window. The relaxation time of 1 is reproduced well by the two relaxation models with a slightly better agreement at low fields when Raman and direct relaxation processes are considered (Figures 4 andS20; with B 1 = 7199(500) s 1 , B 2 = 695(200) T 2 , C = 628(88) K 2.7 s 1 , C 1 = 13(5) T 2 and C 2 = 0.05(5) T 2 and n = 2.7( 5)). It is necessary to underline that the presence of other relaxation processes cannot be excluded in 1 but the experimental ac data do not allow for their detection. Therefore, the present analysis of the relaxation time should be taken with caution even if it suggests that the observed SMM properties in 1 are originating mainly from Raman and direct processes.

The aforementioned results demonstrate an exciting new method in which SMM behavior can be incorporated into mechanically interlocked molecules. The [2]catenane structure reported is the first such example based on an {[Co 4 -(H 2 L) 6 ] 8 + } rectangle complex of an unprecedented topology and exemplifies the importance of understanding weak supramolecular interactions for the synthesis of selfassembled mechanically interlocked molecules. Furthermore, the structure can also exist as the non-interlocked square as shown by the isolation of the non-catenated square structure, 2. Combined dc and ac magnetic susceptibility measurements revealed that 1 displayed slow relaxation of magnetization and therefore behaves as a SMM. Such behavior demonstrates a proof of concept for the arrangement of multiple SMM centers into a complex topology by exploiting metallo-supramolecular mechanically interlocked systems. This may provide an important step in the synthesis of magnetically active molecular machines. S18) and the lognormal distribution as described in reference [24]. The solid red lines are the best fit discussed in the text.

X-Ray Crystallography

General Information

The structural analysis at 120 K was performed on an Agilent dual wavelength SuperNova with monochromated Cu-Kα (λ = 1.54178 Å) or Mo-Kα (λ = 0.70926 Å) radiation. CrysAlisPro was used for the data collection and data processing. S2 The structure was solved using intrinsic phasing with SHELXT S3 and refined on Olex2 S4 using all data by full matrix least-squares procedures with SHELXL. S5 Multi-scan absorption correction using SCALE3 ABSPACK. S6 Hydrogen atoms were included in calculated positions with isotropic displacement parameters 1.2 times the isotropic equivalent of their carrier atoms. For both 1 and 2, no sensible disorder model could be found for the large number of solvent molecules present in each structure. Therefore, the SQUEEZE S7 function of PLATON S8 was applied. Structures were deposited in the Cambridge Structure Database (CCDC 2098246-2098247).

Specific Refinement Details

[Co4(H2L)4]2Br9[ClO4]7 (1)

The single crystals employed immediately began to desolvate after removal from the mother liquor. Swift (<15 sec) handling prior to quenching in the cryostream was required to collect good quality data. The high-resolution data was observed to rapidly fall off, an expected consequence of the supramolecular nature of 1 and the large amount of void space it possessed. Therefore, the completeness of the outer data was less than ideal. Nevertheless, the quality of the data is more than sufficient to establish the identity of the structure. The asymmetric unit contained a quarter of a molecule of the [Co4(H2L)6]2 complex. The bromide and perchlorate anions were found to be disordered with partial occupancies over multiple positions, with the perchlorates requiring thermal parameter restraints to sensibly model. Several AFIX constraints, in conjunction with thermal parameter restraints, were necessary to model the heterocycles in the framework. Due to the rapid desolvation of the complex, the highly disordered solvates could not be adequately identified or modelled and the electron density of which were accounted for using the SQUEEZE routine in PLATON, where the program identified solvent accessible voids totalling 9786.5 Å 3 and 3116.4 electrons per unit cell were recovered.

[Co4(H2L)4]Br4[ClO4]4 2+ (2)
Much like 1, the single crystals employed immediately began to desolvate after removal from the mother liquor. Swift (<15 sec) handling prior to quenching in the cryostream was required to collect good quality data. The highresolution data was observed to rapidly fall off, an expected consequence of the supramolecular nature of 2 and the large amount of void space it possessed, therefore the completeness of the outer data was less than ideal. Nevertheless, the quality of the data is more than sufficient to establish the identity of the structure. The asymmetric unit contained one molecule of the [Co4(H2L)6] complex. The bromide and perchlorate anions were found to be disordered with partial occupancies over multiple positions, with the perchlorates requiring thermal parameter restraints (and in two instances, thermal parameter constraints) to sensibly model. The bond lengths about Co1 and Co3 indicate that they are Co 3+ while Co2 and Co4 are Co 2+ . Due to the large void space resulting in significant disorder of the anions and solvent molecules, the remaining two anions cannot be accurately located and were therefore not modelled. To successfully model the heterocycles of the framework, thermal parameter restraints were applied. The highly disordered solvates could not be adequately identified or modelled and the electron density of which were accounted for using the SQUEEZE routine in PLATON, where the program identified solvent accessible voids totalling 5128.4 Å 3 and 1994.7 electrons per unit cell were recovered. Table S3. Hydrogen bonding parameters for 1. Table S5. Hydrogen bonding parameters for 2.

D-H•

D-H•

••A d(D-H) Å d(D-H•••A) Å d(D•••A) Å <(D-H•••A) ° Symmetry Code N31-H31•••Br7 0.

Magnetic Measurements General Information

Magnetic susceptibility measurements were performed on a Quantum Design SQUID MPMS-XL magnetometer and PPMS-9 susceptometer housed at the Centre de Recherche Paul Pascal at temperatures between 1.8 and 270 K and dc magnetic fields ranging from -7 to +7 T. The ac magnetic susceptibility measurements were performed in an oscillating ac field of 1 to 6 Oe with frequencies between 10 and 10000 Hz and various dc fields (including zero). The measurements were carried out on a freshly-filtered polycrystalline sample of 1 (10.75 mg) suspended in mineral oil and introduced in a sealed polyethylene bag (3 ´ 0.5 ´ 0.02 cm; 21.22 mg). A second polycrystalline sample of 1 (13.28 mg) covered and restrained in a minimum amount of frozen mother liquor within a sealed straw, was also measured for comparison. No evaporation of the mother liquor was observed during the measurement. The mass of the sample was estimated at 13.28 mg after the measurements and after the mother liquor removal/evaporation in air. The measurements on these two samples were found to be virtually identical and thus the extended set of data collected for the freshly-filtered polycrystalline sample are shown in this manuscript. Prior to the experiments, the field-dependent magnetization was measured at 100 K on each sample to exclude the presence of bulk ferromagnetic impurities. In fact, paramagnetic or diamagnetic materials should exhibit a perfectly linear dependence of the magnetization that extrapolates to zero at zero dc field; the samples appeared to be free of any ferromagnetic impurities. The magnetic susceptibilities were corrected for the sample holder, the mineral oil and the intrinsic diamagnetic contributions. -S23-

  catenane, {[Co 4 -(H 2 L) 6 ] 2 16 + }, such that the double pillared sides of one rectangle occupy the cavity of the other (Figures 1, S5 and S6). The interlinking of two {[Co 4 (H 2 L) 6 ] 8 + } rectangles is supported by a plethora of π-π stacking and edge-to-face (C)H•••π interactions (Figures S4, S5

Figure 2 .

 2 Figure 2. a) Single-crystal X-ray structure of 1 showing a single {[Co 4 (H 2 L) 6 ] 8 + } rectangle. The double pillared sides are bridged by two H 2 L ligands (left/right) while the single pillared sides are bridged by a single H 2 L ligand (top/bottom). b) Structure of the [2]catenane {[Co 4 (H 2 L) 6 ] 2 16 + } showing an encapsulated bromide anion disordered over four-positions. c) Space-filling representation of the [2]catenane {[Co 4 (H 2 L) 6 ] 2 16 + } showing the two interlinked {[Co 4 (H 2 L) 6 ] 8 + } rectangles (blue and red) with an encapsulated bromide anion disordered over four-positions. Selected anions and solvent molecules omitted for clarity; cobalt = purple, carbon = grey, nitrogen = pale blue, bromide = orange.

  -based complexes. The χT vs. T and M vs. H data can be simultaneously fitted with the phenomenological Hamiltonian as follows b H à D b S z 2 á gm B b SH, resulting in an isotropic g value of 2.06(1) and an axial zero-field splitting parameter, D/hc = 60.2(

Figure 3 .

 3 Figure3. Temperature dependence of the χT product (where χ is the molar magnetic susceptibility that equals M/H per complex, and T the temperature) collected in an applied dc magnetic field of 0.1 T for 1. Inset: Field dependence of the magnetization for 1 below 8 K. The solid lines are the best fits to the model described in the text.

Figure 4 .

 4 Figure 4. Field (left) and temperature (right) dependence of the relaxation time for 1 estimated from the generalized Debye fits of the ac susceptibility data shown in Figures S15 and S17. The ESD of the relaxation time (vertical solid bars) have been calculated from the α parameters of the generalized Debye fit (Figures S15-S18) and the lognormal distribution as described in reference[24]. The solid red lines are the best fit discussed in the text.

Figure S1 .

 S1 Figure S1. HR-ESI Mass spectrum of 1 corresponding to {(Co4(H2L)6)-5H} 3+ (non-catenated structure) and {(Co8(H2L)12)-10H} 6+ (catenated structure). The top spectrum is the experimentally measured while the middle is the calculated spectrum for the non-catenated structure and the bottom is the calculated spectrum for the catenated structure. The rectangle and catenane peaks overlap to produce a superimposed set of peaks that are observed experimentally.

Figure S2 .

 S2 Figure S2. (Left) Numbering scheme of the 3-pyridyl-1,2,4-triazole ligands used in the following discussion. Four possible tautomers can occur, two of which facilitate chelation of the metal center via the pyridyl nitrogen and N-2 of the triazole (a and b) while two facilitate chelation of the metal center via the pyridyl nitrogen and N-4 of the triazole (c and d). (Middle) The trans-conformation of the ligand with the two bidentate binding regions orientated in opposite directions as it occurs in 1 featuring tautomers b and c. (Right) The two syn-conformation of the ligand with the two bidentate binding regions orientated in the same directions as they occur in 1 for which one features tautomers b and c and the other a and d.

Figure S3 .Figure S4 .

 S3S4 Figure S3. Asymmetric unit of 1 with nitrogen donor atoms and the two crystallographically unique Co(II) centres labelled. Hydrogen atoms, solvent molecules and anions are omitted for clarity.

Figure S5 .Figure S6 .

 S5S6 Figure S5. π-π stacking and C-H•••π interactions occurring between the phenyl and pyridine rings of the interlinked squares π(centroid) shown as red spheres and the π(centroid)•••π(centroid) separation are shown in red. Hydrogen atoms not participating in the illustrated interactions, solvent molecules and anions are omitted for clarity.

Figure S7 .

 S7 Figure S7. Hydrogen bonding interactions of the N-H moieties of the triazole rings with bromide and perchlorate anions in 1 (H•••A separations are shown in blue). Hydrogen atoms, solvent molecules and anions not participating in the illustrated interactions are omitted for clarity.

Figure S8 .

 S8 Figure S8. Crystal packing for 1. (Left) The off-set packing of the catenane units parallel to the crystallographic b-axis (red). Complexes out of the plane are shown in green while complexes into the plane are shown in blue for clarity. (Right) The end-on-end packing of the catenane units in a one-dimensional arrangement parallel to the crystallographic c-axis. The supramolecular chains are made up of catenanes shown in either green or blue.

Figure S9 .

 S9 Figure S9. Asymmetric unit of 2 with labelled nitrogen donor atoms and the four crystallographically unique Co(II) centres. Hydrogen atoms, solvent molecules and anions are omitted for clarity.

Figure S10 .

 S10 Figure S10. (Left) Co•••Co separations (shown in red) and (Right) Co•••Co•••Co angles (shown in red) of the distorted square structure of 2. Hydrogen atoms, solvent molecules and anions omitted for clarity.

Figure S11 .

 S11 Figure S11. Four crystallographically unique π-π interactions between the triazole and phenyl rings for 2 with the π(centroid) shown as red spheres and the π(centroid)•••π(centroid) separations shown in red.

Figure S12 .

 S12 Figure S12. Hydrogen bonding interactions of the N-H moieties of the triazole rings with bromide and perchlorate anions in 2 (H•••A separations are shown in blue). Hydrogen atoms, solvent molecules and anions not participating in the illustrated interactions are omitted for clarity.

Figure

  Figure S13. π-π interaction between the coordinated pyridine ring of one complex and the central phenyl spacer of another for 2 with the π(centroid) shown as red spheres and the π(centroid)•••π(centroid) separation shown in red.

Figure S19 .

 S19 Figure S19. Plot of the average relaxation time (t) vs. the inverse of the temperature (T -1 ) between 1.9 and 7 K at 1000 Oe deduced from the generalised Debye fits S10 of the frequency dependence of the real (c') and imaginary (c'') components of the ac susceptibility shown in Figure S17, for 1. The estimated standard deviations of the relaxation time (vertical solid bars) have been calculated from the a parameters of the generalised Debye fit (Figures S17) and the log-normal distribution as described in reference S11. The solid red line is the best fit with an Arrhenius (thermally activated) law (with ∆/kB = 12(2) K and t0 = 1.6(5) 10 -6 s) considering the data above 4 K (open dots).

Figure S20 .

 S20 Figure S20. Field (left) and temperature (right) dependence of the relaxation time for 1 estimated from the generalised Debye fits S10 of the ac susceptibility data shown in Figures S15 and S17. The estimated standard deviations of the relaxation time (vertical solid bars) have been calculated from the a parameters of the generalised Debye fits (Figures S15-S18) and the log-normal distribution as described in reference S11. The solid red lines are the best fit discussed in the text, including (top) quantum tunneling of the magnetization and Raman relaxation processes (Figure 4) and (bottom) Direct and Raman relaxation processes.

Angew. Chem. Int. Ed. 2022, 61, e202113837 (2 of 5) © 2021 Wiley-VCH GmbH

Angew. Chem. Int. Ed. 2022, 61, e202113837 (3 of 5) © 2021 Wiley-VCH GmbH

Angew. Chem. Int. Ed. 2022, 61, e202113837 (4 of 5) © 2021 Wiley-VCH GmbH

Angew. Chem. Int. Ed. 2022, 61, e202113837 (5 of 5) © 2021 Wiley-VCH GmbH

Acknowledgements

The authors gratefully acknowledge the Royal Society of New Zealand Marsden Fund; the Dumont d'Urville NZ-France Science & Technology Support Programme; the New Zealand France Friendship Fund for the award of an Excellence Scholarship to B.H.W. and the MacDiarmid Institute for financial support. The University of Bordeaux, the CNRS, the Région Nouvelle Aquitaine and the Quantum Matter Bordeaux program are also thanked for their financial support. B.H.W. gratefully acknowledges the receipt of the Roper Scholarship (UC).

Conflict of Interest

The authors declare no conflict of interest.

Supporting Information

Self-assembly synthesis of a [2]catenane Co(II) singlemolecule magnet

Benjamin H. Wilson,* Jas S. Ward, David C. Young, Jun-Liang Liu, Corine Mathonière, Rodolphe Clérac* and Paul E. Kruger*

General Information

All starting materials and reagents were reagent grade and used as received from standard suppliers. Solvents were HPLC grade and used as received. 1 H and 13 C NMR measurements were performed using an Agilent 400 NMR spectrometer operating at 400 MHz for 1 H and 101 MHz for 13 C. Chemical shift values are given in parts per million (PPM) and spectra were referenced to residual solvent peaks. A Bruker ALPHA Platinum ATR FT-IR spectrometer was used to measure samples in the range 4000-400 cm -1 . The following abbreviations were used to describe the signals: s (strong), m (medium), w (weak), br (broad). Melting points were recorded on an Electrothermal melting point apparatus and are uncorrected. Mass spectrometry was performed using a Bruker maXis 4G time of flight spectrometer operating in ESMS+ mode with values are given as MH + .

Syntheses

Synthesis of L

Synthesis of 2-Pyridylamidrazone

Synthesis of 1,2-bis (5-(2-pyridyl)-4H-1,2,4-triazol-3-yl)benzene (H2L) 1,2-bis(5-(2-pyridyl)-4H-1,2,4-triazol-3-yl)benzene (H2L) was synthesised following the literature preparation of Weldon et al. S1 M.pt. >360°C, Lit. >300°C. 1 H-NMR (400 MHz, [D6]-DMSO) δ = 8.72 (2H, d, J = 3. 9 Hz, Ha), 8.16 -8.24 (6H, m, Hd and He), 8.01 (2H, t, J = 7.6 Hz, Hc), 7.49 -7.57 (2H, m, Hb). 13 C-NMR (101 MHz, [D6]-DMSO) δ = 150. 8, 150.1, 138.2, 127.8, 127.0, 125.4, 123.6, 121.9. ESI-MS: [C20H15N8] + meas. 367.1393 calc. 367.1414. !̅ max / cm -1 : 3182 (br, m), 1596 (w), 1478 (s), 1463 (w), 1414 (s), 1142 (s), 1103 (w), 1007 (s).

Synthesis of [Co4(H2L)6]2(ClO4)7Br9, 1

A nitromethane (30 mL) suspension of H2L (55 mg, 0.15 mmol) and Co(ClO4)2•6H2O (37 mg, 0.10 mmol) was stirred at 50°C for several hours to give an orange solution. An aqueous solution of LiBr in H2O (0.125 mol L -1 , 600 µL, 0.075 mmol) was added and the reaction stirred at 50°C for a further 1.5 hours. The cooled solution was filtered to give a clear orange filtrate. Vapour diffusion of chloroform into the nitromethane solution over two days at ambient temperature yielded orange blocks suitable for single crystal X-ray diffraction. Recovered yield = 13 mg (0.002 mmol, 2%). !̅ max / cm -1 : 2917 (w), 2849 (w), 1615 (m), 1585 (w), 1568 (w), 1464 (m), 1409 (br, m), 1287 (w), 1003 (s), 984 (br, s). Elemental: found C, 43. S1).

Synthesis of [Co4(H2L)6]Br4(ClO4)4, 2

A nitromethane (30 mL) suspension of H2L (55 mg, 0.15 mmol) and Co(ClO4)2.6H2O (37 mg, 0.10 mmol) was stirred at 50°C for 1 hour to give an orange solution. An aqueous solution of LiBr in H2O (0.125 mol L -1 , 600 µL, 0.075 mmol) was added and stirred at 60°C for a further 4 hours. The cooled solution was filtered to give a clear orange filtrate. Vapor diffusion of chloroform into the nitromethane spiked with 50 µL m-xylene over three days at ambient temperature yielded orange blocks suitable for single crystal X-ray diffraction, which corresponded to 1. After several weeks, orange flake crystals suitable for single crystal X-ray diffraction grew on top of the blocks corresponding to 2. These crystals were only obtained in trace amounts and therefore no analysis other than single crystal X-ray diffraction was carried out.


Khouloud Fakhfakh

Sarah Ben-Othman

Laetitia Jourdan

Grégoire Smith

Jean-Marie Renard

Slim Hammadi

Hayfa Zgaya

Maala Ab

Jean Marie Re- Nard Bc

Biau Ab

Ontology for Overcrowding Management in Emergency Department

Keywords: Emergency Departments, Domain Ontology, Overcrowding management

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Emergency department overcrowding is a main problem faced by hospitals in France and in developed countries. The management of patient flows, in particular recurrent flows and flows following health crises (influenza, heat wave, exceptional situations) is one of the most important problems that EDs face. To manage this influx of patients, emergency departments need significant human and material resources, as well as a high degree of coordination between these resources. Under these conditions, medical staff is frequently confronted with overcrowding situations that greatly complicate their task and cause stress. Indeed, an emergency is a situation that involves a critical risk to property, life, health or the environment. In emergency scenarios, sharing knowledge and information about emergencies and affected entities (people, infrastructure) is essential to improve safety and infrastructure [START_REF] Othman | Model-driven disaster management[END_REF]. Knowledge management (KM) is responsible for determining what information is needed to recover from a critical situation. Improving the effectiveness of KM can not only help decision makers make faster and better decisions, but also enable various organizations to share and reuse different resources. The main element of the decision support system is the knowledge which can influence and guide the decisions made. This is the main key to the success of real-time decision making [START_REF] Jain | An ontology based earthquake recommendation system[END_REF]. Ontology engineering has become a useful and popular technology in computer science and knowledge science [START_REF] Jain | Ontology-supported rule-based reasoning for emergency management[END_REF]. Ontology is a form of conceptualization of real-world scenarios. It has been applied to decision support systems (DSS) to provide a formal representation of knowledge. It can improve interaction and coordination between different emergency organizations. The domain ontology for emergency management is a mechanism to provide a consistent view of the specific domain that can be used by all relevant authorities. Semantic technology has been used to build an extensible data model (the Resource Description Framework, RDF), in which data is represented as meaningful triples (subject, predicate, and object) [START_REF] Gruber | The role of common ontology in achieving sharable, reusable knowledge bases[END_REF]. The ontology is used to create the knowledge base that stores facts and procedures about the emergency and expert advice. A major aspect of this paper is to define a knowledge representation structure in the form of an ontology that provides information about emergency situations. These are essential to achieve a successful resolution of an evolving situation and to propose adequate solutions according to the severity of the solution. The ontology thus created will be able to represent and capture enough information about situations such as natural disasters, accidents, pandemics and climate data that can influence the demand flows on emergencies. It is a hierarchical model that forms true and faithful representations, so that queries of the model yield reliable results. This hierarchical contingency model indicates the classification of situations and the relationship between situational elements at different levels of granularity. Making quick decisions in the chaos of emergency situations is a very difficult task. The process can become difficult when a decision takes into account several internal and external factors and resources. Before drawing any conclusions or assisting in decision making, the medical staff must be aware of the resources needed and the resources available at a given time. In this context, we propose an ED Overcrowding Management (EDOMO) domain ontology to establish the overcrowding management process and propose solutions for each situation. In addition, determining the level of overcrowding in the ED is crucial to avoid undesirable outcomes. If the level of overcrowding is currently measured, overcrowding plans can be created. Various assessment systems have been developed to detect ED overcrowding. These include real-time analysis of ED demand indicators, the ED Work Index, the National ED Overcrowding Study (NEDOCS), and ED overcrowding rating systems [START_REF] Jones | An independent evaluation of four quantitative emergency department crowding scales[END_REF]. Among these scoring systems, NEDOCS has shown good results [START_REF] Ahalt | Comparison of emergency department crowding scores: a discrete-event simulation approach[END_REF]. However, in another study [START_REF] Ilhan | NEDOCS: is it really useful for detecting emergency department overcrowding today?[END_REF], NEDOCS showed limitations due to not taking into account important real-time factors, such as current ED load and climatic factors. For this purpose, we propose a new overcrowding estimation score (OES) to assess the ED situation by considering all external factors and ED resources. We conduct this work as part of a national project entitled Inter-and intra-hospital logistics optimization supported by the National Research Agency (2019-2022).

Methods

Emergency Department Overcrowding Management Ontology (EDOMO)

In this section, we propose the EDOMO ontology for owercowding management in ED. The ontology is based on an overcrowding estimation score (OES) to evaluate crowding situations in EDs. The implementation of EDOMO is done using the methontology method. We detail each part in the following subsections.

Ontology development methodology

Knowledge engineering is responsible for "ontology modeling" to identify the representation of primitives and meanings that will be used for formal knowledge modeling [START_REF] Sadiche | Profil Utilisateur d'une PLATE-FORME E-Learning[END_REF]. Various methodologies for ontology development exist in the literature [START_REF] Fernández-López | Methontology: from ontological art towards ontological engineering[END_REF], such us METHONTOLOGY, SENSUS, TOVE, IDEF5 and the seven-step method. Ontology construction is an iterative process. It is very important to choose the right methodology for the new ontology. In this paper, we adopte Methontology methodology [START_REF] Fernández-López | Methontology: from ontological art towards ontological engineering[END_REF] to create the domain ontology because it not only has detailed technical support and advantages in model creation, but also has advantages in the detailed modeling process to build the ontology model in the medical domain. This method is composed of the following steps:

1. Specification to deliver a clear description of the target vocabulary, identifying the domain concepts.

2. Conceptualization to enable the organization and structuring of the knowledge acquired in the first step by creating a conceptual model.

3. Formalization of the conceptual model developed in the previous step and of the entire domain glossary built, using a formal ontological language.

4. Implementation to build the ontology in a machinereadable ontology language such as OWL 2 with an ontology development tool; and integrate case scenarios and implement semantic reasoners.

This method can be useful to formalize a multi-model ontology which will presented in the following section.

The EDOMO ontology models

The EDOMO ontology is composed of three models: the Domain model, the case model and the reasoning model.

The Domain model :

The result of our proposed EDOMO ontology contains a single generic concept which is the situation and six main subclasses which define the different situations of ED: Patients, Causes, Overcrowding classes, Context, Solution and Evaluation. The root class of these classes is the Thing class (Table 1). OWL 2 classes are realized as sets of individuals (or sets of objects) and the class Thing represents the set containing all individuals [START_REF] Abeysiriwardana | Ontology based information extraction for disease intelligence[END_REF]. In this context, the EDOMO domain contains two levels of knowledge abstraction that we can qualify by knowledge of surface and deep knowledge:

 The generic level: contains the main concepts of overcrowding situation domain in the ED (Table 1).

 The domain level: describes the ED environment field that influences crowding situations in EDs, defined by EDOMO properties and concepts.

To define the domain concepts, we use standard medical Dictionary of ED and Medical Dictionary of Health in collaboration with the staff of LUHC to build a healthcare domain ontology. Emergency physicians have validated the EDOMO ontology and each element defined and the relations between classes, then we describe all its elements with the OWL 2 language in ontology form. Table 2 presents an overview of the properties defined in EDOMO.

Doctors int

Each property is responsible for defining the relationships between domain concepts in order to create overcrowding situation case scenarios in the ED. Therefore, we define the different data and knowledge in the field of ED by domain concepts and relationships such as context, evaluation and patients. This ontology presents a combination of exact indicators such as the ED capacity at time t and estimated indicators such as the climate forecast. Each domain concept defines information that can influence the ED environment.

The case model :

Based on the FOTS ontology [START_REF] Fakhfakh | Fuzzy Ontology for Patient Emergency Department Triage[END_REF], we developed the EDOMO ontology that represents the ED environment and overcrowding situations. EDOMO provides a case model. The latter presents a detailed description for each ED overcrowding situation scenario containing all data. We describe the different relationships between domain concepts in our EDOMO ontology and set up the case model by defining real ED situation case scenarios. To improve the communication between the case model and the domain model, we integrate these situation cases into the ontology through the data and object properties (Figure 1).

Figure 1-EDOMO case model

The reasonning model :

After creating the domain model and the case model, we define the reasonning model to realize a functional ontology and to integrate into a decision-support system. We use the SWRL (Semantic Web Rule Language) that is a rule language for the semantic web, combining the OWL-DL language and RuleML (Rule Markup Language) to create all possible scenarios of the ED situations. These are integrated into the resulting ontology to reason semantically based on rules, for example:

EDOMO:Situation(?S) ^ EDOMO:Overcrowding_score (?Y) ^ EDOMO:is_evaluated_by (?S,?Y) ^ swrlb:lessThanOrEqual (?Y, "25"^^xsd:long) ^ swrlb:greaterThanOrEqual (?Y, "15"^^xsd:long) -> EDOMO:Overcrowding_classes (EDOMO:Critical_state)

In addition, this model provides rules that assess overcrowding situations and manage these situations by proposing solutions to help healthcare workers. Thus, each rule is described with the properties and instances defined in the ontology. It is based on performance indicators to give an accurate assessment. The defined rule base has been validated by the medical staff of LUHC. The exploitation of semantic rules can also be used to manage missing data.

EDOMO based on overcrowding management process

The overcrowding management process is composed of three steps:

-identify the performance indicators and calculate the overcrowding estimation score (OES).

-Classify the ED situations into four states: normal state, degraded state, critical state and very critical state.

-Propose adequate actions to manage the different levels of overcrowding.

ED performance indicators

The measurable performance indicators that we have selected and validated with the medical staff of the Adult Emergency Department (AED) of Lille and based on the work of Kadri [START_REF] Kadri | A simulationbased decision support system to prevent and predict strain situations in emergency department systems[END_REF] are:

1. PWT: waiting time between the hostess taking charge (Te) and the first medical examination (Tc).

𝑃𝑊𝑇 = 𝑇 𝑒 -𝑇 𝑐

2. T2: waiting time from the hostess (Te) to the nursing consultation (Tnc) (Equation 2).

𝑇 2 = 𝑇 𝑒 -𝑇 𝑛𝑐 (2)
3. Np: number of patients present at the AED when a new patient arrives 4. PM: ratio of the number of patients present at the AED to the number of doctors (Nd) potentially available (Equation 3): As the number of physicians changes according to the period of the day, PM is updated at each period variation.

PM =

𝑁 𝑝 𝑁 𝑑

(3)

5. QS: ratio of the actual stay time in the hospital of a patient in non-emergency state LOSactual, and the theoretical stay time LOSth (Equation 4). The LOSth in the hospital is 210 minutes.

Qs = 𝐿𝑂𝑆𝑎𝑐𝑡𝑢𝑎𝑙 𝐿𝑂𝑆𝑡ℎ (4)
6. Ct: the percentage of the current load at time t. It is the ratio of the number of patients present in the ED and its maximum capacity (N), taking into account the inflow and outflow (Equation 5).

Ct = 𝑁 𝑒 + 𝑁 𝑎 -𝑁 𝑠 𝑁 * 100 ( 5
)
Where Na is the number of patients arriving at the ED, Ne is the patients number in ED and Ns is the number of patients discharged at time t.

The threshold values for each situation class are presented in the following table 3:

Overcrowding Estimation Score (OES)

The OES is proposed to accurately assess the level of crowding in the ED. This score is computed based on the performance indicators mentioned in the previous section (Equation 6). These indicators are selected in collaboration with emergency specialists.

𝑂𝐸𝑆 = ∑ 𝑅𝑆 𝐾 𝐾 1 ( 6
)
Where k is the number of performance indicators. To calculate OES, firstly, we identify the risque score (RSk) for each performance indicator (Table 3) according to Table 4 and then we apply equation ( 6). The RSk is given for each performance indicator according to its ED state.

OES is created using the SWRL rules in order to integrate it into the EDOMO ontology as follows :

EDOMO:Situation(?H) ^ EDOMO:PM(?X) ^ EDOMO:has_risk_score(?X, ?t) ^ EDOMO:Ct(?Y) ^ EDOMO:has_risk_score(?Y, ?S) ^ EDOMO:Np(?N) ^ EDOMO:has_risk_score(?N, ?M) ^ EDOMO:PWT(?F) ^ EDOMO:has_risk_score(?F, ?D) ^ EDOMO:Qs(?R) ^ EDOMO:has_risk_score(?R, ?C) ^ EDOMO:T2(?P) ^ EDOMO:has_risk_score(?P, ?B) ^ swrlb:add(?Z, ?t, ?S, ?M, ?D, ?C, ?B) -> EDOMO:Overcrowding_score(?Z) ^ EDOMO:has_overcrowding_score(?H, ?Z).

Overcrowding management actions

Based on Kadri's work [START_REF] Kadri | A simulationbased decision support system to prevent and predict strain situations in emergency department systems[END_REF] and in collaboration with the health specialists, we selected the following actions according to two categories which are patient flows and resources according to the level of overcrowding specified in the previous step :

Actions on the care load flow (patient flow):

-Incoming patient flow: Decrease of incoming patients (call the EMS 1 to refer patients to other emergency structures).

-Patient flows admitted to the ED: apply priority rules to better manage patient flow in the ED to limit waiting times and length of stay, transfer patients from the STHU2 to other departments and adjust the care provided to patients. These rules can be defined according to different criteria: type of patient, length of stay, progress of care, combination of one or more of the above criteria.

Actions on resources :

-Human resources: add doctors or nurses depending on availability in other departments.

-Material resources: transform one or two STHU rooms into consultation room.

Each action is described in the EDOMO ontology via the SWRL rules by proposing for each scenario an overcrowding situation.

Results

To implement the EDOMO domain ontology, we used Protégé 5.5 (Figure 2). It is an open source software [START_REF] Liu | SOFERS: Scenario ontology for emergency response system[END_REF] that provides a plug-and-play environment for rapid application development. Protégé is the most familiar tool for developing the ontology. Developers can create the ontology easily through its graphical interface without having to worry about the syntax language. Thus we integrate the SWRLTAB tool into protégé for the creation and exploitation of SWRL rules. Thus, we have selected 100 overcrowding scenarios from a real database of the ED in LUHC hospital and we implemented our ontological base in EDOMO. It is a 4-year database including arrival information between 2016 and 2020. This work is part of the OIILH project (2018-2022): Optimization for inter and intra logistics in hospitals. This project is supported by the French research agency and referenced by ANR-18-CE19-0019. The resulting ontology contains 50 classes, 25 object properties, 15 1 Emergency Medical Service data properties, 687 axioms, 546 logical axioms, and 251 concept instances for the 100 overcrowding situations. Each object property and each data property has an instance for every situation case.

Figure 2-EDOMO ontology structure

In addition, the SWRL rules that are created by the SWRLTAB and Protégé tools, are generated with the JESS inference engine. The rule base contains 50 semantic rules (Figure 3).

Discussion

Ontology evaluation requires formal and appropriate evaluation criteria. Therefore, it is essential to select and apply appropriate evaluation approaches that are suitable for the given domain ontology. In the following subsection, we review the different evaluation approaches that have been applied to EDOMO in order to evaluate it. There is no gold standard ontology to measure its similarity to our ontology. But, a comparison with existing ontologies in the same domain is necessary. Thus, we consider the Diabetes ontology (DO) [START_REF] El-Sappagh | A fuzzy ontology modeling for case base knowledge in diabetes mellitus domain. Engineering science and technology[END_REF] for diabetes disease diagnosis. Several criteria for evaluating the quality of ontologies have been defined [START_REF] Djedidi | ONTO-EVO A L an ontology evolution approach guided by pattern modeling and quality evaluation[END_REF][START_REF] Yu | Evaluating ontology criteria for requirements in a geographic travel domain[END_REF]. We also consider the criteria of Djedidi and Aufaure with several metrics. These criteria concern complexity, cohesion, conceptualization, abstraction, completeness and comprehension [START_REF] Djedidi | ONTO-EVO A L an ontology evolution approach guided by pattern modeling and quality evaluation[END_REF] (Table 5).

The comparison between our ontology and the DO shows that EDOMO is a complete, functional and semantically rich ontology. Based on the above criteria, table 5 presents a comparison between the EDOMO and the DO ontology. These indicators presented in this comparison (table 5) assess the reasoning, consistency and applicability of the ontology.

According to these indicators, we can prove that our ontology presents useful practical knowledge considering the vagueness and uncertainty of medical information. These features are very important to put this ontology into a well-functioning DSS. The average number of paths to reach a class starting from the root. [START_REF] Jain | Ontology-supported rule-based reasoning for emergency management[END_REF] 6

The average number of object properties per class.

1.3 4.1

Abstraction

The average depth of the ontology.

2 3

Cohesion

The average number of connected classes

Conclusions

In this paper, we propose a new complete ED domain ontology (EDOMO) to handle the overcrowding in EDs. This ontology is enriched with several types of data (e.g textual and semantic data) which facilitate the development of a DSS. This latter contains semantic reasoning algorithms through SWRL rules to assess the situations of EDs and propose health care personnel to manage them. Thus, the overcrowding estimation score (OES) corresponds to a semantically ontology-based assessment tool with a high coverage of the ED domain and its environment by defining all the useful knowledge. We prove in this paper that our functional ontology presents the necessary knowledge of the emergency domain and can be integrated into a DSS based on semantic reasoning. This allows us to provide very efficient results and to solve the problem of missing data. Thus, this model can make an efficient combination between real and estimation data based on semantic reasoning. Therefore, it can improve the quality of emergency care and help health care workers in critical situations. In future works, we can improve the OES by using fuzzy logic. In addition, we will propose a machine learning algorithm that can be a potential solution to improve the accuracy of the estimated data in order to decrease the uncertainty. Also, it is crucial to test the new score in real time environment and integrate the remainning load as proposed in [START_REF] Chandoul | Conférence francophone gestion et ingénierie des systèmes hospitaliers[END_REF], we will focus on improving the implementation of our ontology using a the current ED system in use. This will allow us to add case-based reasoning and machine learning tools to improve the accuracy of our decision system.

Figure 3 -

 3 Figure 3-SWRL Rules implementation

Table 1 -

 1 Main concepts of EDOMO domain

	Classes	Description
	Situation	presents the generic class of the ontology
		and defines the scenarios of different
		crowding or normal situations in the ED
	Causes	defines the factors that can cause
		overcrowding situations in the ED
	Patients	presents specific data on ED patients
	Overcrowding	classifies the different situations according
	classes	to their level of overcrowding
	Solution	proposes instant solutions to help health
		care personnel manage these situations.

Table 2 -

 2 The EDOMO properties

	EDOMO	Types	Domain	Ranges
	Properties
	has_performanc	Object	Situation	Performance
	e_indicator	property		indicators
	is_defined_by	Object	Overcrow	Overcrowdin
		property	ding_classes	g_scrore
	is_evaluated_by	Object	Situation	Evaluation
		property
	has_temperature	Data	temperature	float
		property
	has_patient_	Data	Patients_admi	int
	admitted number	property	tted
	has_doctors_	Data
	number	property

Table 3 -

 3 The threshold values of Performance indicators

	Perfor-		EDA State
	mance indica-tors	Normal	Degraded	Critical	Very critical
	PWT	PWT<	60<PWT<	90<PWT<	PWT>180
		60	90	180
	T2	T2<25	25<T2<50 50<T2<70 T2>70
	Np	Np<12	12<Np<20 20<Np<40 Np>40
	PM	PM<4	4<PM<7	7<PM<10	PM>10
	Qs	Qs<0.8 0.8<Qs<	1.5<Qs<2	Qs>2
			1.5
	Ct	Ct<50	50<Ct<75	75<Ct<	Ct>120
				120

Table 4 -

 4 The OES score

			EDA State
		Normal	Degraded	Critical	Very
					critical
	(RSk)	1	2	4	5
	OES	[0,7]	[8, 14]	[15, 25]	[26, 30]

Table 5 -

 5 The comparative evaluation table between DO and EDOMO ontology

	Criteria Metrics	DO	EDO
			MO
	Comple-
	xity

Short-term hospitalization unit