Francesco Dell'isola

Maurizio Porfir

Stefano Vidoli

Piezo-ElectroMechanical (PEM) structures: passive vibration control using distributed piezoelectric transducers Structures Piézo-ÉlectroMécaniques (PEM) : contrôle passif de vibrations en utilisant des transducteurs piézo-électriques distribués

Keywords: Control, Electric analog, Electric networks, Vibration damping Mots-clés : Automatique, Vibrations, Analogue électrique, Réseaux électriques, Amortissement de vibrations

A piezo-electromechanical structural member is composed of a host member, a uniformly distributed array of piezoelectric transducers and a passive electric circuit (acting as a controller) interconnecting their electric terminals. Such a circuit has to be designed to assure the most eff cient transduction of mechanical into electrical energy. The needed circuits are synthesized for bars, beams and plates and the performances of the corresponding PEM structures are determined. Once suitable dissipative elements are included in the controller, it is proven that, in PEM structures, mechanical vibrations are the most eff ciently damped.

Résumé

Une structure piézo-électromécanique (PEM) se compose par un élément structurel hôte, une rangée uniformément distribuée de transducteurs piézoélectriques et un circuit électronique passif (agissant comme contrôleur) pour établir leur interconnexion électrique. Un tel circuit doit être conçu pour assurer la transduction la plus eff cace de l'énergie mécanique en électrique. Les circuits nécessaires sont synthétisés pour des barres, des poutres et des plaques et les performances des structures PEM correspondantes sont déterminées. Une fois que des éléments dissipatifs appropriés sont inclus dans le contrôleur on montre que dans les structures PEM les vibrations mécaniques sont atténuées le plus eff cacement possible.

Version française abrégée

Les développements technologiques récents dans les modes de production des transducteurs piézoélectriques et un intérêt général croissant pour l'amortissement de vibrations structurales, sont des facteurs qui ont contribué à intensifie les recherches dans le domaine de l'exploitation des transducteurs piézoélectriques dans des structures réelles (voir [START_REF] Preumont | Vibration Control of Active Structures[END_REF][START_REF] Preumont | Responsive Systems for Active Vibration Control[END_REF]). La technique d'atténuation électronique (electronic damping) attribuée à Olsen [START_REF] Olsen | Electronic control of noise, vibration and reverberation[END_REF], et développée par Swigert et Forward [START_REF] Forward | Electronic damping of orthogonal bending modes in a cylindrical mast-theory[END_REF], est l'une des premières tentatives d'exploitation de l'effet piézoélectrique dans le contrôle structural : un capteur piézoélectrique convertit la contrainte dynamique en courant électrique, ce dernier est amplif é, décalé dans la phase et appliqué à un actionneur piézoélectrique.

Cette technique, qui fut facilement améliorée et généralisée au cas à sorties et entrées multiples, doit être considérée comme active puisque elle exige nécessairement une alimentation en énergie. Si l'on veut obtenir des résultats satisfaisants en termes d'atténuation et stabilité dans cette stratégie d'amortissement active, on doit utiliser, pour le contrôle des capteurs, des amplificateur de puissance sophistiqués et des circuits électroniques très sensibles.

Pour éviter les diff cultés inhérentes au contrôle actif, Hagood et von Flotow [START_REF] Hagood | Damping of structural vibrations with piezoelectric materials and passive electrical networks[END_REF] ont proposé une technique de contrôle passif : un actionneur piézoélectrique est shunté avec une résistance et un inducteur, qui sont eux mêmes accordés de façon optimale sur une fréquence modale donnée de la structure. Ce système n'est performant que dans le contrôle d'un unique mode de vibration de la structure ; en effet, le mode mécaniqueétant choisi, alors l'inductance critique, L * s , et la position optimale du transducteur piézoélectrique sont déterminées uniquement.

Dans le cas de ce contrôle localisé, l'inductance critique L * s doit être proportionnelle à 1/(C p f 2 m ), C p correspondant à la capacité du transducteur piézoélectrique, f m à la fréquence modale mécanique à contrôler. Les valeurs typiques de C p et f m imposent des limitations sérieuses aux inductances à employer : puisque la plage des ces inductances est de 10 2 ÷ 10 4 henry, elles peuvent être obtenues soit par un circuit électronique de simulation [START_REF] Bruton | RC-Active Circuits: Theory and Design[END_REF] soit par des inducteurs à noyau ferroélectrique. Mais des inconvénients technologiques majeurs sont inhérents à ces deux possibilités ; il s'agit, dans le premier cas, de la nécessité d'une alimentation en énergie, dans le second, du fait que l'inducteur ajoute une fraction signif cative de toute la masse du système.

Chercher à réduire l'inductance critique L * s en ajoutant une capacité au circuit de contrôle s'avère être une solution inadéquate puisque cela implique, nécessairement, une diminution de l'eff cacité du couplage piézoélectrique.

Tous les inconvénients mentionnés plus haut peuvent être évités grâce à un système de contrôle plus adapté : si l'on conçoit un contrôleur électrique passif et eff cace sur plusieurs modes structuraux, on peut alors envisager d'exploiter une analogie électromécanique.

Ainsi on peut concevoir une structure PEM [START_REF] Vidoli | Modal coupling in one-dimensional electromechanical structured continua[END_REF][START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF][START_REF] Dell'isola | Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping[END_REF] comme :

-une rangée uniformément distribuée de transducteurs piézoélectriques placés sur la structure à contrôler (voir Fig. 2) ; -un réseau électrique passif pour connecter l'ensemble des transducteurs, dont les propriétés spectrales sont adaptées à celles de la structure à contrôler (voir Figs. 2 et 3).

Il faut, par ailleurs, que le réseau électrique soit conçu pour être résonnant avec toutes les fréquences structurales propres mais aussi de telle sorte que ses formes modales puissent interagir piézoélectriquement avec celles de la structure à contrôler (Fig. 1). Un système de ce type présente l'avantage de contrôler simultanément plusieurs modes sans avoir recours à des éléments actifs ou à de lourds inducteurs. De plus, grâce au comportement synergique des transducteurs piézoélectriques on obtient de très hautes performances en termes d'efficacit de transduction d'énergie mais également en termes de temps d'amortissement, voir formule [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF], pour une largeur de bande de fréquence en principe infi i.

La différence principale entre la stratégie exploitée par les structures PEM et la technique de shuntage passif se situe dans l'interconnexion des transducteurs piézo-électriques distribués.

Si le circuit électrique d'interconnexion est synthétisé pour être analogue à celui de la structure à contrôler, un choix simple des ses paramètres électriques permet l'amortissement de tous les modes mécaniques.

Quel que soit l' élément structural -barres, poutres et plaques -un circuit analogue totalement passif a été synthétisé. Ses performances en tant que contrôleur électrique sont comparées à celles (i) des circuits de shuntage séparés et à celles (ii) des réseaux électriques du second ordre pour toutes les structures présentées. Le contrôle multi-modal n'est possible que si l'on a recours à des circuits analogues et, alors, les inductances critiques nécessaires ont la valeur minimale.

Les structures PEM sont conçues de manière à obtenir une transduction eff cace de l'énergie mécanique ; en effet, une fois que l'énergie a été transformée sous forme électrique, elle peut être dissipée rapidement.

Les temps d'amortissement des vibrations électromécaniques peuvent être optimisées en ajoutant judicieusement, dans le contrôleur électrique, quelques résistances (voyez [START_REF] Maurini | Comparison of distributed vibration absorbers made of piezo-electr(on)ic networks[END_REF] et Figs. 2 et 3). Ils dépendent des coeff cients de couplage piézoélectrique et sont donnés par la formule [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF].

Le développement de ces résultats doit déboucher à terme sur :

-la synthèse des analogues électriques pour des structures plus compliquées, comme coques, poutrages et treillis ; -une analyse précise du procédé d'homogénéisation nécessaire pour obtenir les équations d'évolution pour les structures PEM ; -la conception d'un prototype expérimental pour établir la validité de l'analyse théorique développé.

Introduction

State of the art

The recent technological developments in the production of piezoelectric transducers, and the relevant attention of consumers towards the suppression of structural vibrations, have increased the research efforts in the effective exploitation in actual engineering structures (see [START_REF] Preumont | Vibration Control of Active Structures[END_REF] and [START_REF] Preumont | Responsive Systems for Active Vibration Control[END_REF]). An eff cient control of structural vibrations leads to other benefits such as the precision in mechanisms manoeuvres, reduced fatigue loads, reliability and durability of machineries: these were the main reasons to attract the interest of both the mechanical and aerospace industries to this topic.

Among the f rst attempts to exploit the piezoelectric effect in structural control, one must mention the electronic damping technique -attributed to Olsen [START_REF] Olsen | Electronic control of noise, vibration and reverberation[END_REF], and developed by Swigert and Forward [START_REF] Forward | Electronic damping of orthogonal bending modes in a cylindrical mast-theory[END_REF]. It consists in the following closed loop: a piezoelectric sensor converts the dynamic strain into an electric current, which is amplif ed, shifted in phase and applied to a piezoelectric actuator. This technique, soon improved and generalized to the multi-input multi-output case, can be labeled as active since it necessarily requires a power supply. Within the active control strategy, complex power amplifier and precise sensing electronics are needed to achieve satisfactory results in terms of damping and stability.

Mainly to overcome these drawbacks Hagood and von Flotow [START_REF] Hagood | Damping of structural vibrations with piezoelectric materials and passive electrical networks[END_REF] proposed a passive shunting technique: a piezoelectric transducer is shunted with a resistor and an inductor, optimally tuned to a structural modal frequency. This control strategy electrically parallels the den Hartog theory [START_REF] Hartog | Mechanical Vibrations[END_REF] of tuned-mass damper systems. This approach is effective only for the control of a single vibration mode of the structure; indeed, once the mechanical mode is selected, the critical inductance, say L * s , and the optimal position of the piezoelectric patch are univocally determined. The critical inductance for this lumped control L * s is proportional to 1/(C p f 2 m ), C p being the piezoelectric capacitance, and f m the mechanical modal frequency to be controlled. Typical values for both C p and f m impose severe limitations on the inductances to be used. The subsequent inductance range (10 2 ÷ 10 4 H) can be achieved either by an electronic simulating circuit [START_REF] Bruton | RC-Active Circuits: Theory and Design[END_REF] or by coils wrapped around a magnetic core. In both cases serious technological drawbacks arise: in the former case power supplies are again needed, in the latter case the inductor adds a significan fraction of the total system mass. Attempting to lower the critical inductance L * s by adding capacitance to the shunting circuit turns out to be uneffective since it necessarily implies a decrease of the eff ciency of the piezoelectric coupling.

PEM structures

All the aforementioned drawbacks can be overcome enhancing the design specif cations of the control system. As one compels such an electric controller to be passive and effective on all structural modes, the idea of an electromechanical analogy arises. Thus the conceived net-control technique [START_REF] Vidoli | Modal coupling in one-dimensional electromechanical structured continua[END_REF][START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF][START_REF] Dell'isola | Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping[END_REF] results in:

• a uniformly distributed array of piezoelectric transducers positioned over the host structure;

• an electric passive network, interconnecting the transducers, whose spectral properties are adapted to those of the host structure.

The electric network is designed to be resonant at all the structural characteristic frequencies and so that its modal shapes may piezoelectrically interact with those of the host structure. These design specif cations allow one to control simultaneously all the modes, dispensing with the use of either active elements or heavy inductors. The synergic behavior of the piezoelectric patches leads to a very high perfomance in terms of energy transduction eff ciency over a frequency bandwidth in principle inf nite.

Gallery of net-controlled structures

Within the aforementioned net-control strategy, a gallery of PEM structures is here presented. For some relevant structural members (bars, shafts, beams and plates) several circuital interconnecting schemes are exhibited; for each pair of structure and circuit, the basic dynamic properties are addressed.

In Fig. 1 both the modal frequencies and shapes are sketched for an arbitrary pair of mechanical and electrical one-dimensional sub-systems. The net-control technique introduced is based on the one-to-one correspondence between the modal frequencies and the modal shapes of the vibrating structure and the interconnecting network, assuring the complete transduction of mechanical into electrical energy.

Bars and shafts

The free vibrations of both bar and shaft are governed by the so called D'Alembert equation

ü = α 2 u , α 2 ∈ R + (1)
where u denotes the kinematical descriptor, namely the axial displacement or the twist angle, and superposed dot and prime respectively mean the time and space derivatives. The electrical distributed circuit governed by the D'Alembert equation is the well-known second-order transmission line; a lumped circuit constituted by a set of N grounded capacitors interconnected via f oating inductors represents a f nite difference approximation of the aforementioned distributed circuit. Hence interconnecting the piezoelectric transducers, positioned over the structure, as the capacitors of the circuit in Fig. 2, the following set of coupled evolution equations governing the free vibrations of the net-controlled bar or shaft is derived:

ü = α 2 u + γ 2 ψ , ψ = β 2 ψ -γ 2 u , α 2 , β 2 , γ 2 ∈ R + (2)
ψ being the electric voltage measured with respect of a common ground. Referring to Eq. ( 2), in order to guarantee the one-to-one correspondence between the mechanical and electrical modal characteristics, it is suff cient to set β 2 = α 2 and impose on the electric circuit boundary conditions dual to those of the vibrating structure. The parameter β 2 can be varied tuning the line inductance; let L * 2 be the critical value to get β 2 = α 2 . If, with the same number N of transducers, one uses the passive shunting technique (namely, shunting separately each patch with a single inductance), the multi-modal control is lost. We call L * s2 (k) the critical inductance when the passive shunting technique is employed to control the k-th mode. The ratio [START_REF] Maurini | Comparison of distributed vibration absorbers made of piezo-electr(on)ic networks[END_REF]; this means that for a large number of transducers their interconnection, i.e., the basic concept of PEM systems, sensibly reduces the inductances needed.

L * s2 (k)/L * 2 is proportional to N 2 /k 2 ,

Beams

The elastic equation governing the free vibrations of Euler beam:

ü + α 4 u (iv) = 0, α 4 ∈ R + (3)
does not have a well-known electric analog. However, it is possible to couple the beam with the aforementioned second-order transmission line. The resulting system, discussed in [START_REF] Vidoli | Modal coupling in one-dimensional electromechanical structured continua[END_REF], is governed by:

ü + α 4 u (iv) + γ 3 ψ = 0, ψ -β 3 ψ -γ 3 u = 0, α 4 , β 3 , γ 3 ∈ R + (4)
With a suitable choice of the electric boundary conditions there could be similar electrical and mechanical modal shapes, but the electrical and mechanical spectra can not be superposed. The line inductance can be tuned to match only one pair of electric and mechanical eigenfrequencies, since spectral "spacings" are different (refer to Fig. 1). Nevertheless, the ratio L * s4 (k)/L * 3 (k), between the critical inductances required in the passive-shunting and in the second-order net-control technique (used for the k-th mode), is proportional to N 2 /k 2 . This circumstance represents a sensible technological advantage of the piezoelectric interconnection. In order to synthesize the electric analog of the Euler beam, several approaches have been investigated. The two different circuital schemes in [START_REF] Dell'isola | Bending-waves damping in truss beams by electrical transmission line with PZT actuators[END_REF] and [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF] are characterized by the use of active elements. While in [START_REF] Dell'isola | Bending-waves damping in truss beams by electrical transmission line with PZT actuators[END_REF] some voltage-driven current sources are used, in [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF] the circuital topology is found seeking a f nite-differences symmetric scheme of the elastica, and assuming all the used electric elements to be two-terminal networks. This occurrence necessarily implies the use of negative f oating inductances, which must be simulated by electronic active circuits. A step torwards a feasible passive realization of the analog circuit has been made in [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF] and [START_REF] Dell'isola | Synthesis of electrical networks interconnecting PZT actuators to damp mechanical vibrations[END_REF], where relaxing the two-terminal network hypothesis and considering a suitable truncation of the mechanical impedance matrix of a beam element, a circuit constituted by multiport transformers is obtained. The main drawback of this scheme lies in the complexity of the circuital topology, even if low inductances are required.

A synthesis solution, technologically more convenient in terms of both required inductances and topological complexity, is given in [START_REF] Andreaus | Piezoelectric passive distributed controllers for beam fl xural vibrations[END_REF] and here depicted in Fig. 3.

The proposed analog circuit has been synthesized through a f nite difference approximation of the inf nite dimensional Lagrangian of the Euler beam. The governing equations of the beam net-controlled via the circuits given in [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF][START_REF] Dell'isola | Synthesis of electrical networks interconnecting PZT actuators to damp mechanical vibrations[END_REF][START_REF] Andreaus | Piezoelectric passive distributed controllers for beam fl xural vibrations[END_REF] are:

ü + α 4 u (iv) + γ 4 ψ = 0, ψ + β 4 ψ (iv) -γ 4 u = 0, α 4 , β 4 , γ 4 ∈ R + (5)
Obviously the parameters β 4 and γ 4 depend on the adopted electrical scheme. Eq. ( 5) implies that, once the parameter β 4 is set equal to α 4 and the electric boundary conditions have been chosen to be dual of the mechanical ones, a one-to-one correspondence between the electrical and mechanical modal frequencies and modal shapes is established.

Fig. 3. Circuital scheme for a fourth-order interconnection. Call L * s4 (k) and L * 4 the critical inductances to separately shunt all the N transdurcers for controlling the k-th mode and to equate β 4 to α 4 , respectively, through the circuit in Fig. 3, choosing a unitary turns ratio for the transformers (this choice is required for comparison purposes). The ratio L * s4 (k)/L * 4 is proportional to N 4 /k 4 ; thus increasing the number of the piezoelectric patches results in extremely advantageous inductances with respect to the passive shunting technique. Further the net-controlled beam described by Eqs. ( 5) guarantees the multi-modal control of the mechanical vibrations through a unique choice of the net inductance L * 4 .

Plates

The free vibrations of the Kirchhoff plate are governed by:

ü + A 4 u = 0, A 4 ∈ R + (6)
Similarly to the Euler beam, Eq. ( 6) has not a well known electric analog. The problems arising in the synthesis of the electric analog of the plate parallel, those addressed in the previous section, are used, since again fourth order spatial derivatives are involved. The easiest net-controlled system is realized coupling the Kirchhoff plate with a second-order transmission network, that is the two-dimensional extension of the D'Alembert transmission line. The resulting equations are found in [START_REF] Vidoli | Vibration control in plates by uniformly distributed actuators interconnected via electric networks[END_REF] and here reported:

ü + A 4 u + Γ 3 ψ = 0, ψ -B 3 ψ -Γ 3 u = 0, A 4 , B 3 , Γ 3 ∈ R + (7)
For comparison purposes, let L * sp (h, k) be the critical inductance for the separate resonant shunting relative to the (h, k)-th plate mode. Furthermore let L * 3p (h, k) be the critical inductance needed in the net-controlled system (7) to control the same (h, k)-th mode. Similar considerations concerning Eq. ( 4) hold for this case: a unimodal control is guaranteed employing more advantageous inductances; indeed L * sp (h, k)/L * 3p (h, k) ∝ N/(h 2 + k 2 ). The electric analog of the Kirchhoff plate is instead synthesized in [START_REF] Alessandroni | Optimal piezo-mechanical coupling to control plate vibrations[END_REF] and [START_REF] Alessandroni | A revival of electric analogs for vibrating mechanical systems aimed to their eff cient control by PZT actuators[END_REF] by using active elements to simulate negative f oating inductances. Dispensing with the use of active elements, the one-dimensional circuital topology in Fig. 3 can be extended to the two-dimensional case as done in [START_REF] Alessandroni | A novel-passive electric-network analog to Kirchhoff-Love plate designed to eff ciently damp forced vibrations by distributed piezoelectric transducers[END_REF]. For both the net-controlled systems the following coupled equations hold:

ü + A 4 u + Γ 4 ψ = 0, ψ + B 4 ψ -Γ 4 u = 0, A 4 , B 4 , Γ 4 ∈ R + (8)
Eqs. ( 8) guarantee the multi-modal control of the plate vibrations through a unique choice of the net inductance L * 4p . Once the turns ratio of the transformers, for a fair comparison, has been chosen to be unitary, the ratio L * sp (h, k)/L * 4p becomes proportional to N 2 /(h 2 + k 2 ) 2 : again a large number of patches logically decreases the required inductances.

Conclusions and future developments

The main difference between the net-control strategy and the passive shunting technique lies in the interconnection of the distributed patches. If the interconnecting circuit is synthesized to be analog to the host structure, a single choice of the electric parameters allows for the simultaneous control of all the mechanical modes. For some relevant structural elements -bars, beams and plates -a completely passive analog circuit has been synthesized. Its performances as electric controller are compared with those of (i) separated shunted circuits and (ii) second order transmission lines for all the presented structures. The multi-modal control is obviously possible only using analog circuits and the needed critical inductances result to be lowest in this last case. PEM structures are aimed to get an effective transduction of the mechanical energy since, once the energy has been transformed in the electrical form, it can be stored or rapidly dissipated. The damping ratios for electromechanical vibrations can be optimized by suitably introducing in the electric controller some resistors (see [START_REF] Maurini | Comparison of distributed vibration absorbers made of piezo-electr(on)ic networks[END_REF][START_REF] Andreaus | Piezoelectric passive distributed controllers for beam fl xural vibrations[END_REF] and Figs. 2 and3). For instance for the system (5), introducing a suitable resistances in parallel connection with the f oating ports of the transformers in Fig. 3, the modal damping ratios ζ k turn out to be independent of the mode number k and are given by:

ζ k = γ 4 2 √ α 4 , k = 1, 2, . . . ( 9
)
Future developments of this research will lead to:

-the synthesis of electric analogs for the net-controlling of more complex structures, as frames, trusses with arbitrary shape and shells; -an accurate analysis of the homogenization procedure lying beneath the proposed f eld equations for PEM structures; -an experimental set up to validate the proposed approach.

Fig. 1 .

 1 Fig. 1. Correspondence between mechanical and electrical modal properties.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Correspondance entre les propriétés mécaniques et électriques du modèle.

Fig. 2 .

 2 Fig. 2. Schéma d'un faisceau PEM : l'interconnexion a été faite d'une ligne de transmission du deuxième ordre.

Fig. 3 .

 3 Fig. 3. Schèma d'un circuit d'un interconnexion du quatriéme ordre.


Anja Jaenschke

Falk Olbrich

Dr Ulrich Behrens
email: ubehrens@chemie.uni-hamburg.de

Strukturen von polaren Magnesiumorganylen: Synthese und Struktur von Basen-Addukten des Magnesiumindenids

Keywords: Magnesium, Indenide, Crystal structure Magnesium, Indenide, Crystal structure

An improved X-ray structure determination of magnesium indenide (Mg(C 9 H 7 ) 2 , 1) at low temperature was carried out. Four donor-acceptor complexes of Mg(C 9 H 7 ) 2 (1) with Oand N-donor Lewis bases have been synthesized and characterized by X-ray structure analysis. With dioxane and tetramethylethylenediamine (tmeda) two simple monomeric complexes, [Mg(C 9 H 7 ) 2 (dioxane) 2 ] ⋅ 1.5 dioxane (2a) and [Mg(C 9 H 7 ) 2 (tmeda)] (3), were formed. With the O-donors tetrahydrofuran (thf) and dimethylsulfoxide (dmso) two ionic Mg compounds 4 and 5 could be synthesized which have a [MgL 6 ] 2+ -cation [L = thf and dmso] and two uncoordinated indenide anions.

Einleitung 1) Magnesiumindenid (Mg(C 9 H 7 ) 2 , 1), das, anders als Magnesocen, keine Sandwich-Struktur besitzt, sondern polymer aufgebaut ist [1], bildet mit Tetrahydrofuran (THF) ein monomeres Basen-Addukt der Zusammensetzung [Mg(C 9 H 7 ) 2 (THF) 2 ] mit verzerrt tetraedrischer Koordination am Magnesiumatom [2]. C 2 H 4 -bzw. Me 2 Si-verbrückte Bis-Indenido-Magnesium-Komplexe geben mit Tetrahydrofuran ähnlich gebaute THF-Addukte, [C 2 H 4 (C 9 H 6 ) 2 Mg(THF) 2 ] und [Me 2 Si(C 9 H 6 ) 2 Mg(THF) 2 ] [3]. Auch Magnesocen ist in der Lage, stabile Basen-Addukte mit O-und N-Donatoren zu bilden. Über die Synthese und den Bau solcher Komplexe berichteten wir vor kurzem [4].

In dieser Arbeit beschreiben wir nun die Synthese und strukturelle Charakterisierung von weiteren Basen-Addukten des Magnesiumindenids und bestimmten erneut die Kristallstruktur der Stammverbindung Magnesiumindenid (1), um genauere Strukturparameter zu gewinnen. __________ 1) Verwendete Abkürzungen: DMSO (Dimethylsulfoxid), Ind (Indenid-Anion bzw. Indenido-Ligand, C 9 H 7 ), THF (Tetrahydrofuran), TMEDA (N,N,N´,N´-Tetramethylethylendiamin).

Page 4 of 24

Wiley-VCH

ZAAC

Ergebnisse

Synthese und Charakterisierung

Die Basenaddukte des Magnesiumindenids wurden durch direkte Reaktion von Mg(C 9 H 7 ) 2 (1) mit den entsprechenden Lewis-Basen hergestellt. Auf diese Weise wurde von Brintzinger und Mitarbeiter schon ein THF-Addukt der Zusammensetzung [Mg(C 9 H 7 ) 2 (THF) 2 ] synthetisiert und röntgenographisch charakterisiert [2]. Wir erhielten bei der Umsetzung von Mg(C 9 H 7 ) 2 mit THF ein Produkt der Zusammensetzung Mg(C 9 H 7 ) 2 ⋅ 8 THF (4). Die Kristallzüchtung für die Röntgenstrukturanalyse für alle neuen Basenaddukte gelang durch langsames Abkühlen gesättigter Lösungen. Für die Routineanalytik wurden die jeweiligen Verbindungen mit n-Hexan gewaschen und kurze Zeit im Ölpumpenvakuum getrocknet. Hierbei geben einige der Addukte einen Teil der koordinierten Lewis-Basen wieder ab. Die erhalten Komplexe wurden elementaranalytisch und IR-, sowie 1 H-und 13 C-NMR-spektroskopisch charakterisiert. Die spektroskopischen Daten befinden sich im Experimentellen Teil.

Einkristallstrukturen

Mg(C 9 H 7 ) 2 (1). Da die bekannte, von Atwood und Smith [1] erfolgten auf der Grundlage von Multi-Scans (Programm SADABS [START_REF] Sheldrick | SADABS, Program for area detector absorption correction[END_REF]). Die Strukturen wurden mittels Direkter Methoden gelöst und mit anisotropen Temperaturfaktoren verfeinert (Programme SHELXS-97 und SHELXL-97 [START_REF] Sheldrick | SHELXS-97, Program for the Solution of Crystal Structures[END_REF]). Wasserstoffatome wurden nach dem Reitermodell behandelt.

7 --Abb. 1 Abb. 2

 712 Abb. 1 Asymmetrische Einheit von Mg(C 9 H 7 ) 2 (1, zwei Formeleinheiten).

) 2 (Abb. 3 Schema 3 3 .

 2333 Abb.3 Struktur von [Mg(C 9 H 7 ) 2 (Dioxan) 2 ] ⋅ 1.5 Dioxan (2a). Unkoordinierte Dioxan-Solvens-Moleküle sind nicht dargestellt.

7 -Abb. 5 7 --Abb. 6

 7576 Abb. 5 Struktur von [Mg(THF) 6 ](C 9 H 7 ) 2 ⋅ 2 THF (4). Unkoordinierte THF-Solvens-Moleküle sind nicht dargestellt. Die Fehlordnung der beiden C 9 H 7 --Anionen ist nicht gezeigt, jedoch an den Schwingungsellipsoiden erkennbar. Abstände (pm): Mg(1)-O(1) 208.7(1), Mg(1)-O(2) 209.7(1), Mg(1)-O(3) 209.0(1).

Schema 4 Schema 5 7 --

 457 Bindungslängen [pm] in den beiden freien Indenid-Anionen der Verbindung [Mg(DMSO) 6 ](C 9 H 7 ) 2 (5, Standardabweichungen 0.3 -0.4 pm). Bindungslängen[pm] im Indenid-Anion (gemittelte Werte unter Annahme einer C 2v -Symmetrie im C 9 H Anion; oben: Indenid-Anion eins von Verbindung [Mg(DMSO) 6 ](C 9 H 7 ) 2(5); obere Mitte: Indenid-Anion von Verbindung [Rb(15-Krone-5) 2 ]C 9 H 7[START_REF] Wilde | Private Communication, CSD refcode XUSQOR[END_REF]; untere Mitte: Mittelwerte von beiden Anionen; unten: Werte aus einer DFT-Rechnung[START_REF]Die DFT-Rechnung (B3LYP/cc-pVQZ) wurde von Prof[END_REF].Zusammenfassung. Wie Magnesiumcyclopentadienid ist auchMagnesiumindenid in der Lage, Komplexe mit Lewis-Basen zu bilden. Welche Strukturen dabei im Einzelnen auftreten, wurde im Rahmen dieser Arbeit untersucht. Im Dioxan-Addukt 2a bleiben beide Indenido-Liganden am Magnesium-Ion koordiniert (der erste Indenido-Ligand η 2 -, der zweite nur noch η 1 -koordiniert). Auch im TMEDA-Addukt 3 sind die beiden Indenid-Anionen noch am Magnesium gebunden, ebenfalls mit einer η 2 -Koordination des ersten Indenido-und einer η 1 -Koordination des zweiten Indenido-Liganden. Mit Tetrahydrofuran als Lewis-Base kommt es erstmals zu einer Abspaltung der Indenid-Anionen vom Kation. Es entsteht die ionisch aufgebaute Verbindung [Mg(THF) 6 ](C 9 H 7 ) 2 ⋅ 2 THF (4). Mit Dimethylsulfoxid schließlich, dass eine sehr starke Wechselwirkung mit dem Magnesium(II)-Ion zeigt, wird ebenfalls ein Salz erhalten: Zusammensetzung [Mg(DMSO) 6 ](C 9 H 7 ) 2 (5). Da hier das freie Indenid-Anion nicht fehlgeordnet ist, konnten erstmals genaue Bindungsparameter für dieses Anion bestimmt werden (Schemata 4 und 5). Auch mit Pyridin als Liganden konnte eine ionisch aufgebaute Magnesium-Verbindung isoliert werden: [Mg(Pyridin) 6 ](C 9 H 7 ) 2 . Die erhaltenen Kristalle waren aber von so schlechter Qualität, dass wir die Struktur hier nicht näher diskutiert haben. Da wir alle NMR-Messungen in deuteriertem Pyridin durchgeführt haben, gehen wir davon aus, dass bei allen Komplexen (mit Ausnahme von 5) in Lösung die Substanz [Mg(Pyridin) 6 ](C 9 H 7 ) 2 vorgelegen hat, da sich die Resonanzen der H-und C-Atome vom Indenid-Anion bei den Komplexen 2, 3 und [Mg(C 9 H 7 ) 2 (THF) 2 ] kaum voneinander unterscheiden. Magnesiumindenid spaltet den anionischen Liganden leichter ab als Magnesiumcyclopentadienid. Beim Mg(C 5 H 5 ) 2 gelang uns die Abspaltung des Cyclopentadienido-Liganden nur mit den beiden Chelat-Liganden Pentamethyldiethylentriamin und 15-Krone-5 [4] sowie mit Dimethylsulfoxid [5], während beim Mg(C 9 H 7 ) 2 bereits Tetrahydrofuran und Pyridin freie unkoordinierte Indenid-Anionen liefern, die auch bei der Reaktion mit Pentamethyldiethylentriamin, 15-Krone-5 und mit Dimethylsulfoxid entstehen. Die Kristalle aus der Umsetzung von Mg(C 9 H 7 ) 2 mit Pentamethyldiethylentriamin und 15-Krone-5 waren dabei von so schlechter Qualität, dass wir die Strukturen hier nicht näher diskutiert haben. Experimenteller Teil Alle Arbeiten wurden in Schlenkrohrtechnik unter nachgereinigtem Argonschutzgas durchgeführt. Die verwendeten Lösungsmittel wurden nach gebräuchlichen Methoden getrocknet und unter Inertgas destilliert und aufbewahrt. Die Darstellung der Ausgangsverbindung Mg(C 9 H 7 ) 2 (1) erfolgte aus Dibutylmagnesium und Inden nach [16]. IR-Spektren: PERKIN-ELMER 1420; 1 H-NMR-und 13 C{ 1 H}-NMR-Spektren: BRUKER Avance 400 und VARIAN Gemini 2000BB (aufgenommen in [D 5 ]Pyridin mit TMS als Standard); Röntgenmessungen: BRUKER AXS Smart APEX Diffraktometer. Die Züchtung der Einkristalle der Komplexe 2a, 3, 4 und 5 ist bei den Synthesevorschriften der jeweiligen Substanzen aufgeführt. Die Kristalle wurden in Inertöl auf Glasfäden montiert und in den kalten Stickstoffstrom des Diffraktometers gebracht. Absorptionskorrekturen der Datensätze

und Mg(C 9 H 7 ) 2

	Tabelle 1 Ausgewählte Abstände (pm) der Verbindung Mg(C 9 H 7 ) 2 (1). des Fünfrings beobachtet man weitaus längere Mg-C-Abstände (> 280 pm). Beim THF-
	_______________________________________________ Komplex [Mg(C 9 H 7
	137.8 8 137.8 8	9 9	1 140.8 144.1 1 140.8 144.1	2 2	142.9 142.9
	141.8 141.8		144.7 144.7			3 3
	136.1 7 136.1 7	6 6	141.2 141.2	142.3 5 142.3 5	4 4	139.1 139.1
	137.0 8 137.0 8	9	1 141.2 142.2 141.2 142.2 1	2 2	139.1 139.1
	141.3 141.3		142.8 142.8			3 3
	137.0 7 137.0 7	6 6	141.2 141.2	142.2 5 142.2 5	4 4	139.1 139.1
	Schema 2 Bindungslängen [pm] in den Indenid-Anionen von [Mg(η 1 -C 9 H 7 ) 2 (THF) 2 ] [2]
	(oben; C2 ist koordiniert; Standardabweichungen 0.4 -0.5 pm) und [Mg(CH 3 )(η 3 -
	8 135.4 C 9 H 7 )(TMEDA)] [7] (unten; C2, C3, C4 sind koordiniert; Standardabweichungen 0.3 -0.4 9 140.9 1 2 140.5 142.4 8 9 pm).
	139.8		140.0			3
	7 139.8 7	6 6	141.0	142.1 5	4	141.8
	139.3 139.3 ⋅ 2 Dioxan (2) ⋅ 10 11 141.9 141.4 18 10 11 Mg(C 9 H 7 ) 2 ⋅ 136.2 17 136.2 ⋅ ⋅ ⋅ ⋅ ⋅ 3.5 Dioxan (2a). Bei der Umsetzung von 141.9 141.4 17 18 Magnesiumindenid mit Dioxan wird 2 als farbloses Produkt isoliert. Umkristallisation von 2
	139.9 139.9 aus Dioxan liefert Kristalle der Zusammensetzung Mg(C 9 H 7 ) 2 ⋅ 3.5 Dioxan (2a). Die 12 142.5 12 142.5
	140.4 140.4 Strukturbestimmung ergab, dass die asymmetrische Einheit aus einem Bis(1,4-142.5 134.7 142.6 13 14 15 16 142.5 13 14 15 16 134.7 142.6 dioxan)bis(indenido)magnesium-Komplex (Abb. 3) und anderthalb freien Dioxan-Molekülen
	140.6 21 140.6 besteht. Von den freien Dioxan-Molekülen liegt eines auf einem Symmetriezentrum der 140.1 136.4 19 20 142.6 139.6 143.2 26 27 140.1 136.4 19 139.6 143.2 27 20 21 142.6 26 Raumgruppe P2 1 /c. Aus Abb. 3 ist zu ersehen, dass sich ein monomerer neutraler
	139.0 139.0 Magnesiumkomplex mit zwei Indenido-und zwei Dioxan-Liganden gebildet hat. Damit 142.4 135.1 139.5 22 23 24 25 142.4 22 23 25 24 135.1 139.5 besitzt das Mg 2+ -Ion die Koordinationszahl vier. Die Mg-O-Abstände betragen 204.2(1) und
	138.6 30 138.6 205.6(1) pm und sind damit länger als im Komplex [Mg(C 9 H 7 ) 2 (THF) 2 ] (A) (199.3(2) pm 139.0 136.5 28 29 140.5 144.0 143.9 35 36 139.0 136.5 28 144.0 143.9 36 29 30 140.5 35 [2]). Dafür ist der O-Mg-O-Winkel in 2a (91.83(3)°) deutlich kleiner als im THF-Komplex A
	141.2 141.2 (101.01(12)° [2]). Ein Indenido-Ligand ist η 2 -artig koordiniert mit Mg-C-Bindungslängen 140.9 136.8 143.0 31 32 33 34 140.9 136.8 143.0 32 34 31 33 von 239.7(1) und 243.2(1) pm (weitere Mg-C-Abstände > 260 pm). Der zweite Indenido-
	Ligand koordiniert mit nur einem Kohlenstoffatom an das Magnesiumzentrum. Hier findet
	man eine relativ kurze Bindungslänge von 224.9(1) pm. Zu den anderen Kohlenstoffatomen

  Summenformel C 18 H 14 Mg C 32 H 42 MgO 7 C 24 H 30 MgN 2 C 50 H 78 MgO 8 C 30 H 50 MgO 6 S 6 Es wurde kein Flack-Parameter bestimmt, da die Friedel-Paare für die Verfeinerung gemittelt wurden. Es ist kein schweres Atom in der Struktur vorhanden. Die vollständigen kristallographischen Daten der in dieser TMEDA), 2.15 (s, CH 3 -TMEDA). 13 C-NMR: δ = 132.3 (C1/5), 119.1 (C3 und C6/9), 112.8 (C7/8), 93.3 (C2/4), 58.2 (CH 2 -TMEDA), 47.5 (CH 3 -TMEDA) [19]. Einkristalle der Verbindung fielen direkt bei der Synthese an. THF [2] und Mg(C 9 H 7 ) 2 ⋅ 8 THF (4). Mg(C 9 H 7 ) 2 (1) (0.30 g (1.18 mmol) wurde mit THF (5 mL) versetzt und in der Siedehitze gelöst. Die rote Lösung wurde langsam auf Raumtemperatur abgekühlt und anschließend drei Tage bei einer Temperatur von -22 °C gelagert, wobei sich rote Kristalle bildeten. Die Kristalle wurden zweimal mit jeweils n-Hexan (je 5 mL) gewaschen, dann zehn Minuten lang im Vakuum (0.1 Torr) getrocknet. Ausb. 0.45 g (1.13 mmol, 96%) von Mg(C 9 H 7 ) 2 ⋅ ⋅ ⋅ ⋅ 2 THF, Zers. ab 125 °C. Löslichkeit: mäßig löslich in Pyridin und THF, schwer löslich in Benzol und n-Hexan. Analyse für C 26 H 30 MgO 2 (398.8): C 76.1 (ber. 78.3); H 8.1 (7.6)%. IR (Nujol): 1596, 1573, 1317, 1245, 1217, 1073, 1021, 914, 874, 766, 732 cm -1 . 1 H-NMR: δ = 7.88 (m, H6/9), 7.38 (t, H3), 6.94 (m, H7/8), 6.71 (d, H2/4), 3.66 (m, CH 2 -O), 1.61 (m, CH 2 -CH 2 ). 13 C-NMR: δ = 132.3 (C1/5), 119.5 (C3 und C6/9), 113.2 (C7/8), 94.0 (C2/4), 67.9 (CH 2 -O), 25.8 (CH 2 -CH 2 ) [19]. Das Integral des 1 H-NMR-Spektrums deutet darauf hin, dass Mg(C 9 H 7 ) 2 (1) (0.25 g (0.98 mmol) wurde mit THF (5 mL) versetzt und in der Siedehitze gelöst. Zu der klaren, roten Lösung wurde langsam DMSO (1.0 mL, 14 mmol) getropft, wobei die Lösung eine rot-violette Farbe annahm. Die Lösung wurde langsam auf Raumtemperatur abgekühlt. Es bildeten sich violette Kristalle. Die Kristalle wurden zweimal mit jeweils n-Hexan (je 5 mL) gewaschen, dann mehrere Stunden lang im Vakuum (0.1 Torr) getrocknet. Ausb. 0.59 g (0.82 mmol, 84%), Zers. ab 143 °C. Löslichkeit: mäßig löslich in Pyridin, schwer löslich in THF, Benzol und n-Hexan. Analyse für C 30 H 50 MgO 6 S 6 (723.4): C 56.4 (ber. 49.8); H 6.7 (7.0)%.

	__________________________________________________________________________________________
	Tabelle beschriebenen Strukturen von 1, 2a, 3, 4 und 5 wurden beim Cambridge Crystallographic Data Centre
	unter den Hinterlegungsnummern CCDC-xxxxxx -xxxxxx hinterlegt. Kopien der Daten können kostenlos bei
	Tabelle 3 Kristallographische Daten für Mg(C 9 H 7 ) 2 (1), [Mg(C 9 H 7 ) 2 (Dioxan) 2 ] ⋅ 1.5 Dioxan (2a), [Mg(C 9 H 7 ) 2 (TMEDA)] (3), [Mg(THF) 6 ](C 9 H 7 ) 2 ⋅ 2 THF (4) und [Mg(DMSO) 6 ](C 9 H 7 ) 2 (5). __________________________________________________________________________________________ Verbindung 1 2a 3 4 5 Formelmasse /g mol -1 254.60 562.97 370.81 831.43 723.37 Messtemperatur /K 100 153 153 153 153 Kristallgröße /mm 0.5/0.10/0.07 0.49/0.45/0.41 0.3/0.2/0.2 0.34/0.19/0.19 0.50/0.24/0.17 Kristallsystem orthorhombisch monoklin monoklin triklin monoklin folgender Adresse in Großbritannien angefordert werden: The Director CCDC, 12 Union Road, Cambridge CB2 1EZ, UK (Fax: int.code+(1223)336-033, E-mail: fileserv@ccdc.cam.ac.uk). Synthese von Mg(C 9 H 7 ) 2 ⋅ ⋅ ⋅ ⋅ 2 Dioxan (2). Mg(C 9 H 7 ) 2 (1) (0.30 g, 1.18 mmol) wurde mit Dioxan (5 mL) versetzt und in der Siedehitze gelöst. Anschließend wurde die hellrote Lösung langsam auf Raumtemperatur abgekühlt, wobei sich farblose Kristalle bildeten. Es wurde zweimal mit n-Hexan (je 5 mL) gewaschen und das Produkt für zehn Minuten im Vakuum (0.1 Torr) getrocknet. Ausb. 0.35 g (0.81 mmol, 69%), Zers. ab 230 °C. Löslichkeit: mäßig 7.37 (t, H3), 6.93 (m, H7/8), 6.70 (d, H2/4), 3.62 (s, Dioxan). 13 C-NMR: δ = 132.1 (C1/5), Synthese von Mg(C 9 H 7 ) 2 ⋅ ⋅ ⋅ ⋅ 2 Mg(C 9 H 7 ) 2 ⋅ ⋅ ⋅ ⋅ 2 THF geringfügig mit Komplex 4 verunreinigt ist, da etwa 2.5 Mole THF pro
	Raumgruppe 119.3 (C3 und C6/9), 112.9 (C7/8), 93.9 (C2/4), 67.2 (Dioxan) [19]. P2 1 2 1 2 1 a , Nr. 19 P2 1 /c, Nr. 14 Cc a , Nr. 9 P-1, Nr. 2 Mol Magnesium gefunden werden.	P2 1 /n, Nr. 14
	a /pm b /pm Einkristalle konnten durch mehrtägige Lagerung einer gesättigten Dioxan-Lösung im 2131.1(4) 1139.55(4) 846.6(2) 985.91(9) 1201.68(10) 1230.5(3) 1329.70(5) 2345.7(5) 1091.88(10) 1563.54(13) Einkristalle der THF-reicheren Verbindung Mg(C 9 H 7 ) 2 ⋅ ⋅ ⋅ ⋅ 8 THF (4) konnten aus der
	c /pm Kühlschrank erhalten werden. Die Kristalle haben dabei die Zusammensetzung 1005.9(2) 1971.50(7) 1060.7(2) 1177.42(11) 1984.17(16) Mutterlauge erhalten werden. Diese enthalten neben den sechs am Magnesium(2+)-Ion
	α /° [Mg(C 9 H 7 ) 2 (Dioxan) 2 ] ⋅ 1.5 Dioxan (2a). Sie enthalten neben den beiden koordinierten noch 99.914(2) koordinierten noch zwei weitere zusätzliche freie THF-Moleküle.
	β /° weitere anderthalb freie Dioxanmoleküle, die beim Trocknen im Vakuum leicht abgegeben 101.761(1) 101.34(3) 101.064(2) 90.267(1)
	γ /° Zellvolumen /10 6 pm werden. Synthese von Mg(C 9 H 7 ) 2 ⋅ 2637.9(9) ⋅ ⋅ ⋅ 6 DMSO (5). 2924.6(2)	2065.3(7)	105.321(2) 1166.0(2)	3728.0(5)
	Z	8	4	4	1	4
	D ber /g cm -3 Synthese von Mg(C 9 H 7 ) 2 ⋅ 1.282 ⋅ ⋅ ⋅ TMEDA (3). Mg(C 9 H 7 ) 2 (1) (0.25 g, 0.98 mmol) wurde in 1.279 1.193 1.184 1.289
	µ /mm -1 N,N,N',N'-Tetramethylethylendiamin (10 mL) gelöst, wobei sich die Lösung rot-orange 0.115 0.108 0.097 0.090 0.421
	Beugungsw. (2Θ max /°) verfärbte. Durch Lagerung bei -22 °C wuchsen orange-rote Kristalle, die zweimal mit n-50 (Mo-K α ) 65 (Mo-K α ) 55 (Mo-K α ) 54 (Mo-K α ) 55 (Mo-K α )
	Indexbereich ±h; ±k; ±l Hexan (je 5 mL) gewaschen und anschließend zehn Minuten im Vakuum (0.1 Torr) 25; 14; 11 17; 20; 29 10; 30; 13 12; 13; 15 15; 20; 25
	Reflexe (gem./unabh.) Reflexe mit F o ≥4σ(F o ) getrocknet wurden. Ausb. 0.18 g (0.49 mmol, 50%), Zers. ab 230 °C. Löslichkeit: mäßig 19317/2629 78472/10483 12190/2354 13724/5033 43683/8481 1153 7984 1919 3281 6447
	Parameterzahl löslich in Pyridin und THF, schwer löslich in n-Hexan. 343 364 248	348	410
	Gütefaktor R (F o ≥4σ)	0.047	0.047	0.046	0.041	0.039
	Gütefaktor wR2	0.089	0.132	0.095	0.090	0.093
	Restelektronendichte	0.18/-0.28	0.42/-0.22	0.27/-0.20	0.22/-0.24	0.64/-0.28
	(max/min, e/10 6 pm 3 )

a löslich in Pyridin, Toluol und THF, schwer löslich in n-Hexan. Analyse für C 26 H 30 MgO 4 (430.8): C 72.2 (ber. 72.5); H 7.0 (7.0)%. IR (Nujol): 1587, 1253, 1121, 1050, 870, 765, 739, 721 cm -1 . 1 H-NMR: δ = 7.89 (m, H6/9), Analyse für C 24 H 30 MgN 2 (370.8): C 75.9 (ber. 77.7); H 8.2 (8.2); N 7.4 (7.6)%. IR (Nujol): 3034, 1593, 1335, 1315, 1283, 1242, 1217, 1018, 1005, 946, 744, 716 cm -1 . 1 H-NMR: δ = 7.88 (m, H6/9), 7.36 (t, H3), 6.92 (m, H7/8), 6.70 (d, H2/4), 2.38 (s, CH 2 -IR (Nujol): 1586, 1586, 1435, 1408, 1322, 1254, 1057, 955, 765, 729, 697 cm -1 . 1 H-NMR: δ = 8.00 (m, H6/9), 7.41 (t, H3), 7.01 (m, H7/8), 6.80 (d, H2/4), 2.48 (s, CH 3 ).

Wiley-VCH ZAAC


C E Brooks
email: cathy.brooks@afbini.gov.uk

D A Finlay

W Mcconnell

D A Ball

Culture enrichment assists the diagnosis of cattle botulism by a monoclonal antibody based sandwich ELISA

Keywords: C. botulinum, cattle botulism, ELISA, monoclonal antibodies

Monoclonal antibodies (MAbs) obtained from a mouse immunised with Clostridium botulinum type D toxoid were developed into a sandwich ELISA (sELISA) format that was able to detect type D toxin and types C and D toxin complexes. The sELISA was examined for its potential to replace the mouse bioassay as an alternative in vitro assay for the diagnosis of cattle botulism. Its application directly to intestinal samples collected from suspect cattle botulism cases and prepared for testing for the standard mouse bioassay showed poor correlation and sensitivity with the mouse bioassay results.

However, anaerobic pre-enrichment of the samples after heat treatment at 80 o C for 10 minutes to activate any residual C. botulinum spores greatly improved the sELISA detection rate of the toxin by increasing the sample toxin levels. All of the mouse bioassay positive cattle cases tested were detected by the sELISA from the heated and pre-enriched samples tested after 24 h incubation. Toxin was detected by sELISA and subsequently confirmed by mouse bioassay in samples from an additional 3 cases that had been originally mouse bioassay negative. The results indicate that the application of this procedure for screening intestinal samples for C. botulinum strains that produce types C and D toxins from suspect cattle botulism cases would improve the diagnostic rate as well as significantly reduce the number of mice involved in diagnosis.

Division for diagnostic investigation has risen significantly, and from the 594 cases recorded between 2001-2007, 97 (16.3%) have been confirmed as botulism by the mouse bioassay [START_REF] Scarlatos | Methods for Detecting Botulinum Toxin with Applicability to Screening Foods Against Biological Terrorist Attacks[END_REF]. Although the recommended test sample for confirmation of bovine botulism is serum [START_REF] Dowell | A new Procedure for laboratory diagnosis of botulism. Coproexamination for botulinal toxin and Clostridium botulinum[END_REF], experience at this laboratory has shown that botulinum neurotoxin (BoNT) is detected much more commonly by the examination of intestinal contents (unpublished data, AFBINI). The mouse bioassay remains the 'gold standard' test because of its high analytical sensitivity [(0.8 x 10 8 LD50/mg protein for type C toxin and 1.6 x 10 8 LD50/mg protein for type D toxin [START_REF] Sugiyama | Clostridium botulinum. Pathogenesis of bacterial infections in Animals[END_REF]], however the use of live animals in the test raises obvious welfare considerations and makes the test costly to perform.

The present study was undertaken to develop a monoclonal antibody (MAb) based BoNT sandwich ELISA (sELISA) as a potential replacement for the mouse bioassay. The samples obtained were tested for toxin as received and also after heat shock and anaerobic enrichment. It was postulated that C. botulinum spores as well as the toxin were likely to be present in the intestinal contents in botulism cases, and that a sample enrichment procedure involving heat shock and anaerobic culture could raise the toxin level to a level detectable by sELISA. The detection of toxin from the culture of spores from these samples could be regarded as significant since the organism is not usually found in the absence of botulism (Dowell et al, 1977, Princewell andAgba, 1981). The sELISA results were compared with those of the mouse bioassay. myeloma line SP2/0-Ag14 at a ratio of 5:1 [START_REF] Galfre | Preparation of monoclonal antibodies: Strategies and procedures[END_REF][START_REF] Teh | Generation of monoclonal antibodies to human gonadotrophin by a facile cloning procedure[END_REF].

The subsequent hybridomas were screened by ELISA in microtitre wells (Dynatech, Chantilly, VA, USA) coated with the immunising toxoid antigen. Supernatants from the hybridomas showing a strong optical density (OD) reading were titrated and the five demonstrating the highest titres were selected for cloning. MAbs from the cloned hybridomas were tested by ELISA against microtitre strips coated with BoNT types A, B, C, D, E, F and G (Metabiologics Inc., Wisconsin, USA) to check for specificity.

Sandwich ELISAs

Three of the five cloned hybridomas were adapted to grow in RPMI 1640 (Gibco, 21875) medium containing only 5% (v/v) gamma-globulin-free horse serum (Labtech International, Donor Horse Serum, IGG free, Cat.No. 4-101-500/IGG) and grown in bulk in 200 ml triple layer flasks (Nunclon, Nalge Nunc International, Denmark). The MAbs from these were purified by caprylic acid precipitation [START_REF] Mckinney | A simple, non-chromatographic procedure to purify immunoglobulins from serum and ascites fluid[END_REF] and some of the purified immunoglobulin was biotinylated [START_REF] Hofmann | Avidin binding of carboxylsubstituted biotin and analogues[END_REF].

Combinations of these three MAbs were examined in the following sELISA format using the immunising D toxoid as antigen, their optimal working dilutions being determined by chequerboard titration. Well volumes of 100 l were used in all but the final step of the toxoid antigen as the negative control. The absorbance at 450 nm was determined using an ELISA plate reader (Titertek Multiskan, Helsinki, Finland) and greater than three times the average negative control (PTN) OD value for each plate was taken as a positive reaction.

Combinations of MAbs were examined in the sELISA format for sensitivity for D toxoid and for specificity against types A, B, C, D and E toxoid complexes and types C and D toxin complexes (Metabiologics Inc., Wisconsin, USA), and a selected combination was subsequently used to examine clinical samples. Culture supernatants from heat shocked and cultured Day 1 or Day 5 samples that were sELISA positive but which had been previously negative by the mouse bioassay when tested directly were also tested by the mouse bioassay. Dilutions of 1/5 to 1/7, dependent on available volume, were prepared by filter sterilisation before testing.

Immunoblotting

Statistics

The results were compared with those of the mouse bioassay by analysis in terms of correlation (i.e. the percentage of sELISA results that were the same as the mouse bioassay results), sensitivity (i.e. the percentage of the mouse bioassay positive samples that were found positive by sELISA) and specificity (i.e. the percentage of the mouse bioassay negative samples found negative by sELISA), with the mouse bioassay results being taken as the gold standard [START_REF] Altman | Diagnostic tests. 1: Sensitivity and specificity[END_REF].

A c c e p t e d M a n u s c r i p t 8 3. Results

Antibodies

Forty seven of the 544 hybridomas that developed from the D toxin fusion were reactive to the type D toxoid and the five with the highest antibody titre to the type D toxoid were cloned. Three of these hybridomas, 7A10, 7D10 and 5B5, continued to produce high levels of antibody after cloning and were grown in bulk. These antibodies were specific for type D toxin when tested by direct ELISA against C. botulinum toxin types A, B, C, D, E, F and G.

Sandwich ELISA

Monoclonal antibody reagents prepared from the three bulk cultured MAbs 7A10, 7D10 and 5B5 were tested in various combinations in the sELISA format and 7A10 and 5B5

were selected for further work on the basis of their specificity and sensitivity. Two sELISA combinations (MAb 7A10 capturing with MAb 7A10 biotinylated and MAb 7A10 capturing with MAb 5B5 biotinylated) were specific for type D when tested against types A, B, C, D and E toxoid complexes but detected both types C and D toxin complexes. The analytical sensitivity of a sELISA using MAb 7A10 for both capture and detection was 12.5 ng per ml of the immunising D toxoid. The analytical sensitivity of the sELISA using MAb 7A10 for capture and MAb 5B5 for detection was 3 ng per ml of the immunising D toxoid and 1.5 ng per ml of D toxoid complex or D toxin complex (Metabiologics Inc), and also had a sensitivity of 1.5 ng per ml for the C toxin complex.

Immunoblots

The most prominent staining observed with MAb 5B5 was a 50 kDa protein corresponding to the neurotoxin light chain, and 70 kDa and 33 kDa proteins

Test samples

Preliminary results using MAb 7A10 on both sides of the sELISA for the direct testing of 325 non-enriched samples collected from 115 clinically suspect cattle in Northern Ireland during 2002 and 2003 showed a poor correlation of 72.3% with a sensitivity of 13.8% and specificity of 93.7% relative to the mouse bioassay (results not shown).

Subsequently, the sELISA combination of MAbs 7A10 and 5B5 with improved sensitivity was used to examine additional samples.

The results obtained with the mouse bioassay and this sELISA from the direct testing of 63 non-enriched samples collected from 16 farms during 2006 and 2007 are summarised in Table 1. The comparative results between the mouse bioassay and these sELISA results showed an overall correlation at sample level of 76.2% with a sensitivity and specificity of 42.9% and 85.7% respectively.

Heat treatment and pre-enrichment culture

A total of 28 of the 63 individual samples collected during 2006-2007 were sELISA positive on Day 1 post enrichment as summarised in Table 2. The sELISA detected 13 of the 14 samples that had initially tested positive for toxin by the direct mouse bioassay. In addition, the sELISA indicated the presence of type C or D toxin complexes in a further A c c e p t e d M a n u s c r i p t 10 negative for the mouse bioassay when originally tested directly as samples from clinically suspect botulism cases. Eleven (8 from day 1 and the 3 from day 5) of these 18 samples were from 7 individual animal cases where toxin had been detected by the mouse bioassay before enrichment and 7 were from 3 mouse bioassay negative individual animal cases. All 18 were confirmed as toxin positive by the mouse bioassay neutralisation test.

Discussion

The MAb-based sELISA with the sensitivity of 3 ng per ml of D toxoid and 1.5 ng per ml D and C toxin complexes that was developed in this study applied to 24 h culture enriched samples appears to have the potential of providing a rapid and humane assay for the detection of type C or D toxin producing Clostridium botulinum in intestinal contents samples from suspect cases of cattle botulism. Although the sELISA lacked sufficient sensitivity for the direct detection of toxin from most of the mouse bioassay positive samples, the application of a procedure for the enrichment culture of any spores that may be present in the test samples greatly improved the detection rate of the toxin by increasing the sample toxin levels.

Although MAbs 7A10 and 5B5 were shown to be specific for type D toxin when tested by ELISA against purified toxin, they demonstrated few individual immunoblot staining differences against types C and D toxin complexes (Fig. 1), and did demonstrate a reaction to type C as well as type D toxin complexes by sELISA. The detection of several proteins by each of these MAbs indicates that the epitopes detected in the immunoblots were common to several constituents of the toxin complex. However, the reduction of these toxin complexes during SDS-PAGE may have exposed epitopes which A c c e p t e d M a n u s c r i p t 11 are not available to the MAbs in the intact toxin or toxin complex in the sELISA. It is recognised that C. botulinum type C and D toxin complexes are antigenically similar [START_REF] Oguma | Antigenic similarity of toxins produced by Clostridium botulinum Type C and D Strains[END_REF], but since the BoNT in the mouse bioassay positive samples were typed as D or a chimeric combination of C and D (data not shown), it is uncertain whether this sELISA will detect BoNT C in suspect samples. As far as the diagnosis of botulism in cattle is concerned, since both type C and D toxin are recognised causes [START_REF] Senturk | Outbreak of botulism in a dairy herd in Turkey[END_REF], the distinction between type C and D toxins may be regarded as unnecessary at least for initial diagnosis of the disease.

The analytical sensitivity of the sELISA for the direct testing of suspect samples was poor, with the majority of mouse bioassay positive samples not being detected by the sELISA from the test samples. In addition, the sELISA detected 7 positive samples from the directly tested samples of 2006-2007 (Table 1) that were not detected initially by the mouse bioassay. Only two of these 7 positives were found to be positive by both sELISA and mouse bioassay after heat treatment and enrichment. The sELISA positivity of the non-enriched samples may be attributed to the sELISA antibodies identifying inactive toxin fragments or to non-specific binding of the biotinylated MAb to anti-species antibody or bacterial antigens such as Staphylococcus aureus protein A that may be present in such a complex matrix as faeces.

Although toxin detection is typically used to diagnose botulism, the data presented here demonstrate that the organism is also recoverable, as evidenced by toxin detection post culture in 13/14 samples from 2007 to 2008 in which toxin was originally found by mouse bioassay. Following enrichment, all 18 sELISA positive samples that had initially been mouse bioassay negative were confirmed to be positive for C. botulinum toxin by Botulism in cattle is considered to be caused mainly by intoxication due to ingestion of pre-formed toxin, as opposed to toxicoinfection with neurotoxins derived from growth of C. botulinum in the intestine [START_REF] Smith | Botulism. The Organism, its Toxins, the Disease[END_REF]. The ingested material that subsequently causes botulism is likely to contain toxin and spores, and the results of the present study indicate that the spores may be more persistent and readily detected in the intestinal samples examined than the toxin. However, it is recognised that C. botulinum spores are widely distributed at low levels in the environment, and the culture and testing of a range of environmental and intestinal samples from cattle free from clinical suspicion of botulism is required to fully evaluate the significance of this finding to determine diagnostic specificity and sensitivity. This work is currently being undertaken at this institute and initial results have demonstrated the low occurrence of C. botulinum spores / toxin in intestinal samples collected from cattle free of clinical suspicion of botulism examined by the methods used in the current work (unpublished results).

Conclusion

The mouse bioassay remains as the 'gold standard' assay for the detection of botulinum toxin because of its greater sensitivity for the low levels of the toxins relative to in vitro assays. Its continued use is certainly an animal welfare issue and replacement with reproducible in vitro tests is long overdue. The present results demonstrate that although A c c e p t e d M a n u s c r i p t 13 the heat shock and culture process prior to sELISA failed to detect one botulism sample that had been detected by the mouse bioassay, it did not miss any cases identified by the initial mouse bioassay and was able to detect three new cases missed by the latter after only 24 h enrichment. There remains the possibility that the sELISA positive results that were detected after enrichment may have arisen from the culture of contaminating spores of environmental origin, and further work is required to fully evaluate this approach. This study does indicate that the use of culture enrichment for 24 h and subsequent sELISA for screening samples for toxin produced from group III C. botulinum organisms, with the mouse bioassay being used for confirmation, may improve the diagnostic rate as well as significantly reduce the number of mice involved in the diagnosis of bovine botulism.

  the number of suspect clinical cases submitted to the Veterinary Sciences

  obtained from a type D toxoid (Biodesign International, Saco, ME, USA) immunised BALB/c mouse [carried out under a project licence issued by the Department of Health, Social Services and Public Safety in Northern Ireland in compliance with the 'Animals (Scientific Procedures) Act 1986'] were fused with mouse

  MAb in coating buffer (0.05 M carbonate/bicarbonate buffer, pH 9.5) was used to coat Maxisorp microtitre plate wells (Nalge Nunc International, Denmark) at 37 o C for 2 h. The coating antibody solution was then discarded and a blocking solution of coating buffer containing 1 % (w/v) bovine serum albumin (BSA; Initial fraction by heat shock, Sigma) was added and incubated overnight at 4 o C. The subsequent steps consisting of D toxoid antigen at 0.2 µg/ml, biotinylated MAb and streptavidin-peroxidase (Sigma) were diluted in PTN buffer [0.01 M PBS pH 7.2 (27ml of 0.2 M anhydrous NaH 2 PO 4 , 73ml of 0.2 M Na 2 HPO 4 , 17g NaCl made up to 2 L with dH 2 O), with 0.04% (v/v) Tween 80 and 2% additional NaCl (w/v)] containing 1% BSA (w/v), incubated with shaking for 1 h at 37 o C and washed between steps with ELISA wash [0.01 M PBS, pH 7.2, containing 0.05% (v/v) Tween 20]. The final peroxidase substrate (TMB, Millipore) stage was incubated for 10 min at 37 o C without shaking and stopped with 50 l per well 2.5 M sulphuric acid. PTN buffer in four wells replaced the D

  was carried out using NuPAGE 4-12% BisTris Gel 1.00 x 2D well (Invitrogen Ltd, Paisley, UK) on C. botulinum type C toxin complex and C. botulinum type D toxin complex (Metabiologics Inc., Wisconsin, USA) at 150 µg/ml, under reducing conditions. Western blot transfer of the proteins onto nitrocellulose (Invitrogen) was overnight at 30 mA with subsequent blocking with PTNE (100 ml 0.01 M PBS, 2 g NaCl, 1 ml 0.1 M EDTA, 2.5 ml 20% Tween 80) containing 2% (w/v) BSA (BSA; Initial fraction by heat shock, Sigma) for 1 h at 37ºC. Strips of the nitrocellulose preparations of both type C and type D complexes were used to test biotinylated MAbs 5B5 at 1/25,000 and 7A10 at 1/1000 dilutions in PTNE with 2% BSA for 1 h at 37ºC and washed in PTNE four times. Bound antibodies were detected by incubation of the strips with streptavidin peroxidise at 1/2000 in PTNE and, after washing as above, developed using DAB (3,3-diaminobenzidine tetrahydrochloride; Sigma-Aldrich Company Ltd, Dorset, England) substrate in 0.02 M Tris-HCL buffer containing H 2 O 2 .2.4 Test samplesSixty three bovine samples collected from 21 clinically suspect cattle from 16 farms in Northern Ireland during 2007 and 2008 were tested by the sELISA using MAb 7A10 for capture and biotinylated MAb 5B5 for the detection stage. These samples consisted of 10% (w/v) homogenates in 0.01 M PBS of abomasum contents (n=10), faeces (n=21), rumen contents (n=16) and small intestine contents (n=16) and had been stored at +4ºC for up to 3 months.In addition to direct testing, the 63 bovine field samples were also heat treated and cultured anaerobically for the possible presence of C. botulinum before testing by sELISA. Briefly, 200 µl of each original sample [10% (w/v) homogenates in 0.01M PBS] A c c e p t e d M a n u s c r i p t 7 was heat treated at 80ºC for 10 min and 100 µl of each was added to 20 ml of pre-reduced 1% (w/v) cooked meat medium (CMM, Difco) with Brain Heart Infusion (BHI, Oxoid) and incubated anaerobically at 40ºC. Two ml of broth was removed after overnight (Day 1) and 5 day (Day 5) enrichment and tested by sELISA. 2.5 Mouse bioassay All samples submitted for diagnostic investigation from suspect cattle botulism cases had been tested by the mouse bioassay, carried out under a project licence issued by the Department of Health, Social Services and Public Safety in Northern Ireland in compliance with the 'Animals (Scientific Procedures) Act 1986'.

  toxigenic haemagglutinating proteins, on each of the type C and type D toxin complexes[START_REF] Suzuki | Characterization of the interaction between subunits of the botulinum toxin complex produced by serotype D through tryptic susceptibility of the isolated components and complex forms[END_REF]. MAb 7A10 detected proteins of the same size as MAb 5B5 but also detected a prominent band at 15 kDa and faint bands of approximately 100 kDa corresponding to the BoNT heavy chain on both the type C and D complexes (Fig1).

  . In so far as no false positive sELISA results were obtained from the post enrichment assay, the sample treatment involving heating and diluting appears to reduce the potential for non-specific signals in the sELISA. In addition, three new botulism cases were tentatively confirmed on the basis of the cultural presence of toxin producing organism.

Fig. 1

 1 Fig. 1 Immunoblot of C. botulinum type C and D complexes with MAbs 5B5 and 7A10.

Table 1 .

 1 Correlation between the direct mouse bioassay and the sELISA results on untreated samples collected from suspect cases of cattle botulism from 16 farms during2006-2007.

	Sample	N.	Mouse	sELISA	Correlation	Sensitivity	Specificity
			bioassay	Positive	Negative
			Positive	6	8
	Individual test	63	Negative	7	42	76.2	42.9	85.7
	sample
			Positive	6	2
	Individual	21	Negative	4	9	71.4	75.0	69.2
	animal

Table 2 .

 2 Correlation between the direct mouse bioassay and the sELISA results following heat treatment and enrichment for 1 day on samples collected from suspect cases of cattle botulism from 16 farms during2006-2007.

	Sample	N.	Mouse	sELISA	Correlation	Sensitivity	Specificity
			bioassay	Positive	Negative
			Positive	13	1
	Individual test	63	Negative	15	34	74.6	92.8	69.3
	sample
			Positive	8	0
	Individual	21	Negative	3	10	85.7	100	76.9
	animal

Table 1 .

 1 Correlation between the direct mouse bioassay and the sELISA results on untreated samples collected from suspect cases of cattle botulism from 16 farms during2006-2007.

	Table
	Sample	N.	Mouse	sELISA	Correlation	Sensitivity	Specificity
			bioassay	Positive	Negative
			Positive	6	8
	Individual test	63	Negative	7	42	76.2	42.9	85.7
	sample
			Positive	6	2
	Individual	21	Negative	4	9	71.4	75.0	69.2
	animal

Table 2 .

 2 Correlation between the direct mouse bioassay and the sELISA results following heat treatment and enrichment for 1 day on samples collected from suspect cases of cattle botulism from 16 farms during2006-2007.

	Sample	N.	Mouse	sELISA	Correlation	Sensitivity	Specificity
			bioassay	Positive	Negative
			Positive	13	1
	Individual test	63	Negative	15	34	74.6	92.8	69.3
	sample
			Positive	8	0
	Individual	21	Negative	3	10	85.7	100	76.9
	animal

Table