Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

Kinetic versus thermodynamic control during the formation of [2]rotaxanes by a dynamic template-directed clipping process

A template-directed dynamic clipping procedure has generated a library of nine [2]rotaxanes that have been formed from three dialkylammonium salts-acting as the dumbbell-shaped components-and three dynamic, imino bond-containing, [24]crown-8-like macrocycles-acting as the ring-shaped components-which are themselves assembled from three dialdehydes and one diamine. The rates of formation of these [2]rotaxanes differ dramatically, from minutes to days depending on the choice of dialkylammonium ion and dialdehyde, as do their thermodynamic stabilities. Generally, [2]rotaxanes formed by using 2,6-diformylpyridine as the dialdehyde component, or bis(3,5-bis(trifluoromethyl)benzyl)ammonium hexafluorophosphate as the dumbbell-shaped component, assembled the most rapidly. Those rotaxanes containing this particular electron-deficient dumbbell-shaped unit, or 2,5-diformylfuran units in the macroring, were the most stable thermodynamically. The relative thermodynamic stabilities of all nine of the [2]rotaxanes were determined by competition experiments that were monitored by (1)H NMR spectroscopy.     

Self-assembly of dendrimers by slippage

[reaction: see text] A dendrimer with rotaxane-like characteristics has been assembled under thermodynamic control from complementary wedge-shaped precursors by slippage in CH(2)Cl(2). The driving force for the self-assembly process is the molecular recognition that exists as a result of [N(+)-H.O] and [C-H.O] hydrogen bonds between an NH(2)(+) center in one Fréchet-type benzyl ether wedge and a dibenzo[24]crown-8 unit that links the other two such wedges.     

Can multivalency be expressed kinetically? The answer is yes

Inspired by the concept of multivalency and in pursuit of ever more intricate artificial molecular machines, we investigated the strict self-assembly of a triply threaded two-component superbundle, starting from a tritopic receptor in which three benzo[24]crown-8 macrorings are fused onto a triphenylene core and a trifurcated trication wherein three bipyridinium units are linked 1,3,5 to a central benzenoid core. The result of the investigation was quite unexpected and surprising. It transpired that the rapid formation of a doubly threaded two-component complex was followed by an extremely slow conversion (a week at 253 K in CD3COCD3 to reach equilibrium) of this kinetically controlled product into a thermodynamically controlled one, namely a triply threaded two-component superbundle. This intriguing observation begs the question: are there instances in nature where multivalency is expressed as a kinetically controlled process, prior to an equilibrium state being reached, and if so, what are the biological implications, if any?     

A rotaxane-like complex with controlled-release characteristics

A rotaxane-like complex, based on a dumbbell-shaped component containing an NH(2)(+) recognition site for a [25]crown-8 ring component and a slippage stopper in the form of a p-(tert-butyl)phenyl group, has been synthesized by a "threading-followed-by-stoppering" approach. The half-life for dissociation of this complex, which is very sensitive to its environment, can be varied from minutes to months by changing the temperature and the polarity of the solvent.     

Template-directed dynamic synthesis of mechanically interlocked dendrimers

The versatility and efficiency of dynamic covalent chemistry (DCC) has been exploited in the convergent synthesis of mechanically interlocked dendrimers that are based upon the mutual recognition expressed between secondary dialkylammonium ions and crown ether-like macrocycles. Reversible imine bond formation is employed to clip two acyclic fragments, one of them a diformylpyridine unit bearing a dendritic side chain, and the other a complementary dianiline in the shape of the di(o-aminophenyl)ether of tetraethylene glycol, around each arm of a tritopic trisammonium ion core, thereby affording a branched [4]rotaxane. This template-directed strategy has been demonstrated to work in very high yields (>90%) with successive generations (G0-G2) of a modified Fréchet-type dendritic wedge attached to the 4-position of the diformylpyridine unit. Reduction of these dynamic dendritic systems is achieved upon treatment with borane.THF and results in kinetically stable compounds. The inherent modularity of the overall process should allow for the rapid and straightforward access to many other analogous mechanically interlocked systems in which either the branched core or the dendritic periphery can be modified to suit the needs of any given application of these molecules. Indeed, the dynamic nature of the initial thermodynamically mediated assembly could be utilized in order to amplify particular products from a potential library as a result of a selective recognition process.