Specific ion-molecule interactions of imidazole and 1-methylimidazole in nitrobenzene

We have studied, by conductivity measurements, the formation of hydrogenbonded complexes between imidazoles and ions in the three systems triethylammonium picrate (Et₃NHPic)+imidazole (Im), triethylammonium bromide (Et₃NHBr)+Im, and Et₃NHPic+1-methylimidazole (1-MeIm) in nitrobenzene in order to specify the importance of the two functions of the imidazole molecule, the tertiary nitrogen N₃, and the imino group N₁-H. While 1-MelIm forms only a single complex with the cationic species Et₃NH⁺, imidazole enters into specific interactions as well with the cations through its basic site N₃ and with the anions through its imino group. The complexing of the anions by imidazole, always weaker than the complexing of the cations, is more effective for Br^– than for Pic^–. Moreover, if imidazole is used as ligand, a 1:2 complex is formed between the cation and the imidazole, in which the second molecule of imidazole is bonded to the N-H group of the first by a hydrogen bond at the tertiary N atom. We did not observe a correlation between the equilibrium constants K ₁ ⁺ for the complexing of the cation Et₃NH⁺ by imidazole and pyridines (k ₁ ⁺ for pyridine, 3–4 dimethylpyridine, and imidazole are 8, 24, and 165, respectively) and the pK _a values of these ligands due to the fundamental difference in the structure of the imidazole and pyridine molecules, although both are considered as aromatic nitrogen bases.     

Large Deviations Rate Function for Polling Systems

In this paper, we identify the local rate function governing the sample path large deviation principle for a rescaled process n ^–1 Q _nt , where Q _t represents the joint number of clients at time t in a polling system with N nodes, one server and Markovian routing. By the way, the large deviation principle is proved and the rate function is shown to have the form conjectured by Dupuis and Ellis. We introduce a so called empirical generator consisting of Q _t and of two empirical measures associated with S _t , the position of the server at time t. One of the main step is to derive large deviations bounds for a localized version of the empirical generator. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program. The method seems to have a wide range of application including the famous Jackson networks, as shown at the end of this study. An example illustrates how this technique can be used to estimate stationary probability decay rate.