Micelles for the self-assembly of "off-on-off" fluorescent sensors for pH windows

A micellar approach is proposed to build a series of systems featuring an "off-on-off" fluorescent window response with changes in pH. The solubilizing properties of micelles are used to self-assemble, in water, plain pyrene with lipophilized pyridine and tertiary amine moieties. Since these components are contained in the small volume of the same micelle, pyrene fluorescence is influenced by the basic moieties: protonated pyridines and free tertiary amines behave as quenchers. Accordingly, fluorescence transitions from the "off" to the "on" state, and viceversa, take place when the pH crosses the pK(a) values of the amine and pyridine fragments. To obtain an "off-on-off" fluorescent response in this investigation we use either a set of dibasic lipophilic molecules (containing covalently linked pyridine and tertiary amine groups) or combinations of separate, lipophilic pyridines and tertiary amines. The use of combinations of dibasic and monobasic lipophilic molecules also gives a window-shaped fluorescence response with changes in pH: it is the highest pyridine pK(a) and the lowest tertiary amine pK(a) that determine the window limits. The pK(a) values of all the examined lipophilic molecules were determined in micelles, and compared with the values found for the same molecules in solvent mixtures in which they are molecularly dispersed. The effect of micellization is to significantly lower the observed protonation constants of the lipophilized species. Moreover, the more lipophilic a molecule is, the lower the observed logK value is. Accordingly, changing the substituents on the basic moieties or modifying their structure, tuning the lipophilicity of the mono- or dibases, and choosing among a large set of possible combination of lipophilized mono- and dibases have allowed us to tune, almost at will, both the width and the position along the pH axis of the obtained fluorescent window.     

Martingale convergence,series expansion of Gaussian elements,and strong law of large numbers in Fréchet spaces

The main result of this paper is the derivation of a convergence theorem for certain martingales with values in a separable Fréchet space F. It is shown that this result includes a well known theorem due to Chatterji. Moreover, the series expansion of zero-mean Gaussian elements with values in F and the strong law of large numbers for i.i.d. F-valued random elements also follow as applications of the main theorem.