Prediction of cathodic E1/21 and E1/22 values for viologen-containing conjugated unimers and dimers from calculated pKb values of the aromatic substituents

A library of 18 conjugated, rod-like compounds with either one or two viologen residues were synthesized and characterized electrochemically. Containing up to 8 aromatic/heterocyclic rings in conjugation, the members of the library differ in the substitution pattern of electron-withdrawing or -donating groups on the aromatic substituents of the viologen units. The first and second half-wave potentials of each member were found to be linearly correlated with the calculated pK_b values of the aromatic end-groups. This relationship will enable the half-wave potentials of related, novel, substituted viologen species to be predicted using a simple, empirical formula.     

Two sample applications of a classical isoperimetric problem of the calculus of variations to fluid mechanical problems in fluidization and spouting

This paper is devoted to outlining precisely the basic mathematics of a classical isoperimetric problem of the calculus of variations and showing how significant fluid mechanical problems in fluidization and spouting can be addressed using this approach.     

Bi-velocity transport processes. Single-component liquid and gaseous continua

The present contribution supplements the previous findings regarding the need for two independent velocities rather than one when quantifying mass, momentum and energy transport phenomena in fluid continua. Explicitly, for the case of single-component fluids the present paper furnishes detailed expressions for the phenomenological coefficients appearing in the constitutive equations governing these bi-velocity transport processes. Whereas prior analyses furnished coefficient values only for the case of dilute monatomic gases using data from Burnett’s solution of the Boltzmann equation, the present study furnishes values applicable to all fluids, liquids as well as dense gases. Moreover, whereas prior coefficient calculations derived these values (for dilute monatomic gases) from Burnett’s solution of Boltzmann’s gas-kinetic equation, the latter a molecular theory, the present analysis derives the liquid- and gas-phase values from purely macroscopic data requiring knowledge only of the fluid’s coefficients of thermal expansion, isothermal compressibility, and thermometric diffusivity. In the dilute monatomic gas case common to both levels of analysis, the respective molecularly and macroscopically derived phenomenological coefficients are found to be in excellent agreement, confirming the credibility of both bi-velocity theory and the theory establishing the values of the phenomenological coefficients appearing in the constitutive relations derived therefrom. Whereas the preceding macroscopic calculations invoked Onsager’s reciprocal theorem relating coupled phenomenological coefficients, an alternative scheme is presented at the conclusion of the paper, one that reverses the usual order of things, at least in the present single-component fluid case. This alternate scheme enables Onsager’s nonequilibrium reciprocal relation, originally derived by him using molecular arguments, to be derived using purely macroscopic arguments originating from knowledge of Maxwell’s equilibrium reciprocal relations, the latter fundamental to equilibrium thermodynamics.     

Synthesis of new mono-functionalised tetrathiafulvalene derivatives by reactions of etrathiafulvalenyllithium with aldehydes and ketones: X-ray crystal structures of TTF-CMe(OH)Fc, TTF-CMe(OMe)Fc and TTF-CH(OMe)TTF (Fc = ferrocenyl)

Reactions of tetrathiafulvalenyllithium (TTF-Li) with a range of aldehydes and ketones have been explored for the first time, to provide an efficient route to mono-functionalised TTF derivatives of general formulae TTF-CH(OH)R (R = alkyl, phenyl, tetrathiafulvalenyl and ferrocenyl) and TTF-CR(OH)R′ (R = alkyl, phenyl, R′ = alkyl, phenyl, tetrathiafulvalenyl, ferrocenyl, and R-R′ = fluorenyl). Subsequent transformations involving the reactive alcohol group of some of these compounds are reported. The structures of the three title compounds have been established by single-crystal X-ray analysis.