Titration calorimetric and spectrophotometric studies of micelle formation by alkyltrimethylammonium bromide in aqueous solution

Titration calorimetric data are reported for the deaggregation of micelles in aqueous solution at 298.2 K formed by hexadecyltrimethylammonium bromide (C-16, CTAB), tetradecyltrimethylammonium bromide (C-14, MTAB), dodecyltrimethylammonium bromide (C-12, DOTAB) and decyltrimethylammonium bromide (C-10, DTAB). Critical micellar concentrations (c.m.c.s) determined using calorimetric data are compared with those measured spectrophotometrically using charge-transfer bands for Fe(CN)(4)(bipy)(2-); the c.m.c.s at 298.2 K using the latter probe are 10.5 x 10(-2) (DTAB), 1.35 x 10(-2) (DOTAB), 3.8 x 10(-3) (MTAB) and 0.97 x 10(-3) mol dm(-3) (CTAB). The calorimetric data are accounted for using a model for micellar solutions which envisages a chemical equilibrium between a simple alkylammonium salt, AM(+)Br(-), and a macrosalt, [NAM(+)(N - betaBr-](beta+).beta Br-, where N is the aggregation number and beta measures the degree of counterion binding. For each mole of micelle there are beta moles of 'free' bromide ions in solution. Within each mole of micelles there are N - beta moles of bound bromide ions. With decrease in alkyl chain length the traces obtained from the calorimetric data show increasing relative contributions from the non-ideal properties of simple salt and macrosalt. Key features in the calorimetric traces are successfully reproduced by combining information relating to c.m.c., limiting enthalpy of micelle formation, N and beta together with Fitter equations describing the dependence on ionic strength of the apparent molar enthalpies of simple salts and macrosalts.