The steady-state fluorescence quenching method was used to determine the aggregation number of bound-micelle (N_b) of sodium dodecyl sulfate (SDS) in the ternary mixing system of alkali metal (Li, Na or K) sulfate-SDS-polyethylene glycol (PEG). The altering tendency of N_b with the change of concentration of SDS (c), alkali metal sulfate (c_e) and PEG (c_p) was investigated. The response surface modeling to the N_b of SDS was done, which revealed that the N_b of SDS took approximately the linear increase function of c, the logarithmic function of c_e and in reverse proportion to c_p simultaneously. Consequently the equation including the quadratic interaction terms was established. The coefficients a₀～a₈ in the above equation corresponding to Li₂SO₄, Na₂SO₄ and K₂SO₄ were regressed from the experimental N_b, respectively. The absolute errors between experimental and prospective N_b were less than 3 and the relative ones between them were less than 4%. This equation was useful to anticipate by N_b of surfactants the size and chemical microenvironment of soft template composed by surfactants with macromolecules in the presence of inorganic electrolytes, and to adjust the size of metal-nanoparticles prepared by means of the soft template furthermore.

Key words: steady-state fluorescence quenching, aggregation number of bound-micelle, response surface modeling, sodium dodecyl sulfate, polyethylene glycol, alkali metal sulfate