Adaptive, Bayesian Experimental Design to Efficiently Determine the Critical Micelle Concentration of a Surfactant

Surfactants are widely used for industrial applications, yet more environmentally friendly surfactants with enhanced properties are demanded. A key thermodynamic property governing the behavior of a surfactant in an aqueous solution is its critical micelle concentration (CMC). Below the CMC, increasing the surfactant concentration reduces the surface tension of the solution; above the CMC, the water-air interface becomes saturated with adsorbed surfactant, leading excess surfactant to self-assemble into micelles and the surface tension to plateau. Many physicochemical properties of a surfactant solution exhibit sharp changes at the CMC. The conventional experimental protocol to determine the CMC of a surfactant is labor-intensive and time-consuming: (1) prepare many surfactant solutions spanning a wide concentration range and then (2) measure the surface tension of each solution. Herein, we adopt Bayesian experimental design (BED) to determine the CMC of a surfactant more efficiently─even without prior knowledge of its order of magnitude. BED follows an experiment-model-design feedback loop: (1) prepare a surfactant solution and measure its surface tension; (2) use all surface tension data thus far to obtain a posterior distribution over thermodynamic models of the surface tension isotherm of the surfactant; and (3) pick the surfactant concentration for the next experiment to maximize expected information gain about the CMC. We show that BED efficiently gathers information about the CMC using two surfactants (octyl-β-d-thioglucopyranoside and Triton X-100) as test cases. Broadly, BED can reduce the time, effort, cost, and chemical waste to determine the CMC of surfactants and drive an autonomous laboratory for surfactant discovery and characterization.