= Solution
An <amphiphile> adsorbs at the oil–water interface, reducing the <interfacial tension>. At fixed drop radius and oil volume, $E_s(c)=A\gamma_{ow}(c)$ therefore falls with increasing <concentration> and tends toward a plateau once the interface is nearly saturated and further <amphiphile> mostly enters <micelles>. For an approximately ideal dilute nonionic <surfactant>, the <Gibbs adsorption equation> $d\gamma=-RT\Gamma\,d\ln a$ connects the fall in <interfacial tension> to positive surface excess $\Gamma$. Ionic systems require the appropriate <counterion> activities.
The <critical micelle concentration> gives the familiar break in a tension-versus-log-concentration curve, rather than a fall to zero interfacial <energy>. If mixing creates a different droplet size distribution as <amphiphile> is added, area also changes; a tension <reduction> alone does not determine the total interfacial <energy>. The plotted prediction holds area fixed.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-1-emulsion-energy.png]
{title=Original fixed-area emulsion-energy schematic showing adsorption-driven decrease and an illustrative micellization plateau}
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