= Solution
The composition changes most rapidly across an interface, so $\nabla\phi$ points along its normal. The term
$$
\lambda\mathbf p\mathbin\cdot\nabla\phi
$$
therefore couples the surfactant's head-to-tail orientation to the interface normal. Minimization aligns $\mathbf p$ antiparallel to $\nabla\phi$ when $\lambda>0$ and parallel when $\lambda<0$. The sign is fixed by which fluid component is called positive $\phi$ and by which molecular end defines positive $\mathbf p$, together with the preferential affinity of the head and tail for the two components.
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