Aggregate molecular fraction versus aggregate number fraction ($n_{\alpha }=x_{\alpha }/\alpha$)

If $x_{\alpha }$ counts amphiphile molecules belonging to aggregates of size $\alpha$, the corresponding dimensionless aggregate count is $n_{\alpha }=x_{\alpha }/\alpha$. Its ideal translational chemical potential contains $\ln n_{\alpha }$. Confusing these two distributions drops a factor of $\alpha$ and changes both normalization and the chemical-potential interpretation.