Cetyltrimethylammonium bromide (CTAB) has a measured critical micelle concentration…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Statistical foundations and the equilibrium ensembles

Condensed Matter Physics, Ch Soft matter: when entropy, not bonding, sets the structure

Problem

Cetyltrimethylammonium bromide (CTAB) has a measured critical micelle concentration of

0.92\,\mathrm{mM}

in water at

298\,\mathrm{K}

. ((a)) Chapter 13 wrote the equilibrium vacancy fraction as

n_v=e^{-\varepsilon_v/k_BT}

, where

\varepsilon_v

is the energy cost of forming a vacancy. State the matching quantities in

x_{\rm CMC}\approx e^{-\Delta_{\rm mic}/k_BT}

, and explain why

\varepsilon_v

is a cost while

\Delta_{\rm mic}

is a gain, even though both formulas have the same shape. ((b)) Find

\Delta_{\rm mic}

for CTAB, in

k_BT

and in electronvolts.

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