Sodium dodecyl sulfate ( ) has a CMC of

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Amphiphiles and self-assembly

Problem

Sodium dodecyl sulfate (

C_{12}

) has a CMC of

8.2\,\mathrm{mM}

. Someone wants the CMC of sodium hexadecyl sulfate (

C_{16}

, four more tail carbons) and reasons: 'Each

\mathrm{CH_2}

that leaves water when the surfactant joins a micelle lowers the free energy by the full hydrophobic-effect value,

1.5\,k_BT

. Four extra carbons lower the free energy of joining a micelle by

4\times1.5 = 6\,k_BT

, so the CMC falls by a factor

e^{-6}

\mathrm{CMC}_{16} = 8.2\,\mathrm{mM}\times e^{-6}

.' Calculate this predicted value, then calculate the CMC using the empirical rule that

\log_{10}

CMC falls by about

0.3

per added carbon for sodium alkyl sulfates, and say which is right and why the two disagree.