Cetyltrimethylammonium bromide (CTAB) has a single hexadecyl ( ) tail

PHYSICS · Multi-part · 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

Cetyltrimethylammonium bromide (CTAB) has a single hexadecyl (

n_c=16

) tail. Using Tanford's rules

v=(0.0274+0.0269n_c)\,\mathrm{nm^3}

and

l_c=(0.15+0.1265n_c)\,\mathrm{nm}

, and taking the optimal head area as

a_0 = 0.65\,\mathrm{nm^2}

in pure water and

a_0 = 0.50\,\mathrm{nm^2}

0.3\,\mathrm{M}

KBr (the added salt screens the repulsion between the charged head groups, reducing

a_0

), ((a)) calculate the packing parameter

p

in pure water; ((b)) calculate

p

0.3\,\mathrm{M}

KBr; ((c)) state, with a reason, what shape of aggregate is expected in each case.