Sodium decyl sulfate has a single unbranched tail of carbons

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

Sodium decyl sulfate has a single unbranched tail of

n_c = 10

carbons. Tanford's rules give the tail volume and maximum extended length as

v = (0.0274 + 0.0269\,n_c)\,\mathrm{nm^3}, \qquad l_c = (0.15 + 0.1265\,n_c)\,\mathrm{nm}.

Take the optimal head area for this sulfate head group as

a_0 = 0.58\,\mathrm{nm^2}

. ((a)) Calculate the largest aggregation number

N_{\max} = \tfrac43\pi l_c^3/v

of a spherical micelle this tail could support. ((b)) Calculate the packing parameter

p = v/(a_0 l_c)