Determine an enthalpy of micellization according to the

Question

Fundamental of Nanotechnology-Self Assembly Phenomena

Problem 1

The micellization of surfactant can be represented by a stepwise association process given by the equilibrium reaction below:

S₁ + S_n-1 s_n

For a micellization process with identical equilibrium constant for each step, show that the C, M, W and the polydispersity index are given by the expression below:

(Note: please refer to your notes for more information)

(a) C = |S₁|/(1 - X)                 (c)  W = [S₁](1 + X)/(1-x³)

(b) M = [S₁]/(1-x²)                  (d) N^-_w / N^-_n = 1 + X/(2 - X)²

Where C, M, W, and X are given by:

C = ₁Σⁿ[S_n]     M = ₁Σⁿn[S_n]     w= ₁Σⁿn²[S_n]    X = K[S₁]

Problem 2

(a) The following surface tension were measured for aqueous solutions of the nonionic surfactant CH₃(CH₂)₉(OCH₂CH₂)₅0H at 25 °C

C(10-4mo1/dm-3)	0.1	0.3	1.0	2.0	5.0	8.0	10.0	20.0	30.0
y (mN/m)	63.9	56.2	47.2	41.6	34.0	30.3	29.8	29.6	29.5

Determine the critical micelle concentration and calculate the area occupied by each adsorbed surfactant molecule at the critical micelle concentration.

(b) The critical micelle concentration of nonionic surfactant in water varies with temperature as follows:

Temperature (°C)	15	20	25	30	40
CMC (mmol/dm3)	21.9	20.8	19.9	19.1	17.8

Determine an enthalpy of micellization according to the phase separation model.