Question

(c)      The table below gives the cmc in H_2­O and 0.05mM aq phosphate buffer (NaH₂PO₄/Na₂HPO₄) as well as the aggregation number and Krafft point for tetradecyltrimethylammonium bromide (TTAB) and hexadecyltrimethylammonium bromide (HTAB).

         Substance                         CMC_H2O             CMC_{0.05mM Phosphate}               N_AGG            K_P

         TTAB                             3.8x10^-3             2.5x10^-3                            80               4^oC

         HTAB                             9.1x10^-4             3.0x10^-4                            61               24^oC

         (i)      Explain the type of information provided by each of these parameters above.

         (ii)     Account clearly for the differences in data recorded for the two surfactants.

(d)    Sketch the π-A curve one might expect for either TTAB or HTAB on an aqueous subphase at 25^oC.Explain briefly the behaviour observed for the surface film of surfactant.

Answer 1

Solution (c)(i)

The parameters mentioned for the two compounds are:

1. CMCH2O: In colloidal and surface chemistry, the critical micelle concentration (CMC) is defined as the concentration of surfactants above which micelles form and all additional surfactants added to the system go to form micelles. The CMCH2O is the concentration of the surfactant (in this case, TTAB and HTAB) in water at which the micelles begin to form.
2. CMC0.05mM Phosphate: This is the concentration of the surfactant in the phosphate buffer at which the micelles begin to form.
3. NAGG: This is the aggregation number of the micelle formed i.e., the average number of surfactant molecules in the micelles.
4. Kp: The Krafft point or critical micelle temperature is the minimum temperature at which the surfactants form micelles

Solution (c)(ii)

Why are the CMC values of TTAB>HTAB?

TTAB has a shorter carbon backbone (14 carbons) compared to HTAB (16 carbons). This makes TTAB less hydrophobic compared to HTAB. Which implies that a higher concentration of TTAB can exist without having to form micelles. Hence, TTAB has a larger CMC value (in both solvents) than HTAB.

Why are the CMC values in water > in phosphate buffer?

The presence of the phosphate buffer makes the surfactants more soluble when compared to the other solvent (water). This makes their CMC value in water higher than that in the phosphate buffer.

Why are TTAB aggregation sizes greater than HTAB aggregation sizes?

The smaller hydrophobic chain of TTAB allows it to have a higher aggregation size when compared to HTAB

Why is the Krafft temperature of TTAB lower than HTAB?

The longer the hydrophobic ring, the higher the Krafft temperature.

Solution (d)

π vs A graph

At low surfactant concentration, π and A follow the following relation:

πA = RT; a relation similar to the ideal gas law.

At constant temperature, this shows a hyperbolic curve, as shown.