Oscillations, Waves, and Interactions - GWDG

Liquids: Formation of complexes and complex dynamics 379
Figure 11. Frequency normalized ultrasonic spectra for aqueous solutions of 6methylpurine
without HCl (◦, 0.6 mol/l, pH=6.8) and with HCl added (•, 0.55 mol/l, pH=2)
at 20 ◦ C [64].
where Ni denotes a multimer made of i monomers. For the stack formation, however,
the shape of the size distribution function of the aggregates is different from that
of micelles, particularly as there are no geometrical restrictions for the stack size
[63]. Figure 11 shows ultrasonic attenuation spectra for aqueous solutions of 6methyl-purine
without and with HCl added [64]. The significant effect of pH upon
the attenuation data below 3 MHz suggests the low-frequency relaxation term to be
due to the proton exchange of the ampholytic 6-methylpurine molecules. The term at
higher frequencies has been assigned to the stacking of the polyaromatic molecules.
Unfortunately no clear evidence resulted for a preference of the sequential isodesmic
reaction scheme (Eq. (25)) or the random isodesmic scheme
k f
ij
Ni + Nj ⇋ Ni+j
k r ij
, i, j = 1, 2, . . . , (26)
because, within the concentration range available in the measurements, both models
predict similar concentration dependencies for the relaxation times.
3.2 Micelles
The micelle formation/decay kinetics of nonionic surfactant solutions forming almost
globularly shaped micelles with mean aggregation number m larger than about
50 (proper micelles), typically corresponding with critical micelle concentration cmc
smaller than 10−2 mol/l, can be also well described by the sequential isodesmic
scheme of coupled reactions defined by Eq. (25). It is assumed that the monomer
concentration [N1] is much higher than that of any aggregate so that direct association
of oligomers according to Eq. (26) with i, j > 1 can be neglected. Aniansson
and Wall [65,66] have introduced a symmetrically bell-shaped nearly Gaussian size
distribution � � � � �� � � r r r 2
ki+1 Ni+1 − ki Ni / Ni = − (i − m) k /σ (27)