Oscillations, Waves, and Interactions - GWDG

Liquids: Formation of complexes and complex dynamics 385
Figure 18. Relaxation rate τ −1
max of the Hill relaxation term in the spectra of aqueous
solutions of n-heptylammonium chloride (△ [74]) and of triethylene glycol monohexyl ether
(◦ [81]) at 25 ◦ C displayed versus concentration difference C − cmc. The dashed line represents
the predictions from the extended version of the Teubner-Kahlweit-Aniansson-Wall
model [75].
The curves given in Fig. 17 reveal a particularly broad distribution function at surfactant
concentrations near the cmc, where the content of oligomeric structures is high.
Additionally, the relaxation time τH of the short chain surfactant system shows a
remarkable behaviour (Fig. 18). At variance with the predictions of the Teubner-
Kahlweit-Aniansson-Wall theory (Eq. (31)), the experimental relaxation rate τ −1
max
(and thus τ −1
H ) at surfactant concentrations near the cmc first decreases with C to
increase according to Eq. (31) at higher C only. In order to take properties of short
chain surfactant systems into account, a computer simulation study of the coupled
isodesmic reaction scheme (Eq. (25)) has been performed [75] in which the size distribution
of micelles was not introduced empirically but was derived from reasonable
rate constants, assumed to follow
and
k r i+1 =
�
k r m (1 + sr(i − m)) + k r �
2 1 + exp
k f
i+1 = kf
m (1 − sf (i − m)) (41)
� 1 − ic
d
��� �� � ��
i − ic
1 + exp
.
d
(42)
In these equations the parameters sf and sr define the slopes in the dependencies of
upon i and kf
m as well as krm allow the forward and reverse rate constants,
respectively, to be matched at i = m. Parameter ic defines the aggregation number at
change from a linear dependence upon i to a Fermi
k f
i and kr i
which the reverse rate constants kr i
distribution. The quantities kr 2 and d are additionally used to model the kr i -versus-i
relation at small aggregation numbers. These quantities are thus related to the cmc