Oscillations, Waves, and Interactions - GWDG

Liquids: Formation of complexes and complex dynamics 377
Figure 9. Scheme of relaxation process associated with a chemical equilibrium between
species X and species Y.
equilibrium constant
K = k f /k r . (18)
Within the framework of the simple reaction scheme shown in Fig. 9, the species
on both sides of Eq. (17) differ from one another by the volume difference ∆V and
the enthalpy difference ∆H. They are separated from one another by the enthalpy
barriers ∆H ♯
X and ∆H♯ Y = ∆H♯ X + ∆H, where normally ∆H ≪ ∆H♯ X , thus ∆H♯ Y ≈
∆H ♯
X . Here X and Y denote α − CD + I− and α − CD · I − , respectively. The van’t
Hoff equation
d ln K
= −∆H
d T −1 R
relates the equilibrium constant to the enthalpy difference ∆H, indicating that, according
to our expectations, the larger the reaction enthalpy ∆H the larger K, that
is the more the equilibrium is shifted to the right-hand side of Eq. (17).
The thermal activation relaxation scheme of Fig. 9 predicts ultrasonic excess attenuation
that features Debye-type relaxation characteristics
with the relaxation time τ given by
and the relaxation amplitude following as
(αλ) exc = RD(ν) = Aωτ
1 + ω 2 τ 2
τ −1 = k f � [α − CD] + � I −� + K −1�
(19)
(20)
(21)
A = πΓc(∞)
RT ∆V 2 S . (22)