It is assumed that hexanol will be accessed by cutinase if it is located in the water pool or
in the surfactant (micellar) layer (as S*aot,f), since the micelles are very small and re-size
upon cutinase microencapsulation (Carvalho et al., 1999a).
An adsorption process based on the Langmuir law was considered to define the
concentrations of hexanol in the different micellar constituents. It is considered that the
adsorption is a reversible process that takes place at the micellar interface, with the
adsorbed alcohol molecules unavailable for reaction.
(4)
where qmax represents the monolayer capacity and KL the adsorption equilibrium constant.
The value of q is defined as the molar ratio of substrate (hexanol) to surfactant (AOT).
Partitioning has been mentioned as a key parameter to explain the varying behaviour
of biocatalysts in reversed micelles (Fletcher, 1986; Fletcher et al., 1985).
The partition coefficients (P1–P3) applied in the model are represented schematically
in Figure 7.2 and their definitions as well as the values determined for hexanol are as
follows (Khmelnitsky et al., 1990b; Seeman, 1972):
(5)
(6)
(7)
(8)
In Figure 7.2 the arrows originate in each of the phases and all the processes involved in
substrate distribution are represented; the partition with coefficients P 1 , P 2 and P 3 , the
adsorption (Kad) and the diffusion (Kdif). The hexanol located in the micellar phase, but in
strict contact with the AOT head groups (i.e. with the aqueous core) is considered
accessible to the enzyme while the alcohol molecules interacting or adsorbing to the
hydrophobic chains of the surfactant are not.
The volume fractions, θ, were calculated for the experimental conditions (Wo 2.7 with
150 mM AOT), using the partial specific volume for this W 0 , ρ=0.8831 cm^3 /g (estimated
from Levashov et al., 1982) and the concentrations of constituents AOT (Caot) and water
(Cw).
From eq. 1, it turns that the substrate mass balance is
(9)
where S represents the local concentrations in each ‘‘compartment’’ and the respective
volume fractions.
Reversed micellar bioreaction systems 205