3.1 Dynamic Light Scattering
With 0.1 mM oleic acid in the presence of 5 mM sodium cholate evaluated at different angles: 45°, 60°, 75°, 90°, 105° and 120°. The correlation functions obtained for the oleic acid with sodium cholate system are shown below in Figure 1.
After a mathematical treatment of these results, the correlation functions were normalized and approximated in exponential functions through equation 1.
From this exponential approximation it is possible to designate whether the system is first-order (single exponential) or second-order (double exponential).
Using equation 2 and equation 3,
It can be seen that the relaxation frequency is directly proportional to the square of the scattering vector (q).
After the linear regression of the curve obtained in Fig. 2, the value of the diffusion coefficient was equal to 5.72 x 106. Knowing that the experiments were carried out at room temperature, and using Eq. 3, the RH (Hydrodynamic radius) of this system is calculated. For the concentration of 0.1 mM of oleic acid and 5 mM of sodium cholate, we have particles with a single size distribution (single exponential) of about 38 nm.
Doing the same calculations for all concentrations of sodium cholate, the radius founded for this systems was
Table 1
Hydrodinamic radius of the micelles formed by the interaction of different concentration of oleic acid with sodium cholate
Concentration of Oleic acid
|
Hydrodynamic Radius (nm)
|
0.1 mM
|
38.0
|
-
|
0.5 mM
|
38.5
|
-
|
1.0 mM
|
42.0
|
-
|
5.0 mM
|
57.0
|
-
|
10.0 mM
|
51.0
|
105.0
|
15.0 mM
|
135.0
|
431.0
|
From 10.0 mM of oleic acid in 5 mM de sodium cholate is possible to see a change in the sructure of the system. It became a bi-modal size distribuition, where it is seem 2 different groups of micelles, whith different sizes. The increse of oleic matter seems to increase the effect.
In the table 2, it is possibe to see that this behaviour on other oleic materials.
Table 2
Hydrodinamic radius of the micelles formed by the interaction of different concentration of oleic matter (saponified oelic acid and biodiesel) with sodium cholate
|
Concentration of Oleic matter
|
Hydrodynamic Radius (nm)
|
Saponified oleic acid + 5 mM of Sodium Cholate
|
0.1 mM
|
21
|
-
|
0.5 mM
|
41
|
-
|
1.0 mM
|
35
|
-
|
5.0 mM
|
18
|
44
|
10.0 mM
|
17
|
47
|
15.0 mM
|
26
|
78
|
Biodiesel + 5 mM of Sodium Cholate
|
0.1 mM
|
20
|
-
|
0.5 mM
|
35
|
-
|
1.0 mM
|
41
|
-
|
5.0 mM
|
55
|
-
|
10.0 mM
|
78
|
-
|
15.0 mM
|
92
|
-
|
For the system of saponified oleic acid, it also possible to see the increase of the different populations, but in this case the size of the particles are smaller tha in oleic acid system. Analizing the structures of both species, this distinction can be related to the presence of a conter-ion sodium or hydroxil, respectivelly. The hydroxyl group, present on the sodium cholate give an increase on the size of the micelles whereas that the saponified ones trend to be package in the center of the micelle.
On the other hand the micelles formed by biodiesel and sodium cholate do not presented the same bi-modal particle distribuition. With the increase of the oleic material on the system, the particles also growth, but in a smaller rate than the other systems. This can be explained by the steric hindrance of the methyl groups that harms the proximity and interation of the sodium cholate molecules.[26, 27, 28]
3.2 Electrical Impedance
All the systems have their resistivity determined by this technique, which it fast non destructive and allow the determination of the polarization mechanisms of the materials.
From the Nyquist diagrams it can be traced a semicircle where is obtained the resistence and than the resistivity value can be mathematically determinated through the cell constant. For this work a 0.1 cm-1 constant conductivity cell was used with an amplitude of 0V to 10 mV was applied in a range of 0.01 Hz to 10,000Hz of frequency.
The electric conductivity (s) is the result of a corrent flow of free charges in the material. By definition is the inverse of the resistivity (r).
The Figure 3-5, shows the Nyquist semicircle for all the studyed systems
From those diagrams, the semicicle can be traced with the assistence of the equipment´s software and it is possible to obtain the radius of the semicicle which multiply by the cell constant give us the resistivity value.
The resistivity and condutivity of the micellar systems and 5 mM of the biologicl surfactant (sodium cholate) is in table 3.
All the systems presented a very similar behaviour, do not changing the conductivity with an increase of the oleic matter. According with the conductivity presented, these materials can be rated as semi-conductors. [30]