Results and Discussion

CHAPTER 3: ANALYTICAL EVALUATION OF THE EFFECTS OF

C. Results and Discussion

Table 3 - IV. Reduced Diameter, Number of Reverse Micelles, Number of Surfactant Per Reverse Micelle, and Surface Charge Density Calculated for Additions of Al(NO3)3

Al(NO3)3 (M) 0.1 0.2 0.3 0.4

dh - 0.7 (nm) 7.3 6.1 5.7 5.4

NRM (x 10¹⁹ ) 1.7 3.0 3.7 4.4

NS 680 400 330 280

σo (C/m²) 0.65 0.55 0.52 0.49

Table 3- V. Reduced Diameter, Number of Reverse Micelles, Number of Surfactant Per Reverse Micelle, and Surface Charge Density Calculated for Additions of ZrOCl2

ZrOCl2 (M) 0.1 0.2 0.3

dh - 0.7 (nm) 7.7 6.8 6.3

NRM (x 10¹⁹ ) 1.5 2.2 2.7

NS 800 550 440

σo (C/m²) 0.68 0.61 0.57

The calculated surface charge densities as a function of the added salt concentrations are demonstrated in Figure 3 - 1, which also includes the points of instability. The points of instability correspond to different surface charge densities for the different salts. Previously, the inability to further compress co-ions into the core of the reverse micelle was suggested as the mechanism for destabilization.¹ Alternatively, a mechanism known as salting out has been described for which the reduced surfactant density at the interface increases interfacial tension until single phase reverse micelles are no longer supported.^28,29 The change in interfacial tension with salt concentration, like reverse micelle size, is also proportional to the electrical double layer thickness.³⁰ Thus, the relationship to the electrical double layer thickness cannot rule out either mechanism.

The strong dependence of surface charge density on the electrical double layer thickness does suggest that the interfacial tension is a balancing force. However, the differences in surface charge density at the points of instability suggests that the surface charge density and interfacial tension are not the controlling mechanism by which destabilization occurs or destabilization would occur at the same surface charge density unless the change in interfacial tension with added salt decreases in the order of NH4OH, ZrOCl2, and Al(NO3)3 so that a lower surface charge density can be accommodated in that respective order. However, the change in interfacial tension is not readily available to make any definite conclusions. Resolving this issue can provide valuable insight into the destabilization mechanism, validating or discrediting the destabilization mechanism that is proposed in Chapter 2.

Figure 3 - 1. The surface charge density of AOT reverse micelles in isooctane as a function of added salt concentration. Lines are drawn as a guide for the eye.

The computational steps and values used to evaluate the validity of the model developed in Chapter 2, assuming that sodium counterions do not participate in the electrical double layer, are given in Table 3 - VI. The results indicate that the core size at the point of instability is 3.5 nm, 3.4 nm, and 4.7 nm for NH4OH, Al(NO3)3, and ZrOCl2

containing reverse micelle solutions, respectively, and confirms the feasibility of a central core containing both sodium counterions and electrolyte co-ions.

Table 3 - VI. Point of Instability, Surface Charge Density of Surfactant Film, Electrical Double Layer Thickness, Distance from Surfactant Film to Point of Critical Potential,

Polar Phase Diameter, and Core Size Using a Gouy-Chapman Based Model Electrolyte NH4OH Al(NO3)3 ZrOCl2

P.O.I. (M) 0.6 0.4 0.3

σo (C/m²) 0.64 0.49 0.57

κ^-1 (x10^-9 m) 0.28 0.23 0.2

d/2 (x10^-9 m) 0.9 0.5 0.4

dh-0.7 (x10^-9 m) 7.1 5.4 6.3

dc (x10^-9 m) 3.5 3.4 4.7

The relative concentrations of sodium ions relative to the salt counterions was calculated by equation 12, using the maximum (surface) and minimum (critical) potentials, and the results are given in Table 3 - VII. The value of R at the surface is 25.2, 174, and 206,000 for NH4OH, Al(NO3)3, and ZrOCl2 electrolyte solutions, resepectively and demonstrates the displacement of sodium from the surfactant interface because of the higher valence of the additive and agrees well with the model. However, the R values at the minimum potential are 0.15 for the analysis of all three electrolytes, suggesting surplus sodium ions (~7x) when compared to the electrolyte counterion.

counterion concentration, some of the sodium ions must be displaced outside of the two overlapping electrical double layers according to this analysis. The problem with the analysis is that it was assumed that the sodium counterions are in fact in the electrical double layer and neglects the possibility that there is another sodium position that is more energetically favorable, such as the displacement into the core to screen the electrostatic repulsion between displaced co-ions. Co-ions can also be present in the electrical double layer.⁴ Reality is likely to be somewhere in between, that is, some of the co-ions and sodium counterions participate in the electrical double layer and some of them are displaced to the core. Thus, an analysis excluding sodium counterions from the electrical double layer and including them represent two extremes.

Table 3 - VII. Ratio of Salt Counterion to Sodium Counterion Concentration at the Maximum and Minimum Potential in the Electrical Double Layer

Electrolyte Potential (V) R

NH4OH -0.14 25.2

-0.01 0.15

Al(NO3)3 -0.10 174

-0.01 0.15

ZrOCl2 -0.11 206,000

-0.01 0.15

The computational steps and values that were used to evaluate the validity of the model, but assuming that all sodium counterions and co-ions are included in the electrical double layer, are demonstrated in Table 3 - VIII. In this scenario, the sodium counterions further reduce the electrical double layer thickness and the estimated core size is 5.9 nm, 4.2 nm, and 5.5 nm for the NH4OH, Al(NO3)3, and ZrOCl2 electrolyte solutions,

respectively, which are all larger core sizes than when sodium is assumed to be excluded from the electrical double layer. In this case, the core would consist of water instead of a net-negatively charged core. Two overlapping potentials can still be assumed by considering a slight modification to the model based on the results of Biswas et al. in which the net negative surface is generated by the local orientation of the hydrogen bond network (water molecules).³¹ Alternatively, the intermediate condition in which some of the sodium counterions and the electrolyte co-ions are separated into the core can still generate the net negative surface in the core.

Table 3 - VIII. Point of Instability, Surface Charge Density of Surfactant Film, Electrical Double Layer Thickness (EDL), Distance from Surfactant Film to Point of Critical Potential, Polar Phase Diameter, and Core Size Using a Gouy-Chapman Based Model

and Assuming Sodium Counterions Contribute to the Electrical Double Layer Electrolyte NH4OH Al(NO3)3 ZrOCl2

P.O.I. (M) 0.6 0.4 0.3

σo (C/m²) 0.64 0.49 0.57

κ^-1 (x10^-9 m) 0.15 0.14 0.13 d/2 (x10^-9 m) 0.3 0.3 0.2 dh-0.7 (x10^-9 m) 7.1 5.4 6.3 dc (x10^-9 m) 5.9 4.2 5.5

A similar analysis was performed, but assuming a reduced potential because of the development of a Stern layer. The results, either without or with sodium counterions in the electrical double layer, are presented in Table 3 - IX. Including the Stern model further reduces the electrical double layer thickness and increases the calculated sizes of the core, demonstrated by comparing the results in Table 3 - IX to the results in Table 3 - VI and Table 3 - VIII.

Table 3 - IX. Point of Instability, Surface Charge Density of Surfactant Film, Surface Charge Density at the Stern Layer, Electrical Double Layer Thickness (EDL), Distance

from Surfactant Film to Point of Critical Potential, and Core Size Using a Stern-Based Model Without and With Sodium Counterions Contributing to the Electrical Double

Layer

Condition Electrolyte NH4OH Al(NO3)3 ZrOCl2

P.O.I. (M) 0.6 0.4 0.3

σo (C/m²) 0.64 0.49 0.57 σS (C/m²) 0.32 0.25 0.29 Without κ^-1 (x10^-9 m) 0.28 0.23 0.20 d/2 (x10^-9 m) 0.35 0.19 0.16 dc (x10^-9 m) 5.7 4.6 5.7 With κ^-1 (x10^-9 m) 0.15 0.14 0.13

d/2 (x10^-9 m) 0.10 0.05 0.06

dc (x10^-9 m) 6.7 6.9 6.9