5. Stability against coalescence in nano-dispersion

Though the droplets coalescence rate is sufficiently get reduced for the nanoemulsion due to their smaller size, however, as a consequence of Ostwald ripening, it may results in creaming and ultimately leads to phase separation of the nanoemulsion (Figure 6a). The importance of droplet deformation, surfactant transfer and interfacial rheology for the stability of emulsion is well reported in the literature [28–30]. In the presence of thermal noise, the droplets are allowed to explore space by Brownian motion, and the resulting collisions cause the mean droplet radius R to increase. This process is called coalescence. Stabilization against

#### Figure 6.

(a) Schematic elaboration of various destabilization mechanisms for nanoemulsion and (b) cartoon of dropdrop interaction under two different regions where ligand shell overlaps each other.

coalescence can be effectively achieved, by creating a sufficient repulsive energy barrier between the droplets. This can be done by two ways, such as for O/W nanoemulsion the electrostatic stabilization (due to creation of double layer) by adding ionic surfactants. The formation of an electrical double layer (EDL, thickness δ) barrier is well established in the literature of colloidal stability according to the Derjaguin, Landau, Verwey and Overbeek (DLVO) theory [31]. As a result of this EDL formation when droplets approach a distance h, smaller than twice the double layer extension, strong repulsion occurs against their aggregation; hence, flocculation is prevented. A second and more effective mechanism using non-ionic surfactants or polymer (referred as surfactant) for W/O nanoemulsion is the steric stabilization (due to the presence of adsorbed polymer layer). However, no comparable definitive theory exists till date for the so-called steric stabilization. To date there have been several attempts made to develop the quantitative theory of steric stabilization with a notable success of Fischer's solvency theory [32] which exploits the Flory-Huggins theory [33] to predict the repulsive potential energy between two large flat plates. The total free energy of interaction obtained by Hesselink et al. for two flat plates coated by steric layer is given by [33]

$$\frac{dU\_{\text{total}}}{kT} = (2\pi/\Theta)^{\frac{3}{2}}\gamma^2(a^2 - 1)r\_{rms}M(d) + 2\gamma V(d),$$

interaction parameter and the center-to-center distance between any two

Vm .

The free energy of mixing in this regime can be expressed as [37]

3ln <sup>L</sup>

kT <sup>¼</sup> πγd<sup>2</sup> ð Þ <sup>h</sup> � <sup>1</sup> ln <sup>h</sup> � <sup>1</sup>

Huggin parameter is calculated by Vm

Importance of Surface Energy in Nanoemulsion DOI: http://dx.doi.org/10.5772/intechopen.84201

with molar volume by <sup>δ</sup><sup>2</sup> <sup>¼</sup> <sup>Δ</sup>H�RT

Uel

adsorbed layer becomes small (<5 nm).

Umix kT <sup>¼</sup> <sup>π</sup>d<sup>3</sup> 2V<sup>M</sup> sol φ2 lig 1 <sup>2</sup> � <sup>χ</sup>

Figure 7.

literature.

DLVO interactions.

6. Conclusion

101

approaching spheres, respectively. When χ < 0.5, Gmix is positive and the interaction is repulsive. When χ > 0.5, Gmix is negative and the interaction is attractive. When χ = 0.5, Gmix is zero, which is referred to as the θ–condition. The Flory-

Pictorial representation of distance dependence of pair potential energy between two spheres according to the

Hildebrand solubility parameters [36] of the surfactant and solvent, respectively. Solubility parameter δ<sup>2</sup> of any component is related to its heat of vaporization ΔH

> h � 1

loss in configurational entropy in this region is given by the expression [35]

while the elastic interaction Uel between the surfactant tails resulting from the

<sup>L</sup> � <sup>1</sup> 

where γ is the number of ligands per unit area of the sphere. Therefore, Uel is always repulsive (Figure 7). A pictorial representation of pair potential vs. interparticle distance was shown in Figure 7 elaborating various cases of DLVO and non-

Therefore, the criteria for effective steric stabilization are the following: (1) the particle should be completely covered by the polymer, (2) the polymer should be strongly adsorbed to the particle surface, (3) the stabilizing chain should be highly soluble in the medium and is strongly solvated by its molecules and (4) δ should be sufficiently large to prevent weak flocculation which occurs when the thickness of

This chapter summarizes the most important aspects of nanoemulsion including the composition, structure and physical properties and also provides the glimpses of

Continuing on the droplet-droplet approach within a distance h < 1 þ L, a second regime appears where chains undergo significant interpenetration and compression.

> <sup>þ</sup> <sup>2</sup> <sup>h</sup> � <sup>1</sup> L

þ L ; when, h < 1 <sup>þ</sup> L,

RT ð Þ <sup>δ</sup><sup>s</sup> � <sup>δ</sup><sup>m</sup> <sup>2</sup> <sup>þ</sup> <sup>0</sup>:34, where <sup>δ</sup><sup>s</sup> and <sup>δ</sup><sup>m</sup> are the

� 3 2

, when <sup>h</sup> < 1 <sup>þ</sup> L,

where γ is the number of ligands per unit area, α is the expansion factor, rrms is the root mean square end-to-end distance of the chain in free solution and M dð Þ and V dð Þ are the distance-dependent mixing and elastic function that could be evaluated from segment density distribution function. However, the reason for the failure of Fischer's solvency theory appears to reside in the use of segment density distribution functions relevant to the isolated polymer according to Hesselink calculation [34] which is found unlikely to be applicable here. Smitham, Evans and Napper first pointed out the correction and proposed a simple analytical model to adopt for the segment density distribution function which is a constant segment density step function [35]. Their theory is able to account for many of the qualitative and quantitative features of steric stabilization observed to date. According to this model, the steric repulsion appears from two main origins: the first one (Figure 6b) is the unfavorable mixing of the surfactant chains which depends on their density at the interfacial region, on thickness of the interfacial layer (δ) and on the Flory-Huggin parameter, χ. The second one (Figure 6b) is the reduction in configuration entropy due to elastic stress of the chains which occur when inter-droplet distance becomes lower than δ. This method of stabilization is more effective than electrostatic stabilization in two ways: firstly, the repulsion is still maintained at moderate electrolyte concentration, and, secondly, the repulsion can be maintained at high temperature (provided ligand has solubility at that temperature).

The unfavorable mixing of the surfactant chains (considering the chain-solvent interaction predominates over the chain-chain interaction, like it is in good solvent condition) occurs when the ligand chain starts to interpenetrate within a distance, <sup>1</sup> <sup>þ</sup> <sup>L</sup> <sup>&</sup>lt; <sup>h</sup> < 1 <sup>þ</sup> <sup>2</sup>L, where <sup>L</sup> is the rescaled length of ligand chain <sup>L</sup> <sup>¼</sup> <sup>δ</sup> d , δ is the contour length and d(=2R) is the diameter of the sphere. The free energy of mixing in terms of rescaled parameter can be expressed as [35]

$$\frac{\partial U\_{\text{mix}}}{\partial T} = \frac{\pi d^3}{2V\_{sol}^M} \rho\_{\text{lig}}^2 \left(\frac{1}{2} - \chi\right) \left(h - \left(1 + 2\overline{L}\right)\right)^2; \text{when, } 1 + \overline{L} < h < 1 + 2\overline{L}\_2$$

where V<sup>M</sup> sol, φlig, χ and h are the molar volume of the solvent, the average volume fraction of the ligand segments in the overlapping region, the Flory-Huggin

Importance of Surface Energy in Nanoemulsion DOI: http://dx.doi.org/10.5772/intechopen.84201

Figure 7.

coalescence can be effectively achieved, by creating a sufficient repulsive energy barrier between the droplets. This can be done by two ways, such as for O/W nanoemulsion the electrostatic stabilization (due to creation of double layer) by adding ionic surfactants. The formation of an electrical double layer (EDL, thickness δ) barrier is well established in the literature of colloidal stability according to the Derjaguin, Landau, Verwey and Overbeek (DLVO) theory [31]. As a result of this EDL formation when droplets approach a distance h, smaller than twice the double layer extension, strong repulsion occurs against their aggregation; hence, flocculation is prevented. A second and more effective mechanism using non-ionic surfactants or polymer (referred as surfactant) for W/O nanoemulsion is the steric stabilization (due to the presence of adsorbed polymer layer). However, no comparable definitive theory exists till date for the so-called steric stabilization. To date there have been several attempts made to develop the quantitative theory of steric stabilization with a notable success of Fischer's solvency theory [32] which exploits the Flory-Huggins theory [33] to predict the repulsive potential energy between two large flat plates. The total free energy of interaction obtained by Hesselink et al. for

<sup>2</sup>γ<sup>2</sup> <sup>α</sup><sup>2</sup> � <sup>1</sup> rrmsM dð Þþ <sup>2</sup>γV dð Þ,

where γ is the number of ligands per unit area, α is the expansion factor, rrms is the root mean square end-to-end distance of the chain in free solution and M dð Þ and V dð Þ are the distance-dependent mixing and elastic function that could be evaluated from segment density distribution function. However, the reason for the failure of Fischer's solvency theory appears to reside in the use of segment density distribution functions relevant to the isolated polymer according to Hesselink calculation [34] which is found unlikely to be applicable here. Smitham, Evans and Napper first pointed out the correction and proposed a simple analytical model to adopt for the segment density distribution function which is a constant segment density step function [35]. Their theory is able to account for many of the qualitative and quantitative features of steric stabilization observed to date. According to this model, the steric repulsion appears from two main origins: the first one (Figure 6b) is the unfavorable mixing of the surfactant chains which depends on their density at the interfacial region, on thickness of the interfacial layer (δ) and on the Flory-Huggin parameter, χ. The second one (Figure 6b) is the reduction in configuration entropy due to elastic stress of the chains which occur when inter-droplet distance becomes lower than δ. This method of stabilization is more effective than electrostatic stabilization in two ways: firstly, the repulsion is still maintained at moderate electrolyte concentration, and, secondly, the repulsion can be maintained at high

two flat plates coated by steric layer is given by [33]

Nanoemulsions - Properties, Fabrications and Applications

kT <sup>¼</sup> ð Þ <sup>2</sup>π=<sup>9</sup> <sup>3</sup>

temperature (provided ligand has solubility at that temperature).

in terms of rescaled parameter can be expressed as [35]

Umix kT <sup>¼</sup> <sup>π</sup>d<sup>3</sup> 2V<sup>M</sup> sol φ2 lig 1 <sup>2</sup> � <sup>χ</sup> 

where V<sup>M</sup>

100

<sup>1</sup> <sup>þ</sup> <sup>L</sup> <sup>&</sup>lt; <sup>h</sup> < 1 <sup>þ</sup> <sup>2</sup>L, where <sup>L</sup> is the rescaled length of ligand chain <sup>L</sup> <sup>¼</sup> <sup>δ</sup>

The unfavorable mixing of the surfactant chains (considering the chain-solvent interaction predominates over the chain-chain interaction, like it is in good solvent condition) occurs when the ligand chain starts to interpenetrate within a distance,

contour length and d(=2R) is the diameter of the sphere. The free energy of mixing

<sup>h</sup> � <sup>1</sup> <sup>þ</sup> <sup>2</sup><sup>L</sup> <sup>2</sup>

fraction of the ligand segments in the overlapping region, the Flory-Huggin

sol, φlig, χ and h are the molar volume of the solvent, the average volume

d , δ is the

; when, 1 þ L < h < 1 þ 2L,

Utotal

Pictorial representation of distance dependence of pair potential energy between two spheres according to the literature.

interaction parameter and the center-to-center distance between any two approaching spheres, respectively. When χ < 0.5, Gmix is positive and the interaction is repulsive. When χ > 0.5, Gmix is negative and the interaction is attractive. When χ = 0.5, Gmix is zero, which is referred to as the θ–condition. The Flory-Huggin parameter is calculated by Vm RT ð Þ <sup>δ</sup><sup>s</sup> � <sup>δ</sup><sup>m</sup> <sup>2</sup> <sup>þ</sup> <sup>0</sup>:34, where <sup>δ</sup><sup>s</sup> and <sup>δ</sup><sup>m</sup> are the Hildebrand solubility parameters [36] of the surfactant and solvent, respectively. Solubility parameter δ<sup>2</sup> of any component is related to its heat of vaporization ΔH with molar volume by <sup>δ</sup><sup>2</sup> <sup>¼</sup> <sup>Δ</sup>H�RT Vm .

Continuing on the droplet-droplet approach within a distance h < 1 þ L, a second regime appears where chains undergo significant interpenetration and compression. The free energy of mixing in this regime can be expressed as [37]

$$\frac{\mathcal{U}\_{\text{mix}}}{kT} = \frac{\pi d^3}{2V\_{sol}^M} \rho\_{\text{lig}}^2 \left(\frac{1}{2} - \chi\right) \left[3\ln\left(\frac{\overline{L}}{h-1}\right) + 2\left(\frac{h-1}{\overline{L}}\right) - \frac{3}{2}\right], \text{ when } h < 1 + \overline{L}\_2$$

while the elastic interaction Uel between the surfactant tails resulting from the loss in configurational entropy in this region is given by the expression [35]

$$\frac{U\_{el}}{kT} = \pi \gamma d^2 \left[ (h-1) \left( \ln \frac{h-1}{\overline{L}} - 1 \right) + \overline{L} \right]; \text{when}, h < 1 + \overline{L}, \dots$$

where γ is the number of ligands per unit area of the sphere. Therefore, Uel is always repulsive (Figure 7). A pictorial representation of pair potential vs. interparticle distance was shown in Figure 7 elaborating various cases of DLVO and non-DLVO interactions.

Therefore, the criteria for effective steric stabilization are the following: (1) the particle should be completely covered by the polymer, (2) the polymer should be strongly adsorbed to the particle surface, (3) the stabilizing chain should be highly soluble in the medium and is strongly solvated by its molecules and (4) δ should be sufficiently large to prevent weak flocculation which occurs when the thickness of adsorbed layer becomes small (<5 nm).
