THERMODYNAMICS OF DISPERSED SYSTEMS

3. THERMODYNAMICS OF DISPERSED SYSTEMS

The fundamental thermodynamic property influencing the formation and breakdown of dispersed systems is interfacial tension (refer above).

3.1. Colloids Lyophilic and association colloids are thermodynamically

stable, since these are either large molecules or associations of molecules that are in solution. However, lyophobic colloids are thermodynamically unstable. The instability of lyophobic colloids has a major influence on their formulation and perfor- mance and they must be rendered kinetically stable for a per- iod that constitutes an acceptable shelf-life for the product. The Derjaguin–Landau and Verwey–Overbeek (DLVO) the- ory describes the interaction between particles of a lyophobic colloid. This theory is reviewed in the texts of Hunter (15) and Heimenz (16) and is based on the assumption that the van der Waals interactions (attractive forces) and the electrostatic interactions (repulsive forces) can be treated separately and then combined to obtain the overall effect of both of these forces on the particles. Although this is an oversimplification, it is the easiest way to understand the complex interactions that are occurring between colloidal particles.

3.1.1. Attractive Forces The van der Waals attractive forces between two particles are

considered to result from dipole–dipole interactions and are proportional to 1 6 =H , where H is the separation distance between the particles (17). Consequently, the attractive forces operate over very short distances and the value of these attractive forces is greater the smaller the interparticle dis- tance. The Hamaker summation method is used to calculate

the total van der Waals interaction energy (V A ), assuming that the interactions between individual molecules in two col- loidal particles can be added together to obtain the total inter- action and that these interactions are not affected by the

Physical Stability of Dispersed Systems 11

presence of all the other molecules. The dispersion theory of Lifshitz (18) overcomes the assumptions made in the London theory and is based on the idea that the attractive interac- tion between particles is propagated as an electromagnetic wave over distances that are large compared with atomic dimensions. In the Lifshitz theory, the colloidal particles are considered to be made up of many local oscillating dipoles that continuously radiate energy. These dipoles are also continuously absorbing energy from the electromagnetic fields generated by all the surrounding particles. The reader is referred to the text by Hunter (15) for a full treatment of this theory.

3.1.2. Repulsive Forces The repulsive forces between lyophobic colloids are electro-

static in nature and are a consequence of the charge carried by the particles. All lyophobic colloidal particles acquire a sur- face charge when dispersed in an electrolyte solution: by adsorption of ions from the solution; by ionization of ionizable groups; or by selective ion dissolution from the particle sur- face. These charged particles attract ions of the opposite charge (counter ions), some of which become tightly bound to the particle surface. The counter ions are also pulled away from the particle surfaces by the bulk solution as a result of thermal motion. A diffuse layer of ions builds up as a conse- quence of these two opposing effects so that at a distance from the particle surface, it appears to be electrically neutral ( Fig. 2 ). The tightly bound and the diffuse layers are known collectively as the electrical double layer. The electrical double layer is responsible for the repulsive interaction between two colloidal particles. When two colloidal particles come in close proximity of one another, their electrical double layers over- lap. This causes a free energy change and an increase in osmo- tic pressure as a result of the accumulation of ions between the particles. This repulsive interaction (V R ) decreases exponen- tially with increase in the distance between the particles.

The DLVO theory combines the attractive and repul- sive interactions between lyophobic colloids to explain the

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Figure 2 Diffuse double layer of ions on the particle surface.

aggregative instability of two particles at any given separa- tion distance. The two opposing forces are summed, as shown diagrammatically in Fig. 3, where V T is the summation of V A

and V R (V T ¼V A þV R ). The van der Waals attractive forces dominate at both large and small separation distances. At

Figure 3 Potential energy diagram for two spherical particles. V A is vander Waals attraction energy; V R is repulsive energy; V T is total potential energy obtained by summation of V A and V R (V T ¼V A þV R ).

Physical Stability of Dispersed Systems 13

very small distances, van der Waals attraction increases markedly, resulting in a deep attractive well (known as the primary minimum). However, this well is not infinitely deep due to the very steep short range repulsion between the atoms on each surface (15). The DLVO theory can be applied in a broad sense to most lyophobic colloidal systems. This theory is also applied to particles and droplets outside the colloidal size range and is discussed below for liquid and solid disper- sion stability in the thermodynamics section. (The reader is referred to Chapter 6 in this book for a treatment of the DLVO theory with respect to coarse suspension.

3.1.3. Stabilization of Lyophobic Colloids Lyophobic colloids can be kinetically stabilized by electro-

static and polymeric methods. Electrostatic stabilization results from charge–charge repulsion, as discussed above. Polymeric stabilization is achieved by steric stabilization upon adsorption of macromolecules (lyophilic colloids) at the surface of a lyophobic colloid (19). The lyophilic colloids must extend from the surface of the particles over a distance com- parable to, or greater than, the distance over which van der Waals attraction is effective. Therefore, a molecular weight of at least a few kDa is required and the lyophilic colloids must be present at a sufficiently high concentration so that they saturate the surfaces of the lyophobic particles. The colloidal particles will then repel one another as a result of volume restriction and osmotic pressure effects, as illustrated in Fig. 4 . Lifshitz (18) gives a thermodynamic account of poly- meric stabilization. A polyelectrolyte may stabilize a lyopho- bic colloid by a combination of steric and electrostatic stabilization (electro-steric stabilization).

At low polymer concentrations (and hence low particle surface coverage), lyophilic colloids tend to have multiple points of contact on the lyophobic particle surface and lie along the surface rather than extend from it. Segments of individual molecules may adsorb onto more than one lyopho- bic colloid and hence bridging flocculation may occur ( Fig. 5 ), causing particle aggregation rather than repulsion.

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Figure 4 Stabilization of lyophobic colloidal particles by volume restriction and osmotic pressure effects.

3.2. Thermodynamics of Dispersed Systems Dosage Forms

For the purpose of thermodynamics, dispersed systems can be considered either as liquid dispersions (emulsions) or as solid dispersions (suspensions, liposomes, nano- and microspheres).

Figure 5 Bridging flocculation by adsorption of polymer chains on lyophobic colloid particles.

Physical Stability of Dispersed Systems 15

The term suspension is used in this section to represent suspensions, liposomes, nano- and microspheres.

3.2.1. Emulsions When two immiscible liquids or liquids with very limited

mutual solubility are agitated together, they fail to dissolve. Immiscibility arises since the cohesive forces between the molecules of the individual liquids are greater than the adhe- sive forces between different liquids. Consequently, the force experienced by molecules at the interface between the immis- cible liquids is imbalanced compared to the force experienced by molecules in the bulk (Fig. 6). This imbalance in the force is manifested as interfacial tension (g). When the dispersed phase is broken into droplets, the interfacial area (A) of this liquid becomes large compared to that of the bulk liquid and the surface free energy is increased by an amount gDA. According to the Gibbs equation (20), increase in interfacial free energy causes thermodynamic instability: