Food emulsions are microheterogeneous materials that contain a variety of different structural entities which range in size, shape, and physicochemical properties, including atoms, molecules, molecular aggregates, micelles, emulsion droplets, crystals, and air cells (Dickinson and Stainsby 1982, Dickinson 1992). Many of these structural entities have at least one dimension that falls within the colloidal size range (i.e., between a few nanometers and a few micrometers) (see Figure 1.8). The characteristics of these colloidal particles, and their interactions with each other, are responsible for many of the most important physicochemical and organoleptic properties of food emulsions. The ability of food scientists to understand, predict, and control the properties of food emulsions therefore depends on a knowledge of the interactions that arise between colloidal particles. In this chapter, we examine the origin and nature of the most important types of colloidal interaction, while in later chapters we consider the relationship between these interactions and the stability, rheology, and appearance of food emulsions (Chapters 7 to 9). This is one of the most exciting and rewarding areas of research currently being pursued in emulsion science, and our understanding is rapidly advancing as a result of recent developments in computer modeling, experimental techniques, and the concerted endeavors of individuals working in a variety of scientific disciplines, including mathematics, physics, chemistry, biology, and food science.
The interaction between a pair of colloidal particles is the result of interactions between all of the molecules within them, as well as those within the intervening medium (Hunter 1986, Israelachvili 1992). For this reason, many of the interactions between colloidal particles appear at first glance to be similar to those between molecules (e.g., van der Waals, electrostatic, and steric) (Chapter 2). Nevertheless, the characteristics of these colloidal interactions are often different from their molecular counterparts, because of additional features that arise due to the relatively large size of colloidal particles compared to individual molecules. The major emphasis of this chapter will be on interactions between emulsion droplets, although the same principles can be applied to the various other types of colloidal particles that are commonly found in foods.
Colloidal interactions govern whether emulsion droplets aggregate or remain as separate entities, as well as determine the characteristics of any aggregates formed (e.g., their size, shape, porosity, and deformability) (Dickinson 1992, Dickinson and McClements 1995, Bijsterbosch et al. 1995). Many of the bulk physicochemical and organoleptic properties of food emulsions are determined by the degree of droplet aggregation and the characteristics of the aggregates (Chapters 7 to 9). It is therefore extremely important for food scientists to understand the relationship among colloidal interactions, droplet aggregation, and bulk properties.
In Chapter 2, the interaction between two isolated molecules was described in terms of an intermolecular pair potential. In a similar fashion, the interactions between two emulsion droplets can be described in terms of an interdroplet pair potential. The interdroplet pair potential, w(h), is the energy required to bring two emulsion droplets from an infinite distance apart to a surface-to-surface separation of h (Figure 3.1). Before examining specific types of interactions between emulsion droplets, it is useful to examine the features of colloidal interactions in a more general fashion.
Consider a system which consists of two emulsion droplets of radius r at a surface-to-surface separation h (Figure 3.1). For convenience, we will assume that only two types of interactions occur between the droplets, one attractive and one repulsive:
The overall interaction between the droplets depends on the relative magnitude and range of the attractive and repulsive interactions. A number of different types of behavior can be distinguished depending on the nature of the interactions involved (Figure 3.2):
1. Attractive interactions dominate at all separations. If the attractive interactions are greater than the repulsive interactions at all separations, then the overall interaction is always attractive (Figure 3.2A), which means that the droplets will tend to aggregate (provided the strength of the interaction is greater than the disorganizing influence of the thermal energy).
2. Repulsive interactions dominate at all separations. If the repulsive interactions are greater than the attractive interactions at all separations, then the overall interaction is always repulsive (Figure 3.2B), which means that the droplets tend to remain as individual entities.
3. Attractive interactions dominate at large separations, but repulsive interactions dominate at short separations. At very large droplet separations, there is no effective interaction between the droplets. As the droplets move closer together, the attractive interaction initially dominates, but at closer separations the repulsive interaction dominates (Figure 3.2C). At some intermediate surface-to-surface separation, there is a minimum in the interdroplet interaction potential (hmin). The depth of this minimum, w(hmin), is a measure of the strength of the interaction between the droplets, while the position of the minimum (hmin) corresponds to the most likely separation of the droplets. Droplets aggregate when the strength of the interaction is large compared to the thermal energy, |w(hmin)| >> kT; remain as separate entities when the strength of the interaction is much smaller than the thermal energy, |w(hmin)| << kT; and spend some time together and some time apart at intermediate interaction strengths, |w(hmin)| ~ kT. When droplets fall into a deep
potential energy minimum, they are said to be strongly flocculated or coagulated because a large amount of energy is required to pull them apart again. When they fall into a shallow minimum, they are said to be weakly flocculated because they are fairly easy to pull apart. The fact that there is an extremely large repulsion between the droplets at close separations prevents them from coming close enough together to coalesce.
4. Repulsive interactions dominate at large separations, but attractive interactions dominate at short separations. At very large droplet separations, there is no effective interaction between the droplets. As the droplets move closer together, the repulsive interaction initially dominates, but at closer separations the attractive interaction dominates (Figure 3.2D). At some intermediate surface-to-surface separation (hmax), there is an energy barrier which the droplets must overcome before they can move any closer together. If the height of this energy barrier is large compared to the thermal energy of the system, w(hmax) >> kT, the droplets are effectively prevented from coming close together and will therefore remain as separate entities. If the height of the energy barrier is small compared to the thermal energy, w(hmax) << kT, the droplets easily have enough thermal energy to "jump" over it, and they rapidly fall into the deep minimum that exists at close separations. At intermediate values, w(Amax) ~ kT, the droplets still tend to aggregate, but this process occurs slowly because only a fraction of droplet-droplet collisions has sufficient energy to "jump" over the energy barrier. The fact that there is an extremely strong attraction between the droplets at close separations is likely to cause them to coalesce (i.e., merge together).
Despite the simplicity of the above model (Equation 3.1), we have already gained a number of valuable insights into the role that colloidal interactions play in determining whether emulsion droplets are likely to be unaggregated, flocculated, or coalesced. In particular, the importance of the sign, magnitude, and range of the colloidal interactions has become apparent. As would be expected, the colloidal interactions that arise between the droplets in real food emulsions are much more complex than those considered above (Dickinson 1992). First, there are a number of different types of repulsive and attractive interaction that contribute to the overall interaction potential, each with a different sign, magnitude, and range. Second, food emulsions contain a huge number of droplets and other colloidal particles that have different sizes, shapes, and properties. Third, the liquid that surrounds the droplets may be compositionally complex, containing various types of ions and molecules. Droplet-droplet interactions in real food emulsions are therefore influenced by the presence of the neighboring droplets, as well as by the precise nature of the surrounding liquid. For these reasons, it is difficult to accurately account for colloidal interactions in real food emulsions because of the mathematical complexity of describing interactions between huge numbers of molecules, ions, and particles (Dickinson 1992). Nevertheless, considerable insight into the factors which determine the properties of food emulsions can be obtained by examining the interaction between a pair of droplets. In addition, our progress toward understanding complex food systems depends on first understanding the properties of simpler model systems. These model systems can then be incrementally increased in complexity and accuracy as advances are made in our knowledge.
In the following sections, the origin and nature of the major types of colloidal interaction which arise between emulsion droplets are reviewed. In Section 3.11, we then consider ways in which these individual interactions combine with each other to determine the overall interdroplet pair potential and thus the stability of emulsion droplets to aggregation. A knowledge of the contribution that each of the individual colloidal interactions makes to the overall interaction enables one to identify the most effective means of controlling the stability of a given system to aggregation.
3.3. VAN DER WAALS INTERACTIONS 3.3.1. Origin of van der Waals Interactions
Intermolecular van der Waals interactions arise because of the attraction between molecules that have been electronically or orientationally polarized (Section 2.5). In addition to acting between individual molecules, van der Waals interactions also act between macroscopic bodies that contain large numbers of molecules, such as emulsion droplets (Hiemenz 1986). The van der Waals interactions between macroscopic bodies can be calculated using two different mathematical approaches (Hunter 1986, Derjaguin et al. 1987, Israelachvili 1992). In the microscopic approach, the van der Waals interaction between a pair of droplets is calculated by carrying out a pairwise summation of the interaction energies of all the molecules in one of the droplets with all of the molecules in the other droplet. Calculations made using this approach rely on a knowledge of the properties of the individual molecules, such as polarizabilities, dipole moments, and electronic energy levels. In the macroscopic approach, the droplets and surrounding medium are treated as continuous liquids which interact with each other because of the fluctuating electromagnetic fields generated by the movement of the electrons within them. Calculations made using this approach rely on a knowledge of the bulk physicochemical properties of the liquids, such as dielectric constants, refractive indices, and absorption frequencies. Under certain circumstances, both theoretical approaches give similar predictions of the van der Waals interaction between macroscopic bodies. In general, however, the macroscopic approach is usually the most suitable for describing interactions between emulsion droplets because it automatically takes into account the effects of retardation and the liquid surrounding the droplets (Hunter 1986).
The van der Waals interdroplet pair potential, wVDW(h), of two emulsion droplets of equal radius r separated by a surface-to-surface distance h is given by the following expression (Figure 3.1):
+ ln h2 + 4rh ) I h2 + 4rh + 4r2 ) I h2 + 4rh + 4r2
where ^121 is the Hamaker function for emulsion droplets (medium 1) separated by a liquid (medium 2). The value of the Hamaker function can be calculated using either the microscopic or macroscopic approach mentioned above (Mahanty and Ninham 1976). At close separations (h << r), the above equation can be simplified considerably:
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