ADSORPTION KINETICS

The rate at which an emulsifier adsorbs to an interface is one of the most important factors determining its efficacy as a food ingredient (Magdassi and Kamyshny 1996, Walstra 1996b). The adsorption rate depends on the molecular characteristics of the emulsifier (e.g., size, conformation, and interactions), the nature of the bulk liquid (e.g., viscosity), and the prevail- ing environmental conditions (e.g., temperature and mechanical agitation). It is often conve- nient to divide the adsorption process into two stages: (1) movement of the emulsifier molecules from the bulk liquid to the interface and (2) incorporation of the emulsifier molecules at the interface. In practice, emulsifier molecules are often in a dynamic equilib- rium between the adsorbed and unadsorbed states, and so the rate at which emulsifier molecules leave the interface must also be considered (Hunter 1993, Magdassi and Kamyshny 1996).

5.7.1. Movement of Molecules to an Interface

In this section, we assume that an emulsifier molecule is adsorbed to an interface as soon as it encounters it (i.e., there are no energy barriers that retard adsorption). In an isothermal quiescent liquid, emulsifier molecules move from a bulk liquid to an interface by molecular diffusion, with an initial adsorption rate given by (Tadros and Vincent 1983, Magdassi and Kamyshny 1996): d dt c D t Γ = π (5.10)

where D is the translational diffusion coefficient, Γ is the surface excess concentration, t is the time, and c is the concentration of emulsifier initially in the bulk liquid. The variation of the surface excess concentration with time is obtained by integrating this equation with respect to time:

Γ( )t = 2c Dt

π (5.11)

Thus, a plot of the surface excess concentration versus √t should be a straight line that passes through the origin. This equation indicates that the accumulation of an emulsifier at an interface occurs more rapidly as the concentration of emulsifier in the bulk liquid increases or as the diffusion coefficient of the emulsifier increases. The diffusion coefficient increases as the size of molecules decreases, and one would therefore expect smaller molecules to adsorb more rapidly than larger ones. Experiments with proteins have shown that Equation 5.11 gives a good description of the early stages of adsorption to clean interfaces (Damodaran 1989, Walstra 1996b). After the initial stages, the adsorption rate decreases because the interface becomes saturated with emulsifier molecules and therefore there are fewer sites available for the emulsifier to adsorb to (Figure 5.11). In practice, the rate may be faster than that given by Equation 5.10 because of convection currents caused by temperature gradients within a liquid. Consequently, considerable care must be taken to

ensure that the temperature within a sample is uniform when measuring diffusion-controlled adsorption processes.

The above equations do not apply during the homogenization of emulsions, because homogenization is a highly dynamic process and mass transport is governed mainly by convection rather than diffusion (Dickinson 1992, Walstra 1996b). Under isotropic turbulent conditions, the initial increase of the surface excess concentration with time is given by (Dukhin et al. 1995): Γ( )t Cr c r r t d e d =  +    1 3 (5.12)

where C is a constant which depends on the experimental conditions, and rd and re are the

radii of the droplet and emulsifier, respectively. This equation predicts that the adsorption rate increases as the concentration of emulsifier increases, the size of the emulsion droplets increases, or the size of the emulsifier molecules increases relative to the size of the droplets. This equation implies that when an emulsion is homogenized, the emulsifier molecules initially adsorb preferentially to the larger droplets and that larger emulsifier molecules adsorb more rapidly than smaller ones (which is the opposite of diffusion-controlled adsorp- tion). This explains why large casein micelles adsorb faster than individual casein molecules during the homogenization of milk (Mulder and Walstra 1974).

5.7.2. Incorporation of Emulsifier Molecules at an Interface

So far, we have assumed that as soon as an emulsifier molecule reaches an interface, it is immediately adsorbed. In practice, there may be one or more energy barriers that must be overcome before a molecule adsorbs, and so only a fraction of the encounters between an emulsifier molecule and an interface lead to adsorption (Damodaran 1996, Magdassi and Kamyshny 1996). In these systems, adsorption kinetics may be governed by the height of the energy barrier, rather than by the rate at which the molecules reach the interface (Magdassi and Kamyshny 1996).

There are a number of reasons why an energy barrier to adsorption may exist: 1. As an emulsifier molecule approaches an interface, there may be various types of

repulsion interactions between it and the emulsifier molecules already adsorbed to the interface (e.g., electrostatic, steric, hydration, or thermal fluctuation) (Chap- ter 3).

2. Some surface-active molecules will only be adsorbed if they are in a specific orientation when they encounter the interface. For example, it has been suggested FIGURE 5.11 Adsorption kinetics for a diffusion-controlled system.

that globular proteins which have hydrophobic patches on their surface must face toward an oil droplet during an encounter (Damodaran 1996).

3. The ability of surfactant molecules to form micelles plays a major role in determin- ing their adsorption kinetics (Dukhin et al. 1995, Stang et al. 1994, Karbstein and Schubert 1995). Surfactant monomers are surface active because they have a polar head group and a nonpolar tail, but micelles are not surface active because their exterior is surrounded by hydrophilic head groups. The adsorption kinetics there- fore depends on the concentration of monomers and micelles present, as well as the dynamics of micelle formation–disruption.

Micelle dynamics can be characterized by two relaxation times, one associated with the movement of individual monomers in and out of the micelles (τfast) and the other associated

with the complete dissolution of a whole micelle into a number of individual molecules (τslow)

(Land and Zana 1987). Consider the processes that occur when a fresh oil–water interface is brought into contact with an aqueous solution containing surfactant monomers and micelles (Kabalnov and Weers 1996). When a monomer adsorbs to the surface, the local monomer concentration is depleted, and so there is a concentration gradient between the region in the immediate vicinity of the interface and the bulk solution. This gradient can be equalized by the diffusion of surfactant monomers from the bulk liquid into the depleted zone. However, this disturbs the equilibrium between the monomers and micelles, leading to the partial dissociation of the micelles. Thus the micelles influence the adsorption kinetics indirectly rather than directly. The adsorption kinetics therefore depends on the diffusion coefficient of the monomers and micelles, as well as the dynamic properties of the micelles (i.e., the relaxation times). When the micelle relaxation mechanisms that release the monomers are much slower than the diffusion of the monomers, the adsorption kinetics is governed mainly by the critical micelle concentration, rather than the actual micelle concentration present. On the other hand, if the micelle relaxation mechanisms occur rapidly, then the micelles act as an additional source of monomers, and the adsorption rate is enhanced when the surfactant concentration is increased above the critical micelle concentration.

The adsorption of emulsifier molecules at a surface or interface can be measured using a variety of experimental methods (Couper 1993, Kallay et al. 1993, Dukhin et al. 1995). The most commonly used method is to measure the variation in surface or interfacial tension with time using a tensiometer (Section 5.9). A number of workers have also used radiolabeled emulsifier molecules to measure adsorption kinetics (Damodaran 1989). A radioactivity detector is placed immediately above a water–air surface. The radiolabeled emulsifier is injected into the water and the increase in the radioactivity at the surface is recorded over time by the detector. The radioactivity is highly attenuated by the water, and so only those molecules which are close to the air–water surface are detected. A variety of other experimen- tal methods that can detect changes in interfacial properties due to the adsorption of emul- sifier molecules have also been used to monitor adsorption kinetics, including ultraviolet- visible spectroscopy, infrared spectroscopy, fluorescence spectroscopy, ellipsometry, and interfacial rheology (Kallay et al. 1993).