Aggregates critical packing parameter

The critical packing parameter can be used as a guide to the aggregate architecture for a given surfactant (as shown in Figure 4.6). Typical values and their corresponding aggregate structures are ... 

Figure 4.6 Use of the critical packing parameter to predict aggregate structures.

Chapter 8 has been revised to include a discussion of the critical packing parameter of surfactants and its relation to the structure of resulting surfactant aggregates. This simple geometric basis for the formation of micelles, bilayers, and other structures is intuitively easier to understand for a beginning student. 

Figure 6.25 Influence of the critical packing parameter, CPP = vl(l a], on the type of aggregate formed by surfactants in solution.

A useful concept for characterizing micelle geometry is the critical packing parameter (CPP) [2]. The aggregation number N is the ratio between the micellar core volume, V and the volume of one chain, v. 

The thermodynamic modeling of microemulsions has taken various lines and gave conflicting results in the period before the thermodynamic stability and microstructure were established. It was early realized that a maximal solubilization of oil and water simultaneously could be discussed in terms of a balance between hydrophilic and lipophilic interactions the surfactant (surfactant mixture) must be balanced. This can be expressed in terms of the HLB balance of Shinoda,Winsor s R value, and a critical packing parameter (or surfactant number), as introduced to microemulsions by Israelachvili et al. [37], Mitchell and Ninham [38], and others. The last has become very popular and useful for an understanding of surfactant aggregate structures in general. 

A simple but effective concept described by Israelachvilli et al. predicts the aggregation of surfactants in solution. This model is based on the molecular shape of the surfactant molecules. In this model, the ratio of the size of the hydrophobic and the hydrophilic portion of the molecules is expressed in terms of a critical packing parameter P [9] ... 

Critical packing parameter Approximate molecular shape Expected aggregate structure... 

FIGURE 15.11. The critical packing parameter, allows one to quickly determine the general type of aggregate structure to be expected for a given surfactant molecular composition. 

The critical packing parameter, CPP, is described by eq 2, where v is the average volume of the amphiphile, a is the effective head group area, and / is the effective chain length of the surfactant in the molten state. The CPP can be used to predict the aggregate structures and to correlate stmctural clmges of the surfactant (or PIL) with changes to the self-assembly phases. 

FIGURE 16.1 Surfactant molecules self-assemble into various aggregate shapes, depending on the surfactant molecular structure as described by the critical packing parameter (CPP), which is the ratio of the molecular volume (v) divided by its length (/) times the cross-sectional area of the head group (a) v/al. 

Several ideas have been put forward to explain the driving force for formation of the different liquid crystalline phases. One of the simplest methods for predicting the shape of an aggregated structure is based on the critical packing parameter concept (P) introduced by Israelachvili and his co-workers [22, 23]. This concept will be discussed in detail in the chapter on emulsions (selection of emulsifiers). Basically, P is the ratio between the cross sectional area of the alkyl chain (that is given by v/l, where v is the volume of the hydrocarbon chain and is the maximum length to which the alkyl chain can extend) and the optimum head group area ao, i.e.,... 

The critical packing parameter (CPP) is a simple geometrical concept that determines the shape of any aggregation unit (see Chapter 6). It is simply the ratio of the cross sectional area of the hydrocarbon chain, ao, to the cross sectional area of the hydrophihc head group, a. 

One of the simplest methods for predicting the shape of an aggregated structure is based on the critical packing parameter P [30]. 

Example 5.3. Critical packing parameter and aggregation number of non-ionic surfactants. 

TABLE 4.3. Expected Aggregate Characteristics in Relation to Surfactant Critical Packing Parameter, vlaJc... 

Critical Packing Parameter General Surfactant Type Expected Aggregate Structure... 

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