Critical packing factor

The size, structure, and fluidity of membrane lipids are also important because those aspects of the molecules make it possible for them to pack efficiently into a variety of convoluted bilayer membrane structures with various degrees of curvature and flexibihty. Tliat flexibility also makes possible the inclusion of the various other important components of the cell wall, including proteins, carbohydrates, and cholesterol. In terms of the geometric concepts discussed previously (see Fig. 15.15), one can visualize where one class of lipid will have a critical packing factor. Pc (= v/adc) < 1, which will produce a truncated cone shape, while another will have F > i for an inverted truncated cone. Combinations of the two can then accommodate the inclusion of, for example, proteins and cholesterol, while maintaining an overall planar structure (or a given degree of curvature), or increase curvature to produce a smaller associated unit. 

Figure 11.13 Influence of critical packing factors on aggregated structures.

Tc. The two power-law exponents are not independent but depend on a single parameter, the so-called critical exponent X, which is specific for a given interaction potential (e.g., hard spheres). Actually, the interaction potential enters the MCT equations only indirectly via the structure factor S(q), which fixes the nonlinear coupling in the generalized oscillator equation. It is important to note that the MCT exponents are not universal in contrast to those of second-order phase transitions. In the case of hard spheres, for example, S(q) can be calculated via the Percus-Yevick approximation [26], and the full time and -dependence of < >(q. f) were obtained. As an example, Fig. 10 shows the susceptibility spectra of the hard-sphere system at a particular q. Note that temperature cannot be defined in the hard-sphere system instead, the packing fraction cp is used as a parameter. Above the critical packing fraction 0), which corresponds to T < Tc in systems where T exists, the a-process is absent (frozen) and only the fast dynamics is present. At cp < tpc the a-peak and the concomitant susceptibility minimum shift to lower frequencies with increasing cp, so that the closer cp is to the critical value fast dynamics can be identified (curve c in Fig. 10). 

Surfactant-like lipids adopt either normal (type 1) or inverted (type 2) self-assembled phases, resulting in either oil-in-water (o/w) phases with convex curvature lipid/water interface or water-in-oil (w/o) phases with a concave interface, respectively. The formation of a normal or an inverted self-assembled nanostructure in water mainly depends on the lipid s molecular shape, as discussed in the seventies by Israelachvili and co-workers [78], In this regard, the geometric shape of the lipid can be a useful tool for predicting the water-lipid interface curvature and also can be helpful in imderstanding the phase behavior of binary, ternary, and even multi-component systems [79], For this purpose, the shape factor or more commonly known in the literature as the critical packing parameter CPP) was defined [78] as ... 

Factors Responsible for Formation of Liposomes and Vesides -The Critical Packing Parameter Concept... 

Experience has shown that dispersion and the packing value obtained by linseed oil absorption are closely related to the critical PVC and pigment packing factor for the same pigment in paint and ink films. 

In developing controlled-release matrices, the solubilization capacity of miaoanulsions should be optimized, which depends on various factors, such as the oitical micelle concentration, the surfactant s HLB value, the critical packing parameter and molecular compatibility between the oil, surfactant and co-surfactant (Friberg et al., 1994 Aboofazeli et al., 1995 von Corswant and Soderman, 1998). 

Over the years it has been confirmed that geometric factors control the packing of surfactants and lipids into association structures. The concept has already been introduced, but warrants repetition in the current context for clarity. The packing propensity of a given amphiphilic stmcmre can be conveniently given by the critical packing parameter, denoted here as and given by... 

Metallic packings of aluminum, copper and lead cover a very wide temperature range up to 540°C (1000°F). They should be matched to the shaft material, since shaft finish and tolerance are critical factors in overall efficiency. The great limiting factor in the use of metallic packing is the difficulty of ensuring corrosion resistance with all the likely process materials. 

---