Shape parameters, mesophases

Packing parameter Micellar shape Surfactant Mesophase example... 

Increases in the surfactant concentration lead to changes in the geometric conformation and packing of the micelles in solution. A direct relation between micellar shape and mesophase (surfactant phase in terms of structural properties) has been correlated, and it is known as the packing parameter, g, which describes the geometric parameters of the hydrophobic and hydrophilic sections of the amphiphilic surfactant molecule, and is described as follows ... 

Such surfaces describe the mid-surface of the amphiphilic bilayer. If the bilayer is Type 2, the surface cleaves opposing hydrocarbon chain-ends, and the remaining volume (defining a pair of interwoven 3D cubic labyrinths) are water-filled. Type 1 bicontinuous cubic mesophases consist of a reversed bilayer wrapped on the surfaces, with chains filling the labyrinths (Figure 16.17). As with the other mesophases discussed above, these Types have shape parameters on either side of 1 (roughly equal to 2/3 for Types 1 for Types 2, see Figure 16.8). A brief literature overview of these mesophases can be consulted for further references (10). 

It is impossible to offer estimates for relative locations of mesh mesophases within a phase diagram, due to the extreme variability of shape parameters ( ) with the composition of meshes. Note that Type 1 meshes (stacked layers of 2D apolar labyrinths) can result provided that /2 < s 2/3, and Type 2 meshes (with water labyrinths) can form if s > 2/3, over a range of compositions (Figure 16.8). That means that Type 2 mesh mesophases can be formed in lyotropes containing single-chain amphiphiles in contrast to the other Type 2 mesophases, which form only if s > 1. 

Given the shape parameters, generic equations can be drawn up for the molecular dimensions within the mesophase. We have the following ... 

Table 16.2. Shape parameters (equations (16.1) and (16.4)) and approximate swelling exponents s and s, cf. equation (16.8)) for known lyotropic mesophases. The (variable) constants /i and depend on the specific symmetry of the phase ( /i is the homogeneity index, ideal equal to 3/4 (cf. Table 16.1) / is the interstitial packing fraction for dense sphere and circle packings, equal to unity for ideal homogeneous packings)...

Mesophase Shape parameter. Type 1 Shape parameter. Type 2... 

This parameter corresponds to cylindrical packing shapes. Surfactants and amphiphiles falling in this range often produce planar bilayers and lamellar mesophases. Such cylindrical building blocks also contribute to many... 

It should also be noted that the stability of the distinct mesophases can be quite different. It seems that there is a significant effect of molecular shape and topology, stabilizing SmA phases in the system 41/43 and Colhex phases in the system 35/37. In addition, the mesophase stability is often reduced close to the transition to another mesophase (see Fig. 15). Hence, the order-disorder temperatures can only be roughly estimated based on segmental solubility parameters [24, 25]. 

Despite that the silicate-surfactant mesophase formation resembles the phase separation normally observed in surfactant-polyelecholyte systems, it is interesting to note that it is stiU possible to make qualitative predictions about the influence of inorganic-surfactant phase behavior based on models developed for dilute surfactant systems. The packing parameter concept - is based on a geomettic model that relates the geomehy of the individual surfactant molecule to the shape of the supramolecular aggregate structures most likely to form. N, is defined as... 

The potential of nuclear magnetic resonance spectroscopy for studying liquid crystalline systems is discussed. Typical spectra of nematic, smectic, and cholesteric mesophases were obtained under high resolution conditions. The observed line shape in the cholesteric phase agrees with that proposed on the basis of the preferred orientation of this phase in the magnetic field. The line shapes observed in lyotropic smectic phases appear to be the result of a distribution of correlation times in the hydrocarbon portions of the surfactant molecules. Thermotropic and lyotropic phase transitions are easily detected by NMR and agree well with those reported by other methods. The NMR parameters of the neat and middle lyotropic phases allow these phases to be distinguished and are consistent ivith their proposed structures. 

Through the study of the different topics considered in this article, it was shown how X-ray scattering is a useful tool to characterize the most salient features of the mesophases of LCPs. For instance, a simple procedure can be used to measure the nematic order parameter and it is so far valid for all kinds of LCPs based on rod-like moieties. In the case of main-chain polymers, useful information about the conformation of the repeat unit can also be deduced from the diffuse scattering. In the case of side-chain polymers, not only the smectic period but also the amplitude and shape of the smectic modulation can be derived from the measurement of the smectic reflection intensities. Moreover, fluctuations and localized defects may be detected through their contribution to the diffuse scattering. The average distance between lyotropic LCPs can be measured as a function of concentration which tells us the kind of local packing of the particles. 

Riggs showed the solubility of a pitch in a series of solvents with increasing solubility parameters followed a bell shaped curve, with maximum solubility occurring when the solubility parameter of the solute and solvent were equal( ). In general, non-polar solvents with total solubility parameters ranging from 8.0-9.5 were desirable for extracting mesophase forming fractions from pitches. In this... 

It is known that the trans isomer of azobenzene has elongated rod shape that is favorable for the stabilization of the LC phases, while the cis isomer in bent form is unfavorable and tends to destabilize the LC phases. The trans-cis photoisomerization will decrease the order parameters, if significantly enough, which could lead to the destruction of the ordered LC phase and formation of isotropic state. The reverse transition can be achieved with either visible light irradiation or thermal relaxation as a result of cis-trans isomerization. This principle was initially used to induce the phase transition from nematic to isotropic in azobenzene LCs [39]. Cholesteric mesophase is intrinsically similar to nematic with additional helical arrangement of nematic layers, thus the photoisomerization of azobenzenes can also bring out the phase transition from the cholesteric state to the photoin-duced isotropic (PHI) state. 

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