Crystal phase volume

Samples that are 2 to 3 mm thick are suitable for imaging by CLSM and work well for products with solid fat content (crystal phase volume UNIT D3.1) between -10% and 50%. Fats with higher solid content must be thinner to allow sufficient light penetration. This method does not work well for samples with very high (>75% to 80%) solid fat content, as the samples are generally too opaque to allow sufficient light penetration. 

Quantitative analysis of these images is accomplished in the same manner as for any microscope image, depending on the detail of analysis desired. Automated image analysis software can be used to provide a variety of information. Crystal phase volume (solid fat content UNIT D3.i) can be obtained by counting dark pixels (according to some empirical threshold factor). 

The total number of crystals decreases to balance the increase in crystal size and maintain constant crystal phase volume during recrystallization. For the case of diffusion-limited ripening, the decrease in number of crystals can be written as (Dunning 1973) ... 

The polyamides are soluble in high strength sulfuric acid or in mixtures of hexamethylphosphoramide, /V, /V- dim ethyl acetam i de and LiCl. In the latter, compHcated relationships exist between solvent composition and the temperature at which the Hquid crystal phase forms. The polyamide solutions show an abmpt decrease in viscosity which is characteristic of mesophase formation when a critical volume fraction of polymer ( ) is exceeded. The viscosity may decrease, however, in the Hquid crystal phase if the molecular ordering allows the rod-shaped entities to gHde past one another more easily despite the higher concentration. The Hquid crystal phase is optically anisotropic and the texture is nematic. The nematic texture can be transformed to a chiral nematic texture by adding chiral species as a dopant or incorporating a chiral unit in the main chain as a copolymer (30). 

Miscible Blends. Sometimes a miscible blend results when two polymers are combined. A miscible blend has only one amorphous phase because the polymers are soluble in each other. There may also be one or more crystal phases. Simple theory (26) has supported the empirical relation for the permeabihty of a miscible blend. Equation 18 expresses this relation where is the permeabihty of the miscible blend and ( ) and are the volume fractions of polymer 1 and 2. 

It is clear from the previous discussion that a proportionality between crystallization temperature and the volume of the crystallizing phase has been found for PEO in many cases (Fig. 4), including AB and ABA diblock copolymers however, there have been reports of exceptions to this trend and they have also been included in the data compilation of Fig. 5, in particular the extensive data reported by Xu et al. [96]. In the case of ABC triblock copolymers a different behavior has also been reported and will be analyzed in detail in Sect. 5. 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

The nematic phase (N) is the least ordered, and hence the most fluid liquid crystal phase. The order in this type of LC phases is based on a rigid and anisometric (in most cases rod-shaped or disc-shaped) molecular architecture. Such molecules tend to minimize the excluded volume between them, and this leads to long range orientational order. For rod-like molecules the ratio between molecular length and its broadness determines the stability of the nematic phase with respect to the isotropic liquid state and the stability rises with increase of this ratio. In most cases the rigid cores are combined with flexible chains, typically alkyl chains, which hinder crystallization and in this way retain fluidity despite of the onset of order. 

Thermodynamic Equations. We briefly describe the thermodynamic formalism of Ruckenstein.10 Let us consider a liquid crystal of volume V per unit area, in equilibrium, and denote by <5i the average thickness of the water layer and by d2 the average thickness of the oil layer. The Helmholtz free energy of the system can be written as the sum of a free energy F0 of a hypothetical system in which the lamellae are treated as bulk, planar, phases and a free energy Pi, which accounts for the smallness of the lamellae, the interactions between them, and their thermal undulations. One can write... 

An explanation for this gel formation is sought in the phase transition behavior of span 60. At the elevated temperature (60 °C) which exceeds the span 60 membrane phase transition temperature (50 °C) [154], it is assumed that span 60 surfactant molecules are self-assembled to form a liquid crystal phase. The liquid crystal phase stabilizes the water droplets within the oil. However, below the phase transition temperature the gel phase persists and it is likely that the monolayer stabilizing the water collapses and span 60 precipitates within the oil. The span 60 precipitate thus immobilizes the liquid oil to form a gel. Water channels are subsequently formed when the w/o droplets collapse. This explanation is plausible as the aqueous volume marker CF was identified within these elongated water channels and non-spherical aqueous droplets were formed within the gel [153]. These v/w/o systems have been further evaluated as immunological adjuvants. 

One of the most important uses of phase diagrams in food applications is predict-tion of crystalline yield for a given system. For example, if a sucrose solution of certain concentration is allowed to crystallize to equilibrium, the amount of crystalline solid (yield) can be predicted based on the phase diagram. As will be seen later, crystalline phase volume is one of the most important determinants of food material properties. 

Depending on conditions during processing and storage, a crystalline microstructure develops in many foods that can significantly impact food propaties. Some important characteristics of the crystalline dispersion include the crystalline phase volume, mean size and size distribution of crystals, shape and surface characteristics of the particles, polymorphic characteristics, and any network structure that forms between... 

Crystalline phase volume by itself is generally not sufficient to determine material properties some measure of the dispersion of that crystalline material is also needed. A product that contained all the mass in a few large crystals would have completely different material properties than the same product containing a dispersion of numerous small crystals. Hardness is related to the size of crystals in a system, with more numerous small crystals typically giving a harder product. The product with numerous small crystals has many more interparticle contacts under applied force than a product with the same crystalline phase volume but fewer larger crystals. 

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