Mesophases layered

The existence of the mesophase layer has been proved by infra-red spectroscopy, ESP, NMR, electron microscopy and other experimental methods. Moreover, it has been also proved that the thickness of this layer depends on the polymer cohesion energy, free surface energy of the solid, and on the flexibility of the polymer chains. 

A study of the effect of the mesophase layer on the thermomechanical behaviour and the transfer mechanism of loads between phases of composites will be presented in this study. Suitable theoretical models shall be presented, where the mesophase is taken into consideration as an additional intermediate phase. To a first approximation the mesophase material is considered as a homogeneous isotropic one, while, in further approximations, more sophisticated models have been developed, in which the mesophase material is considered as an inhomogeneous material with progressively varying properties between inclusions and matrix. Thus, improvements of the basic Hashin-Rosen models have been incorporated, making the new models more flexible and suitable to describe the real behaviour of composites. 

In order to solve the system of the above-described equations, and which are derived by applying the self-consistent model, applied for composites by Budiansky 7), it is necessary to evaluate experimentally the moduli of elasticity (tension, shear, bulk) and Poisson s ratios of the constituent phases and the composite. Thus, the only unknown are the radius r of the mesophase layer and its mechanical properties and thermal expansion coefficient, which are then derived. 

A decisive factor for the physical behaviour of a composite is the adhesion efficiency at the boundaries between phases. In all theoretical models this adhesion is considered as perfect, assuming that the interfaces ensure continuity of stresses and displacements between phases, which should be different because of the proper nature of the constituents of composites. However, such conditions are hardly fulfilled in reality, leading to imperfect bonding between phases and variable adhesion between them. The introduction of the mesophase layer has as function to reconcile in a smooth way the differences on both sides of interfaces. 

It is further assumed that the mesophase layer consists of a material having progressively variable mechanical properties. In order to match the respective properties of the two main phases bounding the mesophase, a variable elastic modulus for the mesophase may be defined, which, for reasons of symmetry, depends only on the radial distance from the fiber-mesophase surface. In other words, it is assumed that the mesophase layer consists of a series of elementary peels, whose constant mechanical properties differ to each other by a quantity (small enough) defined by the law of variation of Ej(r). 

In this way, both boundaries of the mesophase layer with the inclusion and the matrix are automatically satisfied and, therefore, Equation (29) is a convenient relationship, yielding the variable Ej(r)-modulus accomodating, in a natural way, the smooth transition from a large Ef-modulus to a reduced Em-modulus for the matrix and vice versa. 

The experimental data show that the magnitude of the heat capacity (or similarly of the specific heat) under adiabatic conditions decreases regularly with the increase of filler content. This phenomenon was explained by the fact that the macromolecules, appertaining to the mesophase layers, are totally or partly excluded to participate in the cooperative process, taking place in the glass-transition zone, due to their interactions with the surfaces of the solid inclusions. 

In order now to evaluate the exponent rp we make recourse to the law of mixtures, given by relation (21), which expresses the elastic modulus of the composite in terms of the moduli and the radii (or volume fractions) of the constituent phases. This relation yields the average elastic modulus for the mesophase Ef. Then, it is valid for the mesophase layer that ... 

It is interesting plotting the variation of the E.(r)-modulus versus polar distance around a typical inclusion. Fig. 10 presents this transition of the moduli from the particulate inclusions to the matrices, exemplifying the important role played by the mesophase layer to the overall mechanical behaviour of the composite. 

These types of models were significant improvements of a previously introduced multilayered model17 based on the same principles, as the unfolding models, and taking into consideration the influence of the mesophase layer to the physical behaviour of the composite2A). 

Indeed, the multi-layered model, applied to fiber reinforced composites, presented a basic inconsistency, as it appeared in previous publications17). This was its incompatibility with the assumption that the boundary layer, constituting the mesophase between inclusions and matrix, should extent to a thickness well defined by thermodynamic measurements, yielding jumps in the heat capacity values at the glass-transition temperature region of the composites. By leaving this layer in the first models to extent freely and tend, in an asymptotic manner, to its limiting value of Em, it was allowed to the mesophase layer to extend several times further, than the peel anticipated from thermodynamic measurements, fact which does not happen in its new versions. 

Fig. 17 presents the variation of the terms E((rf/r)n> and Em(rf/r), i in the mesophase layer for a 65 percent E-glass fiber-reinforced epoxy resin, as they have been derived from Eq. (48). It is wortwhile indicating the smooth transition of the Ermodulus to the Em-modulus at the region r == rf. Similar behaviour present all other compositions. 

A series of models were introduced in this study, which take care of the existence of this boundary layer. The first model, the so-called three-layer, or N-layer model, introduces the mesophase layer as an extra pseudophase, and calculates the thickness of this layer in particulates and fiber composites by applying the self-consistent technique and the boundary- and equilibrium-conditions between phases, when the respective representative volume element of the composite is submitted to a thermal potential, concretized by an increase AT of the temperature of the model. 

Two versions of an alternate model were also introduced, where the mesophase layer was assumed as possessing variable mechanical and physical properties, accomodating a smooth transition of the properties of the inclusions with those of the matrix, by assuring in a very short distance the progressive, from the inclusion-matrix boundaries outwards, change of the characteristic quantities of the one phase, in order to match those of the other phase. 

Proteins for the most part are water soluble but some are not and most have domains along the molecule that differ in their hydrophobicities. There is therefore a strong possibility that some proteins or polypeptides, when added to a sterile emulsion, would distribute themselves into the mesophase layer of the emulsion droplets and remain associated with these droplets on delivery. 

Figure 23. Combination of two +tt disclinations may tilt mesophase layers out of fibrous alignment by formation of a continuous core in the +2tt disclination.

From Figure 14, it can be observed that yield stress increases with an increase in EVA concentration in the binder. One possible explanation for such a phenomenon is by assuming the formation of an immobile absorbed layer of binder molecular chains on the iron particles surface. The formation of such an interface or mesophase layer [53] would effectively increase the apparent size of the particles and in mm increase the effective solid volume fraction of the feedstock [54]. The increase in effective solid volume fraction would in mrn lead to higher suspension yield stress by the same reasoning described in the previous section [51, 52]. The thickness of this absorbed layer corresponds to the random coil dimension for the molecular chains. The chain end-to-end distance, /i, of a polymer molecular chain ranges from 20 to 100 nm and is given by the following expression [55]. 

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