Intimate Contact Model

The Li-Loos intimate contact model was verified for compression molded unidirectional graphite-polysulfone and graphite-PEEK (APC-2) laminae and graphite-PEEK (APC-2) cross-ply laminates. The degrees of intimate contact of the unidirectional and cross-ply specimens were measured by optical microscopy and scanning acoustic microscopy, respectively. The predicted degrees of intimate contact agreed well with the measured values for both the unidirectional and cross-ply specimens processed at different temperature and pressures. 

In the in situ consolidation model of Liu [26], the Lee-Springer intimate contact model was modified to account for the effects of shear rate-dependent viscosity of the non-Newtonian matrix resin and included a contact model to estimate the size of the contact area between the roller and the composite. The authors also considered lateral expansion of the composite tow, which can lead to gaps and/or laps between adjacent tows. For constant temperature and loading conditions, their analysis can be integrated exactly to give the expression developed by Wang and Gutowski [27]. In fact, the expression for lateral expansion was used to fit tow compression data to determine the temperature dependent non-Newtonian viscosity and the power law exponent of the fiber-matrix mixture. 

In the preceding section, a brief review of efforts to model the intimate contact process during consolidation of thermoplastic composites was given. Models based on the original work of 

Lee and Springer [19] and modified by Li and Loos [22,23] to include unidirectional and cross-ply lay-ups will be used to demonstrate the effects of various geometric, material, and processing parameters on the degree of intimate contact. 

Equations 7.2 and 7.3 represent expressions for the degree of intimate contact of a single prepreg ply in contact with a smooth rigid surface (Fig. 7.5). 

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The intimate contact data shown in Figure 7.16 were obtained from three-ply, APC-2, [0°/90o/0o]7- cross-ply laminates that were compression molded in a 76.2 mm (3 in.) square steel mold. The degree of intimate contact of the ply interfaces was measured using scanning acoustic microscopy and image analysis software (Section 7.4). The surface characterization parameters for APC-2 Batch II prepreg in Table 7.2 and the zero-shear-rate viscosity for PEEK resin were input into the intimate contact model for the cross-ply interface. Additional details of the experimental procedures and the viscosity data for PEEK resin are given in Reference 22. 

Ideal adhesion simply means the adhesion expected under one or another model situation of uniform materials having intimate contact over a well-defined area. In these cases, the important quantity is the work of adhesion wab between two phases, which is given by... 

The dominant mechanism of purification for column crystallization of solid-solution systems is recrystallization. The rate of mass transfer resulting from recrystallization is related to the concentrations of the solid phase and free liquid which are in intimate contact. A model based on height-of-transfer-unit (HTU) concepts representing the composition profile in the purification section for the high-melting component of a binary solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 20-10. The column crystallizer was operated at total reflux. The solid line through the data was com-putecfby Powers et al. (op. cit., p. 364) by using an experimental HTU value of 3.3 cm. 

Henry and Fauske (1975, 1976) have proposed a model to describe the events leading to a large-scale vapor explosion in a free contact mode. Their initial, necessary conditions are that the two liquids, one hot and the other cold, must come into intimate contact, and the interfacial temperature [Eq. (1)] must be greater than the homogeneous nucleation temperature of the colder liquid. Assuming the properties of both liquids are not strong functions of temperature, the interface temperature is then invariant with time. Temperature profiles within the cold liquid may then be computed (Eckert and Drake, 1972) as... 

Almost all of the models assume local thermal equilibrium between the various phases. The exceptions are the models of Beming et al., ° who use a heat-transfer coefficient to relate the gas temperature to the solid temperature. While this approach may be slightly more accurate, assuming a valid heat-transfer coefficient is known, it is not necessarily needed. Because of the intimate contact between the gas, liquid, and solid phases within the small pores of the various fuel-cell sandwich layers, assuming that all of the phases have the same temperature as each other at each point in the fuel cell is valid. Doing this eliminates the phase dependences in the above equations and allows for a single thermal energy equation to be written. 

Models of the intimate contact process that have appeared in the literature are commonly composed of three parts or submodels. The first submodel is used to describe the variation in the tow heights (surface waviness or roughness) across the width of the prepreg or towpreg. The second submodel, which is used to predict the elimination of spatial gaps and the establishment of intimate contact at the ply interfaces, relates the consolidation pressure to the rate of deformation of the resin impregnated fiber tow and resin flow at ply surface. Finally, the third submodel is the constitutive relationship for the resin or resin-saturated tow, which gives the shear viscosity as a function of temperature and shear rate. 

Figure 7.8 Representative volume element used in modeling the intimate contact achievement of a cross-ply interply interface...

The unidirectional interply interface model (see Eq. 7.4) was used to calculate the degree of intimate contact versus time for unidirectional samples consolidated at different temperatures and pressures. The surface characterization parameters for T300/P1700 and... 

Considering the complexities involved in the formation of the cross-ply interface during consolidation, the cross-ply interply interface model predicted degrees of intimate contact... 

Consolidation and development of interlaminar bond strength for thermoplastic matrix composites have been modeled by two mechanisms intimate contact and autohesion. Intimate contact describes the process by which two irregular ply surfaces become smooth (Fig. 13.10). In areas in which the ply surfaces are in contact, autohesion occurs, and the long thermoplastic polymer chains diffuse across the ply boundaries. Filament winding with thermoplastic matrix materials is considered an on-line consolidation process in that local... 

A theoretical model for intimate contact for in-situ consolidation has been developed in Reference 21. In this model, the irregular surface of the thermoplastic tow is modeled as a series of rectangular elements, oriented along the fiber axis, which are deformed as local pressure is applied (Fig. 13.11). The amount of flattening is quantified as the degree of intimate contact Dic (Eq. 13.14)... 

An important feature of the cyclodextrins is that they can also accelerate chemical reactions, and therefore serve as models for the catalytic as well as the binding properties of enzymes. The rapid reaction is not catalysis, since the dextrin enters reaction but is not regenerated presumably it arises from approximation, where complex formation forces the substrate and the cyclodextrin into intimate contact. In particular, cyclodextrins can increase the rate of cleavage of phenyl pyrophosphate by factors of as much as 100 (Cramer, 1961). More recent work has improved upon this early example. 

The contribution of the metal to the double layer was discussed in Sections 6.6.7 to 6.6.9. However, we have said little about the ions in solution adsorbed on the electrode and how they affect the properties of the double layer. For example, when presenting the Stem model of the double layer (Section 6.6.6), we talked about ions sticking to the electrode. How does an interface look with ions stuck on the metal What is the distance of closest approach Are hydrated ions held on a hydrated electrode i.e., is an electrode covered with a sheet of water molecules Or are ions stripped of their solvent sheaths and in intimate contact with a bare electrode What are the forces that influence the sticking of ions to electrodes ... 

The theory of Frank and Wen (54) for ion hydration involves the notion that some water molecules intimately contact the ion under consideration and subject to the strong centrosymmetric force field, are highly ordered. Beyond this area is a region of disorder, beyond which, in dilute solutions, unaffected water prevails. Typical literature values for primary hydration numbers range from 2-8 water molecules. For divalent ions, primary hydration numbers range from 10-20 water molecules while some authors have suggested hydration numbers for trivalent ions (based on compressibility data) between 20 and 30 water molecules per ion. Many attempts have been made to extend theories of this type to account better for the hydration of ions. Thus, Azzam (7, 8) and Horne and Birkett (80) have proposed a multilayer model of ion hydration. 

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