Effects of Rigid Inclusions

In Sections 12.1 and 12.2 several important aspects of matrix and interface behavior, such as the effects of an inclusion on modulus and the effect of interfacial adhesion, were described. It is also appropriate to discuss specific molecular effects of rigid inclusions (particulate or fibrous) on a matrix, in order to demonstrate continuity between all types of reinforcements. Effects of environmental exposure on composite behavior are also briefly considered. 

The question is of great importance, for typical expressions for composite behavior (Section 12.1) in terms of constituent properties generally assume that the two components are in close contact (in a state of so-called perfect adhesion ) with a singularity at the interface as one passes from one component to the other. 

A careful reading of the literature [coupled, in this case, with experimental work (Manson and Chiu, 1973a)] reveals that both small and large filler particles can induce significant changes in phenomena such as sorption, permeability, or relaxation behavior of the matrix (notably in the glass transition temperature Tg and in damping characteristics, E or tan 5), in addition to the noninteractive increases in modulus predicted by relationships such as Kerner s equation (12.3). The fact that some exceptions and contradictions continue to exist serves to stimulate further study rather than to deny the tendency toward filler-matrix interaction. Typical evidence may now be summarized. 

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A. R. Boccaccini andE. A. Olevsky, Effect of Rigid Inclusions on Sintering Anisotropy of Composite Glass Powder Compacts,/. Mar. Proc. Technol. 96,92-101 (1999). 

Generally, the presence of rigid inclusions (Gf Gm) of volume fraction Vf in a matrix polymer causes an increase of the elastic modulus of the composite, Gc, resulting from a matrix volume exclusion of an effective volume fraction AVf) (71,123) ... 

In a sense, the effects observed in nanocomposites resemble the behavior of colloidal systems and, in some cases, the behavior of thin polymer films. In comparison to colloids, the long chain charactei- of the liquid phase, however, greatly complicates any theoretical treatment compared to the low molecular weight liquid phase in colloids. Reducing the size of rigid inclusions from... 

Two studies by the present author dealing with the influence of rigid inclusions in crosslinked systems indicate how the effect of a non-uniform distribution of crosslink density of swelling may be studied. The methods of these papers are extended in the following paragraphs in an attempt to consider this problem. 

The description of the averaging in Equation (1) is by no means trivial, and the development of corresponding models for an effective inclusion of flexibility of molecules on various time scales is still an ongoing field of research. We therefore will start out with the most simple case, the averaging of a completely rigid molecule, before going into effects of conformational averaging. 

Polypropylene homopolymer (PP) is a widely used thermoplastic material, despite its brittle behaviour at either low temperature or high loading rates. Improvement in the fi acture toughness of PP can be achieved by either modifying the crystalline structure, or addition of a second phase material [16], The toughening effect and mechanisms of different second phase materials such as stiff fibres, soft rubbery inclusions (EPR, EPDM), and some mineral fillers have been analysed. Recent developments concern the effect of hybrid system consisting of rigid and rubbery inclusions. 

The energy gap law can also be generalized to discuss the effects of inert rigid media upon radiationless transition rates and optical lineshapes of molecules in matrices. This generalization involves the inclusion of both the intra-and intermolecular vibrations in the rate expressions. The simplest type of inert medium is one that can only act as a heat bath, i.e., the intermolecular vibrations may have equilibrium displacements or frequency changes which... 

We present an overview of variational transition state theory from the perspective of the dynamical formulation of the theory. This formulation provides a firm classical mechanical foundation for a quantitative theory of reaction rate constants, and it provides a sturdy framework for the consistent inclusion of corrections for quantum mechanical effects and the effects of condensed phases. A central construct of the theory is the dividing surface separating reaction and product regions of phase space. We focus on the robust nature of the method offered by the flexibility of the dividing surface, which allows the accurate treatment of a variety of systems from activated and barrierless reactions in the gas phase, reactions in rigid environments, and reactions in liquids and enzymes. 

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