Material properties, theoretical

Theoretically, the effects of the manufacturing process on the material property distribution can be determined, shown here for the case when Normal distribution applies. For an additive case of a residual stress, it follows that from the algebra of random variables (Carter, 1997) ... 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

Atomization, or generally speaking droplet generation, is an extremely complex process that cannot yet be precisely predicted theoretically. The lack of general theoretical treatment of droplet processes has led to the development of numerous empirical correlations for droplet properties as a function of process parameters and material properties. In this chapter, empirical and analytical correlations for the prediction of droplet properties, such as droplet size distribution and droplet deformation characteristics will be summarized from experimental observations and theoretical analyses in available literature. 

Higher oxides of nitrogen have been reported (NO3, N206, N2Ot) however, their isolation has been difficult or impossible because of their rapid decomposition. Such materials are theoretically attractive from a performance standpoint, but their use as oxidizers appears remote at present. The properties of NO, N203, N204, and N2Or, are presented for comparison in Table II. 

In contrast to the mechanical and rheological properties of materials, which have defined physical meanings, no such definitions exist for the psychophysical assessment of equivalent textural properties of foods. To identify material properties, or combinations of these, which are able to model sensory assessments requires a mixture of theory and experimentation. Scientific studies of food texture began during the twentieth century by the analysis of the rheological properties of liquid or semi-solid foods. In particular Kokini14 combined theoretical and experimental approaches in order to identify appropriate rheological parameters from which to derive mathematical models for textural attributes of liquid and semi-solid foods, namely, thickness, smoothness and creaminess. 

The main objective of this review article is to demonstrate the analytical capability of SFM techniques in areas of research where SFM gives the most unique and valuable information not accessible by other methods. Complementary to other reviews [65-69], we will focus on recent developments in SFM instrumentation which are particularly useful for polymer systems (Sect. 2) on quantitative characterisation of material properties and structure manipulation on the nanometer scale (Sect. 3) and on visualisation and probing of single macromolecules (Sect. 4). The interested reader can find the theoretical background as well as instrumentation of SFM in text books [52-54,70-72]. 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

---