Material area change

When metals are rolled or forged, or drawn to wire, or when polymers are injection-moulded or pressed or drawn, energy is absorbed. The work done on a material to change its shape permanently is called the plastic work- its value, per unit volume, is the area of the cross-hatched region shown in Fig. 8.9 it may easily be found (if the stress-strain curve is known) for any amount of permanent plastic deformation, e. Plastic work is important in metal- and polymer-forming operations because it determines the forces that the rolls, or press, or moulding machine must exert on the material. 

Chemical deactivation. In chemical deactivation the active surface area changes by strong chemisorption of impurities in the feed, by blocking of active sites by heavy products formed in parallel or sequential reactions, etc. The most important chemical causes of deactivation are poisoning by impurities in the feed and deposition of carbonaceous material, usually referred to as coke . 

When the shape of a particle oscillates, the surface area changes with time. This situation has been modeled by neglecting the motion adjacent to the surface due to the terminal velocity of the particle, i.e., by considering the particle to be oscillating but stationary, with material transferred by transient molecular diffusion over a time equal to the period of oscillation. For Sc 1 the thin concentration boundary layer assumptions are invoked (see Chapter 1). 

Transparency, gloss, color, refractive index, and reflectance are the properties normally associated with aesthetics of plastic materials. In some areas, changes in optical properties, increases in haze after abrasion testing (285), color differences after weathering, and birefringence analysis of residual stress within a transparent part (286) are all used to measure the effects of applied stresses. Measurements of color, gloss, refractive index, and haze apply to many products beyond plastics and use similar techniques. Reference should be made to this general topic for detailed information (see Color). 

The mean curvature is the local rate of interface area change with a local addition of volume.4 This is perhaps the most important aspect of curvature, especially when combined with 7, which is the work required to create an interface per unit area, A. Imagine that in a pure material the addition of a small volume makes an interface develop a localized small bump. The statement above implies that k = AA/AV in the limit of small volumes therefore, the work to create the bump is 7 A A = yuAV, where 7 is the interfacial energy per unit area (see Eq. 3.73). Equating this work to the work done by the system P AV, where P is the net pressure on the interface... 

ROBERT SHAPIRO is professor emeritus and senior research scientist in the Department of Chemistry at New York University. His research has centered on the chemistry of nucleic acids, with emphasis on the reactions of DNA and RNA with carcinogens and mutagens. Dr. Shapiro is author or co-author of over 110 publications, primarily in the area of DNA chemistry. In particular, he and his co-workers have studied the ways in which environmental chemicals can damage our hereditary material, causing changes that can lead to mutations and cancer. 

There are many ways to fabricate and model viscoelastic polymeric materials [22-32]. Fabrication often involves nonlinear flows that are spatially inhomogeneous, nonisothermal, and temporally complex. The flows also may involve material phase changes, and/or a wide range (1-5 decades) of strains and strain rates. Rheology is often the bridge between resin design and fabrication performance, and remains an active area of research [22]. 

As in true strain, the expression above takes into account cross-sectional area changes in a certain cohesive structure (or cake) of powdered material. If the material is isotropic, another possible expression that includes the Poisson s ratio p (the ratio of transverse strain and axial strain resulting from uniformly distributed axial radial stress during static compression of the material in absolute value). The Poisson s ratio, or bulk modulus, permits prediction of the transverse contraction or expansion that occurs when a stress is applied longitudinally. 

The fact that the natural film materials had to be considerably compressed in order to form a coherent film imphes that in the samples examined by Barger et al. (1974) there was insufficient material available to form such a film. Nevertheless, it is apparent from the approximate area changes in Fig. 2 that the concentration of strongly surface active species that remain in the film at high pressure is only a factor of 4 to 8 lower than is expected in visible sea slicks. If the soluble species are added to these, the concentration of organic material at the surface in these samples may not be a great deal lower than in the shcks. 

Thermal influences can often affect the catalyst compositian. In many cases one or more metastable phases are formed from the active components or the support materials. Phase changes can limit the catalyst activity or lead to catalyst- bstrate interactions. We have already dealt with the transformation of y-Al203 into a-Al203 with its lower surface area. Another example is the phase transformation of Ti02 from anatase to rutile in V2O5/ Ti02/corundum catalysts for the oxidation of o-xylene to phthalic anhydride. 

---