Nonblack surfaces

The analysis of radiation transfer in enclosures consisting of black surfaces is relatively easy, as we have seen, but most enclosures encountered in practice involve nonblack surfaces, which allow multiple reflections to occur. Radiation analysis of such enclosures becoroe.s very complicated unless some simplifying assumptions are made. 

NONBLACK SURFACES. The treatment of radiation between nonblack surfaces, in the general case where absorptivity and emissivity are unequal and both depend upon wavelength and angle of incidence, is obviously complicated. Several important special cases can, however, be treated simply. 

Clouds of Nonblack Particles The correction for nonblackness of the particles is complicated by multiple scatter of the radiation reflected by each particle. The emissivity . of a cloud of gray particles of individual surface emissivity 1 can be estimated by the use of Eq. (5-151), with its exponent multiplied by 1, if the optical thickness alv)L does not exceed about 2. Modified Eq. (5-151) would predict an approach of . to 1 as L 0°, an impossibihty in a scattering system the asymptotic value of . can be read from Fig. 5-14 as /, with albedo (0 given by particle-surface refleclance 1 — 1. Particles with a perimeter lying between 0.5 and 5 times the wavelength of interest can be handledwith difficulty by use of the Mie equations (see Hottel and Sarofim, op. cit., chaps. 12 and 13). 

Accuracy of Pyrometers Most of the temperature estimation methods for pyrometers assume that the objec t is either a grey body or has known emissivity values. The emissivity of the nonblack body depends on the internal state or the surface geometry of the objects. Also, the medium through which the therm radiation passes is not always transparent. These inherent uncertainties of the emissivity values make the accurate estimation of the temperature of the target objects difficult. Proper selection of the pyrometer and accurate emissivity values can provide a high level of accuracy. 

Silica is unique among nonblack fillers. Its reinforcing ability is comparable to that of carbon black, especially when mixed with a suitable coupling agent, and its transparency affords many products. Additionally, it is chemically synthesized, which means that a wide range of silica (in terms of diameter, surface area, or surface activity) may be produced depending on the reaction routes and reaction conditions. 

Light. Ultraviolet (uv) light promotes free-radical oxidation at the mbber surface which produces discoloration and a brittle film of oxidized mbber (35). This skin cracks in random directions to form a pattern called crazing, which can be prevented by the addition of carbon black fillers or uv stabilizers. Black stocks are more resistant to uv light than are gum or light-colored stocks. Nonblack compounds require larger quantities of nonstaining antioxidants which should bloom to the surface as the surface uv stabilizers deplete. 

Ultraviolet light initiates free radical oxidation at the exposed surface of an elastomeric product to generate a layer of oxidized rubber. Heat, moisture, or high humidity can then initiate crazing of the surface, which subsequently can be abraded off. Such degradation of the surface is more severe with nonblack stocks than with black compounds. Nonblack compounds such as white tire sidewalls thus require higher levels of nonstaining antioxidants than carbon black-loaded formulations. 

Equation (4.10-2) holds for any black or nonblack solid surface. 

Fig. 4. Reinforcing effect on hardness of nonblack fillers with different surface areas. < Silica, talc, calcium carbonate, x soft clay, hard clay.

Surface Treatment. Carbon black remains the particulate filler of choice for rubber articles since the inherent reinforcing effect of the nonblack fillers in hydrocarbon elastomers is not comparable. This is primarily due to the nonbonded interactions established between the particulate filler and polymer functionality (28). Surface chemistry plays an important role in the interaction of the nonblack fillers and the polymer with contributions ranging from electrostatic interactions to covalent bonding to the polymer backbone. However, surface chemistry also strongly affects the interaction of the nonblack filler with other chemicals in the rubber compound, particularly active metal oxides, curatives, and antidegradants. 

The absorptivity, a, reflectivity, p, and transmissivity, r, are the key radiation properties of a material. The magnitudes of a, p, and r depend on the type of material, its thickness and its surface finish, and also on the wavelength of the radiation. Absorption characteristics are defined in a similar manner to emission characteristics (see Section 10.2). The absorptivity for a nonblack body is the ratio of the nonblack absorption to the black absorption at the same surface temperature. Only the absorbed portion causes heating however, as very few bodies behave as black bodies a more realistic assumption would be to treat those as gray bodies, which have the same absorptivity over the entire wavelength spectrum. 

Mineral fillers are naturally occurring or synthetic nonblack, nonmetallic solid-surface particles. Such fillers have assorted shapes, from nodular to platy to aci-cular. When describing filler shape, the term aspect ratio is employed to describe the relationship of one dimension to another. Mineral fillers for PVC have historically included calcium carbonate (ground and precipitated), alumina trihydrate (ATH), barytes, talc, mica, kaolin, feldspar and nepheline syenite, and wollastonite. 

Plasticizers Polar plasticizers such as esters decrease surface resistivity of nonblack compounds hydrocarbon secondary plasticizers provide increased levels. Unplasticized PVC without a surface coating of paraffin wax has a surface resistivity of about 10 ohm. Addition of 40 phr of ester plastieizer decreases this to 10 °-10 ohm. Phosphate plasticizers can lower surface resistivity by several orders of magnitude. In addition, the mobility (lowering of glass transition temperature) of the plasticizer is a factor. Low-temperature plasticizers are found to have an increased effect in lowering surface resistivity. When substituting, for example, an adipate or oleate for a phthalate to lower surface resistivity (in cases where the application permits), it must be considered that the former are more available microbial nutrients. 

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