Coates equation

The prodncts developed by several additive and specialty chemical suppliers to replace volatile solvents are reviewed. Such solvents have been integral to the coatings equation for a long time. Paints and coatings formnlators have become aware of the role that additives and specialty chemicals play in eliminating these solvents (Chemical Week Assoc., 1994). 

Additional correlations have been developed from amorphous 67] and molten polymers [46]. Griskey and Hubbell [69] showed that Cp data for methacrylic polymers could be correlated using a form of the Sakiadis-Coates equation originally developed for organic liquids. Additionally, it has been shown [46] that the Cp data for molten polyolefins could be correlated as shown in Fig. 2-15. 

Figure 2.29 shows the model applied on low porous carbonate rocks (compare Fig. 2.23). For a better fit, the porosity dependence is empirically modified to following Coates equation. In the calculation no tortuosity...

Method 2 Derivation of Spor from an NMR measurement Coates equation (Coates et al., 1999a,b) for NMR-derived permeability is (see Section 3.5.2)... 

Georgi et al. (1997) and Kasap et al. (1999) describe the calibration of NMR-derived permeability using Coates equation When core (conventional or rotary sidewaU) or wireline formation test data are available, the optimum value for the parameter C can be determined by an error minimization (deviation between core permeability and NMR-derived permeability). Figure 3.10 demonstrates this technique. 

Substrate Properties. It is clear from equation 5 that higher hardness of the substrate lowers friction. Wear rate of the film also is generally lower. Phosphate undercoats on steel considerably improve wear life of bonded coatings by providing a porous surface which holds reserve lubricant. The same is tme for surfaces that are vapor- or sandblasted prior to appHcation of the soHd-film lubricant. A number of typical surface pretreatments are given in Table 13 to prepare a surface for solid-film bonding (61). 

For hquid systems these surface energies expressed in mj/m are numerically equivalent to the surface tensions in mN/m(= dyn/cm). If the adhesive is phase 1 and the release coating is phase 2, then the spreading coefficient, S, of 1 on 2 is as given in equation 2. 

Because the indentation varies with time, the modulus must be specified for a certain indentation time, eg, a 10-s modulus. The Hertz equation holds only for purely elastic materials. However, it has been appHed to viscoelastic materials, including polymers and coatings, with excellent results (249—256). Indentation hardness vs temperature curves are shown in Figure 40 (249,251). 

Layered Structures. Whenever a barrier polymer lacks the necessary mechanical properties for an appHcation or the barrier would be adequate with only a small amount of the more expensive barrier polymer, a multilayer stmcture via coextmsion or lamination is appropriate. Whenever the barrier polymer is difficult to melt process or a particular traditional substrate such as paper or cellophane [9005-81-6] is necessary, a coating either from latex or a solvent is appropriate. A layered stmcture uses the barrier polymer most efficiently since permeation must occur through the barrier polymer and not around the barrier polymer. No short cuts are allowed for a permeant. The barrier properties of these stmctures are described by the permeance which is described in equation 16 where and L are the permeabiUties and thicknesses of the layers. 

The most successful models are based on the finite element method. The flow is discretized into small subregions (elements) and mass and force balances are appHed in each. The result is a large system of equations, the solution of which usually gives the speed of the coating Hquid in each element, pressure, and the location of the unknown free surfaces. The smaller the elements, the more the equations which are often in the range of 10,000 to upward of 100,000. 

Using this equation, the approximate (T — T ) value required for a film of a thermoplastic copolymer to be dry-to-touch, ie, to have a viscosity of 10 mPa-s(=cP), can be estimated (3,4). The calculated (T — T ) for this viscosity is 54°C, which, for a film to be dry-to-touch at 25°C, corresponds to a T value of —29 "C. The calculated T necessary for block resistance at 1.4 kg/cm for two seconds and 25°C, ie, rj = 10 ° mPa(=cP), is 4°C. Because the universal constants in the WLF equation are only approximations, the T values are estimates of the T requited. However, if parameters such as the mass per area appHed for blocking were larger, the time longer, or the test temperature higher, the T of the coating would also have to be higher. 

This lelationship has been shown to hold for a wide variety of coating resins and resin solutions over a wide range of concentrations. A simplification of equation 3 where T is the reference temperature is given in equation 2, which assumes that the viscosity at T is 10 Pa-s. 

Viscosity of Systems with Dispersed Phases. A large proportion of coatings are pigmented and, therefore, have dispersed phases. In latex paints, both the pigments and the principal polymer are in dispersed phases. The viscosity of a coating having dispersed phases is a function of the volume concentration of the dispersed phase and can be expressed mathematically by the Mooney equation (96), a convenient form of which is... 

Polyacetylenes. The first report of the synthesis of a strong, flexible, free-standing film of the simplest conjugated polymer, polyacetylene [26571-64-2] (CH), was made in 1974 (16). The process, known as the Shirakawa technique, involves polymerization of acetylene on a thin-film coating of a heterogeneous Ziegler-Natta initiator system in a glass reactor, as shown in equation 1. 

In a typical experiment, Israelachvili deposited monolayers of surfactants onto cleaved mica sheets, and evaluated the surface energies using the JKR equation. Fig. 11 contrasts results for mica coated with monolayers of (a) L-a-dipalmitoyl-phosphatidylethanolamine (DMPE) where j/a = = 27 mJ/m and (b) hexa-decyltrimethylammonium bromide (CTAB) where = 20 mJ/m and = 50 mJ/m. ... 

---