Resistance center

Here Eq. (21.10) is the usual Navier-Stokes equation. The term yu on the left-hand side of Eq. (21.11) represents the frictional forces exerted on the liquid flow by the polymer segments in the polyelectrolyte layer, and y is the frictional coefficient. If it is assumed that each resistance center corresponds to a polymer segment, which in turn is regarded as a sphere of radius and the polymer segments are distributed at a uniform volume density of in the polyelectrolyte layer, then each polymer segment exerts the Stokes resistance 6nriapU on the liquid flow in the polyelectrolyte layer so that... 

The origin of the spherical polar coordinate system (r, 9, cp) is held fixed at the center of one particle and the polar axis (9 = 0) is set parallel to E. Let the electrolyte be composed of M ionic mobile species of valence zt and drag coefficient A,-(/ = 1, 2,. . . , M), and let nf be the concentration (number density) of the ith ionic species in the electroneutral solution. We also assume that fixed charges are distributed with a density of pflx. We adopt the model of Debye-Bueche where the polymer segments are regarded as resistance centers distributed in the polyelectrolyte... 

As in the case of static electrophoresis, we adopt the model of Debye-Bueche [22, 23] where the polymer segments are regarded as resistance centers distributed in the polyelectrolyte layer, exerting a frictional force on the liquid flowing in the... 

Now we consider the electrokinetic behavior of soft particles, i.e., colloidal particles covered with a polymer layer (Figure 2.2). A number of theoretical studies have been made [34-46] on the basis of the model of Debye and Bueche [47], which assumes that the polymer segments are regarded as resistance centers distributed in the polymer layer, exerting frictional forces y on the liquid flowing in the polymer layer, where u the liquid flow velocity and y a frictional coefficient. The Navier-Stokes equation for the liquid flow inside the polymer layer is thus given by... 

The acconunodation coefficient for Kr on a carbon filament is determined experimentally as follows. The electrically heated filament at temperature 72 is stretched down the center of a cylindrical cell containing Kr gas at 7. Gas molecules hitting the filament cool it, and to maintain its temperature a resistance heating of Q cal sec cm is needed. Derive from simple gas kinetic theory the expression... 

In the case of a polyatomic molecule, rotation can occur in three dimensions about the molecular center of mass. Any possible mode of rotation can be expressed as projections on the three mutually perpendicular axes, x, y, and z hence, three moments of inertia are necessar y to give the resistance to angular acceleration by any torque (twisting force) in a , y, and z space. In the MM3 output file, they are denoted IX, lY, and IZ and are given in the nonstandard units of grams square centimeters. 

These monomers provide a means for introducing carboxyl groups into copolymers. In copolymers these acids can improve adhesion properties, improve freeze-thaw and mechanical stability of polymer dispersions, provide stability in alkalies (including ammonia), increase resistance to attack by oils, and provide reactive centers for cross-linking by divalent metal ions, diamines, or epoxides. 

Heat-Resistant Polymers" in ECT 3rd ed., Vol. 12, pp. 203—225, byj. Preston, Monsanto Triangle Park Development Center, Inc. 

Both phosphoramidate and phosphate triester derivatives have been used as linkers to attach reporter groups to oligonucleotides. These derivatives are not entirely resistant to nucleases and they possess a chiral center. They have not been widely iavestigated as antisense dmgs. 

Most Kaminsky catalysts contain only one type of active center. They produce ethylene—a-olefin copolymers with uniform compositional distributions and quite narrow MWDs which, at their limit, can be characterized by M.Jratios of about 2.0 and MFR of about 15. These features of the catalysts determine their first appHcations in the specialty resin area, to be used in the synthesis of either uniformly branched VLDPE resins or completely amorphous PE plastomers. Kaminsky catalysts have been gradually replacing Ziegler catalysts in the manufacture of certain commodity LLDPE products. They also faciUtate the copolymerization of ethylene with cycHc dienes such as cyclopentene and norhornene (33,34). These copolymers are compositionaHy uniform and can be used as LLDPE resins with special properties. Ethylene—norhornene copolymers are resistant to chemicals and heat, have high glass transitions, and very high transparency which makes them suitable for polymer optical fibers (34). 

Pigments Aftertreatments. The surfaces of pigment particles can have different properties and composition than the particle centers. This disparity can be caused by the absorption of ions during wet milling, eg, the —OH groups, on the surface. In some cases, surfaces are modified intentionaHy to improve the pigments appHcation properties, interaction with the organic matrix, and weather resistance. 

Plant Fireproofing. There is a growing practice in the chemical industry of locating principal equipment out of doors and to enclose only a control room where all instmments and control equipment are centered. The control room should be resistant to potential explosion, fire, and toxicity ha2ards of processes in the vicinity. Prompt and ordedy shutdown of processes following a serious incident is essential in order to minimise personnel-injury and property-loss ha2ards (65,66). 

Fig. 1. Schematic of the hysteresis loop associated with a shape-memory alloy transformation, where M. and Afp correspond to the martensite start and finish temperatures, respectively, and and correspond to the start and finish of the reverse transformation of martensite, respectively. The physical property can be volume, length, electrical resistance, etc. On cooling the body-centered cubic (bcc) austenite (parent) transforms to an ordered B2 or E)02...

Inflated Diaphragm Method (ASTM D3886). This method is appHcable both to woven and knitted fabrics. The specimen is abraded by mbbing either unidirectionally or multidirectionally against an abradant having specified surface characteristics. The specimen is supported by an inflated mbber diaphragm under a constant pressure. Evaluation of abrasion resistance can be either by determination of the number of cycles required to wear through the center of the fabric completely or by visual examination of the specimens after a specified number of cycles. 

Gonorrhea. Gonorrhea, caused by Neisseriagonorrheae is the most commonly reported communicable disease in the United States. Approximately lO cases were reported to the Center for Disease Control (CDC) in 1979, but actual cases could be two to three times higher (99,100). In addition, an increasing number of strains are becoming resistant to penicillin, the antibiotic that is usually used to treat this disease. 

Antimony may be added to copper-base alloys such as naval brass. Admiralty Metal, and leaded Muntz metal in amounts of 0.02—0.10% to prevent dezincification. Additions of antimony to ductile iron in an amount of 50 ppm, preferably with some cerium, can make the graphite fliUy nodular to the center of thick castings and when added to gray cast iron in the amount of 0.05%, antimony acts as a powerflil carbide stabilizer with an improvement in both the wear resistance and thermal cycling properties (26) (see Carbides). 

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