Polymeric liquids

Mate C M, Lorenz M R and Novotny V J 1989 Atomic force microscopy of polymeric liquid films J. Chem. Phys. 90... 

Depending on their constitutive behaviour, polymeric liquids are classified as ... 

Similar relations for other non-Newtouiau fluids may be found in Govier and Aziz and in Bird, Armstrong, and Hassager (Dynamics of Polymeric Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977). 

For laminar flow of power law fluids in channels of noncircular cross section, see Schecter AIChE J., 7, 445 48 [1961]), Wheeler and Wissler (AJChE J., 11, 207-212 [1965]), Bird, Armstrong, and Hassager Dynamics of Polymeric Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977), and Skelland Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). 

Finally, there are an inereasing number of streams of pressurized industrial gases eontaining eontaminants, sueh as eorrosive or polymerizing liquid mist, tar, and the like, on whieh the pressure is being released, and the quantities of available power are signifieant. 

Reduction of the pH of solutions of carbonylate anions yields a variety of protonated species and, from acid solutions, carbonyl hydrides such as the unstable, gaseous H2Fe(CO)4 and the polymeric liquids H2Fe2(CO)g and H2Fe3(CO)n are liberated. The use of ligand-replacement reactions to yield hydrides of higher nuclearity has already been noted. 

Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, 2nd (edn) John Wiley, New York, vol 2, p 58... 

Fig. 27 a and b. Schematic representation of the molecular structure of a side chain polymeric liquid crystals b polymer model membranes studied by 2H NMR... 

Polymeric Liquid Crystals in Materials Science and Technology Series , edited by A. Cifferi, W. R. Krigbaum, R, B, Meyer, Academic Press, N. Y. 1982... 

Since the earliest discoveries of polymeric liquid crystalline melts and solutions a large number of such systems have been reported and this continues to be a vigorous field of research. 

Different molecular theories have been established [27-32] to describe the viscoelasticity of polymeric liquids. Due to their importance, a brief survey of the different theories will be given below. 

In most cases polymer solutions are not ideally dilute. In fact they exhibit pronounced intermolecular interactions. First approaches dealing with this phenomenon date back to Bueche [35]. Proceeding from the fundamental work of Debye [36] he was able to show that below a critical molar mass Mw the zero-shear viscosity is directly proportional to Mw whereas above this critical value r 0 is found to be proportional to (Mw3,4) [37,38]. This enhanced drag has been attributed to intermolecular couplings. Ferry and co-workers [39] reported that the dynamic behaviour of polymeric liquids is strongly influenced by coupling points. 

Non-linear viscoelastic flow phenomena are one of the most characteristic features of polymeric liquids. A matter of very emphasised interest is the first normal stress difference. It is a well-accepted fact that the first normal stress difference Nj is similar to G, a measure of the amount of energy which can be stored reversibly in a viscoelastic fluid, whereas t12 is considered as the portion that is dissipated as viscous flow [49-51]. For concentrated solutions Lodge s theory [52] of an elastic network also predicts normal stresses, which should be associated with the entanglement density. 

In order to evaluate the viscosity of a polymeric liquid at finite rates of deformation, two parameters must be determined, i.e. (i) the critical shear rate y (y=l/7.) at which T) becomes a function of the of deformation, and (ii) the slope in the linear range of the flow curve. 

Curtiss, C. E and Bird, R. B.i Statistical Mechanics of Transport Phenomena Polymeric Liquid Mixtures. Vol. 125, pp. 1-102,... 

Phosphorus vapor consists of tetrahedral P4 molecules, and at higher temperatures also of P2 molecules (P=Pbond length 190 pm). White phosphorus forms by condensation of the vapor it also consists of P4 molecules. Liquid phosphorus normally consists of P4 molecules, but at a pressure of 1 GPa and 100 °C polymeric liquid phosphorus is formed which is not miscible with liquid P4. 

Some years ago, on the basis of the excluded-volume interaction of chains, Hess [49] presented a generalized Rouse model in order to treat consistently the dynamics of entangled polymeric liquids. The theory treats a generalized Langevin equation where the entanglement friction function appears as a kernel... 

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