Isotropic solutions viscosity

If one follows the solution viscosity in concentrated sulfuric acid with increasing polymer concentration, then one observes first a rise, afterwards, however, an abrupt decrease (about 5 to 15%, depending on the type of polymers and the experimental conditions). This transition is identical with the transformation of an optical isotropic to an optical anisotropic liquid crystalline solution with nematic behavior. Such solutions in the state of rest are weakly clouded and become opalescent when they are stirred they show birefringence, i.e., they depolarize linear polarized light. The two phases, formed at the critical concentration, can be separated by centrifugation to an isotropic and an anisotropic phase. A high amount of anisotropic phase is desirable for the fiber properties. This can be obtained by variation of the molecular weight, the solvent, the temperature, and the polymer concentration. 

The zero-shear viscosity r 0 has been measured for isotropic solutions of various liquid-crystalline polymers over wide ranges of polymer concentration and molecular weight [70,128,132-139]. This quantity is convenient for studying the stiff-chain dynamics in concentrated solution, because its measurement is relatively easy and it is less sensitive to the molecular weight distribution (see below). Here we deal with four stiff-chain polymers well characterized molecu-larly schizophyllan (a triple-helical polysaccharide), xanthan (double-helical ionic polysaccharide), PBLG, and poly (p-phenylene terephthalamide) (PPTA Kevlar). The wormlike chain parameters of these polymers are listed in Tables... 

This description is elaborated below with an idealized model shown in Figure 17. Imagine a molecule tightly enclosed within a cube (model 10). Under such conditions, its translational mobility is restricted in all three dimensions. The extent of restrictions experienced by the molecule will decrease as the walls of the enclosure are removed one at a time, eventually reaching a situation where there is no restriction to motion in any direction (i.e., the gas phase model 1). However, other cases can be conceived for a reaction cavity which do not enforce spatial restrictions upon the shape changes suffered by a guest molecule as it proceeds to products. These correspond to various situations in isotropic solutions with low viscosities. We term all models in Figure 17 except the first as reaction cavities even... 

In isotropic solutions of PPT in solvents of the N,N-disubstituted amide/LiCl type, a maximum in limiting viscosity number, [q], has been observed when the lithium chloride content of the solution is chemically equivalent to the secondary amide group content provided by the dissolved polymer 30). Titration of model secondary amides with lithium chloride in tertiary amide solvents confirms that there is a 1 1... 

The Reynolds stress model requires the solution of transport equations for each of the Reynolds stress components as well as for dissipation transport without the necessity to calculate an isotropic turbulent viscosity field. The Reynolds stress turbulence model yield an accurate prediction on swirl flow pattern, axial velocity, tangential velocity and pressure drop on cyclone simulation [7,6,13,10],... 

For a specific polymer, critical concentrations and temperatures depend on the solvent. In Fig. 15.42b the concentration condition has already been illustrated on the basis of solution viscosity. Much work has been reported on PpPTA in sulphuric acid and of PpPBA in dimethylacetamide/lithium chloride. Besides, Boerstoel (1998), Boerstoel et al. (2001) and Northolt et al. (2001) studied liquid crystalline solutions of cellulose in phosphoric acid. In Fig. 16.27 a simple example of the phase behaviour of PpPTA in sulphuric acid (see also Chap. 19) is shown (Dobb, 1985). In this figure it is indicated that a direct transition from mesophase to isotropic liquid may exist. This is not necessarily true, however, as it has been found that in some solutions the nematic mesophase and isotropic phase coexist in equilibrium (Collyer, 1996). Such behaviour was found by Aharoni (1980) for a 50/50 copolymer of //-hexyl and n-propylisocyanate in toluene and shown in Fig. 16.28. Clearing temperatures for PpPTA (Twaron or Kevlar , PIPD (or M5), PABI and cellulose in their respective solvents are illustrated in Fig. 16.29. The rigidity of the polymer chains increases in the order of cellulose, PpPTA, PIPD. The very rigid PIPD has a LC phase already at very low concentrations. Even cellulose, which, in principle, is able to freely rotate around the ether bond, forms a LC phase at relatively low concentrations. 

Isotropic solutions exhibit a monotonic increase in shear viscosity with increasing concentration. The viscosity increases to a maximum when the isotropic to anisotropic transition is approached. Upon formation of the anisotropic phase, the viscosity begins to decrease, after which the viscosity increases strongly as the concentration continues to increase (Fig. 6). In the isotropic state, the hydrodynamic volume is large because of the random polymer orientation. This restricts the polymer diffusivity and causes an increase in viscosity. In the anisotropic phase, the aligned polymer leads to a small hydrodynamic volume and a decrease in viscosity as rotational diffusion is much easier with a net orientation. 

The photoreactivity of phenyl benzoates in which the para positions of both rings are substituted has been examined in liquid crystalline media and compared with the results obtained in isotropic solution.The photoreactivity of phenyl esters of cyclohexane carboxylic acids in which the para position of the phenyl ring and the 4-position of the cyclohexane ring are substituted were also studied under the same conditions.The products were not identified but were assumed to arise from photo-Fries rearrangement based upon the development of absorption in the ultra-violet spectrum assignable to ortho-hydroxyphenyl ketones. The relative quantum yields of the rearrangements were correlated with the viscosity and order of the liquid crystalline phase. 

Mark Houwink exponent of equation relating solution viscosity to molecular weight of the polymer (1.8=ideal value for mesophase to be present, compared to 0.5 for a flexible isotropic polymer) ... 

The effect of NaCl concentration on surfactant solutions was studied at room temperature (25"C 1 C). Upon increasing the NaCl concentration, the isotropic solution changed to an anisotropic state and ultimately to a two phase isotropic system. (Refer to Figures 4 5). In the two phase isotropic system at higher salt concentrations, the upper phase was surfactant rich having high viscosity and the lower phase was aqueous solution of NaCl with trace amounts of the surfactant and alcohol. 

The molecules in such a solution are more readily oriented by shearing than are the molecules in an isotropic solution with the result that the effective viscosity is lower. A more detailed discussion will be found in Ref. 37. 

His theory is applicable to both isotropic and nematic phases, and so can be tested by the peak in viscosity with concentration, which it successfully predicts (see Figure 5 in [23]). Doi recognized a limitation in his theory, in that it assumes a spatially uniform system in which the director vector does not change with position. As will be seen in section 11.6, this is far from reality. Doi does not address negative in this work (it does not appear that he was aware of it), but notes that for small shear rates, normal stress is proportional to shear rate in isotropic solutions and to the square of the shear rate in the nematic phase. 

The steady-state compliance has a minimum at p = p f2 and then increases again by the pretransitional effect. This has indeed been observed by Berry and coworkers. On the other hand the viscosity is unaffected by the pretransitional effect. (This is a result of the cancellation of the effect on the relaxation time t and on the rigidity modulus Gg.) Experimental results on the viscodastidty of the isotropic solution have been reviewed by Baird. ... 

Equations (10.94) and (10.128) give the concentration dependence of j. (Note that eqn (10.128) holds also in the isotropic solution if 5 is put to zero.) The result, shown in Fig. 10.6, indicates that the viscosity takes a maximum near the phase transition point, in agreement with the experimental results. 

The presence of mixed surfactant adsorption seems to be a factor in obtaining films with very viscous surfaces [27], For example, in some cases, the addition of a small amount of nonionic surfactant to a solution of anionic surfactant can enhance foam stability due to the formation of a viscous surface layer possibly a liquid crystalline surface phase in equilibrium with a bulk isotropic solution phase [21, 126], To the extent that viscosity and surface viscosity influence emulsion and foam stability one would predict that stability would vary according to the effect of temperature on the viscosity. Thus, some petroleum industry processes exhibit serious foaming problems at low process temperatures, which disappear at higher temperatures [21],... 

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