Characteristic ratio dilute solution

The dilute solution properties of copolymers are similar to those of the homopolymer. The intrinsic viscosity—molecular weight relationship for a VDC—AN copolymer (9 wt % AN) is [77] = 1.06 x 10 (83). The characteristic ratio is 8.8 for this copolymer. 

Table 2.1 illustrates the magnitudes of the characteristic ratio found for typical polymers in dilute solution. The relatively simple polyethylene oxide), (PEO), chain is fairly flexible whereas the cellulosic chain has... 

The conformation parameter a (=A/Af, where Af is A of a hypothetical chain with free internal rotation) for cellulose and its derivatives lies between 2.8-7.5 2 119,120) and the characteristic ratio ( = A2Mb//2, where Ax is the asymptotic value of A at infinite molecular weight, Mb is the mean molecular weight per skeletal bond, and / the mean bond length) is in the range 19-115. These unexpectedly large values of a and Cffi suggest that the molecules of cellulose and its derivatives behave as semi-flexible or even inflexible chains. For inflexible polymers, analysis of dilute solution properties by the pearl necklace model becomes theoretically inadequate. Thus, the applicability of this model to cellulose and its derivatives in solution should be carefully examined. 

In an experimental study of mixed iron-silica colloids we found the opposite phenomenon, stabilization of colloids of iron hydroxide by silica colloids, which is manifested very clearly in undialyzed iron hydroxide sols of average concentration with a ratio of Fe203 SiOj = 1 3. Colloidal iron in mixed solutions proved to be more resistant to the action of electrolytes than in isolated sols of iron hydroxide. Only colloidal silica shows any stabilizing effect on sols of iron hydroxide dilute solutions undersaturated with Si(OH)4 are not stabilizers. It is characteristic that colloidal silica is capable of stabilizing colloidal iron in the same pH ranges in which pure silica sols are stable in acid (pH < 4) and alkaline (pH > 8) environments. In slightly acid environments (pH = 5-6) iron-silica sols are unstable and decompose to form mixed sediments, which sometimes are not uniform due to different rates of coagulation and deposition. 

Liquid alcohols display an extremely broad absorption near 650 cm (half-width 200-300 cm"" ). Stuart and Sutherland recognized the importance of this band and have attributed it to the hindered rotation perturbed by the formation of the H bond (1967, 1966). They find this band centered at 670 cm"" for pure liquid methanol, and at 475 cm"" for methanol-. The ratio of these frequencies, 1.41, is characteristic of a motion dominated by hydrogen atom movement. The band is present in CCI4 and CS2 solutions of methanol at concentrations above 1 M and is very much weaker at concentrations below 0.1 M. In spectra of dilute solutions, the absorption is presumed to shift below the limit of observation, to about 350 cm . The over-all spectral behavior is as striking and unusual as that of the stretching mode, as shown in Fig. 3-26. In sharp contrast are the relatively minor spectral... 

Coo Characteristic ratio of a polymer chain, usually measured in dilute solutions. 

Some important properties of polymer chains in dilute solutions [steric hindrance parameter, characteristic ratio, persistence length, radius of gyration, statistical chain segment length (introduced earlier, in Chapter 11), intrinsic viscosity, and viscosity at small but finite concentrations] will be discussed, and new correlations will be presented for the steric hindrance parameter and the molar stiffness function, in Chapter 12. 

Step 21. Calculate the key properties of polymers in dilute solutions. The steric hindrance parameter a is predicted by using equations 12.22-12.26. For polystyrene, the result is 0-2.22. The characteristic ratio is predicted from the value of a, by using Equation... 

Relatively few theoretical studies have been devoted to the conformational characteristics of nonlinear block copolymers in different solvent environments. Burchard and coworkers [284] studied theoretically the behavior of the static and dynamic structure factors for regular star-block copolymers in dilute solutions. They considered different cases where the refractive index (n)s of the solvent takes certain values with respect to the corresponding refractive indices of the inner and outer blocks. A different dependence of the ratios... 

Values of the imperturbed dimension can be obtained experimentally from dilute solution measurements made either directly in a theta solvent (see Chapter 9, Section 9.7) or by using indirect measurements in nonideal solvents and employing an extrapolation procedure. The geometry of each chain allows the calculation of ( and results are expressed either as o or as the characteristic ratio = (r )o/ F. Both provide a measure of chain stiffness in dilute solution. The range of values normally foimd for o is from about 1.5 to 2.5, as shown in Table 10.1. 

The monotonic increase in the ratio I (Si-O-Si)/I(Si-OH) with silane concentration (Fig. 2), implies formation of a lower molecular weight product from dilute solutions and a higher molecular weight product from more concentrated solutions. This conclusion is supported by GPC of the polymerized material dissolved in tetra-hydrofuran (Pig. 3). High retention times (low molecular weights) are characteristic of films obtained from dilute solutions (0.2 - 0.5 wt%), while the polymer obtained from the 2.5 wt% solution was eluted in shorter times, and had a distinct bimodal distribution of molecular weight. Such bimodality is characteristic of two different groupings of polymeric species in the specimen. 

Linear polyacrylamides in solution adopt nearly random coil configurations that are partially permeable (draining) to solvent. The coils are unassociated in dilute solution. The average shape of the isolated coils has been described as an ellipsoidal or bean-shaped structure (58). The individual chains are quite flexible, as is common with most vinyl polymers. This is indicated from several parameters shown in Table 2, such as the persistence length, steric hindrance parameter (a), and characteristic ratio (Cco)- The persistence length of 1.52 nm for poly(acrylamide) in water is quite similar to the average intrinsic (bare) persistence length ( 1.4 nm) of many vinyl polymers (59). 

The behaviour of diluted solutions is related to the relation between the viscosity and the chain characteristics (structure, configuration, conformation, etc). Usually, the polymer solutions are treated as two-phase systems, consisting from mechanical elements, the macromolecules, immersed into a continuous media, the solvent. For long time, it was considered that the solvent acts to the polymer macromolecules in the same manner in which a fluid exerts forces about a small particle suspended in it. However, the extension of this model to the polymer solution is not adequate since, the ratio between the dimensions of macromolecules and those of solvent molecules essentially differs by that between the dimensions of a solid immersed particle and solvent molecules. On the other side, the flexible macromolecules, randomly coiled, can not be assimilated with the solid particles and therefore the typical relations applied to solid suspensions in liquids can not be used in this case. 

The conformational properties of a chain are reflected in dilute solution properties, and in particular its characteristic ratio. Coo which was defined in Chapter 1. The characteristic ratio can be detennined experimentally by straightforward methods, or calculated theoretically using rotational isomeric state theory.(219) The characteristic ratios of a large number of polymers have been determined and it is... 

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