Dilute Solution of Linear Polymers

NSE Results from Dilute Solutions of Linear Polymers 0-Conditions... 

These predictions of the Zimm model are compared with experimental data on dilute polystyrene solutions in two -solvents in Fig. 8.7. The Zimm model gives an excellent description of the viscoelasticity of dilute solutions of linear polymers. 

The molecular theory of polymer viscoelasticity rests on the work of Bueche (101-104), Rouse (105), and Zimm (106,107), investigating behavior of diluted solutions of linear polymers. The molecular theory of viscoelasticity has not been very successful in describing viscoelasticity of solid polymers over the whole temperature interval, and thus modified theory of rubber elasticity has to be used... 

Figure 7 The shear (dotted line) and extensional (solid line) viscosities of a dilute solution of linear polymer, showing the coil-stretch transition from coiled to...

With respect to the segmental diffusion, the characteristic frequencies of the cyclic systems vary with Q3 as in the case of the linear chains in dilute solution (see Sect. 5.1.2). The absolute values are independent of the topology of the polymers and their molecular masses, and thus exhibit the same deviations from the theoretical predictions that have just been pointed out for dilute solutions of linear homopolymers. 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

Fig. 6. Reciprocal diffusivity versus concentration in dilute solutions of linear polystyrenes in CC14> for three polymer molecular weights (indicated) (after Ref.4 >, with permission).

Rouse, P.E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21,1272-1280 (1953). 

Here the linear terms in respect to the coefficient of internal viscosity ipa have taken into account only. Averaging with respect to the velocity distribution has been assumed here. One ought to add the stresses (6.13) of carrier viscous liquid to stresses (6.14) to determine the stress tensor for the entire system, that is for the dilute solution of the polymer. 

In this case, equation (F.34) defines, as was shown by Pokrovskii and Chuprinka (1973), the stresses in a dilute solution of a polymers in terms of a linear approximation... 

Pokrovskii VN, Chuprinka VI (1973) The effect of internal viscosity of macromolecules on the viscoelastic behaviour of polymer solutions. Fluid Dyn 8(1) 13-19 Pokrovskii VN, Kokorin YuK (1984) Theory of viscoelasticity of dilute blends of linear polymers. Vysokomolek Soedin B 26 573-577 (in Russian)... 

Pokrovskii VN, Kokorin YuK (1987) The theory of oscillating birefringence of solutions of linear polymers. Dilute and concentrated systems. Polym Sci USSR 29 2385-2393 Pokrovskii VN, Kruchinin NP (1980) On the non-linear behaviour of linear polymer flow. 

Time constants based on molecular theories have been derived for rod hke and bead-spring models (Bird et al., 1977b Ferry, 1980). For example, Whitcomb and Macosko (1978) showed that the conformation of xanthan gum in solution is rod like with some flexibility. The bead-spring model has found extensive use in the literature on polymers. The development of molecular theory for dilute solutions of linear... 

According to dynamic light scattering (DLS) studies, an unusual concentration-dependent LCST was observed. In dilute solutions, single-molecule collapse was observed and this was ascribed to the compact struaure of molecular bmshes. However, when the concentration of the solution of molecular bmshes was increased, intermolecular a egation occurred, as typically observed for solutions of linear polymers (Figure 63). 

Rouse, P.E. Jr. A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers. 

First, we consider the conformation of a random linear chain, which is a model for a dilute solution of a polymer in a solvent [1-6]. Typical examples are polystyrene in benzene or polydimethylsiloxane in toluene or cyclohexane. We assume that the macromolecules are made of N statistical units which are randomly oriented with respect to each other. Because the actual monomers have to respect chemical bond angles, independent units can be regarded as made of several monomers. It is possible to define such independent units which will be used in all cases. This procedure was first presented by Kuhn, who defined the ccmcept of local rigidity of a polymer [1]. Here, we consider the chains as completely flexible, and we do not distinguish between actual monomers and statistically independent units. 

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