Dilute Solutions Flexible Polymers

In dilute solutions the polymer molecule is coiled and swollen (water is a good solvent for PEO). The radius of gyration of a flexible neutral chain in good solvent is given by Flory relation [219,220] ... 

Cates [56] introduced the notion polymer fractal by replacing the rigid bonds in a percolation cluster by flexible (phantom) links. This model can be used to describe the gelation process (Figure 11.2) [57]. Within the framework of this approach, Cates [56] described variations of the structure and the dynamics of dilute solutions of polymers. 

A long flexible polymer chain is a typical object addressed by meso thermodynamics. In dilute solutions a polymer chain can exhibit either a random walk or a self-avoiding walk." These two regimes are separated by the theta point, the point of polymer-solvent phase separation in the limit of infinite degree of polymerization." The random walk occurs when the polymer chain and the solvent form either ideal or quasi-ideal solutions. The ideal polymer chain exhibits Gaussian fluctuations of the distance R between the two ends of the... 

An extensive investigation of the dilute solution properties of several acrylate copolymers has been reported (80). The behavior is typical of flexible-backbone vinyl polymers. The length of the acrylate ester side chain has Httle effect on properties. 

Equation (23) predicts a dependence of xR on M2. Experimentally, it was found that the relaxation time for flexible polymer chains in dilute solutions obeys a different scaling law, i.e. t M3/2. The Rouse model does not consider excluded volume effects or polymer-solvent interactions, it assumes a Gaussian behavior for the chain conformation even when distorted by the flow. Its domain of validity is therefore limited to modest deformations under 0-conditions. The weakest point, however, was neglecting hydrodynamic interaction which will now be discussed. 

The Zimm model predicts correctly the experimental scaling exponent xx ss M3/2 determined in dilute solutions under 0-conditions. In concentrated solution and melts, the hydrodynamic interaction between the polymer segments of the same chain is screened by the host molecules (Eq. 28) and a flexible polymer coil behaves much like a free-draining chain with a Rouse spectrum in the relaxation times. 

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... 

Proper use of LALLS to measure polymer molecular weight requires a dilute solution of optically isotropic flexible macromolecules whose dimensions are of the same... 

The equilibrium structure is considered of flexible polymer chains within the RIS model. This model is solved by an irreducible tensor method which is somewhat different from, and simpler than, the approach of Flory and others. The results are used to compute the light scattering intensities from dilute solutions of flexible polymer chains, and the angle dependence is found... 

Fluorescence is measured in dilute solution of model compounds for polymers of 2,6-naphthalene dicarboxylic acid and eight different glycols. The ratio of excimer to monomer emission depends on the glycol used. Studies as functions of temperature and solvent show that, in contrast with the analogous polyesters in which the naphthalene moiety is replaced with a benzene ring, there can be a substantial dynamic component to the excimer emission. Extrapolation to media of infinite viscosity shows that in the absence of rotational isomerism during the lifetime of the singlet excited state, there is an odd-even effect In the series in which the flexible spacers differ in the number of methylene units, but not in the series in which the flexible spacers differ in the number of oxyethylene units. 

Yamaguchi,N. Sugiura,Y., Okamo,K., WadaE. Non-newtonian viscosity and excluded volume effect of dilute solutions of flexible high polymers. J. Phys. Chem. 75,1141-1149 (1971). 

The conclusion may be drawn that the non-draining values of JeB, as derived by Zimm and by Pyun and Fixman [eqs. (3.62a) and (3.62b)], are very realistic for infinitely dilute solutions of flexible linear chain polymers. The fact that the experimental value of JeR, as given by eq. (3.86), is somewhat too high, can now certainly be ascribed unambiguously to the still insufficient uniformity of molecular weight. 

It is suggested by several equations describing the solution behavior of flexible polymers in good solvents that the second and third virial coefficients of the concentration dependence have a common parameter dependence 12-14). This behavior may be attributed to interchain entanglements for some polymers. In contrast, rigid rods can show completely linear concentration dependence in moderately dilute solution. Here the third virial coefficient is either negligibly small, or it is non-existent—in which case no relation exists between the second and third coefficient. Viscometry of some polyisocyanide solutions shows time-dependent transformations, reflected in pronounced changeovers from parabolic to linear concentration dependencies, and it would be of interest to define the transformations, and to detail their physical descriptions. 

It is evident that due to polymeric specificity of LC polymers most of the information on their molecular parameters, i.e. molecular mass, conformational state, polymeric chain flexibility and mobility, optical anisotropy and others, may be obtained from studies of dilute solutions of these compounds. However, taking into account that this branch of polymer science has already been reviewed 134>172-176> we will here confine our treatment only to the initial steps of LC phase formation in polymer solutions. 

The flow-strength criteria stated in equation (10.2) has been examined experimentally by Fuller and Leal [72] and Dunlap and Leal [149] using four- and two-roll mills, respectively. These devices allow one to systematically vary the flow type (the relative amount of pure extension to pure rotation). The birefringence was measured for dilute and semidilute polymer solutions as a function of both the magnitude and type of the flow. Simple molecular models of flexible polymer chains suggest that such data, when plotted as a... 

The average extension of the chain in space can be modified by its interaction with the environment. This modification will occur in dilute solution, except in the special case where the chain is dissolved in a 0 solvent. The typical dilute solution is prepared using a good solvent, in which case the polymer-solvent interaction produces a positive excluded volume that causes expansion of a flexible chain. The introduction of the consequences of long-range interactions into the conformational description of a linear chain greatly complicates the theoretical description A5-181 The focus is on an expansion factor that can be defined as... 

Figure 11-3. (A) Transfer of a flexible polymer and (B) transfer of a globular molecule of the same size from the condensed pure phase to a dilute solution. The figure is taken from Chan and Dill [20]...

It is now generally accepted that folding is universal for spontaneous, free crystallisation of flexible polymer chains. It was first of all found in crystallisation from very dilute solutions, but it is beyond doubt now, that also spherulites, the normal mode of crystallisation from the melt, are aggregates of platelike crystallites with folded chains, pervaded with amorphous material. "Extended chain crystallisation" only occurs under very special conditions in the case of flexible chains for rigid polymer chains it is the natural mode ("rigid rod-crystallisation" from the melt in case of thermotropic polymers, and from solution in case of the lyotropic liquid-crystalline polymers both of them show nematic ordering in the liquid state). 

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