Intramolecular expansion factor

In a solvent the polymer coil tends to swell to some degree depending on the nature of the solvent. The dimensional expansion is measured by the intramolecular expansion factor,... 

The bonds of the polymer molecule have been considered thus far as volumeless lines in space. In contradistinction, the bonds of real polymer molecules occupy flnite volumes in space. The repulsion between segments that are far removed from one another along the contour of the chain but spatially contiguous will cause the polymer chain to expand beyond the unperturbed dimensions. The magnitude of this dimensional expansion is measured by the intramolecular expansion factor a... 

The dilution parameters are readily determined by a range of experimental measurements, such as the temperature dependence of the second virial coefficient. Alternatively, if the 0-temperature is measured separately, determination of the intramolecular expansion factor a, e.g. by viscometry, allows the values of and k, to be calculated using the Flory relationship, as... 

Flory in his now classic theory of the intramolecular expansion factor a. Despite the expenditure of considerable effort, Flory s theory, or at least the Stockmayer (1960) modified version of it, has scarcely been improved upon in later years if comparison with experiment forms the judgemental basis (Yamakawa, 1971). In any event, the high segment densities often generated in the interpenetrational-plus-compressional domain are difficult to comprehend using the Flory-Huggins theory, especially if the interaction parameter is assumed to be concentration independent. 

Fig. 11.4. The free energy of interaction of two flat plates sterically stabilized by tails of molecular weight 6 000 according to the theory of Hesselink, Vrij and Overbeek (1971). Three different intramolecular expansion factors are shown (after Hesselink, 1977).

Of is the intramolecular expansion factor, which depends on the nature of the solvent. 

More sophisticated approaches to the evaluation of wfr) exist. Some of them are the technique based on the Yoon-Flory expansion, variations of the Gaussian approximation, and an implementation of the Koyama distribution. Freely jointed chains and rotational isomeric chains have also been used as models of chains. Research is actively pursued on the subject of formulating more realistic closure relationships. In considering the choice of an intramolecular structure factor, a paper by McCoy et al. on model polyethylene melts will be useful. 

From Equation 12.71, the intrinsic viscosity depends on the molecular weight as a result of the factor and also through the dependence of the expansion factor on molecular weight. By choosing a theta-solvent or 0 temperature, the influence of the molecular expansion due to intramolecular interactions can be eliminated. Under these conditions, a = 1, and the intrinsic viscosity depends only on the molecular weight. Thus Equation 12.71 is reduced to ... 

The unperturbed dimensions refers to molecular size exclusive of solvent effects. It arises from intramolecular polar and steric interactions and free rotation. The expansion factor is the result of solvent and polymer molecule interaction. For linear polymers, the square of the radius of gyration is related to the mean-square end-to-end distance by the following relationship ... 

In several theories, the effects of excluded volume are combined into a static expansion factor a relating the total, experimentally measured mean square radius of gyration <5 > to the value with no long-range intramolecular forces accounted for,... 

K.—Ordinarily the intrinsic viscosity should depend on the molecular weight not only owing to the factor occurring in Eq. (26), but also as a result of the dependence of the factor on M. The influence of this expansion resulting from intramolecular interactions may be eliminated by suitable choice of the solvent and temperature. Specifically, in an ideal solvent, or -solvent, a = l and Eq. (26) reduces to... 

It must be kept in mind that the Goodrich treatment separates out contributions to intermolecular interactions that arise from film expansion. The differences in film expansion are a reflection of conformation and are accounted for in the pure meso- and ( )-films. However, since ( )- and meso-film components do interact, the intramolecular contribution to film compression may be altered. This effect would arise from conformational perturbations as molecules interact, thereby precluding complete separation of inter- and intra-molecular contributions to the thermodynamics of compression. However, these complicating factors can be mitigated by comparing several molecules with varying structures, as has been carried out in this instance. 

Starting from a multipole expansion of intramolecular Coulomb interactions, we present an efficient configuration interaction calculation for the electron terms = 2,3, 4, and the hole terms (hf)", n = 2-5. We have studied magnetic moments for the electron and hole terms. The coupling of spin and orbital momenta differs from the Lande g-factor scheme of atoms. The magnetic moments do not depend on the orientation of the molecule with respect to an external magnetic field. 

It is weU known that the dimensions of a pol3mer coil in dilute solution are influenced by two factors the polymer solvent interaction and the intramolecular excluded volume effect. The energy of interaction between polymer segments and the molecules of a good solvent tends to increase the chain dimensions, because expansion creates more polymer-solvent contacts. The intramolecular excluded volume effect also increases the dimensions. 

An alternative, and possibly physically more acceptable, interpretation of die intramolecular factors determining the dipole moment changes associated with vibrational motion may be based on consideration involving die electron density function, die spatial part of which is an observable physical quantity. The function p(R) defining the electron density at position R in LCAO expansion reads... 

---