Solvent Systems 1 Polydispersity Effect

Scattering measurements in real polymer/solvent systems 3-5-1. Polydispersity effect. 

Equation 3-43 is valid for monodisperse polymers. However, in naost cases the polymers and soluble conjugated polymers are more or less polydisperse. What is Aen measured is a z-average of the radius of gyration (21). 

The contribution of the highest molecular weight will be predominant for polydisperse samples. Therefore the mass distribution must be included in equation 3-43. R.C. Ob ur (22) has obtained the following expression for chains with pmistence length  

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A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

More emphasis on multicomponent systems including both mixed solvents, blend-solvent systems, as well as the effect of polydispersity... 

Figure 15.5 Effect of molecular weight dispersity ( )) (formerly known as polydispersity) using schematic Gibbs triangle diagrams for polymer-solvent system, generation of cloud point curve and shadow curve in temperature-composition diagram.

The performance of several column packings has been assessed and it has been stressed that low eluent flow rates are necessary for high performance separation. The effects of water contamination in eluents has been studied by Berek et a/. " highlighting the need for rigorou dried systems. Phase equilibria studies in polymer-polymer-solvent systems have proved feasible using a dual detection system and could be extended in the future. Other applications are concerned with copolymer analysis, polydispersity, oligomers, and melamine-formaldehyde and urea— and phenol-formaldehyde resins. New techniques, recycle liquid SEC, phase-distribution chromatography, and the measurement of diffusion coefficients from GPC have been described. 

The foregoing discussion assumed that using a good solvent in place of a solvent has no significant effect on the ratio of viscosities. With some exception (32, 33), the evidence in the case of g shows the validity to be unimpaired for polydisperse as well as monodisperse systems (29, 34-36). It is expected that polymer expansion in good solvents would be in the same direction for branched and linear polymers in dilute and concentrated media so that any errors would be compensating. 

The Debye equation is based on the following physical description of the sample. This is a monodisperse solution of identical particles, which are in random orientations relative to the incident primary beam, and act as independent entities (i.e. there are no interparticle spatial correlations). The above derivation has presumed also that the particles are in vacuo. If they are in solution, they are required to form a two-phase system of solute and solvent. In biology, this corresponds to dilute solutions of pure proteins or glycoproteins in a low-salt buffer. Complications arise in the case of polyionic macromolecules in low-salt buffers, such as nucleic acids. Here, interparticle correlation effects can readily occur and the macromolecule is surrounded by an ion-cloud of opposite charge (i.e. a three-phase system). Other complications can arise in the cases of polydisperse distributions of macromolecules, oligomerization or dissociation phenomena, and conformational changes. Different formuhsms have to be derived for the analyses of these systems. 

Here hence denotes the position of monomer with label i (i= 1,..., N) in the feth chain molecule (fe = 1,..., N ). For simplicity, we have specialized here to a monodisp>erse system of linear homopolymers hut the generalization to polydisperse systems or to heteropolymers or to branched architecture is straightforward, as well as to multicomponent systems (including solvent molecule coordinates, for instance). Typically, the volume in which the S3 tem is considered is a cubic LxLxL box (in d = 3 dimensions, or a square LxL box in d = 2 dimensions), and one chooses periodic boundary conditions to avoid surface effects but if the latter are of interest, the corresponding change of boundary conditions is straightforward. All of what has been said so far applies to lattice models as well as to models in the continuum. 

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