Density of the polymer coil

The intrinsic viscosity [q] has the same unit, [ml g" ], as the reduced viscosity rjred a better understanding, the intrinsic viscosity can be considered as a measure for the volume demand of the single polymer coil in ideally diluted solution. The intrinsic viscosity is proportional to the reciprocal density of the polymer coil in solution according to Eqs. (4.6) and (4.7). 

The chemical structure of a polymer can also cause a contraction of the polymer coil compared to the unperturbed dimensions at theta-conditions. In this case the exponent a of the [ ]]-M-relationship shows values of a<0.5. A contraction of the coil occurs if the attractive intramolecular interactions between the polymer segments become larger than the interactions with the solvent molecules. In extreme cases, the solvent is forced out of the polymer coil and the chain segments start to form compact aggregates. The density of the polymer coil is then independent of the molar mass and the intrinsic viscosity is constant. In this case the exponent a is zero. An example is shown in Fig. 6.12 for compact glycogen in aqueous solution. 

Pequ Equivalent density (density of the polymer coil in the solution... 

The "polymer effect on (f)g.j. - is it generally true that the intersystem crossing rate is diminished (2) Does triplet migration occur in the fluid phase (3) How does the density of the polymer coil affect triplet quenching or sensitization reactions ... 

Here c is the polymer concentration by weight. < the density of the polymer, a an effective bond length or measure of the coil dimensions, and to the monomeric friction factor. The subscript zero indicates the pure polymer. Since 2 (H), the mean-square end-to-end chain separation, the viscosity will be directly proportional to the polymer concentration unless the plasticizer modifies the coil swelling. At high molecular weight the monomeric friction factor is increased by the factor (MIMf)" and M, is increased relative to the undiluted polymer [equation (55)]. Thus... 

At concentrations greater than this value there will be polymer chains at any position in the solution but there will still be large fluctuations in local concentration with position because the density of each polymer coil is greatest at the centre of mass of the coil. The interactions between segments of neighbouring coils due to overlap progressively screen out... 

The Density of a Polymer Coil and Concentration Ranges of a Polymer Solution... 

Values A," l, i=l,distribution density, correspond to the equilibrium state of the polymer coil... 

The volume of the polymer coils l poiymer can be described via the ratio of the mass polymer of t e polymer to its density Pequ- This density p qu does not correspond with the density in the dry state, but with the density of the polymer in solution, where solvent molecules surround the polymer chain ... 

The solvation of the chain of a polymer has a big impact on the expansion of the polymer coil. Figure 5.2 shows that a big solvating envelope increases the effective volume of a polymer segment and therefore the volume fraction of the polymer coil. This leads to a decrease of the polymer density in solution according to... 

The assumption in Determination of the polymer coil dimensions from the intrinsic viscosity in Chap. 7 that the polymer coils in solution behave like hard spheres with a constant density inside the coil and a fixed boundary to the solvent is only a simple approximation. In reality, a polymer chain shows a dynamic behavior with fast and statistically changing conformations. 

Fig. 8.4. Schematic view of the relative segment density of a polymer coil in solution as a function of the distance from the center of gravity 92% of the segments lie within the radius of gyration...

It is stressed again that since is an average quantity, the coil is spherical on average. However, each individnal polymer molecule has a nonspherical asymmetrical shape. Furthermore, the monomer distribntion in the statistical coil is Ganssian that is, the density of the polymer segments decreases outwards from the center. It can be proven that for a random walk conformation, the segmental density distribution Pp(r) is given by... 

The neutron and analogous X-ray measurements can provide density contours from the surface that can be used to understand the way in which the conformational distribution of the chains varies form the surface to the bulk. The conformational distribution defines the size of the polymer coil and hence the density of the material. 

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