Unperturbed dimensions, linear chain

One of the signatures of densely tethered chains is expressed in Eq. 5, namely the linear variation of L with N. This stands in marked contrast with free chains where excluded volume interaction produces, at most, an R N3/5 distortion from the R N1/2 unperturbed dimensions. Tethered layers are stretched and this is the origin of their interesting behavior. 

Kurata, M., Tsunashima, Y., Iwama, M., and Kamada, K., Viscosity-molecular weight relationships and unperturbed dimensions of linear chain molecules, in Polymer Handbook, 2nd ed., Brandrup, J. and Immergut, E. H., Eds, John Wiley Sons, New York, 1975, iv, 1-60. 

The exponent can vary from v=0.33 for hard spheres up to v=1.0 for rigid rods. For linear chains v=0.5 refers to unperturbed coil dimensions in -solvents and v=0.588 [6] to good solvent conditions. Equation (37) maybe re-writ-ten by expressing the molar mass as a function of the radius of gyration, i.e.. 

Additional support for a value of A in the neighborhood of 1.0 10-8 is furnished by the results of our calculations of the unperturbed dimensions of a number of linear polyesters (see Section III C) which consist mainly of methylene chain units and which yield similar values of A. We should also mention an as yet unpublished calculation of Hoeve [quoted in a paper by Ciferri, Hoeve and Flory (66")], according to which such a value of A is in excellent agreement with the observed temperature coefficient, as deduced from intrinsic viscosities and from stress-temperature coefficients for cross-linked polyethylene networks. 

Another important statement of French authors from their neutron scattering experiments was that the size of polystyrene strands in dry model networks is equal to the size of the precursor chains dissolved under -conditions (see Table 1.5). At first sight, this result confirms the idea [136, 137], expressed by Flory [138] in the middle of the last century and later picked up by De Gennes [139], that in bulk polymer the chain retains its unperturbed dimension characteristic of its solution in a -solvent. Flory believed to have experimentally confirmed his idea [140]. By analyzing elastic neutron scattering from a mixture of linear protonated and deuterated polyisobutylene with a molecular weight of 48,000+ 3,000 Da, he found that the gyration radii of the macromolecules... 

Undoubtedly, in the preparation of model networks from rather long polymeric precurson by the end-hnking reactions, the strands between the junction points wid maintain the conformation of coils. In accordance with classical ideas, the cods in the dry model network should acquire unperturbed dimensions, simdar to cods in a -solvent. However, on contacting a model polystyrene network with cyclohexane at room temperature, which is far below the -point for linear polystyrene (34.5°C), its volume increases by a factor of 3. Thus, the solvent breaks some polymer-polymer interactions, stimulates swelling of the network, and may result in an increase of chain dimensions. Hence, even at room temperature, the polystyrene chains prefer replacing the alien chain segments by cyclohexane molecides. 

This follows from the expansion factor, a is greater than unity in a good solvent where the actual perturbed dimensions exceed the unperturbed ones. The greater the value of the unperturbed dimensions the better is the solvent. The above relationship is an average derived at experimentally from numerous computations. Because branched chains have multiple ends it is simpler to describe them in terms of the radius of gyration. The volume that a branched polymer molecule occupies in solution is smaller than a linear one, which equals it in molecular weight and in number of segments. 

Source From Viscosity-molecular weight relationships and unperturbed dimensions of linear chain molecules, in Polymer Handbook. ... 

It is convenient to separate (r ) into its component factors, viz., the unperturbed dimension and a linear expansion faetor for hydrodynamie chain dimensions [ef. Eq. (3.86)]. Equation (3.147) may thus be rewritten as follows ... 

Unperturbed Dimenaons.—The most fundamental model of the statistics of a polymer in solution is the linear Gaussian chain, which exhibits the Markovian property that the mean square end-to-end distance o is directly proportional to the number of chain segments i.e. ounperturbed dimensions , and b is the (Kuhn) statistical segment length. 

The experimentally-measured delays in the gel-point, relative to the predictions of Flory-Stockmayer (F-S) theory, as functions of the initial dilutions of reactive groups, follow the trends predicted by A-R-S theory. Quantitative interpretation of the PDMS gel-points using A-R-S theory yields values for the effective bond length, b (a measure of chain stiffhess), which are in the range expected from the known unperturbed dimensions of linear PDMS chains. 

Viscosity - Molecular Weight Relationships and Unperturbed Dimensions of Linear Chain Molecules... 

MOLECULAR WEIGHT RELATIONSHIPS AND UNPERTURBED DIMENSIONS OF LINEAR CHAIN MOLECULES... 

VII / 12 VISCOSITY - MOLECULAR WEIGHT RELATIONSHIPS AND UNPERTURBED DIMENSIONS OF LINEAR CHAIN MOLECULES TABLE 1. cant d... 

---