Unperturbed dimensions

To use the proportionality between rg and n in this section, we have stipulated unperturbed dimensions-in the sense of item (2)-as indicated by the subscript 0 on the various size parameters. 

Kurata, M. and Stockmayer, W. H. Intrinsic Viscosities and Unperturbed Dimensions of Long Chain Molecules. Vol. 3, pp. 196—312. 

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. 

If we consider the size of a polymer molecule, assuming that it consists of a freely rotating chain, with no constraints on either angle or rotation or of which regions of space may be occupied, we arrive at the so-called unperturbed dimension, written (r)o Such an approach fails to take account of... 

In a sufficiently poor solvent at a given temperature, the condition where a = 1 can be achieved, and the chain attains its unperturbed dimensions. This turns out to be the 6 temperature of Rory and Krigbaum previously described in Section 5.5 of this chapter. 

Theta temperature (Flory temperature or ideal temperature) is the temperature at which, for a given polymer-solvent pair, the polymer exists in its unperturbed dimensions. The theta temperature, , can be determined by colligative property measurements, by determining the second virial coefficient. At theta temperature the second virial coefficient becomes zero. More rapid methods use turbidity and cloud point temperature measurements. In this method, the linearity of the reciprocal cloud point temperature (l/Tcp) against the logarithm of the polymer volume fraction (( )) is observed. Extrapolation to log ( ) = 0 gives the reciprocal theta temperature (Guner and Kara 1998). 

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. 

Deb P.C., Chatterjee S.R. Unperturbed dimension of polymer molecules from viscosity measurements. Die Makromolekulare Chemie 120,1 (1968) 49-57. 

Guner A. 1999. Unperturbed dimensions and theta temperature of dextran in aqueous solutions. Journal of Applied Polymer Science 72, 871-876. 

Studies of the hydrodynamic properties and unperturbed dimensions of fractionated PCL have shown that it is a flexible coil (54,55). The following Mark-Houwink equations have been reported ... 

Koleske, J. V., and Lundberg, R. D., Lactone polymers. II. Hydrodynamic properties and unperturbed dimensions of poly-e-caprolactone, J. Polym. Sci., Part A-2. 7, 897-907, 1969. 

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. 

M Kurata, WH Stockmayer. Intrinsic viscosities and unperturbed dimensions of long chain molecules. Fortschr Hochpolym-Forsch 3 196-312, 1963. 

A preferable system is poly(p-fluorostyrene) doped into poly(styrene). Since rotations about the 1,4 phenyl axis do not alter the position of the fluorine, the F spin may be regarded as being at the end of a long "bond" to the backbone carbon. In standard RIS theory, this polymer would be treated with dyad statistical weights to automatically take into account conformations of the vinyl monomer unit which are excluded on steric grounds. We have found it more convenient to retain the monad statistical weight structure employed for the poly(methylene) calculations. The calculations reproduce the experimental unperturbed dimensions quite well when a reasonable set of hard sphere exclusion distances is employed. 

The fractal dimension measures how open or packed a structure is lower fractal dimensions indicate a more open system, while higher fractal dimensions indicate a more packed system (22). Theories relating the fractal dimension to the relaxation exponent, n, have been put forward and these are based on whether the excluded volume of the polymer chains is screened or unscreened under conditions near the gd point (23). It is known that the excluded volume of a polymer chain is progressively screened as its concentration is increased, the size of the chain eventually approaching its unperturbed dimensions. Such screening is expected to occur near the... 

Flory s viscosity theory also furnishes confirmation of the w temperature as that in which a=V.2, and it permits the determination of the unperturbed dimensions of the Polymer chain. Even if a Q solvent is not available, several extrapolation techniques can be used for the estimating the unperturbed dimensions from viscosity data in good solvents. The simplest of these techniques seems to be that of Stockmayer. 

Note The subscript zero is used to indicate unperturbed dimensions as in(s )y. ... 

Ratio of the root-mean-square end-to-end distance of a macromolecular chain with unperturbed dimensions,, to that of a freely rotating chain with the same structure,... 

As explained earlier (Sect. 1.3.1), macromolecules in a low-molecular-weight solvent prefer a coiled chain conformation (random coil). Under special conditions (theta state) the macromolecule finds itself in a force-free state and its coil assumes the unpertubed dimensions. This is also exactly the case for polymers in an amorphous melt or in the glassy state their segments cannot decide whether neighboring chain segments (which replace all the solvent molecules in the bulk phase) belong to its own chain or to another macromolecule (having an identical constitution, of course). Therefore, here too, it assumes the unperturbed ) dimensions. 

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