Polymers gauche state

Values of the mean-square dipole moment of PNA are determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions are critically interpreted using the RIS model. Good agreement between theory and experiment is obtained by assuming that the gauche states about C(CH3)2— CH2 bonds have an energy 2.5 kJ mol-1 lower than the alternative trans states. 

The gauche states are also observed in crystalline polymers, polyoxymethy-lene6,7,157-160, polyoxyethylene6,7,161,162, poly-1,3-dioxolane163, and poly-1,3-dioxe-pane164 by X-ray analysis. 

In poly-VIII, the favorable conformation of synperiplanar-antiperiplanar-gauche for C-O bonds around the Ci-atom is not accomplished. The labile conformation of the polymer however, is more stable than that of the rigid monomer. In IV, all of the C-O bonds are situated in a gauche state. The polymer can exist as a TGG conformer, in which the position of the chain-methylene is determined by the exo-anomeric effect. 

The kinetic flexibility of a macromolecule is directly related to the ease with which conformational changes between trans and gauche states can take place. The lower the energy barrier AE in Fig. 4-2, the greater the ease of rotation about main chain bonds. Polymers with low chain stiffnesses will have low Tg s in the absence of complications from interchain forces. Chain backbones with... 

Adam-Gibbs equation. Most flexible polymers have energetically favored trans states and disfavored gauche states, with one trans state for every two gauche states. If U is the energy difference per mole between the trans and gauche states, and all such states contribute independently to the energy, then the partition function for these conformations is... 

In the previous section the idea of the conformation of a small molecule, n-butane, was discussed, as was the idea of the local conformation of a polymer chain. It was tacitly assumed that such states were in fact different from each other, i.e. that they each had a certain degree of permanence. The plot in fig. 3.4 shows that the difference in energy between the tram and gauche states is about 3 kJ mol , which is quite close to thermal energies even at room temperature, at which N kT is about 2.5 kJ mol . This means that, even though the tram state has lower energy, there will be a considerable fraction of molecules in the gauche state. 

What matters, however, for ensuring that the states are essentially discrete, is that the energy barrier between the two states is about five times thermal energies at room temperature, so that most of the time the molecule will simply perform small oscillations around a discrete tram or gauche state. The various conformations of a molecule are often called rotational isomers and the model of a polymer chain introduced by Flory in which the chain is imagined to take up only discrete conformational states is called the rotational isomeric-state approximation. 

If it is assumed that the chain is flexible, that is that the barrier between conformational states is sufficiently low that rapid interchange can occur, then the time averaged shape of the polymer will be described by the distribution between the available conformations. This allows a statistical mechanical analysis, called the rotational isomeric model. This indicates that the population of the gauche states causes the chain to adopt a random quasi-spherical shape and not the often pictured zigzag extended aU trans form. The analysis allows calculation of two fundamental parameters the radius of gyration, which is the size of the polymer molecule if it were to undergo free internal rotation, and the related end-to-end distance. These quantities define the shape of the isolated polymer... 

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