Rotational states polymer conformations

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

The conformation of atactic polymers, with any value of the m/r ratio, must be treated as that of a copolymer, wherein the monomer unit statistics are compounded with those of the rotational states. In this case we may either refer to Monte-Carlo type procedures, as done by Floiy, Mark, and Abe (194), or to the pseudostereochemical equilibrium method used by Allegra (195) and Briick-ner (196). In the latter case the atactic polymer is formally considered as a homopolymer that may assume the conformations of either the m or r dyads, with suitable adjusted statistical weights. 

In a typical analysis of a polymer chain, the experimental values of configuration-dependent properties and their temperature coefficients are compared with the results of rotational isomeric state calculations. These comparisons yield values of the energies for the various rotational states about the backbone bonds, and these conformational preferences can then be used to predict other configuration-dependent properties of the chains. It is also possible to obtain such conformational information from potential energy calculations, using the methods of molecular mechanics.39,46 52... 

For polymers with rotational barriers smaller than RT, one may use the RIS model to replace the continuous rotational potential with a discrete sum of rotational states.Nearest-neighbor interactions are important in determining the probability of occurrence of rotational states. This effect is illustrated in the case of n-pentane, where severe repulsive steric interactions between the terminal methyl groups occur in the and g g conformations (see Figure 8). ... 

Some measure of polymer size is obtained from molecular weight, but what is the actual length of the molecule and what is its shape Before trying to answer these questions we should first consider a simple molecule such as butane and examine the behavior when the molecule is rotated about the bond joining two adjacent carbons. This rotation produces different conformational states of the molecule. 

The steric hindrance parameter a is the simplest conformational property of a polymer chain. If o denotes the mean-square end-to-end distance of an unperturbed linear chain molecule in solution, and of denotes the mean-square end-to-end distance of the idealized and hypothetical "freely rotating" state of the chain, o is defined formally by Equation 12.1 ... 

The rotational state parameters are adjusted until the best agreement with several types of experimental data is obtained. The RIS approximation permits the use of matrix methods based on the following considerations. The conformational partition function (Qc) (Appendix 2A) is required for averaging over all possible conformations of a polymer chain. 

The energetics of a polymer chain conformation can be readily specified by its partition function (see Appendix 2A). In the rotational state approximation, the conformational partition function ( gc) can be expressed as the product of the statistical weights for each bond (JJ) fi-om 2 to n- summed over all rotational states. Thus... 

In practice, not aU the combinations of three representative internal rotation states can be accepted along the real polymer chain. For polyethylene chains, there exists the so-called pentane ejfecr (Flory 1993). We know that the summation of two van der Waals radii of carbon atoms is 3.0 A. Two consecutive gauche conformations, g g or g g, bring the end-to-end distance of the pentane segment to 3.6 A. Thus, these two chain ends interleave with each other, which can be acceptable. However, the conformatiOTi g g or g g bring the end distance to 2.5 A,... 

If the interactions between the polymer segments, between a polymer segment and a solvent molecule, and between solvent molecules are equally favorable, all rotational states around the covalent bonds in the polymer chain are equally probable. Assuming that the polymer has no volume, the conformation of the polymer molecule... 

---