Calculation polymer-correlation energy

If one wishes to calculate the correlation energy of a polymer with the aid of equation (68), one has to substitute for (E)/,/ any size consistent expression to compute this quantity (MP2, MP2 + MP3, coupled cluster theory in certain approximations etc.). 

The a transition, which involves motion in long segments of the main polymer chain, is related to the Tg. The P transition involves rotation of short-chain ester side groups in PMMA and therefore occurs below the Tg. The frequency dependency of the p-Tg can be used to calculate the activation energy for the molecular motion, which provides important information for characterising the structure and predicting the performance of polymeric materials. In a dielectric experiment, the calculated activation energy for the P transitions in PMMA was 17.7 kcal/mol. This correlates well with the values calculated from DMA and creep experiments. 

The increase in the number of fluorine atoms is correlated with a shift of about 1 eV per F atom to lower energies for the peak D, while the other peaks do not change appreciably. The spectrum predicted from the calculated band structure for PTFE is in good agreement with experiment, underlining once more that calculations of periodic polymers are quite successful in interpreting ESCA spectra. This agreement will be more comprehensive when allowance is made for the dependence of the ionization cross section of the crystal orbitals on their atomic constituents (intensity calculations), and correlation effects are also taken into account. Furthermore, better-resolved experimental spectra are probably also needed to check the detailed theoretical information obtained for relatively more complex polymers. 

Finally one should point out the occurrence of the basis set superposition effect (each unit cell in a quasi-ID polymer is better described because the basis functions of its neighbours also exert an effect, rather than as a single molecule). The basis set superposition causes only an error if one wants to calculate the cohesion energy of a chain or of a 2D or 3D periodic system, because then one has to calculate the energy difference of the extended system and the sum of its constituents. This basis superposition effect occurs both at the HF and at the correlation corrected (QP) level and causes that already at the MP2 level, if one uses a double basis with polarization functions, and one obtains 70-75% of the correlation energy. 

For the calculation of the correlation energy per unit cell in the ground state of a polymer (either conductor or an insulator) one can use any size-consistent method (perturbation theory /18/, coupled cluster expansion /19/, electron pair theories /20/, etc.). In the case of insulators one can Fourier transform the delocalized Bloch orbitals into site semilocalized Wannier functions (WF-s) and perform the excitations between Wannier functions belonging to near lying sites /4/. (For the generation of optimally localized Wannier functions see /21/.) This procedure is, however,... 

Cohesive energy density and solubility parameters are defined in the section on miscibility of solvents and polymers (Section B). In addition, the applicability of solubility parameters to thermodynamic calculations and their limitations are discussed. Section C contains methods for measuring, calculating and correlating solubility parameters of solvents and polymers. Section D contains... 

Solubility parameters can be determined by direct measurements, indirect calculations, or correlations with other physical parameters. The solubility parameters of solvents usually can be determined directly by measuring the energy of vaporization. The solubility parameters of polymers can only be determined indirectly and may be affected by variations in their chemical constitutions, i.e., the number of crosslinks and the distribution of chain branches or substitutive groups along the polymer backbone. The methods presented in this section can be used to develop correlations of solubility parameters with other physical properties for specific commercial polymer products or to estimate the solubility parameters of new polymers. 

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