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The ab initio molecular computational software GAUSSIAN 03 and TURBOMOLE are supposed to give very similar results for a given input data (choice of the exchange and correlation potential, basis set, etc.). However, partly due to the reason that the TURBOMOLE software runs more efficiently than the GAUSSIAN 03 software, in the CSC - IT Center for Science, Espoo, Finland supercomputer environment, we have done the molecular quantum mechanical calculations presented in Sec. by using the TURBOMOLE software.
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It is well known that the exchange and correlation potential based on the PW91 xc-energy functional that we use in our DFT calculations does not possess the correct long-range asymptotic behavior (∼ -1r for large distances). However, our DFT calculations on acrylic acid grafted polypropylene with the PW91 xc treatment are for large extended systems (large oligomers in molecular modeling and infinite periodic 3-dimensional bulk crystal) where we do not expect this to distort the computed dielectric properties too much. In fact, this functional has been successfully used in our previous molecular based DFT study on dielectric properties for polypropylene (see Ref.) as well as in the DFT studies by Su (see Ref.) for static and dynamical mechanical properties of the ferroelectric polymer poly(vinylidene fluoride) (PVDF) and its copolymer with trifluoro ethylene (TrFE). Finally, it could be argued that as far as the nature of the electronic orbitals (e.g., locality) in the acrylic acid grafted polypropylene are similar to those in the pure polypropylene, there should be no problem in using the PW91 functional also in the grafted polypropylene case.
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Only recently, first-principles computational methods capable of tackling extended Van Der Waals bonded systems, have been developed. Among these we could mention the DFT methods in connection with adiabatic connection fluctuation dissipation theorem (ACFDT) (see, for example, Ref.) and DFT methods exploiting explicitly a nonlocal density functional, called Van der Waals density functional whose correlation part depends nonlocally on the density and accounts for dispersion forces (see, for example, Ref.). However, these methods seemed to have been implemented for total energy calculations only so far, and to our knowledge there seems to be no first-principles computational methods implemented for the response function (e.g., permittivity) incorporating the Van der Waals forces.
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Only recently, first-principles computational methods capable of tackling extended Van Der Waals bonded systems, have been developed. Among these we could mention the DFT methods in connection with adiabatic connection fluctuation dissipation theorem (ACFDT) (see, for example, Ref.) and DFT methods exploiting explicitly a nonlocal density functional, called Van der Waals density functional whose correlation part depends nonlocally on the density and accounts for dispersion forces (see, for example, Ref.). However, these methods seemed to have been implemented for total energy calculations only so far, and to our knowledge there seems to be no first-principles computational methods implemented for the response function (e.g., permittivity) incorporating the Van der Waals forces.
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COOH are the molecular masses of the IPP molecule, hydrogen atom, and carboxyl group, respectively. This expression reflects the fact that the hydrogen atom next to the methyl group bonded to the backbone carbon of the IPP chain (see Fig.) will be removed and replaced by the carboxyl group under the acrylic acid grafting
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COOH are the molecular masses of the IPP molecule, hydrogen atom, and carboxyl group, respectively. This expression reflects the fact that the hydrogen atom next to the methyl group bonded to the backbone carbon of the IPP chain (see Fig.) will be removed and replaced by the carboxyl group under the acrylic acid grafting.
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This is justified as we are interested, in a first place, to see whether any crystalline environment (artificial or real) will cause noticeable changes to electronic and dielectric properties of acrylic acid grafted polypropylene from those computed through the DFT molecular modeling. Interstingly, it turns out (see discussion below) that the artificial tetragonal crystal structure, which comprises a metastable state, causes only minor changes to these properties. Therefore, within the scope of this paper, we will not carry out rather massive DFT and DFPT computations on these properties for possible realistic phases of acrylic acid grafted isotactic polypropylene (the known phases of isotactic polypropylene are the -form monoclinic crystal structure, the -form hexagonal crystal structure, and the -form triclinic crystal structure). However, we have done some calculations (not shown here) for pure isotactic polypropylene with the -form. Conclusions from these calculations are very similar to those from our present calculations based on the tetragonal crystal structure. For example, the band gap energy and permittivity are quite insensitive to the relative positions of the right- and left-handed helical chains along the chain direction, and the permittivity values computed with the DFPT method and molecular DFT modeling (Clausius-Mossotti relation) are very similar.
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bulk in Table).
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g) electronic contribution to the permittivity, i.e., should describe accurately the permittivity behavior in these materials
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g) electronic contribution to the permittivity, i.e., should describe accurately the permittivity behavior in these materials.
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