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van der Waals interaction of simple, parallel polymers
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Image of FIG. 1.
FIG. 1.

The three polymers shown from the top and from the side. The hydrogen atoms are not shown in order to make the helical structure more apparent. the gray spheres are carbon atoms and the dark gray spheres are chlorine atoms. The bottom figures show the corresponding contour plots of the valence electron density averaged along the chain. The contour lines are equally spaced by .

Image of FIG. 2.
FIG. 2.

The calculated static susceptibility of a segment of PE for different angles . The orientation corresponds to the situation shown in Fig. 1 when the electric field is applied in the direction. The diamonds are values obtained from DFT calculations and the full line is obtained by Eq. (6). The dashed line is found using the plasmon-pole approximation and solving the electrodynamic equations with finite element method (FEM) techniques. The inset shows the graph in full scale.

Image of FIG. 3.
FIG. 3.

The orientation-dependent expansion coefficients and for PE, shown as equidistant contours. is the rotation angle of polymer about its center of mass. The initial positions of the polymers are indicated by the contours of the averaged charge densities in Fig. 1. The panels show (a) and (b) , respectively.

Image of FIG. 4.
FIG. 4.

The PE-PE van der Waals interaction energy as a function of separation for the two orientations schematically shown in the inset, corresponding to the minimum and maximum interactions, respectively. The full lines are the results of the 2D numerical interaction integral, while the dotted lines show the results for the seventh order expansion in .

Image of FIG. 5.
FIG. 5.

The PP-PP van der Waals interaction energy as a function of separation in different approximations. The full line corresponds to the evaluation of the 2D-interaction integral while the dotted line shows the expansion of the energy up to the seventh order in inverse distance. The inset shows the PE-PE, PP-PP, and PVC-PVC van der Waals interaction energies as a function of separation . All the polymers are oriented as shown by the density contours in Fig. 1 and separated in the direction.


Generic image for table
Table I.

Geometric data characterizing the polymers: the repetition length (unit-cell length), the average separation of atoms and , and the angle formed by the carbon atoms in the main chain. denotes a carbon atom with an attached subgroup or Cl, stands for or Cl.

Generic image for table
Table II.

Comparison between the expansion coefficients for the full 2D evaluation and the expansion coefficients where cylindrical symmetry is enforced.

Generic image for table
Table III.

Comparison of the coefficients for the PE-PE interaction obtained by other methods with those obtained by our method. Underlined quantities are estimated using Eq. (10).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: van der Waals interaction of simple, parallel polymers