High-density polyethylene can crystallize in both orthorhombic and monoclinic
systems. Here we demonstrate how to build a crystal of orthorhombic polyethylene
using the crystallographic information available in the literature for this polymer.
First we create a cell with the polyethylene lattice parameters and space group,
then one atom of C and H, to model the atoms of the structure, and finally link
the cell with the atoms to build the crystal, using the Wyckoff positions known
for C and H.
Lateral and top views of the polymeric chains, for 2x10x2 conventional cells,
can be seen in the figure at
http://www.gamgi.org/images/screenshot11_6b.png.
Polyethylene
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Press Cell->Create and set Group to 62, the Pnma space
group for orthorhombic polyethylene. As this is an orthorhombic system with
a primitive lattice, System and Lattice are automatically set
to o and P, respectively.
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Set the lattice parameters a, b, c to 7.48,
2.55, 4.97, respectively, the reported values for orthorhombic
polyethylene. The entries for angles ab, ac, bc
are automatically disabled, as they must be 90 degrees.
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With this standard crystallographic orientation, the polymer chains will
be aligned along direction b, so set the number of cells n1, n2,
n3 to 2, 10, 2, respectively. Press Ok
to create the cell.
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Press Atom->Create, write C in the Element entry
and press the mouse over the screen (outside the cell), to create a C
atom. Repeat the task to create a H atom. These two atoms will act as
models to create the structure.
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Press Cell->Link and select the Crystal link method.
Initially, the Wyckoff menu (in Position page) only
has the option, 1 Basis 1, which is the usual crystallographic
base or motif. The first "1" indicates the number of objects that will
be linked to each crystallographic node, and the last "1" the point symmetry.
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Press the mouse over the cell to identify it. As the cell belongs
to space group 62, the Wyckoff menu is automatically updated
to include options for all the Wyckoff positions available for this
space group: 8 d 1, 4 c .m., 4 b -1 and 4 a -1.
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Press the mouse over the C atom, to identify the atom used as a model
to create the C atoms of the crystal.
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According to literature, C atoms occupy Wyckoff positions c, so select
these positions in the Wyckoff menu: 4 c .m.. For these positions,
the y coordinate is known in advance, so the y entry is automatically
disabled.
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Make the x, z coordinates equal to 0.0330, 0.0660,
respectively, and press Ok. 4 atoms of C are added to each node of the
cell (and removed if they fall outside the cell volume).
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Repeat the link procedure, this time to add H atoms. Press the mouse first
over the cell, and then over the H atom. Select again Wyckoff positions c,
make the x, z coordinates equal to 0.1898, 0.0520,
respectively, and press Ok. 4 atoms of H are added to each node of the
cell (and removed if they fall outside the cell volume).
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Repeat the link procedure, to add the remaining H atoms. Press the mouse
first over the cell, and then over the H atom. Select again Wyckoff positions c,
make the x, z coordinates equal to 0.0339, 0.2607,
respectively, and press Ok. 4 atoms of H are added to each node of the
cell (and removed if they fall outside the cell volume).
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The atomic structure is now created. To remove the two C,H atoms used
as models during the building process, press Atom->Remove and
click the mouse over them.
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To create the C-C and C-H polyethylene bonds, press Bond->Create,
select the method Length and press Ok.
- To simplify the visual analysis, press Layer->Modify,
change Projection to Orthographic, and press Ok.
- To reduce visual clutter, press Cell->Modify and change
Borders to Faces or even Edges (in View
page). Set the Euler angles E1,E2,E3 to
0,0,0 and 90,90,90,
(in Position page) to get lateral and top views,
respectively, of the polymer chains. Press Ok to activate
the changes.
- Rotate,move,scale the polyethylene cell with the mouse, to see the
ziz-zag chains (and the partly-formed chains in the outside). Press
Atom->Measure to determine lengths and angles between atoms.
