On the Glass Transition in Polymer Films: Recent Monte Carlo Results
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157 Mat. Res. Soc. Symp. Proc. Vol. 543 0 1999 Materials Research Society
The Bond-Fluctuation Model In the bond-fluctuation model the polymers reside on a simple cubic lattice, each monomer occupies a whole unit cell of the lattice, and the monomers are connected by bond-vectors which fluctuate in length and direction (see Fig. 1). The range of this fluctuation is limited -
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L
.D
.. •
jump forbidden
Figure 1: Sketch of the simulation geometry (left panel) and of the model (right panel). The simulation box is confined by two hard walls in the z-direction, which are a distance D apart (D = 6 - 30 ; (1 - 6)Rg; Rg: bulk radius of gyration). In the x- and y-directions periodic boundary conditions are used (exemplified by the bond leaving the bottom and reentering at the top). The linear dimension in these directions is L = 30. The right panel shows a possible configuration of two different chains. All bonds have energy C (E/kB = 1: this defines the temperature scale) except the bond (3, 0, 0) which is in the ground state (two-level system). This vector blocks four lattice sites (marked by o) due to the excluded volume interaction. This interaction also forbids the jump in direction of the arrow. by the local self-avoidance of the monomers and the uncrossability of the bonds. To simulate a dense melt, a volume fraction of about 53 % of lattice sites is occupied by monomers. The chosen chain length is N = 10 (N < N. • 30; Ne = entanglement length) [4]. A thin film geometry is modeled by two hard walls on opposite sides of the simulation box (z-direction), whereas periodic boundary conditions are used in x, y-directions (see Fig. 1). Effectively, this simulates an infinitely long polymer film embedded between two solid, (chemically) equivalent substrates. In the simulation the distance D between the two hard walls ranges from about once to about 6-7 times the bulk radius of gyration Rg. The sketched model is still completely athermal: there is only chain connectivity and excluded volume interaction. In order to drive the glass transition by temperature, we additionally associate a finite energy with the bond vectors (see Fig. 1). Bonds having a length of three and pointing along the lattice axes are favored energetically. Figure 1 shows that a bond in the ground state blocks four additional lattice sites which cannot be occupied without violating the excluded volume condition. This loss of available volume generates a competition between the stiffening of a chain and the packing constraints of the melt. Therefore, some bonds are forced to remain in the excited state. They are geometrically frustrated [4, 5]. The development of the geometric frustration during the cooling process
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causes the glassy behavior of the model. SELECTED STATIC AND DYNAMIC PROPERTIES Static Properties To exemplify the static properties of the model, Fig. 2 shows the profile of the endto-end vector, measured parallel and perpendicular to the wall. For the interpretation of
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