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The applet runs a 2-dimensional (2D) chain over a wide range of temperature. A 2D model is used instead of the real-world 3D version because the latter model takes much
longer time to compute.
The chain model consists of beads (strictly speaking they are regarded as disks in 2D model but we will stick to beads as a matter of consistency) connected in a successive manner via linkages, each of a
fixed unit length. In order to simulate the solvent conditions we can manipulate the interactions between beads. In this way we do not need to explicitly introduce solvent molecules into our model. This is one of the approach that
is usually employed in computational modellings: we simplify the model to concentrate only on subject of interests, and either ignore or introduce some kind of approximations to other entities.
In this case details on how solvent molecules interact with the polymer chain model are not important. We therefore introduce a mathematical form that describes interactions that implicitly include the temperature-solvent effects. The solvent molecules that we have
ignored can significantly reduce the computational costs.
These mathematical equations are more commonly known as the potential functions. We have chosen one of the simplest and commonest form, namely the Lennard-Jones 12-6 potential functions,V, of which is defined as follows:
Where e is the strength (or 'stickiness') between beads, s is a measure of the size of a bead and r is the distance between two beads. A graph of V versus r is shown below with e = 2.0 and s = 0.8 :
A positive energy V is not favorable while a negative energy is favorable. Note that V = 0 at r = s. The energy quickly climbs to some large positive values when the distance is smaller then s. This means that beads do not like to squeeze with each other too hard when the distance
is smaller then their normal excluded size. However, the most preferred distance between two interacting beads lies around r = 0.9, where the energy is most negative (-e). As the distance increases the energy quickly increases indefinitely towards zero. This means that at large distance a bead
almost does not 'feel' the presence of the other bead.
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