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So where is the temperature parameter? Well, it is in fact indirectly related to the reciprocal of e, or 1/e. So, if temperature is high, then e is
small and this enable the beads to easily 'climb out' from the well depth and move away from other beads. This corresponds to a chain in an expanded conditions. Conversely, if the temperature is small, then e becomes large. The beads would then
prefer to get close to one another and it takes a lot more effort for them to move away from one another. Consequently, you get a chain with compact globular shape.
Notice that we use the term 'well depth' as e is sometimes referred to as the energy well depth. One can imagine by placing a bead in the 'well' of the energy curve on Page 11. The deeper the well (large value of e)
the more difficult for the bead to escape. If there is no external influence, once any pair of beads stick together, what makes them to move apart? Well, remember in our previous discussion the chain structure is constantly changing due to the thermal effects - The molecules are constantly
in motion at any given temperature. Naturally, molecules move faster at higher temperatures and slower at lower temperatures. Furthermore, in a many-body system (a model consists of more than two beads), there is a complex interplay among the beads which constantly repelling and attracting
with one another. Any two beads may not stick to each other at the optimal distance but will be at a distance that is depended upon the positions of other beads.
In the illustrative example of random sampling described in Page 1, we have mentioned of randomly placing disks in a square. A disk is placed in the space without any prior knowledge of any other disks that are already present in the space. This may increase
the chance of unsuccessful insertion (due to overlapping) of a disk as the number of disks already present in space increases. Consequently, this leads to a high rejection rate. In the case of a polymer system, this 'overlapping' problem is called the attrition problem. It becomes more severe
as the chain length is large or the temperature is very low. In other words, the attrition problem is particularly apparent when the density (number of beads occupy per unit volume) is high. In the MCPoly program, a sophisticate MC method is used in order to reduce this problem.
The method is described in details in the following page.
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