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One good starting point to understand the chain-like behavior is to consider dilute polymer solutions. This essentially means a small mount of a polymer dissolves in a
solvent such that a polymer chain is completely surrounded by solvent molecules and it cannot ‘detect’ the presence of other chains. At any temperature, the molecules are moving all the time, in random directions (thermal effects). Consequently, a polymer chain is
constantly evolving to different shapes which are depended on the nature it interacts with the solvent molecules and among the beads within the polymer chain itself.
Diagrams showing different polymer shapes under the influence of thermal effects. The solvent molecules are not show for clarity purposes. Diagram on the left shows 5 arbitrary shapes. On the right, the diagram illustrates the beads’ movement over 5 unit times.
Unlike the example given in Page 1, the beads are very much restricted by chain linkages. However, the diagram on the left shows that a polymer chain can still be conformed to a variety of different shapes, even if the beads do not penetrate (or overlap) one another.
It is therefore obvious that a MC technique can be used to generate these structures. Note that there is no information to show how a polymer structure changes over time. This is where a MC technique excels. It is particularly suited to obtain observables where time elements are not important by
statistically generating chains with a wide range of different arrangements. As a matter of completeness, the diagram on the right illustrates little change in polymer structure as time evolves. That is why simulation techniques that trace out temporal trajectories may not be suitable to calculate time-independent observables
because long simulation times is required to map out a wide range of polymer structure.
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