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MC Polymer
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Universal Behavior
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universal behavior, page 8 Coil-Globule Transition, Page 9 Coil-globule transition, page 10

Note that n for different polymers would be similar only if the conditions such as temperature and space dimension are the same. At a higher temperature interactions between solvent molecules and polymer molecules are more important than interactions among the polymer molecules. As a result, the polymer chain is in expanded form - Beads do not like to come close to each other. In this case, it is found that n has a value of about 0.6 in 3-dimensions.

At a low temperature, interactions between beads now becomes more important than those of between solvent and polymer beads. In this case the polymer collapses to form a compact globular (ball shape) structure with n = 1/3. At an even lower temperature a polymer chain may be completely separated from solution (phase separation). That is, the solution become cloudy and the polymer is no longer soluble in the solution.

Between the extremes there lie a region whereby both competing interactions are equal and cancel each other. At this point the chain is said to exist at the q (theta) point. Theta chains are fascinating because it is a transition or crossway structure between the expanded structure and collapsed globular structure. The change of polymer structure as the the temperature changes is called the coil-globule transition (the expanded form is sometimes referred to as a coiled structure). The graph shows below illustrates the transition.

coil-globule transition curve
An example graph illustrates a coil-globule transition for a given chain length. The green strip refers to the theta region.

Note that at regions of either very high or very low temperatures there is little change in <s2> as the temperature changes. However, dramatic changes in polymer structures (and hence the properties) occur at the theta region. We indicate the approximate location for the theta region as in reality it is difficult to pinpoint the exact location of the theta point.

universal behavior, page 8 coil globule transition, page 10

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