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The inherent universal nature of chains is the fundamental reason why an apparently complicated polymeric material can be studied in a much simpler approach. As we have already
briefly mentioned in Page 5, quite often different polymer chains behave in a similar way even though the intricate bead structures are different. To illustrate this point we will again consider a polymer chain dissolves in a solvent and measure the quantity s.
Provided N is large, the quantity s2 scales as follows:
The first thing one may notice is that the equation to describe the complicated structure of a chain is incredibly simple (you may not like mathematics but believe me, it is really simple!). The quantity n (Greek letter pronounce as ‘nu’) is a universal quantity
which is similar for all types of chains. The quantity 'A' is called the pre-exponential factor. This quantity is NOT universal and is related to the detail chain structures such as the nature of beads and linkages. Different polymer chains will have different values of A
To determine n in computer simulation we can run a series of MC simulations for several values of N to obtain the corresponding values of <s2>. A graph of <s2> versus N can be plotted using a
graph plotting package and the n can be obtained from subsequent graph-fitting procedure using the above mentioned equation.
An example graph of <s2> versus number of links, N. The curve shows the scaling relationship according to the equation shown above with n = 0.6.
The curve can be fitted using, say, 5 or more different sets of data.
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