Characteristic Ratio
Reference: [Sperling-174]
- C is the characteristic ratio.
- l
is the length of the "line", or the length of
the monomer [Sperling-173].
is the theoretical
end-to-end distance
[Sperling-173]. The
bar means that you are taking the average of a set of "simulations."
Maybe you asked a computer to do the "random walk" 500 times.
- the subscript f is a reminder that the math done here is for
the case of a "freely jointed chain", sometimes referred to as a
"random walk." In the freely jointed chain model each monomer is
approximated to be a line of known length, and these lines are
connected end to end, with no regard for the angle at which they
are placed with respect to each other. Said another way, angles
between joined "lines" are completely random.
-
x
is the number of monomers in the the chain,
also known as the degree of polymeriation. [Sperling-173] says
"number of links" instead of number of monomers, and technically
the number of links is one less than the number monomers linked.
- I think Sperling's reference to "foliage" refers to the presence
of side chains.
Last Update- September 16, 1995- wld