Lab Module #11
Structure of Polymer Chains
Noon, Tuesday, November 24
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In this module, you will determine the scaling relationship between the root-mean-square
distance separating the chain ends of a polymer, <
, the number of repeating units
in the chain.
In other words you will determine the value of the exponent ν in the scaling
> ~ NA
How does the end-to-end distance of a polymer chain scale with the
number of repeating units in the chain?
How does VS compare with predictions made by
various chain equations of state?
What is the temperature dependence on the end-to-end
An individual polymer chain can be characterized by its degree of polymerization, N, where N is
the number of monomer units in the chain. This quantity N is proportional to the molecular mass
of the chain and to its contour length (defined as N multiplied by length of a single unit).
The monomer units that compose a polymer chain in solution, however, are rarely aligned in a
Given the chain’s flexibility, it is usually folded.
One of the variables used to
describe the physical state (conformation) of a chain is its spatial size, and this quantity can be
defined in a variety of ways.
Rubinstein & Colby, for instance, characterize the spatial quantity
by the chain’s radius of gyration.
A more straightforward quantity is the root-mean-square end-
to-end distance, which scales with N the same way as the gyration radius.
For example, the conformation of the chain may be very compact; this is likely in the globular
state, and corresponds to a lower value of the end-to-end distance.
The coil state, with its
greater end-to-end distance is much less compact.
Thus, root mean square end-to-end
distance is a useful variable, and polymer scientists are interested in how this distance scales
with N because this yields information about the chain conformation. Also of practical interest,
the end-to-end distance is measurable in experiments.
: The model of an ideal macromolecule plays the same role in polymer physics as
the notion of an ideal gas in traditional molecular physics. This model represents a chain of
immaterial units, each joined with two nearest neighbors and having no interaction either with
solvent molecules or with other monomer units of the same or another macromolecule. There
are several theoretical models of ideal chain; they differ from one another in unit structure and
the type of bonding between the nearest neighbors. The common “ideal” feature of all these
models is the absence of volume interactions. This leads, in particular, to the fact that all these