fall 09 lm _11 polymer structure

# fall 09 lm _11 polymer structure - Chem 481L Lab Module#11...

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N R 2 2 σ = Chem 481L Fall 2009 Lab Module #11 Structure of Polymer Chains Due Date: Noon, Tuesday, November 24 Submit via Blackboard Goal: In this module, you will determine the scaling relationship between the root-mean-square distance separating the chain ends of a polymer, < R 2 > 1/2 , and N , the number of repeating units in the chain. In other words you will determine the value of the exponent ν in the scaling relationship < R 2 > ~ NA ν . Research questions: 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 distance? Introduction 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 linear fashion. 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. Ideal Chains : 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

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## This note was uploaded on 03/03/2010 for the course CHEM 431 taught by Professor Pielak during the Spring '07 term at UNC.

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fall 09 lm _11 polymer structure - Chem 481L Lab Module#11...

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