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Lecture4Notes - Lecture 4 Polymer Conformation Real Chains...

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Lecture 4: Polymer Conformation Real Chains 1 Monday, October 4, 2010
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Recall from last time … A polymer can adopt many conformations Polymers with no interactions between monomers separated by many bonds along the chain are called IDEAL CHAINS The mean square end to end distance for an ideal (long, linear) chain is: C is a characteristic ratio that describes the stiffness of the chain We have defined the Kuhn segment, b , for a polymer chain, which is related to the number of monomers N. From the Kuhn segment, we obtain an expression for the mean square end to end distance for ideal chains Several models of ideal chain conformation exist: freely rotating chain, freely jointed chain, worm-like chain, hindered rotation and rotational isomeric state The mean square radius of gyration, < R g 2 >, is defined as the average square distance from all monomers to the center of mass of the polymer General scaling for IDEAL CHAIN: R 2 C nl 2 2 R N 1 2 Monday, October 4, 2010
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Polymer Conformation The conformation of a polymer chain will be strongly affect by the intra- and intermolecular interactions of the chain with itself and its environment In order to better understand and predict the 3D shape of a polymer chain based on these interactions, we need a starting point (we did this last time) Models of conformation often treat polymers as ideal chains, but the real world (and our experiments) is more complicated DEFINITIONS Ideal chain: no interactions between repeat units far apart along the chain, even if they approach each other in space (do not interact with solvent or itself) Real chain: attractive and/or repulsive interactions between/within repeat units as well as with solvent (interacts with solvent and itself) 3 Monday, October 4, 2010
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Today’s Concepts Real chains do not exist in a vacuum, but rather in a solution with either solvent, or other chains surrounding them Real chains have interactions with the things surrounding them, and between monomers along the chain These interactions can be described in terms of excluded volume , which describes the net two-body interaction between monomers Temperature can affect excluded volume When concentration is high, net three body interactions become important A polymer “solution” can be described as good, theta, and poor; these can change with concentration 4 Monday, October 4, 2010
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Potential Energy r Potential Energy versus Distance Too crowded - repulsion Perfect balance of attraction and repulsion Too far away Potential due to repulsive forces Potential due to attractive forces 5 Monday, October 4, 2010
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Possible interactions of beads on the chain Dispersion forces (van der Waals) Dipole/dipole interactions Hydrogen bonding Coulombic Interactions 6 Monday, October 4, 2010
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van der Waals Forces, dipole dipole interactions weak interactions between dipoles ( δ + and δ - ) alignment of liquid crystals, gecko adhesion φ LJ ( r ) = 4 ε σ r 12 σ r 6 ϕ
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