Random coils ideal

Fig. 10 Equilibrium radius of gyration of a molecule plotted as a function of temperature the molecule is composed of 1000 beads. The radius of gyration shows a steep increase and a large fluctuation above 700 K. The insets show typical chain conformations at indicated temperatures. Note that the ideal random coil state of this fully flexible chain should have the mean-square radius of gyration R2 = 1000 x (1.54/3.92)2/6 = 25.7, the value is around 800 K...

Unfortunately, for some solvent-polymer combinations, even for nearly ideal random coils such as polystyrene, the coefficients are not constant but vary with molar mass. 

The hydrophobic core of worm-like micelles may be further related to the molecular weight of the copolymers hydrophobic block. A fully stretched block of N/ monomer units would theoretically assemble into an object with diameter, d Np,, and blocks of ideal random coils would have d The strong segregation limit (SSL) theory predicts that strong segregation balances the interfacial tension against the chain elasticity and that the core diameter, d, of the worm micelles would scale with ZVai of the hydrophobic block at ... 

For ideal random coils, the relationship between and<5 >(j is simply... 

For example, [p] for an ideal random coil in -solvent conditions is [29]... 

It was shown that for an ideal random coil undergoing random degradation, the number of bonds cleaved per second per g mol of polymer mass is given by [16] ... 

In dilute solution, the properties of the polymer are characterized by the interaction between the solvent and the polymer. In a good solvent, the polymer appears swollen and occupies a large volume. In this scenario, intermolecular forces between the solvent and monomer subunits dominate over intramolecular interactions. In a bad solvent or poor solvent, intramolecular forces dominate and the chain contracts. In the theta solvent, or the state of the polymer solution where the value of the second virial coefficient becomes 0, the intermolecular polymer-solvent repulsion balances exactly the intramolecular monomer-monomer attraction. Under the theta condition (also called the Flory condition), the polymer behaves like an ideal random coil. 

In dilute solutions in a theta solvent, flexible polymer chains are in an isolated, ideal random coil state. For description of the dynamics in such solutions, Zimm model subdivides the chain into subchains (cf Figure 2), represents the friction and elasticity of the subchain by a bead (friction center of the subchain) and the entropic springs conneaing the beads, respectively, and analyzes the motion of this bead-spring chain in the presence of hydrodynamic and thermal... 

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