Polymers statistically coiled

Conformation of macromolecules in solid state and in solution exhibits both many contingencies and restrictions. Coiled conformation of macromolecules is most appropriate for majority of methods employed for molecular characterization of polymers. Statistical coils of macromolecules in equilibrium exhibit large conformational entropy. Any external intervention that leads to a change in the conformation of macromolecules has to surmoimt considerable resistance, which is cormected with the loss of overall conformational entropy. 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

For a statistical coil, the product of polymer intrinsic viscosity and molecular weight is directly proportional to the cube of the root-mean-square radius of gyration RG 77137... 

Flory and Huggins developed an interaction parameter that may be used as a measure of the solvent power of solvents for amorphous polymers. Flory and Krigbaum introduced the idea of a theta temperature, which is the temperature at which an infinitely long polymer chain exists as a statistical coil in a solvent. 

Statistically Coiled Molecules. A polymer such as PVOH contains many single bonds, around which rotation is possible. If the configurations around successive carbon atoms are independent and unrelated, it will be seen that two parts of the polymer chain... 

Most synthetic polymers in which the monomer units are connected via single bonds have rather flexible chains. The bond torsion energy is relatively small and the units can rotate around their bonds [14,30,31]. Each molecule can adopt a large number of energetically equivalent conformations and the resulting molecular geometry is that of a statistical coil, approximately described by a Gaussian density distribution. This coil conformation is the characteristic secondary structure of macromolecules in solution and in the melt. It is entropically favoured because of its... 

The disordered state of a statistical coil is what is displayed by polymers in the molten and amorphous states and also in solution. To describe the conformation of a macromolecule consisting of a main chain N +l atoms, the positions of all them have to be determined. Using vectorial... 

Solid polymers can occur in the amorphous or crystalline state. Polymers in the amorphous state are characterized by a disordered arrangement of the macromolecular chains, which adopt conformations corresponding to statistical coils. The crystalline state is characterized by a long-range three-dimensional order (order extending to distances of hundreds or thousands... 

Kuhn H. Effects of Hampered Draining of Solvent on the Translatory and Rotatory Motion of Statistically Coiled Long-Chain Molecules in Solution. Part II. Rotatory Motion, Viscosity, and Flow Birefringence/i/. Kuhn, W. Kuhn, J. Polymer. Sci. 1952, V. 9,1-33. 

Completely statistical (random) arrangements of the macromolecules without a regular order or orientation, i.e., without constant distances, are known as amorphous states. There is no long-range order whatsoever. The valid model for such states is the statistical coil. This is the dominating secondary structure in synthetic polymers and polymeric solutions. Its determinant parameter is coil density. 

As the radical polymerization model the authors [47] considered the reaction, in which polymer macromolecular coils P were diffused in solution, consisting of statistically located nonsaturating traps T, which were also DMDAACh coils. At coils P and T contact the coil P disappears, forming the larger coil T. Such reactions can be described with the aid of the Eqs. (86) and (88) of Chapter 1. 

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