Jointed Bead-Rod Model, Three Beads

LINEAR FLEXIBLE RANDOM COILS THE BEAD-SPRING 

If external shearing forces are applied to the dilute solution, and they are small enough to correspond to the usual restrictions of linear viscoelastic behavior, the assortment of configurations and the rates of configurational change are only slightly disturbed the Brownian motions go on just the same. But these motions 

A qualitative discussion could be pursued in terms of any of the viscoelastic functions surveyed in Chapter 2. It is convenient for the moment to choose the components of the dynamic modulus, G and G . For a periodic strain, the energy storage per cycle depends on G, and is contributed by the polymeric solute molecules alone the energy dissipation depends on G , and has contributions from both solute and solvent. The relative contributions of the solute to G and G depend on the extent to which the Brownian motions are correlated with the external forces. Force in phase with displacement corresponds to energy storage, but force in phase with velocity corresponds to energy dissipation. 

The complete specification of molecular configuration would require a detailed knowledge of the dimensions and shapes of the monomeric units, local packing effects, and interactions with the solvent molecules. A valuable simplification can be made if one is willing to sacrifice consideration of short-range relationships and attendant behavior at the very highest frequencies. It utilizes the principle from polymer chain statistics that any two points on the chain backbone separated by perhaps 50 or more chain atoms will be related to each other in space in accordance with a Gaussian distribution of vectors, -20 provided the solvent is a 0-solvent. In 

A numerical parameter that is commonly used to characterize molecular dimensions of random coils is the characteristic ratio C = where ro is the mean-square end-to-end distance, n the number of chain bonds (in this expression only), and / the bond length. In terms of C , a = 

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