Elastically-jointed-rod chains

To overcome this shortcoming Warner and Wang (1992c) proposed the theory of elastically-jointed-rod chains in which any deviations of consecutive rods orientation causes an energy penalty. 

For the elastically-jointed-rod chain, the nematic mean field energy is expressed as... 

In the elastically-jointed-rod chain, the mean square end-to-end distance along the director tends to be a rod as q approaches infinity or T is very small, he.,... 

The jointed-rod chain is one-dimensional system of a series of repeated segments and we naturally apply the Transfer matrix technique in the Ising model to obtain the partition function for both the freely-jointed-rods and the elastically-jointed-rods. We will not go into the details of this model but instead will show some results derived from the model. 

If < Iq, it becomes the case of the discrete picture and jointed-rods are applicable. If > lo, however, the elastically discrete polymer evolves into a worm chain, i.e., an elastically homogeneous chain. The orientation change can then take place over a length comparable to Iq. With this continuum of allowed orientational states, the worm chain accurately represents the angular entropy of the real polymer. 

At a given force, the elasticity of covalent bonds of the amino acid backbone gives rise to a length increase. But thermal fluctuations act on the backbone, which on an average pulls the cantilever closer to the membrane, a phenomenon referred to as entropic elasticity of linear polymers. The wormlike chain model [50] describes the polymer as an elastic rod with bending stiffness submitted to thermal fluctuations that decrease the end-to-end distance of the rod. Alternatively, the freely jointed chain model calculates the... 

The available experimental material on the processes which take place in lyotropic nematic systems is very limited. The set of different values of the moduli of elasticity ATn, K22, and K -, obtained in one experiment [54] for solutions of PBG in dioxane with addition of trifluoroacetic acid, should apparently be considered especially approximate due to the possible error in the measurement of the anisotropy of the susceptibility mentioned above. As the theoretical calculations in [58] showed, the elasticity coefficients of the polymeric lyotropic nematic are a function of the degree and mechanism of flexibility of the individual polymer chain. Although all moduli should be of the same order of magnitude for rods and freely jointed chains (but should be slightly higher... 

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