Macromolecules with internal rigidity

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

The pressure p includes both the partial pressure of the gas of Brownian particles n(N +1 )T and the partial pressure of the carrier monomer liquid. We shall assume that the viscosity of the monomer liquid can be neglected. The variables xt k in equation (9.19) characterise the mean size and shape of the macromolecular coils in a deformed system. The other variables ut k are associated mainly with orientation of small rigid parts of macromolecules (Kuhn segments). As a consequence of the mesoscopic approach, the stress tensor (9.19) of a system is determined as a sum of the contributions of all the macromolecules, which in this case can be expressed by simple multiplication by the number of macromolecules n. The macroscopic internal variables x -k and u"k can be found as solutions of relaxation equations which have been established in Chapter 7. However, there are two distinctive cases, which have to be considered separately. 

The lubricity theory explains the resistance of a polymer to deformation. Stiffness and rigidity are explained as the resistance of intermolecular friction. The plasticizer acts as a lubricant to facilitate movement of macromolecules over each other, thus giving the resin an internal lubricity. The gel theory is applied to predominantly amorphous polymers. It proposes that their rigidity and resistance to flex are due to an internal three-dimensional honeycomb structure or gel. The spatial dimensions of the cell in a brittle resin are small because their centers of attraction are closely spaced and deformation cannot be accommodated by internal movement in the cell-locked mass. Thus, the elasticity limit is low. Conversely, a thermoplastic or thermosetting polymer with widely separated points of attachment between its raacroraolecules is flexible without plasticization. 

Additional tests of the force field are also performed on molecules and macromolecules in the condensed phase. As an example of the accuracy of CFF-calculated structures, the results for eight cyclic peptide crystals show that the rms deviation between experimental and calculated positions of all atoms (except hydrogens) is 0.18 A. In contrast to the previously discussed crystal structure calculations with rigid molecules, all degrees of freedom, including the internal coordinates, are relaxed in this result. Thus, this is a validation of both the intramolecular and intermolecular CFF interactions. 

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