Conformational Properties of Bolaform

Average configuration-dependent physical properties have been evaluated for polymethylene chains bearing similarly charged ends. The polymethylene chain contains upward from 20 bonds, and the dielectric constant of the medium ranges upward from 3.5. Configuration-dependent properties evaluated were the persistence vector, average center-of-mass vector, mean-square end-to-end distance, mean-square radius of gyration, averages of corresponding momenta of the inertia tensor, and the probability of observation of a trans placement at an internal bond in the chain. The perturbation produced by the charged ends disappears at sufficiently large chain length. However, a large number of bonds (well in excess of 300) may be required to eliminate the effect of the perturbation. The characteristic ratio goes through a maximum at finite chain contour length in media of low dielectric constant. This behavior is not restricted to bolaform electrolytes formed from polymethylene. I t will be observed with any flexible bolaform electrolyte. Significant expansion of the chain, and alteration in the asymmetry of the distribution of chain atoms, can be observed even when the probability for a trans placement is indistinguishable from that found in the unperturbed chain. While the alteration in the distribution of chain atoms serves to increase the asymmetry, the perturbed molecules are still more accurately described as random coils than as rods with charged ends. Possibly the simplest class of molecules that possess some polyion characteristics are the bolaform electrolytes, i.e., molecules of chemical structure Y-X+(CH2),X+Y-.' Primary (K,) and secondary (K,) dissociation constants for bolaform electrolytes would differ by a factor of 4 if there were no interaction of the identical groups at opposite ends of the polymethylene chain. Electrostatic interaction of the end groups causes K l / K 2 to actually be greater than 4. In addition to modifying the dissociation constants, the electrostatic stress present in the completely dissociated bolaform electrolyte, X+-(CH2),-X+, perturbs configuration-dependent properties of the intervening polymethylene chain. The repulsion between charged ends is minimized when the end-to-end distance is at its upper limit, Le., when the polymethylene chain is in the planar zigzag configuration with all bonds occupying trans states. This configuration could be modeled as a rod with charged ends. The tendency for the bolaform electrolyte to become rodlike is opposed by the tremendous reduction in configurational entropy associated with complete suppression of configurations containing one or more gauche placements. In general, one expects the balance between these two effects to produce configuration-dependent properties lying somewhere between those associated with the unperturbed and fully extended chains. Our objective here is to characterize configuration-dependent properties of bolaform electrolytes in which the only perturbation of the polymethylene chain is that arising from the electrostatic interaction of similarly charged ends. Of particular interest are the magnitudes of the chain expansion, alteration in the probability for observation of a trans placement, and distortion of the average asymmetry of individual chain configurations (including an assessment of the appropriateness of a model in which the bolaform electrolyte is taken to be a rod with charged ends).