Trans Placements , Expansion , and Asymmetry of Starlike Polyethylenes Bearing Similarly Charged Ends

Average configuration-dependent physical properties have been evaluated for tri-, tetra-, and hexafunctional polymethylene stars perturbed by electrostatic repulsion of charges placed at the free chain ends. Configuration-dependent properties evaluated were the probability for a trans placement, expansion of (sl), the mean-square radius of gyration, asymmetry of the distribution of chain atoms, and asymmetry of the distribution described by the atoms considered to bear the charges. Perturbations disappear as n, the number of bonds, becomes infinite. When n is a few hundred, the perturbation no longer affects the probability of a trans placement, but it still produces significant alterations in both (s2) and asymmetry. The characteristic ratio, (s2) /nF, for all three types of stars goes through a maximum as n increases in a medium of low dielectric constant. However, the manner in which the increase in ( s 2 ) is accommodated along the three principal axes depends on both n and the functionality of the branch point. Linear bolaform electrolytes, i.e., molecules with the chemical structure Y-X+(CH2)xX+Y-, are simple molecules which possess some of the characteristics of polyelectrolytes.' Thus electrostatic interaction causes primary and secondary dissociation constants for bolaforms of finite x to differ by more than the ratio (4) expected in the absence of any interaction of the chain ends. The ratio of dissociation constants must become 4 as x becomes infinite. Configuration-dependent properties of the intervening polymethylene chain can be altered by electrostatic interaction of charged chain ends in the completely dissociated bolaform, X+(CH2)xX+. For example, if x is about lo2, interaction of charged chain ends produces an enhanced probability that a bond will occupy a trans placement, an increase in mean-square radius of gyration, and an increased asymmetry of the distribution of chain atomsS2 While these changes are all in the direction which brings about an approach to rodlike behavior, such bolaforms are nevertheless more accurately described as coils than as rods.2 There is another regime, > x >> 102, where there is no significant affect on the probability of a trans placement, but the chain is nonetheless expanded and has a higher asymmetry than that seen in the unperturbed state.2 Chain expansion, in the absence of any alteration in the probability of a trans placement, can also be observed with chains perturbed through attachment of an end to an impenetrable interface3 and in chains expanded by the intramolecular excluded volume e f f e ~ t . ~ ? ~ Our concern here is with branched-molecule equivalents of linear bolaform electrolytes. A general formula for the completely dissociated form of these molecules is Z[(CH2)xX+]f, where Z denotes the branch point of the f-functional star. These stars are perhaps primitive schematic models for micelles formed by aggregation of f molecules of the form H(CH2)xX+. Linear bolaform electrolytes are obtained with Z = CH2, f = 2. Three branched bolaforms are treated here: (a) f = 3, Z = CH; (b) f = 4, Z = C; (c) f = 6, Z = carbon skeleton of benzene. The only perturbation considered is that arising from electrostatic interaction of charged chain ends. Configuration-dependent properties of interest are the molecular expansion, alteration in the probability for observation of a trans placement, distortion of the asymmetry of the distribution of all chain atoms, and asymmetry of the distribution described by atoms at the charged chain ends.