A computer-based lattice model of the step growth reaction of an AB2 monomer, the next elaborate system after an AB monomer, has been devised that allows the simultaneous and explicit occurrence of inter- and intramolecular reactions of A and B groups of the flexible and moving molecules according to Monte Carlo selections of pairs adjacent on the lattice. Though cyclizations are infrequent in comparison to the reactions that develop the branched structures, they do occur, as they accumulate they consume a proportion of the A groups, and so they prevent the development of infinite branched molecules with fractal characteristics. Growth stops when each molecule contains a cycle. For the model explored, in which six lattice sites are used for each monomer, the limiting value of the number average degree of polymerization, 〈x〉n,∞, is 14.6(±0.3) (after infinite time). The occurrence within the system of rings of m residues (m=1,2,3,…) is found to depend upon m and the extent of reaction of the A groups, pa, according to Rm=C0pamm−2.71, the constant C0 reflecting the structure of the lattice and the monomer, and being shown to determine the final degree of polymerization. The exponent of the integers m is apparently −e, so when pa=1 the total number of rings of the molecules is given by the product of C0 and the Euler–Riemann ζ function, ζ(e), a finite number. C0 is obtainable by experiment from 〈x〉n,∞ at the end of the reaction of a real AB2 monomer. Flory’s distribution functions for the numbers and weights of AB2 polymers may be modified to allow for these cyclizations in a procedure which is useful during the early and middle courses of the reaction. However, at the end when cycle formation has come to dominate, the number and weight distribution functions for the first fifty molecules of size x also have the form of a power function [the terms of ζ(χ)] i.e., Nx=Nx,1x−1.5. As each molecule eventually contains one cycle, Nx,1=C0 ζ(e)/ζ(1.5). Since for the weight distribution χw=0.5, the total weight in the system Nx,1Σx−χw diverges, and so there is a limit to the size of x. We present a method for ordering the nodes within a particular structural isomer, priority going to the nodes that bear a loop, and then following its extent of reaction, and if necessary the extent of reaction of its neighbors (and so on). In this way the nodes in each structural isomer of the oligomers of a particular size may be characterized and identified. A mean extent of reaction vector, Px,p, may be obtained for the oligomers of size x at an extent of reaction, pa, to describe the mean extents of reaction of the ordered nodes and to convey the scope for further reactions at those nodes. From the data structures of the model we present information on the proportions of the different structural isomers of the smaller oligomers that are identified by this means, and provide mean connectivity or Kirchof matrices, Kx,p, to describe the patterns of linking between the ordered nodes for examples of certain sizes of the species at selected stages of the reaction.
No abstract
The properties of a 100 penetration grade bitumen are modified considerably, and in a number of ways by the addition of 10 to 40 parts per hundred (pph) of a homopolystyrene and graft, block and random copolymers of styrene with butadiene and acrylonitrile. At low temperatures some blends have a similar stiffness to or even lower stiffness than the bitumen, but generally the blends are more than one order of magnitude stiffer, even when a rubber is added. The contrasting behavior is displayed by a polystyrene and a high impact polystyrene, ∼3% to 4% of grafted rubber on the latter being sufficient to cause the enhancement, even at the 10 pph level, by two different random styrene‐butadiene copolymers, and also by blends consisting of different amounts of SBS block copolymer. Some polymers apparently trigger a Hartley inversion of the micellar structure of the asphaltene micelles. High low temperature stiffness correlates roughly with a lower Tg' as measured by the peak maximum in the E″ plots of the dynamic mechanical thermal analysis (DMTA) and by the steps in the differential scanning calorimetry (DSC) curves at temperatures below O°C. Tan δ maxima and DSC traces detected the glass transition in the continuous phase and in the dispersed phases, but none of these amorphous polymers formed a crystalline phase, though the DSC traces of the polystyrene and the SBS blends suggested that the polymer‐rich phases underwent an aging/ordering process on cooling. Our SBS blends differ in phase inversion behavior and the pattern of loss processes from others that had a smaller asphaltene component.
A study has been performed of the manner in which two structural features of poly(olefin sulfone)s, helical backbones and calamitic side chains, create order in films. For this purpose copolymers were prepared with one (polymer I) or two (polymer III) cyanobiphenyls per residue, and terpolymers were prepared with both such residues diluted to below the 5% level within an otherwise poly(eicosene sulfone) chain (respectively, polymers II and IV). The polymers all have ordered phases according to X-ray powder diffraction studies on samples cooled from the melt, a layer spacing of about 45 Å being detected in the films as in the bulk. Those polymers with mainly eicosene sulfone residues had crystalline phases with large domains, the layers deriving from the helical backbones alone, the smectic A phases of the parent poly(eicosene sulfone) being either suppressed or reduced in extent by the presence of the aromatic moieties, which were almost randomly orientated. Those with one or two cyanobiphenyls per residue were liquid crystalline. In the latter the layer spacing derives from both backbone and side chains and is reduced when the residues bear a second mesogen as a consequence of a constraining effect from the stiff backbone, as a novel model predicts. The spacers give rise to a glass transition and segregate the planes in which the stiff backbones are assembled from the regions in which the aromatic groups aggregate on account of the strong pi-pi interactions. Amorphous and optically isotropic spun cast films of these polymers became ordered on cooling from the melt or just on annealing, with the order, as determined by studies on the optical properties, being homeotropic for the aromatics and being planar for the backbones in a monodomain. For this arrangement we introduce the term homeo-planar smectic. Order parameters as high as 0.63 were measured for polymer I, from a clear film. The cyanobiphenyl chromophores formed H aggregates, with blue shifts in absorption and red shifts in fluoresence, and a little surprisingly these resulted in a circular dichroism, detectable when the films were inspected at an angle of 45 degrees to the normal.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.