Topological Analysis of Long-Chain Branching Patterns in Polyolefins

Patterns in molecular topology and complexity for long-chain branching are quantitatively described. The Wiener number, the topological complexity index, and a new index of 3-starness are used to quantify polymer structure. General formulas for these indices were derived for the cases of 3-arm star, H-shaped, and B-arm comb polymers. The factors affecting complexity in monodisperse polymer systems are ranked as follows: number of arms >> arm length > arm central position approximately equal to arm clustering > total molecular weight approximately equal to backbone molecular weight. Topological indices change rapidly and then plateau as the molecular weight of branches on a polyolefin backbone increases from 0 to 5 kD. Complexity calculations relate 2-arm or 3-arm comb structures to the corresponding 3-arm stars of equivalent complexity but much higher molecular weight. In a subsequent paper, we report the application of topological analysis for developing structure/property relationships for monodisperse polymers. While the focus of the present work is on the description of monodisperse, well-defined architectures, the methods may be extended to the description of polydisperse systems.

[1]  I. Prigogine,et al.  Exploring Complexity: An Introduction , 1989 .

[2]  D. Bonchev,et al.  The problems of computing molecular complexity , 1990 .

[3]  H. Hosoya.  Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons , 1971 .

[4]  Danail Bonchev,et al.  Novel Indices for the Topological Complexity of Molecules , 1997 .

[5]  K. Wagener,et al.  ADMET Modeling of Branching in Polyethylene. The Effect of a Perfectly-Spaced Methyl Group , 1997 .

[6]  Albert H. Widmann,et al.  Simulation of the intrinsic viscosity of hyperbranched polymers with varying topology. 1. Dendritic polymers built by sequential addition , 1998 .

[7]  Holger Frey,et al.  Degree of branching in hyperbranched polymers , 1997 .

[8]  Mircea V. Diudea,et al.  Molecular Topology of Dendrimers , 1999 .

[9]  Jean M. J. Fréchet,et al.  One-step synthesis of hyperbranched dendritic polyesters , 1991 .

[10]  M. Pitsikalis,et al.  Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers , 1997 .

[11]  J. Roovers.  Melt rheology of H-shaped polystyrenes , 1984 .

[12]  D. H. Rouvray.  Concepts in Chemistry: A Contemporary Challenge , 1996 .

[13]  Jozef Bicerano,et al.  Prediction of the Properties of Polymers from Their Structures , 1996 .

[14]  T. McLeish,et al.  Parameter-Free Theory for Stress Relaxation in Star Polymer Melts , 1997 .

[15]  T. McLeish,et al.  Stress Relaxation in Entangled Comb Polymer Melts , 1994 .

[16]  R. Larson,et al.  Molecular constitutive equations for a class of branched polymers: The pom-pom polymer , 1998 .

[17]  Tom C. B. McLeish,et al.  Synthesis and Characterization of H-Shaped Polyisoprene , 1996 .

[18]  W. Graessley,et al.  Melt rheology of some model comb polystyrenes , 1981 .

[19]  D. S. Pearson,et al.  Rheological behavior of star-shaped polymers , 1993 .

[20]  H. Mavridis,et al.  Long-Chain-Branching Index for Essentially Linear Polyethylenes , 1999 .

[21]  A. Balaban,et al.  Topological Indices and Related Descriptors in QSAR and QSPR , 2003 .

[22]  Danail Bonchev,et al.  Long chain branch polymer chain dimensions: application of topology to the Zimm–Stockmayer model , 2002 .

[23]  T. Chung,et al.  Synthesis of Long Chain Branched Polypropylene with Relatively Well-Defined Molecular Structure , 1999 .

[24]  D. Bonchev,et al.  A topological approach to the modelling of polymer properties (The tempo method) , 1992 .

[25]  W. Graessley,et al.  Viscoelasticity and self-diffusion in melts of entangled linear polymers , 1997 .

[26]  M. Gordon,et al.  Configurational Statistics of Highly Branched Polymer Systems , 1964 .

[27]  Nenad Trinajstić,et al.  Topological characterization of cyclic structures , 1980 .

[28]  Dennis H. Rouvray,et al.  The modeling of chemical phenomena using topological indices , 1987 .

[29]  N. Trinajstic,et al.  Information theory, distance matrix, and molecular branching , 1977 .

[30]  Bick,et al.  Topological contributions to nonlinear elasticity in branched polymers. , 1996, Physical review letters.

[31]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[32]  Danail Bonchev,et al.  Topological order in molecules 1. Molecular branching revisited , 1995 .

[33]  M. Pitsikalis,et al.  Well-Defined, Model Long Chain Branched Polyethylene. 1. Synthesis and Characterization , 2000 .

[34]  D. Yan,et al.  Molecular Parameters of Hyperbranched Polymers Made by Self-Condensing Vinyl Polymerization. 2. Degree of Branching† , 1997 .

[35]  Ronald G. Larson,et al.  Theoretical Molecular Rheology of Branched Polymers in Simple and Complex Flows: The Pom-Pom Model , 1997 .

[36]  J. K. Doyle,et al.  Mean distance in a graph , 1977, Discret. Math..

[37]  Steven H. Bertz,et al.  Branching in graphs and molecules , 1988, Discret. Appl. Math..

[38]  A. Balaban,et al.  Topological Indices for Structure-Activity Correlations , 1983, Steric Effects in Drug Design.

[39]  M. Gordon,et al.  Theory of Branching Processes and Statistics of Rubber Elasticity , 1965 .

[40]  Bernard Testa,et al.  Complexity and emergence in drug research , 1995 .

[41]  Danail Bonchev,et al.  Graph—theoretical approach to the calculation of physico-chemical properties of polymers , 1983 .

[42]  D. Bonchev,et al.  Comparability graphs and molecular properties: IV. Generalizations and applications , 1990 .

[43]  H. Wiener.  Relation of the physical properties of the isomeric alkanes to molecular structure; surface, tension, specific dispersion, and critical solution temperature in aniline. , 1948, The Journal of physical and colloid chemistry.

[44]  Dennis H. Rouvray,et al.  The limits of applicability of topological indices , 1989 .

[45]  Danail Bonchev,et al.  Overall Connectivities/Topological Complexities: A New Powerful Tool for QSPR/QSAR , 2000, J. Chem. Inf. Comput. Sci..

[46]  William C. Herndon,et al.  The Similarity of Graphs and Molecules , 1986 .

[47]  Steven H. Bertz,et al.  The first general index of molecular complexity , 1981 .

[48]  J. Seppälä,et al.  Influence of the catalyst and polymerization conditions on the long-chain branching of metallocene-catalyzed polyethenes , 2000 .