Lattice model of living polymerization. I. Basic thermodynamic properties

A Flory-Huggins type lattice model of living polymerization is formulated, incorporating chain stiffness, variable initiator concentration r, and a polymer-solvent interaction χ. Basic equilibrium properties [average chain length L, average fraction of associated monomers Φ, specific heat CP, entropy S, polymerization temperature Tp, and the chain length distribution p(N)] are calculated within mean-field theory. Our illustrative calculations are restricted to systems that polymerize upon cooling [e.g., poly(α-methylstyrene)], but the formalism also applies to polymerization upon heating (e.g., sulfur, actin). Emphasis is given to living polymer solutions having a finite r in order to compare theory with recent experiments by Greer and co-workers, whereas previous studies primarily focused on the r→0+ limit where the polymerization transition has been described as a second order phase transition. We find qualitative changes in the properties of living polymer solutions for nonzero r: (1) L becomes indepen...

[1]  Athanassios Z. Panagiotopoulos,et al.  THERMODYNAMICS OF REVERSIBLY ASSOCIATING POLYMER SOLUTIONS , 1999 .

[2]  Gregory B. McKenna,et al.  Arrhenius-type temperature dependence of the segmental relaxation below Tg , 1999 .

[3]  A. Panagiotopoulos,et al.  Micellization in Model Surfactant Systems , 1999 .

[4]  S. C. Greer.  Physical Chemistry of Equilibrium Polymerization , 1998 .

[5]  R. Ivkov,et al.  The polymerization of actin: Study by small angle neutron scattering , 1998 .

[6]  Steven J. Plimpton,et al.  STRINGLIKE COOPERATIVE MOTION IN A SUPERCOOLED LIQUID , 1998 .

[7]  M. Cates,et al.  Computational confirmation of scaling predictions for equilibrium polymers , 1998, cond-mat/9805261.

[8]  A. P. Andrews,et al.  Living poly(α-methylstyrene) near the polymerization line. V. Heat capacity as a function of temperature , 1997 .

[9]  Vicsek,et al.  Formation of complex bacterial colonies via self-generated vortices. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  P. Schurtenberger,et al.  Enormous concentration-induced growth of polymer-like micelles , 1996 .

[11]  D. Landau,et al.  ADSORPTION OF LIVING POLYMERS ON A SOLID SURFACE : A MONTE CARLO SIMULATION , 1996 .

[12]  Akao.  Percolation in a self-avoiding vortex gas model of the lambda transition in three dimensions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Landau,et al.  Monte Carlo study of semiflexible living polymers. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Milchev,et al.  Monte Carlo study of living polymers with the bond-fluctuation method. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Hald,et al.  Vortex renormalization in three space dimensions. , 1995, Physical review. B, Condensed matter.

[16]  C. Angell,et al.  Formation of Glasses from Liquids and Biopolymers , 1995, Science.

[17]  A. P. Andrews,et al.  Living poly(α‐methylstyrene) near the polymerization line. IV. Extent of polymerization as a function of temperature , 1995 .

[18]  Tainaka.  Vortices and strings in a model ecosystem. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Alexandre J. Chorin,et al.  Vorticity and turbulence , 1994 .

[20]  A. Suto.  Percolation transition in the Bose gas , 1993 .

[21]  K. Zheng,et al.  Living poly-α-methylstyrene near the polymerization line. II. Phase diagram in methylcyclohexane , 1993 .

[22]  A. Milchev.  Phase transitions in polydisperse polymer melts , 1993 .

[23]  S. B. Kiselev,et al.  Crossover approach to global critical phenomena in fluids , 1992 .

[24]  G. Williams.  Vortex rings and the superfluid λ-transition , 1992 .

[25]  P. Janmey,et al.  Distribution of actin filament lengths measured by fluorescence microscopy. , 1992, The American journal of physiology.

[26]  J. Dudowicz,et al.  Effect of monomer structure and compressibility on the properties of multicomponent polymer blends and solutions: 1. Lattice cluster theory of compressible systems , 1991 .

[27]  R. Durrer,et al.  Cosmology in the Laboratory: Defect Dynamics in Liquid Crystals , 1991, Science.

[28]  O. Webster.  Living Polymerization Methods , 1991, Science.

[29]  Lund,et al.  Critical properties of a dilute gas of vortex rings in three dimensions and the lambda transition in liquid helium. , 1990, Physical review. B, Condensed matter.

[30]  S. C. Greer,et al.  Shear viscosity of liquid sulfur near the polymerization temperature , 1989 .

[31]  Shenoy.  Vortex-loop scaling in the three-dimensional XY ferromagnet. , 1989, Physical review. B, Condensed matter.

[32]  Tanaka,et al.  Tricriticality in thermoreversible gels. , 1989, Physical review letters.

[33]  M. Bawendi,et al.  Lattice theories of polymeric fluids , 1989 .

[34]  Pollock,et al.  Path-integral simulation of the superfluid transition in two-dimensional 4He. , 1989, Physical review. B, Condensed matter.

[35]  H. Kleinert,et al.  Self-avoiding random loops versus Ising model in three dimensions , 1988 .

[36]  C. Dasgupta,et al.  Role of topological defects in the phase transition of the three-dimensional Heisenberg model , 1988 .

[37]  David P. Landau,et al.  Computer Simulation Studies in Condensed Matter Physics , 1988 .

[38]  Williams.  Vortex-ring model of the superfluid lambda transition. , 1987, Physical review letters.

[39]  M. Bawendi,et al.  A lattice model for self‐ and mutually avoiding semiflexible polymer chains , 1987 .

[40]  Wills,et al.  Role of vortex strings in the three-dimensional O(2) model. , 1986, Physical review letters.

[41]  G. Faivre,et al.  Viscoelastic properties and molecular structure of amorphous selenium , 1986 .

[42]  J. Israelachvili.  Intermolecular and surface forces , 1985 .

[43]  J. Wheeler.  Symmetric and nonsymmetric tricritical points in liquid sulfur solutions , 1984 .

[44]  J. Wheeler,et al.  Heat capacity of doped liquid sulfur at the polymerization transition, a nonclassical model , 1984 .

[45]  P. Flory.  Molecular theory of liquid crystals , 1984 .

[46]  C. Dasgupta.  Duality maps for a lattice model of the smectic-A-nematic transition , 1983 .

[47]  J. Wheeler,et al.  On the density anomaly in sulfur at the polymerization transition , 1983 .

[48]  J. Wheeler,et al.  Critical and tricritical phenomena in ‘‘living’’ polymers , 1983 .

[49]  A. Hiltner,et al.  Thermoreversible gelation of atactic polystyrene solutions , 1983 .

[50]  W. Helfrich.  Mean-field theory of statistical assemblies of sterically interacting lines , 1983 .

[51]  John Toner,et al.  Renormalization-group treatment of the dislocation loop model of the smectic- A —nematic transition , 1982 .

[52]  H. Stanley,et al.  Solvent effects on polymer gels: A statistical-mechanical model , 1982 .

[53]  D. Y. Yoon,et al.  Theory of nematic systems of semiflexible polymers. I. High molecular weight limit , 1982 .

[54]  B. Halperin,et al.  Phase Transition in a Lattice Model of Superconductivity , 1981 .

[55]  R. Cordery.  Equilibrium Polymerization as an Ising Model , 1981 .

[56]  J. Wheeler,et al.  The n-->0 vector model and equilibrium polymerization , 1981 .

[57]  J. Wheeler,et al.  Critical points and tricritical points in liquid sulfur solutions , 1981 .

[58]  Peter G. Wolynes,et al.  Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids , 1981 .

[59]  V. Privalko.  Excess entropies and related quantities in glass-forming liquids , 1980 .

[60]  Charles Tanford,et al.  The hydrophobic effect , 1980 .

[61]  M. Stone,et al.  Condensed Monopoles and Abelian Confinement , 1978 .

[62]  J. Villain.  Two-level systems in a spin-glass model: II. Three-dimensional model and effect of a magnetic field , 1978 .

[63]  J. Kogut,et al.  Phase transitions in Abelian lattice gauge theories , 1977 .

[64]  A. Polyakov.  Quark confinement and topology of gauge theories , 1977 .

[65]  T. Witten,et al.  Renormalized field theory of polymer solutions. I. Scaling laws , 1977 .

[66]  Fumio Oosawa,et al.  Thermodynamics of the polymerization of protein , 1975 .

[67]  M. Szwarc.  Carbanions, Living Polymers and Electron Transfer Processes , 1968 .

[68]  G. Adam,et al.  On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids , 1965 .

[69]  R. Scott.  Phase Equilibria in Solutions of Liquid Sulfur. I. Theory , 1965 .

[70]  A. Tobolsky,et al.  Equilibrium polymerization of α‐methylstyrene. Part I. Initiation by means of sodium naphthalene and sodium diphenylacetylene at 0°C. , 1960 .

[71]  T. Ooi,et al.  G‐F transformation of actin as a fibrous condensation , 1959 .

[72]  M. Szwarc,et al.  POLYMERIZATION INITIATED BY ELECTRON TRANSFER TO MONOMER. A NEW METHOD OF FORMATION OF BLOCK POLYMERS1 , 1956 .

[73]  P. Flory,et al.  Phase equilibria in solutions of rod-like particles , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[74]  P. Flory,et al.  Statistical thermodynamics of semi-flexible chain molecules , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[75]  Richard Phillips Feynman,et al.  Atomic Theory of the Two-Fluid Model of Liquid Helium , 1954 .

[76]  R. Feynman.  The ?-Transition in Liquid Helium , 1953 .

[77]  P. Flory.  Principles of polymer chemistry , 1953 .

[78]  G. Gee.  The molecular complexity of sulphur in the liquid and vapour , 1952 .

[79]  W. Kauzmann.  The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures. , 1948 .

[80]  K. J. Ivin,et al.  Reversibility of the Propagation Reaction in Polymerization Processes and its Manifestation in the Phenomenon of a ‘Ceiling Temperature’ , 1948, Nature.

[81]  Henry S. Frank,et al.  Free Volume and Entropy in Condensed Systems III. Entropy in Binary Liquid Mixtures; Partial Molal Entropy in Dilute Solutions; Structure and Thermodynamics in Aqueous Electrolytes , 1945 .