Unexpected power-law stress relaxation of entangled ring polymers.

After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers.

[1]  Rae M. Robertson,et al.  Strong effects of molecular topology on diffusion of entangled DNA molecules , 2007, Proceedings of the National Academy of Sciences.

[2]  T. McLeish Hierarchical Relaxation in Tube Models of Branched Polymers , 1988 .

[3]  Hyunjung Lee,et al.  Fractionation of Cyclic Polystyrene from Linear Precursor by HPLC at the Chromatographic Critical Condition , 2000 .

[4]  J. Hinkley,et al.  Mechanical and swelling behaviour of well characterized polybutadiene networks , 1986 .

[5]  Grosberg Critical exponents for random knots , 1999, Physical review letters.

[6]  K.F. Schoch,et al.  Standard Pressure-volume-temperature data for Polymers , 1996, IEEE Electrical Insulation Magazine.

[7]  T. Nagamura,et al.  Comparison of Interdiffusion Behavior between Cyclic and Linear Polystyrenes with High Molecular Weights , 2006 .

[8]  T. McLeish Polymers Without Beginning or End , 2002, Science.

[9]  R. Grubbs,et al.  An "Endless" Route to Cyclic Polymers , 2002, Science.

[10]  T. McLeish Why, and when, does dynamic tube dilation work for stars? , 2003 .

[11]  G. Hadziioannou,et al.  Dilute solution characterization of cyclic polystyrene molecules and their zero-shear viscosity in the melt , 1987 .

[12]  Limits of analogy between self-avoidance and topology-driven swelling of polymer loops. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[14]  J. Klein Dynamics of entangled linear, branched, and cyclic polymers , 1986 .

[15]  G. McKenna,et al.  The viscosity of blends of linear and cyclic molecules of similar molecular mass , 1986 .

[16]  G. Szamel,et al.  Influence of topological constraints on the statics and dynamics of ring polymers. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Huggins Viscoelastic Properties of Polymers. , 1961 .

[18]  S. Shanbhag,et al.  What Is the Size of a Ring Polymer in a Ring−Linear Blend? , 2007 .

[19]  Obukhov,et al.  Dynamics of a ring polymer in a gel. , 1994, Physical review letters.

[20]  Michael Rubinstein,et al.  Network Modulus and Superelasticity , 1994 .

[21]  J. A. Semlyen,et al.  Studies of cyclic and linear poly(dimethylsiloxanes): 34: Preparation, fractionation and characterisation of the first per-deuterated macrocyclic poly(dimethylsiloxanes) , 1999 .

[22]  J. Roovers Viscoelastic properties of polybutadiene rings , 1988 .

[23]  J. E. Mark,et al.  Physical properties of polymers handbook , 2007 .

[24]  Philip J. Cox,et al.  Physical properties of polymers handbook , 1997 .

[25]  J. A. Semlyen,et al.  Studies of cyclic and linear poly(dimethylsiloxanes): 27. Bulk viscosities above the critical molar mass for entanglement , 1988 .

[26]  C. Strazielle,et al.  Cyclic macromolecules. Synthesis and characterization of ring-shaped polystyrenes , 1983 .

[27]  M. Rubinstein,et al.  Dynamics of ring polymers in the presence of fixed obstacles. , 1986, Physical review letters.

[28]  M. Isichenko Percolation, statistical topography, and transport in random media , 1992 .

[29]  P. Gennes Reptation of a Polymer Chain in the Presence of Fixed Obstacles , 1971 .

[30]  J. Roovers The melt properties of ring polystyrenes , 1985 .

[31]  S G Whittington,et al.  Statistical topology of closed curves: Some applications in polymer physics , 2007 .

[32]  D. Vlassopoulos,et al.  Linear Melt Rheology of Pom-Pom Polystyrenes with Unentangled Branches , 2007 .

[33]  D. J. Walsh,et al.  Standard Pressure Volume Temperature Data for Polymers , 1995 .

[34]  S. Edwards,et al.  Dynamics of concentrated polymer systems. Part 1.—Brownian motion in the equilibrium state , 1978 .

[35]  P. Gennes Reptation of stars , 1975 .

[36]  J. A. Semlyen Cyclic polymers , 1981 .

[37]  Wittmer,et al.  Topological effects in ring polymers: A computer simulation study. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  B. Trathnigg,et al.  Hplc of Polymers , 1998 .

[39]  N. Hadjichristidis,et al.  A study of the linear viscoelastic properties of cyclic polystyrenes using creep and recovery measurements , 1989 .

[40]  T. C. B. McLeish,et al.  Polymer Physics , 2009, Encyclopedia of Complexity and Systems Science.

[41]  P. E. Rouse A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers , 1953 .

[42]  J. Viovy,et al.  Constraint release in polymer melts: tube reorganization versus tube dilation , 1991 .

[43]  G. Marrucci Relaxation by reptation and tube enlargement: A model for polydisperse polymers , 1985 .

[44]  J. M. Deutsch,et al.  Conjectures on the statistics of ring polymers , 1986 .

[45]  J. Roovers,et al.  Synthesis of high molecular weight ring polystyrenes , 1983 .

[46]  M. Doi,et al.  Rheology of star polymers in concentrated solutions and melts , 1980 .

[47]  E. Kramer,et al.  Diffusion of polymer rings in linear polymer matrices , 1987 .

[48]  Muthukumar,et al.  Knottedness in ring polymers. , 1991, Physical review letters.

[49]  J. Roovers,et al.  Synthesis and characterization of ring polybutadienes , 1988 .

[50]  S. Nechaev,et al.  Dynamics of a polymer chain in an array of obstacles , 1987 .