Macromolecular topology and rheology: beyond the tube model

Abstract

The motion of entangled polymers is marked by their ability to make conformational adjustments, which is mediated by their free ends. A credible account of the basic features of entanglement release in linear and nonlinear rheology is offered by the tube model which, despite its limitations and shortcomings, is considered as the “standard” model in the field, accounting for the dynamics of linear and branched polymers with homogeneous monomer density. Here, we challenge the two central elements of the molecular picture of entanglements by exploiting the consequences of absence of free ends and monomer density distribution. Non-concatenated ring polymers of high molar mass do not form an entanglement network with plateau modulus, but instead relax stress self-similarly, while they deform much less than their linear counterparts in nonlinear shear flow. Their rheology is extremely sensitive to the presence of unlinked linear chains. On the other hand, star polymers with many arms have a dual nature: polymeric, which governs arm relaxation, and colloidal, which controls their subsequent center-of-mass motion and completes the stress relaxation process. Appropriate choice of number and size of arms allows to tune their dynamic and structural properties, and therefore bridge the gap between polymers and colloids. These examples demonstrate a different manifestation of topological interactions, with distinct linear and nonlinear rheology, which cannot be described in full by the tube model. They also provide an avenue for taking advantage of macromolecular architecture in order to engineer the rheology of polymeric structures and soft composites. Still, a number of outstanding issues remain and we outline some perspectives in this exciting field of molecular rheology.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. Adams JM, Fielding SM, Olmsted PD (2011) Transient shear banding in entangled polymers: a study using the Rolie-poly model. J Rheol 55:1007–1032

    Article  Google Scholar 

  2. Agarwal P, Srivastava S, Archer LA (2011a) Thermal jamming of a colloidal glass. Phys Rev Lett 107:268302

    Article  Google Scholar 

  3. Agarwal P, Archer LA (2011b) Strain-accelerated dynamics of soft colloidal glasses. Phys Rev E 83:041402

    Article  Google Scholar 

  4. Ahmadi M, Bailly C, Keunings R, Nekoomanesh M, Arabi H, van Ruymbeke E (2011) Time marching algorithm for predicting the linear rheology of monodisperse comb polymer melts. Macromolecules 44:647–659

    Article  Google Scholar 

  5. Alvarez NJ, Marín JMR, Huang Q, et al. (2013) Creep measurements confirm steady flow after stress maximum in extension of branched polymer melts. Phys Rev Lett 110:168301

    Article  Google Scholar 

  6. Andreev M, Schieber JD (2015) Accessible and quantitative entangled polymer rheology predictions, suitable for complex flow calculations. Macromolecules 48:1606–1613

    Article  Google Scholar 

  7. Antonietti M, Pakula T, Bremse W (1995) Rheology of small spherical polystyrene microgels: a direct proof for a new transport mechanism in bulk polymers besides reptation. Macromolecules 28:4227–4233

    Article  Google Scholar 

  8. Archer LA, Juliani (2004) Linear and nonlinear viscoelasticity of entangled multiarm (pom-pom) polymer liquids. Macromolecules 37:1076–1088

    Article  Google Scholar 

  9. Auhl D, Ramirez J, Likhtman AE, Chambon P, Fernyhough C (2008) Linear and nonlinear shear flow behavior of monodisperse polyisoprene melts with a large range of molecular weights. J Rheol 52:801–835

    Article  Google Scholar 

  10. Bach A, Rasmussen HK, Hassager O (2003) Extensional viscosity for polymer melts measured in the filament stretching rheometer. J Rheol 47:429–441

    Article  Google Scholar 

  11. Bacova P, Lentzakis H, Read DJ, Moreno AJ, Vlassopoulos D, Das C (2014) Branch-point motion in architecturally complex polymers: estimation of hopping parameters from computer simulations and experiments. Macromolecules 47:3362–3377

    Article  Google Scholar 

  12. Bent J, Hutchings LR, Richards RW, Gough T, Spares R, Coates PD, Grillo I, Harlen OG, Read DJ, Graham RS, Likhtman AE, Groves DJ, Nicholson TM, McLeish TCB (2003) Neutron-mapping polymer flow: scattering, flow visualization, and molecular theory. Science 301:1691–1695

    Article  Google Scholar 

  13. Berry GC, Fox TG (1968) The viscosity of polymers and their concentrated solutions. Adv Polym Sci 5:261–357

    Article  Google Scholar 

  14. Bielawski CW, Benitez D, Grubbs RH (2002) An “endless” route to cyclic polymers. Science 297:2041–2044

    Article  Google Scholar 

  15. Bras AR, Pasquino R, Koukoulas T, Tsolou G, Holderer O, Radulescu A, Allgaier J, Mavrantzas VG, Pyckhout-Hintzen W, Wischnewski A, Vlassopoulos D, Richter D (2011) Structure and dynamics of polymer rings by neutron scattering: breakdown of the rouse model. Soft Matter 7:11169–11176

    Article  Google Scholar 

  16. Briels WJ (2009) Transient forces in flowing soft matter. Soft Matter 5:4401–4411

    Article  Google Scholar 

  17. Cao J, Likhtman AE (2015) Simulating start-up of entangled polymer melts. ACS Macro Lett 4:1376–1381

    Article  Google Scholar 

  18. Cates ME, Deutsch JM (1986) Conjectures on the statistics of ring polymers. J Phys 47:2121–2128

    Article  Google Scholar 

  19. Cates ME (2003) Arrest and flow of colloidal glasses. Ann Henri Poincaré 4(Suppl. 2):S647–S661

    Article  Google Scholar 

  20. Chambon P, Fernyhough CM, Im K, Chang T, Das C, Embery J, McLeish TCB, Read DJ (2008) Synthesis, temperature gradient interaction chromatography, and rheology of entangled styrene comb polymers. Macromolecules 41:5869–5875

    Article  Google Scholar 

  21. Chang T (2005) Polymer characterization by interaction chromatography. J Polym Sci B Polym Phys 43:1591–1607

    Article  Google Scholar 

  22. Chen Q, Gong S, Moll J, Zhao D, Kumar SK, Colby RH (2015) Mechanical reinforcement of polymer nanocomposites from percolation of a nanoparticle network. ACS Macro Lett 4:398–402

    Article  Google Scholar 

  23. Chen X, Lee H, Rahman MS, Lee H, Mays J, Chang T, Larson RG (2011) Combined synthesis, TGIC characterization, and rheological measurement and prediction of symmetric H polybutadienes and their blends with linear and star-shaped polybutadienes. Macromolecules 44:7799–7809

    Article  Google Scholar 

  24. Chisholm MH, Gallucci JD, Yin H (2006) Cyclic esters and cyclodepsipeptides derived from lactide and 2, 5-morpholinediones. Proc Natl Acad Sci (PNAS) 103:15315–15320

    Article  Google Scholar 

  25. Chremos A, Douglas JF (2015) When does a branched polymer become a particle? J Chem Phys 143:111104

    Article  Google Scholar 

  26. Chremos A, Panagiotopoulos AZ, Koch DL (2012) Dynamics of solvent-free grafted nanoparticles. J Chem Phys 136:044902

    Article  Google Scholar 

  27. Cogswell FN (1969) Tensile deformations in molten polymers. Rheol Acta 8:187–194

    Article  Google Scholar 

  28. Cordier P, Tournilhac F, Soulié-Ziakovic C, Leibler L (2008) Self-healing and thermoreversible rubber from supramolecular assembly. Nature 451:977–980

    Article  Google Scholar 

  29. Costanzo S, Huang Q, Ianniruberto G, Marrucci G, Hassager O, Vlassopoulos D (2016) Shear and extensional rheology of polystyrene melts and solutions with the same number of entanglements. Macromolecules 49:3925–3935

    Article  Google Scholar 

  30. Cremer T, Cremer M, Dietzel S, Müller S, Solovei I, Fakan S (2006) Chromosome territories—a functional nuclear landscape. Curr Opin Cell Biol 18:307–316

    Article  Google Scholar 

  31. Cromer M, Fredrickson GH, Leal LG (2014) A study of shear banding in polymer solutions. Phys Fluids 26:063101

    Article  Google Scholar 

  32. Das C, Inkson NJ, Read DJ, Kelmanson MA, McLeish TCB (2006) Computational linear rheology of general branch-on-branch polymers. J Rheol 50:207–234

    Article  Google Scholar 

  33. des Cloizeaux J (1988) Double reptation vs. simple reptation in polymer melts. Europhys Lett 5:437–442

    Article  Google Scholar 

  34. Daniel WFM, Burdyńska J, Vatankhah-Varnosfaderani M, Matyjaszewski K, Paturej J, Rubinstein M, Dobrynin AV, Sheiko SS (2016) Solvent-free, supersoft and superelastic bottlebrush melts and networks. Nat Mater 15:183–190

    Article  Google Scholar 

  35. Daoud M, Cotton JP (1982) Star shaped polymers: a model for the conformation and its concentration dependence. J Phys (Paris) 43:531–538

    Article  Google Scholar 

  36. Dealy JM, Wissbrun KF (1990) Melt rheology and its role in plastics processing. Van Nostrand Reinhold, New York

    Google Scholar 

  37. Dealy JM, Larson RG (2006) Structure and rheology of molten polymers. Hanser Publications, New York

    Google Scholar 

  38. Dessi C, Tsibidis GD, Vlassopoulos D, De Corato M, Trofa M, D’Avino G, Maffettone PL, Coppola S (2016) Analysis of dynamic mechanical response in torsion. J Rheol 60:275–287

    Article  Google Scholar 

  39. Dhont JKG, Lettinga MP, Dogic Z, Lenstra TAJ, Wang H, Rathgeber S, Carletto P, Willner L, Frielinghausb H, Lindner P (2003) Shear-banding and microsctructure of colloids in shear flow. Faraday Discuss 123:157–172

    Article  Google Scholar 

  40. Doi M (1983) Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model. J Polym Sci Polym Phys Ed 21:667–684

    Article  Google Scholar 

  41. Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, New York

    Google Scholar 

  42. Doi Y, Matsubara K, Ohta Y, Nakano T, Kawaguchi D, Takahashi Y, Takano A, Matsushita Y (2015) Melt rheology of ring polymers with ultra-high purity. Macromolecules 48:3140–3147

    Article  Google Scholar 

  43. Dullaert K, Mewis J (2005) Stress jumps on weakly flocculated dispersions: steady state and transient results. J Colloid Interface Sci 287:542–551

    Article  Google Scholar 

  44. Ederle Y, Naraghi KS, Lutz PJ (1999) In: Cahn RW, Haasen P, Kramer EJ (eds) Materials science and technology, volume: synthesis of polymers (Schlüter AD, ed.). Wiley, New York

  45. Eisenberg A, Eu BC (1976) Mechanical spectroscopy: an introductory review. Annu Rev Mater Sci 6:335–359

    Article  Google Scholar 

  46. Erwin BM, Colby RH (2002) Temperature dependences of relaxation times and the length scale of cooperative motion for glass-forming liquids. J Non-Cryst Solids 307-310:225–231

    Article  Google Scholar 

  47. Erwin BM, Vlassopoulos D, Cloitre M (2010) Rheological fingerprinting of an aging soft colloidal glass. J Rheol 54:915–939

    Article  Google Scholar 

  48. Fetters LJ, Kiss AD, Pearson DS, Quack GF, Vitus FJ (1993) Rheological behavior of star-shaped polymers. Macromolecules 26:647–654

    Article  Google Scholar 

  49. Fetters LJ, Lohse DJ, Milner ST, Graessley WW (1999) Packing length influence in linear polymer melts on the entanglement, critical, and reptation molecular weights. Macromolecules 32:6847–6851

    Article  Google Scholar 

  50. Freeman SM, Weissenberg K (1948) Some new rheological phenomena and their significance for the constitution of materials. Nature 162:320–323

    Article  Google Scholar 

  51. Fuchs M, Cates ME (2009) A mode coupling theory for Brownian particles inhomogeneous steady shear flow. J Rheol 53:957–1000

    Article  Google Scholar 

  52. Ge T, Panyukov S, Rubinstein M (2015) Self-similar conformations and dynamics in entangled melts and solutions of nonconcatenated ring polymers. Macromolecules 49:702–722

    Google Scholar 

  53. de Gennes PG (1996) Soft adhesives. Langmuir 12:4497–4500

    Article  Google Scholar 

  54. Gohr K, Pakula TP, Tsutsumi K, Schärtl W (1999) Dynamics of copolymer micelles in an entangled homopolymer matrix. Macromolecules 32:7156–7165

    Article  Google Scholar 

  55. Gooßen S, Krutyeva M, Sharp M, Feoktystov A, Allgaier J, Pyckhout-Hintzen W, Wischnewski A, Richter D (2015) Sensing polymer chain dynamics through ring topology: a neutron spin Echo study. Phys Rev Lett 115:148302

    Article  Google Scholar 

  56. Goot RD, Madden TJ (1998) Dynamic simulation of diblock copolymer microphase separation. J Chem Phys 108:8713–8724

    Article  Google Scholar 

  57. Graessley WW, Hazleton RL, Lindeman LR (1967) The shear-rate dependence of viscosity in concentrated solutions of narrow-distribution polystyrene. Trans Soc Rheol 11:267–285

    Article  Google Scholar 

  58. Graessley WW (2008) Polymeric liquids & networks: dynamics and rheology. Garland Science, New York

    Google Scholar 

  59. Graham RS, Likhtman AE, McLeish TCB, Milner ST (2003) Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release. J Rheol 47:1171–1200

    Article  Google Scholar 

  60. Graham RS, Henry EP, Olmsted PD (2013) Comment on “New experiments for improved theoretical description of nonlinear rheology of entangled polymers”. Macromolecules 46:9849–9854

    Article  Google Scholar 

  61. de Greef TFA, Meijer EW (2008) Supramolecular polymers. Nature 453:171–173

    Article  Google Scholar 

  62. Grest GS, Kremer K, Milner ST, Witten TA (1989) Relaxation of self-entangled many-arm polymers. Macromolecules 22:1904–1910

    Article  Google Scholar 

  63. Grest GS, Fetters LJ, Huang JS, Richter D (1996) Star polymers: experiment, theory and simulation. Adv Chem Phys XCIV: 67–164 (Prigogine I, Rice SA eds) Wiley, New York

  64. Grosberg AY (2014) Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: towards the physics of crumpling. Soft Matter 10:560–565

    Article  Google Scholar 

  65. Hachmann P, Meissner J (2003) Rheometer for equibiaxial and planar elongations of polymer melts. J Rheol 47:989–1010

    Article  Google Scholar 

  66. Halperin A (1987) Polymeric micelles: a star model. Macromolecules 20:2943–2946

    Article  Google Scholar 

  67. Halperin A, Tirrell M, Lodge TP (1992) Tethered chains in polymer microstructures. Adv Polym Sci 100:31–71

    Article  Google Scholar 

  68. Halverson JD, Lee WB, Grest GS, Grosberg AY, Kremer K (2011a) Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. J Chem Phys 134:204904

    Article  Google Scholar 

  69. Halverson JD, Lee WB, Grest GS, Grosberg AY, Kremer K (2011b) Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics. J Chem Phys 134:204905

    Article  Google Scholar 

  70. Halverson JD, Grest GS, Grosberg AY, Kremer K (2012) Rheology of ring polymer melts: from linear contaminants to ring-linear blends. Phys Rev Lett 108:038301

    Article  Google Scholar 

  71. Halverson JD, Smrek J, Kremer K, Grosberg AY (2014) From a melt of rings to chromosome territories: the role of topological constraints in genome folding. Rep Prog Phys 77:022601

    Article  Google Scholar 

  72. Harmandaris VA, Kremer K (2009) Predicting polymer dynamics at multiple length and time scales. Soft Matter 5:3920–3926

    Article  Google Scholar 

  73. Hassager O, Mortensen K, Bach A, Almdal K, Rasmussen HK, Pyckhout-Hintzen W (2012) Stress and neutron scattering measurements on linear polymer melts undergoing steady elongational flow. Rheol Acta 51:385–394

    Article  Google Scholar 

  74. Hassell DG, Lord TD, Scelsi L, Klein DH, Auhl D, Harlen OG, McLeish TCB, Mackley MR (2011) The effect of boundary curvature on the stress response of linear and branched polyethylenes in a contraction–expansion flow. Rheol Acta 50:675–689

    Article  Google Scholar 

  75. Hatzikiriakos SG (2015) Slip mechanisms in complex fluid flows. Soft Matter 11:7851–7856

    Article  Google Scholar 

  76. Hawke LGD, Ahmadi M, Goldansaz H, van Ruymbeke E (2016) Viscoelastic properties of linear associating poly(n-butyl acrylate) chains. J Rheol 60:297–310

    Article  Google Scholar 

  77. Hild G, Strazielle C, Remp P (1983) Cyclic macromolecules. Synthesis and characterization of ring-shaped polystyrenes. Eur Polym J 19:721–727

    Article  Google Scholar 

  78. Holmes CB, Sollich P, Fuchs M, Cates ME (2005) Glass transitions and shear thickening suspension rheology. J Rheol 49:237–269

    Article  Google Scholar 

  79. Hutcheson SA, McKenna GB (2008) The measurement of mechanical properties of glycerol, m-toluidine, and sucrose benzoate under consideration of corrected rheometer compliance: an in-depth study and review. J Chem Phys 129:074502

    Article  Google Scholar 

  80. Ianniruberto G (2015a) Quantitative appraisal of a new CCR model for entangled linear polymers. J Rheol 59:211–235

    Article  Google Scholar 

  81. Ianniruberto G (2015b) Extensional flows of solutions of entangled polymers confirm reduction of friction coefficient. Macromolecules 48:6306–6312

    Article  Google Scholar 

  82. Inn YW, Wissbrun KF, Denn MM (2005) Effect of edge fracture on constant torque rheometry of entangled polymer solutions. Macromolecules 38:9385–9388

    Article  Google Scholar 

  83. Jia Z, Monteiro MJ (2012) Cyclic polymers: methods and strategies. J Polym Sci A Polym Chem 50:2085–2097

    Article  Google Scholar 

  84. Kapnistos M, Semenov AN, Vlassopoulos D, Roovers J (1999) Viscoelastic response of hyperstar polymers in the linear regime. J Chem Phys 111:1753–1759

    Article  Google Scholar 

  85. Kapnistos M, Vlassopoulos D, Roovers J, Leal LG (2005) Linear rheology of architecturally complex macromolecules: comb polymers with linear backbones. Macromolecules 38:7852–7862

    Article  Google Scholar 

  86. Kapnistos M, Lang M, Vlassopoulos D, Pyckhout-Hintzen W, Richter D, Cho D, Chang T, Rubinstein M (2008) Unexpected power-law stress relaxation in entangled ring polymers. Nat Mater 7:997–1002

    Article  Google Scholar 

  87. Keshavarz M, Engelkamp M, Xu J, Braeken E, Otten MBJ, Uji-I H, Schwartz E, Koepf M, Vananroye A, Vermant J, Nolte RJM, De Schryver F, Maan JC, Hofkens J, Christianen PCM, Rowan AE (2016) Nanoscale study of polymer dynamics. ACS Nano 10:1434–1441

    Article  Google Scholar 

  88. Kim SA, Mangal R, Archer LA (2015) Relaxation dynamics of nanoparticle-tethered polymer chains. Macromolecules 48:6280–6293

    Article  Google Scholar 

  89. Kinloch AJ, Young RJ (1995) Fracture behavior of polymers. Springer, Dordrecht

    Google Scholar 

  90. Klein J (1986) Dynamics of entangled linear, branched and cyclic polymers. Macromolecules 19:105–118

    Article  Google Scholar 

  91. Kobelev V, Schweizer KS (2005) Strain softening, yielding, and shear thinning in glassy colloidal suspensions. Phys Rev E 71:021401

    Article  Google Scholar 

  92. Kossuth MB, Morse DC, Bates FS (1999) Viscoelastic behavior of cubic phases in block copolymer melts. J Rheol 43:167–196

    Article  Google Scholar 

  93. Kotaka T, Kurata M, Tamura M (1962) Non-Newtonian flow and normal stress phenomena in solutions of polystyrene in toluene. Rheol Acta 2:179–186

    Article  Google Scholar 

  94. Kumar SK, Jouault N, Benicewicz B, Neely T (2013) Nanocomposites with polymer-grafted nanoparticles. Macromolecules 46:3199–3214

    Article  Google Scholar 

  95. Larson RG (1992) Instabilities in viscoelastic flow. Rheol Acta 31:213–263

    Article  Google Scholar 

  96. Larson RG, Winey KI, Patel SS, Watanabe H, Bruinsma R (1993) The rheology of layered liquids: lamellar block copolymers and smectic liquid crystals. Rheol Acta 32:245–253

    Article  Google Scholar 

  97. Larson RG (2001) Combinatorial rheology of branched polymer melts. Macromolecules 42:4556–4571

    Article  Google Scholar 

  98. Larson RG, Sridhar T, Leal LG, McKinley GH, Likhtman AE, McLeish TCB (2003) Definitions of entanglement spacing and time constants in the tube model. J Rheol 47:809–818

    Article  Google Scholar 

  99. Lee HC, Lee H, Lee W, Chang T, Roovers J (2000) Fractionation of cyclic polystyrene from linear precursor by HPLC at the chromatographic critical condition. Macromolecules 33:8119–8121

    Article  Google Scholar 

  100. Le Meins J-F, Moldenaers P, Mewis J (2003) Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow. Rheol Acta 42:184–190

    Article  Google Scholar 

  101. Lentzakis H, Vlassopoulos D, Read DJ, Lee H, Chang T, Driva P, Hadjichristidis N (2013) Uniaxial extensional rheology of well-characterized comb polymers. J Rheol 57:605–625

    Article  Google Scholar 

  102. Levental I, Georges PC, Janmey PA (2007) Soft biological materials and their impact on cell function. Soft Matter 3:299–306

    Article  Google Scholar 

  103. Li SW, Park HE, Dealy JM, Maric M, Im K, Chang T, Lee H, Choi H, Rahman MS, Mays J (2011) Detecting structural polydispersity in branched polybutadienes. Macromolecules 44:208–214

    Article  Google Scholar 

  104. Li Y, Hu M, McKenna GB, Dimitriou CJ, McKinley GH, Mick RM, Venerus DC, Archer LA (2013) Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions. J Rheol 57:1411–1428

    Article  Google Scholar 

  105. Li Y, Hsiao K-W, Brockman C-A, Yates DY, Robertson-Anderson RM, Kornfield JA, San Francisco MJ, Schroeder CM, McKenna GB (2015) Macromolecules 48:5997–6001

    Article  Google Scholar 

  106. Ligoure C, Mora S (2013) Fractures in complex fluids: the case of transient networks. Rheol Acta 52:91–114

    Article  Google Scholar 

  107. Likos CN (2001) Effective interactions in soft condensed matter physics. Phys Rep 348:267–439

    Article  Google Scholar 

  108. Likhtman AE, McLeish TCB (2002) Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 35:6332–6343

    Article  Google Scholar 

  109. Likhtman AE (2005) Single-chain slip-link model of entangled polymers: simultaneous description of neutron spin-echo, rheology, and diffusion. Macromolecules 38:6128–6139

    Article  Google Scholar 

  110. Likhtman AE (2009) Whither tube theory: from believing to measuring. J Non-Newtonian Fluid Mech 157:158–161

    Article  Google Scholar 

  111. Likhtman AE, Ponmurugan M (2014) Microscopic definition of polymer entanglements. Macromolecules 47:1470–1481

    Article  Google Scholar 

  112. Lindenblatt G, Schärtl W, Pakula T, Schmidt M (2000) Synthesis of polystyrene-grafted polyorganosiloxane microgels and their compatibility with linear polystyrene chains. Macromolecules 33:9340–9347

    Article  Google Scholar 

  113. Lindenblatt G, Schärtl W, Pakula T, Schmidt M (2001) Structure and dynamics of hairy spherical colloids in a matrix of nonentangled linear chains. Macromolecules 34:1730–1736

    Article  Google Scholar 

  114. Liu C-Y, Halasa AF, Keunings R, Bailly C (2006) Probe rheology: a simple method to test tube motion. Macromolecules 39:7415–7424

    Article  Google Scholar 

  115. Liu C-Y, Yao M, Garritano RG, Franck AJ, Bailly C (2011) Instrument compliance effects revisited: linear viscoelastic measurements. Rheol Acta 50:537–546

    Article  Google Scholar 

  116. Lo WC, Turner MS (2013) The topological glass in ring polymers. Europhys Lett 102:58005

    Article  Google Scholar 

  117. Lord SJ, Leed H-ID, Moerner WE (2010) Single-molecule spectroscopy and imaging of biomolecules in living cells. Anal Chem 82:2192–2203

    Article  Google Scholar 

  118. Maia JM, Covas JA, Nóbrega JM, Dias TF, Alves FE (1999) Measuring uniaxial extensional viscosity using a modified rotational rheometer. J Non-Newtonian Fluid Mech 80:183–197

    Article  Google Scholar 

  119. Mandare P, Winter HH (2006) Ultraslow dynamics in asymmetric block copolymers with nanospherical domains. Colloid Polym Sci 284:1203–1210

    Article  Google Scholar 

  120. Marrucci G (1985) Relaxation by reptation and tube enlargement: a model for polydisperse. J Polym Sci B Polym Phys 23:159–177

    Article  Google Scholar 

  121. Marrucci G (1996) Dynamics of entanglements: a nonlinear model consistent with the Cox–Merz rule. J Non-Newtonian Fluid Mech 62:279–289

    Article  Google Scholar 

  122. Masubuchi Y, Watanabe H (2014) Origin of stress overshoot under start-up shear in primitive chain network simulation. ACS Macro Lett 3:1183–1186

    Article  Google Scholar 

  123. McConnell GA, Gast AP, Huang JS, Smith SD (1993) Disorder-order transitions in soft sphere polymer micelles. Phys Rev Lett 71:2102–2105

    Article  Google Scholar 

  124. McKenna GB, Plazek DJ (1986) The viscosity of blends of linear and cyclic polymers of similar molecular mass. Polymer Comm 27:304–306

    Article  Google Scholar 

  125. McKenna GB, Hostetter BJ, Hadjichristidis N, Fetters LJ, Plazek DJ (1989) A study of the linear viscoelastic properties of cyclic polystyrenes using creep and recovery measurements. Macromolecules 22:1834–1852

    Article  Google Scholar 

  126. McKenna GB (2006) Commentary on rheology of polymers in narrow gaps. Eur Phys J E 19:101–108

    Article  Google Scholar 

  127. McLeish TCB (1988) Hierarchical relaxation in tube models of branched polymers. Europhys Lett 6:511–516

    Article  Google Scholar 

  128. McLeish TCB (2002) Tube theory of entangled polymer dynamics. Adv Phys 51:1379–1527

    Article  Google Scholar 

  129. McLeish TCB, Allgaier J, Bick DK, Bishko G, Biswas P, Blackwell R, Blottière B, Clarke N, Gibbs B, Groves DJ, Hakiki A, Heenan RK, Johnson JM, Kant R, Read DJ, Young RN (1999) Dynamics of entangled H-polymers: theory, rheology, and neutron-scattering. Macromolecules 32:6734–6758

    Article  Google Scholar 

  130. McLeish TCB (2008a) Molecular polymeric matter, Weissenberg, Astbury and the pleasure of being wrong. Rheol Acta 47:479–489

    Article  Google Scholar 

  131. McLeish TCB (2008b) Floored by the rings. Nat Mater 7:933–934

    Article  Google Scholar 

  132. McLeish TCB, Clarke N, de Luca E, Hutchings LR, Graham RS, Gogh T, Grillo I, Fernyhough CM, Chambon P (2009) Neutron flow-mapping: multiscale modelling opens a new experimental window. Soft Matter 5:4426–4432

    Article  Google Scholar 

  133. Meissner J, Garbella RW, Hostettler J (1989) Measuring normal stress differences in polymer melt shear flow. J Rheol 33:843–864

    Article  Google Scholar 

  134. Meissner J, Hostettler J (1994) A new elongational rheometer for polymer melts and other highly viscoelastic liquids. Rheol Acta 33:1–21

    Article  Google Scholar 

  135. Mewis J, Wagner NJ (2012) Colloidal suspension rheology. Cambridge University Press, New York

    Google Scholar 

  136. Michieletto D, Turner MS (2016) A topologically driven glass in ring polymers. Proc Natl Acad Sci (PNAS). doi:10.1073/pnas.1520665113

    Google Scholar 

  137. Michieletto D, Marenduzzo D, Orlandini E, Alexander GP, Turner MS (2014) Threading dynamics of ring polymers in a gel. ACS Macro Lett 3:255–259

    Article  Google Scholar 

  138. Mills PJ, Mayer JM, Kramer EJ, Hadziioannou G, Lutz P, Strazielle C, Remp P, Kovacs JA (1987) Diffusion of polymer rings in linear polymer matrices. Macromolecules 20:513–518

    Article  Google Scholar 

  139. Milner ST, McLeish TCB (1997) Parameter-free theory for stress relaxation in star polymer melts. Macromolecules 30:2159–2166

    Article  Google Scholar 

  140. Milner ST, McLeish TCB (1998) Arm-length dependence of stress relaxation in star polymer melts. Macromolecules 31:7479–7482

    Article  Google Scholar 

  141. Milner ST, Newhall JD (2010) Stress relaxation in entangled melts of unlinked ring polymers. Phys Rev Lett 105:208302

    Article  Google Scholar 

  142. Montarnal D, Capelot M, Tournilhac M, Leibler L (2011) Silica-like malleable materials from permanent organic networks. Science 334:965–968

    Article  Google Scholar 

  143. Moorcroft RL, Fielding SM (2014) Shear banding in time-dependent flows of polymers and wormlike micelles. J Rheol 58:103–147

    Article  Google Scholar 

  144. Moore NT, Grosberg AY (2005) Limits of analogy between self-avoidance and topology-driven swelling of polymer loops. Phys Rev E 72:0161803

    Article  Google Scholar 

  145. Münstedt H (1979) New universal extensional rheometer for polymer melts. Measurements on a polystyrene sample. J Rheol 23:421–436

    Article  Google Scholar 

  146. Mzabi S, Berghezan D, Roux S, Hild F, Creton C (2011) A critical local energy release rate criterion for fatigue fracture of elastomers. J Polym Sci Polym Phys Ed 49:1518–1524

    Article  Google Scholar 

  147. Neugebauer D, Zhang Y, Pakula T, Sheiko SS, Matyjaszewski K (2003) Densely-grafted and double-grafted PEO brushes via ATRP. A route to soft elastomers. Macromolecules 36:6746–6755

    Article  Google Scholar 

  148. Nielsen JK, Rasmussen HK, Hassager O (2008) Stress relaxation of narrow molar mass distribution polystyrene following uniaxial extension. J Rheol 52:885–899

    Article  Google Scholar 

  149. Obukhov S, Rubinstein M, Duke T (1994) Dynamics of a ring polymer in a gel. Phys Rev Lett 73:1263–1266

    Article  Google Scholar 

  150. Obukhov S, Lohner A, Baschnagel J, Meyer H, Wittmer JP (2014) Melt of polymer rings: the decorated loop model. Europhys Lett 105:48005

    Article  Google Scholar 

  151. Orrah DJ, Semlyen JA, Ross-Murphy SB (1988) Studies of cyclic and linear poly(dimethylsiloxanes): 27. Bulk viscosities above the critical molar mass for entanglement. Polymer 29:1452–1454

    Article  Google Scholar 

  152. Osaki K (1993) On the damping function of shear relaxation modulus for entangled polymers. Rheol Acta 32:429–437

    Article  Google Scholar 

  153. Pakula T, Geyler S, Edling T, Boese D (1996) Relaxation and viscoelastic properties of complex polymer systems. Rheol Acta 35:631–644

    Article  Google Scholar 

  154. Pakula T (1998a) Static and dynamic properties of computer simulated melts of multiarm polymer stars. Comput Theor Polym Sci 8:21–30

    Article  Google Scholar 

  155. Pakula T, Vlassopoulos D, Fytas G, Roovers J (1998b) Structure and dynamics of melts of multiarm polymer stars. Macromolecules 31:8931–8940

    Article  Google Scholar 

  156. Pakula T (2000) Collective dynamics in simple supercooled and polymer liquids. J Mol Liq 86:109–121

    Article  Google Scholar 

  157. Pakula T (2003) In: Kremer F, Schönhals A (eds) Broadband dielectric spectroscopy. Springer, Heidelberg

    Google Scholar 

  158. Park SJ, Desai PS, Chen X, Larson RG (2015) Universal relaxation behavior of entangled 1,4-polybutadiene melts in the transition frequency region. Macromolecules 48:4122–4131

    Article  Google Scholar 

  159. Park SJ, Shanbhag S, Larson RG (2005) A hierarchical algorithm for predicting the linear viscoelastic properties of polymer melts with long-chain branching. Rheol Acta 44:319–330

    Article  Google Scholar 

  160. Pasquino R, Vasilakopoulos TC, Jeong YC, Lee H, Rogers S, Sakellariou G, Allgaier J, Takano A, Brás AR, Chang T, Gooβen S, Pyckhout-Hintzen W, Wischnewski A, Hadjichristidis N, Richter D, Rubinstein M, Vlassopoulos D (2013) Viscosity of ring polymer melts. ACS Macro Lett 2:874–878

    Article  Google Scholar 

  161. Puaud F, Nicol E, Brotons G, Nicolai T, Benyahia L (2014) Liquid–solid transition and crystallization of mixtures of frozen and dynamic star-like polymers. Macromolecules 47:1175–1180

    Article  Google Scholar 

  162. Pusey PN (1991) In: JP H, Levesque D, Zinn-Justin J (eds) Liquids, freezing and glass transition. North Holland, Amsterdam

    Google Scholar 

  163. Qin J, Milner ST (2016) Tube dynamics works for randomly entangled rings. Phys Rev Lett 116:068307

    Article  Google Scholar 

  164. Ravindranath S, Wang S-Q (2008a) Universal scaling characteristics of stress overshoot in startup shear of entangled polymer solutions. J Rheol 52:681–695

    Article  Google Scholar 

  165. Ravindranath S, Wang S-Q (2008b) Steady-state measurements in stress plateau region of entangled polymer solutions: controlled-rate and controlled-stress modes. J Rheol 52:957–980

    Article  Google Scholar 

  166. Read DJ, Auhl D, Das C, den Doelder J, Kapnistos M, Vittorias I, McLeish TCB (2011) Linking models of polymerization and dynamics to predict branched polymer structure and flow. Science 333:1871–1874

    Article  Google Scholar 

  167. Robertson RM, Smith DE (2007) Strong effects of molecular topology on diffusion of entangled DNA molecules. Proc Natl Acad Sci 104:4824–4827

    Article  Google Scholar 

  168. Roovers J (1979) Synthesis and dilute solution characterization of comb polystyrenes. Polymer 20:843–849

    Article  Google Scholar 

  169. Roovers J, Graessley WW (1981) Melt rheology of some model comb polystyrenes. Macromolecules 14:766–773

    Article  Google Scholar 

  170. Roovers J, Toporowski PM (1983) Synthesis of high-molecular weight ring polystyrenes. Macromolecules 16:843–849

    Article  Google Scholar 

  171. Roovers J (1985) Melt properties of ring polystyrenes. Macromolecules 18:1359–1361

    Article  Google Scholar 

  172. Roovers J (1988a) Viscoelastic properties of polybutadiene rings. Macromolecules 21:1517–1521

    Article  Google Scholar 

  173. Roovers J, Toporowski PM (1988b) Synthesis and characterization of ring polybutadienes. J Polym Sci B Polym Phys 26:1251–1259

    Article  Google Scholar 

  174. Roovers J (1991) Viscoelastic properties of 32-arm star polybutadienes. Macromolecules 24:5895–5896

    Article  Google Scholar 

  175. Roovers J, Zhou L-L, Toporowski PM, van der Zwan M, Iatrou H, Hadjichristidis N (1993) Regular star polymers with 64 and 128 arms. Models for polymeric micelles. Macromolecules 26:4324–4331

    Article  Google Scholar 

  176. Roovers J (2000) In: Semlyen JA (ed) Cyclic polymers. Kluwer, Amsterdam

    Google Scholar 

  177. Rosa A, Everaers R (2014) Ring polymers in the melt state: the physics of crumpling. Phys Rev Lett 112:118302

    Article  Google Scholar 

  178. Rubinstein M (1986) Dynamics of ring polymers in the presence of fixed obstacles. Phys Rev Lett 24:3023–3026

    Article  Google Scholar 

  179. Rubinstein M, Zurek S, McLeish TCB, Ball RC (1990) Relaxation of entangled polymers at the classical gel point. J Phys Fr 51:757–775

    Article  Google Scholar 

  180. Rubinstein M, Obukhov S (1993) Power-law-like stress relaxation of block copolymers: disentanglement regimes. Macromolecules 26:1740–1750

    Article  Google Scholar 

  181. Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, New York

    Google Scholar 

  182. Ruocco N, Dahbi L, Driva P, Hadjichristidis N, Allgaier J, Radulescu A, Sharp M, Lindner P, Straube E, Pyckhout-Hintzen W, Richter D (2013) Microscopic relaxation processes in branched-linear polymer blends by rheo-SANS. Macromolecules 2013:9122–9133

    Article  Google Scholar 

  183. Ruzette A-V, Leibler L (2005) Block copolymers in tomorrow’s plastics. Nat Mater 4:19–31

    Article  Google Scholar 

  184. Ryu CY, Lee MS, Hajduk DA, Lodge TP (1997) Structure and viscoelasticity of matched asymmetric diblock and triblock copolymers in the cylinder and sphere microstructures. J Polym Sci Polym Phys 35:2811–2823

    Article  Google Scholar 

  185. Schlüter AD, Halperin A, Kröger M, Vlassopoulos D, Wegner G, Zhang B (2014) Dendronized polymers: molecular objects between conventional linear polymers and colloidal particles. ACS Macro Lett 3:991–998

    Article  Google Scholar 

  186. Schweizer T, Bardow A (2006) The role of instrument compliance in normal force measurements of polymer melts. Rheol Acta 45:393–402

    Article  Google Scholar 

  187. Schweizer T, Hostettler J, Mettler F (2008) A shear rheometer for measuring shear stress and both normal stress differences in polymer melts simultaneously: the MTR 25. Rheol Acta 47:943–957

    Article  Google Scholar 

  188. Schweizer T, Schmidheiny W (2013) Cone-partitioned plate rheometer cell with three partitions (CPP3) to determine shear stress and both normal stress differences for small quantities of polymeric fluids. J Rheol 57:841–856

    Article  Google Scholar 

  189. Sebastian JM, Lai C, Graessley WW, Register RA (2002b) Steady-shear rheology of block copolymer melts and concentrated solutions: disordering stress in body-centered-cubic systems. Macromolecules 35:2707–2713

    Article  Google Scholar 

  190. Sebastian JM, Graessley WW, Register RA (2002a) Steady-shear rheology of block copolymer melts and concentrated solutions: defect-mediated flow at low stresses in body-centered-cubic systems. J Rheol 46:863–879

    Article  Google Scholar 

  191. Sefiddashti MN, Edwards B, Khomami B (2015) Individual chain dynamics of a polyethylene melt undergoing steady shear. J Rheol 59:119–153

    Article  Google Scholar 

  192. Seghrouchni R, Petekidis G, Vlassopoulos D, Fytas G, Semenov AN, Roovers J, Fleischer G (1998) Controlling the dynamics of soft spheres: from polymeric to colloidal behavior. Europhys Lett 42:271–276

    Article  Google Scholar 

  193. Sentmanat ML (2004) Miniature universal testing platform: from extensional melt rheology to solid-state deformation behavior. Rheol Acta 43:657–669

    Article  Google Scholar 

  194. Shi X, McKenna GB (2006) Mechanical hole-burning spectroscopy: demonstration of hole burning in the terminal relaxation regime. Phys Rev B 73:014203

    Article  Google Scholar 

  195. Shin EJ, Jeong B, Brown HA, Koo BJ, Hedrick JL, Waymouth RM (2011) Crystallization of cyclic polymers: synthesis and crystallization behavior of high molecular weight cyclic poly(ε-caprolactone)s. Macromolecules 44:2773–2779

    Article  Google Scholar 

  196. Skorski S, Olmsted PD (2011) Loss of solutions in shear banding fluids driven by second normal stress differences. J Rheol 55:1219–1246

    Article  Google Scholar 

  197. Smerk J, Grosberg AY (2015) Understanding the dynamics of rings in the melt in terms of the annealed tree model. J Phys Condens Matter 27:064117

    Article  Google Scholar 

  198. Snijkers F, Vlassopoulos D (2011) Cone-partitioned-plate geometry for the ARES rheometer with temperature control. J Rheol 55:1167–1186

    Article  Google Scholar 

  199. Snijkers F, van Ruymbeke E, Kim P, Lee H, Nikopoulou A, Chang T, Hadjichristidis N, Pathak J, Vlassopoulos D (2011) Architectural dispersity in model branched polymers: analysis and rheological consequences. Macromolecules 44:8631–8643

    Article  Google Scholar 

  200. Snijkers F, Cho HY, Nese A, Matyjaszewski K, Pyckhout-Hintzen W, Vlassopoulos D (2014) Effects of core microstructure on structure and dynamics of star polymer melts: from polymeric to colloidal response. Macromolecules 47:5347–5356

    Article  Google Scholar 

  201. Snijkers F, Pasquino R, Olmsted PD, Vlassopoulos D (2015) Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers. J Phys Condens Matter 27:473002

    Article  Google Scholar 

  202. Sridhar T, Acharya M, Nguyen DA, Bhattacharjee PK (2014) On the extensional rheology of polymer melts and concentrated solutions. Macromolecules 47:379–386

    Article  Google Scholar 

  203. Stiakakis E, Wilk A, Kohlbrecher J, Vlassopoulos D, Petekidis G (2010) Slow dynamics, aging and crystallization of concentrated multiarm stars. Phys Rev E 81:020402(R)

    Article  Google Scholar 

  204. Sui C, McKenna GB (2007) Instability of entangled polymers in cone and plate rheometry. Rheol Acta 46:877–888

    Article  Google Scholar 

  205. Sussman DM, Schweizer KS (2013) Entangled polymer chain melts: orientation and deformation dependent tube confinement and interchain entanglement elasticity. J Chem Phys 139:234904

    Article  Google Scholar 

  206. Tanner RI, Keentok M (1983) Shear fracture in cone-plate rheometry. J Rheol 27:47–57

    Article  Google Scholar 

  207. Tantakitti F, Boekhoven J, Wang X, Kazantsev RV, Yu T, Li J, Zhuang E, Zandi R, Ortony JH, Newcomb CJ, Palmer LC, Shekhawat GS, Olvera de la Cruz M, Schatz GC, Stupp SI (2016) Energy landscapes and functions of supramolecular systems. Nat Mater 15:469–477

    Article  Google Scholar 

  208. Tezel AK, Oberhauser JP, Graham RS, Jagannathan K, McLeish TCB, Leal LG (2009) The nonlinear response of entangled star polymers to startup of shear flow. J Rheol 53:1193–1214

    Article  Google Scholar 

  209. Tsalikis DG, Mavrantzas VG, Vlassopoulos D (2016) Threading of ring poly(ethylene oxide) molecules by linear chains in the melt. ACS Macro Lett 5:755–760

    Article  Google Scholar 

  210. Tsalikis DG, Mavrantzas VG (2014) Analysis of slow modes in ring polymers: threading of rings controls long-time relaxation. ACS Macro Lett 3:763–766

    Article  Google Scholar 

  211. Tsenoglou C (1991) Molecular weight polydispersity effects on the viscoelasticity of entangled linear polymers. Macromolecules 24:1762–1767

    Article  Google Scholar 

  212. Tsolou G, Stratikis N, Baig C, Stephanou PS, Mavrantzas VG (2010) Melt structure and dynamics of unentangled polyethylene rings: Rouse theory, atomistic molecular dynamics simulation, and comparison with the linear analogues. Macromolecules 43:10692–10713

    Article  Google Scholar 

  213. Truzzolillo D, Vlassopoulos D, Munam A, Gauthier M (2014) Depletion gels from dense soft colloids: rheology and thermoreversible melting. J Rheol 58:1441–1462

    Article  Google Scholar 

  214. van Oosten ASG, Vahabi M, Licup AJ, Sharma A, Galie PA, MacKintosh FC, Janmey PA (2016) Uncoupling shear and extensional elastic moduli of semiflexible biopolymer networks: compression-softening and stretch-stiffening. Sci Report. doi:10.1038/srep19270

    Google Scholar 

  215. van Ruymbeke E, Keunings R, Bailly C (2005) Prediction of linear viscoelastic properties for polydisperse mixtures of entangled star and linear polymers: modified tube-based model and comparison with experimental results. J Non-Newtonian Fluid Mech 128:7–22

    Article  Google Scholar 

  216. van Ruymbeke E, Bailly C, Keunings R, Vlassopoulos D (2006) A general methodology to predict the linear rheology of branched polymers. Macromolecules 39:6248–6259

    Article  Google Scholar 

  217. van Ruymbeke E, Coppola S, Balacca L, Righi S, Vlassopoulos D (2010) Decoding the viscoelastic response of polydisperse star/linear polymer blends. J Rheol 54:507–538

    Article  Google Scholar 

  218. van Ruymbeke E, Slot JJM, Kapnistos M, Steeman PAM (2013) Structure and rheology of polyamide 6 polymers from their reaction recipe. Soft Matter 9:6921–6935

    Article  Google Scholar 

  219. van Ruymbeke E, Lee H, Chang T, Nikopoulou A, Hadjichristidis N, Snijkers F, Vlassopoulos D (2014) Molecular rheology of branched polymers: decoding and exploring the role of architectural dispersity through a synergy of anionic synthesis, interaction chromatography, rheometry and modeling. Soft Matter 10:4762–4777

    Article  Google Scholar 

  220. Venerus DC, Shiu T-Y, Kashyap T, Hostettler J (2010) Continuous lubricated squeezing flow: a novel technique for equibiaxial elongational viscosity measurements on polymer melts. J Rheol 54:1083–1095

    Article  Google Scholar 

  221. Vermant J, Moldenaers P, Mewis J, Ellis M, Garritano R (1997) Orthogonal superposition measurements using a rheometer equipped with a force rebalanced transducer. Rev Sci Instrum 68:4090–4096

    Article  Google Scholar 

  222. Vermant J, Moldenaers P, Mewis J (1998) Orthogonal versus parallel superposition measurements. J Non-Newtonian Fluid Mech 79:173–189

    Article  Google Scholar 

  223. Viovy JL, Rubinstein M, Colby RH (1991) Constraint release in polymer melts: tube reorganization versus tube dilation. Macromolecules 24:3587–3596

    Article  Google Scholar 

  224. Vlassopoulos D, Fytas G, Pakula T, Roovers J (2001) Multiarm star polymer dynamics. J Phys Condens Matter 13:R855–R876

    Article  Google Scholar 

  225. Vlassopoulos D, Cloitre M (2014) Tunable rheology of dense soft deformable colloids. Curr Opin Colloid Interface Sci 19:561–574

    Article  Google Scholar 

  226. Vrentas CM, Graessley WW (1982) Study of shear stress relaxation in well-characterized polymer liquids. J Rheol 26:359–371

    Article  Google Scholar 

  227. Wang S-Q (1999) Molecular transitions and dynamics at polymer/wall interfaces: origins of flow instabilities and wall slip. Adv Polym Sci 138:227–275

    Article  Google Scholar 

  228. Wang S-Q, Ravindranath S, Wang Y, Boukany P (2007) New theoretical considerations in polymer rheology: elastic breakdown of chain entanglement network. J Chem Phys 127:06490

    Google Scholar 

  229. Wang S-Q, Liu G, Cheng S, Boukany PE, Wang Y, Li X (2014) Letter to the editor: sufficiently entangled polymers do show shear strain localization at high enough Weissenberg numbers. J Rheol 58:1059–1069

    Article  Google Scholar 

  230. Wang S-Q (2015) Nonlinear rheology of entangled polymers at turning point. Soft Matter 11:1454–1458

    Article  Google Scholar 

  231. Watanabe H (1997) Rheology of diblock copolymer micellar systems. Acta Polym 48:215–233

    Article  Google Scholar 

  232. Watanabe H, Sato T, Osaki K, Hamersky MW, Chapman BR, Lodge TP (1998) Diffusion and viscoelasticity of copolymer micelles in a homopolymer matrix. Macromolecules 31:3740–3742

    Article  Google Scholar 

  233. Watanabe H (1999) Viscoelasticity and dynamics of entangled polymers. Prog Polym Sci 24:1253–1403

    Article  Google Scholar 

  234. Watanabe H, Ishida S, Matsumiya Y, Inoue T (2004) Test of full and partial tube dilation pictures in entangled blends of linear polyisoprenes. Macromolecules 37:6619–6631

    Article  Google Scholar 

  235. Watanabe H, Matsumiya Y (2005) Rheology of diblock copolymer micellar dispersions having soft cores. Macromolecules 38:3808–3819

    Article  Google Scholar 

  236. Watanabe H, Matsumiya Y, Ishida S, Takigawa T, Yamamoto T, Vlassopoulos D, Roovers J (2005) Nonlinear rheology of multiarm star chains. Macromolecules 38:7404–7415

    Article  Google Scholar 

  237. Weissenberg K (1924) Ein neues Röntgengoniometer. Z Phys 23:229–238

    Article  Google Scholar 

  238. Wen YH, Lu Y, Dobosz KM, Archer LA (2014) Structure, ion transport, and rheology of nanoparticle salts. Macromolecules 47:4479–4492

    Article  Google Scholar 

  239. Wilner L, Jucknischke O, Richter D, Roovers J, Zhou LL, Toporowski PM, Fetters LJ, Huang JS, Lin MY, Hadjichristidis N (1994) Structural investigation of star polymers in solution by small-angle neutron scattering. Macromolecules 27:3821–3829

    Article  Google Scholar 

  240. Winkler RG, Fedosov DA, Gompper G (2014) Dynamical and rheological properties of soft-colloid suspensions. Curr Opin Colloid Interface Sci 19:594–610

    Article  Google Scholar 

  241. Witten TA, Pincus PA, Cates ME (1986) Macrocrystal ordering in star polymer solutions. Europhys Lett 2:137–140

    Article  Google Scholar 

  242. Yamamoto T, Ohta Y, Takigawa T, Masuda T (2002) Stress relaxation of multi-arm star polystyrenes in the molten state. J Soc Rheol Jpn 30:129–132

    Article  Google Scholar 

  243. Yan ZC, Costanzo S, Jeong Y, Chang T, Vlassopoulos D (2016) Linear and nonlinear shear rheology of a marginally entangled ring polymer. Macromolecules 49:1444–1453

    Article  Google Scholar 

  244. Yaoita T, Isaki T, Masubuchi Y, Watanabe H, Ianniruberto G, Marrucci G (2012) Primitive chain network simulation of elongational flows of entangled linear chains: stretch/orientation-induced reduction of monomeric friction. Macromolecules 45:2773–2782

    Article  Google Scholar 

  245. Zamponi M, Pyckhout-Hintzen W, Wischnewski A, Monkenbusch M, Willner L, Kali G, Richter D (2010) Molecular observation of branch point motion in star polymer melts. Macromolecules 43:518–524

    Article  Google Scholar 

  246. Zhang B, Wepf R, Fischer K, Schmidt M, Besse S, Lindner P, King BT, Sigel R, Schurtenberger P, Talmon Y, Ding Y, Kröger M, Halperin A, Schlüter DA (2011) The largest synthetic structure with molecular precision: towards a molecular object. Angew Chem Int Ed 50:737–740

    Article  Google Scholar 

  247. Zhou Q, Larson RG (2007) Direct molecular dynamics simulation of branch point motion in asymmetric star polymer melts. Macromolecules 40:3443–3449

    Article  Google Scholar 

Download references

Acknowledgments

This overview reflects interactions with many present and past collaborators, to whom I am deeply indebted: Jacques Roovers, Wim Briels, Taihyun Chang, Michel Cloitre, Ralph Colby, Jan Dhont, Mario Gauthier, Nikos Hadjichristidis, Savvas Hatzikiriakos, Giovanni Ianniruberto, Sanat Kumar, Gary Leal, Christos Likos, Pino Marrucci, Kris Matyjazewski, Vlasis Mavrantzas, Tom McLeish, Wim Pyckhout-Hintzen, Dieter Richter, Michael Rubinstein, Sasha Semenov, Dieter Schlüter, Norm Wagner, Hiroshi Watanabe, and the late friends Tadeusz Pakula, Paul Callaghan, and Alexei Likhtman. The work presented is based on the dedicated efforts of several gifted students and postdocs: Evelyne van Ruymbeke, Frank Snijkers, Rossana Pasquino, Domenico Truzzolillo, Michael Kapnistos, Emmanuel Stiakakis, Salvatore Costanzo, Zhi-Chao Yan, Helen Lentzakis, Salvatore Coppola, Samruddhi Kamble, Brian Erwin, and Simon Rogers. Very special thanks to my colleagues in Crete, George Fytas, Benoit Loppinet, and George Petekidis, to Jan Mewis and Ole Hassager, and, of course, to Gerry Fuller and Jan Vermant.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Dimitris Vlassopoulos.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vlassopoulos, D. Macromolecular topology and rheology: beyond the tube model. Rheol Acta 55, 613–632 (2016). https://doi.org/10.1007/s00397-016-0948-1

Download citation

Keywords

  • Entanglement
  • Ring polymer
  • Soft colloids
  • Star polymer
  • Topological caging