Science China Chemistry

, Volume 58, Issue 9, pp 1471–1477 | Cite as

Coil to globule transition of homo- and block-copolymer with different topological constraint and chain stiffness

  • Wei Wang
  • Yanchun Li
  • Zhongyuan LuEmail author


In this paper, we present the coil-to-globule (CG) transitions of homopolymers and multiblock copolymers with different topology and stiffness by using molecular dynamics with integrated tempering sampling method. The sampling method was a novel enhanced method that efficiently sampled the energy space with low computational costs. The method proved to be efficient and precise to study the structural transitions of polymer chains with complex topological constraint, which may not be easily done by using conventional Monte Carlo method. The topological constraint affects the globule shape of the polymer chain, thus further influencing the CG transition. We found that increasing the topological constraint generally decreased CG transition temperature for homopolymers. For semiflexible chains, an additional first-order like symmetry-broken transition emerged. For block copolymers, the topological constraint did not obviously change the transition temperature, but greatly reduced the energy signal of the CG transition.


coil-to-globule transition topological constraint chain stiffness molecular dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dulbecco R, Vogt M. Evidence for a ring structure of polyoma virus DNA. Proc Natl Acad Sci USA, 1963, 50: 236–243CrossRefGoogle Scholar
  2. 2.
    Vinogard J, Lebowitz J. Physical and topological properties of circular DNA. J Gen Physiol, 1966, 49: 103–125CrossRefGoogle Scholar
  3. 3.
    Craik DJ, Daly NL, Bond T, Waine C. Plant cyclotides: a unique family of cyclic and knotted proteins that defines the cyclic cystine knot structural motif. J Mol Biol, 1999, 294: 1327–1336CrossRefGoogle Scholar
  4. 4.
    Craik DJ, Conibear AC. The chemistry of cyclotides. J Org Chem, 2011, 76: 4805–4817CrossRefGoogle Scholar
  5. 5.
    Mallam AL, Jackson SE. Folding studies on a knotted protein. J Mol Biol, 2005, 346: 1409–1421CrossRefGoogle Scholar
  6. 6.
    Hsieh T. Knotting of the circular duplex DNA by type II DNA topoisomerase from Drosophila melanogaster. J Biol Chem, 1983, 258: 8413–8420Google Scholar
  7. 7.
    Trigueros S, Roca J. Production of highly knotted DNA by means of cosmid circularization inside phage capsids. BMC Biotechnol, 2007, 7: 94CrossRefGoogle Scholar
  8. 8.
    Oike H. Supramolecular approach for synthesis and functionalization of cyclic macromolecules. React Funct Polym, 2007, 67: 1157–1167CrossRefGoogle Scholar
  9. 9.
    Jia Z, Monteiro MJ. Cyclic polymers: methods and strategies. J Polym Sci A: Polym Chem, 2012, 50: 2085–2097CrossRefGoogle Scholar
  10. 10.
    Xiong XQ, Yi C. Application of click chemistry in the synthesis of cyclic polymers. Sci China Chem, 2013, 43: 783–800Google Scholar
  11. 11.
    Ohta Y, Kushida Y, Matsushita Y, Takano A. SEC-MALS characterization of cyclization reaction products: formation of knotted ring polymer. Polymer, 2009, 50: 1297–1299CrossRefGoogle Scholar
  12. 12.
    Ohta Y, Nakamura M, Matsushita Y, Takano A. Synthesis, separation and characterization of knotted ring polymers. Polymer, 2012, 53: 466–470CrossRefGoogle Scholar
  13. 13.
    Cates ME, Deutsch JM. Conjectures on the statistics of ring polymers. J Phys France, 1986, 47: 2121–2128CrossRefGoogle Scholar
  14. 14.
    Baiesi M, Orlandini E. Universal properties of knotted polymer rings. Phys Rev E, 2012, 86: 031805CrossRefGoogle Scholar
  15. 15.
    Rosa A, Orlandini E, Tubiana L, Micheletti C. Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology. Macromolecules, 2011, 44: 8668–8680CrossRefGoogle Scholar
  16. 16.
    Rawdon EJ, Kern JC, Piatek M, Plunkett P, Stasiak A, Millett KC. Effect of knotting on the shape of polymers. Macromolecules, 2008, 41: 8281–8287CrossRefGoogle Scholar
  17. 17.
    Millett KC, Plunkett P, Piatek M, Rawdon EJ, Stasiak A. Effect of knotting on polymer shapes and their enveloping ellipsoids. J Chem Phys, 2009, 130: 165104CrossRefGoogle Scholar
  18. 18.
    Rawdon E, Dobay A, Kern JC, Millett KC, Piatek M, Plunkett P, Stasiak A. Scaling behavior and equilibrium lengths of knotted polymers. Macromolecules, 2008, 41: 4444–4451CrossRefGoogle Scholar
  19. 19.
    Kanaeda N, Deguchi T. Universality in the diffusion of knots. Phy Rev E, 2009, 79: 021806CrossRefGoogle Scholar
  20. 20.
    Orlandini E, Stella AL, Vanderzande C, Zonta F. Slow topological time scale of knotted polymers. J Phys A Math Theor, 2008, 41: 122002CrossRefGoogle Scholar
  21. 21.
    Narros A, Moreno AJ, Likos CN. Effects of knots on ring polymers in solvents of varying quality. Macromolecules, 2013, 46: 3654–3668CrossRefGoogle Scholar
  22. 22.
    Chen WD, Chen JZ, Liu LJ, Xu XL, An LJ. Simulation study on conformational and dynamical properties of individual ring polymers in good solution. Sci China Chem, 2014, 44: 320–326CrossRefGoogle Scholar
  23. 23.
    Ivanov VA, Paul W, Binder K. Finite chain length effects on the coil-globule transition of stiff-chain macromolecules: a Monte Carlo simulation. J Chem Phys, 1998, 109: 5659CrossRefGoogle Scholar
  24. 24.
    Ivanov VA, Stukan MR, Vasilevskaya VV, Paul W, Binder K. Structures of stiff macromolecules of finite chain length near the coil-globule transition: a Monte Carlo simulation. Macromol Theor Simul, 2000, 9: 488–499CrossRefGoogle Scholar
  25. 25.
    Bachmann M, Janke W. Thermodynamics of lattice heteropolymers. J Chem Phys, 2004, 120: 6779–6791CrossRefGoogle Scholar
  26. 26.
    Bachmann M, Arkın H, Janke W. Multicanonical study of coarse-grained off-lattice models for folding heteropolymers. Phys Rev E, 2005, 71: 031906CrossRefGoogle Scholar
  27. 27.
    Wang L, Chen T, Lin X, Liu Y, Liang H. Canonical and microcanonical analysis of nongrafted homopolymer adsorption by an attractive substrate. J Chem Phys, 2009, 131: 244902CrossRefGoogle Scholar
  28. 28.
    Chen T, Wang L, Lin X, Liu Y, Liang H. Microcanonical analysis of adsorption of homopolymer chain on a surface. J Chem Phys, 2009, 130: 244905CrossRefGoogle Scholar
  29. 29.
    Wang Z, He X. Phase transition of a single star polymer: a Wang-Landau sampling study. J Chem Phys, 2011, 135: 094902CrossRefGoogle Scholar
  30. 30.
    Guo J, Liang H, Wang ZG. Coil-to-globule transition by dissipative particle dynamics simulation. J Chem Phys, 2011, 134: 244904CrossRefGoogle Scholar
  31. 31.
    Seaton DT, Schnabel S, Landau DP, Bachmann M. From flexible to stiff: systematic analysis of structural phases for single semiflexible polymers. Phys Rev Lett, 2013, 110: 028103CrossRefGoogle Scholar
  32. 32.
    Arkin H, Janke W. Gyration tensor based analysis of the shapes of polymer chains in an attractive spherical cage. J Chem Phys, 2013, 138: 054904CrossRefGoogle Scholar
  33. 33.
    Wang Z, Wang L, He X. Phase transition of a single protein-like copolymer chain. Soft Matter, 2013, 9: 3106CrossRefGoogle Scholar
  34. 34.
    Chi P, Wang Z, Yin Y, Li BH, Shi AC. Finite-length effects on the coil-globule transition of a strongly charged polyelectrolyte chain in a salt-free solvent. Phy Rev E, 2013, 87: 042608CrossRefGoogle Scholar
  35. 35.
    Wang W, Zhao P, Yang X, Lu ZY. Coil-to-globule transitions of homopolymers and multiblock copolymers. J Chem Phys, 2014, 141: 244907CrossRefGoogle Scholar
  36. 36.
    Swetnam A, Brett C, Allen MP. Phase diagrams of knotted and unknotted ring polymers. Phys Rev E, 2012, 85: 031804CrossRefGoogle Scholar
  37. 37.
    Zhao Y, Ferrari F. A numerical technique for studying topological effects on the thermal properties of knotted polymer rings. J Stat Mech-Theory E, 2012: P11022Google Scholar
  38. 38.
    Zhao Y, Ferrari F. A study of polymer knots using a simple knot invariant consisting of multiple contour integrals. J Stat Mech-Theory E, 2013: P10010Google Scholar
  39. 39.
    Yang L, Gao YQ. A selective integrated tempering method. J Chem Phys, 2009, 131: 214109CrossRefGoogle Scholar
  40. 40.
    Yang L, Shao Q, Gao YQ. Comparison between integrated and parallel tempering methods in enhanced sampling simulations. J Chem Phys, 2009, 130: 124111CrossRefGoogle Scholar
  41. 41.
    Zhao P, Yang LJ, Gao YQ, Lu ZY. Facile implementation of integrated tempering sampling method to enhance the sampling over a broad range of temperatures. Chem Phys, 2013, 415: 98–105CrossRefGoogle Scholar
  42. 42.
    Zhu YL, Liu H, Li ZW, Qian HJ, Milano G, Lu ZY. GALAMOST: GPU-accelerated large-scale molecular simulation toolkit. J Comput Chem, 2013, 34: 2197–2211CrossRefGoogle Scholar
  43. 43.
    Roovers J, Toporowski PM. Synthesis of high molecular weight ring polystyrenes. Macromolecules, 1983, 16: 843–849CrossRefGoogle Scholar
  44. 44.
    Roovers J. Dilute-solution properties of ring polystyrenes. J Polym Sci Polym Phys Ed, 1985, 23: 1117–1126CrossRefGoogle Scholar
  45. 45.
    Takano A, Kushida Y, Ohta Y, Masuoka K, Matsushita Y. The second virial coefficients of highly-purified ring polystyrenes in cyclohexane. Polymer, 2009, 50: 1300–1303CrossRefGoogle Scholar
  46. 46.
    des Cloizeaux J. Ring polymers in solution: topological effects. J Phys Lett, 1981, 42: L–433Google Scholar
  47. 47.
    Tanaka F. Osmotic pressure of ring-polymer solutions. J Chem Phys, 1987, 87: 4201CrossRefGoogle Scholar
  48. 48.
    Iwata K. temperature of ring polymers: another evidence of topological interaction. Macromolecules, 1989, 22: 3702–3706CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.State Key Laboratory of Supramolecular Structure and Materials; Institute of Theoretical ChemistryJilin UniversityChangchunChina

Personalised recommendations