Scaling Analysis of Real-Chain Conformations

  • Wenbing HuEmail author


Scaling analysis is a powerful tool to learn non-ideal-chain conformations. Several examples are introduced by considering the volume repulsion and its concentration effect, the attraction in a single chain, the charge interactions and their concentration effect, the stretching, the compression, and the adsorption, respectively. The blob model reflects the local thermal energy against the external disturbance. The Flory mean-field treatment derives the optimized coil size.


Single Chain Chain Conformation Polymer Coil Collapse Transition Entropy Loss 
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  1. Barrat JL, Joanny JF (1996) Theory of polyelectrolyte solutions. In: Rice S, Prigogine I (eds) Advances in chemical physics. Wiley, New York, pp 1–66CrossRefGoogle Scholar
  2. Daoud M, Cotton JP, Farnoux B, Jannink G, Sarma G, Benoit H, Duplessix R, Picot C, de Gennes PG (1975) Solutions of flexible polymers: neutron experiments and interpretation. Macromolecules 8:804–818CrossRefGoogle Scholar
  3. De Gennes PG (1972) Exponents for excluded volume problem as derived by Wilson method. Phys Lett A 38:339–340CrossRefGoogle Scholar
  4. De Gennes PG (1976) Scaling theory of polymer adsorption. J Phys 37:1445–1452CrossRefGoogle Scholar
  5. De Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, IthacaGoogle Scholar
  6. De Gennes PG (1981) Polymer solutions near an interface. 1. Adsorption and depletion layers. Macromolecules 14:1637–1644CrossRefGoogle Scholar
  7. De Gennes PG (1983) Scaling theory of polymer adsorption: proximal exponent. J Phys Lett 44:L241–L246CrossRefGoogle Scholar
  8. De Gennes PG, Pincus P, Velasco RM, Brochard F (1976) Remarks on polyelectrolyte conformation. J Phys (Paris) 37:1461–73CrossRefGoogle Scholar
  9. Dobrynin AV, Rubinstein M (2001) Counterion condensation and phase separation in solutions of hydrophobic polyelectrolytes. Macromolecules 34:1964–1972CrossRefGoogle Scholar
  10. Dobrynin AV, Rubinstein M (2005) Theory of polyelectrolytes in solutions and at surfaces. Prog Polym Sci 30:1049–1118CrossRefGoogle Scholar
  11. Dobrynin AV, Rubinstein M, Obukhov SP (1996) Cascade of transitions of polyelectrolytes in poor solvents. Macromolecules 29:2974–2979CrossRefGoogle Scholar
  12. Edwards SF (1965) The statistical mechanics of polymers with excluded volume. Proc Phys Soc Lond 85:613–624CrossRefGoogle Scholar
  13. Edwards SF (1966) The theory of polymer solutions at intermediate concentration. Proc Phys Soc Lond 88:265–280CrossRefGoogle Scholar
  14. Eisenriegler E, Kremer K, Binder K (1982) Adsorption of polymer-chains at surfaces: scaling and Monte-Carlo analyses. J Chem Phys 77:6296–6320CrossRefGoogle Scholar
  15. Fleer GJ, Cohen-Stuart MA, Scheutjens JMHM, Cosgrove T, Vincent B (1993) Polymers at interfaces. Chapman and Hall, LondonGoogle Scholar
  16. Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, IthacaGoogle Scholar
  17. Freed KF (1987) Renormalization group theory of macromolecules. Wiley, New YorkGoogle Scholar
  18. Freed KF, Dudowicz J, Stukalin EB, Douglas JF (2010) General approach to polymer chains confined by interacting boundaries. J Chem Phys 133:094901CrossRefGoogle Scholar
  19. Fuoss RM, Katchalsky A, Lifson S (1951) The potential of an infinite rod-like molecule and the distribution of the counter ions. Proc Natl Acad Sci USA 37:579–589CrossRefGoogle Scholar
  20. Golestanian R, Kardar M, Liverpool TB (1999) Collapse of stiff polyelectrolytes due to counterion fluctuations. Phys Rev Lett 82:4456–4459CrossRefGoogle Scholar
  21. Guggenheim EA (1952) Mixtures. The Clarendon Press, OxfordGoogle Scholar
  22. Hansen CM (1967) Three dimensional solubility parameters and solvent diffusion coefficients. Danish Technology Press, CopenhagenGoogle Scholar
  23. Helfand E (1975) Theory of inhomogeneous polymers: fundamentals of the Gaussian random-walk model. J Chem Phys 62:999–1005CrossRefGoogle Scholar
  24. Hildebrand JH (1936) The solubility of non-electrolytes. Reinhold, New YorkGoogle Scholar
  25. Hoy KL (1985) Tables of solubility parameters. Union Carbide Corporation, Solvent and Coatings Materials Research and Development Department, South CharlestonGoogle Scholar
  26. Hu WB (1998) Structural transformation in the collapse transition of the single flexible homopolymer model. J Chem Phys 109:3686–3690CrossRefGoogle Scholar
  27. Ishinabe T (1982) Critical exponents for surface interacting self-avoiding lattice walks. I. Three-dimensional lattices. J Chem Phys 76:5589–5594CrossRefGoogle Scholar
  28. Israelachvili JN (1985) Intermolecular and surface forces. Academic, LondonGoogle Scholar
  29. Joanny JF, Leibler L, de Gennes PG (1979) Effects of polymer solutions on colloid stability. J Polym Sci Polym Phys Ed 17:1073–1084CrossRefGoogle Scholar
  30. Kuhn W, Kunzle O, Katchalsky A (1948) Verhalten polyvalenter fadenmolekelionen in lösung. Halvetica Chemica Acta 31:1994–2037CrossRefGoogle Scholar
  31. Le Guillou JC, Zinn-Justin J (1977) Critical exponents for the n-vector model in three dimensions from field theory. Phys Rev Lett 39:95–98CrossRefGoogle Scholar
  32. Madras N, Slade G (1993) The self-avoiding walk. Birkhaeuser, BaselGoogle Scholar
  33. Mandelbrot BB (1983) The fractal geometry of nature. Freeman W.H, New YorkGoogle Scholar
  34. Manning GS (1969) Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J Chem Phys 51:924–933CrossRefGoogle Scholar
  35. Miller-Chou BA, Koenig JL (2003) A review of polymer dissolution. Prog Polym Sci 28:1223–1270CrossRefGoogle Scholar
  36. Odijk T (1977) Polyelectrolytes near the rod limit. J Polym Sci Polym Phys Ed 15:477–483CrossRefGoogle Scholar
  37. Odijk T, Houwaart AC (1978) On the theory of the excluded-volume effect of a polyelectrolyte in a 1-1 electrolyte solution. J Polym Sci Polym Phys Ed 16:627–639CrossRefGoogle Scholar
  38. Pincus P (1976) Excluded volume effects and stretched polymer chains. Macromolecules 9:386–388CrossRefGoogle Scholar
  39. Potemkin II, Khokhlov AR (2004) Nematic ordering in dilute solutions of rodlike polyelectrolytes. J Chem Phys 120:10848CrossRefGoogle Scholar
  40. Potemkin II, Limberger RE, Kudlay AN, Khokhlov AR (2002) Rodlike polyelectrolyte solutions: effect of the many-body Coulomb attraction of similarly charged molecules favoring weak nematic ordering at very small polymer concentration. Phys Rev E 66:011802CrossRefGoogle Scholar
  41. Rayleigh L (1882) On the equilibrium of liquid conducting masses charged with electricity. Philos Mag 14:184–186CrossRefGoogle Scholar
  42. Rubin RJ (1965) Random walk model of chain polymer adsorption at a surface. J Chem Phys 43:2392–2407CrossRefGoogle Scholar
  43. Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, OxfordGoogle Scholar
  44. Scheutjens JMHM, Fleer GJ (1980) Statistical theory of the adsorption of interacting chain molecules. 2. Train, loop, and tail size distribution. J Phys Chem 84:178–190CrossRefGoogle Scholar
  45. Semenov A, Joanny JF (1995) Structure of adsorbed polymer layers: loops and tails. Europhys Lett 29:279–284CrossRefGoogle Scholar
  46. Skolnick J, Fixman M (1977) Electrostatic persistence length of a wormlike polyelectrolyte. Macromolecules 10:944–948CrossRefGoogle Scholar
  47. Wu C, Zhou S (1996) First observation at the molten globule state of a single homopolymer chain. Phys Rev Lett 77:3053–3055CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Department of Polymer Science and Engineering School of Chemistry and Chemical EngineeringNanjing UniversityNanjingChina, People’s Republic

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