SPECIAL ISSUE: Proceedings of the 17th National Conference on Condensed Matter Theory and Statistical Physics (CMTS12); 23–26 July 2012, Lanzhou, ChinaNo Access

ON THE STRUCTURE OF STATISTICAL FIELD THEORY OF POLYMERS

BING MIAO

BING MIAO

College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China

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https://doi.org/10.1142/S0217979213610092Cited by:1 (Source: Crossref)

Abstract

We examine several widely used statistical field theoretic methods in theoretical polymer physics. A systematic derivation for the polymer field theoretic model is given within the framework of the effective Landau theory. After constructing the field theoretic model, we perform a perturbative expansion of the model, and then the mean-field approximation and the Gaussian fluctuation approximation are introduced into the treatment of the model in order. We also outline a derivation for the self-consistent Hartree theory in polymer physics within a variational scheme. The applications of these methods are also discussed accordingly.

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References

R. A. L. Jones , Soft Condensed Matter ( Oxford University Press , New York , 2002 ) . Crossref, Google Scholar
P. G. de Gennes , Scaling Concepts in Polymer Physics ( Cornell University Press , Ithaca , 1979 ) . Google Scholar
M. Doi and S. F. Edwards , The Theory of Polymer Dynamics ( Oxford University Press , New York , 1986 ) . Google Scholar
G. H. Fredrickson , The Equilibrium Theory of Inhomogeneous Polymers ( Oxford University Press , New York , 2006 ) . Google Scholar
T. A. Vilgis, Phys. Rep. 336, 167 (2000), DOI: 10.1016/S0370-1573(99)00122-2. Crossref, Web of Science, ADS, Google Scholar
D. C. Morse, Ann. Phys. 321, 2318 (2006). Crossref, Web of Science, ADS, Google Scholar
D. J. Amit , Field Theory, The Renormalization Group, and Critical Phenomena ( World Scientific , Singapore , 1984 ) . Google Scholar
M. Kardar , Statistical Physics of Fields ( Cambridge University Press , New York , 2007 ) . Crossref, Google Scholar
N. Goldenfeld , Lectures on Phase Transitions and The Renormalization Group ( Addison-Wesley , New York , 1992 ) . Google Scholar
M. W. Matsen and M. Schick, Phys. Rev. Lett. 72, 2660 (1994), DOI: 10.1103/PhysRevLett.72.2660. Crossref, Web of Science, ADS, Google Scholar
M. W. Matsen, J. Phys.: Condens. Matter 14, R21 (2002), DOI: 10.1088/0953-8984/14/2/201. Crossref, Web of Science, Google Scholar
L. Leibler, Macromolecules 13, 1602 (1980), DOI: 10.1021/ma60078a047. Crossref, Web of Science, ADS, Google Scholar
T. Ohta and K. Kawasaki, Macromolecules 19, 2621 (1986), DOI: 10.1021/ma00164a028. Crossref, Web of Science, ADS, Google Scholar
K. Kawasaki, T. Ohta and M. Kohrogui, Macromolecules 21, 2972 (1988), DOI: 10.1021/ma00188a014. Crossref, Web of Science, Google Scholar
K. Kawasaki and T. Kawakatsu, Macromolecules 23, 4006 (1990), DOI: 10.1021/ma00219a022. Crossref, Web of Science, ADS, Google Scholar
B. Miaoet al., J. Chem. Phys. 124, 144902 (2006), DOI: 10.1063/1.2187492. Crossref, Web of Science, ADS, Google Scholar
B. Miaoet al., Polymer 48, 4278 (2007), DOI: 10.1016/j.polymer.2007.05.045. Crossref, Web of Science, Google Scholar
I. Erukhimovich and A. Johner, Eurephys. Lett. 79, 56004 (2007), DOI: 10.1209/0295-5075/79/56004. Crossref, Google Scholar
I. Erukhimovichet al., J. Chem. Phys. 134, 054906 (2011), DOI: 10.1063/1.3537978. Crossref, Web of Science, Google Scholar
A.-C. Shi, J. Noolandi and R. C. Desai, Macromolecules 29, 6487 (1996), DOI: 10.1021/ma960411t. Crossref, Web of Science, ADS, Google Scholar
M. Laradjiet al., Macromolecules 30, 3242 (1997), DOI: 10.1021/ma9618437. Crossref, Web of Science, ADS, Google Scholar
A.-C. Shi, J. Phys.: Condens. Matter 11, 10183 (1999), DOI: 10.1088/0953-8984/11/50/311. Crossref, Web of Science, Google Scholar
G. H. Fredrickson and E. Helfand, J. Chem. Phys. 87, 697 (1987), DOI: 10.1063/1.453566. Crossref, Web of Science, ADS, Google Scholar
I. W. Hamley and V. E. Podneks, Macromolecules 30, 3701 (1997), DOI: 10.1021/ma961679n. Crossref, Web of Science, ADS, Google Scholar
B. Miao and R. A. Wickham, J. Chem. Phys. 128, 054902 (2008), DOI: 10.1063/1.2827472. Crossref, Web of Science, Google Scholar
P. Grzywacz, J. Qin and D. C. Morse, Phys. Rev. E 76, 061802 (2007), DOI: 10.1103/PhysRevE.76.061802. Crossref, Web of Science, Google Scholar
J. Qin and D. C. Morse, J. Chem. Phys. 130, 224902 (2009), DOI: 10.1063/1.3124799. Crossref, Web of Science, ADS, Google Scholar