Theory of directed polymers
Abstract
We develop a theory of polymers in a nematic solvent by exploiting an analogy with twodimensional quantum bosons at zero temperature. We argue that the theory should also describe nematic polymers in an isotropic solvent. The dense phase is analyzed in a Bogoliubovlike approximation, which assumes a broken symmetry in the phase of the boson order parameter. We find a stiffening of the longitudinal fluctuations of the nematic field, calculate the densitydensity correlation function, and extend the analysis to the case of ferro and electrorheological fluids. The boson formalism is used to derive a simple hydrodynamic theory which is indistinguishable from the corresponding theory of nematic polymers in an isotropic solvent at long wavelengths. We also use hydrodynamics to discuss the physical meaning of the boson order parameter. A renormalizationgroup treatment in the dilute limit shows that logarithmic corrections to polymer wandering, predicted by de Gennes, are unaffected by interpolymer interactions. A continuously variable Flory exponent appears for polymers embedded in a twodimensional nematic solvent. We include free polymer ends and hairpin configurations in the theory and show that hairpins are described by an Isinglike symmetrybreaking term in the boson field theory.
 Publication:

Physical Review A
 Pub Date:
 June 1992
 DOI:
 10.1103/PhysRevA.45.8727
 arXiv:
 arXiv:condmat/9204007
 Bibcode:
 1992PhRvA..45.8727K
 Keywords:

 36.20.Ey;
 05.40.+j;
 Conformation;
 Condensed Matter
 EPrint:
 29 pages (small)  requires harvmac.tex (16 figures, not included)