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Numéro
J. Phys. II France
Volume 6, Numéro 5, May 1996
Page(s) 587 - 591
DOI https://doi.org/10.1051/jp2:1996199
References of J. Phys. II France 6 587-591
  1. Grest G.S., Fetters L.J., Huang J.S. and Richter D., Adv. Chem. Phys., Vol. 94, E. Prigogine and S. A. Rice Eds. (New York, 1996).
  2. Daoud M., Cotton J.-P., J. Phys. France 43 (1982) 531 [CrossRef] [EDP Sciences].
  3. Raphaël E., Pincus P. and Fredrickson G.H., Macromolecules 26 (1993) 1996-2006 [CrossRef].
  4. The results (1) and (2) are easily generalized to the case P > N ; see the upper part of Figure 1.
  5. Consider an isolated linear chain, with degree of polymerization N, dissolved in a melt of shorter, chemically identical chains with degree of polymerization P. The chain behaves like a string of subunits, usually called melt blobs, each containing gc = P2 monomers. Within one melt blob the behavior is ideal, leading to a blob size lc = aP. Different melt blobs repel each other, and the resulting self-avoiding chain (of unit step lc) has a size $R \cong (N/g_{c})^{\nu}l_{c}$ where ${\nu} = 3/5$ is the Flory 3-dimensional exponent. See, e.g., de Gennes P.-G., "Scaling Concepts in Polymer Physics" (Cornell University Press, Ithaca, Fourth Printing, 1985).
  6. Aubouy M., Fredrickson G.H., Pincus P., Raphaël E., Macromolecules 28 (1995) 2979-2981 [CrossRef].
  7. Note that the results concerning the star radius R may be recovered by minimizing the Flory free energy per arm $\displaystyle\frac{F_\textrm{{arm}}}{kT} \cong$ $\displaystyle\frac{R^{2}}{Na^{2}}$ + $N\displaystyle\frac{a^{3}}{P}c$ + $N\displaystyle\frac{a^{6}}{P}c^{2}$ (where $c \cong Nf/R^{3}$ is the average monomer concentration of the star), keeping in mind the conditions $a^{3}c \leq 1$ (i.e. $N f a^{3} \leq R^{3})$ and $R \geq aN^{1/2}$
  8. A somewhat similar Gaussian behavior was described by Birshtein and Zhulina for stars with a small number of semiflexible branches in low molecular weight solvents. See Birshtein T.M., Zhulina E.B., Polymer 25 (1984) 1453-1461 [CrossRef].