In the concentrated solutions, multiple chains are adsorbed on the substrate, and
the distances away from the substrate surface can be roughly separated into three
regions: the proximal region,x<d, which is basically similar to the single chain
adsorption in the dilute solutions; the central region,d<x<xb, which reflects the
hydrodynamic thickness of the adsorption layer beyondd, with the decay of
monomer concentrations in a scaling exponent of4/3 to the distancex, where
xbis the correlation length in the bulk solution; the distal region,x>xb, which
exhibits an exponential decay of monomer concentrations down to the bulk solution
(De Gennes 1981 ). In the central region, de Gennes proposed the so-called “self-
similar grid” construction that the correlation lengths for a mesh size of the loops
were in the same scales of distancesxaway from the substrate, while the correlation
lengthxscaled with the concentrationCin semi-dilute solutions with an exponent
of 3/4, see (4.32), and thus inversely derived the above exponent of –4/3
(De Gennes 1981 ).
Question Sets
- What kind of polymer physics process roughly corresponds to the rice cooking?
- Why does the scaling analysis work well in polymer physics?
- Why can we say that polymer chains are their own theta solvent?
- Why can the poly(acrylate acid) chain change its flexibility with the pH values in
aqueous solutions? - Why can long DNA chains be stored in a small room of cell nucleus?
- Why does the collapse transition of a polyelectrolyte chain show the bead-string
structure?
References
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Advances in chemical physics. Wiley, New York, pp 1–66
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 8:804–818
De Gennes PG (1972) Exponents for excluded volume problem as derived by Wilson method.
Phys Lett A 38:339–340
De Gennes PG (1976) Scaling theory of polymer adsorption. J Phys 37:1445–1452
De Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca
De Gennes PG (1981) Polymer solutions near an interface. 1. Adsorption and depletion layers.
Macromolecules 14:1637–1644
De Gennes PG (1983) Scaling theory of polymer adsorption: proximal exponent. J Phys Lett
44:L241–L246
De Gennes PG, Pincus P, Velasco RM, Brochard F (1976) Remarks on polyelectrolyte conforma-
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Dobrynin AV, Rubinstein M (2001) Counterion condensation and phase separation in solutions of
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Polym Sci 30:1049–1118
72 4 Scaling Analysis of Real-Chain Conformations