Collapse of polymer brushes grafted onto planar ... - Wageningen UR

For small particles with radius R < R ≅ 1/2
o aN , the two effects give rise to the novel “pseudo-star”
conformation of polyampholyte chain (Zhulina 2001). Here, the equilibrium structure of the complex is
determined by the interplay of three factors: the polarization of the loops, the stretching of the loops, and the
ternary contacts between monomers (theta-solvent conditions). The analysis (Zhulina 2001; Dobrynin 2001)
indicates that in the pseudo-star conformation, the loops have a bimodal distribution. The smaller loops of
size ~ R decorate the particle (the core of the pseudo-star). The larger loops of size H ~ aN1/2( Q2f ) −1/
6 form
the “branches” of the pseudo-star. The number of branches P ~( Q2f ) 2/3 does not depend on chain length N
and is determined solely by particle charge Q and degree of chain ionization f.
In excess of polyampholyte molecules in the bulk solution, each complex is comprised of many chains.
One can envision such a situation as formation of a semi-dilute adsorbed layer near the charged particle. The
structure of the adsorbed layer (the polymer density profile, the distribution of loops, etc.) depends on the
particle size and the surface charge density. For small particles with R < R ≅ 1/2
o aN , the internal part of the
adsorbed layer is found in the pseudo-star conformation. (It contains P chains each forming a single branch
of the pseudo-star). The polymer density profile cr ()~ P1/2r −1
decays inversely proportional to the distance r
from the particle. The exterior part of the layer is formed by the less polarized chains (“poles” stretched in the
electric field of spherical symmetry). For very large particles, adsorption occurs as on a planar surface
(Dobrynin 1999). We calculate the adsorption isotherms for particles of different sizes and obtain the
thickness of the adsorbed layer as a function of bulk polymer concentration. The results are compared with
the experimental data on adsorption of gelatin.
3. Interaction of ionized micelles with oppositely charged polyions
We consider the association of an ionized quenched polymer micelle with an oppositely charged polyion.
The star-like micelle consists of a neutral core and a charged corona. The respective degrees of ionization of
the corona and of the polyion, α and β, are assumed to be relatively small to ensure the stability (solubility) of
the complex. The number of polymer chains in the micelle is fixed, and the length of the polyion varies. An
analytical self-consistent-field model indicates that when the polyion is long enough, the complex is virtually
electroneutral as a whole (Simmons 2001). The compensating amount of oppositely charged polyion is
dragged inside the micelle to release the small counterions from the corona. The structure of the equilibrium
complex is rationalized in terms of the effective second ( v eff ) and third ( w eff ) virial coefficients of monomermonomer
interactions, v = + α β 2
eff v (1 / ) + χα/ β and w = + α β 3
eff w (1 / ) . Here, v and w are the actual virial
coefficients of monomer-monomer interactions of the corona chains, and χ is the Flory interaction parameter.
We then use the numerical Scheutjens and Fleer model to explore the structure of the micelle/polyion
complex in more detail. By performing calculations at various values of v, α, β, χ, and different amounts of
added polyion, we demonstrate that the equilibrium properties of the complex can be rationalized in terms of
the theory of neutral star-like polymers. We also focus on the effect of charge distribution on the polyion and
consider three different cases: (1) a homopolymer with the smeared distribution of charge, (2) a diblock
copolymer with a charged and a neutral block, and (3) a multi-block copolymer. Although the fine details of
polyion distribution in the micelle/polyion complex are different in the three cases, the Scheutjens and Fleer
model confirms the essential electroneutrality of the complex. The numerical findings are in reasonable
agreement with predictions of the analytical self-consistent-field theory.
Acknowledgements
The results presented in this lecture were obtained in collaboration with Dr. Andrey Dobrynin (UNC), Prof.
Michael Rubinstein (UNC), Chris Simmons (UT), Prof. Steve Webber (UT), Dr. Jan van Male (WU) and Dr.
Frans Leermakers (WU). The financial support from the National Science Foundation USA (grants DMR-
9973300 and DMR-9730777) and NWO Project 047.009.016 “Self-Organization and Structure of Bionanocomposites”
is greatly acknowledged.