Adsorption Desorption Limit Complex Configurations

Equilibrated configurations as a function of Ct and kang are presented in Table 5. No adsorption is observed when Ct > 1 M whereas adsorption is always ob-

FIG. 15

am ratio,

Net charge |Q* | = |Q -i q | variation as a function of particle charge, ap / and ionic concentration C.. Charge inversion increases with charge screening.

the data do not fit the linear variations because the chain is too small to attain the asymptotic conditions of the Nguyen-Shklovskii analytical theory.

FIG. 15

am ratio,

Net charge |Q* | = |Q -i q | variation as a function of particle charge, ap / and ionic concentration C.. Charge inversion increases with charge screening.

the data do not fit the linear variations because the chain is too small to attain the asymptotic conditions of the Nguyen-Shklovskii analytical theory.

TABLE 5 Monte Carlo Equilibrated Conformations of Semiflexible Polyelectrolyte-Particle Complexes as a function of C and kang>

[kBT/deg]

0

0,01

0.1

0.3

1

0

n

ft

OKh^:

m

0.001

JÉL

«

0.005

I

On

IK

o

» N/"

0.01

1

#

o

«

0,02

'2X

)

aBy increasing the chain stiffness, solenoid conformations are progressively achieved at the particle surface.

aBy increasing the chain stiffness, solenoid conformations are progressively achieved at the particle surface.

served when Ct < 0.1 M. At Ct = 0.3 M, Table 5 clearly demonstrates that adsorption is strongly controlled by the value of kmg. Hence, adsorption is promoted by (1) decreasing the chain stiffness (and subsequently the required energy to confine the semiflexible polyelectrolyte at the particle surface) and (2) decreasing the ionic concentration (thus increasing the electrostatic attractive interactions between the monomer and the particle surface that we consider as the driving force for the adsorption). Because of charge screening in the highsalt regime, monomer-particle interactions are not large enough to overcome the polyelectrolyte confinement near the particle.

A quantitative picture of adsorption-desorption is achieved by calculating the critical ionic concentration Cct vs. ktmg at which the adsorption-desorption process is observed (Fig. 16). The adsorption-desorption limit is determined by monitoring the ionic concentration required to satisfy the adsorption-desorption criteria (for a constant kang value). We found that CC is rapidly decreasing with kang from 0.38 M to a plateau value at 0.22 M when kang > 0.01 kBT/deg2. In that plateau region, as the polyelectrolyte conformation is similar to that of a rigid rod, the polyelectrolyte is in contact with the particle surface with a few consecutive monomers only, with two polymer arms extended in opposite directions from the particle. We also calculated vs. Ct the critical chain stiffness kcmg at which adsorption-desorption is observed (inset of Fig. 16). We found that kOmg ~ k-5 (with 8 = 14.5), revealing that the increase of chain stiffness rapidly promotes chain desorption on curved surfaces.

The monomer distribution at the particle surface is largely controlled by the value of kang. When the chain flexibility is important (kang < 0.001 kBT/deg2), "tennis ball" conformations are achieved, whereas when rigid chains are consid-

FIG. 16 Plot of the critical ionic concentration C\ vs. kmg at the adsorption-desorption limit. The critical stain stiffness value kacng, at which desorption is observed, is shown in the inset vs. k.

ered (kang > 0.00l kBT/deg2), the intrinsic flexibility forces the polyelectrolyte to adopt solenoid conformations such as those predicted by the analytical model of Nguyen and Shklovskii. Both the strong electrostatic repulsions between the neighboring turns and intrinsic chain rigidity keep the turns parallel to each other and a constant distance between them. It is worth noting that the polymer ends are not adsorbed at the particle surface in all cases.

When Ci > 0.01 M, large changes in the chain dimensions are now observed with increasing the chain stiffness. As long as kang < 0.001kBT/deg2, loops and tail are promoted (Table 5; Ct = 0.3 M and kang = 0.0005kBT/deg2), resulting in an increase of the thickness of the adsorption layer. When kang > 0.005kBT/deg2 and with increasing Ci, the polyelectrolyte starts to leave the surface by winding off. Extended tails in solution are formed concomitantly with a decrease in the number of turns of the solenoid and monomers in trains (Table 5; Ci = 0.1 M and kang = 0.01kBT/deg2). By further increasing the ionic concentration or chain intrinsic flexibility, the polyelectrolyte becomes tangent to the particle surface with dimensions close to its free unperturbed dimensions.

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