Number of Monomers in Trains Loops and Tails

The number of monomers in trains, loops, and tails as a function of op/am and different Ct values is presented in Fig. 12 to provide insight into the structure of adsorbed layer. The number of monomers in trains increases rapidly when particle size increases from op /am = 2 to 10. Then, by further increasing the op / <5m ratio to 50, it reaches a plateau value that is close to the total number of monomers of the polyelectrolyte (in particular when Ct = 0 M). Thus, in the presence of large particles the chains have a tendency to flatten and to be fully extended on the particle surface since this lowers the free energy most. Under such conditions, the electrostatic excluded volume of the monomers does not play a key role in the limitation of the amount of adsorbed monomer on the particle surface.

FIG. 12 Quantitative description of the adsorbed monomer layer; number of monomers in trains, loops, and tails vs. ap/<5m and Ct. The monomer fraction in trains increases with the ap/<5m ratio, then reaches a plateau value, whereas the monomer fraction in tails decreases with ap/<5m The monomer fraction in loops exhibits a maximal value when the surface area of the particle is large enough to attract only a few monomers.

FIG. 12 Quantitative description of the adsorbed monomer layer; number of monomers in trains, loops, and tails vs. ap/<5m and Ct. The monomer fraction in trains increases with the ap/<5m ratio, then reaches a plateau value, whereas the monomer fraction in tails decreases with ap/<5m The monomer fraction in loops exhibits a maximal value when the surface area of the particle is large enough to attract only a few monomers.

When increasing Ct, and when the particle surface is large enough (op/om > 10), the number of monomers in trains is less than in the salt-free case due to the formation of loops and tails. When curvature effects become significant (8 < <5p/<5m < 15), the fraction of monomers in trains decreases whereas that in the loops increases, the monomers being transferred to loops but not to tails. Figure 12b illustrates that the number of monomers in loops reaches a maximum when op/am is close to 8, the ratio at which maximal chain deformation occurs. By decreasing the op /am ratio (op /om < 8), monomer desorption becomes critical and the monomers are transferred in tails.

Further insight into the adsorption properties of the polyelectrolyte on the surface is gained by examining particle surface coverage or the amount of adsorbed polymer. The effect of Ct and op/am presented in Fig. 13 clearly demonstrates that the amount of adsorption r generally increases as the op /am ratio increases and Ct diminishes. Nonetheless, it is important to note that r does not take on monotonic behavior because of the competition between the attractive monomer-particle interactions and an increase in the electrostatic excluded volume of the polyelectrolyte at the particle surface. The monomer excluded electrostatic volume is expected to limit the number of monomers confined close to the particle surface in the low-salt regime and when 4 < op/am < 15.

FIG. 13 Adsorbed amount r of the polyelectrolyte vs. Ci and ap/om. r increases by increasing the size of the particle and reaches a maximal value in the low-salt regime. However, although monomer-particle interactions are promoted in the low-salt regime, the excluded electrostatic volume between monomers at the particle surface strongly limits the number of adsorbed monomers in particular when ap /om = 10, 8, 7, 6, 5. Data with the coordinates log(Ci) = -4 correspond to the salt-free case.

FIG. 13 Adsorbed amount r of the polyelectrolyte vs. Ci and ap/om. r increases by increasing the size of the particle and reaches a maximal value in the low-salt regime. However, although monomer-particle interactions are promoted in the low-salt regime, the excluded electrostatic volume between monomers at the particle surface strongly limits the number of adsorbed monomers in particular when ap /om = 10, 8, 7, 6, 5. Data with the coordinates log(Ci) = -4 correspond to the salt-free case.

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