Number of Monomers in Trains Loops and Tails

The number of monomers in trains, loops, and tails as a function of kang and Ci is presented in Fig. 17a-c. Monomer fraction in trains has a maximal value when kang = 0.005kBT/deg2, i.e., when semiflexible chains are considered. Below that value, i.e., when flexible chains are considered, the solenoid conformation is lost and monomers move from the first layer to the others to form loops. Above that value, when rigid chains are considered, most of the monomer entropy is lost and ordered solenoid conformations are obtained. By decreasing the attractive monomer-particle interactions, rigid chains desorb to form tails.

Competition between the attractive electrostatic energy and the increase in the torsional energy to control the final complex structure is well illustrated when Ci = 0.1 M. By increasing kang, we obtain a transition from a disordered and strongly bound complex to a situation where the polymer touches the particle over a finite length while passing by the formation of a solenoid structure. Complexes exhibit a significant monomer loop fraction only when kang < 0.001kBT/deg2. In the other cases, the fraction of monomers in train decreases while that of the tails increases, monomers being transferred to tails but not to loops. The amount of chain adsorption r, which is commonly used experimentally to derive adsorption isotherms, is presented in Fig. 18. r is decreasing with increasing ionic concentration because of monomer desorption. On the other hand, the amount of monomer adsorption has a maximal value when kang = 0.005kBT/deg2 (i.e., for semiflexible chains) according to the formation of a solenoid without parts extending in the solution. Because of the displacement of the adsorption-desorption limit with kang, curves cross each other.

FIG. 17 Number of monomers in trains, loops, and tails vs. kang at various ionic concentration values (N = 100). Monomers in loops are promoted by decreasing the chain rigidity whereas monomers in trains exhibits a maximal value for semiflexible chains (i.e., when kang = 0.005 kBT/deg2).
Latex Particle Nbr

FIG. 18 Adsorbed amount r and surface coverage 8 of the polyelectrolyte and particle, respectively, vs. C for different kang values. r reaches a maximal value for the semiflexible chain kang = 0.005 kBT/deg2 (and with decreasing C). Above that value both chain rigidity (by forcing the chain to be extended in solution) and flexibility (monomers are transfered to loops) limit the amount of adsorbed monomers in the first adsorption layer.

FIG. 18 Adsorbed amount r and surface coverage 8 of the polyelectrolyte and particle, respectively, vs. C for different kang values. r reaches a maximal value for the semiflexible chain kang = 0.005 kBT/deg2 (and with decreasing C). Above that value both chain rigidity (by forcing the chain to be extended in solution) and flexibility (monomers are transfered to loops) limit the amount of adsorbed monomers in the first adsorption layer.

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