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The interplay of the polyelectrolyte-surface electrostatic and non-electrostatic interactions in the polyelectrolytes adsorption onto two charged objects – A self-consistent field study
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10.1063/1.4748815
/content/aip/journal/jcp/137/10/10.1063/1.4748815
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/10/10.1063/1.4748815

Figures

Image of FIG. 1.
FIG. 1.

A schematic representation of the cross-sections of the system under study. The two charged columns are immersed in a polyelectrolyte solution.

Image of FIG. 2.
FIG. 2.

(a) Effect of the salt on the degree of charge compensation at different strengths of monomer-surface non-Coulombic interaction for a specified system parameters of α P = 0.2, σa 2 = 0.04762, H = 4 × 2.887a, and a system size of (20.0 × 2.887a) × (19.0 × 2.887a). In the figure, the legends B-I correspond to u 0 = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1.0, respectively. (b) Effect of the strength of the monomer-surface non-Coulombic interaction on the degree of charge compensation at different salt concentrations for the same system as in Figure 2(a). In the inset, the boundary layer thickness is plotted against the strength of the monomer-surface non-Coulombic interaction at three different salt concentrations. (c) The logarithmic (base 10) plot of the total amount of the bridging chain conformation against the strength of the monomer-surface non-Coulombic interaction at different salt concentrations for the same system as in Figure 2(a). Please note that, in this figure and the subsequent figures, Σ is in the unit of Rg 2.

Image of FIG. 3.
FIG. 3.

(a) The double logarithmic plot of the boundary layer thickness against the charge fraction of PE chains at a surface charge density of σa 2 = 0.04762 and u 0 = 0 for the same system as in Figure 2(a). There is no added salt in the system. In the inset, the double logarithmic plot of the boundary layer thickness against the surface charge density at a PE chain charge fraction of α P = 0.2 and u 0 = 0 is displayed. (b) The plots of the degree of charge compensation against the charge fraction of PE chains at different monomer-surface non-Coulombic interactions for the same system as in Figure 2(a) with a surface charge density of σa 2 = 0.04762. There is no added salt in the system. In the inset, the total amounts of the adsorbed PE chains are plotted against the charge fraction of PE chains at different monomer-surface non-Coulombic interactions. The legends in the inset are the same as in the figure. Please note that, for all the data points at different α P and u 0 in the inset, the total amount of the adsorbed chains is normalized by that at α P = 0.05 and u 0 = 0.

Image of FIG. 4.
FIG. 4.

(a) The plots of the degree of charge compensation against the surface charge density at different monomer-surface non-Coulombic interaction strengths for the same system as in Figure 2(a) with a PE charge fraction of α P = 0.2. There is no added salt in the system. In the figure, the legends B-E correspond to u 0 = 0.0, 0.3, 0.5, 1.0, respectively. In the inset, the total amounts of the adsorbed PE chains are plotted against the surface charge density at different strengths of the monomer-surface non-Coulombic interaction. The legends in the inset are the same as in the figure. Please note that in the inset, for all the data points at different u 0 and σa 2, the total amount of the adsorbed PE chains is normalized by that at a surface charge density of σa 2 = 0.02381 and u 0 = 0.0. (b) The plots of the total amounts of the adsorbed PE chains against the surface charge density at different monomer-surface non-Coulombic interaction strengths (the lower and the upper curves correspond to u 0 = 0.3 and u 0 = 1.0, respectively) for the same system as in Figure 4(a) with a PE charge fraction of α P = 0.4. In the lower right inset, the total amounts of the adsorbed PE chains are plotted as a function of the surface charge density at different monomer-surface non-Coulombic interaction strengths for the same system as in Figure 4(a) with a PE charge fraction of α P = 0.05. The legends in the lower right inset are the same as in the figure. Please note that in both the figure and the lower right inset, the total amount of the adsorbed PE chains corresponding to different data points is normalized by the total adsorbed amount at a surface charge density of σa 2 = 0.02381 and u 0 = 0.3. In the upper left inset, the monomer density distributions along the central horizontal line (x-axis) at different PE charge fractions (α p = 0.05, 0.2, 0.4) at the same monomer-surface non-Coulombic interaction of u 0 = 1.0 and the surface charge density of σa 2 = 0.02381 for the same system as in Figure 4(a) are displayed. In the upper left inset, the curves with the peak value in a decreasing order correspond to increasing PE chain charge fraction. (c) The plot of the total amount of the bridging chain conformation against the surface charge density for the same system as in Figure 4(a) at u 0 = 0.0. In the inset, the total amounts of the bridging chain conformation are plotted against the surface charge density at different monomer-surface non-Coulombic interaction strengths. The legends C-E in the inset are the same as in Figure 4(a).

Tables

Generic image for table
Table I.

The various enthalpic and entropic contributions to the free energy per chain of a polyelectrolyte salt-fee solution with immersed two charged objects at different gap spacings. The system parameters are: N = 50, χ PS = 0.0, , u 0 = 0.5,α P = 0.05, σa 2 = 0.04762, L o = 2.887a, and the system size of (12.0 × 2.887a) × (5.0 × 2.887a). In solving the self-consistent field equations, the size of the time step is 0.002, and the mesh size is 0.015625 Rg. In the table, U sr  / k B T, U e  / k B T, S P  / k B , S S  / k B , S + / k B , S  / k B denote, respectively, the short-range monomer-surface enthalpic contribution, the electrostatic part, the entropic contributions of polymer chains, solvent, counter-ions, and co-ions. Please refer to Ref. 30 for the definitions of the enthalpic and entropic terms.

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/content/aip/journal/jcp/137/10/10.1063/1.4748815
2012-09-13
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The interplay of the polyelectrolyte-surface electrostatic and non-electrostatic interactions in the polyelectrolytes adsorption onto two charged objects – A self-consistent field study
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/10/10.1063/1.4748815
10.1063/1.4748815
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