Parsons-Zobel plots

FIG. 7 Parsons-Zobel plot of 1/Q as a function of the inverse Gouy-Chapman capacitance 1 /Cqc- The plot is calculated analytically from Eqs. (54) and (85) at zero charge density. The straight line represents the case = a = For the upper... 

Parsons-Zobel plot Measurements of the extent of monolayer adsorption of an indicator species 226-231... 

The idea in these papers67,223,224 was to identify the potential of the capacitance minimum in dilute electrolyte solutions with the actual value of Ea=o (i.e., <7ge0m( min) = Ofor the whole surface) and to obtain the value of R as the inverse slope of the Parsons-Zobel plot at min.72 Extrapolation of Cwom vs- to Cgg0m = 0 provides the inner-layer capacitance in the / C geom, and not C ea as assumed in several papers.67,68,223,224 In the absence of ion-specific adsorption and for ideally smooth surfaces, these plots are expected to be linear with unit slope. However, data for Hg and single-crystal face electrodes have shown that the test is somewhat more complicated.63,74,219,247-249 More specifically,247,248 PZ plots for Hg/... 

Schmidder and Henderson282 have studied several solvents and metals, using the jellium model for the metal and the MSA for the solution. Deviations of the Parsons-Zobel plot from linearity in the experimental results72,286-288 at the highest concentration have been attributed to the onset of ion-specific adsorption. However, data at other electrode charges... 

The local solvent structural information inherent in deviations from Parsons-Zobel plots suggests that this effect deserves further experimental investigation.126,283 284 The reported accuracy of recent capacitance data (5%) for dilute solutions,285 however, must be improved before unambiguous conclusions about deviations can be drawn. 

In concentrated NaOH solutions, however, the deviations of the experimental data from the Parsons-Zobel plot are quite noticeable.72 These deviations can be used290 to find the derivative of the chemical potential of a single ion with respect to both the concentration of the given ion and the concentration of the ion of opposite sign. However, in concentrated electrolyte solutions, the deviations of the Parsons-Zobel plot can be caused by other effects,126 279"284 e.g., interferences between the solvent structure and the Debye length. Thus various effects may compensate each other for distances of molecular dimensions, and the Parsons-Zobel plot can appear more straight than it could be for an ideally flat interface. 

Parsons-Zobel plots have been constructed for all the systems at a = 0 in the range 0.02 < c < 0.2 M. These plots were linear, with the value of the slope very close to unity. The values of C, obtained by extrapolation of the C-1, C plots to C a = 0 were in good agreement with those calculated from the C,E curves for the 0.1 M NaC104 + DMF system according to the GCSG model.358 The value of Q increases in the sequence of electrodes Hg < Tl(Ga) < In(Ga) < Ga as the hydrophilicity of the electrode surface rises. 

The applicability of the GCSG model has been tested by the Parsons-Zobel approach the Parsons-Zobel plots were linear for all systems, with the value of /re very close to unity. The values of Cf30 obtained by extrapolation of the 1/C(1/Q) curves to 1 /Cd = Owere in good agreement with the values of Cf calculated by Grahame s method. The C/,01 curves for Ga, In(Ga), Tl(Ga), and Hg apparently merge at [Pg.67]

The electrical double layer at Hg, Tl(Ga), In(Ga), and Ga/aliphatic alcohol (MeOH, EtOH) interfaces has been studied by impedance and streaming electrode methods.360,361 In both solvents the value ofis, was independent of cei (0.01 < cucio4 <0.25 M)and v. The Parsons-Zobel plots were linear, with /pz very close to unity. The differential capacity at metal nature, but at a = 0,C,-rises in the order Tl(Ga) < In(Ga) < Ga. Thus, as for other solvents,120 343 the interaction energy of MeOH and EtOH molecules with the surface increases in the given order of metals. The distance of closest approach of solvent molecules and other fundamental characteristics of Ga, In(Ga), Tl(Ga)/MeOH interfaces have been obtained by Emets etal.m... 

Hz, where the capacity dispersion does not exceed 10%. According to the experimental results, depends slightly on cNacio4 and at o Oit decreases with the dilution of the solution. The Parsons-Zobel plot at showed an inverse slope, /pz = 2.22. The values of Cf"° and Cf<<0, calculated according to the GCSG model, are noticeably lower than those for PC-A11/H2O481 or for Hg/PC.312 In contrast to pc-Au/H20, thedepend-... 

Later, polished and unpolished pc-Pb electrodes were studied600 and the Parsons-Zobel plots at c > 0.005 M NaF were found to be linear, with the value of/re = 1.15 for the polished electrode. At c 0.005 M NaF, nonlinear Parsons-Zobel plots, which are characteristic of solid pc electrodes, were observed. The Ch a curves, calculated for polished pc-Pb taking into account the roughness of the surface (Cf ° = 0.26 F m-2, cr = 0.18 F m 2), were compared with those obtained on the basis of the GCSG theory for liquid Hg. C, E curves were obtained for NaF + H20 solutions with the addition of various amounts of thiourea (TU). The... 

Parsons-Zobel plot was linear, with fn equal to unity for pure NaF solution and somewhat lower for a solution with the addition of thiourea. 

Parsons-Zobel plot for NaF solutions was linear (Table 12). The value of Cf"0,determined by the extrapolation of the Cl, Q1 curve to Cjl = 0 and corrected by the value of /pz, has been obtained (Cf 0 - 0.32 F m 2). Adsorption studies of (C l at a polished pc-Pb show splitting of the adsorption-desorption peaks, which can be explained by the energetic inhomogeneity of the surface. The difference between Ea=Q values of various Pb faces has been estimated to be on the order of50-60 mV.604... 

V (SCE in H20). A very well-defined diffuse layer minimum is observed at fmin = -0.82 0.02 V (SCE), independent of v and cCh,coon The Parsons-Zobel plot and Ch a curve have not been derived. 

Vitanov and Popov et al.156 660-662 have studied Cd(0001) electrolyti-cally grown in a Teflon capillary in an aqueous surface-inactive electrolyte solution. The E is independent of ce) and v. The capacity dispersion is less than 5%, and the electrode resistance dispersion is less than 3%. The adsorption of halides increases in the order Cl" < Br" < I".661 A comparison with other electrodes shows an increase in adsorption in the sequence Cd(0001) < pc-Cd < Ag( 100) < Ag(l 11). A linear Parsons-Zobel plot with /pz = 1.09 has been found at a = 0. A slight dependence has been found for the Cit a curves on ce, ( 5%) in the entire region of a. Theoretical C, E curves have been calculated according to the GCSG model. 

Parsons-Zobel plots show a remarkable curvature at cel < 0.05 M KF (Table 16). At c < 0.01 M, a more remarkable deviation from linearity has... 

The BiDER/DMSO + LiC104 interface has been studied by impedance and a very well-developed diffuse layer minimum has been observed, with ,niB independent of cyao/75 The capacitance dispersion was no greater than 2 to 3% in the region -1.5 E< -0.3 V (SCE in H20). Linear Parsons-Zobel plots with/pz very close to unity were obtained, Q was independent of cya0j. 

The electrical double layer at BiDER/PrOH and BiDER/2-PrOH interfaces with the addition of various electrolytes (LiC104> Lil, LiSCN, KSCN) has been studied using impedance.691-693 The Emj was independent of cei and v. A weak dependence of C on v has been found at cucio4 < 0- 1 M and at a > -0.03 C m 2, and the equilibrium differential capacitance C o has been obtained by linear extrapolation of C vs. tu,/2 to co1/2 = 0. Parsons-Zobel plots at a = 0 are linear, with/pz = 1.01 0.01. The values of cf have been obtained according to Grahame and Soder-... 

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