Surface differential double layer capacity

Various methods have been employed for the determination of E of liquid and solid metals. Besides purely electrochemical ones (e.g. measurement of the differential double layer capacity (see also chapter 4.2)) further techniques have been used for the investigation of the surface tension at the solid/electrolyte solution phase boundary. The employed methods can be grouped into several families based on the meas-... 

In its most simple form, this means without effects such as adsorption or formation of coatings at the electrode surface36. The resistance, Rc, represents electrical conductivity of the electrolyte and is not a property of the electrode itself. The differential double-layer capacity, Cmetal surface of the metal-electrolyte interface, which is in equilibrium with an equal excess of charge but opposite in sign at the side of the electrolyte. 

Area, constant, optical absorption Activity, absorption coefficient Debye length Cyclic voltammogram Capacitance / j,F Double layer capacity / 0.F Differential double layer capacity Integral double layer capacity Concentration / M Surface concentration Bulk concentration / M Diffusion coefficient / cm s ... 

Electrochemical techniques such as chronocoulometry, integrated cyclic voltammetry curves, or differentiating double-layer capacity measurements as a function of bulk concentrations can be used to estimate FA however, these types of determinations may still be in error since they measure the total number of surface species, while the number of molecules at active sites which exhibit both the EM and CT effects may be much smaller. Thus, the estimates of Gsers 10 to 10 found at pretreated Ag, for example, may err on the low side if special active sites are involved in SERS. It has been estimated that only 3% of the surface sites are SERS active. " ... 

Figure 7. Comparison of (a, solid) electrochemical and (b, dashed) UHV measurements of the H, coverage/potentiaI differential versus potential on Pt(lll).1.) cathodic sweep (25 mV/s) voltammogram in 0.3 M HF from Ref. 20, constant double layer capacity subtracted, b.) dB/d(A ) versus A plot derived from A versus B plot of Ref. 26. Potential scales aligned at zero coverage. Areas under curves correspond to a.) 0.67 and b.) 0.73 M per surface Pt atom.

The simplest model is that of a plate capacitor developed very early by Helmholtz. The idea is that the ions of the electrolyte, which form the excess charge there, can approach the metal surface only up to the distance of the radius which includes the irmer solvation sphere in liquid solutions. Measurements of the differential capacity of smooth electrodes yielded values for the Helmholtz double-layer capacity, Ch, on tlie order of 20 to 30 pF cm . The model of a plate capacitor gives for the differential capacity... 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

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... 

Measurement of the differential capacitance C = d /dE of the electrode/solution interface as a function of the electrode potential E results in a curve representing the influence of E on the value of C. The curves show an absolute minimum at E indicating a maximum in the effective thickness of the double layer as assumed in the simple model of a condenser [39Fru]. C is related to the electrocapillary curve and the surface tension according to C = d y/dE. Certain conditions have to be met in order to allow the measured capacity of the electrochemical double to be identified with the differential capacity (see [69Per]). In dilute electrolyte solutions this is generally the case. 

FIG. 8 Inverse differential capacity at the zero surface charge vs. inverse capacity Cj of the diffuse double layer for the water-nitrobenzene (O) and water-1,2-dichloroethane (, ), interface. The diffuse layer capacity was evaluated by the GC ( ) or the MPB (0,)> theory. (From Ref. 22.)... 

Of the quantities connected with the electrical double layer, the interfacial tension y, the potential of the electrocapillary maximum Epzc, the differential capacity C of the double layer and the surface charge density q(m) can be measured directly. The latter quantity can be measured only in extremely pure solutions. The great majority of measurements has been carried out at mercury electrodes. 

Fig. 6-96. Change in differential capacity of an interfadal double layer leading or not leading to interfadal lattice transformation in anodic and cathodic potential sweeps for a gold electrode surface (100) in perchloric add solution Ey = critical potential beyond which the interfadal lattice transforms from (5 x 20) to (1 x 1) E = critical potential below which the interfadal lattice transforms from (1 x 1) to (5 x 20) Ejm = potential of zero charge VacE = volt referred to the saturated calomel electrode. [From Kolb-Schneider, 1985.]...

Naneva and Popov et al. [4, 5] have studied Cd(OOOl) grown electrolytically in a Teflon capillary in NaF aqueous solution. A value of fpzc equal to —0.99 V (versus saturated calomel electrode (SCE)) was evaluated from minimum potential (Amin) on the differential capacity C-E curves obtained in dilute electrolyte. The zero charge potential was found to be practically independent of the crystallographic orientation. The Apzc and the irmer layer capacity of Cd(OOOl) single crystals were determined in KF solution as a function of temperature [5]. The positive values of AApzc/AT indicated that the water dipoles in the inner part of the double layer were orientated with their negative part to the electrode surface. It was found that the hydrophilicity of the electrodes was increasing in the order Cd(OOOl) < Ag(100)[Pg.768]

The differences between various Ag surfaces can be distinguished by comparing their surface morphology (generally, the surface of (110) crystal is more folded than that of (111)) and other properties, such as the surface density of atoms, the PZC, and double-layer capacitance. The double-layer properties of single-crystal Ag electrodes have been studied very intensively [3, 22-27]. Selected characteristics of various Ag surfaces are compared in Table 1, which shows that the higher the surface density of atoms, the more positive PZC becomes. Furthermore, Fig. 2 exemplifies differential capacity data of those Ag surfaces. 

Fig. 3.3 Schematic plots of the double layer region, (a) Electrocapillary curve (surface tension, y, vs. potential) (b) Charge density on the electrode, aM, vs. potential (c) Differential capacity, Cd, vs. potential. Curve (b) is obtained by differentiating curve (a), and (c) by differentiation of (b), Ez is the point of zero...

The capacity C of the double layer per square centimetre, or the rate of change of the charge with the applied potential E, can be found from the electrocapillary curve, for it is equal to the second differential coefficient of the surface tension with respect to the potential. This follows at once from (13), since... 

The charge density of a -> double layer is Q = C(E - Ezc)> where C is the differential capacity and Ezc is a -+ potential of zero charge, i.e., the potential of electro-capillary maximum. By integrating the Lippmann equation a relationship between the surface tension and the electrode potential is obtained y = ymax -C(E - Ezc)212. This is a parabola symmetrical about ymax> if C is independent of E [ii]. 

Experimentally, the -> electric double layer at ITIES has been studied mainly by -> surface tension [x, xi] and differential capacity [xii] measurements. Experimental results and theoretical models were reviewed [xiii]. 

Capacitance, C, provides direct information on the structure of the adsorbed layer (10, 11). The change in the differential capacity of the electrical double layer between a polarized mercury surface and a 0.15 M NaCl solution containing various concentrations of protein... 

F. 1.1.1 A simple electronic scheme equiveilent to the electrochemical cell Ru, resistance uncompensated in the regular three-electrode system Q, differential capacity of the double layer Rf, resisttmce to faradaic current at the electrode surface Rq, solution resistemce compensated in the three-electrode system... 

The values of surface charge density obtained by numerical differentiation of the electrocapillary curve agreed well with those obtained by numerical integration of the differential capacity curve [17,29] (Fig. 3). These results indicate that the interface between a nitrobenzene solution of TBATPB and an aqueous solution of LiCl actually behaves as an ideal-polarized interface in a certain potential range and also that the differential capacity measurements should give essentially the same information on the electrocapillarity and the double layer structure of nitrobenzene/water interfaces as the electrocapillary curve measurements, provided that their electrocapillary maximum potential which is now equal to the potential of zero charge (pzc) and interfacial tension at the pzc (y J known. 

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