Electric double layer inner part

The model more generally accepted for metal/electrolyte interfaces envisages the electrical double layer as split into two parts the inner layer and the diffuse layer, which can be represented by two capacitances in series.1,3-7,10,15,32 Thus, the total differential capacitance C is equal to... 

For a long time, the electric double layer was compared to a capacitor with two plates, one of which was the charged metal and the other, the ions in the solution. In the absence of specific adsorption, the two plates were viewed as separated only by a layer of solvent. This model was later modified by Stem, who took into account the existence of the diffuse layer. He combined both concepts, postulating that the double layer consists of a rigid part called the inner—or Helmholtz—layer, and a diffuse layer of ions extending from the outer Helmholtz plane into the bulk of the solution. Accordingly, the potential drop between the metal and the bulk consists of two parts ... 

The electric double layer can be regarded as consisting of two regions an inner region which may include adsorbed ions, and a diffuse region in which ions are distributed according to the influence of electrical forces and random thermal motion. The diffuse part of the double layer will be considered first. 

Electrokinetic measurements at 25°C on silver iodide in 10 3 mol dm-3 aqueous potassium nitrate give d /d(pAg) = -35 mV at the zero point of charge. Assuming no specific adsorption of K+ or NO3 ions and no potential drop within the solid, estimate the capacity of the inner part of the electric double layer. Taking the thickness of the inner part of the double layer to be 0.4 nm, what value for the dielectric constant near to the interface does this imply Comment on the result. 

Eiectrokinetic motion occurs when the mobile part of the electric double layer is sheared away from the inner layer (charged surface). There are several types of eiectrokinetic measurements ... 

This statement requires explanation in terms of the electrical double layer at the surface of all cells, including at the sarcolemma of myofibers and the plasma membrane of neurons. The inner part of this double layer (Stmt layer) can be regarded as a condenser with its complement of ions largely giving it a certain numerical value for permittivity (dielectric constant). This is charged when the membranes of muscle and nerve are at rest (resting potential). 

Figure 1. Part a Surface complex formation of an ion (e.g., cation) on a hydrous oxide surface. The ion may form an inner-sphere complex (chemical bond), an outer-sphere complex (ion pair), or be in the diffuse swarm of the electric double layer. (Reproduced with permission from reference 2. Copyright 1984.) Part h Schematic portrayal of the hydrous oxide surface, showing planes associated with surface hydroxyl groups (s), inner-sphere complexes (a), outer-sphere complexes ( 3), and the diffuse ion swarm (d). In the case of an inner-sphere complex with a ligand (e.g., F or HPOfi ), the surface hydroxyl groups are replaced by the ligand (ligand exchange). (Modified from reference 3.)...

Unsymmetrical solute molecules usually re-orientate on the adsorbing surface [38,50-58]. In addition, electrochemical studies on the properties of the inner part of the electrical double layer have shown that the solvent molecules are likely to re-orientate at the surface solution during an adsorption process [1,59,60]. Thus, the re-orientation of adsorbed species on the adsorbing surface is a feature which cannot be ignored, at least at certain cases. Here, for simplicity we restrict our study to the adsorption behaviour of a neutral solute, the molecules of which exhibit two distinct orientations at the adsorbed layer. 

The potential difference across the electrode/solution interface is dropped by the accumulation of ions of opposite charge in the solution immediately adjacent to the electrode surface in the electrochemical double layer. The spatial distribution of ions gives a potential profile across the double layer into the solution over a distance that is dependent upon the electrolyte concentration. Given this position-dependent potential profile, it is possible that species undergoing electrochemical reaction, which are assumed to reside in the outer Helmholtz plane of the electrical double layer adjacent to the substrate electrode (otherwise known as the plane of closest approach of nonspecifically adsorbed ions), may not actually be at ([is and hence would not experience the full electrical field corresponding to the electrode/solution potential difference. The result of this is that only a part of the measurable applied r] affects the Gibbs energy of activation of the process. The potential at the OHP with respect to solution, (t)s, is denoted t /i and is known as the potential of the (inner limit... 

Certain model assumptions are necessary in order to reveal the surface concentration of specifically adsorbed ions in the total surface excess F,-. Usually, the ionic component of the electrical double layer (EDL) is assumed to consist of the dense part and the diffuse layer separated by the so-called outer Helmholtz plane. Only specifically adsorbing ions can penetrate into the dense layer close to the surface (e.g. iodide ions), with their electric centers located on the inner Helmholtz plane. The charge density of these specifically adsorbed ions ai is determined by their surface concentration F Namely, for single-charged anions ... 

A charged particle in solution provokes an increased eoneentration of counter ions (ions of opposite eharge to that of the partiele) close to its surface, generating an electrical double layer around this partiele. The liquid layer surrounding the particle exists as two parts an inner region (the Stern... 

In the inner part of the electrical double layer, adjacent to the (solid) surface, the structure of the hydration water differs from that in the bulk solution, and at the surface the environment is even more different. Hence, the surface potential /o cannot be established as the work of charging the surface. 

Because in an aqueous environment, under most conditions, the potential decays for the largest part across the inner region of the electrical double layer (i.e., in the region enclosed by the plane of shear), usually does not exceed a few tens of millivolts. 

An indication of the surface potential can be obtained through electrokinetic measurements. Electrokinetic motion occurs when the mobile part of the electric double layer is sheared away from the inner layer (charged surface). Of the four types of electrokinetic measurements, electrophoresis, electro-osmosis, streaming potential, and sedimentation potential, the first finds the most use in industrial practise. In electrophoresis, an electric field is applied to a sample causing charged dispersed species, and any attached material or liquid, to move towards the... 

Electro-osmosis is an important process in capillary electrophoresis. When the separation capillary is filled with a working electrolyte, an electric double layer is always formed on the inner wall surface due to ionizable groups of the capillary wall material and/or ions absorbed on to the capillary wall. For example, in quartz capillaries, the silanol groups present at the surface form the fixed negative part of the electric double layer. The positive part is then formed by ions present in the solution. A fraction of the ions forming the electrolyte part of the electric double layer is always fixed by electrostatic forces near the capillary wall and forms the so-called Stern layer the rest of these ions form, however, the mobile diffuse layer. The potential this creates between the Stern layer and the bulk solution is termed the zeta potential (in V), and is given by... 

Let s now examine the second important mechanistic point. As the surface of the oxidic supports is charged in electrolytic solutions, an electrical double layer is formed between the support surface and the solution. Various models have been developed to describe the oxide/solution interface [43, 56-63]. It has been widely accepted that the triple layer model describes better this interface in the most of cases [33-39, 41]. A simplified picture of this model is illustrated in fig. 9. It should be noted that the SOH2+. SOH and SO groups are considered to be localized on the surface of the support (zero plane). On the other hand the centers of the water molecules surrounding the surface of the support particles constitute the so called Inner Helmholtz Plane (IHP). Moreover, the counter ions (of the indifferent electrolyte) are located on the Outer Helmholtz Plane (OHP). Very near to this plane is the shear plane and then the diffuse part of the double layer and the bulk... 

Zeta Potential Zeta (Q potential is a parameter used to describe the electrophoretic mobility of colloidal particles. Charged colloidal particles are slightly different from ions in that colloidal particles are surrounded by an electric double layer which is similar but not identical to the ionic atmosphere. The inner part of the double layer moves as a unit in transport experiments. The ( potential is the surface potential of the inner part of the double layer, as shown in Figure 13.10. It is defined as... 

In the case of block copolymer micelles with weak polyelectrolyte shells, the situation is much more complex. Firstly, the amphiphilic pH indicators do not bind only at the core/shell interfacial layer, but they can be solubihzed also in the inner part of the shell. Secondly, the electric field surrounding the indicator probe cannot be described by the simple electric double layer as in the case of ionic surfactant micelles, because the shell thickness is typicaUy several tens of nm with the degree of dissociation (or protonation) of the polyelectrolyte block and consequently the charge density graduaUy increasing with the increasing radial distance from the core-shell micelles. 

Model a is the constant-capacitance model, which may be used in analogy to the constant ionic medium approach in aqueous chemistry Restriction to one value of high ionic strength (in terms of composition and concentration of the electrolyte) assures constancy of activity coefficients of aqueous species and a model of the sohd-hquid interface, which is sufficiently described by a compact layer. It is assumed that the drop in potential in the inner part of the electric double layer at the high electrolyte concentrations is quite extensive so that the difluse part can be completely neglected. 

The value of the electric permittivity of water in the inner part of the double layer is commonly accepted as equal to 6. A much higher capacity of the inner layer at the Ga/solution interface was explained by the weak interaction of gallium with water, leading to a high value of As shown... 

According to the capacitor model of the double layer, assuming constant thickness and electric permittivity, the dependence of AG° on <7m should be linear. " Deviations from linearity can be viewed as resulting from changes of X2 and/or e in the inner part of the double layer. A linear plot ofAG° vs. is observed for adsorption of ions and thiourea. ... 

The electric field which actually affects the charge transfer kinetics is that between the electrode and the plane of closest approach of the solvated electroactive species ( outer Helmholtz plane ), as shown in Fig. 2.2. While the potential drop across this region generally corresponds to the major component of the polarization voltage, a further potential fall occurs in the diffuse double layer which extends from the outer Hemlholtz plane into the bulk of the solution. In addition, when ions are specifically absorbed at the electrode surface (Fig. 2.2c), the potential distribution in the inner part of the double layer is no longer a simple function of the polarization voltage. Under these circumstances, serious deviations from Tafel-like behaviour are common. 

Especially for polar solvents the dielectric permeability may be reduced under the influence of the electric field in the double layer. We Introduced this dielectric saturation In secs. 1.5. Id and I.5.3e. The consequence Is a reduced screening power of the solvent, especially In the inner part of the double layer where the field is high. 

Three interface layers occur within the electrical or the diffuse double layer (DDL) of a clay particle the inner Helmholtz plane (IHP) the outer Helmholtz plane (OHP) with constant thicknesses of Xi and X2, respectively and third is the plane of shear where the electro kinetic potential is measured (Rg. 2.10). This plane of shear is sometimes assumed to coincide with the OHP plane. The IHP is the outer limit of the specifically adsorbed water, molecules with dipoles, and other species (anions or cations) on the clay solid surface. The OHP is the plane that defines the outer limit of the Stem layer, the layer of positively charged ions that are condensed on the clay particle surface. In this model, known as the Gouy-Chapman-Stera-Grahame (GCSG) model, the diffuse part of the double layer starts at the location of the shear plane or the OHP plane (Hunter, 1981). The electric potential drop is linear across the Stem layer that encompasses the three planes (IHP, OHP, and shear planes) and it is exponential from the shear plane to the bulk solution, designated as the reference zero potential. 

If E, and 2 are assumed to be constant. Eqs. [32[ and [33] predict a linear potential drop within each part of the inner double layer, as shown in Fig. (10b). The dependence of the electric potential with distance, in the region from x = d to the bulk solution, i.e, in the diffuse part of the double layer, will be exponential if the surface potential is moderate, as predicted by Eq. 124). In the case of higher surface potentials, the dependence is that shown in Eq. [26], substituting tpn by yj at X = ti. Similarly, the surface charge density, O is related to y by an equation of the type [28]. 

In a fused silica capillary, the surface is negatively charged when the pH is >3. The positive counterions dose to the surface are tightly bound, while the more loosely bound cations in the diffuse part of the double layer can move under the influence of an applied electric field. Because these cations are solvated, and the solvent molecules can hydrogen bond to other solvent molecules, the solvent is pulled toward the cathode. It should be mentioned that this effect occurs only in surface-charged capillaries with a rather narrow inner diameter (ID). 

The timed delivery of oxygenated blood to all parts of the body is the function of the four-chambered pump, the heart. It is enclosed in a double-layered sac, the pericardium, with the inner layer, the visceral pericardium, anchoring the heart and the outer layer attached to the sternum. A cardiac skeleton anchors the foiu heart valves and the atria and ventricles. The thick wall separating the two ventricles, the interventricular septum, houses the Purkinje fibers, which play an important part in the electrical activity of the heart. 

The Galvani potential difference (GPD) is defined as the difference of the inner electric potentials within the Helmholtz part of the double layer. " However, in solutions with ionic strengths above approximately 0.1 mol/(im, the difference of the inner electric potentials between the outer plane of the Helmholtz layer and the bulk of the solution is close to zero. In such cases, the GPD may be approximated by the difference of the inner electric potentials of the electrode material and the solution, with the inner electric potential of the solution as the relative zero point in the evaluation of... 

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