Stern plane

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Sterilization, in fermentation, 11 35-36 Sterilization-in-place (SIP), 11 40 Stern-Langmuir equation, 24 139 Stern-Langmuir isotherm, 24 138 Stern plane, 7 285-286 Steroidal ketones, dehydrogenation of,... 

Figure 9. Formation of Stern plane and diffuse layer on particle surface ( I 0 = surface or Nernst potential, = potential of inner Flelmholtz plane, I 5 = Stern potential, l = thickness of Stern plane, ZP = zeta potential at surface of shear, d = distance from particle surface).

Figure 7.4. Schematic model of the Electrical Double Layer (EDL) at the metal oxide-aqueous solution interface showing elements of the Gouy-Chapman-Stern-Grahame model, including specifically adsorbed cations and non-specifically adsorbed solvated anions. The zero-plane is defined by the location of surface sites, which may be protonated or deprotonated. The inner Helmholtz plane, or [i-planc, is defined by the centers of specifically adsorbed anions and cations. The outer Helmholtz plane, d-plane, or Stern plane corresponds to the beginning of the diffuse layer of counter-ions and co-ions. Cation size has been exaggerated. Estimates of the dielectric constant of water, e, are indicated for the first and second water layers nearest the interface and for bulk water (modified after [6]).

Specifically adsorbed ions are those which are attached (albeit temporarily) to the surface by electrostatic and/or van der Waals forces strongly enough to overcome thermal agitation. They may be dehydrated, at least in the direction of the surface. The centres of any specifically adsorbed ions are located in the Stern layer - i.e. between the surface and the Stern plane. Ions with centres located beyond the Stern plane form the diffuse part of the double layer, for which the Gouy-Chapman treatment outlined in the previous section, with 0o replaced by (f/d, is considered to be applicable. 

In the absence of specific ion adsorption, the charge densities at the surface and at the Stern plane are equal and the capacities of the Stern layer (Ct) and of the diffuse layer (C2) are given by... 

A refinement of the Stern model has been proposed by Grahame89, who distinguishes between an outer Helmholtz plane to indicate the closest distance of approach of hydrated ions (i.e. the same as the Stern plane) and an inner Helmholtz plane to indicate the centres of ions, particularly anions, which are dehydrated (at least in the direction of the surface) on adsorption. 

At low surface potentials Eq. (5.5) reduces to Eq. (5.2). Secondly, an inner layer exists because ions are not really point charges and an ion can only approach a surface to the extent allowed by its hydration sphere. The Stern model specifically incorporates a layer of specifically adsorbed ions bounded by a plane termed the Stern plane (see Figure 4.3). In this case the potential changes from ip° at the surface, to ip(d) at the Stern plane, to ip = 0 in bulk solution. 

The first four methods are described in Refs. [81,253,254] and the electroacoustical methods in [130,255-257]. Of these, electrophoresis finds the most use in industrial practice. The electroacoustic methods are perhaps the best suited to studying concentrated suspensions and emulsions without dilution [258], In all of the electro-kinetic measurements, either liquid is made to move across a solid surface or vice versa. Thus the results can only be interpreted in terms of charge density (a) or potential (zeta potential, ) at the plane of shear. The location of the shear plane is generally not exactly known and is usually taken to be approximately equal to the potential at the Stern plane, = W d), see Figure 4.9. Several methods can be used to calculate zeta potentials [16,81,253], Some of these will be discussed here, in the context of electrophoresis results. 

Figure 4.9 Schematic representation of the positions of the Stern plane and the Zeta potential in the electric double layer. From Shaw [60]. Copyright 1966, Butterworths.

In practice the situation may be more complicated. The shear plane may actually lie about 20 nm further away from the surface than the Stern plane, closer to the Gouy plane [271]. Also, if particle surfaces are covered by long chain molecules (physically or chemically bonded to the surface) then steric repulsion between particles may be significant. This repulsion is due to an osmotic effect caused by the high concentration of chains that are forced to overlap when particles closely approach, and also due to the volume restriction, or entropy decrease, that occurs when the chains lose possible conformations due to overlapping. 

Figure 8. Effects of pH, ionic strength, and total lead on potential at the 2.17 A Stern plane, as predicted by VSC-VSP model...

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Fig. 1. The potential at the surface (i/ o) linearly decreases in the Stern layer with respect to the value of the zeta potential ( ). This is the electric potential at the plane of shear between the Stern layer (plus that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear, a small distance further out from the surface than the Stem plane, renders the zeta potential marginally smaller in magnitude than the potential at the Stern plane (i//g). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume identity of ifig and f, and the bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

Fig.l Schematic representation of the electric double layer at a solid-liquid interface and variation of potential with the distance from the solid surface if/Q, surface potential potential at the Stern plane potential at the plane of share (zeta potential) 8, distance of the Stern plane from the surface (thickness of the Stern layer) k, thickness of the diffuse region of the double layer. 

Figure 7.3 Representation of the conditions at a negative surface, with a layer of adsorbed positive ions in the Stern plane. The number of negative ions increases and the number of positive ions decreases (see upper diagram) as one moves away from the surface, the electrical potential becoming zero when the concentrations are equal. The surface potential, and the potential at the Stern plane, are shown. As the particle moves, the effective surface is defined as the surface of shear, which is a little further out from the Stern plane, and would be dependent on surface roughness, adsorbed macromolecules, etc. It is at the surface of shear that the zeta potential, is located. The thickness of double layer is given by 1 /k.

The equations do not take into account the finite size of the ions the potential to be used is ipi, the potential at the Stern plane (the plane of closest approach of ions to the surface), which is difficult to measure. The nearest experimental approximation to is often the zeta potential (0 measured by electrophoresis. 

In the Stern-Gouy-Chapman (SGC) theory the double layer is divided into a Stern layer, adjacent to the surface with a thickness dj and a diffuse (GC) layer of point charges. The diffuse layer starts at the Stern plane at distance d] from the surface. In the most simple case the Stern layer is free of, charges. The presence of a Stern layer has considerable consequences for the potential distribution across the Stern layer the potential drops linearly from the surface potential V s to the potential at the Stern plane, V>d- Often is considerably lower than especially in the case of specific adsorption (s.a.). 

In the presence of s.a. ions one has to decide at which plane these ions adsorb. The most simple choice is that the s.a. ions are located at the Stern plane. This choice is appropriate for ions that form outer sphere complexes with the surface sites or for ions that have no affinity for the proton sites. Specifically adsorbing counterions that are forming inner sphere complexes with the surface groups screen the primary surface charge very effectively and the difference between primary and secondary surface charge becomes vague. In this case it is appropriate to place the s.a. charge at the surface plane, or partly at the surface plane and partly at the Stern plane. 

In all situations discussed so far only one Stern layer capacitance is required. In literature it is however often assumed [7, 8, 22] that diffuse ions can approach the surface up to the Stern plane and that s.a. ions are located at a newly defined adsorption plane, the inner Helmholtz plane. The inner Helmholtz plane is located in between the surface plane and the Stern or outer Helmholtz plane. The double layer model composed of an inner and outer Helmholtz layer plus a diffuse layer is generally called the triple layer (TL) model. 

For gibbsite type surfaces the characteristic protonation reaction is given by Eq. (43) and the surface charge by Eq. (62). In the presence of a simple 1-1 electrolyte of s.a. ions that weakly adsorb at the Stern plane Eqs. (62) and (55) to (59) can be combined to give... 

Stern [4] introduced the concept of the nondiffuse part of the double layer for specifically adsorbed ions, the remainder being diffuse in nature this is shown schematically in Figure 7.4, where the potential is seen to drop linearly in the Stern region, and then exponentially. Grahame distinguished two types of ions in the Stern plane, namely physically adsorbed counterions (outer Helmholtz plane) and chemically adsorbed ions that lose part of their hydration shell (inner Helmholtz plane). 

Shear plane Stern plane Particle surface... 

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