scholarly journals On the diffuse double layer

1933 ◽  
Vol 139 (839) ◽  
pp. 596-603 ◽  
Keyword(s):  
Double Layer ◽  
Colloidal Particles ◽  
Mutual Influence ◽  
Streaming Potential ◽  
Specific Adsorption ◽  
Double Layers ◽  
Diffuse Double Layer ◽  
Plane Parallel ◽  
Parallel Surfaces

1. The formulæ derived by Gouy for the diffuse double layer hold only in the case of a single surface in an infinite amount of medium. In practice they are not very suitable, for very frequently we have to deal either with capillaries, as in streaming potential measurements, or with colloidal particles which may be near enough to influence one another. In these cases it is too difficult to calculate the effect of the mutual influence of two double layers, though in less complicated systems it is possible. Suppose we have two plane parallel surfaces separated by a distance 2 h and charged both to the same potential, in a solution of an electrolyte. If the dimensions of the surfaces are large compared with the distance h there will be no drop of potential between the two. We therefore need to make the assumption (which was superfluous in Gouy’s case) of a specific adsorption by the surface of one or more of the ions in the solution, otherwise there will be no double layer at all; the same effect will also be obtained if ions of the surface dissolve.

The double layer in the absence of specific adsorption

1996 ◽  
Author(s):  
Wolfgang Schmickler
Keyword(s):  
Metal Surface ◽  
Double Layer ◽  
Specific Adsorption ◽  
Perfect Conductor ◽  
Diffuse Double Layer ◽  
Capacity Curves ◽  
Plane Passing ◽  
Constant Potential ◽  
Two Phases ◽  
Solvent Molecules

One of the fundamental problems in electrochemistry is the distribution of the potential and of the particles at the interface. Here we will expand on the subject of Chapter 3, and consider the interface between a metal and an electrolyte solution in the absence of specific adsorption. Until about 1980 a simple model of this interface prevailed, which was based on a particular interpretation of the interfacial capacity. The metal was assumed to be a perfect conductor in the classical sense, and hence a region of constant potential right up to the metal surface. As was pointed out in Chapter 3, the inverse capacity can be split into two terms, a Gouy-Chapman and a Helmholtz term: l/C = l/CGc + 1/CH. It was argued that these two terms pertain to two different regions in the solution: the space charge or diffuse double layer, which is already familiar to us, and the Stern or outer Helmholtz layer giving rise to the Helmholtz capacity. Since the latter does not depend on the concentration of the ions, the Stern layer was supposed to consist of a monolayer of solvent molecules adsorbed on the metal surface. The plane passing through the centers of these molecules was called the outer Helmholtz plane. Rather elaborate models were developed for the dielectric properties of this layer in order to explain Helmholtz capacity curves such as those shown in Fig. 3.3. This Gouy-Chapman-Stern model, as it was named after its main contributors, is a highly simplified model of the interface, too simple for quantitative purposes. It has been superseded by more realistic models, which account for the electronic structure of the metal, and the existence of an extended boundary layer in the solution. It is, however, still used even in current publications, and therefore every electrochemist should be familiar with it. In the remainder of this chapter we will present elements of modern double-layer theory. Two phases meet at this interface: the metal and the solution. We will consider each phase in turn.

Ionic motion in a compacting filtercake

1992 ◽  
Vol 437 (1901) ◽  
pp. 607-627 ◽  
Keyword(s):  
Double Layer ◽  
Transport Coefficients ◽  
Streaming Potential ◽  
Ionic Concentration ◽  
Double Layers ◽  
Clay Particles ◽  
Clay Concentration ◽  
Selective Membrane ◽  
Order Of Magnitude ◽  
Double Layer Theory

Electrical double layer theory is used to predict ionic transport coefficients in the fluid between two parallel charged plates, which represent clay particles. The compaction of a finite quantity of mud (clay suspended in water), to form a clay filter cake, is then modelled, using double layer theory to predict the forces between the clay particles. The path followed by the water and ions is taken to be a smoothly varying channel, which is widest at the upper (least-compacted) surface of the cake, and narrowest at the (most-compacted) cake base. There is a constant surface charge density over the walls of the channel. The electrical double layers surrounding the clay particles overlap one another at the base of the cake, and act as an ion-selective membrane. When filtration commences, the ionic concentration in the filtrate is initially lower than that in the clay suspension. The mean ionic concentration of the suspension increases during the compaction: that of the filtrate first increases and then decreases. Such variations have been previously reported, and may be responsible for the observed time dependence of the clay concentration at the base of clay filtercakes. Predictions are also made of the streaming potential generated across the cake by the motion of the filtrate: these are of the same order of magnitude as those obtained experimentally.

NOTE ON THE THEORY OF ELECTROLYTIC DOUBLE LAYERS

1949 ◽  
Vol 27b (7) ◽  
pp. 682-687
Author(s):  
A. J. Dekker
Keyword(s):  
Double Layer ◽  
Double Layers ◽  
Diffuse Double Layer ◽  
Diffuse Part ◽  
Convenient Formula

The mechanism suggested by Gurney for the formation of a double layer at the interface of a metal and a solution containing its ions is applied to a diffuse double layer. The diffuse part of the double layer is treated in a way that differs from Stern's method, leading to a more convenient formula for the potential ψδ of the diffuse part. Numerical values and a comparison with Stern's results are given.

Salt diffusion in charged porous media

2020 ◽  
Author(s):  
Pavan Cornelissen ◽  
Anton Leijnse ◽  
Vahid Joekar-Niasar ◽  
Sjoerd van der Zee
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Double Layer ◽  
Effective Diffusion ◽  
Pore Network ◽  
Salt Transport ◽  
Double Layers ◽  
Diffuse Double Layer ◽  
Low Salinity ◽  
Charged Surfaces

<p>Some porous media such as clay have charged surfaces. The presence of these charged surfaces results in a complex system where water flow, salt transport, and the electric field are coupled. This system is important in many fields, such as geotechnical engineering, storage of radioactive waste in clay barriers, enhanced oil recovery, and irrigation with marginal water. The charged surfaces alter the transport properties of ions. For example, clay minerals are often negatively charged due to isomorphous substitution. Cations are therefore attracted to the mineral surface, while anions are repelled, creating a diffuse double layer around the clay particle. Cations are therefore transported preferably over anions through such charged pores. To conserve electroneutrality, a streaming potential develops to counteract diffusion by electromigration. This results in smaller effective diffusion coefficients compared to uncharged porous media. We developed a pore-network model to quantify the effect of the double layer processes on the effective diffusion coefficient. Pore-network models are a suitable tool to include the heterogeneity of pore sizes and surface charge densities seen in nature. In pore-network modeling, the geometry of the pore space is simplified, but the network properties are based on realistic statistics such as pore size distribution and connectivity. The larger scale behavior can be identified by averaging over a large number of pores. The results were strongly dependent on the salinity, as this controls the thickness of the double layers. At high salt concentrations, the diffuse double layer is thin and the differences between charged and uncharged porous media are negligible. However, at low salinity, the double layers are thick and the effective diffusion coefficient of salt was reduced by 25% in charged porous media compared to uncharged porous media, due to salt transport being slowed down to conserve electroneutrality. Hence, the presence of charged mineral surfaces can significantly alter transport rates under low salinity conditions.</p>

RAPIDLY CONVERGENT SERIES FOR THE COMPUTATION OF THE INTERACTION BETWEEN DISSIMILAR PLANE PARALLEL DOUBLE-LAYER (y0 > 0 > yd ≥ -y0)

2005 ◽  
Vol 12 (02) ◽  
pp. 145-153 ◽  
Author(s):  
SHIMIN ZHANG
Keyword(s):  
Power Series ◽  
Interaction Energy ◽  
Double Layer ◽  
Surface Potential ◽  
Convergent Series ◽  
Integration Constant ◽  
Double Layers ◽  
Absolute Value ◽  
Plane Parallel ◽  
Significant Figures

Several rapidly-convergent series for the computation of the interaction energy between dissimilar plane parallel double layers (y0 > 0 > yd ≥ -y0) are derived by expanding the interaction energy in the power series of ω0[ω0 < tanh (y0/64)]. The series terms required to obtain the interaction energy with six significant figures do not exceed 1 when the dimensionless surface potential of colloid particles y0 is less than or equal to 2.00000 × 10. The results of Devereux and de Bruyn are discovered to be incorrect when the integration constant C and absolute value of the surface potential is larger or the integration constant C is smaller.

How to use alum with cationic dispersed rosin size

TAPPI Journal ◽  
2016 ◽  
Vol 15 (5) ◽  
pp. 331-335 ◽  
Author(s):  
LEBO XU ◽  
JEREMY MYERS ◽  
PETER HART
Keyword(s):  
Zeta Potential ◽  
Colloidal Particles ◽  
Streaming Potential ◽  
Excessive Amount ◽  
Paper Machine ◽  
Optimum Amount ◽  
Potential Measurement ◽  
Streaming Current ◽  
Wide Range ◽  
Laboratory Results

Retention of cationic dispersed rosin size was studied via turbidity measurements on stock filtrate with different alum and dispersed rosin size dosages. Stock charge characteristics were analyzed using both an analysis of charge demand determined via a streaming current detector and an evaluation of zeta potential of the fibers by streaming potential measurement. The results indicated that an optimum amount of alum existed such that good sizing retention was maintained throughout a wide range of dispersed rosin size dosages. However, when an excessive amount of alum was used and fines and colloidal particles were transitioned from anionic to cationic, the cationic size retention was reduced. Laboratory results were confirmed with a paper machine trial. All data suggested that a stock charge study was necessary to identify optimal alum dosage for a cationic dispersed rosin sizing program.

Cracking at the fold in double layer coated paper: the influence of latex and starch composition

TAPPI Journal ◽  
2019 ◽  
Vol 18 (2) ◽  
pp. 93-99
Author(s):  
SEYYED MOHAMMAD HASHEMI NAJAFI ◽  
DOUGLAS BOUSFIELD, ◽  
MEHDI TAJVIDI
Keyword(s):  
Mechanical Properties ◽  
Double Layer ◽  
Starch Content ◽  
Single Layer ◽  
Double Layers ◽  
Coated Paper ◽  
Coated Papers ◽  
Coating Layers ◽  
Scanned Images ◽  
Packaging Paper

Cracking at the fold of publication and packaging paper grades is a serious problem that can lead to rejection of product. Recent work has revealed some basic mechanisms and the influence of various parameters on the extent of crack area, but no studies are reported using coating layers with known mechanical properties, especially for double-coated systems. In this study, coating layers with different and known mechanical properties were used to characterize crack formation during folding. The coating formulations were applied on two different basis weight papers, and the coated papers were folded. The binder systems in these formulations were different combinations of a styrene-butadiene latex and mixtures of latex and starch for two different pigment volume concentrations (PVC). Both types of papers were coated with single and double layers. The folded area was scanned with a high-resolution scanner while the samples were kept at their folded angle. The scanned images were analyzed within a constant area. The crack areas were reported for different types of papers, binder system and PVC values. As PVC, starch content, and paper basis weight increased, the crack area increased. Double layer coated papers with high PVC and high starch content at the top layer had more cracks in comparison with a single layer coated paper, but when the PVC of the top layer was low, cracking area decreased. No measurable cracking was observed when the top layer was formulated with a 100% latex layer.

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