Using the Einstein relation to find the distance an ion can diffuse during the dissipation time scale, we have This dissipation is due to ion attraction and repulsion. The charge density is accumulated when the time scale for the transport of the ion to the charged surface is much smaller than the time scale for the dissipation of the charge density in the solution. Here, let us consider the diffusion coefficient of the ions,, and the characteristic charging time scale. Many equations exist to define or derive the Debye length in terms of different properties.

The distance that the diffuse double layer extends is called the Debye length. Since electrical attractions and repulsions encourage the restoration of electroneutrality, the double layer only extends a very short distance away from a charged surface. The absolute permittivity of water is a little less than 10 -9 F m -1, so for typical conductivities of electrolytes of the order of 1 S m -1, this time scale is of the order of nanoseconds.

The rate constant is the inverse of a characteristic charge dissipation time scale, given by the ratio of a solution's permittivity ( ) to conductivity ( ). This is a first-order rate equation for the space charge density. The concentration of the repelled cations is lowered close to the electrode surface correspondingly, the concentration of the attracted anions is raised. The schematic graph below shows the concentration profiles normal to a positively charged electrode. The net charge on a surface - whether a conductor or a dielectric - is counterbalanced by a region of space charge in the solution, where ions of opposite charge to the surface are accumulated and ions of like charge to the surface are depleted. For example, chemical modification of silica or carbon surfaces can alter the surface charge density. Surface chemistry can give solids a net surface charge density too. When we place an electrolyte in contact with an electrical conductor, the conductor typically acquires a net surface charge, which can be altered by polarization of the electrochemical cell. Electroneutrality is violated, however, in the very close vicinity of a charged region, such as an electrode. In the graph above, we observe electroneutrality over scales of hundreds of and timescales of many seconds. (See this page for the reasons why.) The majority of the current in the cell is then delivered by migration of the protons in an evolving electric field so that their concentration profile remains relatively unperturbed. This is because the mobility of protons is much higher than the mobility of potassium ions. Note that the K + concentration is changed significantly, whereas the H + concentration hardly changes. For all points in space and time, the total space charge adds up to zero that is, the sum of the H + and K + concentrations equals the Cl - concentration. The animation below shows 10 s of change in concentrations across a 0.5 mm distance from the surface where Cl - is depleted. Removing chloride ions will create extra positive charge density, which will repel both the H + and K + ions and attract oppositely charged Cl - ions so that electroneutrality is maintained. For example, an electrode might drive electrolysis to oxidize the chloride into chlorine gas that bubbles out of solution. Let us now imagine that the concentration of chloride is depleted at the right-hand side of a cell modeled in 1D. The concentrations of 10 mM H +, 10 mM K +, and 20 mM Cl - (half from acid and half from salt) add up to a net zero charge.

In solution, these chemicals dissociate into three ions: solvated protons (H +), sodium (Na +) cations, and chloride (Cl -) anions. We can imagine an aqueous solution containing 10 mM hydrochloric acid (HCl) and 10 mM potassium chloride (KCl). Normally, this effect leads to electroneutrality, where the concentrations of positive and negative ions balance out locally, leaving no net charge density. How Does the Diffuse Double Layer Form?Īccording to Coulomb's law, regions with a certain charge density repel ions of like charge and attract ions of opposite charge. The diffuse double layer is a thin layer of electrolyte solution close to a charged surface, in which the solution acquires a local space charge density due to accumulation or depletion of the dissolved ions. If there are more positive ions in a certain region of space than negative ions, then there will be a local positive space charge density. In an electrolyte solution, ions are dissolved in a polar solvent, such as water. Fluid Flow, Heat Transfer, and Mass Transport Diffuse Double Layer What Is the Double Layer?

Water in motion creates negative ions