Electric Double Layer Potential

When a solid surface is placed in contact with an electrolytic solution, it often acquires a charge. This charge can be due to various reasons, such as:

• Adsorption of ions from the solution.
• Dissociation of surface functional groups.
• Isomorphic substitution in crystal lattice.

This surface charge attracts ions of opposite charge (counterions) from the solution, forming an electric double layer near the surface. This double layer is typically described in models like the Stern model.

The electric double layer consists of two main parts:

• Fixed Layer (Stern Layer): This layer is immediately adjacent to the charged surface and contains ions that are strongly adsorbed or electrostatically attracted and held relatively rigidly. Water molecules are also present in this layer. The potential drops linearly or sharply across this layer.
• Diffuse Layer (Gouy-Chapman Layer): Beyond the fixed layer is a region where counterions are still attracted to the surface charge, but they are also subject to thermal motion. Coions (ions with the same charge as the surface) are repelled but are also present due to random motion. This layer is less ordered than the fixed layer, and the concentration of counterions decreases with distance from the surface until it reaches the concentration in the bulk solution. The potential drops exponentially across this layer.

The potential difference between the charged surface and the bulk solution is sometimes referred to as the surface potential or the total double layer potential (often denoted as $\psi_0$). However, the question asks for the potential difference between the "fixed part" of the double layer and the bulk solution.

Understanding Zeta Potential

The concept of the electric double layer is crucial for understanding the stability of colloidal dispersions. When a particle with an electric double layer moves through a liquid, or when the liquid flows around a stationary particle, a "slipping plane" or "shear plane" exists. This plane separates the liquid that is tightly bound to the particle surface and moves with it (including the fixed layer and a part of the diffuse layer) from the bulk liquid that is free to move. The potential at this slipping plane relative to the bulk solution is called the Zeta potential ($\zeta$).

The potential difference between the fixed part of the double layer and the bulk solution is essentially the potential at the boundary of the fixed layer and the mobile part of the diffuse layer, measured relative to the bulk. This potential is the Zeta potential. While the potential at the *very outer edge* of the fixed layer might technically be the potential at the beginning of the diffuse layer (often denoted as $\psi_\delta$), the Zeta potential is the electrokinetic potential measured at the slipping plane, which is very close to or just outside the Stern layer, representing the effective potential influencing particle interactions and motion in the fluid.

Evaluating the Options

• Zeta potential: This is the potential at the slipping plane within the diffuse layer, relative to the bulk solution. It represents the potential difference between the region considered to move with the particle (including the fixed layer and some inner diffuse layer) and the bulk solution. This fits the description provided in the question.
• Double layer potential: This term can sometimes refer to the total potential drop from the surface to the bulk ($\psi_0$), which is different from the potential between the fixed part and the bulk.
• Sedimentation potential: This is an electrokinetic phenomenon where a potential difference is created when charged particles move through a stationary liquid under the influence of gravity or centrifugal force. It is not a measure of the potential distribution within the double layer itself.
• Chemical potential: This is a thermodynamic concept that describes the energy change when adding a particle to a system at constant temperature and pressure. It is related to the concentration of species and phase equilibria, not directly to the potential distribution in the electric double layer due to charge separation.

Based on the definitions, the potential difference between the fixed part of the double layer and the bulk solution corresponds to the Zeta potential, which is the potential at the slipping plane.