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Isothermal and Thermal Liquid Junction Potentials - Theory Isothermal Liquid Junction Potential Theory A very common method for checking a Class 2 reference electrode is to compare its half cell voltage to that of another reference electrode known to be behaving properly. The two electrodes are immersed in the same environment. That environment usually has a different ionic strength from that in the compartments surrounding the reference electrodes being used. The electrodes are then connected through a high impedance voltmeter which measures the voltage difference. That voltage difference is compared to the "expected" difference. One artifact that can affect the voltage is the isothermal liquid junction potential. This potential is caused by the differences in cation and anion mobilities through the porous frits. The diffusion process is caused by the difference in concentration between the fluid directly surrounding the electrode and the environment on the other side of the frit. The result is a potential difference across the frit. The magnitude is a function of the relative mobilities of the salt constituents through the frit. An example of estimating this potential is in the section entitled Isothermal and Thermal Liquid Junction Potentials - Calculation.This figure )
is an illustration of the geometry creating the isothermal liquid junction potential.
In this case, two identical salts of differing concentration at the same
temperature are separated by a membrane (frit) that allows very restricted
diffusion between the compartments. In this case the ions are singly charged
but any charge is possible as long as electrical neutrality exists in the
compartments. The theory behind the junction potential for this case is as follows.
The concentration gradient between the two compartments creates diffusion through the frit. The diffusion process itself is irreversible. But, if the interface movement is slow relative to the experimental time as, for example, when a frit is present, then the system can be assumed to be at "equilibrium". The boundary motion can be ignored. A potential is developed across this boundary because M+ and A- ions travel at different speeds (have different ionic mobilities). This potential is the isothermal liquid junction potential. The potential is actually an irreversible contribution to the overall cell potential. Values can be very high depending on the differences in mobility of the ions through the boundary. The equation for the isothermal liquid junction potential can be written as 
(12)where VLJ is the potential, a is the activity of each ion, t is the transference number of each cation or anion, z is the charge, and the summation is over all charged species passing through the frit. The transference number is the fraction of the charge carried by the ion. It depends on the ion activity and its diffusion coefficient. The value cannot be easily calculated. Several models exist for estimating the liquid junction potential. The simplest is as follows. The integration of equation (12) is carried out across the junction with the activities being a function of position. The junction normally encountered in corrosion studies involves an actual separation of the two fluids .
The assumption made in this simple development is the transference number
is independent of activity (concentration). If the diffusion is rapid enough,
the boundary may be considered to be a series of mixtures of the two solutions.
The assumption results in two equations depending on whether the two sides of the
frit have the same or different ionic constituents. Note that these equations should
be used with caution. Their applicablility decreases as systems become more
complex.
If the two solutions have the same univalent electrolyte, the equation for the liquid junction potential becomes 
(13)where t+ is the transference number of the cation. Since the two transference numbers are a fraction, if they are about equal their value is close to 0.5 and the liquid junction potential approaches zero. If two univalent electrolytes are present and they have a common ion, for example NaCl and KCl, then the liquid junction potential becomes 
(14)where Λ is the equivalent conductance for each salt. The conductance is a function of concentration. Conductance values along with a review of the theory of conductance can be found in, for example R. Fernandez-Prini, "Conductance and Transference Numbers", ch. 5, in "Physical Chemistry of Organic Solvent Systems", (Covington and Dickinson, ed.), Plenum, 1973. The liquid junction potential can be expressed in terms of the transference numbers for the special case that the sum of species remains constant through the regions of restricted transport. 
(15a)where 
(15b)In equations (15), A and B denote the two solutions, tj is the transference number in solution A or B depending on superscript, and aj is the activity coefficient of constituent j. Many of these values are difficult to estimate. Other theories exist but they often result in equations far too difficult to evaluate on a routine basis. Some conclusions about junction potentials are as follows:
Thermal Liquid Junction Potential Theory The corrosion practitioner is often faced with evaluating corrosion at elevated temperatures. Sometimes these temperatures are higher than the laboratory reference electrode can withstand. A common approach is to keep the reference electrode outside of the electrochemical cell with communication being through a filled capillary between the reference electrode and the cell. A temperature gradient exists along this capillary because the reference electrode and cell are at different temperatures. So-called pressure balanced external reference electrodes as used in autoclave studies tend to have these characteristics. An example of estimating this potential is in the section entitled Isothermal and Thermal Liquid Junction Potentials - Calculation.This temperature gradient causes material to migrate between the two temperatures. This migration creates a diffusion gradient. This process has a name, the Soret effect and falls under the general category of irreversible thermodynamics. For the case of a single salt which dissolves into two types of ions, the Soret coefficient σ is given by 
(16)where m is the molality of the salt, T is the absolute temperature, and the derivative is taken at steady state (signified by the subscript "st"). Since the ionic mobilities of the salt constituents differ, the diffusion gradient establishes a potential difference between the hot and cold ends of the capillary. This potential difference is the thermal liquid junction potential. Values can be of the order of 0.05V depending on electrolyte, concentration, and temperature difference. The case of the single electrolyte in a solvent has been presented in the literature (A. A. Seys, et al., "The Value of the Thermal Diffusion Potential in Corrosion Experiments at High Temperature Introduction of a Thermal Diffusion Coefficient", in "High Temperature High Pressure Electrochemistry in Aqueous Systems", NACE-4, 1976). For that case, the potential gradient along the capillary can be expressed in terms of the mole fraction gradients or temperature gradients as 
(17a)and 
(17b)where n is the mole fraction of constituents 1 and 2 in the salt, h is the heat of transport, t is the transference number, z is the valence, and x is the distance. The third term in equation (17a) is the Soret effect. Calculation of the thermal liquid junction potential in the absence of any measurements is often not possible. But certain properties of this potential can have a large effect on the corrosion measurement.
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David C. Silverman, Ph.D. - Primary Consultant |