Advantages of the Cell Model Approach

A key advantage of this approach is that all quantities involved in the equations describing electrolyte transport through a porous layer—namely thermodynamic fluxes and forces—can be directly measured in experiments.

Figure 1. Breakthrough Discovery Challenges 1931 Thermodynamic Law.

When determining the kinetic coefficients LijL_{ij}Lij of the Onsager matrix, the independent thermodynamic forces applied during experiments involving the transport of an electrolyte solution through a thin, infinitely extended charged porous layer (or membrane) are the gradients of pressure (dp/dxdp/dxdp/dx), chemical potential (dμ/dxd\mu/dxdμ/dx), and electric potential (dϕ/dxd\phi/dxdϕ/dx) taken perpendicular to the surface of the layer. Figure 1 shows Breakthrough Discovery Challenges 1931 Thermodynamic Law.

Dependent Thermodynamic Parameters and Experimental Observations

In experiments, the dependent thermodynamic parameters are taken as the flux densities:

• UUU: solvent flux (e.g., water),
• III: mobile charge flux (electric current density),
• JJJ: solute flux (diffusion flux density of the electrolyte).

Experimental Observations

Experiments conducted with heterogeneous MK-40 and homogeneous MF-4SK cation-exchange membranes have shown that, at low concentrations of aqueous NaCl solutions (up to 0.1 M), the cross kinetic coefficients differ only slightly.

However, at higher concentrations, significant quantitative and qualitative differences emerge between the reverse osmotic coefficient (L13L {13}L13) and the capillary osmotic coefficient (L31L_{31}L31), as well as between the electrodiffusion coefficients (L23L_{23}L23 and L32L_{32}L32). In contrast, the cross coefficients L12L_{12}L12 (associated with electroosmosis) and L21L {21}L21 (associated with the streaming current) remain nearly equal, even at elevated electrolyte concentrations.

These findings demonstrate that within the cell model framework, the Onsager reciprocity principle does not hold—the matrix of kinetic coefficients is asymmetric. As a result, special care must be taken when evaluating the transport properties of membranes, especially since these properties are influenced by the cross coefficients, which may not mirror each other.

This study highlights that the coupled cross coefficients can differ not only in magnitude but also in behavior. This distinction is critical when analyzing the transport characteristics of charged membranes.

What Is the 1931 Thermodynamic Law?

In 1931, physicist Lars Onsager introduced a foundational principle in non-equilibrium thermodynamics called Onsager’s Reciprocal Relations. This law states that in systems near equilibrium, the cross effects of thermodynamic processes are symmetrical. For example, if an electric field can cause heat flow (thermoelectric effect), then a temperature gradient should induce an electric current (Seebeck effect), and both are mathematically connected by equal coefficients. This reciprocity was long thought to be universally valid for linear systems with microscopic reversibility.

The Discovery—Asymmetry in Kinetic Coefficients

Recent experimental studies on cation-exchange membranes, such as MK-40 (heterogeneous) and MF-4SK (homogeneous), revealed that Onsager reciprocity breaks down under certain conditions. At low salt concentrations (e.g., < 0.1 M NaCl), the symmetry holds well. But at higher concentrations, researchers observed that cross-coefficients such as L13L {13}L13 and L31L {31}L31 or L23L {23}L23 and L32L_{32}L32 diverge significantly—both quantitatively and qualitatively. This means the flux driven by one force doesn't match the reverse effect, violating the expected reciprocity.

Why Does This Violation Matter?

The violation of Onsager reciprocity suggests that the traditional assumptions of near-equilibrium linear thermodynamics may not apply in complex, real-world systems like charged membranes with high ionic strength. It challenges long-standing models of transport phenomena and indicates that other factors—such as structural heterogeneity, nonlinear interactions, or surface charge effects—might disrupt symmetry. This discovery forces researchers to rethink how they model and predict transport in systems ranging from batteries to biological cells.

Implications for Science and Technology

This breakthrough has broad implications. In theoretical physics, it motivates the development of new frameworks that go beyond Onsager’s original theory. In applied fields, it could affect how engineers design membranes, biosensors, electrochemical devices, or drug delivery systems. It also opens the door for further research into conditions under which reciprocity fails and how such violations might be exploited—for instance, in designing more efficient energy conversion systems or achieving one-way transport in synthetic membranes.

Source: SciTECHDaily

Cite this article:

Priyadharshini S (2025), Scientists Uncover Breach of 1931 Thermodynamic Law, AnaTechMaz, pp. 289