Solving Lyapunov equations for electrically driven ternary electrolytes: Application to long-range van der Waals...

Area of Science:

• Physical Chemistry
• Computational Chemistry
• Condensed Matter Physics

Background:

• Stochastic density-functional theory (SDFT) is crucial for studying out-of-equilibrium electrolyte solutions, including electrical conductivity and van der Waals interactions.
• Linearizing SDFT leads to complex Lyapunov equations, with complexity scaling quadratically with the number of ionic species (N).
• Analytical solutions for ternary electrolytes (N=3) are scarce due to this complexity.

Purpose of the Study:

• To simplify the Lyapunov equations governing steady-state correlation functions in SDFT for electrolytes.
• To develop a method for calculating van der Waals interactions in ternary electrolytes under external electric fields.
• To investigate the out-of-equilibrium properties of driven ternary electrolyte solutions.

Main Methods:

• Developed a reduction technique for Lyapunov equations specific to electrolyte systems, transforming N(N+1)/2 equations into N linear equations.
• Applied this reduction to compute the long-range van der Waals interaction between two slabs containing a ternary electrolyte.
• Simulated the system under an applied electric field parallel to the slabs.

Main Results:

• Successfully reduced the complexity of Lyapunov equations for ternary electrolytes.
• Calculated the van der Waals interaction between slabs with ternary electrolytes under an electric field.
• Demonstrated that the van der Waals interaction in this driven ternary electrolyte system depends on ionic diffusion coefficients.

Conclusions:

• The developed reduction method significantly simplifies the analysis of out-of-equilibrium ternary electrolytes.
• The van der Waals interaction in driven ternary electrolytes is intrinsically linked to ionic diffusion, unlike in binary systems.
• This work provides a pathway for analytical studies of complex, driven electrolyte solutions.