Potential of bio-inspired materials for efficient mass transfer boosted by new version of century-old theory

The natural vein structure found in leaves, which has inspired the structural design of porous materials capable of maximizing mass transfer, could unlock improvements in energy storage, catalysis and sensing through a new twist of a century-old biophysical law.

An international team of researchers, led by the NanoEngineering Group at the Cambridge Graphene Centre, has developed a new materials theory based on ‘Murray’s Law’, applicable to a wide range of next-generation functional materials, with applications in all areas, from rechargeable batteries to high-performance gas sensors. The results are reported in the journal Natural communications.

Murray’s Law, proposed by Cecil D. Murray in 1926, describes how natural vascular structures, such as the blood vessels of animals and the leaf veins of plants, efficiently transport fluids with minimal energy expenditure.

“But while this traditional theory works for cylindrical pore structures, it often struggles to create synthetic networks of various shapes, a bit like trying to fit a square peg into a round hole,” explains the first author, Cambridge Ph.D. student Binghan Zhou.

Dubbed “Murray’s Universal Law,” the researchers’ new theory bridges the gap between biological vessels and artificial materials and is expected to benefit energy and environmental applications.

“The original Murray’s law was formulated by minimizing energy consumption to maintain laminar flow in blood vessels, but it was not suitable for synthetic materials,” says Zhou.

“To broaden its applicability to synthetic materials, we expanded this law by considering resistance to flow in hierarchical channels. The universal Murray’s law we propose works for pores of any shape and is suitable for all types of transfer currents, including laminar flow, diffusion and ionic migration.

Ranging from everyday use to industrial production, many applications involve ion or mass transfer processes through highly porous materials – applications that could benefit from universal Murray’s law, the researchers say.

For example, when charging or discharging batteries, ions physically move between the electrodes through a porous barrier. Gas sensors rely on the diffusion of gas molecules through porous materials. Chemical industries often use catalytic reactions, involving laminar flow of reactants through catalysts.

“Using this new biophysical law could significantly reduce the flow resistance in the above processes, thereby increasing the overall efficiency,” adds Zhou.

The researchers proved their theory using graphene airgel, a material known for its extraordinary porosity. They carefully varied the size and shape of the pores by controlling the growth of ice crystals in the material. Their experiments showed that microscopic channels following Murray’s new universal law provide minimal resistance to fluid flow, while deviations from this law increase flow resistance.

“We designed a reduced hierarchical model for numerical simulation and found that simple shape changes following the proposed law effectively reduced the flow resistance,” says co-author Dongfang Liang, professor of hydrodynamics in the Department of Energy. ‘engineering.

The team also demonstrated the practical value of Murray’s universal law by optimizing a porous gas sensor. The sensor, designed in accordance with the law, has a significantly faster response than sensors following a porous hierarchy, which are traditionally considered very efficient.

“The only difference between the two structures is a slight variation in shape, demonstrating the power and ease of application of our proposed law,” explains Zhou.

“We incorporated this particular natural law into synthetic materials,” adds Tawfique Hasan, professor of nanoengineering at the Cambridge Graphene Centre, who led the research. “This could be an important step toward theory-guided structural design of functional porous materials. We hope our work will be important for next-generation porous materials and contribute to applications for a sustainable future.”