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Materials with continuous dissipation can exhibit responses andfunctionalities that are not possible in thermodynamic equilibrium. While thisconcept is well-known, a major challenge has been the implementation: how torationally design materials with functional non-equilibrium states and quantifythe dissipation? Here we address these questions for the widely used colloidalnanoparticles that convey several functionalities. We propose that usefulnon-equilibrium states can be realised by creating and maintaining steady-statenanoparticle concentration gradients by continuous injection and dissipation ofenergy. We experimentally demonstrate this with superparamagnetic iron oxidenanoparticles that in thermodynamic equilibrium form a homogeneous functionalfluid with a strong magnetic response (a ferrofluid). To create non-equilibriumfunctionalities, we charge the nanoparticles with anionic charge control agentsto create electroferrofluids where nanoparticles act as charge carriers thatcan be driven with electric fields and current to non-homogeneous dissipativesteady-states. The dissipative steady-states exhibit voltage-controlledmagnetic properties and emergent diffuse interfaces. The diffuse interfacesrespond strongly to external magnetic fields, leading to dissipative patternsthat are not possible in the equilibrium state. We identify the closestnon-dissipative analogues of these dissipative patterns, discuss thedifferences, and highlight how pattern formation in electroferrofluids islinked to dissipation that can be directly quantified. Beyond electricallycontrolled ferrofluids and patterns, we foresee that the concept can begeneralized to other functional nanoparticles to create various scientificallyand technologically relevant non-equilibrium states with optical, electrical,catalytic, and mechanical responses that are not possible in thermodynamicequilibrium.

Electroferrofluids with non-equilibrium voltage-controlled magnetism, interfaces, and patterns