A system will generally move towards equilibrium when a change is made to it in a process called relaxation. To predict the state of the system after some period of time, we only need to know its current state and the external conditions. However, some polymers have memory behaviours where the evolution of the system is not only dependent on the current state, but also on previous states. This is known as the Kovacs effect.

In this work, the researchers investigated the Kovacs effect in a system consisting of suspensions of rod-like nanoparticles. By applying an electric field to these nanoparticles they align, therefore the particles change the liquid’s optical anisotropy, which can be measured as birefringence, which is how the liquid changes light polarization. More birefringence means the particles are more aligned. Importantly, there are faster- and slower-relaxing nanoparticles because of their polydispersity and different sizes, meaning they align at different rates. By changing the strength of the electric field, the faster and slower nanoparticles become out of sync with each other. The future behaviour will then depend on the system’s previous history that is overall hidden by the global birefringence measurement; this is the Kovacs effect.

The researchers modelled the orientational dynamics using the Smoluchowski equation, which describes rotational diffusion of particles. They found that relaxation is not determined by a single timescale or relaxation mode. When some of the modes are fast and some are slow, memory effects will occur. The Kovacs effect is important because it shows that a simple strategy of applying a strong electric field before switching to the target field does not necessarily speed up relaxation. Due to memory effects arising from particles relaxing at different rates, the system overshoots the target state, reducing the expected gain in speed.

To overcome this, the researchers designed improved two- and three-step protocols that suppress the slowest relaxation modes rather than simply matching the average birefringence. These protocols reduce the memory effect, produce a smoother approach to equilibrium, and achieve faster relaxation, although the benefit of additional switching steps becomes progressively smaller. This research improves our understanding of memory effects in complex systems and provides a practical strategy for controlling nanoparticle dynamics more quickly and efficiently.

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Scientific developments of liquid crystal-based optical memory: a review by Jai Prakash, Achu Chandran and Ashok M Biradar (2016)