Periodic Reporting for period 2 - CONIN (Effects of confinement on inhomogeneous systems) Reporting period: 2019-01-01 to 2022-06-30 Summary of the context and overall objectives of the project The objective of the project is determination of universal features and specific properties of systems spontaneously ordering into spatially inhomogeneous structures, with special focus on effects of confinement. We pay particular attention to systems spontaneously forming ordered patterns, from thin films on solid surfaces through particles on interfaces to biological membranes and arid ecosystems. Our studies can help to understand origin of life, for which a confinement is believed to play an essential role, and can be exploited in innovative technology. In addition, we investigate ionic liquids/ionic-liquid mixtures near charged surfaces and in porous media, and mobile ions in intercalation compounds that are important in innovative electrochemistry. In particular, we search for systems and conditions that allow for efficient energy storage. The new results and theoretical approaches will help in future studies that may find applications in medicine, information technology, energy conversion and storage, and functional fabrics.Spontaneous pattern formation occurs on different length scales, and typically is caused by competing tendencies in interactions between the considered objects – from ions through nanoparticles, proteins, colloid particles to trees in semi-arid ecosystems. We focus on modeling the systems whose elements attract each other at short distances, but repel each other at larger distances (SALR interactions). In the case of particles, the repulsion is of electrostatic origin and the attraction can be induced by the solvent. Particles that attract each other at short distances can form clusters, but the repulsion at larger separation prevents the clusters from further growth. In the case of such particles different patterns were observed. Our purpose is on the one hand to develop new theoretical and simulation methods suitable for investigation of such systems. On the other hand, we try to find out how the fluctuations that destroy the order can be suppressed, and we investigate the effects of confinement and obstacles.We are also interested in systems with weaker heterogeneities, in particular in room-temperature ionic liquids (RTIL) and mobile ions in solids. The properties of ionic liquids are determined by the specific interactions as well as by the Coulomb potential.There is competition between structure making and structure breaking effects which may have different manifestation next to interfaces. We intend to study structure of RTIL near a flat or a porous electrode, and effects of confinement on charging-discharging processes. Another open question is the vapour-liquid and/or liquid-liquid phase equilibria in ionic liquids and in the mixtures of RTILs with neutral components. Mutual effects of the phase transitions and the charge accumulated near an electrode are important for supercapacitors and energy storage devices. In addition, we plan experimental study of nanostructured surfaces by electrochemistry methods. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far We have developed new theoretical methods and simulation procedures for systems with spontaneous inhomogeneities on different length scales or with hyperuniformity. With these new methods, we investigated well-established and new models of: (i) concentrated ions in different solvents and in solids (ii) core-shell particles (iii) charged particles with effective short-range attraction and (iv) mixtures of such particles. We determined thermodynamic, structural, electrostatic and kinetic properties of the above systems in bulk and in confinement on flat or curved surfaces, in single pores with different sizes and shapes as well as in various ordered and disordered porous materials.For particles with short-range attraction long-range repulsion (SALR) we discovered in particular: (i) anomalous decrease of adsorption from bulk reservoir for increasing gas pressure when clusters dominate in bulk (ii) chains of clusters in dilute- and alternating layers of particles in a mixture of SALR particles with particular cross-interaction (Fig.1a)(ii) thick dense layer with particles forming ordered patterns adsorbed on a selective surface from a dilute mixture of SALR particles(iii) formation of chiral structures made by worm-like clusters in pipes with different cross-section (Fig.1c) spherical shells (Fig. 1d) or inside a hexagon with a small obstacle attached to a vertex (Fig.1b) (iv) formation of new ordered patterns by SALR particles inside ordered porous materials (Fig.2)(v) appearance of disordered hyperuniformity in mixtures of dipolar particles that can lead to invisible materials.For core-shell particles we predicted formation of many regular patterns on a fluid interface and a strong dependence of the number and the type of the patterns on the thickness of the polymeric shell and on cross-linking distribution. The sensitivity to the details of the interactions is in strong contrast to the universal behavior of the SALR particles and block copolymers.Using the new theories for ionic systems we have determined (i) strong effect of the demixing phase transition in mixtures of ionic liquid and neutral solvent on capacitance of the double layer (Fig.3a)(ii) jumps of the stored energy at the ionization/deionization transition in slits (Fig.4)(iii) phase transitions of ionic liquids and ionic liquid mixture with anisotropic solvent confined in porous medium (Fig.3b) (iv) distribution of ions and electrostatic potential in ionic liquids, ionic liquid mixtures and solid electrolyte near a charged surface and between flat electrodes (v) the effect of finite pore length on ion structure and charging (vi) the effect of the crystal field variation on the screening effects and electro-physical characteristics.Our results were published in over 50 articles, presented at conferences as 60 lectures (including 17 invited or plenary lectures) and 30 posters, and in scientific institutions as 12 invited seminars. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) We have developed new theoretical approaches and simulation procedures suitable for inhomogeneous systems, and introduced several new models. We have obtained numerous results concerning phase transitions and effects of confinement, and discovered new phenomena, such as: (i) anomalous adsorption in cluster-forming systems that may play an important role for implants (ii) new ordered structures self-assembled in various types of confinement or by core-shell particles that may guide tailored patterns for different smart materials (iii) new shape of the capacitance curve close to the phase separation having strong effect on the energy and charge storage (iv) disordered hyperuniformity in mixtures of dipolar particles on a surface that may lead to invisible materials. We have shown how the size and shape of the confining walls can modify the patterns formed by the particles and induce patterns absent in bulk. Our new theories and computer simulations will be used in continuing studies of inhomogeneous or hyperuniform systems that are ubiquitous in soft- and living matter. Experimental studies of nanoparticles production and their assembly during formation of nanostructured surfaces can find applications in anti-corrosion coatings. Fig.2 Fig.3 Fig.1 Fig.4
