Alexander Chervanyov

The main focus of my current research is to investigate how different filler materials affect the static, dynamic, and electrical properties of selected polymer-based nanocomposites. As one representative example, I have recently explored how variations in the morphology of diblock copolymer systems influence the structure of networks formed by embedded conductive fillers, such as carbon nanotubes and carbon black. These morphological changes can lead to drastic variations in the electrical conductivity of the resulting composites. This line of research is primarily motivated by its broad practical relevance to industrial applications, including filler agglomeration in tires and piezoresistive effects in sensors based on carbon-nanotube-filled elastomers. To ensure the realism and applicability of my theoretical studies, I work in close collaboration with experimental research groups.

I have extensive experience in modeling various types of effective interactions acting between solid inclusions in polymer host systems . Polymer-mediated interactions often play a key role in determining the macroscopic properties of technologically relevant polymer-based nanocomposites, ranging from dynamic mechanical moduli to piezoresistive behavior. Due to their practical importance, these interactions have attracted increasing attention over the past decades. To address the associated mathematical and theoretical challenges, I employ a broad range of analytical approaches, including polymer self-consistent field theory , liquid-state theory , and potential theory , including methods developed by myself.

As a relatively new direction of my research, I develop phase-field models for pattern formation in various systems of active particles. As one representative example, I investigate the emergence of moving and resting patterns in systems of self-propelled particles as a function of orientational correlations between particles, temperature, and the magnitude of the active driving force. The interplay of these factors gives rise to a rich variety of crystalline states, both dynamic and static. Such ordered phases provide a promising basis for the design of novel active materials. Selected two-dimensional examples of these states are illustrated in the figure.