Polymers in Physics, Chemistry and Biology: Behavior of Linear Polymers in Fractal Structures.

We start presenting an overview on recent applications of linear polymers and networks in condensed matter physics, chemistry and biology by briefly discussing selected papers (published within 2022-2024) in some detail. They are organized into three main subsections: polymers in physics (further subdivided into simulations of coarse-grained models and structural properties of materials), chemistry (quantum mechanical calculations, environmental issues and rheological properties of viscoelastic composites) and biology (macromolecules, proteins and biomedical applications). The core of the work is devoted to a review of theoretical aspects of linear polymers, with emphasis on self-avoiding walk (SAW) chains, in regular lattices and in both deterministic and random fractal structures. Values of critical exponents describing the structure of SAWs in different environments are updated whenever available. The case of random fractal structures is modeled by percolation clusters at criticality, and the issue of multifractality, which is typical of these complex systems, is illustrated. Applications of these models are suggested, and references to known results in the literature are provided. A detailed discussion of the reptation method and its many interesting applications are provided. The problem of protein folding and protein evolution are also considered, and the key issues and open questions are highlighted. We include an experimental section on polymers which introduces the most relevant aspects of linear polymers relevant to this work. The last two sections are dedicated to applications, one in materials science, such as fractal features of plasma-treated polymeric materials surfaces and the growth of polymer thin films, and a second one in biology, by considering among others long linear polymers, such as DNA, confined within a finite domain.