Introduction

A macromolecule is a molecule composed by a great number of covalently bonded atoms[1]. The most common class of macromolecules is that of polymers, which are molecules composed by smaller subunits, the monomers, covalently linked together. If the monomers are all of the same type, the resulting molecule is a homopolymer, while if they are different, the molecule is a heteropolymer. In general, monomers can be connected in different ways, giving raise to unidimensional structures such as chains or rings, or to more complicated topologies such as brushes, stars, networks, etc.

Focussing on chains, the number of repeating units (also known as residues) composing a polymer is called degree of polymerisation $N$, and for common plastic materials is rather large ($N \sim 10^3 - 10^5$). The simplest polymer is the hydrocarbon polyethylene, $(-CH_2-)_n$, which is used to make cheap bags and bottles and accounts for more than $30%$ of the plastic produced worldwide (see e.g. here). Other very common polymers used to build everyday objects are polypropilene, $-CH_2-CH(CH_3)-$, which is heat- and fatigue-resistant and therefore used to make hinges, piping systems, containers, and polystyrene, $-CH_2-CH(C_6H_5)-$, used to make plastic cutlery, containers or insulating foams. The skeletal formulas of these three polymers are shown in the figure below.

Polymers are fascinating systems for several reasons. First, their large size and flexible architecture give rise to a rich variety of conformations and dynamic behaviors, which are strongly influenced by temperature, solvent quality, and molecular interactions. Second, the sheer diversity of possible monomer types and connectivity patterns allows for a vast design space of materials with tailored mechanical, optical, and chemical properties. From DNA and proteins in biology to plastic packaging and high-performance composites in industry, polymers play a central role in both natural and engineered systems.

A particularly interesting feature of polymers is that, despite their chemical complexity, many of their macroscopic properties, such as elasticity or viscosity, emerge from relatively simple physical principles. For example, the entropic elasticity of a rubber band or the slow relaxation of entangled polymer melts can often be understood in terms of statistical physics and coarse-grained models, without requiring detailed chemical knowledge.