This chapter summarizes the various models to treat isolated uncharged flexible chains and outlines the properties of the chains with a comparison with experimental results. The summary presented in this chapter is the first step to enter into the field of charged macromolecules.

Starting from a general description of model gels and key experimental variables, thermodynamics and swelling equilibria are described. Based on the fundamentals, behaviors of gels under tension, shear, and temperature variation are explained using a combination of theory and experiments. Phase transitions of gels, where volume changes of several orders of magnitude are of common occurrence, are presented in details to enable researchers to design new hydrogels for their intended industrial purpose.

This chapter reviews basics of electrostatics in vacuum and dielectric media, ion solvation, hydrophobic effect, and thermodynamic properties of electrolyte solutions. Debye-Huckel theory is presented with emphasis on electrostatic screening and corrections to ideal solution properties.

Using the Flory-Huggins theory for uncharged polymer solutions, key concepts of the critical point, coexistence curve, and spinodal curve are presented. These concepts are then generalized to charged systems by explicitly considering restricted primitive model for electrolytes and new developments for polyelectrolyte solutions that include the liquid-liquid phase separation invoked in the formation of membrane-less organelles. Fibrillization in amyloids and collagen is discusses with a focus of electrostatic effects.

This chapter describes the importance of charge regularization using titration curves, basic models of charged macromolecules, experimental and simulation results on isolated charged macromolecules, and theories based on scaling, mean field and self-consistent field methods. Based on these inputs, thermodynamic properties of charged macromolecules in dilute solutions are described. As special classes of charged macromolecules, polyampholytes, polyzwitterions, and intrinsically disordered proteins are described.

This chapter presents salient concepts to understand a vast literature on dynamics of charged macromolecules. Starting from a description of hydrodynamic interaction, dynamics of folded proteins, colloids, flexible polyelectrolytes, DNA are described. For flexible macromolecules, the models of Rouse, Zimm, reptation, and entropic barrier are developed in increasing order of complexity. Using this groundwork, the phenomena of ordinary-extraordinary transition, electrophoretic mobility, and topologically frustrated dynamical state are explained.

Basic principles of assembly processes of charged macromolecules complexing with oppositely charged interfaces and macromolecules are described. Specific examples include adsorption at planar and curved interfaces, charged brushes, genome assembly inside RNA viruses, intermolecular complexation, coacervation, and membrane-less organelles.