Statistical mechanics of macromolecular complexation

The self-assembly of macromolecules through molecular association has attracted long-standing attention in soft-condensed matter physics. The hierarchical formation from small-scale building blocks into larger-scale complex structures often leads to very rich phase behavior controlled by various ambient conditions. The understanding and control of the phase behavior of self-assembling systems require detailed knowledge about the entropy and enthalpy contributions to the free energy of the system. However, this knowledge is limited at the present time because a comprehensive theoretical description of molecular association is still lacking. In this thesis, four tales of achievements in developing theories of macromolecular complexation are presented. (1) We begin with an analytically solvable model of the self-assembly of rigid macromolecules with surface adsorption. A generic understanding of the driving force and the role of entropy is obtained from the exact solutions. (2) We move on to further development of the theory in order to study the complexation between polymers and ionic molecules. The extension of the first model to chain-like molecules is performed using a well-established method in polymer physics, the self-consistent field theory (SCFT) of polymers. We also discuss gelation in this system within the scope of mean-filed approximations. (3) Then, a ladder-like polymer-polymer complexation is studied. Unconventional phase diagrams are predicted from the modified SCFT, indicating a large effect of variations in entropy due to the complexation on bulk properties. (4) Finally, the kinetic aspect of macromolecular binding reactions is discussed.