Abstract
Treatments of the statistical thermodynamics of rigid rod-like particles have generally assumed that the distribution of rod lengths is fixed, and have therefore been concerned only with the equilibration of particle orientations. Since many systems of biological interest involve the reversible linear polymerization of proteins, we have been concerned with the joint equilibration of the distributions of rod lengths and rod orientations. Accordingly, we have combined earlier lattice model calculations of the statistics of particle orientation with free energies of polymerization, and located the equilibrium with respect to both polymer growth and alignment. We have initially assumed simple linear polymerization in which the free energy of monomer addition to an existing polymer is independent of polymer length. The phase behavior is found to be more sensitive to the value of the free energy of polymerization than to the nature of the interactions between polymers, to such a degree that the effects of temperature on the system are most likely felt primarily through the temperature dependence of the free energy of polymerization. As a consequence, the form of the temperature phase diagram predicted for reversibly polymerizing systems is distinctly different from that predicted for irreversibly polymerized systems.