We present a Landau theory for large-$l$ orientational phase transitions and apply it to the assembly of icosahedral viral capsids. The theory predicts two distinct types of ordering transitions. Transitions dominated by the $l=6,10,12$, and 18 icosahedral spherical harmonics resemble robust first-order phase transitions that are not significantly affected by chirality. The remaining transitions depend essentially on including mixed $l$ states denoted as $l=15+16$ corresponding to a mixture of $l=15$ and $l=16$ spherical harmonics. The $l=15+16$ transition is either continuous or weakly first-order and it is strongly influenced by chirality, which suppresses spontaneous chiral symmetry breaking. The icosahedral state is in close competition with states that have tetrahedral, $D_5$, and octahedral symmetries. We present a group-theoretic method to analyze the competition between the different symmetries. The theory is applied to a variety of viral shells.

• Received 18 January 2017

DOI:https://doi.org/10.1103/PhysRevE.95.062402