  Inspired to understand the complex spectrum of space-filling organizations
the dsDNA genome within the capsid of bacterial viruses, we study a minimal,
coarse-grained model of single chains densely-packed into a finite spherical
volume. We build the three basic elements of the model--i) the absence of chain
ends ii) the tendency of parallel-strand alignment and iii) a preference of
uniform areal density of chain segments--into a polymer nematic theory for
confined chains. Given the geometric constraints of the problem, we show that
axially symmetric packings fall into one of three topologies: the coaxial
spool; the simple solenoid; and the twisted-solenoid. Among these, only the
twisted-solenoid fills the volume without the presence of line-like
disclinations, or voids, and are therefore generically preferred in the
incompressible limit. An analysis of the thermodynamics behavior of this simple
model reveals a rich behavior, a generic sequence of phases from the empty
state for small container sizes, to the coaxial spool configuration at
intermediate sizes, ultimately giving way, via a second-order,
symmetry-breaking transition, to the twisted-solenoid structure above a
critical sphere size.
