  Poly-vinlyacetate (PVAc) forms very stable and reproducible monolayers on the
surface of water, a model system to understand polymer physics on two
dimensions. A recently introduced technique is applied here to to study
viscoelasticity of PVAc monolayers. The method is based on measurement of
surface tension in two orthogonal directions during anisotropic deformation.
Compression and shear moduli are explored over a very large concentration
range, highlighting a series of four different regimes. At low concentration
the polymers are in a dilute gas. Above the overlap concentration $\Gamma^\ast$
there is a fluid semi-dilute region, where the monolayer properties are
described by scaling laws. At a threshold concentration $\Gamma^{\ast\ast}$, a
decrease in the gradient of pressure with concentration is observed, and we
argue that there is still a large fraction of free area on the surface.
Compressing further, we then identify close packing as the point where the
pressure gradient rises sharply and a shear modulus emerges. This is
interpreted as a transition to a soft-solid due to the kinetic arrest of
close-packed monomers. The reological properties of PVAc above
$\Gamma^{\ast\ast}$ have not been studied previously. Discussion includes
possible explanations for the observed behaviour in terms of both equilibrium
and non-equilibrium conditions, and the relation to microscopic chain
properties. Temperature dependent effects around $\Gamma^{\ast\ast}$ are also
observed and described.
