Universality in the nematic lyotropic phase space

Here, we propose that some aspects of the phase diagram of nematic lyotropic materials can be put in a universal form. We will show that a simple combination of the order parameter invariants in the uniaxial and biaxial nematic phase is enough to revel the existence of a singular and unique phase space topology, which is common to all nematic lyotropic system. This universal lyotropic topology lies fused with individual properties of the specific compound in the nematic phase space. As an application, we will use these concepts on the lyotropic mixture of potassium laurate, decanol and heavy water to exemplify the occurrence of these universal phase space properties on nematic lyotropic materials.