A singular value decomposition approach for investigation of liquid crystal phase transitions

This study uses a texture-based Singular Value Decomposition technique to examine the phase transitions of p-n-alkyloxy benzoic acids (nOBA, where n = 10 and 12). Using this method, the textures of liquid crystals are analysed in relation to temperature. The texture of liquid crystal phases was processed through the Singular Value Decomposition technique, and the first derivative of the dominant singular value was computed to detect structural changes associated with phase transitions. Maximum rate of change in singular values reflecting the subtle shifts in molecular alignment and the temperatures corresponds to shifts that give the transition temperatures. The sensitivity of phase transition detection is increased by this method. Furthermore, structural difference heatmaps and singular value entropy, two measures based on SVD, offer complementary insights into the phase and temperature behavior of liquid crystals. These findings show the SVD methods are reliable and efficient for describing phase behavior in liquid crystals.