| The Sr14-xCaxCu24O41 compounds possess a layered structure of alternating planes of Cu2O3 spin ladders and CuO2 spin chains. The two sub-systems have incommensurate translation vectors in the ladder-chain direction, and their mutual influence induces incommensurate structural distortions of both subsystems. The low energy properties of these compounds are different both from uniform ladder physics and chain physics. Moreover these properties are strongly modified by the isovalent substitution of the strontium by the calcium counter-ion. This work studies the influence of the incommensurate structural modulations on the low energy physics of the Sr14-xCaxCu24O41 copper-oxides. An effective t-J+V model has been determined for both subsystems using ab-initio calculations. This model includes on-site, an both nearest neighbor and next nearest neighbor effective parameters. The structural modulations appear to be the key degree of freedom, responsible for the low energy properties, such as the electron localization, the formation of dimers in the chains of the x=0 compound or the anti-ferromagnetic order in the x=13.6 compound. This microscopic model however put into question the pertinence of the uniform ladder model as the origin of the superconductivity in the x=13.6 compound. |