We provide a new approach to describe the component segmental dynamics of miscible polymer blends combining the concept of chain connectivity, expressed in terms of the self-concentration, and the Adam-Gibbs model. The results show an excellent agreement between the prediction of our approach and the experimental data. The self-concentrations obtained yield length scales between 1 and 3.2 nm depending on the temperature, the flexibility of the polymer, expressed in terms of the Kuhn segment, and its concentration in the blends, at temperatures above the glass transition range of the blend.