Scattering from Thermal Concentration Fluctuations

Abstract

This chapter describes scattering from solutions of binary mixtures of molecules which are nonuniform with respect to spatial concentration (composition) distribution due to thermal fluctuations. The chapter presents Ginzburg–Landau/Cahn–Hilliard theory for the nonuniform solutions which provides the physical basis of the Ornstein–Zernike (OZ) scattering formula for the thermal concentration fluctuations of the mixtures. Critical scattering and critical temperature are described based on the OZ scattering together with the mean-field Flory–Huggins theory of polymer mixtures and with the non-mean-field theory which incorporates the renormalization effects of random thermal noise on the concentration fluctuations driven by the thermodynamic driving force. The general theory of the scattering from thermal concentration fluctuations is also presented based on Random Phase Approximation (RPA). The RPA provides the scattering formula not only for polymer mixtures A/B but also for block copolymers A-b-B. The scattering from the two systems (A/B and A-b-B) are compared to elucidate the profound effects of the single chemical link between the two chain ends of A and B on the thermal concentration fluctuations and resultant scattering and also on phase transition and nature of phase transition through its effects on the random thermal force.