Polymers at Surfaces-Reflection

Neutrons can be reflected from planar surfaces according to the usual laws of specular optics. The rdractive index n for neutrons is given by  

This equation indicates that for most materials the refractive index will be very close to, but generally slightly less than, unity. The condition in optics known as total internal reflection will thus be replaced by total external reflection [60]. This will occur at low angles, typically about one degree for thermal neutrons. At angles larger than the critical angle, the reflectivity is reduced, and it is this variation that provides information about the structure of the interface. 

The intensity of a neutron beam reflected from a surface can be calculated exactly using the optical matrix approach of approximating the interface to a series of thin layers and calculating the reflection at each boundary in the manner described by Bom and Wolf [61], Heavens [62] or Abeles [63]. It is perhaps more instructive to consider an alternative procedure based on the kinematic theory of scattering [64] which gives the following approximate expression for the reflectivity R(0 as a function of Q the momentum transfer normal to the interface  

This technique has emerged only recently but is rapidly growing. Reviews of the experimental technique [66] and the application to polymers [67] have already appeared. The application of neutrons to the study of polymer surfaces or interfaces can be divided into two categories. First, the study of polymers adsorbed or spread at liquid interfaces secondly, the study of polymers in thin films. This second category provides interesting models for measurements on polymer compatibility and inter-diffiision. Reports of ordering of copolymers at surfaces [68], phase separation [69] and the width of polymer/polymer interfaces during diffusion [70] have been made. 

The results on adsorbed polymers using neutron reflection provide a useful complement to studies of adsorption by small angle scattering and other classical techniques. Measurements of the excess polymer at both solution/vapour [71-73] and solution/solid [74-76] interfaces have been described. Other studies 

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