Self-Assembly of Synthetic and Biological Polymeric Systems of ...

It is normal to represent them as two moduli that determine the component of stress in phase
with the applied strain (storage modulus) and the component out of phase by 90 0 . In an
experiment, the amplitudes of the oscillation input ( ) and output ( ), and the phase angle
( ) are measured. Therefore, each oscillatory shear flow measured at a given provides two
independent quantities, amplitude ratio and phase angle:
The storage and loss moduli are subtle descriptions of the material properties of the system.
These two properties are related to the phase angle and complex modulus. These are both
functions of the applied frequency and represent an alternative description of the system.
The phase angle changes with the frequency, from 90 degrees at low frequency, to 0 degrees
at the high frequency limit; thus, as the frequency increases the sample becomes more elastic,
and the phase difference between the stress and the strain reduces.
2.10.- X-ray diffraction
X-ray diffraction (XRD) is a versatile, powerful and non destructive technique that reveals
detailed information about the chemical crystallographic structure of natural and
manufactured materials. Diffraction effects are observed when an electromagnetic radiation
impinges on periodic structures with geometrical variations on the length scale of the radiation
wavelength. The inter-atomic distances in crystal and molecules is around to 0.15 – 0.5 nm,
which correspond in the electromagnetic spectrum with the wavelength of X-rays, having
photon energies between 3 and 8 keV (3).
There are three different types of interactions between X-rays and matter. First, the
photoionization, where electrons may be liberated from their bound atomic states during the
process, and which falls into the group of inelastic processes. In addition, other inelastic
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