Equations for less flexible molecules

As discussed in Chapter 2, xanthan has a structure that is not quite a rigid rod since it has some degree of flexibility. This type of structure was described by Porod and Kratky as the worm-like chain model (Richards, 1980, p. 88). Although this may be visualised intuitively to be rather like a semi-flexible string of plastic pop-in beads, it requires the definition of the persistence length, /p, in order to develop the idea in a more quantitative way. This quantity is defined for an infinite polymer chain as follows  

Alternatively, for short rigid rods, /p L, and therefore 1, and Equation 3.41 reduces quite straightforwardly to the result in Equation 3.39 above (since the quantity 2q —q - -qQxp( — 1/ ) 1 as q- co). 

The above theory was developed basically for flexible molecules which may have some degree of stiffness. However, if it is assumed that xanthan molecules may be modelled as rigid rods to a first approximation, then a theory has been developed which allows the determination of molecular dimensions from viscometric measurements in a similar way to the flexible coil case. The relationship between intrinsic viscosity and macromolecular shape has been derived theoretically for rigid rods (Layec and Wolff, 1974). When the ratio of the length to the diameter of the molecule, p, is large (p 50), the model gives a relationship between the zero shear intrinsic viscosity, Mq, and p of the form  

Following the treatment of Benoit et al (1967) on the properties of rigid rods, it is possible to derive a molecular weight for the xanthan from the expression  

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