Conformational calculations of charged polysaccharides

A combination of the molecular polyelectrolyte theory with the methods of statistical mechanics can be used at least for the description of the chain expansion due to charges along the polysaccharide chain. The physical process of the proton dissociation of a (weak) polyacid is a good way to assess the conformational role of the poly electrolytic interactions, since it is possible of tuning poly electrolyte charge density on an otherwise constant chemical structure. An amylose chain, selectively oxidized on carbon 6 to produce a carboxylic (uronic) group, has proved to be a good example to test theoretical results.  

If the real semi-flexible chain of infinite length is replaced by a sequence of segments, the average end-to-end distance r of each segment defines the average distance b between charges  

The probability function W (r) of the end-to-end displacement r of a charged segment can be obtained by multiplying its a priori (non-ionic) probability W(r) with the Boltzmann 

The calculation of the averaged (electrostatic) functions is reached in two steps. At the first, the proper flexibility of the polymer is evaluated either from conformational calculation or from suitable models, then the mean value of each property is calculated through the averaging procedure described below. 

The conformational (non-ionic) free energy, obtained from the radial distribution function for non-ionic chains by Monte Carlo calculations, was used in conjunction with the electrostatic free energy to calculate the actual distribution function of the charged chain segments. The resulting expansion justifies almost quantitatively in many cases the experimental thermodynamic properties (such as pK, H i, etc.) and the dimensional properties (viscosity) of the ionic polysaccharides to which the approach has been applied. 

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The chapter, however, does not give extensive references to the experimental determination of the polysaccharide shape and size in different solvents, but rather it attempts to focus on the molecular reasons of these perturbations. A digression is also made to include the electrostatic charges in polyelectrolytic polysaccharides, because of their diffusion and use and because of interesting variations occurring in these systems. Thus, provided that all the interactions are taken into account, the calculation of the energetic state of each conformation provides the quantitative definition of the chain dimensions. 

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