Comparison of PDC with Other Column Methods

1 The surface of the beads is usually treated with (CH3)2SiCl2 to avoid sorption. 

2 The elution and migration effects are also found in PDC, but not the compression effect, since no precipitant and temperature gradients are applied. Unlike BWF, no simple transport Equation is applied in PDC because the replacement of the linear Eq. (3b) by the non-linear (17c) would lead to an integrodifferential equation similar to (41 a-b), but more complicated, if some explicit formulation were used instead of the implicit one, based on a flow-equilibrium and on a perturbation calculus, applied to an integrated transport Equation 

Moreover, no general valid mathematical expression is available for the GPC-calibration curve because the GPC-resolution mechanism has not yet been described mathematically to a sufficient extent. However, as the GPC-calibration curve is temperature-independent, spline polynomials 16) can well be used here, or a 4-para-meter-formula propsed by Yau and Malone 281 can be applied (cf. also the papers of Rosen and Provder quoted in Ref. 27i). 

There is however, a way conceivable to avoid these difficulties, namely the combination of GPC- and PDC-measurements performed with the same sample for which the resolution of the GPC-column is good at a possibly narrow MWD. Since the mathematical structure of the spreading functions of the GPC- and the PDC-column is the same, the parameters of Eq. (44a) (e.g. D(P), ctD(P), yD(P) and SD(P)) can then be fitted for GPC by comparing the MWDs calculated from GPC- and PDC-measurements on the same sample by the standard method shown below. Although inverted integral transforms would have to be included in such a non-linear fit, it should not be too hard to find a suitable mathematical algorithm for that iteration. However, so far no efforts have been made in this direction. 

The method applied to the calculation of the MWD from GPC- and PDC-measurements is formally the same it is based on the inversion of compact integral operators in the Hilbert space in a numerical way. Like the treatment of the problems connected with the analytical solution of the integrodifferential Eq. (41a b), also the treatment of this inversion method cannot be given here in all details it can be found in Ref. 8). Here, only an orientation in this universal and therefore somewhat abstract theory, stated by Greschner on the basis of a general superposition principle, will be given in a form specified for PDC and GPC, enabling easy application. 

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