화학공학소재연구정보센터
Macromolecules, Vol.36, No.26, 10021-10028, 2003
Masterfunctions providing a sound theoretical basis for the extraction of accurate k(p) data from PLP-SEC chain-length distributions exhibiting Poissonian and Gaussian broadening
The positions of the maxima l(max) of the first "extra peak" that appears in chain-length distributions (CLDs) evaluated by the pulsed laser polymerization-size exclusion chromatography (PLP-SEC) method, and the positions of the points of inflection on the low-molecular-weight side of this peak (l(LPI)), are known to be approximate, but more-or-less inaccurate, representatives of the characteristic chain length (L-0) needed for the determination of the rate constant of chain propagation (k(p)), according to the relation k(p) = L-0/([M]t(0)), where [M] is the monomer concentration and to is the separation of two successive laser pulses. The deviation Of l(LPI) and l(MAX) from L-0 depends on the reaction conditions and, above all, the extent of the axial dispersion (sigma(ad,k)) caused by the size exclusion chromatography (SEC) device. On the basis of simulated CLDs that cover a wide range of reasonable experimental conditions, considering Poissonian (due to the fluctuation of propagation) and Gaussian (due to axial dispersion) broadening, the correction factors L0/l(LPI) and L0/l(MAX) first were shown to be unique functions of a quantity that can be used to compare the experimental and theoretical peak broadness for each sigma(ad,k) value (Uad,k = 0.00, 0.025, 0.050, 0.075). As a next step, masterfunctions were developed, which allow calculation of the correction factors L-0/l(LPI), and L-0/l(MAX) for any arbitrary Uad,k value. These factors are able to reduce the remaining error in L-0 to < 1%, on average, L-0/l(LPI) is used and the mode of termination (disproportionation or combination) is known. However, in the other cases (Lo/l(MAX), and/or lacking knowledge about the mode of termination), the error that remains is only slightly larger. In one case, a masterfunction could be developed (for L-0/l(MAX), in this case) in which sigma(ad,k) does not enter as a parameter explicitly. Because of this feature, it is this masterfunction that is probably best-suited for an a posteriori improvement of older kp data, although the remaining error here is somewhat larger (, 2%).