Some recursion relations for solutions of a class of equations
This work presents some recursion relations for solutions of a class of singular partial differential equations. The equations consist of iterated differential operators each of which involves real parameters.
On a class of partial differential equations of even order
SummaryThe general solution for a class of equations of even order is expressed as a sum of solutions of equations of second order.
MAS-NMR spectroscopy studies in the setting reaction of glass ionomer cements.
OBJECTIVES
The main objective is the characterisation of the setting reaction in glass ionomer cements based on experimental ionomer glasses with different fluorine content and a commercial glass ionomer cement liquid by using 13C CP/MAS-NMR, 29Si, 27Al and 31P MAS-NMR spectroscopy in order to receive information specifically about the cross-linking process.


METHODS
Different fluorine containing glass compositions based on 4.5SiO2-3Al2O3-1.5P2O5-(5-z)CaO-zCaF(2) where z=0-3, were mixed with a commercially available polymer liquid to form glass ionomer cements. The cements were subjected to 27Al, 13C CP/MAS, 29Si, and 31P MAS-NMR analysis.


RESULTS
The 27Al spectra showed clearly the formation of six-fold coordinate Al(VI), that may crosslink the carboxyl groups in the poly-acid molecules. A shift towards to more positive values of the carboxyl peak in the 13C CP/MAS-NMR spectra showed clearly the proton dissociation of the carboxyl groups. A shift towards more negative values was observed in the 29Si MAS-NMR spectra, suggesting formation of hydrated silica gel and consequently formation of additional Si-O-Si bonds. 31P MAS-NMR spectra also reflected changes in the coordination state around a PO4(3-) tetrahedron. Increasing the fluorine content of the glasses resulted generally in increased reactivity during setting, due to promoting cross-linking and repolymerisation of the silicate phase, followed by clear changes in the MAS-NMR spectra.


CONCLUSIONS
The cross-linking process during the setting reaction of glass ionomer cements can be followed by MAS-NMR spectroscopy observing the conversion of Al(IV) to Al(VI). The acid base setting reaction is completed in 1 day and no further significant changes in the MAS-NMR spectra can be observed. Further study is required in order to understand the role of phosphorus.