Study of post-gelation reaction by differential scanning calorimetry Zoran S. Petrovi6* and Jaroslava Budinski-Simendi6 Institute for Petrochemistry, Gas, Oil and Chemical Engineering, Faculty of Technology, Novi Sad, Yugoslavia and Tatjana Malava~,i6 Chemical Institute Boris Kidri~, Ljubljana, Yugoslavia and William J. MacKnight Department of Polymer Science and Engineering, University of Massachusetts, Amherst. USA (Received 22 March 1989; revised 28 August 1989; accepted 3 October 1989) Determination of conversion in the polycondensation of polyfunctional monomers above the gel point is complicated by insolubility of the polymer. The use of d.s.c, can overcome this difficulty if it affords sufficient accuracy. The aim of this work was to estimate the accuracy of the d.s.c, determination of conversion in the reaction of tris(4-isocyanatophenyl) thiophosphate and polypropyleneglycol of M W= 1000 model system. The calibration of the d.s.c, conversion values was carried out by titration of the isocyanate groups at different conversions in the pre-gel state. The results were then used to compare the conversion measured by d.s.c, with that from sol fraction measurements in the post-gel state. The relationship between the sol fraction and the degree of conversion for our system was obtained from cascade theory. Reasonable agreement between the d.s.c, and sol fraction methods was found below 90% conversion. (Keywords: gelation; d.s.c.; model polyurethanes) INTRODUCTION The study of the gelation of polyfunctional monomers beyond the gel point is difficult because such materials are insoluble and not amenable to most of the standard techniques for measurement of conversion. In the case of a difunctional polyol and a triisocyanate, it is, in principle, possible to measure conversion beyond the gel point by infra-red red spectroscopy, following the absorption of the very strong isocyanate group at 2275-2240cm-1. However, experience shows that the reaction in the very thin film, suitable for infra-red, does not proceed in the same way as in bulk. Also, the process of sample preparation for i.r. measurements after gelation occurred, is extremely difficult and time consuming. With the development of modern high precision instru- mentation, differential scanning calorimetry (d.s.c.) is offering new possibilities for studying the later stages of gelation. In order to examine the precision and applic- ability of the method to gelation study, a model system consisting of the polypropylene glycol (PPG), having MW= 1000, and tris(4-isocyanatophenyl) thiophosphate was reacted and the degree of conversion measured by d.s.c, and titration before the gel point, and by d.s.c, and sol fraction measurement after the gel point. Conversion beyond the gel point can be obtained from sol fraction measurements and gelation theories. Gelation theories can be divided into several groups. The first is the *To whom correspondence should be addressed at: Tehnologki Fakultet, 21000 Novi Sad, V. Vlahovira 2, Yugoslavia 0032-3861/90/0815144)5 © 1990 Butterworth-Heinemann Ltd. 1514 POLYMER,1990, Vo131, August probability theory of Flory-Stockmayer 1, the second is cascade (or branching) theoriesZ; the third, percolation theories 3 and the fourth, kinetics theories 4. This fact alone indicates that there are still some unsolved problems and different approaches offer new insights into the phenomenon. One of the unsolved problems is associated with the assessment of the degree of intra- molecular reactions 5. However, if intramolecular reaction is present then the theories mentioned may be adapted to take approximate account of such reaction. The resulting approximations become less accurate, the greater the degree of intramolecular reaction. Experi- mentally, the degree of intramolecular reaction can be assessed by measuring the dependence of molecular weight on conversion. Intramolecular reactions increase conversion without increasing the molecular weight of the polymer. In order to study intramolecular reactions after the gel point one can compare the sol fraction from theory (for the ideal case without intramolecular reac- tions) with the experimental value at a given conversion. Thus, the precise degree of conversion is required. Conversion, p, from d.s.c, can be calculated directly by measuring the enthalpy of the unreacted part at a given time, H, and using the initial enthalpy Ho, according to the relationship: p = (no - n)/no (1) This equation is correct provided the reaction heat is independent of the substitution in the triisocyanate. If the reaction is slow then samples can be taken at regular times and simultaneous d.s.c, analysis and titration can