Ultrasonic Investigation of Polyurethane Gel Forming Systems Pierre-Yves Baillif, Mohamed Tabellout,* and Jacques R. Emery Groupe UltrasonssU.M.R. 6515, Chimie et Physique des Mate´ riaux Polyme` res, Universite´ du Maine, Av. O. Messiaen, 72085 Le Mans Cedex 9, France Received August 24, 1998; Revised Manuscript Received January 29, 1999 ABSTRACT: Polyurethane systems corresponding to different reaction extents of the gelation process are investigated by ultrasonic methods in order to apprehend their high-frequency dynamical properties and their evolution during formation. The longitudinal moduli M calculated from the measurement of the longitudinal velocity and absorption exhibit a relaxation behavior which is attributed to the R process. The results are analyzed by comparison with low-frequency rheological data, allowing a more complete description of this relaxation by the Tamman-Vogel-Hesse-Fulcher equation. As moduli M are obtained versus temperature at a single frequency, data are treated by a transformed Havriliak-Negami function. The R relaxation process probed by ultrasonics is larger than the rheological one, which has been interpreted in terms of the influence of a secondary relaxation merging at high temperature. I. Introduction In gel forming systems, two main transitions can occur during the growth process: the sol-gel transi- tion, 1 which is a transition of connectivity, and the vitrification 2 process associated with chain mobility. The gelation occurs through the growth of branched polymer units. As the reaction proceeds, the viscosity increases and diverges for a critical reaction extent at which an infinite cluster is formed and a static elastic modulus appears. The increase of connectivity leads also to a decrease in mobility and thus to an increase of the glass transition temperature. These two aspects have been studied using ultrasonic methods in some polymers. 3-6 While the vitrification process is clearly pointed out by ultrasonic measurement, 7 the sol-gel transition passes without any particular incidence on the velocity and absorption. In the general frame of the study of the structure- mechanical properties relationships of polymers, poly- urethane systems (PU) are of special interest because of their well-known chemistry and so can be considered as model systems. On the basis of trifunctional poly- (propylene glycol)triol and difunctional hexamethylene diisocyanate, they lead to tridimensional networks. Four relaxation processes have already been reported in PU systems: the normal mode which characterizes the conformational relaxation of the molecular backbone, the R relaxation which characterizes segmental motion, and two sub-glass relaxation processes  and γ. These relaxations have been pointed out by different experi- mental techniques such as mechanical, 7 dielectrical, 8 and optical 9 methods in polyurethane. We focused in this paper on the dynamics of R relaxation, a phenom- enon related to glass transition, involving polymer chain units and resulting in cooperative movements. In a previous work 9 it has been shown on a single system that ultrasonic methods associated with rheology allow a complete and a better description of the R relaxation. The relaxation times associated with this process follow a so-called Tamman-Vogel-Hesse-Fulcher (TVHF) 11 law. However, only relative values were determined, leading to some uncertainties. In the present study, both velocity and absorption obtained for all samples are absolute values, allowing a better comparison between low and high frequency. It is therefore interesting to study the evolution of these dynamics with the reaction extent from the starting materials to the fully cured polyurethane. It is further interesting to see how the prepolymer influences the dynamics of the final mate- rial. With this aim, several samples are prepared corresponding to different steps of the gel formation. The influence of cross-link density on R relaxation dynamics is investigated using different molecular masses of the prepolymer. As these samples are very attenuative media, the measurements have been carried out at a single fre- quency but at a very large temperature range. To get information on the evolution of the relaxation time distribution, the data have been analyzed using the Havriliak-Negami empirical function in the tempera- ture domain. II. Experimental Section Samples. Polyurethane (PU) systems were formed by condensation of a prepolymer poly(propylene glycol) triol with hexamethylene diisocyanate (HMDI). The reaction catalyzed by dibutyltin dilaurate leads to a tridimensionnal network. To study the system dynamics during its formation, quenched samples corresponding to different steps of the reaction were prepared at various initial stoichiometric ratios r ) 0, 0.2, 0.4, 0.6, 0.8, and 1 defined as the initial relative concentration of NCO groups to OH groups: while the reaction extent p, representing the rate of formed links, is defined as For all samples, the reaction was carried out at 25 °C for 24 h until complete comsumption of NCO groups (p ) 1). To understand the influence of molecular size on dynamics properties, three different molar masses are used for precur- sors: 260, 720, and 6000 g/mol. A gel is obtained for r g 0.569 in the case of systems based on triol 260 and 720 and r g 0.76 for the triol 6000. The critical stoichiometries have been * Corresponding author. E-mail: Mohamed.Tabellout@univ- lemans.fr. r ) [NCO] initial /[OH] initial (1) p ) [NCO] reacted /[NCO] initial (2) 3432 Macromolecules 1999, 32, 3432-3437 10.1021/ma981324z CCC: $18.00 © 1999 American Chemical Society Published on Web 04/28/1999