Combination of high-performance refractometry and infrared spectroscopy as a probe for chemically induced gelation and vitrification of epoxies

A combination of infrared spectroscopy and high-performance refractometry was used to investigate the chemically induced sol–gel and glass transition during the polymerization of epoxies. Representations of the refractive index versus chemical conversion reveal an interesting insight into the optical properties accompanying gelation and vitrification. Whereas the electronic polarizability of the liquid state of small average molecular mass and the glassy state is dominated by the mass density, an unexpected excess polarizability observed during the gelation is attributed to cooperative dipole–dipole interactions.


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As model systems, we chose different epoxy compositions based on the resin diglycidyl ether of bisphenol A (DGEBA) and the hardener diethylene triamine (DETA), which undergo either no, one or both isostructural phase transitions during isothermal polymerization.
In the following, we focus on the evolution of the refractive index during the chemically driven gelation and vitrification of the different epoxy compositions. Special interest is paid to the role of mass density and the other aforementioned polarizability contributions during the initial liquid state of small molecular weight, the gelation and the glassy state.

Samples and sample preparation
The epoxy system consists of the resin DGEBA DER 332 from Dow Chemical and (at room temperature) the liquid hardener diethylene triamine (DETA) from Fluka Chemie GmbH (Switzerland). The functional chemical groups of the resin are two oxirane rings. The functional groups of the hardener are five amine hydrogens, distributed on two primary and one secondary amine groups.
First the constituents are degassed. Then sample preparation is performed by mixing the constituents for 5 min by means of a magnetic stirrer at 55 • C in order to exceed the melting temperature of DGEBA. After mixing, the samples are cooled down quickly to ambient temperature in a water bath and applied to the infrared spectrometer and the refractometer. In this way, simultaneous measurements can always be performed on the same sample batch. The isothermal polymerizations are studied at 295 K. The moment of adding the hardener to the resin is taken as the start time of polymerization (all times in the graphical representations of the measured data are shifted appropriately). The problem of removing glassy adhesives from the prisms after room temperature polymerization is solved by applying a suitable treatment with the solvent dimethyl formamide.

Experimental methods
Both experimental techniques, the Abbe refractometry and the attenuated total reflection infrared spectroscopy, are based on the total reflection of an electromagnetic wave incident from the prism to the optically less dense sample. Fresnel's formulae accurately describe the relevant reflection and absorbance processes [45]. The evanescent wave that propagates in the case of total reflection along the interface before entering the prism again carries the information about the sample's optical properties. The evanescent wave's penetration depth into the sample d depth depends on the vacuum wavelength λ 0 and the angle of incidence ϕ of the incident electromagnetic wave and on the ratio between the refractive indices n λ 0 S/P = n λ 0 Sample /n λ 0 Prism , Consequently, information about the sample's optical properties is obtained from the sample layer adjacent to the prism. This layer's thickness lies in the several hundred nanometer range for refractometry and several micrometer range for infrared spectroscopy. For the infrared spectroscopic investigations, the imaginary part of the refractive index is an especially important property as it allows the description of the wavelength-dependent absorbance of the incident electromagnetic wave via excitation of molecular degrees of vibration.

Refractometry.
The used high-precision refractometer Abbemat from Anton Paar OptoTec GmbH (Germany) possesses the high absolute accuracy of 10 −5 and a relative accuracy of 10 −6 . The refractometer's optical wavelength equals 589.3 nm (sodium D-line). The measurement chamber was specially sealed in order to avoid additional demixing processes of the reactants because of moisture [46]. The temperature stabilization of the measurement chamber is better than 0.1 K.
The refractive index is related to the dielectric susceptibility at optical frequencies ε ∞ via n = √ ε ∞ . Note that generally no simple relationship exists between the refractive index and the molecular structure in terms of mass density, being roughly proportional to the electronic dipole number density, and other contributions of electronic polarizability at optical frequencies.
Relevant contributions of the latter type may be the strength of the dipoles at optical frequencies, the molecular shape and the molecular arrangement [36]- [38], [44].
Although there is no model relating mass density ρ and refractive index n for polymers, for many systems a good approximation is given by the well-known Lorenz-Lorentz [33,34] relation, where r is the specific refraction. The specific refraction roughly reflects molecular properties like molecular shape, arrangement and dipole strength. In the surely approximate frame of the group contribution method, the specific refraction, considered from the contributions of chemical groups, is almost a constant during the polymerization of epoxies at ambient temperature [1,47].

Infrared spectroscopy.
All measurements were carried out by the technique of attenuated total reflection on a Biorad/Digilab FTS 3000 Excalibur infrared spectrometer. The modification of the spectrometer consisted in the automation of the detector's cooling. Softwarecontrolled recording of the infrared spectra took place every 15 min during the polymerization of the samples. The parameters of the measurement configuration were s-polarization of the incident beam, angle of incidence ϕ = 60 • , and a prism made of zinc selenide [28,29]. The calculation of the chemical conversion from the infrared spectra is described in detail in [28,29]. The temporal diminishing of a band's height, belonging to a molecular group that reacts during the polymerization, is determined. As usual, the oxirane band at 915 cm −1 is chosen for this purpose. For each spectrum, the height of the oxirane band h oxirane (t) is divided by the height of a reference band, the phenylene band at 1510 cm −1 h phenylene (t), which is independent of the polymerization process. Firstly, this manipulation allows for excluding atmospheric influences on the evaluation resulting, for example, from small temperature fluctuations inside the measurement chamber. Secondly, as the refractive index grows during the polymerization, the penetration depth of the beam into the sample increases continuously, i.e. also the information volume. This effect is accounted for by the division of the oxirane band's height by that of the reference band h phenylene (t).
Finally, the chemical conversion, given in per cent, equals The heights h oxirane (t = 0 h) and h phenylene (t = 0 h) are estimated by a superposition of the spectra of the reactants [28,29].
The evaluation of the chemical conversion u suffers an absolute error lower than 8%, and the relative error is significantly lower [28,29]. In addition, the temperature of the measurement chamber may be subject to long-term variations of several tenths of a kelvin around 295 K. According to experience with temperature-modulated calorimetry, the influence of these fluctuations can be regarded as non-significant for the general polymerization process. For understoichiometric compositions, i.e. below (100/12), the chemical conversion is calculated with respect to the maximum possible oxirane consumption.

Results and discussion
For the sake of clarity, only the datasets of a representative selection of compositions are displayed in some figures; but all of them are taken into account for the general discussion. Figure 1(a) shows the temporal evolution of the chemical conversion for a wide-stretched range of compositions of the reactants DGEBA and DETA measured at room temperature T = 295 K. All curves roughly show the same time dependence: at the beginning of the polymerization process they increase more or less steeply and tend to become asymptotic for longer polymerization times.
Room-temperature-polymerized epoxy mixtures based on DGEBA and DETA are known to vitrify in the neighborhood of the stoichiometric composition. As vitrification strongly hinders the chemical reaction, it can be assumed that all systems that do not reach a chemical conversion of 100% vitrify. In figure 1(a), this statement is valid for the compositions (100/7), (100/14) and (100/30). Under strongly understoichiometric and overstoichiometric conditions, a chemically induced glass transition is no longer possible at ambient temperature and thus the degree of polymerization is expected to develop to u = 100% [7,15,16]. The latter behavior is observed for the epoxies (100/5), (100/40) and (100/61). Hence the habit and especially the asymptotic end values of the curves presented in figure 1(a) give indeed a first hint of which systems undergo a chemically induced glass transition during polymerization at 295 K. In contrast, no hints regarding chemically induced sol-gel transitions are obtained from the temporal development of the chemical conversion.
A deeper insight into the transition behavior accompanying the polymerization process is gained from calculations of the chemical reaction velocity versus the conversion v r (u) = (du/dt) (u) that represents the kinetics of the polymerization process. All chemical reaction velocity curves v r (u) indicated in figure 1(b) follow the same general shape: they start at a finite value, go through a maximum and tend towards zero afterwards. The increase in v r (u) for low conversions is attributed to catalysis of the epoxy reaction provoked by the rising number of hydroxyl groups [16,24,30,48,49]. Vitrifying compositions exhibit an inflection point and a subsequent strong change in slope on approaching v r (u) = 0% h −1 . This strong change in slope, marked by the black bars in figure 1(b), is interpreted as the onset of the chemically induced glass transition. The finite value of the v r (u) curves after the glass transition shows that the polymerization process still proceeds in the glassy network. In other words, molecular transport and network formation are not completely stopped by vitrification. The strongly overstoichiometric systems (100/40) and (100/61), which according to their visco-elastic consistency surely do not vitrify during room temperature curing, go straight to v r (u) = 0% h −1 . Figure 1(b) suggests that the system (100/30) still freezes and that the epoxy (100/5) is at least close to freezing. As deduced from the asymptotic u(t) values of figure 1(a), the maximum degree of polymerization at 295 K is strongly reduced in the range of the stoichiometric composition (100/12). The asymptotic values of all room-temperature-polymerized compositions are plotted in figure 2 as black squares. The red line of the same figure corresponds to the chemical conversion of 100% measured after post-polymerization at 393 K for 1 h, a treatment that is known to achieve the complete possible consumption of the oxirane groups. The significant deviation between the datasets of the room-temperature-polymerized and the post-polymerized samples suggests that the aforementioned glass transition occurs probably in the concentration range of (100/7) to (100/30).
Simultaneously to the infrared measurements, the evolution of the refractive index n(t) was recorded for all compositions. Unfortunately, the continuous and monotonous habits of the n(t) curves shown in figure 3 are rather unspectacular concerning evidence for chemically induced sol-gel or glass transitions. Figure 3 shows that there is a systematic increase in the initial slope of n(t) and a systematic decrease in the starting value n(t = 0) with increasing DETA concentration. The former reflects the increase in reaction velocity already depicted in figure 1(b).
As the chemical conversion rather than the polymerization time reflects the state of the chemical network formation, we plot in figure 4 the refractive index versus chemical conversion n(u). Figure 4(a) contains the curves for all studied epoxies that vitrify, and figure 4(b) those of the other systems. These refractive index curves n(u) show features that are not visible in the temporal representations of either n(t) or u(t).
The curves in figure 4 can be divided into up to three distinctive conversion intervals as exemplarily shown for the epoxy (100/30) in figure 4(a). In a first conversion interval (I1), which is a common feature of all compositions, the evolution of the refractive index behaves almost linearly. Mathematically, this linear regime I1 can be described by n| I1 x (u) = a x + b x · u, where a x and b x are specific constants for the composition (100/x). The extrapolated intercept values a x agree well with predictions based on a linear volume mixing rule concerning the refractive indices of both epoxy reactants (see table 1). The predicted values are slightly lower than the extrapolated values. At this point it cannot be decided whether the model is unsuitable or whether the volume additivity is violated.
Except for the strongly understoichiometric compositions (100/3) and (100/5), there is a subsequent polymerization range (I2), where the n(u) curves increase in a nonlinear way with dn| I2 x /du > b x . For the vitrifying compositions, a third range (I3) is observed in which the n| x (u) curves flatten after the preceding nonlinear increase. This flattening results in a slope of n| I3 x (u) being smaller than b x .
The different behavior in slope observed for the three intervals suggests that the increase in the refractive index with the chemical conversion u is determined by several optical polarization mechanisms being specific to I1, I2 and I3. As stated in section 2, qualitatively there are a number of contributions to the refractive index: the molecular dipole strength, the molecular shape and arrangement, and the dipole number density being roughly proportional to mass density. The goal of the following discussion is to tentatively relate the measured evolution of the refractive index to different structural formation processes, including the phase transitions accompanying the polymerization.
The interpretation of interval I3 seems the clearest and most obvious compared with the others. As the onset of flattening at the beginning of interval I3 apparently coincides with the kink in the reaction velocity v r (u) (compare the black vertical bars in figures 1(b) and figure 4(a)), this flattening is attributed to the chemically induced glass transition. Since a rather rigid molecular network has formed during the ongoing isothermal polymerization in  the glassy state, the volume shrinkage is much more hindered in that state than in the liquid or gel state. Thus, in the course of the chemically induced vitrification and in the glassy state, n(u) is dominated by the saturation of the mass density. The current investigations do not allow an interpretation of the remaining finite slope dn| I3 x /du in the glassy state. It may be dominated either by a slight increase in mass density or by changes in molecular polarizability at an almost constant mass density.
In order to get a clearer view of the influence of the mass density ρ(u) on n(u), for an epoxy-based nanocomposite, the role of nanoparticles in the refractive index evolution n(u) is Table 1. Investigated compositions: mass ratios of resin DGEBA to hardener DETA, molar ratios of the functional groups oxirane and amine, extrapolated n(u = 0)-values, estimated n(u = 0)-values according to a linear volume mixing rule of the refractive indices of DETA (n = 1.4846) and DGEBA (n = 1.5688), and Flory-Stockmayer prediction [12,16] of the critical chemical conversion for the sol-gel transition u sg .

Mass ratio
Molar ratio n(u = 0) n(u = 0) u sg DGEBA/DETA oxirane amine/hydrogens extrapolated calculated Flory-Stockmayer  [50]. For this purpose, silanized precipitated silica nanoparticles with a spherical shape and an average diameter of 14 nm (Nanoresins AG, Geesthacht), which are generally supposed to have mostly a topological impact on the epoxy network but essentially no chemical influence on the polymerization, are added to the epoxy reactants [25,51]. In figure 5, the n(u) curves of the pure, almost stoichiometric epoxy (100/14) and a nanocomposite based on the same epoxy composition but containing 67 mass parts of silica nanoparticles are compared. Obviously, the presence of nanoparticles neither removes the flattening of the n(u) curve caused by the density saturation in I3 nor changes the slope in I1. From these observations we conclude that the effects of mass density on the refractive index are essentially not modified by the nanoparticles. It is plausible that the linear increase in n(u) in I1 is solely linked to an increase in mass density with chemical conversion. However, in interval I2 the positive excess refractive index, which adds to the purely linear n(u)-background observed in I1, vanishes in the presence of the nanoparticles, so that for the nanocomposite the linear n(u)-behavior of zone I1 extends until I3. Also in I2 the linear background of the electronic polarizability at optical frequencies is attributed to the dipole number density, being roughly proportional to the mass density. Other contributions of optical polarizability, which are responsible for the positive excess refractive index in I2, have to be added for the pure epoxy (100/14). At the moment, it seems that the origins of the latter contributions can be disturbed by the nanoparticles so that the positive excess polarizability in I2 vanishes for the nanocomposite. It appears that the linear increase in n(u), i.e. ρ(u), in I1 is observed for epoxies still possessing low average molecular weights. At this early stage of polymerization, a heterogeneous formation of dimers, trimers and m-mers that in essence do not interact with each other takes place. For strongly understoichiometric and overstoichiometric pure epoxy compositions, this linear regime I1 extends to rather high degrees of polymerization as the increase in the sample's average molecular weight as a function of chemical conversion is slowed down. As shown in table 1, for these highly unstoichiometric systems the percolation threshold of the epoxy network is either obtained for high chemical conversions or is even impossible. It seems that the linear regime can also spread to higher average molecular weights for almost stoichiometric samples when the macroscopically extended molecular network becomes strongly coarse grained due to the presence of 25 vol.% silica nanoparticles. Thus, the negligible electromagnetic interaction of molecules observed for small molecular groups in I1 can also be suppressed in a macroscopic network (i.e. in I2) in the presence of a sufficient amount of silica nanoparticles.
The linear increase in the refractive index as a function of mass density suggests the applicability of the Lorentz-Lorenz equation [33,34,41,42] (see equation (2)) with a constant specific refraction r for the given epoxy composition. Since for this epoxy n is a weakly varying function of u (total change smaller than 2%), it follows that dn/du is in good approximation proportional to dρ/du by The accuracy of this approximation scales with the total change in n, i.e. here roughly 2%. Obviously, the slope of n(u) for the various systems depends on several effects, such as e.g. dilution effects for a high DGEBA or DETA concentration, compared to the stoichiometric composition, and the respective molecular structural formation. Of course, the molecular structure depends also on the reactant's composition, but is also affected by the unequal reactivity of primary and secondary amines [16,48,52].
The remaining question concerns the interpretation of the nonlinear increase in n(u) in the interval I2 (see figure 4). It should be stressed that this n(u)-anomaly is a specific property of certain DGEBA/DETA systems as it is not noticed in other gelating polymers, such as polyurethanes [53] and polydimethylsiloxanes (unpublished). As explained above, the cause of this increase in I2 most probably lies in a combination of an increasing average strength of the dipoles and an increasing dipole number density. From the above debate about the action of silica nanoparticles on the n-anomaly, we conclude that the linear background caused by the mass density augmentation is supposed to continue from I1 until the end of I2. Secondly, this linear contribution is superimposed by a nonlinearly increasing contribution to n due to an increasing effective strength of the optical dipole system. In order to separate both these contributions in I2, the linear n(u)-relationship visible in I1 is extrapolated until the highest degree of polymerization and subtracted from the measured curves. A representative choice of the resulting excess refractive index curves n(u) = n(u) − n| I1 figure 6. In interval I1, all n-curves are, of course, equal to zero within the margin of error. Except for the composition (100/5), the subsequent excess polarizability contribution leads to a strong, monotonous augmentation of n. Finally, for the vitrifying epoxies from (100/7) to (100/30), n shows a maximum that reflects the leveling of n(u) close to the glass transition. The subsequent apparent decrease in n(u) in I3 is an artifact of the data treatment. In fact, it is due to the ignorance of the density-determined refractive index saturation in the chemically induced glassy state where indeed n(u) becomes constant. According to figure 6, the most remarkable increases in n occur for systems with no or little interference with the chemically induced glass transition. In those cases, an almost diverging increase in n(u) is experimentally evidenced. Since vitrification can be excluded as an inherent cause of n(u), it is reasonable to discuss the question whether the sol-gel transition could be at the origin of the quasi-diverging n. Indeed, the significant growth in n(u) seems to be inherently connected to network formation in the course of gelation. In order to get a rough overview of the location of the critical conversion u sg , a suitable gelation theory like the one of Flory and Stockmayer [12,16] will be applied. The critical conversion is calculated according to with N E and N A denoting the mole numbers of oxirane rings and amine hydrogens, and f A and f E being their respective functionalities. Using f A = 5 and f E = 2, the values of u sg were calculated for the studied epoxy compositions and listed in table 1. Figure 6 shows for most systems a rough correlation between the onset of the steepest part of n(u) and u sg . On the other hand, it turns out that the strongly overstoichiometric systems (100/61) and (100/80) surely do not reach the gel state (see table 1). It is therefore likely that the actual appearance of the sol-gel transition is not a prerequisite for the existence and growth of n(u). It remains unclear whether the sol-gel transition modifies the habit of the n(u)curves. That the onset of n(u) is observed for the smallest chemical conversion in the case of the stoichiometric composition gives a clear hint that the excess polarizability is linked to the formation of larger network aggregates.
For the vitrifying compositions from (100/7) to (100/30), the glass transition obviously truncates the n(u) increase being characteristic for I2. As, for these systems, the sol-gel transition probably suffers a few per cent conversion prior to the glass transition, an interference of both transitions is likely. The chemically induced glass transition limits the further growth of n, but does not seem to reduce the currently existing excess polarizability. Interestingly, n is maximal for the composition (100/30), which freezes only when an almost full degree of polymerization is reached. In other words, the gelation, i.e. the necessary condition for the excess polarizability contribution, could largely develop in this epoxy. In contrast with the influence of vitrification on n(u), figure 5 shows that the addition of a sufficient amount of silica nanoparticles destroys the excess refractive index.
According to these statements, the origin of the optical excess polarization leading to n(u) remains puzzling and the interpretation of this effect is necessarily speculative: it is argued that the optically excited molecular dipoles do cooperatively interact as long as they are arranged closely in an undisturbed molecular epoxy network. Apart from densification effects due to the structural formation accompanying the polymerization process, dipole-dipole interactions create the observed surplus of n(u) in I2. In other words, the formation of large molecular network aggregates as well as structure-specific interactions between the molecular dipoles produce a dielectric situation in which positive feedback between these dipoles exists. However, these cooperative dipole interactions are weak since a sufficient amount of small topological and dielectric defects like silica nanoparticles are able to destroy them completely.
On the background of the 'feedback hypothesis', the interesting issue arises whether the onset of n is gradual as a function of the chemical conversion or whether a critical size and/or density of the molecular network aggregates is needed in order to activate the excess polarization process. The data given in figure 6 seem to be in favor of a sudden onset of n. Although for the highly understoichiometric epoxy (100/5) the sol-gel transition is predicted for u = 77% according to the Flory-Stockmayer theory, no excess refractive index n is observed. Probably the necessary critical size and/or density of molecular aggregates cannot be reached for this composition.
The fact that strongly overstoichiometric compositions like the epoxy (100/80), which do not percolate, still develop a significant excess refractive index is related to the presence of a sufficient amount of adequate molecular network aggregates (microgels). As expected, figure 6 reveals that the amplitude of n decreases significantly for an increasing overstoichiometry.

Conclusion
Different compositions of DGEBA/DETA-based epoxies were investigated by infrared spectroscopy and refractometry. The representations of the chemical conversion u as well as of the refractive index n versus time both give a rough view of the structural formation during the polymerization process. The reaction velocity v r (u) derived from the chemical conversion gives, in addition, a good overview of the composition-dependent chemically induced vitrification, but no indication of the gelation process.
On the other hand, the representation of the refractive index versus the chemical conversion turned out to be sensitive not only to the freezing but also to the gelation process. The evolution of n(u) can be divided into three distinctive intervals reflecting different stages of structural formation. The first interval reflects the initial growth of the epoxy network molecules. The linear increase in the refractive index is related to the accompanying increase in mass density. The third interval, which is close to maximum conversion, is attributed to the chemically induced freezing process. In this interval, the refractive index evolution is predominantly coupled to that of the mass density that is triggered by the chemical freezing process.
Finally, in the intermediate interval, in which predominantly gelation takes place, two astonishing different processes contribute to the optical polarizability and consequently to the refractive index. As in the first interval, the increase in mass density accompanying the polymerization still yields a linear increase in the refractive index n(u). In addition to this contribution, an unexpected nonlinear contribution to the refractive index is identified that is attributed to feedback between optically induced dipoles specific for molecular epoxy network aggregates, which are sufficiently large and/or dense. A unique relation between the evolution of the excess refractive index and the sol-gel transition was not found.