Notice: Wiley Online Library will be unavailable on Saturday 30th July 2016 from 08:00-11:00 BST / 03:00-06:00 EST / 15:00-18:00 SGT for essential maintenance. Apologies for the inconvenience.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
Mixtures of tetraglycidyl-4,4′-diamino diphenylmethane (TGDDM) and 4,4′-diamino diphenylsulfone (DDS) are the preferred resin systems for use as matrices in high-performance fiber composites for aerospace applications and for the encapsulation of microcircuitry in the electronic industry. The widespread success of TGDDM/DDS resin mixtures is due to the excellent properties of the derived products, such as high tensile strength and modulus, very high glass-transition temperatures (Tg ∼ 270 °C), outstanding resistance to solvents, and good thermooxidative stability.1–4
One major deficiency of products based on these cured resins is the absorption of relatively large amounts of water in high humidity environments, which brings about a general deterioration of properties. At equilibrium, a typical TGDDM/DDS-cured resin may absorb between 4.0 and 7.0 wt % water,5–7 depending on the molar ratio of the two components, the curing conditions and, obviously, the water vapor activity of the environment. The absorbed moisture acts as a very effective plasticizer, lowering the Tg value of the cured resin, which is estimated to be approximately 20 °C for every 1% absorbed water. Moreover, water sorption may cause irreversible damage to the material by the formation of microcracks through repeated sorption/desorption cycles.4, 6, 7
NMR studies have indicated that the water dispersed within an epoxy network may be present as bound water (hydrogen-bonded) and as mobile water (free).8, 9 Recent work has shown that the levels of both bound and free water can be estimated by Fourier transform infrared (FTIR) spectroscopy in the mid-infrared (MIR; 4000–400 cm−1) and near-infrared (NIR; 8000–4000 cm−1) ranges.10
Systems comprising 4,4′-bismaleimide-diphenylmethane (BMI), TGDDM, and DDS have attracted considerable attention both in industrial applications11 and in scientific research12–15 because of their relatively low water absorption characteristics and the dual mechanism for curing reactions. A detailed spectroscopic analysis of the curing reactions has shown, in fact, that TGDDM and BMI form individual networks without intercrosslinks. Although TGDDM will crosslink through a reaction with DDS, the BMI component will only homopolymerize through thermally induced reactions, even although it is inherently capable of reacting also with DDS.14, 15 Despite the apparent lack of interactions between the original components of the resin mixture, which prevents the system from forming intercrosslinks between TGDDM and BMI, dynamic mechanical analysis has revealed a substantial degree of physical interpenetration of the two networks insofar as only one Tg could be identified.14, 15 This observation also indicated that the curing process produced a single-phase, molecularly homogeneous system, at least to the scale of the aforementioned technique, that is, to the size of the chain segments responsible for the primary relaxation mechanism. This conclusion was supported by scanning electron microscopy measurements; in fact, no evidence of phase-separated domains was found, even at very high magnifications.14, 15
The presence of a rigid BMI homonetwork within the looser network formed by the reactions of TGDDM with DDS increases the Tg, modulus, and yield strength of the final products.15 Furthermore, a BMI homonetwork would have a low affinity for water, so its presence as an interpenetrating network within the two-component epoxide network is expected to reduce the level of water absorbed, if no increase in microvoids is experienced during curing. Both the equilibrium level of absorbed water and its rate of diffusion through the network, in fact, depend not only on the molecular interactions (bound water) but also on the amount of microvoids present. Consequently, the modification of the TGDDM/DDS network with the incorporation of a BMI network could bring about, in a nonpredictable manner, substantial changes in the transport properties of the material. This has been confirmed by preliminary sorption measurements carried out at 70 °C. The water diffusivity into the bulk of the sample, however, was hardly affected.15
Vibrational spectroscopy, particularly NIR spectroscopy, is one of the best suited techniques for probing hydrogen-bonded molecular structures.16 In a previous contribution10 on water sorbed in TGDDM/DDS networks, there were identified, in the infrared spectrum, signals arising from mobile water localized in microvoids and from water molecules firmly bound to the network by hydrogen-bonding interactions. The stoichiometry of the interaction was determined, and the most likely proton-accepting groups along the network were identified. A method was also identified for the quantitative evaluation of the amount of bound water in the system according to spectroscopic data for water in different solvents.
In this study, this molecular spectroscopy analysis is extended to TGDDM–DDS–BMI interpenetrating networks and to a BMI homogeneous network to obtain a deeper understanding of the molecular basis of the diffusion properties of these systems. Sorption and desorption characteristics are subsequently examined by conventional gravimetric techniques and by a spectroscopic method based on time-resolved Fourier transform (FT)-NIR measurements.17 A qualitative comparison is made among the diffusion behaviors of the pure epoxy resin and two compositions of the ternary mixture, with the different molecular structures of the investigated systems taken into account. The results are interpreted in the light of a diffusion model that takes into account the information on molecular interactions obtained by the spectroscopic analysis.
The tetraglycidyl-4,4′-diamino-diphenylmethane (TGDDM) resin was supplied by Ciba-Geigy (Basel, Switzerland). This resin has an epoxy equivalent weight of 124.1 g equiv−1, which is 15% lower than the calculated stoichiometric value because of partial hydrolysis of the oxirane rings, as evidenced by the presence of a readily detectable band of hydroxyl groups in the 3600–3300-cm−1 range of the FTIR spectrum.
The resin hardener was 4,4′ diaminodiphenylsulfone (DDS), supplied by Aldrich (Milwaukee, WI). The bismaleimide resin component was N,N′-bismaleimide-4,4′-diphenylmethane, also from Aldrich.
All reagents were used without further purification.
The structures of these components are as follows:
TGDDM and DDS were mixed at 120 °C in a weight ratio of 1/0.3 (corresponding to a molar ratio of 1/0.5) under vigorous mechanical stirring to obtain a homogeneous (visually transparent) solution. The mixture was then degassed for 15 min in vacuo, and the appropriate amount of BMI was added. Mixing was continued at 100 °C until the bismaleimide powder was completely dissolved. The mixture was then poured into a stainless steel mold and cured at 140 °C for 16 h. Postcuring was carried out at 200 °C for 4 h. The respective codes and compositions of the network systems are reported in Table 1.
Table 1. Codes and Compositions of the Investigated Network Systems
Water Absorption and Desorption
To investigate the transport of water at different temperatures by FT-NIR spectroscopy, we used an isothermal desorption mode so that spectroscopic interference due to liquid water could be eliminated.
Samples 0.15–0.25 mm thick were previously equilibrated with respect to the amount of absorbed water by immersion in a deionized water bath, which was thermostatically controlled at 22 ± 0.1 °C. The desorption of water was monitored by the equilibrated samples being placed in an environmental chamber fitted to an FTIR spectrometer (PerkinElmer System 2000).17 This instrument was equipped with a high-temperature tungsten halogen NIR source, a multilayer calcium fluoride beam splitter, and a deuterated triglycine sulfate detector.
The measurements were carried out over several time intervals at temperatures well below the Tg values: 22, 35, 45, and 60 °C for the TGDDM/DDS network samples and 22, 39, 54, and 60 °C for samples produced from the ternary mixture (TGDDM/DDS/BMI). Measurements were made under an atmosphere of N2 and a pressure of 760 Torr.
The instrumental parameters adopted for the FTIR-monitored desorption tests were as follows: resolution, 4 cm−1; optical path difference velocity, 0.2 cm s−1; and spectral range, 8000–4000 cm−1, which corresponded to 4001 collected data points. Eight data collections were taken and averaged for any single spectrum.
To obtain meaningful and reproducible results, we performed the NIR measurements in the νOH region on samples 3.5–4.0 mm thick because of the reduced absorptivity of the OH stretching modes in comparison with the water band used for monitoring its concentration (5215 cm−1). For these samples, 300 spectra were signal-averaged for each measurement. A calibration plot of the recorded absorbance against the concentration of sorbed water was constructed with the following procedure.
Pieces 3.0 mm long and 2.0 mm wide were cut from 3.5-mm-thick slabs immediately after postcuring. To prevent water from being absorbed from the environment, we transferred the samples to a vacuum oven and stored them overnight at 100 °C, to ensure that they were completely dry. The first NIR spectrum collected confirmed the total absence of sorbed water [shown later in Figs. 2(B) and 3(B)]. This spectrum was taken as a reference for the spectral subtraction analysis (discussed later). The samples were accurately weighed (±0.1 mg) and placed in a deionized water bath thermostatically controlled at 70 ± 0.1 °C. Periodically, the samples were removed from the bath, reweighed, and transferred to the FT-NIR spectrometer to record the spectra (the surface water being previously removed through blotting with a paper tissue). This procedure was continued until no further changes in weight were observed; it took about 180 days to complete.
Gravimetric sorption measurements were carried out with the so-called pat-and-weight technique with 0.10–0.25-mm-thick samples previously dried overnight at 100 °C in vacuo for the complete removal of absorbed water. This was confirmed by FT-NIR spectroscopy. The dried specimen was immersed in a deionized water bath thermostatically controlled at 22 ± 0.1 °C. Periodically, the sample was removed, blotted, and reweighed until it reached a constant weight.
RESULTS AND DISCUSSION
Molecular Interactions of Water with Epoxide Networks
Before discussing the spectroscopic characterization of the molecular interactions, we should consider the principal features of the FT-NIR spectra of both investigated networks. In Figure 1 are reported the transmission FT-NIR spectra of the uncured TGDDM/DDS mixture (trace A) and the same mixture after curing and postcuring (trace B). Trace C represents the spectrum of the latter sample after absorption of the equilibrium amount of water. The residual content of epoxy groups (absorption band at 4525 cm−1) for the postcured samples is negligible. The vanishing of the primary amine doublet located at 5070 and 5008 cm−1 and of the peak at 6676 cm−1 is also worth noting. The doublet originates from ν + δ and ν + δ combinations, and the peak comes from a ν overtone. A residual absorption characteristic of secondary amine (νNH overtone) is detected at 6680 cm−1, indicating incomplete conversion of the secondary amines.18 A comparison of spectra B and C in Figure 2 reveals a characteristic peak for absorbed water at 5215 cm−1, which is assigned to a combination of asymmetric stretching (νas) and in-plane deformation (δ) of water that occurs at 3755 and 1595 cm−1 in the vapor-phase spectrum.10
The 5215-cm−1 peak is reasonably well resolved, that is, free from interference by the polymeric substrate and sufficiently intense for quantitative determination of the water content in the sample.10, 17 It is known that another multicomponent band for water occurs around 6900 cm−1 resulting from the combination of νas and νs fundamentals. This profile is superimposed onto a much stronger absorption due to of the first OH overtone of the hydroxyl groups within the TGDDM/DDS network, producing only a slight increase in the intensity and breath of the band in the 7200–6200-cm−1 range.
In Figure 2 are reported the spectra of the N3 system (data in Table 1) before curing (trace A), after curing (trace B), and after equilibration in water (trace C). Although the main features of these spectra are identical to those of the binary TGDDM/DDS system, the water sorbed in the TGDDM/DDS/BMI ternary network produces a main absorption at 5231 cm−1, that is, slightly above the peak maximum observed for the binary epoxide network.
Stretching and bending vibrations are very sensitive to the occurrence of hydrogen-bonding interactions. For a typical proton donor such as the hydroxyl group, hydrogen bonding reduces the force constant of the OH bond, thereby producing a decrease in its stretching frequencies to a degree that is directly related to the strength of the interaction. However, hydrogen-bonding interactions, having a highly directional character, act as constraints on both in-plane and out-of-plane deformation vibrations and, therefore, will produce frequency shifts in the opposite direction (i.e., toward higher frequencies) for these modes.16, 19
For a first overtone or a combination of two stretching fundamentals, the frequency shift caused by hydrogen bonding is either twice or the sum of the shifts occurring for the fundamental vibrations. This effect greatly helps in improving the resolution and separation of those individual components that remain unresolved in the MIR spectrum. Conversely, for a combination of stretching and bending fundamentals, the resulting shift is equal to the difference between the shifts produced on the aforementioned vibrations. Therefore, the resolution in the NIR interval will be worse than that in the MIR frequency range. Because the effect on stretching vibrations is stronger than that on bending modes, the shift of the combination takes place in the direction of lower frequencies.
A further important advantage of NIR spectroscopy over MIR for studies of extensively hydrogen-bonded systems arises from the fact that, in the overtone and in the combination region, the absorptivities are very similar in magnitude. In the fundamental region, however, the absorptivities of bonded species are generally much larger than those of nonbonded species. Against these advantages is the higher uncertainty of the NIR assignments.
In Figure 3 are shown the ν + δ combination peaks for water absorbed in the three different networks of this study. Spectrum A refers to the binary TGDDM/DDS network with an equilibrium water content of 6.2 wt %, spectrum B refers to the TGDDM/DDS/BMI network (N3, 1/0.5/1.2 molar ratio) with an equilibrium water content of 4.6 wt %, and spectrum C is for a BMI homonetwork containing equilibrium water equal to 2.5 wt %.
A BMI homonetwork is to be considered essentially hydrophobic in character because of the negligible tendency of the imide carbonyls to act as proton acceptors.20 The spectra in Figure 3 reveal a shift in the peak frequency toward lower wave numbers, that is, 5244 and 5231 cm−1 for the BMI homonetwork and the TGDDM/DDS/BMI ternary system, respectively, and 5215 cm−1 for the binary TGDDM/DDS system. Furthermore, the absorption band for the networks containing TGDDM and DDS components develops a well-defined shoulder in the low wave-number side of the peak, which is more pronounced in the spectrum of the binary TGDDM/DDS network than in that of the corresponding TGDDM/DDS/BMI system. These spectral features can be readily explained. The multicomponent profiles observed in spectra A and B, for instance, are merely indicative of the presence of different water species in the respective networks. In particular, the shoulder at the lower frequency is due to water molecules involved in quite strong hydrogen-bonding interactions, whereas the main peak can be attributed to noninteracting water molecules. This assignment is confirmed by the spectrum of water in the BMI homonetwork, where no hydrogen bonding with the polymeric substrate is expected to occur. For this system, a relatively sharp, symmetrical, and fully resolved peak is found at 5244 cm−1; the low-intensity satellite band occurring around 5120 cm−1 can be explained by the spectral features observed in the νOH wave-number range.
The downward shift of the main component from spectrum A to spectrum C is also related to the increasing intensity of the unresolved shoulder, which causes the broadening of the whole profile and the displacement of the position of the maximum.
From an inspection of the spectra in Figure 3, it is clear that, for the TGDDM-based networks, the amount of interacting water decreases considerably when BMI is introduced to the system (compare spectra A and B). Although the 5500–4800-cm−1 region is useful for gathering qualitative information on the molecular level, it is less suitable for quantitative analysis because hydrogen bonding has an opposite effect on stretching and bending vibrations, which reduces the capability of resolving the various components of the complex profile. It is, therefore, worth analyzing in more detail the 7800–6000-cm−1 interval, which corresponds to the region in which the combination of the two stretching fundamentals (νas + νs) is expected to occur. In this wave-number range, the TGDDM-containing networks display an intense and complex νOH overtone band due to the hydroxyl groups of the epoxy resin, which obscure the water spectrum. In fact, the presence of water in the network causes a general increase in the total absorbance area, particularly around 6800 and 6400 cm−1 [compare the spectra in Fig. 4 (A,B) and Fig. 5 (A,B)].
To isolate the spectrum of sorbed water by eliminating the interference of the network, we performed a spectral subtraction analysis. The spectrum of the completely dry specimen was subtracted from that of the same specimen containing a given amount of sorbed water, with the complex multiplet in the 6100–5300-cm−1 interval as the reference band to be reduced to the baseline. The vibrational origin of these modes (nearly 100% CH stretching) makes the absorptions in this range insensitive to the presence of water. The results of the spectral subtraction analysis are reported in spectrum C of Figure 4 for the TGDDM/DDS network and in spectrum C of Figure 5 for the TGDDM/DDS/BMI system. The two difference spectra show that the νCH multiplet is completely eliminated and a three-component profile emerges, consisting of two sharper peaks centered at 7075 and 6820 cm−1 and a broader band at lower wave numbers (ca. 6535 cm−1). Although the peak positions remain approximately the same for the two difference spectra, the relative intensities of the three components change (discussed later).
The subtraction spectra characteristic of sorbed water are very reproducible. This is demonstrated in Figure 6, in which are reported the difference spectra for the TGDDM/DDS/BMI ternary networks containing various amounts of sorbed water. Therefore, the results of the spectral subtraction analysis indicate that the spectrum of the networks in the absence of water matches exactly the spectrum of the systems after water sorption, particularly in the OH stretching region, regardless of the amount of water present in the sample. This implies that the secondary network of hydrogen-bonding interactions formed among the hydroxyl groups of the epoxy network is not perturbed by the presence of absorbed water. A similar conclusion was reached by Jelinski et al.21 from quadrupole-echo NMR measurements.
The interpretation of the NIR spectrum for sorbed water is based on a simplified association model that identifies three distinct water species directly from spectroscopic measurements.10, 22–27
The peak at 7075 cm−1 is assigned to a combination of the νas and νs modes of non-hydrogen-bonded water (S0 molecules), whereas the peak at 6820 cm−1 is attributed to a combination of νnb and νb fundamentals in S1 molecules (self-associated dimers). The presence of a small fraction of individual water molecules forming a single hydrogen-bonding interaction with the network cannot be entirely ruled out. Finally, the broad component centered at 6535 cm−1 is attributed to a νas + νs combination of water molecules whose hydrogens are both involved in strong hydrogen-bonding interactions with proton-accepting groups located on the polymeric network (S2 molecules). The breath of this band (three times larger than the 7075 cm−1 peak and four times larger than the peak at 6820 cm−1) is related to the occurrence of different interactions (i.e., with different proton-accepting groups) that produce a comparatively large distribution of hydrogen-bonding strengths. The proton-accepting groups of the network that have been identified in previous work are the amino alcohol functionalities and the SO2 groups.10
For high-Tg materials, the plasticizing efficiency of the various water species depends ultimately on whether or not they are molecularly dispersed within the polymeric network and on their molecular mobility. S0 species, together with S1 dimers, are expected to have low plasticizing efficiency, as they are confined into excess free-volume elements (i.e., microvoids) and are much more mobile than the hydrogen-bonded species. The nonbonded species are desorbed well below the onset of long-range molecular motion: at temperatures around 180 °C, where the α relaxation of a wet TGDDM/DDS samples is observed, the only water molecules present are those hydrogen-bonded to the network14, 15 (S2 species), and these are the species that actually determine the depression of the network's Tg.
In Figure 7 (C) is reported the spectrum of the BMI homonetwork containing 2.5 wt % absorbed water. For this system, only two water peaks are observed, corresponding to the S0 and S1 species. These peaks are equivalent in shape and position to those assigned to the same water species in the TGDDM-based networks (compare the values of the spectral parameters reported in Table 2). The BMI homonetwork has no interfering absorptions in the 8000–5800-cm−1 range, so the spectrum of water can be directly observed without the need of spectral subtraction. The coincidence of the peaks characteristic of S0 and S1 water species in the BMI homonetwork with those in the TGDDM-based systems confirms the proposed assignments and the reliability of the spectral subtraction analysis. However, the complete absence of a third low-frequency band demonstrates that, for the BMI network, the sorbed molecules do not form any hydrogen-bonding interactions with the polymeric network because of the negligible propensity of the imide carbonyls to act as proton acceptors. The dimeric water species (S1) is likely responsible for the low-intensity satellite band observed at 5120 cm−1 (a (ν + δ combination).
Table 2. Results of the Curve-Fitting Analysis of the Spectra of Water in Different Environments in the Wave-Number Range 8000–4000 cm−1
A quantitative analysis of the spectra of water absorbed in the various investigated networks was performed with a curve-fitting algorithm described elsewhere.10 The results of this analysis are shown in Figure 7(A–C), and the parameters evaluated therefrom are summarized in Table 2.
Previous studies27 have demonstrated that the molar absorptivity values, ϵ, for S0, S1 and S2 species are very close to one another. In particular, it was found that
It is possible to estimate the relative concentration of each species according to the following relationship:10
Analogous relationships hold for the other two species.
With these equations, the relative amounts of nonbonded (Cnb = C + C) and bonded (Cb = C) water were estimated and are plotted as a function of the total water content in Figure 8. These data show that for the TGDDM/DDS system the amount of bonded water increases linearly with increasing total water content in the resin but remains lower than the amount of free water. The ratio Cnb/Cb goes from approximately 2.5 for a water content tending to zero to 1.5 at the maximum water content of 6.0 wt %. Conversely, for the TGDDM/DDS/BMI system, the Cnb/Cb ratio is essentially independent of the total water content, and its average value is equal to 2.5. The amount of water absorbed at equilibrium in microvoids (Cnb) can be taken as a qualitative measure of the amount of excess free volume in the networks. A comparison of the initial Cnb values (3.7 wt % for the control resin and 3.2 wt % for the BMI-containing network) indicates that the free volume is slightly larger in the TGDDM/DDS resin.
Further relevant information resulting from Figure 8 is the considerable reduction of bound water in the ternary TGDDM/DDS/BMI system in comparison with the binary TGDDM/DDS network over the whole range of water concentrations investigated. Therefore, the presence of BMI in the network reduces not only the overall amount of absorbed water but also the fraction of absorbed water molecularly bound to the network, which is responsible for plasticization of the resin and for other detrimental physical effects.
Gravimetric Measurements of Water Diffusion
In Figure 9 is reported the gain in weight due to water absorption as a function of time for the three systems investigated, that is, the binary composition (N1) and two ternary compositions (N2 and N3). These diagrams show that the binary (control) epoxide network absorbs the greatest amount of water (6.2 wt %), reaching equilibrium after approximately 66 h. The network N3 (1/0.5/1.2 TGDDM/DDS/BMI molar ratio) displays a sorption curve notably different from that of the control. That is, the incorporation of the BMI network within the TGDDM/DDS network reduces the level of water absorption to 4.6 wt % from the original 6.2 wt %, whereas the initial sorption rate increases from 9.8 × 10−3 to 2.8 × 10−2 wt % min−1. The ternary composition N2 (1/0.5/0.6 TGDDM/DDS/BMI molar ratio) displays an intermediate behavior.
The equilibrium water uptake and the Fickian diffusion coefficients at room temperature, calculated from the initial slopes of the gravimetric sorption curves, are reported in Table 3.
Table 3. Diffusion Coefficients from Gravimetric Sorption Measurements at Room Temperature
D × 109 (cm2 s−1)
W∞ (wt %)
Spectroscopic Determination of the Water Diffusion Parameters
To obtain more detailed information about the transport of water in the systems under investigation, we had to increase substantially the amount of collected data points. To this end, a technique was developed, based on time-resolved FTIR measurements in the NIR range, that permits the continuous monitoring of the diffusion process.17 The study was conducted at different temperatures on both the TGDDM/DDS network system and a BMI-containing network (N3 composition).
In Figure 10 are reported the calibration curves for the absorbance areas of the main water absorption band, normalized for the sample thickness (reduced absorbance), as a function of the water content in the sample for the binary epoxide network (curve A) and the ternary N3 system (curve B). These diagrams demonstrate that the absorption data follow the Beer–Lambert law for both systems and can be used, therefore, to measure directly the water content of the samples by spectroscopic means. The calibration curves are also insensitive to sample thickness over a wide thickness range, as demonstrated by the solid symbols that were obtained for specimens 2.70–2.80 mm thick, whereas the open symbols refer to samples 0.150–0.220 mm thick. The difference in the slopes of the two straight lines is a manifestation of the discrepancy in the molar absorptivity for water, which originates from the different molecular interactions established with the two networks.
According to Fick's second law of diffusion, the flux of a penetrant through a slab can be described in terms of its change in mass, M, with time, t, with the following expression:
where Mt is equal to (wt − wd)/wd, wt is the weight of the specimen at time t, wd is the weight of the dry specimen, D is a concentration-independent diffusion coefficient, L is the sample thickness, and n is an integer.
According to Shen and Springer,28 the diffusion equation (eq 3) can be approximated to
Expressions similar to eqs 3 and 4 can be used for desorption processes by the water content at time t being replaced with the amount of water desorbed at time t:
where wi is the initial weight of the specimen (water-saturated sample).
Furthermore, the ratio Mt/M∞ can be conveniently expressed in terms of absorbance (A) in accordance with the Beer–Lambert law:
For a purely Fickian process, the penetrant will desorb completely at t → ∞, so that w∞ = wd, M∞ = (wi − wd) wd, and A∞ = 0. Rearranging eq 6, one obtains
The desorption data are plotted in Figures 11 and 12. These reveal that for both binary and ternary networks, the absorbance reaches a residual limiting value that becomes smaller with increasing temperature.
This behavior can be modeled by a two-mode desorption process originally put forward by Jacob and Jones29, 30 and later modified by Maggana and Pissis31 to describe the diffusion of water in epoxy networks. These authors adopted the Shen and Springer equation originally used for the diffusion of vapors through glass-fiber composites, assuming that epoxy networks contain two phases, differing only with respect to their density and each having a different diffusivity.
The total flux of diffusant through the bulk, therefore, was assumed to be the sum of the fluxes through each of the two phases:
where the subscript 1 and 2 refer to phases 1 and 2 and M∞ is equal to M1 + M2.
The rational of this equation hinges on the premise that the concentration gradient along the direction of the flux is the same for both phases, which is valid if the two phases are cocontinuous. This assumption also justifies the use of the same thickness value for the two terms of the equation, which is equal to the sample thickness. Furthermore, it is to be expected that most of the water is likely to diffuse through the phase that forms only weak interactions with water. The other phase would have a much more hydrophilic character and will only allow a very slow diffusion of water. It is not necessary, however, to assume a two-phase morphology to explain that diffusion can take place by two simultaneous mechanisms, that is, a fast diffusion process associated with the free movement of water without interaction with the network and a much slower mode of diffusion taking place via associations at the hydrogen-bonding sites of the network. In any case, the size of the domains that provide the vehicle for the transportation of the water by the two mechanisms is only relevant if there is interference from interphases in relation to the premise of a constant concentration gradient in the flux direction.
From the previous discussion, it can be deduced that the diffusion equation can also be based on absorbance data if we assume complete desorption by the two modes for t → ∞ (i.e., A∞,1 = A∞,2 = 0) and consider that Ai = Ai,1 + Ai,2. On this basis, the absorbance equation can be rearranged and written as follows:
This equation provides the basis for a least-squares curve-fitting analysis of the spectroscopic desorption data to determine the values of the parameters D1, D2, Ai,1, and Ai,2. The results of such an analysis are summarized in Table 4 for experiments carried out at various temperatures on N1 and N3 network systems.
Table 4. Diffusion Parameters Evaluated According to Eq 9 for the N1 and N3 Networks from Spectroscopic Desorption Measurements at Various Temperatures
D1 (cm2 s−1)
Wi,1 (wt %)
D2 (cm2 s−1)
Wi,2 (wt %)
Wi (wt %)
1.5 × 10−9
2.6 × 10−11
2.1 × 10−9
7.0 × 10−12
3.4 × 10−9
7.4 × 10−9
4.1 × 10−9
6.0 × 10−9
1.0 × 10−8
1.1 × 10−8
In Figure 11, the experimental data collected in the range 22–60 °C for the binary TGDDM/DDS system are fitted to the two-mode diffusion model with eq 9. The excellent agreement with experimental data (R2 = 0.999) confirms the validity of the model. From these data, the calculated values for the respective diffusion coefficients at 22 °C are D1 = 1.5 × 10−9 cm2 s−1 and D2 = 2.6 × 10−11 cm2 s−1. The much lower D2 value refers to the diffusion of bound water. The values of D2 decrease more rapidly than D1 values with increasing temperature and become negligible above 36 °C. The D1/D2 ratios are 580 at 22 °C and 3000 at 36 °C, rising to infinity at 45 °C and higher temperatures.
The parameters Wi,1 and Wi,2 denote the initial amount of water involved in the two diffusion processes, that is, free and bound water. At 22 °C, the initial weight ratio of free and bound water is 1.67, and it increases to 9.82 at 35 °C, remaining approximately at this level at higher temperatures.
The observed effect is likely to result from the dissociation of bound water from the weaker hydrogen-bonding sites, becoming available for participation in the main diffusion process (mode 1). This deduction is supported by the results of the previously discussed spectroscopic analysis of molecular interactions. In fact, various types of hydrogen-bonding interactions were detected in the system, differing in the interaction strength. A residual amount of bound water, however, remains associated with the network even after the outer diffusion of the free water is complete. The diffusion of bound water becomes extremely slow at this point because of energetic constraints imposed on its dissociation from the network, so that a concentration gradient required for Fickian diffusion can no longer be set up.
The desorption curves obtained for the ternary TGDDM/DDS/BMI system are shown in Figure 12. These confirm the validity of the model, but the D2 values are extremely small even at room temperature: D2 ≈ 0 at all temperatures. At 22 °C, the ratio of free and bound water is 2.2, and it gradually increases to 28 at 60 °C. The D1 values for the ternary network system are approximately double the values for the corresponding binary TGDDM/DDS system at all temperatures.
It is worth noting the satisfactory agreement between the free/bound water ratio obtained from the two-phase model applied to the diffusion kinetics (1.7 for the binary N1 network and 2.2 for the ternary N3 network) and the same ratio evaluated from the spectroscopic analysis of the molecular interactions (1.5 for the N1 network and 2.5 for the N3 network).
With the Arrhenius equation, the activation energy for the diffusion coefficient (Ea) and the pre-exponential factor (D0) were calculated. For the binary TGDDM/DDS network, Ea = 8.2 kcal mol−1 and D0 = 1.62 × 10−3 cm2 s−1. These values are similar to those reported in the literature for gravimetric measurements carried out on analogous systems. Majerus et al.5 reported, for instance, an Ea value of 8.8 kcal mol−1 and a D0 value of 1.56 × 10−3 cm2 s−1. The presence of the BMI network in the N3 system lowered Ea by about 25% (6.1 kcal mol−1) and D0 by an order of magnitude (1.42 × 10−4 cm2 s−1).
The higher diffusivity values and the lower activation energy for diffusion observed for the N3 network in comparison with the binary system can be at least partially attributed to topological effects, that is, to the formation of a more defective and less dense network. Relevant in this respect is the greater propensity of the epoxide component to undergo etherification reactions in ternary systems,14, 15 which result in a reduction of the crosslink density and in the formation of a less homogeneous TGDDM–DDS network.
The effect of the BMI homonetwork on the diffusion behavior of the ternary system may also be related to molecular interactions. In fact, the polar groups forming hydrogen-bonding association with the diffusing water provide trapping sites that slow down its movements within the network. Therefore, a decrease in the concentration of these trapping sites will produce a corresponding acceleration of the diffusion process. Essentially, the same effect is found in anhydride-cured diglycidyl ether of bisphenol A resins, which exhibit diffusivities larger by nearly one order of magnitude than those of the corresponding resins cured with amine hardeners.32 This is because anhydride-cured resins contain ether and ester groups that are far less interactive toward water than the amino alcohol functionalities present in the amine cured resins.
Gravimetric sorption tests and FT-NIR spectroscopy measurements of desorption have demonstrated that the presence of a BMI network within an epoxide TGDDM/DDS network decreases the equilibrium water uptake, increases the water diffusivity, and lowers the activation energy for diffusion. A dual-mode model can be used to describe the diffusion behavior of water in the investigated networks. This can discriminate between two different populations of water molecules present in the systems, that is, those not involved in molecular interactions with the network (free water) and those molecularly bound to specific sites along the network (bound water). The results of the model simulations made it possible to obtain a quantitative estimation of the ratio between the two water populations.
From the FT-NIR spectra in the νOH region, it was possible to separately detect the presence of mobile water localized into excess free-volume elements (microvoids), that is, species that do not interact with the polymer network, and water molecules bound to specific sites through hydrogen-bonding interactions. Spectroscopic measurements also provided an accurate estimate of the relative fraction of bound water in the binary TGDDM/DDS and ternary TGDDM/DDS/BMI networks. The results obtained were in close agreement with those from the dual-mode diffusion model. The fraction of bound water was about 40% of the total (i.e., 2.5 wt %) in the binary TGDDM/DDS network and 30% of the total (i.e., 1.4 wt %) for the ternary TGDDM/DDS/BMI system. Therefore, the presence of the BMI homonetwork produces two beneficial effects: it reduces the equilibrium water uptake and considerably reduces the fraction of bound water that is responsible for plasticization of the system and subsequent degradation in structural properties.