Broadband dielectric relaxation spectroscopy in interpenetrating polymer networks of polyurethane-copolymer of butyl methacrylate and dimethacrylate triethylene glycol

Polymer Gels and Networks 6 (1998) 83—102

Broadband dielectric relaxation spectroscopy in interpenetrating polymer networks of polyurethane-copolymer of butyl methacrylate and dimethacrylate triethylene glycol A. Kanapitsas!, P. Pissis!, L. Karabanova", L. Sergeeva", L. Apekis! ! National Technical University of Athens, Department of Physics, Zografou Campus, 15780 Athens, Greece " Institute of Macromolecular Chemistry of National Academy of Sciences of Ukraine, Kharkov Road 48, Kiev 253660, Ukraine Received 1 October 1996; accepted 10 May 1997

Abstract The electrical and dielectric properties of interpenetrating polymer networks (IPNs) based on crosslinked polyurethane (PUR) and a copolymer of butyl methacrylate and dimethacrylate triethylene glycol were studied by means of broadband AC dielectric relaxation spectroscopy to obtain information on the morphology and phase separation in these IPNs. Three relaxation processes were observed: a secondary b relaxation due to the copolymer, the a relaxation due to the glass—rubber transition of the PUR phase and a conductivity current relaxation due to charge carriers trapped at the interfaces in the microheterogeneous samples. The a relaxation due to the glass—rubber transition of the copolymer is masked by conductivity effects and is revealed after a fitting treatment. The dipolar a and b mechanisms and the AC conductivity mechanism were studied in detail at several IPN compositions, by analysing the dielectric susceptibility data within the complex permittivity formalism, the modulus formalism and power law forms. For the copolymer network, the dielectric loss eA(u) shows a strong secondary b relaxation which becomes faster in the IPNs. The PUR network displays a relatively broad a-relaxation process which becomes slower in the IPNs. The energy and shape parameters of the response were determined for both mechanisms at several temperatures. From AC conductivity measurements we extracted information about the morphology and local structure of the IPNs. It is concluded that the IPNs studied are two-phase systems, but phase separation is incomplete in these materials. ( 1998 Elsevier Science Ltd. All rights reserved. 0966-7822/98/$—see front matter ( 1998 Elsevier Science Ltd. All rights reserved. PII S 0 9 6 6 - 7 8 2 2 ( 9 7 ) 0 0 0 1 8 - X

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1. Introduction Interpenetrating polymer networks (IPNs) have been investigated extensively, as evidenced by a number of reviews and monographs [1—5] At present there are two lines of research in these systems. In the first, emphasis is put on obtaining new types of IPN (three-component, ionomer-containing, gradient, reinforced, etc.) and studying their characteristics; in the second, the interest is focused on the processes of formation of these complex multicomponent systems. The formation of IPNs is determined by two factors: the kinetics of the chemical reaction of crosslinking of the two independent networks; and the conditions of phase separation that arise because of the immiscibility of the two constituent networks. It was shown [6] that the formation kinetics of IPNs and the ratio of curing rates of the constituent networks determine the rate and degree of microphase separation in incompatible systems. Many factors play an important role in determining the properties of IPNs: compatibility of the polymers, overall composition, method of synthesis, crosslink density in both polymers, crystallinity and glass transition temperatures. In the case of highly incompatible polymers, the thermodynamic forces leading to phase separation are so powerful that it occurs before the kinetic processes can prevent it. As a result, little phase mixing takes place. If polymers with better compatibility are used there is almost no phase separation, which is effectively controlled by permanent entanglement chains. For cases between these two extremes, an intermediate or complex phase behaviour results. Thus, IPNs with dispersed phase domains ranging from a few micrometres (incompatible) to a few tens of nanometres (intermediate) can be obtained. The dielectric study of such complex systems can reveal details of the phase structure and provide information about modes of motion in the IPN [7,8]. Dielectric measurements often reveal more details of the various relaxation processes than the relatively broader features observed in dynamic mechanical spectroscopy, volume dilatometry and differential scanning calorimetry [9,10]. This work deals with detailed investigations of molecular mobility in IPNs of polyurethane/copolymer of butyl methacrylate and dimethacrylate triethylene glycol by means of broadband AC dielectric relaxation spectroscopy. The wide ranges of frequency (10~2 to 2]109 Hz) and temperature (from !100°C to 90°C) of the measurements allow us to study the dynamics of the secondary (b) mechanism of the copolymer, of the main (a) mechanism of the polyurethane network and of the conductivity current relaxation reflecting the inhomogeneous nature of the system under investigation [11]. Systematic variation of the composition of the IPNs allows us to follow changes in the dynamics of the aforementioned processes and, thus, to draw conclusions on the morphology and the local structure of the resulting IPNs. 2. Experimental 2.1. Materials The interpenetrating polymer networks were prepared on the basis of crosslinked polyurethane (PUR) and a copolymer of butyl methacrylate and dimethacrylate

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triethylene glycol by the sequential method. For preparation of the polyurethane, a three-functional oligoglycol was first synthesized by the reaction of poly(oxypropylene) glycol of molecular mass 1052 and phenyl triethoxy silane. The polyurethane elastomer network was then formed from the three-functional oligoglycol and an adduct of trimethylol propane and toluylene diisocyanate (ratio 1:1.5 g equiv.) at a temperature of 80°C. The matrix network (polyurethane) was swelled to the equilibrium state in a monomeric mixture of butyl methacrylate and dimethacrylate triethylene glycol with benzoin isobutyl ether (3.5 wt %) as initiator. The second network was cured by photopolymerization. By this procedure IPNs with wide range of composition were obtained. 2.2. Dielectric relaxation measurements AC dielectric measurements were carried out by using three different experimental set-ups. In the frequency range from 5 to 2]109 Hz and the temperature range !100°C to 90°C, two Hewlett—Packard Network Analysers (HP 3755B and HP8510B) were used. The samples were placed in a shielded capacitor-like measurement cell, which was inserted into a transmission line, in a home-made thermostatic oven, and the transmission coefficient was measured. The dielectric parameters can be determined via these impedance measurements [12]. In the frequency range from 102 to 107 Hz and the temperature range 30°C to 120°C, a Hewlett—Packard HP 4192A Impedance Analyser was used combined with an Ando type TO-19 thermostatic oven and an Ando SE-70 dielectric cell. We performed complex admittance measurements with a two-terminal electrode configuration. For both set-ups the samples were clamped between nickel-coated stainless steel electrodes. A Schlumberger frequency response analyser (FRA 1260) supplemented by a buffer amplifier of variable gain were used for measurements in the 10~2—106 Hz frequency region, the samples being clamped between gold-coated electrodes. The samples were in form of discs 13 mm in diameter and 1.30 mm thick. We also used the Hewlett—Packard 4339 High Resistance Meter to measure the DC conductivity values of the samples at ¹"20°C.

3. Results and discussion The dielectric behaviour of a material is usually described in terms of the dielectric function, e* ("e@!ieA). In Figs. 1—3 we show on log—log plots the dielectric loss tangent, tan d ("eA/e@) against frequency, f, for the PUR network (Fig. 1), for the copolymer network (Fig. 2) and for the IPN sample with 80 wt % copolymer (Fig. 3) over a wide range of temperatures (0°C to 90°C) and frequencies (5 Hz to 2]109 Hz). Because of the wide range of frequencies and temperatures studied, the dielectric spectra of Figs. 1—3 include practically all the dielectric relaxations observed in the IPN materials. At low temperatures and high frequencies we observe a broad loss peak (Fig. 1), which shifts to higher frequencies with increasing temperature. The position and

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Fig. 1. Dielectric loss tangent, tan d, vs. frequency, f, for the pure polyurethane (PUR) network at several temperatures between !20 and #90°C in steps of 10°C.

Fig. 2. Loss tangent, tan d, vs. frequency, f, for the pure copolymer network measured at several temperatures given in the plots.

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Fig. 3. Frequency dependence of tan d for the 80 wt% copolymer IPN at several temperatures given in the plot.

magnitude of this peak allow us to relate it to the main glass—rubber transition (a relaxation) of the polyurethane network (glass transition temperature, ¹ "!38°C). ' This peak does not exist in the spectra of the pure copolymer network (Fig. 2). As the temperature increases a second relaxation mechanism appears in our frequency window, which shifts to higher frequencies with increasing temperature (Fig. 2). This peak does not exist in the spectra of the pure polyurethane network (Fig. 1). The transition corresponding to this peak is a secondary b-relaxation process and is due to rotation of the polar side groups in the copolymer main chain [8] which is in the glassy state (copolymer ¹ defined at ¹"70°C from thermomechanical ' analysis measurements) [13]. For the IPN samples (Fig. 3) we observe three dielectric relaxation processes. The loss peak observed at high frequencies and low temperatures (105 to 107 Hz and 0°C and 20°C in Fig. 3) is due to the a relaxation of the polyurethane phase in the IPN. At high temperatures (40, 60 and 90°C) we observe in the region from about 102 to 105 Hz a loss peak which correlates with the b-relaxation process in the copolymer phase of the IPN. The high values of dielectric losses and of e@ (not shown in the figure) at low frequencies and high temperatures indicate the existence of space charge polarization [14] due to the ‘free’ charge motion within the material [11]. 3.1. ¹he a relaxation of the polyurethane in the IPNs Fig. 4 shows the dielectric loss against frequency for the PUR network and for the IPNs with 20 wt % and 80 wt % of copolymer at ¹"!10°C. The a-relaxation peak

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Fig. 4. Dielectric losses vs. frequency for PUR and the IPNs with 20 wt% and 80 wt% copolymer at ¹"10°C.

due to the glass—rubber transition of the PUR phase is well distinguished in the high-frequency region of the spectra. We can also observe the b-relaxation process of the copolymer phase in the IPNs at low frequencies; at this temperature the PUR phase in the IPNs is in a rubber state (¹ "!38°C) while the copolymer phase is in ' a glassy state (¹ "70°C). With increasing copolymer content in the IPNs, the peak of ' the a relaxation of the PUR phase shifts to lower frequencies (Fig. 4), i.e. the a process becomes slower in the IPNs. Isochronal plots of dielectric loss against temperature are presented in Fig. 5 for a frequency of 107 Hz. The spectra are dominated by the strong a-relaxation process of the PUR phase. The position of the PUR glass transition peak shifts to higher temperatures as the copolymer content increases in the IPNs, in agreement with studies by calorimetry and thermomechanical analysis [13]. The magnitude of the peak reduces almost linearly with decreasing PUR phase in the IPNs, indicating that only the PUR phase is involved in this process. We can also observe a broadening in the shape of the a-relaxation peak with increasing copolymer content in the IPNs. Broadening of the peak of the glass transition and the shift of ¹ compared with the ' pure polymer network usually reflect the interpenetration between networks in IPNs [15]. They demonstrate the mutual influence of components in these systems. Thus, the broadening in shape of the a-relaxation peak in the IPNs under investigation is

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Fig. 5. Isochronal plots of tan d vs temperature at 107 Hz for PUR (L) and for the IPNs with 20 wt% (h), 50 wt% (£) and 80 wt% (e) copolymer.

a manifestation of the physical restriction imposed by the rigid polymer component (copolymer) on the molecular segmental mobility of the PUR local regions in the IPNs [16]. Fig. 6 shows Arrhenius plots for the temperature dependence of the peak frequency of the dielectric loss for the a- and b-relaxation mechanisms of the IPNs. We have used the Vogel—Tammann—Fulcher (VTF) Eq. [8] q"q exp[B/(¹!¹ )] (q"1/2nf) 0 0

(1)

to fit the experimental points in Fig. 6 for the a relaxation of the PUR phase (solid lines). In this equation, q is the characteristic relaxation time and q , B and 0 ¹ constants. We can observe the antiplasticizing action of the copolymer phase on 0 the a relaxation of PUR in the IPNs (shifting to higher temperatures at a fixed frequency and to lower frequencies at a fixed temperature), which is practically independent of the copolymer content in the range studied (20—80 wt % copolymer content). For the pure PUR network we obtain a limiting high-temperature value q "0.5]10~14 s, the activation parameter B"1338 K and the ideal glass transi0 tion temperature ¹ "!108°C (¹ +¹ !50).[8] For comparison, the corres0 0 ' ponding parameters for the 20 wt% and 80 wt% copolymer IPNs are listed in Table 1.

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Fig. 6. Arrhenius plot of peak frequency of tan d for the PUR network (r), the IPNs with 20 wt% copolymer (L), 50 wt% copolymer (h) and 80 wt% copolymer (£) and the pure copolymer network (e). The lines are fits of the VTF equation, Eq. (1), and the Arrhenius equation, Eq. (4), to the data for the a and b process, respectively.

Table 1 Best least-squares fitting parameters of the VTF equation, Eq. (1), for a relaxation of the PUR phase in the IPNs Sample

q (s) 0

B (K)

¹ (K) 0

PUR IPN with 20 wt % copolymer IPN with 80 wt % copolymer

0.5]10~14 0.9]10~12 0.6]10~12

1338 865 994

165 209 203

The apparent activation energy, E, calculated from the VTF equation [Eq. (1)] is [17]: E L ln q B¹2 " " (2) k L(1/¹) (¹!¹ )2 0 For the PUR network, calculated values of E decrease from 1.3 eV to 0.8 eV over the temperature range from !20°C to #20°C. For IPNs E was found to decrease from 2.5 eV to 0.9 eV for the 20 wt % copolymer IPN and from 2.2 eV to 0.9 eV for the 80 wt % copolymer IPN over the same temperature range. It follows that, as the

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a process becomes slower for the IPNs, we observe also that its activation energy, E, increases compared with the corresponding value for the pure PUR network. 3.2. ¹he secondary b-relaxation of the copolymer in the IPNs The contribution of the b relaxation of the copolymer regarding the dielectric loss of the IPNs can easily be defined (Fig. 3). In the pure copolymer network near and below ¹ , the b process dominates the experimental dielectric loss (tan d) spectra ' (Fig. 2). In Fig. 2 we have used three different experimental set-ups to follow the b relaxation of the copolymer, resulting in different frequency regions at different temperatures: the Frequency Response Analyser at 30°C, the Network Analysers at 40 and 50°C, and the Impedance Analyser from 60 to 120°C. The b relaxation in the pure copolymer is due to local motion of the polar ester side groups on the polymer main chain [8]. In the IPN this process arises from such motions within the copolymer-rich regions. For the well-defined b relaxation in the pure copolymer network and the IPNs, the experimental eA(u) data can be represented by a single Havriliak—Negami (HN) function [18] to extract the characteristic relaxation parameters: *e e*(u)!e " = [1#(iuq)1~a]b

(3)

In this equation e* is the complex dielectric function, e*"e@!ieA; u is the angular frequency; e "e@(u) for uA1/q; *e is the relaxation strength, *e"e@(0)!e@(R); q is = the relaxation time; and a and b are shape parameters describing the slope of the eA(u) curve below and above the frequency of the peak (04a(1, 0(b41). For the pure copolymer network a single HN function could be fitted to the experimental eA(u) with parameters: a"0.35—0.30 and b"0.45—0.40, over the temperature range between 80 and 100°C. The results of the fitting procedure applied in the whole frequency range of the spectra for the 50/50 IPN are shown in Fig. 7. We used a sum of Havriliak—Negami functions with the lowest possible number of terms plus a conductivity term, eA(u)"Au~s, to fit the low-frequency region [19]. The fitting procedure gives us two single HN peaks. The peak located at about 105 Hz is the well-defined secondary relaxation of the copolymer phase, while it is reasonable to assign the peak located at about 103 Hz to the primary relaxation due to the glass—rubber transition of the copolymer phase, which is masked by the contribution of conductivity to eA(u) values at low frequencies (¹ "70°C for the pure copolymer network [13]). The upward ' swing in the low-frequency region of the spectra with slope s"!1 results from the pure DC conductivity of the PUR phase, eA(u)"p/ue . From the fitting parameter 0 A of the conductivity term (Au~s) we calculate p"3.23]10~8 S m~1, which is in good agreement with the conductivity determined from AC measurements at low frequencies, p ( f"5 Hz)"3.27]10~8 S m~1. For the IPN with 50 wt% copolymer !# in Fig. 7 the HN parameters of the b relaxation of the copolymer phase have the values a"0.20 and b"0.45 at ¹"80°C.

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Fig. 7. Dielectric losses, eA( f ), for the 50 wt% copolymer IPN measured at ¹"80°C. The solid line is a fit of a sum of two single HN functions and a conductivity term (details in the text).

In Fig. 6 we can observe the Arrhenius behaviour of the temperature dependence of the frequency of the loss peak of the b relaxation. By fitting the Arrhenius equation f "f exp(!E /k¹) (4) . 0 !#5 (where f is the frequency of loss peak, f is the pre-exponential parameter, k is . 0 Boltzmann’s constant and E is the apparent activation energy) to the experimental !#5 points (solid straight lines in Fig. 6), E of the b mechanism in the IPNs was !#5 calculated. For the pure copolymer network E "1.07 eV. In the IPNs E is lower !#5 !#5 and probably decreases with decreasing polymer content if we ignore the data for the sample with 20 wt % copolymer, which are less accurate. E "0.86 eV for the !#5 80 wt % copolymer and E "0.79 eV for the 50 wt % copolymer. !#5 These results suggest that the copolymer-rich regions in the IPNs experience somewhat lower potential energy barriers than the pure copolymer network. The molecular motions involved in the b-relaxation loss peak are faster in the IPNs than in the pure copolymer network. The plasticizing action of the PUR phase on the b relaxation of the copolymer is clearly visible in Fig. 8, where the peak shifts to higher frequencies with increasing PUR content in the IPNs while its magnitude (the magnitude of the peak, not eA at maximum) decreases. The shift is already significant with 10 wt % PUR added to the copolymer, similar to what we observed for the a relaxation of the polyurethane. In addition, the shape of the response changes with composition. As we observe from the scaled plot in Fig. 9 the peak becomes broader in the IPNs, reflecting a broader distribution of relaxation times. In the IPNs each

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Fig. 8. Dielectric loss, eA, vs. frequency, f, measured on the 50 wt% and 90 wt% copolymer IPNs and on the pure copolymer network at ¹"80°C.

Fig. 9. Scaling plot of the secondary loss peak measured on the 80 wt% copolymer IPN (h) and on the pure copolymer network (L) at 80°C.

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dipole of the side ester group is surrounded by a different environment in comparison with the pure copolymer network [20]. This distribution of potential energy barriers to rotation is expected to yield a greater distribution of relaxation times, so that we have broader peaks as a result. Thus, in the systems investigated, two relaxation processes were observed for all the IPNs corresponding to the presence of two constituent networks, which is typical of a two-phase system [1]. However, in the IPNs the temperature (or frequency) of both the PUR a- and the copolymer b-relaxation processes in the spectra is shifted in relation to the position for the two pure networks. In addition, both peaks become broader in the IPNs. The shift and broadening are a result of incomplete phase separation in the IPNs accompanied by the formation of two phases with varying composition [5]. If the phase separation was complete, the relaxation processes in the IPNs would be described by the same values as those in the pure components. In the IPNs studied there are two phases, one of them enriched in PUR and the second enriched in copolymer. The investigation of conductivity effects in the IPNs will provide further support for this result. 3.3. Conductivity relaxation in the IPNs and the constituent networks At low frequencies and relatively high temperatures the values of e@ and eA become very high. The high values of dielectric losses at low frequencies do not correspond to the bulk dielectric function but are rather due to ‘free’ charge motion within the material. The build-up of charges at the boundaries of conductivity species in the material and at the ends of conductivity paths leads to so-called ‘conductivity relaxation’ and reflects, in fact, the distribution of the conductivity relaxation times [21,22]. In this case the effective dielectric function of the material is characterized by the topology of the conducting paths and the dipolar relaxation mechanisms of the material, if the latter are not masked by the contribution of the motion of ‘free’ charges. The data in Fig. 10 show a frequency-independent conductivity for low frequencies followed by an increase in conductivity for higher frequencies. The switch from the frequency-independent to the frequency-dependent region signals the onset of the conductivity relaxation phenomena. At constant temperature the frequency of this transition becomes lower with increasing copolymer content in the IPNs (Fig. 10). The PUR network is more conductive than the copolymer network. In order to relate conductivity to relaxation of the mobile charge carriers, one can rely on the phenomenological nature of the electric modulus [21,23]. By using the formalism of complex electric modulus, M* ("1/e*), the MA(u) spectra show peaks which are related to the ionic conductivity and their peak frequencies show the same temperature dependence as the DC conductivity [17]. The results of the analysis are analogous to those obtained by using the mechanical modulus in solids [24]. Fig. 11 shows the imaginary part, MA, of the electric modulus for the IPN with 80 wt % copolymer in the temperature range from 0 to 90°C. In the high-frequency region we observe two peaks, which correspond to the dipolar a and b relaxations of the IPNs already discussed above in detail. The spectra are dominated by an intense

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Fig. 10. Real part of the AC conductivity, p , vs. frequency, f, for the pure PUR and pure copolymer !# networks, and for the IPNs with 20, 50 and 80 wt% copolymer at ¹"90°C.

Fig. 11. Imaginary part of electric modulus, MA, vs. frequency, f, for the 80 wt% copolymer IPN measured at several temperatures between 0 and 90°C in steps of 10°C.

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Fig. 12. Conductivity relaxation peak for the PUR, the copolymer and IPNs with 20, 50 and 80 wt% copolymer at ¹"90°C.

peak at low frequencies. This peak, which is the region of the knee in Fig. 10, corresponds to the contribution of conductivity in eA(u). The shift of the frequency of maximum MA with temperature corresponds to the so-called ‘conductivity relaxation’ [21,22]. We note that the effects of space charge polarization are minimized in the electric modulus representation [21]. In Fig. 12 we show the MA(u) spectra for the pure PUR and copolymer networks as well as for IPNs at ¹"90°C. The frequency position of this peak is proportional to the DC conductivity of the sample, [25] so we can conclude that there is a decrease in conductivity of the IPNs with increasing copolymer content. This is in agreement with the results shown in Fig. 10 and with DC conductivity measurements at ¹"20°C shown in Fig. 13. The peak frequency of the MA(u) spectra of the IPNs is plotted against reciprocal temperature in Fig. 14(b). For the pure PUR network the solid line is the best least-squares fitting of the VTF equation to the data: f "A exp[!B/(¹!¹ )] .M‘‘ 0

(5)

where A, B and ¹ constants. The values of A, B and ¹ determined by the fitting 0 0 procedure are listed in Table 2. In terms of the strong—fragile classification scheme proposed by Angell and coworkers, [26,27] we used the modified VTF equation to fit our experimental data f "A@ exp[!D¹@ /(¹!¹@ )] 0 0 .M’’

(6)

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Fig. 13. DC conductivity of the IPNs at ¹"20°C (L) (obtained from direct resistance measurements) and ¹"90°C (v) (obtained from AC measurements) vs. copolymer content.

with A@, D and ¹@ being constants. In this equation D is the ‘strength’ parameter from 0 which we can define also the ‘fragility’ parameter, m [28] (m has previously been called the steepness index [29]): m"17#580/D

(7)

A@, ¹@ , D and m are listed in Table 2. The D (and m) values suggest that the pure PUR 0 network is a ‘fragile’ system (D(10). Fragile systems show the largest deviations from the Arrhenius law; for D'100 a graphical representation of the VTF equation is hard to distinguish from that of the Arrhenius law [30]. It is interesting to note that for the a relaxation of PUR we received D"4.83 and 4.98 by fitting the data of tan d and MA, respectively. Contrary to the VTF temperature dependence of the conductivity relaxation in the pure PUR network, in the IPNs the peak frequency of MA follows Arrhenius behaviour [Fig. 14(b)]. By fitting an Arrhenius equation similar to Eq. (4) to the experimental points [solid straight lines in Fig. 14(b)] we calculated the activation energy, E, of this mechanism in the IPNs. For the 20 wt % copolymer network we obtained E"0.71 eV, while for the 80 wt % copolymer we found E"0.61 eV. In order to study the distribution of conductivity relaxation times, the full-width at half-maximum, w, of the MA(u) peak (from Fig. 12) related to the conductivity mechanism, was calculated. The corresponding value of the stretched exponential parameter b in the Kohlrausch—Williams—Watts equation is approximately estimated by using the equation [31]: b"1.14/w

(8)

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Fig. 14. Arrhenius plots of DC conductivity (a) and peak frequency of the MA( f ) peak related to the conductivity relaxation (b) for PUR and IPNs indicated on the plots. The lines are best fittings of the VTF equation, Eq. (1), and the Arrhenius equation, Eq. (4), for PUR and the IPNs, respectively.

For ¹"90°C we found b"0.62 for the pure PUR network, for the 50 wt % copolymer IPN we found b"0.84 while b"0.85 for the 80 wt % copolymer IPN. The increase of b towards the value of unity for Debye behaviour means that the distribution of relaxation times becomes narrower in the IPNs [21]. We can also observe in Fig. 12 that the shape of the peak changes in the IPNs, becoming narrower (close to Debye) compared with that of the pure PUR network. This result can be understood as a limitation in the diversity of geometrical shapes of the conductivity paths. The peak shape of MA(u) (Fig. 12) for the pure PUR network is asymmetric, centred approximately in the dispersion region of M@. The region to the left of the peak is where the charge carriers are mobile over long distances and the region to the right is

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Table 2 Best least-squares fitting parameters for the conductivity relaxation for the pure PUR network VTF [Eq. (5)] f A .M

Fragility scheme [Eq. (6)] log A

B (K)

¹ (K) 0

log A@

D

¹@ (K) 0

m

7.55

982

148

7.55

6.6

148

106

VTF [Eq. (10)] p $#

Fragility scheme [Eq. (11)] log p

0

!2.45

B (K)

¹ (K) 0

log p@ 0

D

¹@ (K) 0

m

801

162.7

!2.45

4.9

162

137

where the charge carriers are confined spatially to their potential wells; in the peak region a transition from long-range to short-range mobility occurs [32]. The shape of the conductivity relaxation peak is best described by using the empirical Cole—Davidson (CD) expression to fit the experimental points [8]: MA(u)"*M@(cos u)b sin(bu)

(9)

where *M@"M !M , u"arctan(uq ), q is a characteristic relaxation time and = 0 0 0 b is a shape parameter. (For b"1 the CD equation reduces to the Debye form.) The CD expression gives an asymmetric peak describing better the distribution of short relaxation times. From the best fitting procedure we obtain b"0.40 for the pure PUR network, while b"0.67 for the 20 wt % copolymer IPN at ¹"90°C (i.e. more close to Debye behaviour as mentioned above). The DC conductivity, p values, evaluated from frequency-independent conductiv$# ity values of conductivity spectra (the plateau value in Fig. 10) or alternatively from complex impedance plots, [33] are also plotted against reciprocal temperature in Fig. 14(a) for the pure PUR network and the IPNs. We observe that the temperature behaviour of DC conductivity in Fig. 14(a) is seen to be very similar to that of the conductivity relaxation modulus peak frequency in Fig. 14(b). The VTF equation p "p exp[!B/(¹!¹ )] $# 0 0

(10)

with constants p , B and ¹ was used to fit the conductivity data of the pure PUR 0 0 network, suggesting that the charge carrier transport mechanism is governed by the cooperative motion of polymer chain segments. The results are listed in Table 2 together with those obtained with the fragility scheme [26,27]: p "p@ exp[!D¹@ /(¹!¹@ )] 0 0 0 $#

(11)

with constants p@ , D and ¹@ . Within the p formalism it follows again that the pure 0 $# 0 PUR network is a fragile system (D"4.9).

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By using the BENSH equation, [34] which is a generalized Vogel law applied to ionic conductivity, p "AA exp[!BA/(¹!¹ )3@2] (12) $# # with constants AA, BA and ¹ , we found log AA"!3.25, BA"12015.8 and # ¹ "121.4 K. In this equation BA is a constant proportional to the concentration of # mobile defects, which are proposed to be responsible for ionic conductivity, and ¹ is # the critical temperature for condensation of defects. The BENSH fit was equally as good as those of the VTF and modified VTF equations, Eqs. (10) and (11) respectively, suggesting that the defect model provides an alternative interpretation of the free volume picture [34,35]. For the IPNs the temperature dependence of the DC conductivity in Fig. 14(a) changes from VTF to Arrhenius type: p "p exp(!E/k¹) (13) $# 0 where E is the apparent activation energy and k is Boltzmann’s constant. The values of E, obtained by least-squares fitting of the Arrhenius equation to the data [straight lines in Fig. 14(a)], are 0.67 eV for the 20 wt % copolymer IPN and 0.57 eV for the 80 wt% copolymer IPN. These results are in a good agreement with those found within the modulus formalism. We note here the slight decrease of conductivity activation energy with increasing amount of copolymer phase in the IPNs. In Fig. 13 we show the DC conductivity values of the IPNs at ¹"20°C and ¹"90°C. The values at ¹"20°C were obtained by using an HP4339 High Resistance Meter, while those at ¹"90°C were obtained from the frequency-independent limits of the p values (Fig. 10). As we can see, the pure PUR network is more !# conductive than the copolymer network. In the IPNs the DC conductivity decreases compared with that of the PUR network. The conductivity values of the IPNs are almost independent of composition over a wide range of composition (Fig. 13). Obviously, the polyurethane network has phase continuity for a copolymer content less than about 80 wt % in the IPN system. This result is in agreement with data of stress—strain measurements for the same IPNs [36].

4. Conclusions The dielectric study of interpenetrating polymer networks (IPNs) based on crosslinked polyurethane (PUR) and a copolymer of butyl methacrylate and dimethacrylate triethylene glycol has shown that there are three distinct dielectric relaxation processes in this system. The a relaxation, associated with the glass—rubber transition of PUR in the IPNs, shifts to higher temperature at constant frequency (or to lower frequencies at constant temperature) with increasing copolymer content in the system. The results show a broadening in the shape of the a-relaxation peak in the IPNs compared with the pure PUR network.

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The a relaxation of the copolymer in the IPNs is masked by the contribution of the conductivity of the PUR phase at low frequencies. This relaxation is revealed by fitting a sum of Havriliak— Negami functions and a conductivity term to the experimental eA(u) data. The secondary b relaxation of the copolymer in the IPNs shifts to higher frequencies at constant temperature and the loss peak becomes broader with increasing PUR content in the IPNs. The molecular motions involved in the brelaxation loss peak are faster in the IPNs than in the pure copolymer network, while the a-relaxation process of PUR becomes slower in the IPNs compared with pure PUR. These results suggest that the IPNs studied are two-phase systems, but the phase separation is incomplete in these materials. The phase separation is accompanied by the formation of two phases with varying composition. Thus, in the IPNs investigated in this work, two phases are formed: one of them enriched by PUR and the second enriched by the copolymer. The phase composition of this multiphase system depends on the ratio of the constituent networks in the IPNs. The third relaxation process clearly observed in the IPNs is a conductivity current relaxation. The PUR phase is more conductive than the copolymer phase. In the IPNs the DC conductivity decreases compared with that of the PUR network. As a result of incomplete phase separation in the IPNs we have a narrower distribution of conductivity relaxation times, reflecting a limitation of the diversity of conductive paths, and a decrease in DC conductivity values. The dependence of DC conductivity on composition suggests that, for copolymer contents lower than about 80 wt %, the PUR phase is the continuous one in the IPNs. Within the fragility scheme, investigation of both the a relaxation due to the glass—rubber transition and the conductivity current relaxation classifies the PUR network as a fragile one.

Acknowledgements One of us (L. Karabanova) gratefully acknowledges financial support from the NATO Science Fellowship Programme at the National Technical University of Athens and thanks the research group for their hospitality during her stay. Financial support by INTAS (INTAS 93-3379) is gratefully acknowledged.

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