J. MATER. CHEM., 1991, 1(6), 919-922 Dielectric Relaxation in Hydroxypolyesters Enrique Sanchez Martinez,a Ricardo Diaz Calleja" and Klaus Wilhelm Lienertb a E.T.S.I.I. (U.P. V.), E-46071 Valencia, Spain BASF Lacke und Farben Ag, GroBmannstraBe 105, Postfach 280180, 0-2000Hamburg 28, Germany Dielectric spectra of a hydroxypolyester (I)and an imide-modified hydroxypolyester (11) are presented. In both cases two clearly defined zones of relaxation are shown. At the high-temperature side of the spectrum the a relaxation zone is produced by micro-Brownian motion of the main backbone and by free charges, and below room temperature, a complex fi secondary relaxation zone, showing indications of structure, is detected. Detailed analysis of the subglass relaxation zone is given and activation energies from an Arrhenius plot (In f vs. T-') are calculated for both polymers.By application to the low-frequency (high-temperature) side of the a relaxation of a transformation which converts permittivity E* into polarizability a* a new relaxation peak appears; this is attributed to the conductivity in the liquid state. Keywords: Hydroxypolyester; Dielectric relaxation; Polarizabilify Polymers have great importance in the electrical industry as by butyltitanate. The number-average molecular weight as insulators. From this point of view the analysis of the dielectric measured by GPC was 1758. relaxation ' behaviour gives crucial information for the devel- opment of these materials. In this paper we present a study Imide-modijied hydroxypolyester I1 of the dielectric relaxation in two polymers used as electrical In a standard three-neck flask, equipped with a stirrer, con- wire coatings.denser and a nitrogen inlet tube a mixture of ethylene glycol (4.6g), trihydroxyethyl isocyanurate (1 1.9 g), dimethyl tereph- Experimental thalate (1 0.2 g), 4,4'-diaminodiphenylmethane(6.9 g), trimel- litic anhydride (13.5 g) and butyl titanate (0.04 g) was heated The polymers are a hydroxypolyester (I) and an imide-to 200 "C. An imide-modified polyester with an OH number modified hydroxypolyester (11) and were synthesised as of 160-170 mg g-' KOH was obtained. The imide-modified follows. polyester dissolved in solvents such as N-methylpyrrolidone or cresol and dissolution was catalysed by butyl titanate.The H ydrox ypol yester I number-average molecular weight measured by GPC was In a standard three-neck flask, equipped with a stirrer, con- 1598. denser and a nitrogen inlet tube a mixture of ethylene glycol Molecular weight was measured using a gel-permeation (6.7 g), trihydroxyethyl isocyanurate (14.8 g), dimethyl tereph- chromatograph equipped with two PL-gel columns (25 cm thalate (25 g) and butyl titanate (0.04 g) was heated to 200 "C. long, particle size 5 pm, 1000 8, and 100 8, pore size), operated A polyester with an OH-number of 200-210 mg g-' KOH at 40 "C at a flow rate of 0.5 cm3 min-' N-methylpyrrolidone, was obtained. The polyester dissolved in solvents such as N-using polystyrene as standard. Tg for I and I1 were 71 and methylpyrrolidone or cresol, and dissolution was catalysed 132 "C, respectively. 0 I-0-CH2-CH2-N I ,c\ N-CH2-CH2-0-C '~~-O-CH2-CH2-OH 0 0o+c. CH2-CH2-O-~~~-O-CH2-CH2-OHY 'O 0 II 0 -CH2-N /c, N-CH2-CH2-O-!e!-O-CH2-CH2-OH I1A,.p=o 0 0 0 0 II Scheme 1 Dielectric measurements were carried out using a GENRAD 1620 bridge with a three-terminal cell from -130 "C to +130 "C or +180 "C in the frequency range 0.1-100 kHz.The samples were prepared by curing the products at 180 "C for 1 h in an oven. The films obtained were coated with silver to ensure good electrical contact. A three-terminal cell was used in a thermostatic vessel built by us. Experimental values were recorded from the bridge after 15 min, after which time thermal equilibrium had been reached.tan 6 reproducibility was > +2% and the permittivity values were reproducible to > &5%, taking into account the uncertainties in the micrometer measurements of the thickness and width of the sample. Results and Discussion The dielectric permittivity and loss of I and I1 are shown in Fig. 1 and 2. For the sake of clarity the permittivity is presented at only two frequencies and the high-temperature tail of the loss curve of I at 100 kHz is also omitted. The spectrum is complex in both cases. Two clearly distinguished zones of relaxation are seen in both polymers: at low tempera- tures a broad fl loss peak was observed which showed evidence of structure.This seems to be a complex relaxation process with several overlapping dielectric absorptions. A detailed description of the p zone for I as an example is shown in Fig. 3. In order to characterize the absorptions appearing in the p zone we have calculated the activation energy by means of an Arrhenius equation from a plot of lnf us. T-' (Fig. 4). The values obtained and the temperatures of the peaks at 1 kHz are given in Table 1 together with an estimate of the uncertainty in the activation energies. The higher temperature cr-relaxations in the two polymers are assigned to the cooperat- ive motions around Tg and because of this they possibly follow a Williams-Landel-Ferry (WLF) behaviour for the corresponding relaxation times. The loss curve for I shows two relaxation peaks at frequencies higher than 1 kHz at temperatures above 80 "C.The loss curves of I1 (10 kHz and 100 kHz) show a rapid increase above 140 "C indicating the high contribution of the conductivity to the loss curves. 21k -100 80 I60 -40 -20 cc) -10 p18 -6 -4 1' Fig. 1 Dielectric permittivity E' and loss E" of I: 0, 0.1 kHz; x, 1 kHz; 0,10 kHz; V, 100 kHz J. MATER. CHEM., 1991, VOL. 1 12 6-E' 4-2-1--120-80 40 0 40 80 120 160 TI'C Fig. 2 Dielectric permittivity and loss of 11: 0,0.1 kHz; x, 1 kHz; 0,10 kHz; V. 100 kHz 14. I 1 -140 -120-100 -80 -60 -40 -20 0 20 40 TI0C Fig. 3 tan 6 vs. temperature for I in the fl zone showing the complex structure of this absorption.0, 0.1 kHz; 0,1 kHz; 0,10 kHz; A, 100 kHz In order to characterize the a relaxation, we suppose that all the relaxation times around Tghave the same temperature dependence, and the same shift factor ~,=z~/z~,~,where T~ is,~ the relaxation time at To,given by the Voge12 equation mIn a,=A+-T-T, where a, is calculated from the horizontal shift of the exper- imental curves and m is related to the relative free volume 4 by B m= -4 (T-T,) (2) J. MATER. CHEM., 1991, VOL. 1 12-11 10-$‘9-* = 8-7 6-5-i“ I 41 2 3 4 5 6 7 lo3 KIT Fig. 4 Relaxation map for I (0)and I1 (0).a shows the relaxations associated to T,. p’, P” and 8”’ show successiverelaxations in decreasing order of temperature. (a) a (11), (b)a (I), (c) p’ (11), (6)p’ (I), (e)B” (I), (f)P”’(~),(dB”‘(~I) Table 1 Characteristics of the relaxations for I and I1 I I1 T/”C E,/kJ mol-’ T/”C E,/kJ mol-’ a 98 WLF 140 WLF B’ B” -24 -48 170f10 108& 10 -37 - 72f5 - p’” -128 26f2 -130 17+2 according to the Doolittle3 equation BIn q=A’+-4 (3) where B is assumed to be unity and q is the viscosity.On the other hand, the expansion coefficient of the free volume at T, is given by (4) where 4, is the free volume at the glass-transition temperature. Values for 4, and a, for both polymers are given in Table 2. The values for 4gare close to 2.5 x lop2,the predicted value by the theory. On the other hand a, values are slightly higher than the predicted ones.Returning to the a relaxation in 11, it is possible to obtain more information by using polarizability a* instead of permit-tivity &*. a* and &* are related by &*-1a*=---&*+2 (5) as proposed by S~aife.~This transformation has been exten-sively used ’q6 for charge-transfer complexes in order to show up relaxations hidden by the high conductivity on the low-frequency side of the loss permittivity, because they tend to highlight the low-frequency absorptions. In this sense it is valuable in helping to clarify the experimental results. The use of polarizability instead of permittivity has been Table 2 $K and aKvalues for I and I1 I 3.O 6.0 I1 3.7 7.4 921 where &,--I -4zN~ &,+2 3v and considering the response of a macroscopic sphere in terms of a time-dependent correlation of the dipole moment of the sample.The first term on the right-hand side of eqn. (6) represents the instantaneous polarization of the sphere, (p(O)M(O))is the equilibrium induced moment of the sphere, L is the Laplace transform, is the decay function and the left-hand side of eqn.(6) is the complex polarization of the sphere under consideration. The polarizability provides a macroscopic quantity, a*, by use of eqn. (5). Moreover, S~aife,~considering the relaxation behaviour in a spherical specimen, has pointed out that the effects observed in a non-periodic field are not present in a periodic one and for this reason the transformation E* into a* is fully justified.A polarizability representation of the macroscopic dielectric data give us the opportunity to com-pare different materials according to the fact that eqn.(5) is a method for ‘normalizing’ the data and a Cole-Cole plot of the two components of the polarizability (a” us. d)gives more weight to the low-frequency absorptions than those with shorter relaxation times. Accordingly, values of a’ and cl” for I1 have been calculated by means the of equations 3El‘(E’ -1)(d +2)+&”2. ,,, = &I‘ - (E’ +2)2+El’* ’ (&’ +2)2 +&“2 (7) the real and imaginary parts of a* are given by eqn. (5). The results are shown in Fig. 5 at three frequencies. Higher frequencies do not show significant peaks. Two peaks are clearly distinguished in a* at 0.1 kHz.The first corresponds 1.oc 100 120 140 160 180 T/”C Fig. 5 Dielectric and loss polarizabilities of I1 at three frequencies: 0,0.1 kHz; x, 0.2 kHz; 0,0.5 kHz to the inflexion in E" at 0.1 kHz, i.e. the a relaxation. A second peak ca. 10 times higher than the first can be seen at 163.5 "C; this corresponds to the high-conductivity (low-frequency) zone. The results are striking, but they are consistent with our previous experience of high-conductivity compo~nds.~,~ Thus the transformation given by eqn. (5) appears to be applicable also to polymeric systems for detecting relaxation peaks hidden by conductivity effects. R.D.C. and E.S.M. acknowledge Stiftung Volkswagenwerk for financial support. J. MATER. CHEM., 1991, VOL. 1 References N. G. McCrum, B. E. Read and G. Williams, Inelastic and Dielectric Eflects in Polymeric Solids,Wiley, Chichester, 1967. H. Vogel, 2.Phys., 1921, 22, 645. A. K. Doolittle and D. B. Doolittle, J. Appl. Phys., 1957, 28, 901. B. K. P. Scaife, Proc. Phys. Soc., 1963, 81, 124. E. Sanchez Martinez, R. Dim Calleja, W. Gunsser, P. Berger and G. Klar, Synth. Met., 1989, 30, 67. E. Sanchez Martinez, R. Diaz Calleja and G. Klar, Synth. Met., 1990,38, 93. R. H. Cole, J. Chem. Phys., 1965, 42, 637. Paper 1/00877C; Received 25th February, 1991