influence of the molecular structure on the dynamics in poly(ester-imide)s

Macromol. Chem. Phys. 198,2817-2824 (1997) 2817

Influence of the molecular structure on the dynamics in poly (ester-imide)s

Merenga Abdallah, Herbert Groothues, Friedrich Kremer*

Fakultat fiir Physik und Geowissenschaften, Universitat Leipzig, Linnestr. 5, D-04103 Leipzig, Germany

Hans R. Kricheldorf

Institut fur Technische und Makromolekulare Chemie, D-20146 Hamburg, Germany

(Received: January 29, 1997; revised manuscript of March 7, 1997)

SUMMARY Dielectric spectroscopy in the frequency range from 0.1 to lo5 Hz was employed to

study the molecular dynamics of main-chain poly(ester-imide)s (PEIMs) with varying spacer lengths from 5 to 12 methylene units. For all samples three relaxation processes were observed. The B-process shows an Arrhenius-like temperature dependence with activation energies between 50 and 55 kJ/mol. This process is assigned to a local libration of the ester groups. The a*-process shows a WFL-like temperature dependence. It is assigned to a main-chain-coupled motion of the mesogens around their short molecular axes. The a-process also follows a WFL-like temperature dependence. It is assigned to cooperative main-chain motion of PEIM and it is correlated to the glass transition.

Introduction

Poly(ester-imide)s (PEIMs) with even-numbered methylene spacers can form three different kinds of solid phases, including a smectic glass and a crystalline smectic state. The main difference of poly(ester-imide)s with odd-numbered spacers are the decreased phase transition temperatures between the LC phases and the isotropic phase (the glass transition temperature does not show such an odd-even effect)').

The primary relaxation process and the related glass transition phenomena are at present an interesting problem in condensed matter physics. The strong increase of the viscosity, 7, near the calorimetric glass transition temperature (T,) is the most important characteristic of this relaxation process*).

Secondary relaxation processes taking place within the glassy state strongly affect the macroscopic proper tie^^.^). These relaxations lead, for instance, to stepwise var- iations of elastic moduli, dielectric constants or thermal expansions. Of particular interest is the question, how the width, the strength and the frequency range of such processes can be related to the ductility of main chain polymers.

Since primary and secondary relaxations are known to originate from chain and local motion, respectively, the identification and characterization of the different motional processes that may occur in these thermotropic LC polymers is of major interest for the understanding of their dynamic behaviour.

In this paper the dynamics of six PEIMs with varying spacer length from 5 up to 12 methylene groups are investigated by dielectric spectroscopy in the frequency

0 1997, Hiithig & Wepf Verlag, Zug CCC 1022-1352/97/$10.00

2818 M. Abdallah, H. Groothues, F. Kremer, H. R. Kricheldorf

range from 10-I to lo5 Hz. Temperature variation from 140 to 430 K enabled the analysis of molecular and local dynamics in the isotropic, liquid crystalline and crystalline phases.

0 II

Experimental part

Materials

The synthesis of these polymers is described elsewhere]). Tab. 1 shows the measured compounds and their phase transition temperatures derived from differential scanning calorimetry (DSC) measurements') (heating rate: 20 "C/min). T,, and Tm2 represent melting temperatures of liquid crystalline modification I and 11, respectively. It should be noted that in this series of PEIMs the mesogenic group is asymmetric. The sequences of head-to-head and head-to-tail are randomly distributed along the polymer chain.

Tab. 1. Glass transition and melting temperatures of PEIMs as determined by DSC

n 5 6 7 8 9 10 12

Tg/ "C TmlI0C Tm21 "C

89 82 79 75 55 59 44 127 203 123 177 111 I23 122 175 223 164 I96 161 171 158

Measurement set-up

Dielectric measurements were performed in the frequency range between 0.1 and lo5 Hz, using a Stanford Lock-in amplifier (SR-830). The samples were melted between two gold plated brass electrodes which had a diameter of 20 mm and were seperated by 50 pm. The measurements were made in the temperature range from -130" to 150°C with a precision of kO.01 "C usin a temperature-controlled nitrogen gas jet (Novocon-

fitted with a generalized relaxation function according to Havriliak and Negami? trol) and a custom made cryostat 5 . For a quantitative analysis, the measured data were

A& & * ( W ) = E m +

(1 + ( iWzHN)a)Y In this equation, the parameters a and y describe the symmetric and asymmetric broadening of the relaxation time distribution function, respectively, and At is the relaxation strength ( E ~ - E-). On the low frequency side the experimental data are superimposed by a conductivity contribution due to small amounts of ionic impurities in the samples. Within a limited frequency range the influence of charge transport in amorphous materials on the imaginary part of the dielectric function can be described by Eq. (2)":

Influence of the molecular structure on the dynamics in poly(ester-imide)s 2819

(T ."(w) = - to id

where (T and s are fit parameters (0 I s I 1). In the case of s = 1, Q corresponds to the D.C. conductivity.

Results and discussion For all compounds in Tab. 1 the dielectric spectra are in principle similar. They

are composed of a conductivity contribution and three relaxation processes, labeled a, a*, and p. In Fig. 1 the real and imaginary part of the dielectric function for P E N (n = 5 ) is plotted versus frequency at three different temperatures. The dashed and dotted lines show the single contributions of the relaxations and the conductivity contribution. Each relaxation process will be discussed separately.

Fig. 1. (a) Real (E') and (b) imaginary (E") part of the complex dielectric function E* (w) versus frequency at 165 K, 387 K and 401 K of PEIM n = 5. The dotted lines represent the contributions of each relaxation process. The Havriliak-Negami fit parameters are: (P-process [ 165Kl): A t = 0.34; t = 6.1 x 10-3s ;~=0 .24 ;8= 0.74; (a*-process [387K]): A~=2.15; t = 1.5 x lo4 s; u = 0.81; /? = 0.2; (a-process [387K]): (T = 3.6 x lO-''s - m-'; s = 0.8; AE = 3.71; t = 8.7 x S; u = 0.57; /3 = 1

40 0 electrode polarisation

165K

a'-process

a-process I L

'"1 I 4

lo-' loo 10' lo2 lo3 lo4 lo5 f l Hz

a-Process

The analysis of the a-process is difficult due to the conductivity contribution. Considering the long relaxation times near Tg, the dielectric loss data is covered in this temperature region by the conductivity slope and the fitting procedure fails. At higher temperatures the a-process can be separated, but still the uncertainty in deter- mination of the mean relaxation time and dielectric strength is relatively high,


Fig. 2. Activation plot of the a- (filled symbols) and a*-process (open symbols) for all PElMs investigated. The dotted vertical lines indicate the glass temperatures derived from DSC measurements

because of a strong broadening of the dielectric loss peak. In Fig. 2 the temperature dependence of the mean relaxation time is shown in an activation plot. It can be described by the Williams-Landel-Ferry-(WLF-) equation (3)”:

t(Tg) is the mean relaxation time at the dynamic glass temperature having a value of 100 s. The WLF-parameters C,, C2 and the dynamic glass temperature Tg were obtained by fitting the experimental data (solid lines in Fig. 2 and Tab. 2). Alterna- tively the Vogel-Fulcher-Tamann-equation (4) can be used for describing the temperature dependence of the a-process. The corresponding fitting parameters are included in Tab. 2.

Within the experimental error the dynamic glass temperature and the calorimetric glass temperature from DSC measurements are in agreement. Hence this process corresponds to the dynamic glass transition and is assigned to a fluctuation of the repeating units of the polymer chain.


Tab. 2. WLF- and VlT-fitting parameters for the a- and the a*-process

Sample WLF-constants VFT-constants Cl c2 T, A B TO

n = 5 n = 7 n = 8 n = 9

n = 5 n = 7 n = 8 n = 9 n = 10 n = 12

19.0 85.1 14.2 54.3 25.0 129.0 18.0 70.2

17.2 35.1 12.4 11.5 15.8 26.5 9.8 5.3

10.0 20.3 24.6 48.1

386.3 368.8 360.9 356.2

389.5 356.4 340.4 341.5 323.8 323.4

a-relaxation 10.2 8.1

11.6 9.8

9.5 7.4 8.8 6.3 6.7

12.7

a*-relaxation

1613.4 770.0

2 505 .O 1263.2

603.4 142.3 418.4 52.8

217.4 1185.1

301.1 314.5 248.0 286.5

334.4 344.9 313.8 336.0 303.3 274.9

a*-Process

The a*-process is faster compared to the a-process and consequently better separated from the conductivity contribution. This process has also a broad relaxation time distribution and the mean relaxation time does not show an Arrhenius-like temperature dependence, too (Fig. 2). Comparison of all compounds shows a systematic variation of the relaxation time with the number of methylene units. With increasing number of methylene units the a*-process becomes faster (only the PEIM with n = 6 deviates from this regularity; for this compound the a*-process is much faster than expected). The molecular origin of the a*-process must be a librational motion of the rigid aromatic imide unit about its short axis. With increasing number of methylene units the decoupling of the rigid imide groups becomes more effective and hence relaxation time decreases. Approaching the calorimetric glass transition temperature, the chain motion slows down rapidly. The motion of the rigid imide unit is coupled to the polymer chain motion because it is connected to the main chain via head and tail. Consequently the slowing down of the chain motion near the glass transition temperature must lead to a slowing down of the imide unit motion around its short molecular axis, too. Below the glass temperature the a*-process has van- ished. The anomal dynamic behaviour of the polymer with n = 6 is not thoroughly understood. It is probably caused by the phase structure, which depends strongly on the thermal history of the sample'). Only for n = 6 the polymer does not show a lamellar phase when annealed at 160°C'). Unfortunately, wide angle X-ray scatter- ing and dielectric measurements can not be done in parallel, so this hypothesis can- not be verified.

/I-Process

The P-process is weak in its dielectric strength (0.3 < A& < 0.4) compared to the a- and a*-process and shows an Arrhenius-like temperature dependence. Fig. 3 dis-

2822

0,032 -

0,030 -

0,028 -

0,026 - -W

0,024 -

M. Abdallah, H. Groothues, F. Krerner, H. R. Kricheldorf

0,022

0,020

lo-' loo 10' lo2 103 lo4 lo5 f / Hz

Fig. 3 . The solid lines are Havriliak-Negami fits

Frequency and temperature dependence of the dielectric loss for PEIM (n = 5).

plays the dielectric function at different temperatures for the polymer with n = 5 . The process is strongly broadened corresponding to a wide relaxation time distribution. Fig. 4 is an activation plot for all PEIMs investigated. The activation energies range from 50 W/mol to 55 W/mol (Tab. 3). These values are in the range of what is expected for the local motion of the ester groups9-"). Relaxation time and dielectric

n=5 0 n=6 A n=7 v n=8 0 n=9 + n=10 % n=12

t s + +

B O

8 " 0

0 0

i ' l ' l ' l ' l ' l ' l ' l ' l '

1 0 3 . ~ - ' K-' 5,4 5,6 5,8 6,O 6,2 6,4 6,6 6,8 7,O

Fig. 4. Activation plot of the P-process for all PEIMs investigated


Tab. 3. Activation energies and prefactors of the P-process for all PEIMs investigated

n 5 6 7 8 9 10 12

E,/(kJ/mol) 51.8 54.0 50.2 54.7 51.9 53.9 50.2 I~[T,-’/HZ-’I 33.6 35.0 36.4 36.4 34.8 37.1 34.1

strength are similar for the different chain length. There is an odd-even effect in the activation energy, but not very pronounced. The thermal history of the samples also effects the P-process. When the samples are quenched from the isotropic liquid into the glassy state rapidly, dielectric strength of the P-process is increased compared to slow cooling. These observations demonstrate the difficulties in the interpretation of the dielectric data. In the glassy state the sample consists of a mixture of amorphous and crystalline regions, the ratio is determined by the thermal history and the molecular structure. It is suggested that the P-process exists only in the amorphous domains and is suppressed in the crystalline regions. Fast cooling increases the frac- tion of amorphous regions and thus the dielectric strength of the P-process.

Conclusion

For all PEIMs under investigation three relaxation processes were detected. The low freguency relaxation (a-process) is correlated to the glass transition temperature and originates from a motion of the polymer chain. The second relaxation (a*-process) only exists above Tg. The number of methylene units clearly influences the mean relaxation time of this process. Increasing spacer length lead to a systematic decrease in the relaxation times. This process also slows down near Tg The molecular assignment is a libration of the rigid aromatic imide units around the short axis, coupled via head and tail to the polymer chain. The irregular behaviour of PEIM (a = 6 ) probably originates from an anomalous phase structure. The high frequency relaxation (P-process) has an Arrhenius-like temperature dependence with activation energies ranging from 50 kJ/mol to 55 kJ/mol. When the amorphous portion in the sample is increased (by quenching), the relaxation time decreases and furthermore the relaxation strength increases. This process is assigned to a localised libration of the carbonyl units in the amorphous regions.

H. R. Kricheldorf, G. Schwarz, J. Abajo, J. G. Campa, Polymer 32,942 (1991)

N. G. McCrum, B. E. Read, G. Williams, “Anelastic and Dielectric Effects in Poly- meric Solids”, J. Wiley, New York 1967

2, K. L. Ngai, G. B. Wright,J. Non-Cryst. Solids, 131 (1991)

4, J. D. Ferry, “Kscoelastic Properties of Polymers”, J. Wiley, New York 1980 5, F. Kremer, D. Boese, G. Meier, E. W. Fischer, Prog. Colloid Polym. Sci. 80, 129

6, S. Havriliak, S. Negami, Polymer 8,161 (1967) ’) N. F. Mott, E. A. Davis, “Electronic Processes in Non Crystalline Materials”, 2nd

(1989)

edition, Clarendon Press, Oxford 1979


*) M. L. Williams, R. F. Landel, J. D. Ferry, J. Am. Chem. SOC. 77,3701 (1955) 9, J. C. Coburn, R. H. Boyd, Macromolecules 19,2238 (1986)

lo) T. A. Ezquerra, F. J. Balta-Calleja, H. G. Zachmann, Acta Polym. 44, 18 (1993) ‘ I ) P. Hedwig, “Dielectric Spectroscopy of Polymers”, Adam Hilger Ltd., Bristol 1977

influence of the molecular structure on the dynamics in poly(ester-imide)s

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