Application of NMR in the Tire Industry

Transcription

1 PRÜFEN UND MESSEN TESTING AND MEASURING Molecular mobility DMTA NMR-relaxation WLF-equation Mastercurve A series of unfilled elastomers, consisting of different polymers and crosslink densities is investigated by dynamic mechanical thermal analysis (DMTA) and NMR relaxation. A broad range of 8 decades of molecular mobilities is covered with polymers differing in their side groups and the measurement temperatures. With the help of the WLF-equation the molecular jump frequency is derived by dynamic mechanical analysis, which correlates with the NMR quantity T 2. An empirical power law describes the data quite well on a log-log plot. Anwendung von NMR in der Reifenindustrie Molekulare Beweglichkeit DMTA NMR-Relaxation WLF-Gleichung Masterkurve Eine Reihe ungefüllter Elastomere, bestehend aus unterschiedlichen Polymeren und Vernetzungsdichten wurde mit dynamisch mechanisch thermischer Analyse (DMTA) und NMR-Relaxation untersucht. Ein großer Bereich von 8 Dekaden molekularer Beweglichkeit wird durch Polymere mit unterschiedlichen Seitengruppen und dem Einsatz unterschiedlicher Temperaturen während des Experiments abgedeckt. Mittels der WLF-Gleichung wird die molekulare Sprungfrequenz von der dynamisch mechanischen Analyse abgeleitet, welche mit der NMR- Größe T 2 korreliert. Ein empirisches Potenzgesetz beschreibt die Daten hinreichend genau bei doppelt logarithmischer Darstellung. Application of NMR in the Tire Industry In recent years, diverse NMR-techniques proved to be a useful tool for soft matter analysis and for the investigation of polymers in particular [1]. For tire materials NMR-Imaging and NMR-relaxation techniques are of great interest. A mobile equipment for the measurement of NMR-relaxation is the NMR-MOUSE [2]. Therefore measurements on the tire are possible without cutting the tire. An established and common method to obtain information about the dynamic behavior and damping properties of tire materials is the dynamic mechanical thermal analysis (DMTA) [3]. Normally strip samples are investigated, which means the tire has to be destroyed for analysis. A mobile indentation tester was developed [4], to obtain dynamic mechanical data of the surface of the tire in a non-destructive way. Therefore, since NMR-relaxation data and dynamic mechanical data can be obtained non-destructively from the very same spot of a tire surface, the general question about the correlation of both arises. Interpretation of the molecular mobility [5] The molecular mobility is interpreted in terms of the free volume theory according to Doolittle [6]. Due to the thermal energy of the polymer chain, a segment of the chain jumps from one equilibrium position to another. The conditions for the realization of such a jump are: 1) enough free volume for the segment to fit in, 2) the segment has enough energy to break off from its surroundings and move into the free volume space, and 3) movement of the segment in the proper direction at just the right time [7]. The molecular motion results in a viscosity g for the system which can be described by eq. (1), often called the Doolittle equation : m * k 2 g ¼ k 1 e m f ; ð1þ where v f is the free volume of the polymer, v * the required free volume to perform a jump, and k 1 and k 2 are constants. Therefore Doolittle s equation describes the viscosity in terms of free and required volumes without regarding temperature. However, the temperature dependence of the viscosity is introduced by the dependence of the free volume v f on temperature T according to eq. (2): m f ¼ m g þ m m DaðT T g Þ; ð2þ where v g is the free volume at the glass transition temperature T g. v m is a fictitious volume of the molecule at absolute zero without free volume, and Da the difference of the thermal expansion coefficients in the glassy and the liquid phases, respectively. With the assumption that v m is independent of temperature, with k 2 ¼ 1 [8], and regarding equations 1 and 2 for two different temperatures eq. (3) is obtained following rearrangement of terms: C 1 zfflfflffl} fflfflffl{ log g g g ¼ ðm* =m g ÞðT Tg Þ : ð3þ ðm g =m m DaÞ þt T g fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} C 2 Using the results of many different authors, Williams, Landel and Ferry could empirically show [9] that C 1 17,44 and C 2 51,6 K, which nowadays are well recognized as the WLF-parameters. Therefore the WLF-parameters are not only empirical constants, but have a physical meaning as stated above. As mentioned by Ferry, these universal values should be considered as a first approximation, obtained as an average for a large number of different polymers [10]. Interpretation of the viscosity of the system in terms of molecular mobility leads to the formulation of a so V. Herrmann, K. Unseld, T. Böhner, Hanau B. Blümich, Aachen Corresponding author: Dr. V. Herrmann Dunlop GmbH u. Co. KG Dunlopstr Hanau Tel.: / Fax: / Volker.Herrmann@Dunlop.de 22 KGK Kautschuk Gummi Kunststoffe 57. Jahrgang, Nr. 1-2/2004

2 called molecular jump frequency f, which can be described by eq. (4) [11]: log f ¼ C 1 ðt T g Þ f g C 2 þ ðt T g Þ ; ð4þ where f g is the jump frequency in the glassy state. From dielectrical measurements a reasonable number of f g ¼ 0,1 Hz is obtained [7], which means in general a lower limit for f. That means in the sense of the present interpretation, a polymeric chain segment performs one jump every 10 seconds in the glassy state. An upper limit is set by the vibration frequency of molecules at f ¼ Hz [7, 8]. Frequencies at Hz e.g. are typical for molecular vibrations which can be detected by IRspectroscopy. Fig. 1. Microstructure of the polymers investigated and extrapolated glass transition temperatures at 0,1 Hz (crosslinking agents: 1 phr sulphur, 1 phr TBBS) Experimental Sample formulation and preparation The systems investigated consist of unfilled rubber types, which cover a broad range of molecular mobility, see Fig. 1. All polymers are free of oil, which can be regarded as a low molecular weight impurity leading to a further contribution in T 2. All samples are sulphur crosslinked and a crosslink series within every polymer was available for measurements. For the particular formulation of the samples see Table 1. All samples were mixed in a laboratory Brabender Banburymixer according to Table 1 and sheeted out through a mill afterwards. The samples were vulcanized in a laboratory press at 160 8C to maximum crosslink density according to a Monsanto MDR2000E vulcameter. NMR-relaxation measurements The NMR-relaxation measurements were carried out with an NMR-MOUSE and an mq20 minispec analyzer (Bruker Optic GmbH, Karlsruhe). Tab. 1. Compound formulation and mixing data Polymer 100 phr ZnO phr Stearic acid 2 phr Sulphur 1,2,3,4,5 phr TBBS 1,2,3,4,5 phr mixing process: 0 0 Polymer 8 0 Zinc oxide þ Stearic acid þ TBBS þ Sulphur 18 0 dump NMR-MOUSE j : All measurements were carried out at room temperature (23 28C). The samples were cylindrical in shape with a diameter of 20 mm and a thickness of 2 mm. To improve the signal-to-noise ratio, two samples, one on top of the other were investigated together. The 1 H spin-spin relaxation time T 2 was investigated by Hahn echo experiments [1]. Care was taken to avoid heating of the samples by the pulse sequence, therefore the measurement of one sample took 24 hours. Mq20 minispec: The investigations were performed under temperature control in the range of 60 8C þ 60 8C in steps of 20 8C. Strip samples were cut in portions of 400 mg and placed inside the homogeneous magnetic field. For the determination of the relaxation time T 2, CPMG-pulse sequence experiments [1] were applied, in order to shorten the influence of oxygen aging of the samples on T 2, due to higher temperatures [12]. In both cases the magnetization decay for every measurement was fitted by a single exponential curve. Dynamic mechanical thermal analysis (DMTA) The DMTA investigations were performed by a VES-F3-Iwamoto -viscoelastic spectrometer in tensile mode. The dimensions of the samples were ðl w tþ mm 3. The measurements were carried out under 10 % prestrain with a dynamical amplitude of 0,15 %. This condition was chosen with respect to the force limit and the force resolution of the spectrometer at low and high temperatures. With these parameters the maintenance of constant strain amplitude over the whole range of temperature was assured. The investigated temperature range started at least 20 8C below the respective glass transition temperature and went up to 100 8C for all samples. The measurements were performed at frequencies of 1, 10, and 50 Hz. Results NMR-MOUSE j : Fig. 2, top, shows the transverse relaxation times T 2 over the respective glass transition temperatures T g at 0,1 Hz. The T g values were extrapolated (maximum of the damping curve) from the 1, 10, 50 Hz measurements [8], due to the value for f g. It is a well known fact, that T 2 decreases, as T g increases for a constant temperature T [1, 13], irrespective of the microstructure of the polymers and crosslink density. This is a result of the lower molecular mobility due to a steric hindrance of the polymer segments. The background signal of the resin around the coil, used in the NMR-MOUSE j here, KGK Kautschuk Gummi Kunststoffe 57. Jahrgang, Nr. 1-2/

3 thermal temperatures (see legend). Again, T 2 decreases with higher glass transition temperatures for a constant temperature T. Another feature is, the higher the temperature T, the higher T 2 for a certain sample, respectively for a fixed T g. In a summary one can say, both lower glass transition temperatures T g and higher temperatures T lead to higher transverse relaxation times T 2. By referencing to difference of T T g, which, in practice means a shift of the isothermal curves along the T g axis one obtains the diagram in the top, right corner. According to the procedure above, the molecular jump frequency f can be calculated for every sample and every temperature T with the help of the WLF-equation to obtain a log-log plot. Again, an empirical power-law according to eq. (5) fits the data well with a regression coefficient of r ¼ 99 %. Table 2 shows the empirical parameters resulting from the fit procedure. poses a lower limit to the range of proper evaluation of T 2 at 0,039 ms. With the help of the WLF-equation (4) and the specific WLF-constants [5], the molecular jump frequency f can be calculated for T ¼ 238C. Here, the specific C 1 and C 2 values for every system were evaluated according to the 2nd method of Ferry, p.305 [10]. Figure 2, bottom, shows T 2 over f for T ¼ 238C in a double logarithm plot. The empirical equation logt 2 a þ b ðlogfþ c ð5þ Fig. 2. Measurements with DMTA and NMR-MOUSE: Top: T 2 at room temperature T ¼ 238C over the glass transition temperatures T g of all samples. Bottom: T 2 at room temperature over the molecular jump frequency f, calculated with the WLF-equation fits the data with a regression coefficient of r ¼ 93 %. For the resulting values of a; b and c see Table 2. Mq20 minispec: In the top left corner of Fig. 3, T 2 of all samples contained in Fig. 2, is displayed as a function of the glass transition temperature T g for different iso- Discussion Since the transverse relaxation time T 2 is a measure for the molecular mobility, it depends on the thermal energy and thus on temperature. The glass transition temperature T g of a polymeric sample represents a characteristic lower limit for molecular motion. Therefore it turns out, that the difference of T T g determines the absolute value of T 2. As a first approach this is valid for all investigated elastomers, irrespective of the chemical structure and the crosslink density. When plotted versus T T g, all isothermal curves coincide to a mastercurve. The fact that T 2 is independent of the absolute value of T g indicates, that T 2 may follow the WLF-equation. Williams, Landel and Ferry found the same shift factors to construct a mastercurve for polymers with different glass transition temperatures as well as for inorganic glasses with melting points of a few hundred degrees celcius. With the help of the WLF equation the T T g axis can be interpreted as a frequency axis, i.e. the molecular jump frequency axis. Therefore shifts of isothermal curves along a frequency axis are performed in Fig. 3, which is very similar to the original shift procedure of Williams, Landel and Ferry. In these terms the log-log-plot in Fig. 3, bottom represents a mastercurve for the transverse relaxation time T 2. The variable of this mastercurve is the molecular jump frequency f, which turns out to be a suitable entity for the correlation of dynamic mechanical data and NMR data. But we have to keep in mind, that f represents an average value of all possible molecular motions within the regarded volume and does not account for variations in the molecular net- Tab. 2: Parameters a; b and c according to the power law for the different types of NMRequipment and pulse sequences a b c NMR-MOUSE â, Hahn Echo 7,58 5,53 0,165 Mq20 minispec, CPMG 2,03 0,064 1, KGK Kautschuk Gummi Kunststoffe 57. Jahrgang, Nr. 1-2/2004

4 Fig. 3. Measurements with DMTA and mq20 minispec: Top, left: T 2 over the glass transition temperatures T g of all samples for different temperatures between 60 8C and þ 60 8C. Plotting the same data versus T T g leads to the top, right diagram. Bottom: T 2 over the molecular jump frequency I at different temperatures T, according to the WLF-equation on the NMR equipment used and the pulse sequence applied. The practical application which arises, is the following: by a combination of eq. (4) and eq. (5) one obtains the temperature dependence of T 2 : h 2,303 aþb C1 T 2 ¼ e ðt TgÞ C 2 þt T g 1 c i ð6þ In general, according to eq. (6) T 2 increases as the temperature T increases (since C 1 > 1 and c > 0). This was found in earlier investigations [14]. Furthermore, this increase should show an exponential behavior. This was verified for two samples in the range of 30 to þ 150 8C as depicted in Fig. 4. The points are the experimental values and the lines represent the fitted curves according to eq. (6). The regression coefficients in both cases were r ¼ 99 %, whereas the parameters a; b and c are given in Table 2 (Mq20 minispec), the T g s of the samples were determined by DMTA and the WLF-parameters C 1 and C 2 were the fitted variables. Therefore, with the knowledge of a; b and c, the specific WLF-constants of the sample can be determined, if T g is known at a frequency of 0,1 Hz. Furthermore, with a temperature controlled measurement of T 2, one can estimate the glass transition temperature of the sample by the help of eq. (6), when the universal WLF-constants (C 1 ¼ 17,44; C 2 ¼ 51,6 K) are used. work. Slower, respectively faster motions that occur, are not considered in f, but can be illustrated by a mechanical relaxation time spectrum. For polymers, such a spectrum covers a broad range of molecular mobilities over many decades [5]. Since the log-log-plots in Fig. 2 and Fig. 3 cover a few decades of molecular jump frequencies as well, this indicates that T 2 accounts well for the dominant time scale of motion within the sensitive volume of the sample. From the physical point of view, the nuclear dipolar coupling is the determining Fig. 4. T 2 as a function of temperature for two samples in the range of < 30 þ 150 8C. The points are the experimental values, the lines represent the fitted curves according to eq. (6) factor for the value of the transverse relaxation. Since the 1 H-protons are located on the segments of the polymer chains, the segmental motion influences the interaction of the protons. Therefore, the higher the molecular jump frequency, which is a measure of the molecular mobility, the better the averaging of the nuclear dipolar coupling. This leads to slow spin-spin relaxation and therefore to high values for T 2 as the log-log-plots show. The parameters of the power laws are of empirical nature and apparently depend Conclusion The transverse relaxation time T 2 measured by NMR (NMR-MOUSE j as well as Mq20 minispec) is sensitive to the microstructure of polymers and the crosslink density at isothermal conditions. Temperature controlled measurements in a homogeneous field show that T 2 increases with temperature, which arises from a better averaging of the nuclear dipolar coupling, due to higher molecular mobility at higher thermal energy. It could be shown, that the difference temperature T T g is the determining factor for T 2. Once referenced to T T g, T 2 is independent of the microstructure of the polymers and the crosslink density. The molecular jump frequency f, obtained by dynamic mechanical analysis, correlates with T 2 and this correlation can be described by a power law. This power law represents a mastercurve for the NMR quantity T 2. The parameters a; b and c of this power law depend on the NMR equipment used and the applied pulse sequence. By combining the power law with the WLF equation the temperatu- 26 KGK Kautschuk Gummi Kunststoffe 57. Jahrgang, Nr. 1-2/2004

5 re dependence of T 2 can be predicted and an exponential curve is obtained. This is especially of interest when the mobile NMR equipment (NMR-MOUSE) is used at different environments and temperatures. The molecular jump frequency f is a characteristic quantity of the molecular mobility, and it accounts likewise for the molecular restrictions of the elastomer (side groups, crosslink density) and the thermal energy. It has been shown in this work to be a suitable entity to correlate dynamic-mechanical data (DMTA) with NMR relaxation data. References [1] B. Blümich, NMR imaging of materials, Clarendon Press, Oxford (2000), 1. Aufl. [2] G. Eidmann, R. Savelsberg, P. Blümler and B. Blümich, J. Magn. Reson. A 122 (1996) 104. [3] DIN53513 (1983). [4] PAT (2000), Dunlop GmbH, Erf. K.-H. Jakob, K. Unseld, V. Herrmann, H.-B. Fuchs. [5] V. Herrmann, K. Unseld, H.-B. Fuchs and B. Blümich, Coll. Pol. Sci. 280 (2002) 758. [6] A.K. Doolittle, J. Appl. Phys. 22 (1951) [7] F. Bueche, Physical properties of polymers, Wiley, New York (1962), 1. Aufl. [8] U. Eisele, Introduction to polymer physics, Springer, Berlin, Heidelberg, New York (1990), 1. Aufl. [9] M.L. Williams, R.F. Landel and J.D. Ferry, J. Am. Chem. Soc. 77 (1955) [10] J.D. Ferry, Viscoelastic properties of polymers, Wiley, New York (1970), 2. Aufl. [11] A.V. Tobolsky, Properties and structure of polymers, Wiley, New York (1960), 1. Aufl. [12] C. Fülber, B. Blümich, K. Unseld and V. Herrmann, Kautsch. Gummi Kunstst. 48 (1995) 254. [13] G. Zimmer, A. Guthausen and B. Blümich, Solid State Nucl. Magn. Res. 12 (1998) 183. [14] P. Blümler and B. Blümich, Rubb. Chem. & Technol. 70 (1997) 468. The authors Dr. Volker Herrmann is Manager Advanced Analytical Methods, Dr. Klaus Unseld is Manager Physical Test Methods and Dipl.-Ing. Thomas Böhner works at the Chemical Technology of Goodyear Dunlop Tires Germany GmbH, Hanau, Germany. Prof. Dr. Bernhard Blümich is head of the Chemistry Department at RWTH Aachen and of AixNMR, Zentrum für Magnetische Resonanz, Rott, Germany. KGK Kautschuk Gummi Kunststoffe 57. Jahrgang, Nr. 1-2/