Plasticheskie Massy, No. 4, 2009, pp. 34 40 Influence of the thermodynamic state of bisphenol A and aliphatic epoxy oligomers on the temperature dependences of Newtonian viscosity E.F. Kolesnikova, 1 P.G. Babaevskii, 1 E.S. Zhavoronok, 2 and A.E. Chalykh 2 1 MATI K.E. Tsiolkovskii Russian State Technological University 2 A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences Selected from International Polymer Science and Technology, 37, No. 4, 2009, reference PM 09/04/34; transl. serial no. 16178 Translated by P. Curtis Abstract A generalised analysis is made of experimental and published data on the temperature dependences of the Newtonian viscosity of bisphenol A and aliphatic oligomers of different molecular weight in a wide temperature range, with account taken of the departure of the experimental temperature from the hypothetical (calculated) crystallisation temperature T cr. It is shown that the deviation of the temperature dependence of the Newtonian viscosity of epoxy oligomers from the theoretically expected dependence in accordance with activation theory and free volume theory is greater the lower the temperature range of the experiment by comparison with T cr, and accordingly the greater the probability of formation of solid-like molecular associates or clusters. The use of T cr as a parameter of the corresponding state (the temperature of reduction) makes it possible to plot a universal generalised curve of viscosity for epoxy oligomers with account taken of the dependence of their Newtonian viscosity on molecular weight. The viscosity of reactive oligomers, including bisphenol A and aliphatic epoxy oligomers, is directly related to their molecular and supermolecular structure and to the dynamics of molecular rearrangements [1, 2]. It is extremely sensitive to change in temperature and is a key factor as regards the processing properties of thermosetting composites both in the production process and at the initial stages of processing. Therefore, investigation of the temperature dependence of the viscosity of epoxy oligomers (primarily bisphenol A oligomers) at low shear rates excluding relaxation effects is of great scientific and practical importance, and it has been the subject of a considerable number of studies [3 8]. Analysis of the results obtained for epoxy oligomers is normally based on the same theoretical approaches as for melts of crystallising polymers or for non-crystallising polymers in the viscous flow state. These approaches include activation theory and free volume theory, which use the Arrhenius Frenkel Eyring (AFE) equation and the Williams Landel Ferry (WLF) or Vogel Fulcher (VF) equation respectively. In the WLF and VF equations the glass transition temperature T g or the associated temperature corresponding to the lower limit of the appearance of a large-scale form of thermal motion and viscous flow is normally adopted as the characteristic temperature serving as a parameter of the corresponding state (the temperature of reduction). In this case, no account is taken of the thermodynamic state of oligomers and polymers equilibrium or non-equilibrium, or metastable in relation to their phase states. In the case of non-crystallising oligomers, including many reactive oligomers, one of these states (crystalline) cannot be achieved on account of steric constraints, but the leaning towards it in the metastable state should greatly affect the supermolecular structure of the oligomers and accordingly their molecular dynamics and viscosity. The supermolecular structure of non-crystallising (amorphous) oligomers, like polymers, has historically 2010 Smithers Rapra Technology T/15
always been examined from two viewpoints. In accordance with the first of these [9], based mainly on statistical analysis, such a structure is considered to be statistically homogeneous with possible random (labile) fluctuations in density, the lifetime of which is determined by the correlation time of the main form of molecular thermal motion. According to the second viewpoint [10], based mainly on experimental data, this structure is microheterogeneous, with the presence of stable supermolecular aggregates domains, packs, associates, or solid-like clusters, the thermodynamic motive force of formation of which is not always clear. It seems that the decisive influence in this case is rendered by the state of the non-crystallising oligomer or polymer in relation to its hypothetical (calculated) crystallisation temperature T cr. When T > T cr, the amorphous (liquid or viscous flow) state is thermodynamically equilibrium, and the supermolecular structure in this state should most probably be statistically homogeneous with labile fluctuations in density. At T < T cr, the amorphous state is thermodynamically non-equilibrium supercooled and metastable in relation to the liquid and crystalline states respectively, and the supermolecular structure should most likely contain thermodynamically stable microheterogeneities. As, in the first case, the formation of fluctuations in density is random in nature, and their lifetime for oligomers of low molecular weight is very short on account of the considerable departure from the glass transition temperature T g, they should not markedly affect the viscosity at low shear rates, while the temperature dependence of viscosity can adequately be described by activation theory or free volume theory. In the second case, the formation of solid-like clusters is governed thermodynamically by the tendency to form crystalline phase nuclei, which can be fairly stable even at a size smaller than the critical on account of sharp increase in the correlation time of molecular motion to singularity during fairly strong supercooling. Therefore, in this case, molecular associates, or solid-like clusters, the number and size of which are determined by the departure from T cr (degree of supercooling), should have a considerable influence on the Newtonian viscosity, increasing its temperature dependence and resulting in deviation from the AFE and WLF equations. The VF equation takes into account the singularity of the correlation time of molecular motion during strong supercooling [11], and, evidently, can adequately describe the behaviour of non-crystallising oligomers and polymers in the metastable state. The aim of the present work is a generalised analysis of experimentally determined and published data on the temperature dependences of the Newtonian viscosity of bisphenol A and aliphatic epoxy oligomers of different molecular weight in a wide temperature range with allowance for the departure of the experimental temperature from the hypothetical (calculated) crystallisation temperature T cr, which determines the thermodyamically equilibrium or non-equilibrium (supercooled metastable) state of oligomers, and accordingly the probability of formation of solid-like molecular associates or clusters. EXPERIMENTAL The investigation was conducted on epoxy oligomers of two types: on bisphenol A diglycidyl ether (aromatic epoxy oligomer) EPIKOTE 828 and on oligooxypropylenetriol polyglycidyl ether (aliphatic epoxy oligomer) Laproxides 503M, 603, and 703 with different molecular weights. The molecular structure and characteristics of the investigated oligomers are given in Table 1. In parallel, published data for bisphenol A epoxy oligomers, the characteristics of which are also presented in Table 1, were analysed. The glass transition temperature T g of the epoxy oligomers was determined by differential scanning calorimetry on a TA Instruments DSC Q-100 instrument in a dynamic regime, with increase in temperature at a rate of 2.5 K/min. The instrument was calibrated with respect to indium (T m = 429 K), and the samples weighed ~2.0 8.0 mg. Data were processed using the TA Universal Analysis 2000 program (v.4.2). It had already been shown (Figure 1) that, for epoxy oligomer EPIKOTE 828, T g = 17.0 C and T cr = +35.2 C, so that the ratio T cr /T g = 1.20. This quantity was the basis for calculating the hypothetical crystallisation temperature T cr of other epoxy oligomers. The flow curves of the epoxy oligomers were obtained in the temperature range 293 333 K using a Rheotest-2 rotation viscometer with a temperature-controlled cone plane working unit at a shear rate D of up to 5000 s -1 and a shear stress t of up to 400 Pa. It had already been shown that the regime of change in the shear rate (gradual increase or reduction) had no influence on the result of measurement. In the entire investigated range of temperatures and shear rates and stresses, the flow curves were linear, i.e. Newtonian flow was observed. RESULTS AND DISCUSSION The experimentally obtained temperature dependences of the viscosity of the epoxy oligomers are presented in coordinates of the AFE equation (Figure 2) [12]: η = A exp E η RT where E h is the activation energy of viscous flow, and A is a constant. For comparison, published data for bisphenol A epoxy oligomers of different molecular weight [3, 6, 7] are also (1) T/16 International Polymer Science and Technology, Vol. 37, No. 8, 2010
Table 1. Chemical structure and characteristics of bisphenol A and aliphatic epoxy oligomers Epoxy oligomer Degree of polymerisation x or a + b + c M n T g, K T cr,* K EPIKOTE 828 [6] 0.1 366 257 311 EPIKOTE 828 0.1 375 255 309 EPIKOTE 828 [3] 0.1 376 258 312 EPIKOTE 834 [6] 0.5 479 273 330 EPIKOTE 1001 [3] 1.9 875 303 367 EPIKOTE 1001 [6] 2.0 898 303 367 EPIKOTE 1001F [7] 2.2 953 304 368 EPIKOTE 1002 [6] 2.8 1147 312 378 EPIKOTE 1002F [7] 3.0 1179 315 381 EPIKOTE 1004 [3] 4.1 1495 323 391 EPIKOTE 1004 [6] 4.2 1538 327 396 EPIKOTE 1004F [7] 5.2 1821 330 399 EPIKOTE 1007 [3] 7.1 2355 343 415 EPIKOTE 1009 [3] 9.4 3020 352 426 Laproxide 503M 4.5 480 198 240 Laproxide 603 7.0 645 200 242 Laproxide 703 8.7 730 202 244 * Values of T cr were calculated on the basis of experimental and published data on T g Calculated for the ideal general chemical formula of the epoxy oligomer Figure 1. Typical DSC thermogram for epoxy oligomer EPIKOTE 828 containing an amorphous and a crystalline phase (rate of increase in temperature = 2.5 K/min) Figure 2. Temperature dependences of the viscosity of epoxy oligomers in coordinates of the AFE equation. 1 EPIKOTE 828 [4]; 2 EPIKOTE 828 experiment; 3 EPIKOTE 828 [1]; 4 EPIKOTE 834 [4]; 5 EPIKOTE 1001 [4]; 6 EPIKOTE 1001 [1]; 7 EPIKOTE 1001F [5]; 8 EPIKOTE 1002 [4]; 9 EPIKOTE 1002F [5]; 10 EPIKOTE 1004 [4]; 11 EPIKOTE 1004 [1]; 12 EPIKOTE 1007 [1]; 13 EPIKOTE 1009 [1]; 14 Laproxide 503M; 15 Laproxide 603; 16 Laproxide 703 2010 Smithers Rapra Technology T/17
Table 2. Constants of the WLF and VF equations for bisphenol A epoxy oligomers, oligooxypropylenetriol glycidyl ethers, and some other oligomers and polymers High-molecular-weight Temperature WLF equation VF equation compound range, K T g, K C 1 C 2 T 0, K B, K A 10 3, Pa s Bisphenol A epoxy oligomers EPIKOTE 828 290 334 257 14.7 18.4 236 294 0.3 DGEBA [8] 175 ED-16 [8] 230 ED-8 [8] 250 EPIKOTE 828 [3] 270 357 258 231 339 1.2 EPIKOTE 1001 [3] 323 417 303 273 393 0.8 EPIKOTE 1004 [3] 345 455 323 282 467 2.2 EPIKOTE 1007 [3] 370 476 343 303 471 6.2 EPIKOTE 1009 [3] 385 476 352 310 539 18 EPIKOTE 828 [6] 278 357 257 11.27 25.8 EPIKOTE 834 [6] 294 400 273 12.23 36.0 EPIKOTE 1001 [6] 333 426 303 13.89 45.7 EPIKOTE 1002 [6] 345 444 312 15.36 42.2 EPIKOTE 1004 [6] 370 488 327 14.99 50.0 EPIKOTE 1001F [7] 335 378 304 14.10 49.2 EPIKOTE 1002F [7] 353 398 315 14.13 50.7 EPIKOTE 1004F [7] 330 14.94 43.2 Aliphatic epoxy oligomers Laproxide 703 290 334 198 15.7 22.8 179 356 0.23 Laproxide 603 290 334 200 16.0 24.3 177 384 0.12 Laproxide 503M 290 334 202 16.3 25.7 178 415 0.06 given in Figure 2. As expected, increase in the molecular weight of epoxy oligomers (both bisphenol A oligomers and Laproxides) leads to a regular increase in viscosity in the entire temperature range. Furthermore, for all the dependences presented there is pronounced non-linearity, which is more marked in the case of bisphenol A epoxy oligomers, the T cr of which is comparable with the experimental temperature, whereas the T cr of Laproxides is below it. The non-linearity of the dependences (Figure 2) means that E h changes with temperature. Calculations show that, in the investigated temperature range, the E h of Laproxides changes from 56 to 27 30 kj/mol, while the E h for E828 changes from ~125 to ~70 kj/mol. At the same time, judging by published data, with increase in the molecular weight and in the temperature range of the experiment, this change is more significant: thus, for EPIKOTE 1004 (M h = 1495), E h in the range 398 343 K is ~100 kj/mol and at 333 343 K ~400 kj/mol [3], and for bisphenol A epoxy oligomer DER-663U (M w = 1800 2000, T g = 360 380 K) it ranges from ~150 to ~10 kj/mol in the temperature range ~288 413 K [13]. On the other hand, the examined temperature dependences of viscosity of epoxy oligomers can be presented in the coordinates of the WLF equation [12]: lg η η = C (T T ) 1 g g C 2 + (T T g ) where h and h g are the viscosities at the experimental temperature T and at the glass transition temperature T g. The viscosity at the glass transition temperature was assumed to be h(t g ) ~ 10 12 Pa s [14]. The experimentally obtained temperature dependences of the viscosity of epoxy oligomers in coordinates of the WLF equation are practically linear (Figure 3), which makes it possible to calculate the constants C 1 and C 2 from them. The corresponding values, combined with published data for some other epoxy oligomers, are given in Table 2. It must be pointed out that the real values of C 1 and C 2 differ from the universal values: C 1 = 17.44, C 2 = 51.6 [12, 15]; however, with increase in the molecular weight of the oligomer, a leaning towards these values is evidently observed. Finally, in Figure 4 the temperature dependences of the viscosity of the investigated oligomers are approximated (2) T/18 International Polymer Science and Technology, Vol. 37, No. 8, 2010
by straight lines in coordinates of the VF equation [3, 12]: lg η = lg A + B T T 0 (3) where A and B are constants, and T 0 is the characteristic temperature: at T 0 = 0 the VF equation is transformed into the AFE equation, while at T 0 = T g it is transformed into the WLF equation. As indicated in reference [12], the temperatures T 0 and T g are connected by the relation T 0 = T g - C 2. The values of constants A and B, calculated from these straight lines, combined with published data, are also given in Table 2. It must be pointed out that the ratios B/T g and T 0 /T g, judging by published [3] and experimental data, are near-constant and amount to 1.3 1.5 and 0.9 for bisphenol A epoxy oligomers and to 1.8 1.9 and 0.9 for Laproxides. This means that the temperature dependences of viscosity in the coordinates lg h T/T g (or T g /T) should differ only in position relative to the vertical axis, and consequently can be reduced to a single generalised curve by vertical shift. One of the variants of such shift, with the aim of obtaining a generalised curve, is the use of the reduced viscosity, which is related to viscosity at the prescribed temperature by the equation [15]: Figure 3. Experimental temperature dependences of the viscosity of epoxy oligomers in coordinates of the WLF equation. 1 EPIKOTE 828; 2 Laproxide 503M; 3 Laproxide 603; 4 Laproxide 703 lg η* = lgη(t) A + B (4) where A and B are constants characteristic of each highmolecular-weight compound, and lg h* is a universal function of T g /T [15]. On the basis of the above, in the capacity of the characteristic temperature as a parameter of the corresponding state, it is expedient to use the hypothetical crystallisation temperature T cr rather than T g. The ratio of T cr to the actual temperature T determines the thermodynamic state of non-crystallising oligomers (the degree of supercooling) and accordingly the magnitude of the motive force causing the formation in them of associates or solid-like clusters, which in turn influence the time of correlation of molecular motion and Newtonian viscosity of oligomers. The corresponding generalised curve in the coordinates lg h T cr /T is presented in Figure 5, while the values of the constants of reduction A and B are presented in Table 3. It is evident that both experimental and published data for the Newtonian viscosity of bisphenol A and aliphatic epoxy oligomers fit well on the universal curve. The quantity A is practically the same for bisphenol A and aliphatic epoxy oligomers, irrespective of their molecular weight, i.e. can be considered to be universal. The quantity B seems to depend on the molecular weight and the type of oligomer, decreasing markedly with Figure 4. Experimental temperature dependences of the viscosity of epoxy oligomers in coordinates of the VF equation. 1 EPIKOTE 828; 2 Laproxide 503M; 3 Laproxide 603; 4 Laproxide 703 Figure 5. Generalised curve of the viscosity of oligomers and polymers. Continuous line universal curve for polymers according to data of [10]. 1 EPIKOTE 828 [4]; 2 EPIKOTE 828 experiment; 3 EPIKOTE 828 [1]; 4 EPIKOTE 834 [4]; 5 EPIKOTE 1001 [4]; 6 EPIKOTE 1001 [1]; 7 EPIKOTE 1001F [5]; 8 EPIKOTE 1002 [4]; 9 EPIKOTE 1002F [5]; 10 EPIKOTE 1004 [4]; 11 EPIKOTE 1004 [1]; 12 EPIKOTE 1007 [1]; 13 EPIKOTE 1009 [1]; 14 Laproxide 503M; 15 Laproxide 603; 16 Laproxide 703 2010 Smithers Rapra Technology T/19
Table 3. Values of the constants of reduction from equation (4) for bisphenol A and aliphatic epoxy oligomers Epoxy oligomer M n T cr, K A B Bisphenol A epoxy oligomers EPIKOTE 828 366 311 1.7 2.5 EPIKOTE 828 375 309 1.7 2.4 EPIKOTE 828* 376 312 1.9 2.8 EPIKOTE 834 479 330 1.8 2.2 EPIKOTE 1001* 875 367 2.1 1.8 EPIKOTE 1001 898 367 1.9 2.2 EPIKOTE 1001F 953 368 2.5 1.9 EPIKOTE 1002 1147 378 2.4 1.8 EPIKOTE 1002F 1179 381 2.5 1.9 EPIKOTE 1004* 1495 391 2.3 1.6 EPIKOTE 1004 1538 396 1.6 1.8 EPIKOTE 1007* 2355 415 1.6 1.5 EPIKOTE 1009* 3020 426 1.9 1.4 Aliphatic epoxy oligomers Laproxide 503M 480 240 1.5 2.1 Laproxide 603 645 242 1.4 2.0 Laproxide 703 730 244 1.3 2.0 Calculated from data of: * Ref. [3]; Ref. [6]; Ref. [7] increasing M n for bisphenol A epoxy oligomers. With similar values of molecular weight, the values of B of bisphenol A and aliphatic epoxy oligomers are similar to each other. Thus, to obtain a universal generalised curve of viscosity of all epoxy oligomers, it is necessary to take into account the dependence of their Newtonian viscosity on molecular weight. It is known that the dependence of Newtonian viscosity on molecular weight for melts of polymers and oligomers has the form of an exponential function [15, 12]: lgh = lga + a lg M (5) where a and a are constants. The corresponding dependences for bisphenol A epoxy oligomers and Laproxides, plotted from experimental and published [6, 7] data, are presented in Figure 6. They can be approximated by straight lines, which makes it possible to calculate constant a, the values of which are presented in Table 4. It is believed [15] that constant a for oligomers should have a magnitude of the Figure 6. Dependence of viscosity on molecular weight in double logarithmic coordinates according to Refs [4] and [5] and experimental data. 1 4 bisphenol A epoxy oligomers; 5, 6 Laproxides. Temperature: 1, 5 298 K; 2, 6 333 K; 3 383 K; 4 403 K order of 1, while for polymers with a molecular weight higher than a certain critical value it is about 3.4 3.5 [13]. However, for bisphenol A epoxy oligomers, a is far greater than these values, and here, with reduction in the experiment temperature, i.e. with increasing departure from T cr, this difference increases considerably (Table 4). In the case of aliphatic epoxy oligomers, for which the experimental temperature exceeds T cr, a = 1. All this once again confirms the stated assumption concerning the key influence of the thermodynamic associated state on the laws governing the Newtonian viscous flow of epoxy oligomers. Acknowledgement The authors are grateful to IFKhE colleagues M.R. Kiselev and I.N. Senchikhin for help in conducting the experiment. REFERENCES 1. S.M. Mezhikovskii, Physical Chemistry of Reactive Oligomers: Thermodynamics, Kinetics, Structure. Nauka, Moscow, 1998, 233 pp. 2. S.M. Mezhikovskii et al., Oligomeric State of a Substance. Nauka, Moscow, 2005, 252 pp. Table 4. Values of constant a of equation (5) for bisphenol A and aliphatic epoxy oligomers Oligomers Range of M n T, K a Bisphenol A epoxy oligomers 375 3020 298 19.6 333 11.8 383 7.6 403 7.1 Oligooxypropylenetriol glycidyl ethers 480 730 298 1.0 333 1.0 T/20 International Polymer Science and Technology, Vol. 37, No. 8, 2010
3. A. Ghijsels et al., Temperature dependence of the zero-shear melt viscosity of oligomeric epoxy resins. Polymer, 25, 1984, pp. 463 466. 4. L.G. Nechitailo et al., Dependence of the viscosity of epoxy bisphenol A oligomers on temperature and molecular weight. Ukr. Khimich. Zhurnal, 53, No. 9, 1987, pp. 997 1000. 5. L.G. Nechitailo et al., Temperature dependence of viscosity and parameters of the free volume of epoxy compounds. Ukr. Khimich. Zhurnal, 54, No. 6, 1988, pp. 634 638. 6. T. Koike, Relationship between melt viscosity and dielectric relaxation time for a series of epoxide oligomers. J. Appl. Polym. Sci., 47, 1993, pp. 387 394. 7. T. Koike, Melt viscosity at glass transition temperature for some epoxide oligomers. J. Appl. Polym. Sci., 56, No. 9, 1995, pp. 1183 1186. 8. Yu.S. Zaitsev et al., Epoxy Oligomers and Adhesive Composites. Naukova Dumka, Kiev, 1990, 200 pp. 9. P.J. Flory, Levels of order in amorphous polymer. Organization of Macromolecules in the Condensed Phase: Faraday Discussion of the Chemical Society, No. 68, 1979, pp. 14 25. 10. V.A. Kargin and G.L. Slonimskii, Short Essays on the Physical Chemistry of Polymers. Khimiya, Moscow, 1967, 230 pp. 11. J.P. Sethna et al., Scaling Theory for the Glass Transition. 12. G.V. Vinogradov and A.Ya. Malkin, Rheology of Polymers. Khimiya, Moscow, 1977, 439 pp.; Phys. Rev. B, 44, No. 10, 1991, pp. 4943 4959. 13. A.N. Krasovskii et al., Investigation of the relaxation transitions in epoxy oligomers. Kompozitsionnye Polimernye Materialy, No. 46, 1990, pp. 30 36. 14. A.A. Tager, Physical Chemistry of Polymers. Khimiya, Moscow, 1978, 544 pp. 15. D.V. Van Krevelen, Properties and Chemical Structure of Polymers. Khimiya, Moscow, 1976, 416 pp. 2010 Smithers Rapra Technology T/21