Plasticheskie Massy, No.,, pp. 19 Using the thermal electrical fluctuation method to investigate molecular mobility in structurally inhomogeneous polymer systems Yu. V. Zelenev, V. A. Ivanovskii, and D. D. Valgin D. I. Mendeleev Russian Chemico-Technological Institute Selected from International Polymer Science and Technology, 9, No. 9,, reference PM //19; transl. serial no. 1481 Translation submitted by P. Curtis This work demonstrates the relationship between the intensity of electrical fluctuations and features of the structural organisation of polymer systems of different classes. The results of analysing processes of molecular mobility in the polymers polyvinyl chloride (PVC), polystyrene (PS), polymethyl methacrylate (PMMA), low-density polyethylene (LDPE), polytetrafluoroethylene, natural rubber, and SKMS-1 butadiene methylstyrene rubber and in the copolymer vinylidene fluoride + tetrafluoroethylene (VDF + TFE) have been interpreted in accordance with the theory of temperature transitions in solids, according to which they can be observed after 1. K. An investigation was made of the dependence of the spectral density of the stress of electrical fluctuations on the frequency in the range.1 1. MHz. The thermal electrical fluctuation method was used to determine the physical quantities of polymer systems that are connected with their structural organisation: dielectric characteristics, effective dipole moment, internal pressure. The correlation was shown between the physical characteristics of PVC when modifier MBS is introduced and the thickness-related spectral density of the stresses of electrical fluctuations. Molecular mobility in polymers is due to vibrations of individual groups and fragments of macromolecules which are represented by different subsystems: the set of elements of supermolecular structures, macromolecules of identical or different length, free and combined segments, and different quasiparticles [1]. In a study of molecular motions in polymers of different structure by methods of relaxation spectrometry in wide temperature and frequency ranges it was established that the temperature values at which temperature transitions appear depend considerably on the types of force field and their strengths. With increase in the strength of the force field (as with increase in the frequency of external action), the regions of relaxation that appear are displaced towards higher temperatures, which makes it difficult to assess the true values of the temperature coefficients of the relaxation times and the effective size of the kinetic units. Furthermore, not all temperature transitions can be recorded by existing methods used to study relaxation effects in polymeric materials and systems. It is known [ 4] that the temperatures of the transitions in solids can be placed in the series T i = m T (1) where m is an integer and T = 1. K. Thus, in the range 4 K, up to temperature transitions can appear. However, in real polymers no more than 1 1 are recorded. This is due firstly to the structural inhomogeneity of the polymer systems, and secondly to the insensitivity of the existing methods of relaxation spectrometry that are used for analysis. In this context, to analyse processes of molecular mobility, it is expedient to use methods that make it possible to carry out tests in the absence of any force fields, and that are sensitive to the appearance of as large a number of temperature transitions of the m T series as possible. One such method is the thermal electrical International Polymer Science and Technology, Vol., No., T/1
fluctuation method []. Essentially, this method is fairly simple [6]. The material to be investigated is placed between the plates of a primary capacitance pick-off and, as the temperature rises, the change in the mean square stress of electrical fluctuations of the polymer on the clamps of this sensor are measured and recorded. In [6] it was shown that, on the dependences of the mean square stress of electrical fluctuations, U, on time t and temperature T, regions of anomalous change in U are observed, which is due to temperature transitions in the polymer. Here, the value of U can be presented by the following relationship [7]: U U T (t,t) + U ri (t,t), t is t t if = () U T (t,t), t [t is,t if] where U T (t, T) is a component proportional to the intensity of internal friction the mean square stress of thermal electrical fluctuations, and U ri (t, T) is the relaxation component the fluctuations over and above the thermal fluctuations. The latter are due to temperature transitions and appear when new types of motion of the available relaxers (kinetic units) appear. Subscript s stands for the start and subscript f stands for the finish of appearance of the corresponding transition. Table 1 gives the results of experimental investigations of U (t, T) at a frequency f = 1. x 1 Hz in the band f = 1 Hz for polymers of different classes at a heating rate of K/min. It also compares the minimum temperature of appearance of transition according to data of the thermal electrical fluctuation method and the value of T i calculated by means of formula (1). An analysis of the data obtained makes it possible to state the following. In the investigated temperature range 78 4 K, the greatest number of temperature transitions are possessed by a vulcanisate of natural rubber and SKMS-1. The smallest number are possessed by noncrystalline solid polymers PVC, PS, and PMMA. Crystalline LDPE and PTFE lie in an intermediate position in terms of the number of regions of appearance of processes of molecular mobility. Unvulcanised natural rubber has a greater number of transitions than PVC, PS, and PMMA but a smaller number than LDPE and PTFE. Thus, the structural organisation of the polymers has a considerable influence on the number of processes of molecular mobility that appear. Here, polymers possessing a more ordered structure also have a greater number of temperature transitions. Comparison of the temperatures of the series T i = m T with values of T imin indicates that T imin differs from T i in most cases by no more than ±K (Figure 1). This is also due to the structural inhomogeneity of the specimens investigated. Depending on the ordering of the kinetic units within the polymer, unfreezing of each type of their molecular motion (for example, longitudinal or torsional vibrations) can proceed either as entirely independent processes (Figure 1a) or as combined processes (Figure 1b). If a single combined process appears, then the number of possible temperature transitions can be defined as N = (T imax - T imin ) T () where T imin and T imax are the minimum and maximum temperatures of appearance of transitions that are recorded from the variance of the mean square stress of thermal electrical fluctuations of the polymer, and T = 1. K. Table gives the results of analysing fluctograms of U (t, T) of polarised and unpolarised copolymer V F + TFE and assigning the temperature transitions observed to the series n T. It is well known that polarisation leads to ordering of the structure of the polymer. The data in Table and the results of IR spectroscopy [8] confirm the thesis that a greater number of temperature transitions of the series ndt appear in the more ordered structure. The effective activation energy of unfreezing of the mobility of relaxers, determined using the thermal fluctuation method, is equal to [9] E i t f lg t j =. R 1 1 T T f j where R is the universal gas constant, t f and T f are the finish time and temperature of the process being analysed, and t j and T j are the time and temperature corresponding to the middle of the appearance of the jth process of molecular mobility. If the material being investigated is structurally homogeneous, then when it is heated at a constant rate, the temperature transitions will appear in accordance with the series m T. Considering that the processes of unfreezing of the corresponding molecular motions Figure 1 Modifications of the appearance of temperature transitions in polymers on fluctograms of U (t, T): (a) two independent processes; (b) combined process governed by two temperature transitions (4) T/ International Polymer Science and Technology, Vol., No.,
Table 1 Calculated data for T, i K m m T PVC 1 1. 7. 4 6. Experimental values of minimum temperatures of appearance of processes of molecular mobility ccording to data of thermal electrical fluctuation method T, K PS a imin PMMA LDPE PTFE Natural rubber Vulcanisate Natural rubber SKM S-1 6 7 78 78 7 87. 91 8 1 9 99 98 9 11. 111 19 1 1 18 1 11 17 141 1 1 147 11 1 147 148 1 16. 16 17 16 14 17 17 17 17 181 168 1 187. 189 189 18 19 191 16 4 19 198 17 1. 9 16 17 17 9 8 11 18 9 19 7. 44 1 41 46 4 49 48. 1 6. 8 61 68 6 64 7 7 77 79 74 78 7 76 87. 81 94 87 87 4 6 97 96 4 9 97 9 1. 8 14 1 6 19 4 7 7. 4 6 4 9 8 4 1 9 6. 6 61 7 78 71 76 71 begin at T j and end at T f = m T + 1, where T i = m T = m x 1. K, where T i = m T = m x 1. for W m we will obtain the following relationship: W = 1 + 16m + 69 J/ mol () m m The value of W m with m = corresponds to the energy of zero vibrations of the relaxers (i.e. at T = ). The estimate obtained, W = 69 J/mol, is similar in magnitude to the energy of dipole dipole interaction of atoms 1 ev or 96 J/mol at T = [1]. International Polymer Science and Technology, Vol., No., T/
Table m T j = m T, K Unpolarised DF + TFE T, V jmin With account taken of the above, it is possible to propose a scheme of appearance of processes of α-, β-, γ-, and δ-relaxation, and variants of their break-up for non-crystalline and crystalline solid polymers (Figure ) with indication of the values of the energy barriers for the occurrence of different molecular motions. K Polarised DF + TFE T V jmin 87. 9 4 1. 1 6 6 9 7 7. 8 46 9 6. 69 7 1 87. 87 4 4 97 41. 416 41 4 4 47. 4 44 6 4 4 7 46. 8 47 9 487. 491, K Figure Scheme of appearance of temperature transitions in polymers and variants of break-up of α-, β-, γ-, and δ- relaxation processes Thus, the thermal electrical fluctuation method is extremely informative and sensitive to temperature transitions existing in the polymer. The number of recorded transitions in the polymer system depends on its structural organisation. Structurally inhomogeneous materials have fewer transitions. Each of the processes of α-, β-, γ-, and δ relaxation breaks up into corresponding subprocesses appearing at temperatures of the series m T. A second aspect of using the thermal electrical fluctuation method for analysis of structurally inhomogeneous polymer systems is the determination of their physical properties, which is possible on the basis of measuring the mean square stress of thermal electrical fluctuations U T (t, T). As shown in [, 6], U T (t, T) can be written in the form 8K d f ε UT = T (6) επ D f ( ε ) + ( ε ) where K is the Boltzmann constant, ε is the electrical constant, d is the thickness of the polymer specimen, D is the diameter of the potential electrode of the primary pickoff, f and f are the frequency and band of frequencies of U T measurement, and ε and ε are the dielectric permittivity and coefficient of dielectric losses. With T = const, U T characterises the structural organisation of the polymers. For comparison of polymer systems of different classes in terms of U T, it is necessary to introduce into the examination the thickness-related spectral density of the stress of thermal electrical fluctuations S d UT Sd = V Hz m fd, / (7) As follows from Figure, S d of all the polymers investigated obeys the law 1/f, which confirms the thesis concerning the thermal nature of the processes of electrical fluctuations at a fixed test temperature T = 9 K and the band of frequencies f = 1 Hz. Here, crosslinked polymers (cured epoxy resin ED-4M) have the lowest value compared with all other polymer systems. The highest value of S d is possessed by PVC, which is due to the polarity of this polymer. Of note is the identical nature of change in S d of PVC and in the mechanical characteristics (tensile elastic modulus E t and yield point σ) when modifier MBS is introduced into the polymer (Figure 4). The formation of a three-dimensional structure of the polymer system also has a marked effect on the behaviour of S d. Figure gives comparative characteristics of ED- 4M specimens with increase in the degree of curing: the spectral density S d and the dielectric permittivity ε measured in the normal way (measurements of ε of specimens in a variable electric field were carried out using an E1- instrument and a VR 49 dielectric T/4 International Polymer Science and Technology, Vol., No.,
holder). As follows from Figure, ε changes little with increase in the degree of curing, while S d decreases by more than a factor of.. Measurements of U T make it possible to determine the dielectric characteristics ε and ε of polymer systems without exposing the specimen to an external electric field [6]. From the values of ε and ε it is possible to determine the effective dipole moment in polymers by a formula following from the fluctuation dissipation theorem [11] Figure Dependence of thickness-related spectral density of stress of electrical fluctuations S d on frequency for polymers of different structural organisation: 1 PVC; PMMA; PC; 4 PS; ED-4M Figure 4 Dependence of (1) spectral density S d, () tensile elastic modulus E t and () yield point σ on content of modifier MBS in PVC M ε ( 1+ ε )( ε 1) µ eff = KT (8) ρ 4πNA ε where M is the molecular weight of the recurrent unit of the polymer, ρ is density, and N A is Avogadro s constant. The internal pressure ρ was determined according to []. Table gives the results of estimating the physical characteristics of polymer systems of different structural organisation and chemical composition by the thermal electrical fluctuation method. The necessary values of the molecular parameters were taken from [1]. To compare the data obtained, use was made of the results of calculating µ eff by the procedure described in [1]. As follows from Table, ε, ε, and tg δ = ε /ε determined without an external electric field are an order of magnitude greater than the values measured under normal conditions. This indicates the intensity of processes of molecular mobility of relaxers of the polymer system being studied and its polarity. Polyethylene and polystyrene have the lowest values of ε and tg δ. The high values of ε and tg δ for PTFE are caused by a phase transition connected with change in the structure of the elementary cell of the crystal in the temperature region T = 9 K. The magnitude of the effective dipole moment for PVC,.1 D, reflects the dipole moment of the C Cl bond with µ =. D [14]. For PMMA, the obtained value µ eff = 1.89 D may be due to the methyl ether group COOCH, for which there are polar bonds C O with µ = 1.1 D and C=O with µ =.7 D. The obtained values of the internal pressure ρ reflect fairly well the cohesive energy of the polymers being analysed. REFERENCES Figure Change in (1) spectral density S d and () dielectric permittivity ε as function of degree of curing of ED-4M 1. E. N. Zadorina et al., Dokl. Akad. Nauk SSSR, 7, No. 6, 1981, p. 16. Yu. N. Venevtsev et al., Dokl. Akad. Nauk SSSR,, No. 1, 1976, p. 11. V. I. Muromtsev et al., Systems of special temperature points of solids (Eds. Yu. N. Venevtsev and V. I. Muromtsev), Moscow, 1986, p. 94 4. G. A. Lushcheikin, Methods for investigating electrical properties of polymers, Moscow, 1988, p. 11 International Polymer Science and Technology, Vol., No., T/
Table P olymer ε ε t g δ µ ef, D µ f e ff, D [14] ρ, MPa PMMA. 89. 7. 8 1.89.6 47 PVC 117. 7 8.. 4.1.41 7 PS 94. 6. 1. 4 1. 1.6 74 PE 6. 6 1. 8. 8. 87 PTFE 61. 1 189.. 1 1..4 46. Yu. V. Zelenev and V. A. Ivanovskii, Vys. Soed., A, No. 7, 199, p. 16 6. V. A. Ivanovskii, M. Tech. Sci. thesis, Moscow, 1986, 6 pp. 7. Yu. V. Zelenev et al., Vys. Soed., B8, No. 9, 1986, p. 697 8. V. G. Sokolov et al., Vys. Soed., 9, No., 1987, p. 9. Yu. V. Zelenev and V. A. Ivanovskii, Modern methods and instruments for monitoring product quality, Moscow, 1989, p. 119 1. Yu. S. Barash, Van der Waals forces, Moscow, 1988, p. 11. M. M. Bredov et al., Classical electrodynamics, Moscow, 198, p. 6 1. A. A. Askadskii and Yu. I. Matveev, Chemical structure and physical properties ofpolymers, Moscow, 198, 48 pp. 1. D. V. Van Krevelen, Properties and chemical structure of polymers, Moscow, 1976, 416 pp. 14. M. V. Vol kenshtein, Structure and physical properties of molecules, Moscow, 19, p. 4 (No date given) T/6 International Polymer Science and Technology, Vol., No.,