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Orientational diffusion of the toluene-d3methyl group in solutions and polymer matrices
Specrrochimica Acm. Vol. 49A. No. Il. Printed in Great Britain
Orientational
pp. 1651-1657.
1993
05~8539193 $6.00 + 0.00 @ 1993 Pergamon Pres Ltd
diffusion of the toluene-d, methyl group in solutions and polymer matrices
A. A. STOLOV, F. T. KHAFIZOV, D. I. KAMALOVA,A. I. MOROZOV and A. B. REMIZOV Chemical Department, Kazan State University, Lenin st. 18, Kazan, 420008, Russia (Received
26 October
1992; accepted 26 November 1992)
Abstract-IR spectra of solutions of selectively deuterated toluene C,H,CD, in the region of the asymmetric stretching vibrations of the CD, group are studied. Pentane, non-deuterated toluene, dibutyl phthalate, acetone and polymers: polybutadiene (PBD), polypropylene (PP) and polymethyl methacrylate (PMMA) are used as solvents. In order to determine activation enthalpy AH* and entropy AS* of the orientational diffusion of the CD, group the temperature dependencies of the absorption band widths 6 of the asymmetric vibrations of this group are studied. An original method of estimating the errors in determining the values AH* and AS* within Rakov’s approach is propsed and checked. The values obtained for AH* do not exceed 1 kcal mol-‘. No correlation of AH* with either the dielectric permittivity or the viscosity of the medium was observed. The glass transition in dibutyl phthalate and PBD, as well as relaxation transitions in PP and PMMA,do not affect the dependence 6 =f( T).
INTRODUCTION NOTWITHSTANDING the progress in studying vibrational and orientational dynamics of molecules in condensed phase, little attention is paid to studying the effect of medium on these processes. As a rule, the study of the solvent effect is restricted to comparison of data obtained for a pure liquid and a solution in an inert solvent [l-5]. Only a few papers in which the molecular dynamics of one compound are studied in a series of solvents are known [6-91, and most of them are concerned with studying the rotation diffusion of radicals by means of ESR [lo]. The influence of medium on the orientation diffusion of small molecular fragments (OH-, CH,-, etc.) is practically not studied. It is well known that the rapid reorientation of small groups considerably contributes to the broadening of the vibrational bands: therefore methods of vibrational spectroscopy are most suitable for studying these systems. In this paper we use IR spectroscopy in order to determine the parameters of orientational diffusion of the toluene-d, methyl group. Selective deuteration enables one to study the region of stretching vibrations of the CD3 group (24OO-21OOcm-‘) in which most of the solvents are transparent. The rotation of the toluene methyl group in the gaseous phase is nearly free (the barrier of - 10 cal/mol) [ll, 121, and in condensed phase the barrier of reorientation of the group will be mainly determined by the intermolecular interactions. It should be noted that glass-forming low-molecular liquids and polymers may be used as solvents (or matrices). The mobility of polymer chains and lateral groups is different for various temperature ranges, the changes in the mobility being accompanied by relaxation transitions. The relaxation transitions are investigated by different experimental methods, and the information about the process occurring at such transitions is important. Thus, the influence of the relaxation process in solvent on the barriers of orientational diffusion is of particular interest. Therefore, apart from traditional solvents, glass forming low molecular liquids and polymers were used. Activation energies for orientational diffusion were determined according to RAKOV’S method [13] which we modified in Ref. [14]. We pay a lot of attention to analyzing the accuracy of the determination of activation barriers using IR spectra. EXPERIMENTAL Selectively deuterated toluene C&CD3 (I) was produced by the firm IZOTOP (St Petersburg). The purity of the product was not lower than 99.5%. The purity was confirmed by mass 1651
1652
A. A.
STOLOV
et al.
spectroscopy. Pentane, non-deuterated toluene, acetone, and dibuthyl phthalate purified according to Ref. [15] were used as solvents. Polypropylene (PP), polymethyl methacrylate (PMMA) and polybutadiene (PBD) with the following isomeric composition: 67% l,Ctruns, 27% 1,2-cb and 6% l,Zisomer, were used as polymer matrices. PP and PMMA films were prepared by milling, PBD film was prepared by pressing the drop of PBD between two KBr windows. The thickness of the films was about 0.1 mm. Concentration of I both in liquid solvents and polymer matrices was of 2-5 volume per cent. In PP film I was introduced from gaseous phase. The film was saturated with vapours of I for abut 20 h; afterwards it was kept at room temperature for 2 h. The samples I in PMMA and PBD were prepared from the soluton of PMMA in I by evaporating the latter for about 60 h. IR absorption spectra were measured with a SPECORD M-80 spectrometer combined with a computer. Spectra were registered at the width of slit function of 1.5 cm-‘. As far as the minimum width of the studied bands was 12 cm-‘, it was not necessary to account for apparatus distortions
WI. Low temperature measurements were carried out with a one-beam cryostat cooled by liquid nitrogen. Temperature was measured by copper-constantan thermocouple with the accuracy of 0.5 K. All experiments were carried out in two stages. At first, IR spectra of solutions were registered at various temperatures. Then the same measurements were repeated for a pure solvent (matrix). Subtraction of the spectra was performed with computer. A Raman spectrum was obtained for pure I. Spectrometer DFS-24 at 1,x, = 488.11 nm and the width of slit function 2 cm-’ was used.
APPROACHES
TO DETERMININGTHE BARRIERSOF ORIENTATIONALDIFFUSIONAND TREATMENTOF EXPERIMENT
Information about the orientational diffusion of the band shapes and widths of its asymmetric vibrations. The cm-’ of asymmetric stretching vibration of the group spectra is the sum of contributions from vibrational and
methyl group is present in the band width at half maximum 6, in IR and anisotropic Raman orientational relaxation:
(1) where r,, is the time of orientation relaxation. The temperature dependence of r,, is determined by the activation energy of orientational diffusion. RAKOV proposed [13] to use the Arrhenius’ dependence 6,,(T): d=&,+A
exp(-UJRZ’),
(2)
where U,, is the activation energy, and A is a constant. The dependence (2) was used to determine U,, in some papers (for example, Refs [3,13, 17-221). However, in Ref. [14] it was noted that the dependence 6 =f( T) must have an inflection point at Ti”a= UJ2R, if it is defined by Eqn (2). No inflection was observed in the experiment. Since then it was proposed [14] to use the expression in Eyring form:
where k, h are Boltzman and Planck constants, respectively; c is the light velocity; and AH* and AS* are the enthalpy and entropy of the activaton of the process. To determine the quantities AH* and AS* is the aim of our investigation. The problem is considerably simplified if the value of 8vibis known. In order to determine Bvibthe following approaches are proposed in the literature: (i) the use of both isotropic and anisotropic Raman spectra [22,23]. Unfortunately, this method is not applicable to totally depolarized bands of the perpendicular vibrations of the methyl group; (ii) the extrapolation of the function 6 =f(q-‘) to the infinite viscosity 11[13]. This method is not applicable to solutions in glassy liquids and polymers. In addition, the dependence of 6 on 7 requires a reliable theoretical interpretation;
Orientational diffusion of the toluene-d, methyl group
1653
(iii) in Refs [24,25], an approach which is actually based on supposing the equality of the activation barrier of molecular reorientation and the activation energy of the viscous flow was proposed. This supposition is, generally speaking, not justified, and, as will be shown later, it is not applicable to our case; (iv) in Ref. [26] the dependencies bib)
ln(h_,,i-
=.f(T’)
are studied for different possible values of dvib. Here bexpiis the experimental magnitude of the width, and i is the number of the experimental points. It is assumed that the dependence (4) with the maximum value of the linear correlation coefficient corresponds to the true value of Gvib.The approach [26] is seriously criticized. In Ref. [14] it is noted that taking the logarithm of the differences (6,,; - &,) which for several temperatures are close to zero distorts the normal distributions of random errors of 6, and, in turn, it considerably affects the results of calculation. It should be noted that the methods (ii)suppose the independence of 6 of the temperature. According to the theoretical ideas [27,28] and experimental data [20-223, the value 8vibdecreases by l-2 cm-’ when the temperature is decreased by 100 K. Such changes are by an order of magnitude smaller than that observed for the band corresponding to the asymmetric vibration of toluene-da methyl group, and, consequently, this assumption in our case is justified. We propose the following approach to determining the quantities AH*, AS* and S,,. Let us assume that the band width 6 has a normal error distributed according to the normal law, and the dispersion errors of one measurement are the same in the whole region of 6 values. In addition, let us assume that the dependence of 6 on T is determined by Eqn (3) in which AH*, AS* and Bvibare temperature independent. In order to find parameters of (3) we minimize the sum of error squares
without going into logarithmic coordinates. algorithm. Let us write the expression (3) in the form
It is convenient
to use the following
d=d,,+ax
(6)
where a = (k/&c)
exp(AS*lR);
X= Texp( - AH*IRT).
(7)
Taking AH* = 0, we calculate the values Xi corresponding to the experimental temperatures Ti. Then using a least-squares method we find optimal parameters a, Bvibof the straight line (6) and the dispersion of points D. Let us add a step (in our case 20 cal/mol) to AH* and once more calculate a, &, and D. The latter procedure is continued until the upper limit for AH* (in our case 10 kcal/mol) is reached. From the obtained sets of parameters we chose the optimum 01and dvib(corresponding to the minimal dispersion). The errors of determining Bvib,AH* and AS* are estimated as follows. The normally distributed random noise with dispersion equal to that in experiment is added to the optimal values of the function 6 = F(T). Using the above algorithm, the optimal parameters &,,, AH* and AS* are found. This procedure is repeated 100 times, and a histogram of the values avib, AH* and AS* is built according to the results. Five boundary values are rejected, and the remaining ones show the limits of errors in determination (the probability 0.95). The advantage of this method is that it enables one to carry out the exhaustive search of all possible values of AH* (with a given step) and thus to find the global minimum of the sum of error squares.
A. A. STOLOV et
1654
al.
c
A&& 2300
2200
2100
v (cm-')
Fig. 1. IR (a), Raman I, (b) and 4, (c) spectra of pure toluene-d,. RESULTS AND DISCUSSION
We have studied the bands corresponding to asymmetric stretching vibrations of the CD3 group. Fragments of IR and Raman spectra for pure I are given in Fig. 1. Taking into account the depolarization ratios in Raman spectrum, only the bands in the range 2160-2270 cm-’ may be attributed to asymmetric vibrations. The analysis of the fourth derivative of the IR spectrum shows the presence of at least four bands in this range.
2300
2270
2240
2180
2190
2230 v (cm-')
Fig. 2. IR spectra of toluene-d, in nondeuterated toluene fitted by Eqn (8). Circles show the experimental spectra, solid lines-the rebuilt one. (a) T=293 K; (b) T= 163 K.
Orientational diffusion of the toluene-d, methyl group
1655
16
1
‘i
E s
I
I
I
I
100
160
220
280
I
I 160
I 220
I 280
I
100
T (K) Fig. 3. The dependencies 6 upon T for the band 2211 cm-’ of toluene-d, in different solvents: (a) 0, PP; pentane; A, -.-. acetone; +, --- nondeuterated toluene. (b) 0, + , --- dibutyl phthalate; A, -.-. PBD; E-. .- PMMA.
The IR spectrum in the region 2270-2160 cm-’ was resolved into four components having the following form: D(Y) =x
Ad2
#+4(Y-Q)*
+(l--)Aexp
4 In 2 -~(Y-~Q)*
(8)
, >
with A, vo, 6 and x being the variable parameters. In this way there was a good agreement with the experimental spectra (Fig. 2). As the temperature is lowered, approximately the same narrowing of all four components (2240, 2230, 2211 and 2175 cm-‘) is observed, the position of the bands changing slightly (Fig. 2). The relative contribution of the Lorentzian component in Eqn (8) was practically temperature independent and was x = 0.5-0.7. The widths of the bands 2230 and 2170 cm-’ at lowest attainable temperature (77 K) were equal to each other (with accuracy of 1 cm-‘). It enables us to assume the equality of the widths when treating the contours obtained at higher temperatures. Table 1. Orientational relaxation parameters of toluene-d, in solutions
Pentane Toluene Dibutylphthalate Acetone PBD PP PMMA
w
4ib
cw(PSI
&
(290K)
TW
(cm-‘)
(290K)
1.8 2.4 8.5 21.5 2.2 2.15 3.15
0.24 0.58 2.10 0.33 -104 - 10’5 - 1on
138-293 163-293 80-293 183-2% 80-290 77-213 77-295
5.1kl.l 7.3kO.9 12.0+ 1.3 lO.lk3.4 8.8+ 1.8 13.5kO.5 13.4kO.2
tl
Solvent
0.50+0.04
0.72 f 0.06 1.04f0.18 0.79f0.23 0.79kO.12 0.84+0.10 1.4lkO.12
-2.2+0.1 -2.9kO.2 -2.6f0.5 -0.8f0.8 -2.7kO.2 -1.lf0.6 -2.3kO.3
0 0
0.30+0.18 0.71+ 0.32 0.10+0.10 0.58kO.14 0.58kO.08
A. A. STOLOV et al.
1656
Two asymmetric stretching IR bands of the methyl group must be assumed for one conformation of toluene [29]. For &D&D3 these bands were found to occur at one and the same frequency: 2212 cm-’ [30]. In our opinion, the most intense bands 2230 and 2211 cm-’ refer to the asymmetric stretching vibrations of the CD3 group. It is possible that the weak bands at 2240 and 2175 cm-’ correspond to overtones or combination vibrations. The existence of different conformations of I is also possible, having slightly different frequencies of stretching asymmetric vibrations of the CD3 group. Weak bands 2240 and 2175 cm-’ cannot be explained by the admixture of C&15CD2H (according to mass spectroscopy data, the admixtures do not exceed 0.5%; these do not agree with sufficiently large intensities of these bands). The temperature changes of the spectra do not enable us to attribute these bands to the unresolved rotational structure of more intense components and to hot transitions. The temperature dependencies of the band widths for 2230 (and 2211) cm-’ of I in different media are given in Fig. 3. The dependencies are well described by Eqn (3). Optimal values of the parameters of Eqn (3) and characteristics of solutions: dielectric permittivity E and viscosity t7 are given in Table 1. The curves in Fig. 3 correspond to the optimum values of the parameters. The cases AH* = 0 refer to practically linear dependencies 6 =f(T) when, according to Eqn (3) the time of reorientation of the CD, group is due only to the entropy factor. It is difficult to find any correlations between the barrier AH* and the properties of the medium (Table 1). However, the accuracy we achieved enables us to note that ail the values AH* are smaller than 1 kcal mall’. In addition, the absence of considerable dependence of AH* on the viscosity of the medium is noticeable. According to the Debye-Stokes-Einstein theory [31], 6,,=-
3kT 2 ln(2alb) - 1 &r2ctj
a3
’
(9)
where a and b are the lengths of the principal axes of the top. As follows from Eqn (9), the band width must be inversely proportional to 77at constant temperature. Compounds we studied cover the range of viscosity from 10-l to 1Ol5cP. According to the theory, the quantity 6,, must decrease by 16 orders of magnitude when going from penthane to PMMA. It is not observed (cf. Fig. 3 and Table 1). Apparently, the Debye-Stokes-Einstein theory is not applicable to the orientation diffusion of methyl groups. Thus, it is not correct in our case to put the activation barriers of orientational diffusion and viscosity equal to each other, as is done in Refs [24,25]. As far as large viscosity of PMMA and PP is connected with their glassy state, it is of interest to study the influence of glass transition on the dependence of 6 =f(T). It is convenient to use the solutions of I in dibutyl phthalate (glass transition temperature Tg= 173.5 K) and PBD ( Tg= 200 K). As is seen in Fig. 3, the dependencies 6 =f( T) have no peculiarities (steps or inflections) at temperatures Tg. It should be noted that rotational diffusion of nitroxyl radicals (method of spin probes [lo]) is sensitive to glass transition of the matrix: the dependence In r=f(r’) (t is the time of rotational correlation) has an inflection at Tg In our case the absence of inflectin is probably due to the methyl group being smaller in volume than nitroxyl radicals. It should be noted that the dependencies 6 =f( T) for I in PP, PBD and PMMA do not manifest any relaxation transitions (relaxation transitions are not observed in the method of spin probes as well). It is seen for I in PMMA in particular: the relaxation transition at T- 180-200 K [32] observed by various physical methods is not manifested in the dependence 6 = f( T) . Acknow/edgement-The
authors are grateful to S. F.
Mironovfor obtaining the Raman spectrum of I.
REFERENCES [l] C. Dreyfus, C. Brouillard, T. Nguyen Tan, A. Grosjean and J. Vincent-Geisse, /. Mofec. Srrucr.47, 41 (1978).
Orientational diffusion of the toluene-d, methyl group [2] [3] [4] [5]
1657
J. Yarwood, Adu. Molec. Rel. Proc. 5, 375 (1973). J. Yarwood, R. Arndt and G. Doge, Chem. Phys. 25,387 (1977). V. E. Pogorelov, A. I. Lizengvich, I. I. Kondilenko and G. P. Buyan, Usp. Fiz. Nauk 127, 683 (1979). N. N. Kravetz, V. E. Pogorelov, G. I. Salivon, V. N. Sushii and I. B. Estrela-Liopis, Spectroskopiya Nemetallitcheskikh Kristallov (Spectroscopy of Nonmetal Crystals), p. 135. Kiev (1990). (61 A. Heranz, An. Quim. A/Real. Sot. Esp. Quim. 84,327 (1988). [7] J. Yarwood, J. Molec. Liq. 36, 237 (1987). [8] A. Heranz, J. Molec. Liq. 39, 111 (1988). [9] A. Purkayastha, R. Das and K. Kumar, J. Raman Specrrosc. 21, 227 (1990). [lo] A. M. Vasserman and A. L. Kovarskii, Spinoviye Metki i Zondi u Fizikokhimii Polimerov (Spin Labels and Probes in Physical Chemistry of Polymers). Moscow (1986). [ll] H. D. Rudolph, H. Dreizler, A. Jaeschke and P. Wendling, Z. Naturforsch 22A, 940 (1%7). [12] C. M. Pol, P. K. Panja and B. Sibsankar, /. Molec. Struct. 189, 287 (1988). [13] A. V. Rakov, Trudi Fiz. Inst. Akad. Nauk 27, 111 (1964). [14] N. N. Vakhrusheva, A. B. Remizov, A. A. Stolov and A. I. Fishman, Zh. Prikl. Spektr. 51,273 (1989). [15] D. D. Perrin, W. L. F. Armarego and D. R. Pert-in, Purification of Laboratory Chemicals. Pergamon Press, Oxford (1980). [16] K. Tanabe and J. Hiraishi, Spectrochim. Acta 36A, 341 (1980). [17] J. M. Janik, J. A. Janik, A. Migdal-Mikuli and G. Pytasz, Acta Phys. Polonica 4lA, 741 (1971). (181 J. M. Janik, A. Migdal-Mikuli and J. A. Janik, Acta Phys. Polo&a 46A, 299 (1974). [19] R. C. Leech, D. B. Powell and N. Sheppard, Spectrochim. Acta 22, 1931 (1966). [20] A. B. Remizov, N. N. Vakhrusheva, I. S. Pominov and I. Ya. Kuramshin, Opt. Spektr. 46, 184 (1977). [21] A. B. Remizov, N. N. Vakhrusheva and I. S. Pominov, Zh. Prikl. Spektr. 35,299 (1981). [22] F. J. Bartoli and T. A. Litovitz, J. Chem. Phys. 56, 404 (1972). [23] F. J. Bartoli and T. A. Litovitz, J. Chem. Phys. 56, 413 (1972). [24] S. Hashimoto, T. Ohba and S. Ikawa, Chem. Phys. 13863 (1989). [25] A. Sugitiani, S. Ikawa and S. Konaka, Chem. Phys. 142,423 (1990). [26] S. A. Kirillov and I. Ya. Rivelis, Zh. Prikl. Spektr. 19,934 (1973). [27] R. Kubo, Fluctuation, Relaxation and Resonance in Magnetic Systems, p. 23. Edinburgh (1962). [28] W. G. Rothschild, 1. Chem. Phys. 65,455 (1976). [29] A. B. Dempster, D. B. Powell and N. Sheppard, Spectrochim. Acta UIA, 373 (1972). [30] L. M. Sverdlov, M. A. Kovner and E. P. Krainov, Kolebatelniye Spektri Mnogoatomnykh Molekul (Vibrational Spectra of Polyatomic Molecules). Moscow (1970). [31] F. G. Dijkman, Chem. Phys. Left. 57,450 (1978). [32] 0. E. Zgadzai, D. I. Kamalova, A. B. Remizov, A. A. Stolov and A. I. Fishman, Zh. Fiz. Khim. 64,1029 (1990).
Orientational
pp. 1651-1657.
1993
05~8539193 $6.00 + 0.00 @ 1993 Pergamon Pres Ltd
diffusion of the toluene-d, methyl group in solutions and polymer matrices
A. A. STOLOV, F. T. KHAFIZOV, D. I. KAMALOVA,A. I. MOROZOV and A. B. REMIZOV Chemical Department, Kazan State University, Lenin st. 18, Kazan, 420008, Russia (Received
26 October
1992; accepted 26 November 1992)
Abstract-IR spectra of solutions of selectively deuterated toluene C,H,CD, in the region of the asymmetric stretching vibrations of the CD, group are studied. Pentane, non-deuterated toluene, dibutyl phthalate, acetone and polymers: polybutadiene (PBD), polypropylene (PP) and polymethyl methacrylate (PMMA) are used as solvents. In order to determine activation enthalpy AH* and entropy AS* of the orientational diffusion of the CD, group the temperature dependencies of the absorption band widths 6 of the asymmetric vibrations of this group are studied. An original method of estimating the errors in determining the values AH* and AS* within Rakov’s approach is propsed and checked. The values obtained for AH* do not exceed 1 kcal mol-‘. No correlation of AH* with either the dielectric permittivity or the viscosity of the medium was observed. The glass transition in dibutyl phthalate and PBD, as well as relaxation transitions in PP and PMMA,do not affect the dependence 6 =f( T).
INTRODUCTION NOTWITHSTANDING the progress in studying vibrational and orientational dynamics of molecules in condensed phase, little attention is paid to studying the effect of medium on these processes. As a rule, the study of the solvent effect is restricted to comparison of data obtained for a pure liquid and a solution in an inert solvent [l-5]. Only a few papers in which the molecular dynamics of one compound are studied in a series of solvents are known [6-91, and most of them are concerned with studying the rotation diffusion of radicals by means of ESR [lo]. The influence of medium on the orientation diffusion of small molecular fragments (OH-, CH,-, etc.) is practically not studied. It is well known that the rapid reorientation of small groups considerably contributes to the broadening of the vibrational bands: therefore methods of vibrational spectroscopy are most suitable for studying these systems. In this paper we use IR spectroscopy in order to determine the parameters of orientational diffusion of the toluene-d, methyl group. Selective deuteration enables one to study the region of stretching vibrations of the CD3 group (24OO-21OOcm-‘) in which most of the solvents are transparent. The rotation of the toluene methyl group in the gaseous phase is nearly free (the barrier of - 10 cal/mol) [ll, 121, and in condensed phase the barrier of reorientation of the group will be mainly determined by the intermolecular interactions. It should be noted that glass-forming low-molecular liquids and polymers may be used as solvents (or matrices). The mobility of polymer chains and lateral groups is different for various temperature ranges, the changes in the mobility being accompanied by relaxation transitions. The relaxation transitions are investigated by different experimental methods, and the information about the process occurring at such transitions is important. Thus, the influence of the relaxation process in solvent on the barriers of orientational diffusion is of particular interest. Therefore, apart from traditional solvents, glass forming low molecular liquids and polymers were used. Activation energies for orientational diffusion were determined according to RAKOV’S method [13] which we modified in Ref. [14]. We pay a lot of attention to analyzing the accuracy of the determination of activation barriers using IR spectra. EXPERIMENTAL Selectively deuterated toluene C&CD3 (I) was produced by the firm IZOTOP (St Petersburg). The purity of the product was not lower than 99.5%. The purity was confirmed by mass 1651
1652
A. A.
STOLOV
et al.
spectroscopy. Pentane, non-deuterated toluene, acetone, and dibuthyl phthalate purified according to Ref. [15] were used as solvents. Polypropylene (PP), polymethyl methacrylate (PMMA) and polybutadiene (PBD) with the following isomeric composition: 67% l,Ctruns, 27% 1,2-cb and 6% l,Zisomer, were used as polymer matrices. PP and PMMA films were prepared by milling, PBD film was prepared by pressing the drop of PBD between two KBr windows. The thickness of the films was about 0.1 mm. Concentration of I both in liquid solvents and polymer matrices was of 2-5 volume per cent. In PP film I was introduced from gaseous phase. The film was saturated with vapours of I for abut 20 h; afterwards it was kept at room temperature for 2 h. The samples I in PMMA and PBD were prepared from the soluton of PMMA in I by evaporating the latter for about 60 h. IR absorption spectra were measured with a SPECORD M-80 spectrometer combined with a computer. Spectra were registered at the width of slit function of 1.5 cm-‘. As far as the minimum width of the studied bands was 12 cm-‘, it was not necessary to account for apparatus distortions
WI. Low temperature measurements were carried out with a one-beam cryostat cooled by liquid nitrogen. Temperature was measured by copper-constantan thermocouple with the accuracy of 0.5 K. All experiments were carried out in two stages. At first, IR spectra of solutions were registered at various temperatures. Then the same measurements were repeated for a pure solvent (matrix). Subtraction of the spectra was performed with computer. A Raman spectrum was obtained for pure I. Spectrometer DFS-24 at 1,x, = 488.11 nm and the width of slit function 2 cm-’ was used.
APPROACHES
TO DETERMININGTHE BARRIERSOF ORIENTATIONALDIFFUSIONAND TREATMENTOF EXPERIMENT
Information about the orientational diffusion of the band shapes and widths of its asymmetric vibrations. The cm-’ of asymmetric stretching vibration of the group spectra is the sum of contributions from vibrational and
methyl group is present in the band width at half maximum 6, in IR and anisotropic Raman orientational relaxation:
(1) where r,, is the time of orientation relaxation. The temperature dependence of r,, is determined by the activation energy of orientational diffusion. RAKOV proposed [13] to use the Arrhenius’ dependence 6,,(T): d=&,+A
exp(-UJRZ’),
(2)
where U,, is the activation energy, and A is a constant. The dependence (2) was used to determine U,, in some papers (for example, Refs [3,13, 17-221). However, in Ref. [14] it was noted that the dependence 6 =f( T) must have an inflection point at Ti”a= UJ2R, if it is defined by Eqn (2). No inflection was observed in the experiment. Since then it was proposed [14] to use the expression in Eyring form:
where k, h are Boltzman and Planck constants, respectively; c is the light velocity; and AH* and AS* are the enthalpy and entropy of the activaton of the process. To determine the quantities AH* and AS* is the aim of our investigation. The problem is considerably simplified if the value of 8vibis known. In order to determine Bvibthe following approaches are proposed in the literature: (i) the use of both isotropic and anisotropic Raman spectra [22,23]. Unfortunately, this method is not applicable to totally depolarized bands of the perpendicular vibrations of the methyl group; (ii) the extrapolation of the function 6 =f(q-‘) to the infinite viscosity 11[13]. This method is not applicable to solutions in glassy liquids and polymers. In addition, the dependence of 6 on 7 requires a reliable theoretical interpretation;
Orientational diffusion of the toluene-d, methyl group
1653
(iii) in Refs [24,25], an approach which is actually based on supposing the equality of the activation barrier of molecular reorientation and the activation energy of the viscous flow was proposed. This supposition is, generally speaking, not justified, and, as will be shown later, it is not applicable to our case; (iv) in Ref. [26] the dependencies bib)
ln(h_,,i-
=.f(T’)
are studied for different possible values of dvib. Here bexpiis the experimental magnitude of the width, and i is the number of the experimental points. It is assumed that the dependence (4) with the maximum value of the linear correlation coefficient corresponds to the true value of Gvib.The approach [26] is seriously criticized. In Ref. [14] it is noted that taking the logarithm of the differences (6,,; - &,) which for several temperatures are close to zero distorts the normal distributions of random errors of 6, and, in turn, it considerably affects the results of calculation. It should be noted that the methods (ii)suppose the independence of 6 of the temperature. According to the theoretical ideas [27,28] and experimental data [20-223, the value 8vibdecreases by l-2 cm-’ when the temperature is decreased by 100 K. Such changes are by an order of magnitude smaller than that observed for the band corresponding to the asymmetric vibration of toluene-da methyl group, and, consequently, this assumption in our case is justified. We propose the following approach to determining the quantities AH*, AS* and S,,. Let us assume that the band width 6 has a normal error distributed according to the normal law, and the dispersion errors of one measurement are the same in the whole region of 6 values. In addition, let us assume that the dependence of 6 on T is determined by Eqn (3) in which AH*, AS* and Bvibare temperature independent. In order to find parameters of (3) we minimize the sum of error squares
without going into logarithmic coordinates. algorithm. Let us write the expression (3) in the form
It is convenient
to use the following
d=d,,+ax
(6)
where a = (k/&c)
exp(AS*lR);
X= Texp( - AH*IRT).
(7)
Taking AH* = 0, we calculate the values Xi corresponding to the experimental temperatures Ti. Then using a least-squares method we find optimal parameters a, Bvibof the straight line (6) and the dispersion of points D. Let us add a step (in our case 20 cal/mol) to AH* and once more calculate a, &, and D. The latter procedure is continued until the upper limit for AH* (in our case 10 kcal/mol) is reached. From the obtained sets of parameters we chose the optimum 01and dvib(corresponding to the minimal dispersion). The errors of determining Bvib,AH* and AS* are estimated as follows. The normally distributed random noise with dispersion equal to that in experiment is added to the optimal values of the function 6 = F(T). Using the above algorithm, the optimal parameters &,,, AH* and AS* are found. This procedure is repeated 100 times, and a histogram of the values avib, AH* and AS* is built according to the results. Five boundary values are rejected, and the remaining ones show the limits of errors in determination (the probability 0.95). The advantage of this method is that it enables one to carry out the exhaustive search of all possible values of AH* (with a given step) and thus to find the global minimum of the sum of error squares.
A. A. STOLOV et
1654
al.
c
A&& 2300
2200
2100
v (cm-')
Fig. 1. IR (a), Raman I, (b) and 4, (c) spectra of pure toluene-d,. RESULTS AND DISCUSSION
We have studied the bands corresponding to asymmetric stretching vibrations of the CD3 group. Fragments of IR and Raman spectra for pure I are given in Fig. 1. Taking into account the depolarization ratios in Raman spectrum, only the bands in the range 2160-2270 cm-’ may be attributed to asymmetric vibrations. The analysis of the fourth derivative of the IR spectrum shows the presence of at least four bands in this range.
2300
2270
2240
2180
2190
2230 v (cm-')
Fig. 2. IR spectra of toluene-d, in nondeuterated toluene fitted by Eqn (8). Circles show the experimental spectra, solid lines-the rebuilt one. (a) T=293 K; (b) T= 163 K.
Orientational diffusion of the toluene-d, methyl group
1655
16
1
‘i
E s
I
I
I
I
100
160
220
280
I
I 160
I 220
I 280
I
100
T (K) Fig. 3. The dependencies 6 upon T for the band 2211 cm-’ of toluene-d, in different solvents: (a) 0, PP; pentane; A, -.-. acetone; +, --- nondeuterated toluene. (b) 0, + , --- dibutyl phthalate; A, -.-. PBD; E-. .- PMMA.
The IR spectrum in the region 2270-2160 cm-’ was resolved into four components having the following form: D(Y) =x
Ad2
#+4(Y-Q)*
+(l--)Aexp
4 In 2 -~(Y-~Q)*
(8)
, >
with A, vo, 6 and x being the variable parameters. In this way there was a good agreement with the experimental spectra (Fig. 2). As the temperature is lowered, approximately the same narrowing of all four components (2240, 2230, 2211 and 2175 cm-‘) is observed, the position of the bands changing slightly (Fig. 2). The relative contribution of the Lorentzian component in Eqn (8) was practically temperature independent and was x = 0.5-0.7. The widths of the bands 2230 and 2170 cm-’ at lowest attainable temperature (77 K) were equal to each other (with accuracy of 1 cm-‘). It enables us to assume the equality of the widths when treating the contours obtained at higher temperatures. Table 1. Orientational relaxation parameters of toluene-d, in solutions
Pentane Toluene Dibutylphthalate Acetone PBD PP PMMA
w
4ib
cw(PSI
&
(290K)
TW
(cm-‘)
(290K)
1.8 2.4 8.5 21.5 2.2 2.15 3.15
0.24 0.58 2.10 0.33 -104 - 10’5 - 1on
138-293 163-293 80-293 183-2% 80-290 77-213 77-295
5.1kl.l 7.3kO.9 12.0+ 1.3 lO.lk3.4 8.8+ 1.8 13.5kO.5 13.4kO.2
tl
Solvent
0.50+0.04
0.72 f 0.06 1.04f0.18 0.79f0.23 0.79kO.12 0.84+0.10 1.4lkO.12
-2.2+0.1 -2.9kO.2 -2.6f0.5 -0.8f0.8 -2.7kO.2 -1.lf0.6 -2.3kO.3
0 0
0.30+0.18 0.71+ 0.32 0.10+0.10 0.58kO.14 0.58kO.08
A. A. STOLOV et al.
1656
Two asymmetric stretching IR bands of the methyl group must be assumed for one conformation of toluene [29]. For &D&D3 these bands were found to occur at one and the same frequency: 2212 cm-’ [30]. In our opinion, the most intense bands 2230 and 2211 cm-’ refer to the asymmetric stretching vibrations of the CD3 group. It is possible that the weak bands at 2240 and 2175 cm-’ correspond to overtones or combination vibrations. The existence of different conformations of I is also possible, having slightly different frequencies of stretching asymmetric vibrations of the CD3 group. Weak bands 2240 and 2175 cm-’ cannot be explained by the admixture of C&15CD2H (according to mass spectroscopy data, the admixtures do not exceed 0.5%; these do not agree with sufficiently large intensities of these bands). The temperature changes of the spectra do not enable us to attribute these bands to the unresolved rotational structure of more intense components and to hot transitions. The temperature dependencies of the band widths for 2230 (and 2211) cm-’ of I in different media are given in Fig. 3. The dependencies are well described by Eqn (3). Optimal values of the parameters of Eqn (3) and characteristics of solutions: dielectric permittivity E and viscosity t7 are given in Table 1. The curves in Fig. 3 correspond to the optimum values of the parameters. The cases AH* = 0 refer to practically linear dependencies 6 =f(T) when, according to Eqn (3) the time of reorientation of the CD, group is due only to the entropy factor. It is difficult to find any correlations between the barrier AH* and the properties of the medium (Table 1). However, the accuracy we achieved enables us to note that ail the values AH* are smaller than 1 kcal mall’. In addition, the absence of considerable dependence of AH* on the viscosity of the medium is noticeable. According to the Debye-Stokes-Einstein theory [31], 6,,=-
3kT 2 ln(2alb) - 1 &r2ctj
a3
’
(9)
where a and b are the lengths of the principal axes of the top. As follows from Eqn (9), the band width must be inversely proportional to 77at constant temperature. Compounds we studied cover the range of viscosity from 10-l to 1Ol5cP. According to the theory, the quantity 6,, must decrease by 16 orders of magnitude when going from penthane to PMMA. It is not observed (cf. Fig. 3 and Table 1). Apparently, the Debye-Stokes-Einstein theory is not applicable to the orientation diffusion of methyl groups. Thus, it is not correct in our case to put the activation barriers of orientational diffusion and viscosity equal to each other, as is done in Refs [24,25]. As far as large viscosity of PMMA and PP is connected with their glassy state, it is of interest to study the influence of glass transition on the dependence of 6 =f(T). It is convenient to use the solutions of I in dibutyl phthalate (glass transition temperature Tg= 173.5 K) and PBD ( Tg= 200 K). As is seen in Fig. 3, the dependencies 6 =f( T) have no peculiarities (steps or inflections) at temperatures Tg. It should be noted that rotational diffusion of nitroxyl radicals (method of spin probes [lo]) is sensitive to glass transition of the matrix: the dependence In r=f(r’) (t is the time of rotational correlation) has an inflection at Tg In our case the absence of inflectin is probably due to the methyl group being smaller in volume than nitroxyl radicals. It should be noted that the dependencies 6 =f( T) for I in PP, PBD and PMMA do not manifest any relaxation transitions (relaxation transitions are not observed in the method of spin probes as well). It is seen for I in PMMA in particular: the relaxation transition at T- 180-200 K [32] observed by various physical methods is not manifested in the dependence 6 = f( T) . Acknow/edgement-The
authors are grateful to S. F.
Mironovfor obtaining the Raman spectrum of I.
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Orientational diffusion of the toluene-d, methyl group [2] [3] [4] [5]
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J. Yarwood, Adu. Molec. Rel. Proc. 5, 375 (1973). J. Yarwood, R. Arndt and G. Doge, Chem. Phys. 25,387 (1977). V. E. Pogorelov, A. I. Lizengvich, I. I. Kondilenko and G. P. Buyan, Usp. Fiz. Nauk 127, 683 (1979). N. N. Kravetz, V. E. Pogorelov, G. I. Salivon, V. N. Sushii and I. B. Estrela-Liopis, Spectroskopiya Nemetallitcheskikh Kristallov (Spectroscopy of Nonmetal Crystals), p. 135. Kiev (1990). (61 A. Heranz, An. Quim. A/Real. Sot. Esp. Quim. 84,327 (1988). [7] J. Yarwood, J. Molec. Liq. 36, 237 (1987). [8] A. Heranz, J. Molec. Liq. 39, 111 (1988). [9] A. Purkayastha, R. Das and K. Kumar, J. Raman Specrrosc. 21, 227 (1990). [lo] A. M. Vasserman and A. L. Kovarskii, Spinoviye Metki i Zondi u Fizikokhimii Polimerov (Spin Labels and Probes in Physical Chemistry of Polymers). Moscow (1986). [ll] H. D. Rudolph, H. Dreizler, A. Jaeschke and P. Wendling, Z. Naturforsch 22A, 940 (1%7). [12] C. M. Pol, P. K. Panja and B. Sibsankar, /. Molec. Struct. 189, 287 (1988). [13] A. V. Rakov, Trudi Fiz. Inst. Akad. Nauk 27, 111 (1964). [14] N. N. Vakhrusheva, A. B. Remizov, A. A. Stolov and A. I. Fishman, Zh. Prikl. Spektr. 51,273 (1989). [15] D. D. Perrin, W. L. F. Armarego and D. R. Pert-in, Purification of Laboratory Chemicals. Pergamon Press, Oxford (1980). [16] K. Tanabe and J. Hiraishi, Spectrochim. Acta 36A, 341 (1980). [17] J. M. Janik, J. A. Janik, A. Migdal-Mikuli and G. Pytasz, Acta Phys. Polonica 4lA, 741 (1971). (181 J. M. Janik, A. Migdal-Mikuli and J. A. Janik, Acta Phys. Polo&a 46A, 299 (1974). [19] R. C. Leech, D. B. Powell and N. Sheppard, Spectrochim. Acta 22, 1931 (1966). [20] A. B. Remizov, N. N. Vakhrusheva, I. S. Pominov and I. Ya. Kuramshin, Opt. Spektr. 46, 184 (1977). [21] A. B. Remizov, N. N. Vakhrusheva and I. S. Pominov, Zh. Prikl. Spektr. 35,299 (1981). [22] F. J. Bartoli and T. A. Litovitz, J. Chem. Phys. 56, 404 (1972). [23] F. J. Bartoli and T. A. Litovitz, J. Chem. Phys. 56, 413 (1972). [24] S. Hashimoto, T. Ohba and S. Ikawa, Chem. Phys. 13863 (1989). [25] A. Sugitiani, S. Ikawa and S. Konaka, Chem. Phys. 142,423 (1990). [26] S. A. Kirillov and I. Ya. Rivelis, Zh. Prikl. Spektr. 19,934 (1973). [27] R. Kubo, Fluctuation, Relaxation and Resonance in Magnetic Systems, p. 23. Edinburgh (1962). [28] W. G. Rothschild, 1. Chem. Phys. 65,455 (1976). [29] A. B. Dempster, D. B. Powell and N. Sheppard, Spectrochim. Acta UIA, 373 (1972). [30] L. M. Sverdlov, M. A. Kovner and E. P. Krainov, Kolebatelniye Spektri Mnogoatomnykh Molekul (Vibrational Spectra of Polyatomic Molecules). Moscow (1970). [31] F. G. Dijkman, Chem. Phys. Left. 57,450 (1978). [32] 0. E. Zgadzai, D. I. Kamalova, A. B. Remizov, A. A. Stolov and A. I. Fishman, Zh. Fiz. Khim. 64,1029 (1990).