Rotational isomeric relaxation in poly(ethylene glycols) studied by acoustic spectroscopy.
1. INTRODUCTIONGlycols are dihydric alcohols that constitute an important class of organic compounds and are used widely in basic and applied research. However, structure of these compounds in the liquid state, the kinetics, and the molecular mechanisms of their restructuring processes caused by heating are practically unknown. Such information is of great value for the development of the liquid state theory, in particular in studies of molecular nature of highly-viscous liquids, in the theory of vitrification, etc.
Bihydric alcohols can serve as model objects in studies of properties of liquids with net-like structure formed by intermolecular hydrogen bonds, as well as in high-molecular analogues of polyethyleneoxides (PEOs). PEO is a thermoplastic polymer which has the formula OH-[(C[H.sub.2]-C[H.sub.2]-O).sub.m]-H, where m is the degree of polymerization. In the literature a polymer of low molecular mass is generally also called poly(ethylene glycol) (PEG).
Acoustic properties of ethylene glycol (and, to a lesser extent, those of poly(ethylene glycols)) have been studied extensively (1-6). Nevertheless, there is currently no clear understanding of the mechanisms of acoustic relaxation in materials. Extant studies have been performed only in limited frequency and temperature ranges.
2. EXPERIMENTAL PROCEDURES
We have conducted measurements of the acoustic properties (velocity of sound propagation (c) and coefficient of attenuation ([Alpha][f.sup.-2]) in poly(ethylene glycols) with molecular masses of 200, 400, and 600 purchased from Merck and designated as PEG-200, PEG-400, and PEG-600, correspondingly, in temperature interval from 278 to 343 K.
Coefficient of sound attenuation ware measured by a pulse method in the frequency interval from 5 to 2500 MHz with 2-5% error. Velocity of sound propagation was determined with the pulse phase method by using a home-made thermoregulated ([+ or -]0.1 [degrees] C) acoustic interferometer. The accuracy of the experimental velocity measurements is better than [+ or -] 0.1%.
The solutions were prepared using ultrapure PEG and twice distilled and deionized water.
3. EXPERIMENTAL RESULTS AND DISCUSSION
Acoustic spectra of PEG-200 at temperatures below 303 K, as well as spectra of PEG-400 and PEG-600 at temperatures above 303 K, comprise two dispersion regions. The frequency dependence of ([Alpha][f.sup.-2]) values is given by (7, 8)
[Mathematical Expression Omitted] (1)
where c is velocity of sound propagation; the frequency [Mathematical Expression Omitted]; [b.sub.i] and [[Tau].sub.i] are relaxation strength and relaxation time for the i-th simple dispersion region, correspondingly, B denotes the high-frequency limit of [Alpha][f.sup.-2] while co is the low-frequency limit of sound velocity [Mathematical Expression Omitted].
Identification of the acoustic spectra has been achieved by iterational approximation approach. Frequency dependence of the ([Alpha][f.sup.-2]) parameter was approximated by an empirical equation accounting for two relaxation times (7, 8):
[Alpha][f.sup.-2] = [A.sub.1] / 1 + [([Omega][[Tau].sub.1]).sup.2] + [A.sub.2] / 1 + [([Omega][[Tau].sub.2]).sup.2] + B (2)
where [A.sub.i] is a low-frequency limit of [Alpha][f.sup.-2] values [Mathematical Expression Omitted].
Values of parameters defining the simple dispersion regions are listed in Table 1. The Table includes also estimated values of sound attenuation determined from the shear viscosity [Alpha][c.sub.1], and maximum sound attenuation per wavelength [Mathematical Expression Omitted] as defined by the following relationships (7, 8)
[Mathematical Expression Omitted] (3)
[Mathematical Expression Omitted] (4)
The values of the shear viscosity [[Eta].sub.s] and density used in the present calculations have been previously reported by us (9).
[TABULAR DATA FOR TABLE 1 OMITTED]
It is seen from the Table 1 that the values of [A.sub.1], [A.sub.2], [b.sub.1], [b.sub.2], and [[Mu].sub.max] decrease monotonously with temperature. Such behavior is characteristic of liquids with acoustic dispersion due to changes of molecular conformation or restructuring processes (7, 8). In order to establish molecular mechanisms which could be responsible for the simple dispersion regions we have subsequently carried out experiments PEG-400. The results show that the position of the low-frequency relaxation region is independent of water content. [[Mu].sub.max] values decrease linearly with increase in the water concentration, while the relaxation frequency [f.sub.1] is independent of the concentration [ILLUSTRATION FOR FIGURE 1 OMITTED]. Such concentration dependencies of [[Mu].sub.max] and [f.sub.1] can only appear as consequences of the rotational isomeric relaxation. By contrast, frequency of the high-frequency region of the acoustic relaxation is dependent on the water content. The frequency shifts to the high-frequency region on increasing water concentration, what is typical for structural relaxation.
Consider now the low-frequency relaxation region. It can be assumed that polyoxyethylene (POE) is a conformational analog of PEG (10, 11).
Using the equivalence principle and assuming the conformation of the repetitive unit defined by two C-C and C-O bonds to be the same along the chain, we find that potential of internal rotation about any bond can be obtained by adding up of three-fold potential and superimposing interaction effects due to interactions of the carbon and oxygen atoms with hydrogen atoms of methylene groups and oxygen atoms. The most important parameters in the present case comprise coordinates of five minima: one of trans-trans (TT) conformation, two of trans-gauche (TG) conformations ([Phi] = [+ or -] 120 [degrees]), and two of gauche-gauche (GG) conformations ([Phi] = [+ or -] 240 [degrees]). Conformational transitions in the three-state model are described by the following system of relations:
[Mathematical Expression Omitted] (5)
[Mathematical Expression Omitted] (6)
[Mathematical Expression Omitted] (7)
where each [k.sub.ij] is the rate constants of a given spontaneous reaction.
In accordance with the above, there should be two independent relaxation processes in the system, namely two normal reactions with degrees of completeness [[Zeta].sub.1] and [[Zeta].sub.2] defined as linear combinations of the degrees of completeness [[Xi].sub.1] and [[Xi].sub.2] respectively of the natural reactions 5 and 6 (8).
The low-frequency region of the acoustic relaxation can be described within experimental error limits by an equation with single relaxation time. We can further assume, in accordance with theory of relaxation processes, that the region under examination is created by one of the reactions 5, 6, or 7.
Isobaric-isoentropic times of relaxation for normal reactions, as defined by the acoustic spectra (Eq 1), can be evaluated as solution of the problem for the following eigenvalues (8)
[Mathematical Expression Omitted] (8)
Proper vectors [Mathematical Expression Omitted] form columns of linear transformation matrix X from the degrees of completeness [Xi] = X[Zeta] of the normal reactions [Xi] into degrees of completeness [Zeta] of the natural reactions 5 and 6. L is the diagonal matrix which consist of the rate constants of the natural reactions 5 and 6, and P is a positively defined square matrix of elements representing second derivatives of the Gibbs function with respect to the degrees of completeness of the natural reactions 5 and 6.
The LP matrix is of the form
[Mathematical Expression Omitted]. (9)
Here [c.sub.1], [c.sub.2] and [c.sub.3] represent respectively concentration of the TT, TG, and GG conformers.
Taking into account relationship 9, Eq 8 may be rewritten as
[Mathematical Expression Omitted] (10)
Thus, the problem is reduced to the determination of eigenvalues for the matrix LP, the determinant of which is given by
[Mathematical Expression Omitted] (11)
By solving Eq 11 we obtain
[Mathematical Expression Omitted] (12)
Here [a.sub.11] = [k.sub.12] + [k.sub.21] and [a.sub.12] = [k.sub.21]. With [a.sub.22] = [k.sub.23] + [k.sub.32] we have
[Beta] = 4([a.sub.11][a.sub.22] - [a.sub.12][a.sub.21]) / [([a.sub.11] + [a.sub.22]).sup.2]. (13)
[TABULAR DATA FOR TABLE 2 OMITTED]
Since [a.sub.11] [greater than] [a.sub.12], and [a.sub.22] [greater than] [a.sub.21], [Beta] is always positive. As discussed by Papulov and Khalatur (11), in the general case [[Tau].sub.ps, 1] and [[Tau].sub.ps, 2] cannot be related each to one of the reactions 5 and 6. The relationship between these reactions is characterized by elements [a.sub.12] and [a.sub.21] of the matrix LP. In the present case [a.sub.12] [not equal to] [a.sub.21], [a.sub.12] [not equal to] 0, [a.sub.21] [not equal to] 0. Consequently, the elements are interrelated.
Calculations of the conformers concentration were performed using the following relationships in the Gibbs function changes [Delta][G.sup.0] and entropy changes [Delta][S.sup.0]:
[Mathematical Expression Omitted], (14)
[Mathematical Expression Omitted], (15)
[Mathematical Expression Omitted], (16)
Values of [Delta][S.sup.0] were calculated from the following equation (11):
[Delta][S.sup.0] = R ln q + R ln [Sigma], (17)
where q is the statistical weight of the conformer and [Sigma] is the order of symmetry.
The difference in enthalpy [Delta][H.sup.0] of the conformers was determined from the experimentally determined values of the relaxation part of the heat capacity, as well as from the results of Papulov and Khalatur (11). The resulting values are 17.3 kJ/mol for [Mathematical Expression Omitted] and 5.8 kJ/mol for [Mathematical Expression Omitted]. The values of [Delta][H.sup.0] and the respective conformers concentrations are listed in Table 2. We have assumed in the calculations of the conformers concentrations that the volume effects in the reactions 5-7 are equal to zero. Since relaxation frequencies of the rotational isomeric transformations differ from those of the structural relaxation by more than an order of magnitude, they exert no influence on one another.
Basing on analysis of the experimental data available for the rotational barriers and that of the Stewart models, evaluation of relaxation rates ratio was performed. It has shown that, in the first approximation, one can assume that [k.sub.21] [approximately equal to] [k.sub.32]. In the present case (see Eq 12) for the temperature range studied we have [T.sub.2]/[[Tau].sub.1] [approximately equal to] 3, so that it is impossible to distinguish between the relaxation regions.
By assuming that the low-frequency region of the dispersion observed is brought about by reactions 5 and 6, we obtain
[b.sub.exp][[Tau].sub.exp] = [b.sub.1][[Tau].sub.1] + [b.sub.2][[Tau].sub.2]. (18)
Using the experimental values of the relaxation strengths [b.sub.exp], relaxation times and [[Tau].sub.2]/[[Tau].sub.1] ratio, relaxation strengths can be defined (8) as
[Mathematical Expression Omitted]. (19)
Here [Gamma] denotes ratio of beat capacities at constant pressure [Mathematical Expression Omitted] to that at constant volume [Mathematical Expression Omitted], and [Mathematical Expression Omitted] is the relaxing part of heat capacity.
Contribution of the normal reactions 5 and 6 to the dispersion of [Alpha][f.sup.2] value is defined by relationship (8):
[Mathematical Expression Omitted]. (20)
Results of calculations of the [b.sub.i], [[Tau].sub.i] and [Delta]([Alpha][f.sup.-2]) values are listed in Table 2. It follows from the data listed that main contribution to the sound attenuation caused by rotational isomeric relaxation comes from reaction 5.
4. CONCLUSIONS
Acoustic spectra of poly(ethylene glycols) showed that the low-frequency dispersion region is caused by conformational restructuring processes in PEG molecules. The main contribution to the sound attenuation was shown to be caused by rotational isomeric relaxation of reaction trans-transtrans-gauche. Thermodynamical and kinetic parameters for the low-frequency relaxation region are reported.
REFERENCES
1. M. I. Shakhparonov, P. K. Khabyboulaev, K. Parpiev, and V. V. Levin, Vestnik Moskovskogo Gosudarstvennogo Universiteta (Bulletin of Moscow State University). 6, 633 (1972).
2. L. B. Verblian, V. S. Sperkach, and M. I. Shakhparonov, Akust Zhurn, 3, 441 (1973).
3. Yu. S. Manucharov, S. A. Manucharova, R. K. Rakhmonov, and V. A. Solovev, Vysokomol. Soedin, A33, 8, 597 (1991).
4. M. P. Janelli, S. Magazu, and G Maisano, Physica Scripta, 50, 215 (1994).
5. M. P. Janelli, S. Magazu, and G. Maisano, J. Mol. Struct., 322, 337 (1994).
6. V. Cruppi, M. P. Janelli, S. Magazu, Nuovo Cimento, 15D, 7, 809 (1994).
7. I. G. Mikhailov, V. A. Solovev and Yu. P. Syrnikov, Foundations of Molecular Acoustics (in Russian), Nauka, Moscow (1964).
8. M. I. Shakhparonov, Mechanisms of Fast Processes in Liquids (in Russian), Vysshaya Shkola, Moscow (1980).
9. V. S. Sperkach and A. L. Stribulevich, Ukr. Fiz. Zhurn, 9, 945 (1995).
10. Yu. S. Lipatov, V. V. Shylov, Yu. P. Gomza, and N. E. Krugliak, Roentgenographycal Methods of Investigations of Polymer Systems (in Russian), Naukova dumka, Kyiv, Ukraine (1982).
11. Yu. T. Papulov and P. G. Khalatur, Calculations of Conformations (in Russian). Kalinin, Kalininskiy Gosudarstvenniy Universitet (Kalinin State University) 1980.
 Printer friendly
 Cite/link
 Email
 Feedback
| |
| Title Annotation: | 5th International Conference on Polymer Characterization |
|---|---|
| Author: | Striboulevich, Anatoly; Sperkach, Volodymyr; Sperkach, Yaroslav |
| Publication: | Polymer Engineering and Science |
| Date: | Mar 1, 1999 |
| Words: | 2114 |
| Previous Article: | Brittle to ductile: fracture toughness mapping on controlled epoxy networks. |
| Next Article: | Controlled release PVC membranes: influence of phthalate plasticizers on their tensile properties and performance. |
| Topics: | |