1610
GORDON G. HAMMES AND THOMAS B. LEWIS
Ultrasonic Absorption in Aqueous Polyethylene Glycol Solutions1
by Gordon G. Hammes and Thomas B. Lewis Department of Chemistry, Cornell University, Ithaca, New York, and Department of Chemistry and Research Laboratory of Etectronics, Massachusetts Institute of Technology, C a m b r a e , Massachusetts (Received December 9,1966)
The ultrasonic absorption and velocity in aqueous solutions of polyethylene glycol of molecular weights 20,000 and 7500 have been measured over the frequency range 10 to 185 Mc/sec. A single relaxation process is observed over the concentration, temperature, and frequency range investigated. The high-frequency limiting value of the absorption always exceeds that of water, which suggests that the water structure is altered owing to the presence of polymer and/or further relaxation processes occur at higher frequencies than employed in this investigation. The relaxation times determined from the data are essentially independent of concentration, temperature, and molecular weight; the maximum of the absorption per wavelength is approximately proportional to the polymer concentration. Viscosity measurements on the polymer solutions and use of the Zimm theory of viscous relaxation indicates that viscous relaxation is not being observed. The relaxation process is attributed to a perturbation of the hydrogen-bonding equilibrium between polymer and solvent. Minimum volume changes of approximately k0.6 ml/ mole of monomer are associated with this equilibrium. The general use of ultrasonic absorption measurements as a probe of microscopic solvent structure is considered.
Introduction Ultrasonic attenuation measurements in poly-Lglutamic acid (PGA) solutions have been recently reported.2 The observed chemical relaxation was attributed primarily to solvent-polymer interactions, that is, to perturbation of an equilibrium between solvent molecules bound to the polymer and the bulk solvent. Since PGA is a quite complex polymer, such an interpretation is difficult to make with certainty, and a simpler polymer, polyethylene glycol, has been selected for further study. Only three sources of ultrasonic relaxation are possible in aqueous polyethylene glycol solutions: macromolecule-macromolecule interactions, solvent-polymer interactions, and viscosity. These three processes can be distinguished experimentally, and the results obtained indicate solvent-polymer interactions are responsible for the observed ultrasonic relaxation. The use of ultrasonic attenuation measurements as a probe of microscopic solvent structure in the neighborhood of solutes is considered. Experimental Section Polyethylene glycol, E-6000 (E6) of Lot V-75 and The Journal of Physical ChemGtry
E20,000 (E20) of Lot A200, with average molecular weights of 7500 and 20,000 respectively, were obtained from the Dow Chemical Co., Midland, Mich. Both polymers are characterized by a sharply peaked molecular weight distribution. At the temperatures used in this work, the bulk polymers are highly watersoluble solids. Ultrasonic measurements were made on 1.98 and 1.20 m (moles of monomer/1000 g of solvent) solutions at 10 and 25". All solutions were prepared with doubly distilled water. Calibrated CannonFenske viscometers were used to measure the solution viscosities. The absorption and velocity measurements were obtained with the ultrasonic pulse system previously describede2 A 2-RiIc/sec X-cut quartz transducer was used for the measurements between 10 and 42 Mc/sec, while two 5-Mc/sec X-cut quartz crystals were used in the frequency range 35 to 185 Mc/sec. The procedure (1) This work was supported in part by the Joint Services Electronics Program under Contract DA 36-039-AMC-O320O(E) and in part by grants from the National Institutes of Health (GM07803 and 13292). (2) J. J. Burke, G. 0 . Hammes, and T. B. Lewis, J. Chem. Phys., 42, 3520 (1965).
ULTRASONIC ABSORPTION IN AQUEOUS POLYETHYLENE GLYCOL SOLUTIONS
for determining the amplitude absorption coefficients and the ultrasonic velocities has been described in detail e l ~ e w h e r e . ~The , ~ absorption coefficients were reproducible to within j=2%, with the data at low frequencies being somewhat less accurate owing to the decreased attenuation of the solutions. The measured velocities were reproducible to within 0.5%. The instrument was checked for absolute accuracy a t periodic intervals using water and the accepted literature values for the absorption coefficient4and velocity.6 These results were always within the limits of the quoted reproducibility. The temperature was maintained to ZtO.05" with a Bronwill thermostating unit and a Whirlpool thermoelectric immersion cooler. Results and Treatment of Data Ultrasonic measurements of the pressure amplitude absorption coefficient, a, and the velocity of propagation, v, were obtained for the two molecular weights of the poly mer at two concentrations and temperatures. The data are presented in Figures 1 and 2 in plots of a / f 2 us. f, where f is the frequency. If only a single relaxation process is being observed in the frequency range investigated8
1611
'Ot
ob
I
I
I
5
IO
20
I
I
I
I 1 1 1 1
I
70 100
40
I
200
f (Mclsrc)
Figure 1. Ultrasonic absorption of aqueous solutions of polyethylene glycol of molecular weight 7500 as a function Best-fit single-relaxation of frequency a t 10' ( 0 )and 25' (0). curves are indicated by the solid lines for the 1.98 m solutions and by dashed lines for the 1.20 m solutions.
AT
= 1
+ (wr)Z + B
where A and B are amplitude parameters, r is the characteristic relaxation time, and w is equal to 27rf. Very often when chemical relaxation effects are observed B is equal to the value of a / f z of the pure solvent; however, in the polyethylene glycol solutions this constant always exceeded the value characteristic of the pure solvent. For an analysis of the results, a useful procedure is to consider the absorption per wave length, p = 2CYRX, where X is the wavelength and (YR is equal to (cy/? B)?. This quantity can be represented by 11 =
211,
wr
1
+
(wT)z
where pmis equal to Av/2a. The data can be characterized by the three independent constants, B, pm, and r . Values of pm and r are obtained from plots of log p us. log f, which are symmetrical about f = 1/27rr. A typical plot of the data is presented in Figure 3 along with the corresponding theoretical curve. In practice, the three constants are varied to obtain a best fit of the data to a single relaxation curve. In all cases assumption of a single relaxation process is sufficient to characterize the data. The values of pm/co, B, and r obtained by this procedure, where co is the polymer concentration in moles of
lot I
5
I
IO
I
I
I I 1 1 1 1
I
20 40 f (Mc/src)
70 Do
I
I
200
I
Figure 2. Ultrasonic absorption of aqueous solutions of polyethylene glycol of molecular weight 20,000 as a function of frequency a t 10" ( 0 )and 25" (0).Best-fit single-relaxation curves are indicated for the 1.98 m solutions by the solid lines, and for the 1.20 m solutions by the dashed lines.
monomer/1000 g of solvent, are listed in Table I, together with the measured ultrasonic velocities. The ~
~
~~~~~~
(3) T. B. Lewis, "Relaxation Spectra in Polymer Solutions," Ph.D. Thesis, Massachusetts Institute of Technology, 1965. (4) J. H.Pinkerton, Nature, 160, 128 (1947). (5) M. Greenspan and C. E. Tschiegg, J. Res. Natl. Bur. Std., 59, 249 (1957). (6) K. F. Herefeld and T. A. Litovitz, "Absorption and Dispersion of Ultrasonic Waves," Academic Press Inc., New York, N. Y., 1959.
Volume 70,Number 6 May 1966
1612
GORDON G. HAMMES AND THOMAS B. LEWIS
Table I1 : Viscosities of Polyethylene Glycol Solutions
tOMc/uc)
Figure 3. The absorption per wavelength of 1.20 rn aqueous solution of polyethylene glycol, molecular weight 20,000, vs. frequency at 10'. The single-relaxation curve which best fits the data is indicated. Error brackets correspond to a f 2'3, variation of the measured values of a / j 2at each frequency.
estimated uncertainties in T are flo%, in PJCO f15%, and in B =k3Y0. Theoretical curves calculated with these parameters and eq 1 are included in Figures 1 and 2. Table I : Ult,rasonic Parameters eo,
T,
m
eo, m-1
IOL'B, seca/cm
io^, seo
10:r-,L" sec
cm/sec
3.1 1.7 3.1 1.7
1.48 1.53 1.51 1.54
10-5~,
E6 1.20 1.20 1.98 1.98
IO 25 10 25
3.0 2.3 2.9 2.7
39.8 24.1 43.2 25.8
6.9 5.5 6.4 4.7
1.20 1.20 1.98 1.98
10 25 10 25
2.9 2.3 3.4 2.9
E20 40.1 24.1 42.6 26.0
7.6 5.7 5.9 4.5
18 10 18 10
1.48 1.52 1.50 1.54
Calculated from the theory of Zimm.'
Viscosities of the polyethylene glycol solutions were measured a t five concentrations for both molecular weights a t both temperatures. The intrinsic viscosities, [ q ] , were determined by an extrapolation of (q/qHI0 - l)/C' and In (?/?H,o)/C' to zero concentrations. Here is the solution viscosity, qH,O the viscosity of water, and C' the concentration in grams per deciliter. A summary of the viscosity results is given in Table 11.
Discussion In all cases the absorption data can be ascribed to a single relaxation process. A consideration of the variations of the relaxation time, 7 , and the maximum of the absorption per wavelength, pm, can provide some insight into the nature of the process The Journal of P h & d
Chemietry
Polymer
'C
1.98
1.20
0.46
0.23
0.11
dl/g
E6 E6 E20 E20
10 25 10 25
5.43 3.40 11.2 6.88
3.42 2.19 5.80 3.62
1.96 1.30 2.60 1.68
1.62 1.09 1.89 1.25
1.46 0.98 1.58 1.06
0.22 0.19 0.39 0.34
T,
--c-
171,
occurring. The relaxation time is almost constant for the different conditions of molecular weight, concentration, and temperature. However, a slight trend to shorter times occurs as the temperature and concentration are increased; unfortunately, the precision of the measurements is not sufficient to establish these trends with certitude. The maximum of the absorption per wavelength divided by the monomer concentration, pLm/cO,is also roughly constant within the experimental uncertainties. The concentration and temperature ranges investigated were limited by the fact that a t lower concentrations and higher temperatures the amplitude of the relaxation process was too small to measure with precision, while at higher concentrations the polymer begins to influence the bulk solution properties and the variation of activity coefficients with concentration (which is unknown) is of importance in interpreting the data. If the observed relaxation process is primarily due to viscous effects, the relaxation times should be comparable to those predicted by the theory of Zimm7 for the motion of a flexible polymer molecule in solution. This theory predicts a spectrum of relaxation times, although the amplitude associated with the longest relaxation tjme is expected to be much greater than that associated with shorter times. Values of the longest relaxation time calculated according to Zimm7 are included in Table I; the theoretical relaxation times are more than an order of magnitude longer than those observed. Moreover, if the observed process were due to a spectrum of viscosity relaxation times, the relaxation times should depend markedly on molecular weight. This is clearly inconsistent with the observed experimental results. A final possibility is that a "local viscosity" effect is being observed which would be independent of molecular weight. In this case, the same relaxation process should be observed in dielectric relaxation. Dielectric relaxation experiments have been carried out on solutions of polyethylene glycol in benzene and water.8j9 (7) B. H. Zimm, J. Chem. Phys., 24, 269 (1956).
ULTRASONIC ABSORPTION IN AQUEOUS POLYETHYLENE GLYCOL SOLUTIONS
Relaxation has not been detected in the frequency range under consideration here although a dielectric relaxation effect attributed to orientation of short chain segments ("local viscosity" relaxation) has been observed in benzene at much shorter times (-lo-" see). I n the case of water as the solvent, the observed dielectric relaxation was attributed primarily to water, rather than to polymer. The "local viscosity" relaxation is a possible cause for the constant B being higher than that found for the pure solvent. That is, CY/$; would presumably decrease further a t very high frequencies due to this relaxation. Alternatively, the presence of polymer might change the relaxation characteristics of water itself, causing the observed increase in B.* Polymer-polymer interactions also are probably not the source of the observed effect. A more distinct concentration dependence of the relaxation parameters would be expected if this were the case: the relaxation times would decrease markedly with increasing concentration and the maximum of the absorption per wave length, kLmlwould not be simply proportional to the polymer concentration. Moreover, some dependence of y on molecular weight would be expected. The primary process observed here most likely corresponds to solvent-polymer interactions. The perturbation by the sound wave would have the effect of shifting the equilibrium between water molecules bound to the polyethylene glycol and water in the bulk solvent. This would involve the breakdown of the water structure around the polymer and solvation of the polyethylene glycol by the water and is probably related to hydrogen-bonding interactions between the oxygens of the polymer and the hydrogens of the water. If this chemical process were rate limiting for the "local viscosity" dielectric relaxation, the dielectric and ultrasonic relaxation times would be identical. If the ultrasonic relaxation is due to a chemical process] the maximum of the absorption per wavelength can be written :do
where AVO and AH" are the standard volume and changes associated with the process' p is the solution density, /3 is the thermal expansion Coefficient of the SOlUtiOn, c, iS the COnStant-preSSUre T specific heat of the solution, R is the gas is the absolute temperature, co is the solute concentration, and is a function of the equilibrium constant (and concentrations in general). For the process A S B, Eigen and de Maeyerloshow that the function r has a maximum value of about 0.25. Minimumvalues of the
1613
bracketed quantity in eq 3 can be calculated with eq 3 and r equal to 0.25. The results, which are essentially independent of concentration, are summarized in Table 111. Very often for aqueous solutions, the value of p is sufficiently small and AVO sufficiently large (10 to 20 ml/mole) so that the effect of the enthalpy term
Table III : Minimum Values of f[AV (PEG)
*
1.20 1.20 1.98 1.98
- (p/pcp)AH]
T," C
E5
E20
10 25 10 25
0.6 0.6 0.6 0.6
0.6 0.6 0.7 0.6
'
a Milliliters per mole of monomer. Polyethylene glycol concentration in moles per 1000 g of solvent.
can be neglected. However, in the present case, no final conclusion concerning the magnitude of the volume and/or enthalpy change associated with the relaxation process can be reached, except that both are probably very small. The volume change associated with the solvent-polymer interactions can be roughly identified with the volume change which occurs on mixing polymer and solvent. Thermodynamic mixing properties for aqueous solutions of polyethylene glycol at 65" have been reported" and the results indicate that the volume change associated with mixing is approximately -1 ml/mole of monomer, which is of the same order of magnitude as the volumes reported in Table
___
111.
The ultrasonic relaxation process observed in PGA solutions exhibited a distribution of relaxation times, but this relaxation was also attributed primarily to polymer-solvent interactions.' The results reported here tend to confirm this interpretation. The distribution of relaxation times in the case of PGA solutions is probably due to the presence of several different solvating sites and/or to a superposition of other relaxation processes which can occur in PGA solutions (cy. ref 2 for a more comprehensive discussion of this point). Recently, Zana" made acoustic studies of polymers (8) M. Davies, G. Williams, and G. D. Loveluck, 2. Elektrochem., 64,575 (1960). (9) W. H. Stockmayer, H. Yu, and J. E. Davis, Abstracts, 145th National Meeting of the American Chemical Society, New York, N . Y . ,Sept 1963, p 7U. M. Eigen and de Maeyer in of Organic Chemistry," Vol. 8, Part 2, S. L. Frieas, E. S. Lewis, A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y . , 1963. (11) G. N . Malcolm and J. S. Rowlinson, Trans. Faraday Soc., 53, 921 (1957). (12) R. Zana, J. Chim. Phys., 62,612 (1965).
Volume 70,Number 6 May 1966
GORDON G. HAMMES AND THOMAS B. LEWIS
1614
in organic solvents. Many of the results he reported cannot be explained in terms of a simple relaxation process, but others strongly suggest polymer-solvent interactions are being observed. This type of interaction is certainly not limited to macromolecules. Ultrasonic relaxation effects have been observed in alcohol-water solutions with data obtained over a limited frequency range.l3,l4 This relaxation behavior can also be attributed to a perturbation of intermolecular hydrogen bond equilibria. More definitive information about solvent-solute interactions, e.g., local solvent structure and rates of elementary processes, can be found with appropriate small molecule solutes by use of the ultrasonic r n e t h ~ d . ~ The ~ J ~ study of
The J o u r d of Physical Chemistry
solute-solvent interactions with ultrasonic attenuation measurements on a more extensive scale may prove to to be of general utility in the investigation of microscopic solvent structure. Further experiments with other systems are currently in progress.
Acknowledgements. The authors wish to thank Mr. Michael H. Auerbach for carrying out some preliminary experiments on the polyethylene glycol-water system. (13) L. R. 0.Storey, Proc. Phys. SOC.(London), B65, 943 (1952). (14) D.Sette, Nuovo Cimento, 1, 800 (1955). (15) G.G.Hammes and H. 0. Spivey, J. Am. Chem. SOC.,8 8 , 1621 (1966). (16) G. G. Hammes and W. Knoohe, in preparation.
