Article pubs.acs.org/JPCB
A Comparative Ultrasonic Relaxation Study of Lower Vicinal and Terminal Alkanediols at 298.15 K in Relation to Their Molecular Structure and Hydrogen Bonding Edward Zorębski* and Michał Zorębski Institute of Chemistry, Silesian University, Szkolna 9, 40-006 Katowice, Poland S Supporting Information *
ABSTRACT: Ultrasonic relaxation spectra were determined for lower vicinal and terminal alkanediols at ambient pressure and a temperature of 298.15 K. The ultrasound absorption measurements were made by means of the standard pulse technique for 1,2ethanediol, 1,2-propanediol, 1,3-propanediol, 1,2-butanediol, 1,4-butanediol, 2,3-butanediol, and 1,5-pentanediol within the frequency range of 5−300 or 10−300 MHz. Relaxation processes were observed for all compounds except 1,2-ethanediol. The relaxation regions were dependent on both the carbon chain length and the position of hydroxyl groups. In addition, the terminal diols showed lower absorption than the adequate vicinal diols did. The results are discussed in terms of molecular structure and molecular interactions, as well as compared with the behavior of adequate lower 1alkanols. A comparison with classical absorption is also made. The results are discussed in term of shear viscosity relaxation.
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previously,2 three reasons for this seem dominant: (i) an essentially poorer uncertainty than with the measurement uncertainty of the speed of sound, (ii) more complicated measurements (apparatus and procedure), and (iii) practically, there is a lack of commercially available equipment available at a moderate price. It also appears that the publications are scattered across a variety of sources that are difficult to acquire. Moreover, the data that are available are old and often unavailable in English. A good example is 1,2-ethanediol. As has been reported recently,2 for this diol in closed conditions (at room temperature), ultrasound absorption values from (120 to 386) × 10−15 m−1·s2 are reported. This prompted us to investigate the ultrasound absorption in the megahertz range for lower alkanediols, which are liquids that are capable of forming both inter- and intramolecular hydrogen bonds. In this type of liquid, hydrogen bonds constitute the most important interactions in determining the structural properties and microdynamics.3 Simultaneously, such interactions, which are generally dependent on the carbon chain, number, and position of the hydroxyl groups, are prominent forces in biological materials. For such materials, alkanediols can be treated as simple bifunctional model substances (model structural units with two donor and two acceptor functions). An additional reason is that such investigations are connected with pressure−temperature studies of thermodynamic properties by means of the acoustic method.4 This is because such
INTRODUCTION Knowledge of the liquid structure, molecular dynamics, and the kinetics of elementary processes occurring in liquid systems is very important for a variety of reasons. For example, it is important for a fundamental understanding of many phenomena not only in chemistry, physics, physical chemistry, and biochemistry but also for chemical engineering and process control. From the many experimental techniques that have been applied to study the mentioned properties of liquids, the utility of acoustic methods is difficult to overestimate. Since ultrasonic waves are coupled to basic thermodynamic parameters and to transport properties, they constitute a versatile and almost universal research tool for investigation of a large variety of diverse molecular processes at an almost ideal thermal equilibrium. As is known, propagation of ultrasonic waves in liquids induces periodic perturbations in pressure and temperature. Such perturbations can shift the equilibriums that exist in liquids. Consequently, the energy dissipation results in characteristic spectra of ultrasound absorption and velocity dispersion. An analysis of such spectra yields valuable information about thermodynamic and kinetic parameters of the particular system, which is often difficult to obtain through other methods. Thus, ultrasound absorption can be a significant and integral source of information on the molecular structure of the liquid, as well as on the physical and the chemical processes occurring in the liquid phase. This is especially true when measurements are performed over a broad frequency range.1 However, measurements of ultrasound absorption are rather rare (a concise review can be found in ref 1), especially in comparison with measurements of speed of sound. As stated © 2014 American Chemical Society
Received: August 22, 2013 Revised: May 7, 2014 Published: May 7, 2014 5934
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sample. Exactly, the α values are obtained from the slope of the straight line ln I(li)/I(li+1) = −α(li − li+1), where I(li) and I(li+1) are the amplitudes of the received pulses measured for the distances li and li+1, respectively. Thus, this method enables absolute measurements of the absorption coefficient α by the use of the amplitude of the first transmitted pulse and variation of the sample thickness. This is advantageous over cavity resonator methods, where calibration measurements are needed due to instrumental losses. Since details concerning construction of the measuring set and the measurements procedure have been reported previously,11,12 we only present a brief description here. In the present measurements, the available frequencies cover the range from 5 or 10 to 300 MHz. The measurements within this frequency range were executed for chosen discrete frequencies by the use of two or three sets of broadband ultrasonic heads (LiNbO3 transducers with a diameter of 16 mm connected with waveguides (fused quartz) through a thin metal layer) at 298.15 K and at atmospheric pressure. The received pulses were analyzed and recorded by means of an analogue LeCroy LA314 oscilloscope. The distances li were measured with a resolution of ±0.1 μm using a vertical length meter from Zeiss. The propagation distance of an ultrasonic pulse passing through the liquid (sample thickness) was varied by moving the receiving head. In each case, at least six measurements at different sample thicknesses were made and the absorption coefficient α was obtained from the above-mentioned slope of the straight line. The temperature of the sample was maintained with an uncertainty ±0.05 K. During the experiment, the glass measuring cell (a total volume ca. 20 cm3) was filled with argon to avoid contact of the sample with air (the majority of alkanediols are hygroscopic). The uncertainty of the αf−2 data is estimated to be ±2.5%. Some supplementary speed of sound measurements (T = 298.15 K, atmospheric pressure) needed for the calculations were made by means of a pulse-echo-overlap method that is routinely used in our laboratory.4 Our own measuring set (OPE-4F, two transducers per measuring cell) operated at a fixed frequency of 2 MHz. The uncertainty of the measured speeds of sound was estimated to be ±0.5 m·s−1.
studies must be carried out outside of the relaxation regions. Moreover, a priori knowledge of sound absorption is necessary in some methods that are used for the determination of the acoustic nonlinearity parameter,5−7 which is a basic measure of the nonlinearity of a medium. It should also be noted that lower alkanediols are compounds that are increasingly used in many areas, especially propanediols and butanediols, because, unlike 1,2-ethanediol, they are considerably less toxic (e.g., according to the FDA, 1,2propanediol is classified as GRAS [Generally Recognized as Safe]). Propane and butanediols are compounds that have numerous applications in the biochemical field (e.g., cryobiology, protein-stabilizing agents)8,9 and in industry (e.g., food, tobacco, cosmetics).10 In this work, a study of the ultrasound absorption and related properties at 298.15 K for a few lower alkanediols (namely, 1,2ethanediol, 1,2-propanediol, 1,3-propanediol, 1,2-butanediol, 1,4-butanediol, 2,3-butanediol, and 1,5-pentanediol) is presented. From the measurement results, the ultrasonic relaxation spectra, the difference between the experimental absorption and the classical absorption, the relaxation strength, and the ratio of volume and shear viscosity are calculated and analyzed in terms of differences between vicinal and terminal (α,ω-) alkanediols. The results are compared with the behavior of lower 1-alkanols with the same carbon chain length (i.e., ethanol, 1-propanol, 1butanol, 1-pentanol). To this end, the ultrasound absorption measurements in the same experimental conditions were made, or in the case of ethanol,12 recently reported data were used.
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EXPERIMENTAL SECTION Apart from degassing by means of ultrasound (ultrasonic cleaner), the chemicals were used without further purification. Provenance, purity, and the acronyms for the alkanediols studied are summarized in Table 1. Table 1. Provenance, Purity, Acronyms, and Water Content for the Alkanediols Studied chemical name 1,2ethanediol 1,2propanediol 1,3propanediol 1,2butanediol 1,4butanediol 2,3butanediola 1,5pentanediol
acronym
CAS
1,2ED
10721-1 5755-6 50463-2 58403-2 11063-4 51385-9 11129-5
1,2PrD 1,3PrD 1,2BD 1,4BD 2,3BD 1,5PD
supplier
mass fraction purity
water content (mass fraction)
Fluka
>0.995
0.995
0.990
0.99
0.995
2.6 × 10−4b
Fluka
>0.990
6.6 × 10−4c
Fluka
≥0.97
1.3 × 10−4c
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MEASUREMENT RESULTS AND CALCULATIONS For the alkanediols studied, the ultrasound absorption coefficients of α per squared frequency f (i.e., the quotients αf −2) are plotted against log f in Figures 1 and 2 (excluding 1,2ED, and the raw data are summarized in Tables S1 and S2 in the Supporting Information). It appears that, within the investigated frequency range, the dependence of the quotient αf−2 on frequency is different for the diols studied. The details are discussed below and in the next section. Generally, the attenuation of an ultrasound wave in liquids is usually composed of two contributions according to the relation
a
Mixture of the meso form and racemate of the d,l-isomers. Determined by the Karl Fisher method and reported in ref 4. c Determined in this work by the Karl Fisher method. b
αf −2 = (αf −2 )cl + (αf −2 )ex
(1)
where the classical part is denoted by the subscript “cl” and the excessive part is denoted by the subscript “ex”. To represent the ultrasonic absorption data for 1,3PrD, 1,2PrD, 1,4BD, 1,2BD, and 1,5PD, we applied the following function
The ultrasound absorption measurements were carried out using a measuring set designed and constructed in our laboratory. The measuring set is based on the standard pulse method with a variable path length. In this method, the dependence of the amplitude of the first transmitted pulse is recorded as a function of the propagation distance in the
αf −2 = A(1 + (f /frel )2 )−1 + B 5935
(2)
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(2πf rel)−1) and the relaxation strengths r are also given. The relaxation strength is calculated from r = Ac/(2π 2τrel)
(3)
where c is the speed of sound. In the case of 2,3BD, to represent the ultrasonic absorption data, we applied the function with two relaxation frequencies αf −2 = A1(1 + (f /f1,rel )2 )−1 + A 2 (1 + (f /f2,rel )2 )−1 + B (4)
and the obtained values of A1, A2, f1,rel, f 2,rel, and B, as well as relaxation strengths (calculated according to eq 3), are summarized in Table 3. Figure 1. Ultrasound absorption coefficient per squared frequency αf −2 plotted against log f at T = 298.15 K for terminal alkanediols: (○) 1,2ED, (▲) 1,3PrD, (■) 1,4BD, and (◆) 1,5PD. The dashed lines (sequence as above) indicate the classic absorption contributions according to eq 5.
Table 3. Parameters of the Relaxation Equation (Eq 4) Together with Standard Mean Deviation δa and Relaxation Strength r for the 2,3BD at the Temperature 298.15 K
a
1015B/ m−1·s2
1015A1/ m−1·s2
f1,rel/ MHz
1015A2/ m−1·s2
f 2,rel/ MHz
1015δ/ m−1·s2
104r2
102r1
737.8
891.1
217.6
31.2
4.9
12
0.72
9.1
See footnote in Table 2.
Since according to Stokes, the dissipative part in the Navier− Stokes formula is determined only by static shear viscosity (2πf → 0), a classical absorption coefficient αcl can be calculated from the formula αcl = 8π 2ηs(3ρc 3)−1f 2
where ηs is the static shear viscosity (Newtonian) and ρ is the density. Kirchhoff has shown that a finite coefficient of heat conduction will lead to additional energy dissipation αK. However, because for most liquids (excluding liquid metals) αK is very small in comparison to the values calculated from eq 5, αK can be neglected. Thus, the values of αcl f −2 are calculated according to a rearranged eq 5, and the obtained values of αcl f −2 are summarized in Table 4. For the calculations, the values of
Figure 2. Ultrasound absorption coefficient per squared frequency αf −2 plotted against log f at T = 298.15 K for vicinal alkanediols: (○) 1,2ED, (△) 1,2PrD, (□) 1,2BD, and (+) 2,3BD. The dashed lines (sequence as above) indicate the classic absorption contributions according to eq 5.
Table 4. Classical Ultrasound Absorption αcl f−2 According to Stokes Formula (Eq 5), the Ratios α/αcl of the Observed to the Classical Absorption in the Nondispersion Regiona and the Ratios of the Volume Viscosity to the Static Shear Viscosity ηv/ηs in the Nondispersion Region,a and Relaxation time τ for the Liquids Studied
where A is the relaxation amplitude and f rel is the relaxation frequency of the discrete single relaxation process. B represents the sum of the classical part of the absorption and the contributions from possible processes with relaxation frequencies considerably higher than f rel. The values of the parameters A, B, and f rel are estimated by the least-squares method and are collected in Table 2. In Table 2, the relaxation times τrel (τrel = Table 2. Parameters of the Relaxation Equation (Eq 2) Together with Standard Mean Deviation δa and Relaxation Strength r for the Liquids Studied at the Temperature 298.15 K liquid
1015B/m−1·s2
1015A/m−1·s2
f rel/MHz
1015δ/m−1·s2
102r
1,2PrD 1,3PrD 1,2BD 1,4BD 1,5PD
360.7 329.9 194.5 302.3 501.6
287.2 70.7 673.4 404.5 525.6
437 393 458 388 191
3.8 1.5 3.8 5.8 9
6.0 6.7 14.2 8.0 5.1
(5)
a
liquid
1015αcl f−2/m−1·s2
α/αcl
ηv/ηs
τ/ns
1,2PrD 1,3PrD 1,2BD 1,4BD 2,3BD 1,5PD
322.5 234.3 457.1 443.9 996.0 621.5
2.01 1.71 1.89 1.58 1.65 1.65
1.35 0.95 1.19 0.77 0.87 0.87
0.36 0.41 0.35 0.41 0.75 0.83
At frequencies below the relaxation region.
densities, speeds of sound, and static shear viscosities taken from our own previous reports4,13−15 and the literature were used.16−18 In the case of 2,3BD and 1,5PD, however, the speeds of sound measured in this work were used. As a result, at T = 298.15 K, the obtained c values are 1486.28 and 1589.90 m·s−1, respectively. In the case of 1,2ED, where the quotient αf −2 is independent of frequency, the mean value is calculated and listed in Table 5.
δ = (∑ni=1((αf−2)i − (αf−2)cal)2/(n − m))1/2, where n and m are the number of experimental points and fitted parameters, respectively. Subscript “cal” denotes calculated values.
a
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permittivity εr because on comparing the obtained (αf−2)0 values with the literature εr values19 it appears that the (αf−2)0 increases roughly with decreasing εr (Figure S1 in the Supporting Information). This implies that ultrasound absorption of alkanediols is closely related with their polar properties. Since 1,2ED is known as a so-called nonrelaxing liquid, it is not surprising that, in the case of 1,2ED, the quotient αf−2 is independent of frequency over the entire frequency range investigated. This finding is in accordance with previous reports.2 However, as mentioned in the Introduction, the values reported by various authors often show considerable differences, and these differences are difficult to understand.2 In the case of the remaining alkanediols, the lack of data makes it impossible to make a direct comparison. However, comparison with the limited data reported by Litovitz et al.20 shows that our αf2 values are generally at least qualitatively consistent with those reported. Note that, apart from 1,2ED, Litovitz et al.20 reported data at T = 293 K and 22.5 MHz only. Generally, the obtained ultrasonic spectra can be discussed assuming aggregation processes determined by hydrogen bonding. The idea of the hydrogen-bonded chainlike and/or ringlike aggregates is well documented and supported by dielectric relaxation studies.21,22 Generally, this technique has been used extensively by various research groups because, compared to other techniques used to study the hydrogenbonding behavior, dielectric spectroscopy is especially advantageous for an investigation of the cooperative nature of Hbonding liquids.23 Remarkable are numerous investigations of diols and their aqueous mixtures.24−26 However, in spite of numerous studies, a good understanding of the nature of this effect at the molecular level is still lacking. Also the nature of the primary dielectric relaxation process which exhibits Debyetype relaxation is still unclear. Assuming that liquid alcohol can be treated as a mixture of monomers A1 and chain structures Ap (p = 2, 3, 4, ...), Shakhparonov and Khabibullaev27 proposed a theory of ultrasonic relaxation, which is based on a chemical equilibrium between associates of different sizes Am and An with the reaction scheme
Table 5. Mean Ultrasound Absorption Coefficients Per Squared Frequency αf −2 with Standard Deviations in the Frequency Range f = 10−300 MHz and at T = 298.15 K for the Liquids Studied and Comparison with the Literature, and Classical Ultrasound Absorption αcl f−2 According to Stokes Formula (Eq 5), the Ratios α/αcl of the Observed to the Classical Absorption, and the Ratios of the Volume Viscosity to the Static Shear Viscosity ηv/ηs 1015αf−2/m−1·s2 (this work)
1015αcl f−2/ m−1·s2
α/αcl
ηv/ηs
1,2ED ethanol
153.8 ± 0.5 49.2c
88.7a 24.6d
1.73 1.99
0.98 1.34
1propanol 1-butanol
68.4 ± 0.2
36.4d
1.88
1.17
80.7 ± 0.3
43.0h
1.88
1.17
93.4 ± 0.4
52.1k
1.79
1.06
1-pentanol a
1015αf−2/ m−1·s2 (lit.) 157.1 ± 1.5b 55e, 46.8 ± 0.1f 75g, 71.3 ± 4.2f 80i, 80.1 ± 1.5j 102l
b
Reference 2. 30−80 MHz, ref 2. cReference 12. dCalculated from data in ref 38. e8−220 MHz, ref 43. f0.15−1600 MHz, ref 38. g15−280 MHz, ref 43. hReference 39. i4−200 MHz, ref 43. j10−80 MHz, ref 39. k Calculated from data in ref 18. l21 MHz, ref 43.
Table 5 also shows the results obtained at T = 298.15 K for 1propanol (Fluka, mass fraction purity 0.998), 1-butanol (SigmaAldrich, anhydrous, mass fraction purity 0.995), and 1-pentanol (Lancaster, mass fraction purity >0.98) because for these liquids, the αf−2 is also independent of frequency within the investigated frequency range 10−300 MHz. In Table 5, the data reported previously for ethanol12 are also included.
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DISCUSSION It appears that, apart from 1,2ED, within the investigated frequency range, the quotient αf−2 is dependent on frequency (Figures 1 and 2). 2,3BD and 1,5PD show dependence on frequency as early as below and above ca. 40 MHz, respectively, whereas the 1,3PrD shows a weak dependence on frequency above 100 MHz. In the cases of 1,4BD, 1,2BD, and 1,2PrD, the dependence on frequency is not observed before ca. 100 MHz. In other words, in each case (except 1,2ED) the relationship d(αf −2)/df < 0 is observed. Figures 1 and 2, as well as Tables 2 and 3, show also that, as the alkyl chain length increases, the relaxation regions shift toward lower frequencies. Generally, both the carbon chain length and the position of the OH groups cause the differences in ultrasound absorption spectra of the alkanediols studied. The magnitude of the αf2 values in the nonrelaxation region, denoted below as (αf −2)0, increases in the order 1,2ED < 1,3PrD < 1,2PrD < 1,4BD < 1,2BD < 1,5PD < 2,3BD (i.e., from rather weakly absorbing 1,2ED to highly absorbing 2,3BD; the values of αf2 at T = 298.15 K and f = 10 MHz are 153.8 × 10−15 and 1641 × 10−15 m−1·s2, respectively). It should be clearly noted, however, that excluding 2,3BD, in the case of the diols studied, the ultrasound attenuation at low frequencies (i.e., at the frequencies used in typical speed of sound measurements, for example at 2 MHz) is small enough for the correct use of the Newton−Laplace relation. In other words, c may be still treated as a thermodynamic equilibrium property because the effects of attenuation on the speed of sound may be ignored. This results from the fulfilled inequality αc/(2πf) ≪ 1 (the left side changes from 0.81 × 10−4 to 5.2 × 10−4 for 1,2ED and 1,5PD, respectively.). It is also remarkable that the magnitude of the (αf−2)0 values can be connected with the static relative
Am + An ↔ Ap
(6)
where p = m + n, with m = 1,2,3,... and n = 1,2,3,.... If an average degree of associates is p ≥ 3, and all bonds in the associate are equivalent, the same forward and backward rate constants, kf and kb, can be used for all steps of association according to eq 6. In consequence, various equlibria are reduced to one reaction, which can be described by the discrete relaxation frequency (time) according to eq 2 (i.e., by a single Debye-type relaxation term). In analyzing the relaxation strengths (Table 2), it is visible that the greatest r value is observed in the case of 1,2 BD. Since the relaxation strength depends on the enthalpy ΔH and volume ΔV change connected with the process disturbed by the acoustic wave (e.g., eq 6), the above changes (at least one) must be large in the case of the different signs. The same signs of ΔV and ΔH changes, however, lead in principle to decrease the r value but if one or the other strongly predominates, relatively large r can be observed. This finding can be better understood by taking into account that 1,2BD shows both high compressibility (reflects volume changes in relation to pressure) and isobaric heat capacity (reflects enthalpy changes in relation to temperature).4,14 5937
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Figure 3. (a) Values of the ultrasound absorption coefficient per squared frequency in the nonrelaxation region (αf −2)0 plotted against carbon chain length for 1,2ED, 1,3PrD, 1,4BD, and 1,5PD. The line plotted according to eq 6. (b) Values of the absorption coefficient per squared frequency in the nonrelaxation region (αf −2)0 plotted against static shear viscosity ηs for (○) 1,2ED (ηs from ref 17), (▲) 1,3PrD (ηs from ref 15), (■) 1,4BD (ηs from ref 16), (◆) 1,5PD (ηs from ref 18), (△) 1,2PrD (ηs from ref 15), (□) 1,2BD (ηs from ref 16), (+) 2,3BD, and (∗) 1,3-butanediol, ref 32. Lines are arbitrary. All data at T = 298.15 K.
substantially, and the difference is clearly far outside of the declared experimental error. Unfortunately, the lack of raw data makes it impossible to compare the relaxation spectra directly. In our opinion, the disagreement can be connected to differences in densities and viscosities. Especially, the differences in the values of shear viscosity are extremely and seem crucial. In point of fact, extracted from the data given in ref 28, the value of ηs = 47.3 mPa·s at T = 298 K is much smaller than the value that we obtained during a measurement check (Ubbelohde viscometer, uncertainty ±1%), that is, ηs = 129.8 mPa·s, which accords with data in ref 16. It may be that this difference is connected with the differential composition of isomers in the samples studied (e.g., for the most part, the levo2,3BD isomer). We believe that this is a plausible explanation because shear viscosity plays a very important role in compressional wave propagation (shear wave as well). According to Durov et al.,28,29 the low-frequency term is connected with conformation equlibria and the high-frequency term can be connected with a rearrangement of the local structures of the postulated 3D H-bond network. Here, it should be noticed that only if the relaxation times associated with the two coupled processes differ sufficiently from each other would the relaxation function be made up of two parts. Sometimes, it may be impossible to resolve the contributions to the absorption spectrum from two processes (e.g., similar relaxation times), and the absorption data will have the appearance of a single relaxation curve. Therefore, the fact that the absorption data fit a single relaxation curve does not necessarily mean that there is a single relaxation process. It has been shown that two overlapping relaxation times can be clearly detected only when the ratio of the relaxation times fulfills the inequality τ1/τ2 > 4.30 At the same time, the ratio of the relaxation amplitudes should be 0.25 < A2/A1 < 4.30 In our case,
Inspection of Figures 1 and 2, as well as Table 2, shows that α,ω-diols have lower absorption than adequate vicinal 1,2-diols. This is also related to relaxation amplitude (Table 2). It is also interesting to note that for α,ω-diols (αf −2)0 increases linearly with the number of methylene groups n in the molecule (Figure 3a). Thus, the (αf −2)0 shows (within the accuracy of the measurements) an additive character here. To describe above dependence the following simple approximating function was used (αf −2 )0 = C + D(n(CH 2) − 2) −15 2
(7) −1
where C = (134 ± 22) × 10 s ·m and D = (292 ± 12) × 10−15 s2·m−1. The C and D coefficients of eq 7 were determined by the unweighted least-squares method. From all the alkanediols studied, the highest (αf −2)0 shows 2,3BD (formally also a vicinal diol). Since a molecule of 2,3BD has two asymmetric carbon atoms, two optically active isomers and an inactive meso form exist. As shown in Table 1, we examined a mixture of the above isomers in this work. Thus, it is not surprising that the spectrum of ultrasonic absorption indicates both the relaxation process connected with chainrotational isomerization (relatively very slow relaxation process with τ = 33 ns) and a structural relaxation process connected with association and rearrangement in the local structures (τ = 0.75 ns) according to eq 6. The relatively very slow relaxation process in the first dispersion region is most likely caused by the conformational transition that is accompanied by a rearrangement of the local surroundings. It is interesting that, in the case of 2,3BD, Durov et al.28,29 reported two relaxation times also (for example, at T = 303 K, τ1 = 3.8 ns and τ2 = 0.14 ns, respectively) in the temperature range 293−333 K. Thus, although both spectra show some similarity (two relaxation processes), the spectra differ 5938
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the first condition is fulfilled but the second one is not. This can be related to the very small energy activation (very small relaxation amplitude) for such conformation transitions in the molecule. Note also that a discrete very slow (τ1 = 180 ns at T = 313 K) ultrasound relaxation process connected with conformational equlibria has also been reported for 2,3-dimethylbutane2,3-diol.31 The chain rotational isomerization has been suggested for 2-methyl-2,4-pentanediol as well. In the case of 2-methyl-2,4-pentanediol and its aqueous solutions in the high concentration range, however, Nishikawa and Nakao32 suggested that two relaxations (near 100 MHz) with very close frequencies may be superimposed at 298.15 K even if the absorption spectrum appears to be single relaxation and it is not possible to distinguish these two relaxations in the ultrasonic spectrum. According to the mentioned authors, apart from association, the second possible mechanism may be associated with rotational isomerization about the C2−C3 bond. This is confirmed by ultrasonic absorption measurements of 2-methyl2,4-pentanediol in toluene mixtures where the relaxation times are independent of concentration. An additional feature in the case of 1,5PD and 2,3BD is observed; i.e., as Figures 1 and 2 show, above some frequency, the values of αf−2 are smaller than those predicted by classical theory (exactly, the Stokes relation (eq 5)). In other words, the absorption curves for 1,5PD and 2,3BD shown in Figures 1 and 2 indicate that α > αcl at lower frequencies (below 300 MHz) and α < αcl at higher frequencies (above 300 MHz). Thus, the frequency for which α = αcl is ca. 300 MHz at T = 298.15 K. This means that in this frequency range a relaxation mechanism of the viscous type should be present. As known, the static shear viscosity values are used in the Stokes relation (i.e., the shear viscosities with a shear rate ≈0). Thus, a shear viscosity relaxation in the megahertz range can be supposed, and the dependence of αf −2 on frequency can also be attributed to a relaxation behavior of the shear viscosity. In other words, it is obvious that ηs must decrease with frequency. The same can be related to a certain degree to 1,2BD and 1,4BD for frequencies above 630 MHz. In the past, similar results at room temperature have been reported for 1-dodecanol,33,34 castor oil,35 and recently for ionic liquid.12 It is not surprising that, for lower temperatures, α < αcl has been observed also for other liquids.36 Note that the ultrasonic relaxation is not a suitable tool to investigate the microscopic origin of the shear viscosity because it is difficult to separate the contributions of volume and shear viscosities to the ultrasonic relaxation and separate determination of the shear viscosity behavior requires the study of the shear ultrasound wave. However, it is general agreement that if α < αcl, the shear viscosity relaxation can be supposed.27,33−36 On the supposition that the shear viscosity relaxation is present, and taking into account the simple Maxwell model, the real part of the relaxing shear viscosity can be expressed as η′(ω) = ηs(1 + ω 2τM 2)−1
In the case of 1,5PD, fortunately, an independent shear relaxation experiment has been done by Kono et al.37 It appears that our conclusions from ultrasound absorption measurements are accordant with the reported by Kono et al.37 shear relaxation in megahertz range with a relatively narrow distribution of shear relaxation times (b = 0.75, where b is the width of the Gaussian distrubution of the relaxation times for a generalized Maxwell model). Taking into account the value of G∞ = 0.13 × 109 Pa estimated from shear relaxation data for 1,5PD37 and the value of ηS = 0.095 Pa·s, the τM is 0.73 ns at T = 298.15 K. As known, when ωτM = 1, the region is viscoelastic and η′(ω) = 0.5ηs. Accordance between relaxation frequency obtained from our ultrasound absorption measurements (191 MHz) and those estimated for shear viscosity (218 MHz) from shear relaxation data37 is excellent. However, it should be noted that the uncertainty ±0.15 ns of the estimated τM is related mainly with the uncertainty of the G∞ which is declared by Kono et al.37 as ±15%. Figure 4 shows the
Figure 4. Frequency-dependent shear viscosity η′ plotted against frequency (continuous line) for 1,5PD at 298.15 K together with the uncertainty range (dotted lines). For calculation, the simple Maxwell model (eqs 8 and 9) and literature data18,37 were used. For comparison, the static shear viscosity ηs is plotted as the horizontal dashed line (Newtonian behavior).
calculated dependence of η′ on frequency for 1,5PD. Unfortunately, in the case of 2,3BD the reliable shear data are lacking and similar calculation is not possible. However, it seems that similar behavior can be supposed with great probability. To illustrate the general relation between ηs and αf −2 in the nonrelaxation region, Figure 3b shows (αf −2)0 plotted against ηs. Inspection of the figure leads to some interesting conclusions. First of all, the terminal alkanediols show a linear dependence. A nearly linear dependence is also observed for 1,2-alkanediols. Moreover, a nearly linear dependence is also observed for 1,2BD, 1,3-butanediol, and 2,3BD, whereas 1,4BD shows a lower value of (αf−2)0 in relation to its static shear viscosity. It should be mentioned, however, that generally only terminal alkanediols do not have stereoisomers. As a result, there is likely lower 1,4BD absorption in relation to its 1,2-, 1,3-, and 2,3-isomers (assuming contributions from rotational isomerization). The values of the ratios (Table 4) of the observed absorption with respect to those calculated from the Stokes rule (i.e., classical absorption) in the nondispersion region are typical and characteristic of structural relaxation (for alkanediols studied, α/αcl ranged from 1.58 to 2.01). From the ratio α/αcl, the ratio
(8)
where ω = 2πf and τM are the angular frequency and the Maxwell relaxation time, respectively. The Maxwell relaxation time is given as the ratio of the static shear viscosity and the limiting shear modulus G∞
τM = ηsG∞−1
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dx.doi.org/10.1021/jp502700k | J. Phys. Chem. B 2014, 118, 5934−5942
The Journal of Physical Chemistry B
Article
of the volume viscosity to shear viscosity ηv/ηs can be estimated from the following relationship20 ηv /ηs = 4/3(α /αcl − 1)
rotational isomerization is observed. For the higher n-alkanes and their derivatives, however, the configurational diversity increases with carbon chain length. It seems also that the above-mentioned linearity between the values of (αf−2)0 and the carbon chain length for α,ωalkanediols (Figure 3a) suggests that intramolecular hydrogen bonding can be neglected or that this effect is much the same for all the α,ω-alkanediols studied. According to Klein,45,46 however, 1,4BD has the strongest intramolecular bonding of all the α,ω-alkanediols up to 1,6-hexanediol. Recent reports47−49 about conformers existing in alkanediol molecules are consistent with this conclusion of Klein. Generally, however, intramolecular hydrogen bonding in the liquid phase of the pure α,ω-alkanediols does not appear to be very important thermochemically 50 and our results show that minor importance of the intramolecular hydrogen bonding can be stated in the case of ultrasound absorption as well. It has also been reported that the behavior of lower alkanediols in aqueous solutions at room temperatures depend on the molecular structure of the solute.51−53 Thus, relaxation processes have been found in aqueous 1,2BD solutions (the composition dependence of αf2 shows maximum),51 whereas no relaxation processes have been found in aqueous solutions of 1,2ED, 1,3PrD, 1,4BD, and 1,5PD in the frequency ranges of 15−220 or 1.5−230 MHz (monotonic composition dependence).51−53 From the above ultrasonic relaxation studies, it was concluded that the hydrophobicity of the 1,2BD is the greatest, and that the greater the hydrophobicity of the diol, the more effectively it promotes the water structure.51,53 In the case of 1,2-diols, this effect increases clearly from 1,2ED (no relaxation53) via 1,2PrD (some indications for relaxation53) to 1,2BD (relaxation51) with the increase of separation between the polar and the nonpolar parts of the molecule.
(10)
where volume viscosity ηv is a measure of the resistance of the liquid to a pure expansion or compression. Here, it should be noted that acoustic data are the only way to determine values of ηv, as they cannot be measured directly. Inspection of Tables 4 and 5 shows that the obtained ηv/ηs values scatter around 1. Thus, the magnitude of the ηv values is very close to the ηs values. This finding is consistent with reports in the literature, as a survey of the literature shows that the ratio of ηv/ηs scatters around 1 for different pure alcohols.2,27,38−41 Additionally, for solutions of KCl and NaBr in glycerol,41 as well as for binary mixtures of alcohols,2,39 such scattering of ηv/ηs has been reported. According to Brai and Kaatze,38 differences in the ηv/ηs ratio (from 1.28 to 0.36) are reported for the lower alkanols, which may be related to a structural relaxation process in the gigahertz range. Generally, if ηv/ηs is near 1 and approximately temperature independent, a similar activation enthalpy for both viscosities can be supposed. Although temperature dependence of ηv/ηs was not tested, the above supposition can be accepted because all of the alcohols studied have a linear carbon chain. An exception is 2,3BD where a small contribution from rotational relaxation process was detected. As known, in the case of isomeric rotational relaxation processes, the ηv/ηs values are generally large and change with temperature.42 It is interesting to compare the ultrasound absorption data obtained for alkanediols with those of 1-alkanols with similar carbon chain lengths. It appears that, for the 1-alkanols studied (Table 5), the αf−2 is independent of the frequency within the investigated frequency range (10−300 MHz). This finding is not surprising and accords with literature reports.38,43 In the case of 1-butanol, however, a broadband ultrasonic study shows that at T = 298.15 K, a relaxation process at a frequency of 1.3 GHz is present.38 In the case of ethanol and 1-propanol, no relaxation process has been found under similar conditions.38 For 1-pentanol,44 however, in addition to the ultrasonic relaxation process, a second relaxation process near 10 GHz has been observed. This discrete relaxation has been assigned to conformational equilibria (strictly, an equilibrium of rotational isomers). Generally, the lower relaxation region in alkanols can be assigned to fluctuations in the structure of hydrogen-bonded alcohol clusters, whereas only the higher relaxation region can be connected with intramolecular conformational isomerism.33 The results obtained in this work for 1-alkanols are generally consistent with the above literature reports because the experimental absorption has a higher value than those from classical absorption. This means that other relaxation processes can be present in the higher frequency range. Nevertheless, some quantitative differences in the αf−2 values obtained in this work and those given in the literature are present (Table 5). Comparison of the ultrasonic spectra for 1-alkanols and spectra for linear alkanediols with the same carbon chain lengths leads to the conclusion that the presence of a second hydroxyl group moves the relaxation region toward lower frequencies. However, this effect is not observed in the case of 1,2ED. In the experimental range, no indication of a relaxation can be detected. As already mentioned, this result is not surprising, as for ethane and some of its derivatives, the conformers (three stable configurational positions exist) have the same energy and no relaxational acoustic effect due to
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CONCLUSIONS Apart from 1,2ED (1-alkanols as well), above some frequencies, the experimental data clearly do not define a constant αf−2, but instead exhibit dependence on frequency (i.e., d(αf2)/d f < 0). The relaxation region is dependent on both carbon chain length and the position of hydroxyl groups. Moreover, alkanediols with smaller values of εr tend to exhibit larger values of (αf −2)0. If, for 1-alkanols, the magnitude of αf−2 increases clearly as the carbon chain length increases (i.e., in the order ethanol
