J. Phys. Chem. 1996, 100, 6801-6807
6801
Structural Relaxation and H Bonding in Isomeric Octanols and Their LiCl Solutions by Calorimetry G. Sartor,† K. Hofer,‡ and G. P. Johari* Department of Materials Science and Engineering, McMaster UniVersity, Hamilton, Ontario, Canada L8S 4L7 ReceiVed: NoVember 14, 1995; In Final Form: January 22, 1996X
Isomeric octanols show a variety of dielectric behavior. At low temperatures, some behave as nonpolar liquids, others as polar liquids. This results from the extent of steric hindrance for intermolecular H bonding when the CH3 group is in the proximity of the OH group in the seven-membered -C-C- chain. Differential scanning calorimetric studies of nine isomeric octanols and LiCl solutions of two of them are reported here. These are discussed in terms of structural relaxation, glass transition temperature Tg, configurational contribution to the heat capacity ∆Cp, and distribution of structural relaxation times parameter β. Tg of the isomers of octanols lies between 148 and 168 K, ∆Cp between 35 and 82 kJ/mol, and β between 0.33 and 0.93. Those octanols that behave dielectrically as nonpolar liquids have a broader distribution of relaxation times, or lower β, than those isomers that behave dielectrically as highly polar liquids. Addition of 5 mol % LiCl increases Tg and ∆Cp in the former case but decreases both in the latter case, and the distribution of relaxation times broadens in both cases. An analysis in terms of configurational contributions to Cp shows that steric hindrance of the OH group determines the H-bonded motifs formed in liquid octanols near their glass-liquid transition temperature.
Introduction On the basis of their extensive dielectric studies, Dannhauser and co-workers1 concluded that, depending upon the steric hindrance to intermolecular H bonding, isomeric octanols associate by intermolecular H bonds to form two types of motifs: (i) linear chains and (ii) molecular ring dimers. Measurements of the compressibility2 of the isomeric octanols and the effect of dissolved electrolytes on their static permittivity s3 seem to confirm that the position of the OH relative to the CH3 group in the molecules’ C-C chain has a pronounced effect on the type of H-bonded motifs that form in the structure of liquid alcohols. The temperature dependence of s and of the deduced Kirkwood-Fro¨hlich4,5 dipolar orientation correlation factor g showed that, for octanols with sterically less hindered OH groups, the g factor was greater than unity and increased with decreasing temperature. This indicated, according to the Kirkwood-Fro¨hlich theory,4,5 that parallel alignment of nearneighbor dipole vectors occurred in linear chains. However, for octanol molecules with sterically more hindered OH groups, the g factor was found to be less than unity and decreased with decreasing temperature. This indicated antiparallel alignment or canceling of the near-neighbor dipole vectors in a manner similar to that which occurred in the dimer rings formed by intermolecular H-bond association in dicarboxylic acids and in amides dissolved in nonpolar solvents.6 Vij et al.7 and Scaife8 preferred to interpret their observation of a similar dielectric study differently. They considered that there is only one H-bonded motif, namely, the linear chains. Steric hindrance to intermolecular H bonding in octanol isomers, with sterically hindered OH groups, creates a less ordered arrangement of neighboring H-bonded chains as a result of inefficient chain packing, and that this tends to cause a partial cancellation of the dipole moments. Hence, their static dielectric †
Schro¨dinger Research Fellow, 1994-1996. Postdoctoral Research Fellow, 1990. Permanent address: Institut fu¨r Allgemeine, Anorganische und Theoretische Chemie, Universita¨t Innsbruck, A-6020 Innsbruck, Austria. X Abstract published in AdVance ACS Abstracts, March 15, 1996. ‡
0022-3654/96/20100-6801$12.00/0
permittivity, s, is similar to those of nonpolar liquids. Under a hydrostatic pressure, the packing of intermolecular H-bonded chains becomes more efficient, with the net effect being that the long-range dipolar correlation increases and s increases. Vij et al.7 also pointed out that these alcohols exist as enantiomorphic invariants; i.e., the hydroxyl group in them can be attached to either of the two different bonds on a given carbon atom. Thus, they pointed out that there is a possibility that, depending upon the proportions of the optically active species in the octanol liquid, the H bonding between the alcohol molecules would not produce straight chains because of the steric hindrance produced by the CH3 group attached to the neighboring carbon atom. It is conceivable that, from the point of view of molecular packing at high densities of an alcohol under a hydrostatic pressure, the two optical species would separate out locally. To resolve this issue, Hofer and Johari3 studied the effect of ions on the intermolecular association in isomeric octanols by dielectric measurements. Ions break the intermolecular H bonds and, therefore, alter the structure of H-bonded motifs from ring dimers to linear dimers or monomers, and long, linear chain, n-mers to shorter chains or oligomers. Their studies did show that the presence of ions increased the s of those octanols which behaved dielectrically like a nonpolar liquid but decreased the s of those octanols which behaved like a polar liquid. In the former case, nonpolar ring dimers were broken into linear dimers or monomers; in the latter case, linear chainmers were broken into shorter chains or monomers. The configurational contribution to the enthalpy, entropy, volume, heat capacity, and expansivity of a liquid is determined by the structure of the liquid, i.e., by the nature of intermolecular H bonding in the case of octanols. This configurational contribution becomes vanishingly small when a liquid becomes a rigid glass. So one expects that the thermodynamics of glass transition, i.e., the change in the heat capacity and the nature of its structural relaxation, can be useful in investigating whether or not there is a difference between the intermolecular H-bonded motifs in various isomeric octanols and whether the dissolved © 1996 American Chemical Society
6802 J. Phys. Chem., Vol. 100, No. 16, 1996
Sartor et al.
ions affect the population of such motifs. Some aspects of these effects have been described on pp 358 and 359 of ref 9, which may be consulted. In this paper, we report on a calorimetric study of the glass f liquid transition of nine isomeric octanols and of solutions of LiCl in two of them. The analysis of the differential scanning calorimetric (DSC) data near the glass transition of isomeric octanols show that different types of intermolecularly associated motifs are produced as a result of intermolecular H bonding when the OH group is sterically hindered. The work reported here is part of our continuing studies on the use of calorimetry for distinguishing amorphous solids from microcrystalline solids10,11 and characterizing their nature, for investigating the amount of liquid present at the grain junctions of polycrystalline solids,12-14 under conditions of a thermodynamic equilibrium, for studying the glass relaxation phenomena, e.g., enthalpy crossover or memory effect,15 and for development of procedures, such as anneal and scan, for detecting the glassiness of cold biomaterials,16 a technique that has found immediate acceptance for studying simpler polypeptides in aqueous solutions.17
[(
τ(T,Tf) ) A exp
The isomeric octanols used for this study were the same samples as in previous studies1-3 (Professor W. Dannhauser,1 who had kept them stored in sealed bottles since 1966, donated these to us). LiCl was purchased from Aldrich Chemical Co. and was used without further purification. The solutions of LiCl in the isomeric alcohols 2-methyl-6-heptanol and 4-methyl-3heptanol were prepared by dissolving accurately weighed amounts at room temperature. A Perkin-Elmer differential scanning calorimeter, DSC 4, with the TADS data acquisition system was used. The instrument’s background signal was measured as a baseline in all cases and subtracted during each scan (SAZ function). This baseline was obtained with empty sample pans. The data obtained were transferred to a PC via a serial interface and then analyzed. Samples (6-24 mg) were sealed in aluminum pans. The samples were cooled in the instrument at a cooling rate of 20 K/min except the sample that was used for curve 2 in Figure 3. This sample was cooled by dropping the Al pan containing the sample into liquid nitrogen, which gives a cooling rate of ≈1500 K/min. All other samples were cooled to 103 K in the DSC instrument and heated at a rate of 20 K/min during which their DSC scans were obtained. Results and Data Analysis The DSC data obtained for all isomeric octanols were normalized in the form of Cp, the heat capacity, and then analyzed by the Tool-Narayanaswamy-Moynihan procedure.18-20 The equations and the details of the normalization and data analysis are described in a previous study.21 Briefly, the analysis was carried out in terms of a reduced time formalism by using a stretched exponential relaxation function
[ ( ) ] { [∫ ] } tβ ) exp τ
dt′ τ(Tf)
T
0
β
(1)
where t is the time, β is a parameter which characterizes the width of the distribution of relaxation times, and τ is referred to as a characteristic time that depends both on the actual temperature, T, and the fictive temperature,18 Tf, i.e., one corresponding to the instantaneous equilibrium state of a glass. τ has been related to T and t by a variety of equations, but Kovacs and co-workers22,23 have shown that all can be written
]
(1 - x)∆h* x∆h* + RT RTf
)
(2)
where A is the relaxation time when T and Tf formally approach infinity (but is referred to as that at some arbitrary temperature) and ∆h* is an activation enthalpy. x (1 g x g 0) is an empirical parameter which separates the temperature dependence from the structural dependence of τ. For x ) 1, eq 2 becomes an Arrhenius equation. By combining eqs 1 and 2, transforming t to T using the relation q ) (dT/dt), where q is the heating rate, and summing over all instantaneous T jumps, according to the Boltzmann superposition,
[
{ [∫
Tf(t) ) T0 + ∫T dT′ 1 - exp T 0
T
dT′′
T′ qτ(T,T ) f
] }] β
(3)
where T0 is a starting temperature well above Tg and T′ and T′′ are dummy (chosen for convenience) variables. By definition,
Cp,norm )
Experimental Section
Φ(t) ) exp -
in the form originally developed by Narayanaswamy,19
( ) dTf dT
(4)
Equation 2 was developed by Narayanaswamy;19 Moynihan and co-workers20 developed procedures for its use by combining it with eq 1. The use of these equations in analyzing the DSC data is often referred to as the Tool-NarayanaswamyMoynihan procedure.18-20 Hodge24,25 has recently reviewed this subject and has summarized the calorimetric studies that were used to examine this formalism. The Cp,norm data were fitted to eqs 1-4 as follows. Approximate values of the parameters A, ∆h*, x, and β were determined by visually comparing the calculated and measured values of Cp,norm at 0.2 K intervals on a monitor display, as in an earlier study.21 ∆h* was not measured from the usual method of plotting the heating rate against the reciprocal Tg, because such plots are found to be often curved.26 So each of the four parameters was varied until the best agreement between the calculated and experimental data was found over the range of temperature Tg ( 20 K. The algorithm used was similar to that developed by Hodge and co-workers27,28 but was extended for convenience of data manipulation. The best values of ln A, x, ∆h*, and β are listed in Table 1, where the values of Tg, obtained by the intersection of lines as illustrated in Figure 1, for each octanol and its LiCl solution are included. As noted in ref 29, this procedure is not unique in data fitting. The fact that the various procedures of fitting equations based on different theories and models yield almost the same agreement of the equations with the experimental data only supports the view that there is a fundamental formulation underlying this phenomena which is yet to be developed. For this reason, we refrain from seeking a molecular interpretation of the parameters A, ∆h*, and x here. Figure 1 shows the normalized DSC data of the three isomeric octanols in which the OH group is sterically less hindered, i.e., in which the CH3 group is not in close proximity to the OH group along the C-C chain. On it, curves 1-3 show the normalized DSC data (data points) and the best fitting curves (continuous lines) for 5-methyl-3-heptanol (1), 6-methyl-3heptanol (2), and of 3-octanol (3). An endothermic step owing to a glass-liquid transition can be seen in all curves. Here the manner by which Tg was determined from the intersection point of lines drawn to the DSC data is also shown for the three cases. The effect of the addition of 5 mol % LiCl to the DSC scans of octanols is shown in Figures 2 and 3, where the data for
Relaxation and H-Bonding in Isomeric Octanols
J. Phys. Chem., Vol. 100, No. 16, 1996 6803
TABLE 1: Calorimetric Data and the Structural Relaxation Parameters for Isomeric Alcohols and Their LiCl Solutions substance
Tg/K
∆Cp/(J/(K mol))
β
ln A
x
∆h*/(kJ/mol)
τ at Tg/s
T at τ ) 20 s
2-methyl-1-heptanol 4-methyl-1-heptanol 6-methyl-1-heptanol 5-methyl-3-heptanol 6-methyl-3-heptanol 3-octanol 2-methyl-6-heptanol 2-methyl-6-heptanol with 5 mol % LiCl 2-methyl-3-heptanol 4-methyl-3-heptanol 4-methyl-3-heptanol with 5 mol % LiCl
151.0 147.9 148.6 167.7 166.7 163.2 158.4 153.6 161.5 153.2 158.9
81.6 40.7 34.9 73.9 47.7 63.0 73.4 65.3 71.8 55.7 75.0
0.50 0.93 0.87 0.53 0.54 0.58 0.45 0.39 0.33 0.36 0.31
-157 -161 -160 -139 -140 -144 -150 -153 -145 -155 -150
0.59 0.52 0.38 0.58 0.43 0.55 0.91 0.91 0.92 0.55 0.90
200.5 200.5 200.0 200.0 200.0 201.0 201.0 201.0 201.0 202.4 204.5
13.2 12.2 16.0 44.7 45.2 31.5 12.1 59.7 83.9 11.8 91.8
150.4 147.1 148.1 169.2 168.4 164.5 158.0 154.8 163.1 152.2 160.5
Figure 1. Normalized DSC data (data points) and best fitting curves (continuous lines) of (1) pure 5-methyl-3-heptanol, (2) pure 6-methyl3-heptanol, and (3) pure 3-octanol.
Figure 2. Normalized DSC data (data points) and best fitting curves (continuous lines) of (1) pure 2-methyl-1-heptanol, (2) pure 2-methyl6-heptanol, and (3) 2-methyl-6-heptanol containing 5 mol % LiCl.
other pure octanols are also plotted. Figure 2 shows the normalized DSC data (data points) and the best fitting curves (continuous lines) of pure 2-methyl-1-heptanol (curve 1), pure 2-methyl-6-heptanol (curve 2), and 2-methyl-6-heptanol containing 5 mol % LiCl (curve 3). In both of these octanols, the OH group is sterically less hindered, much like in the octanols whose DSC data and best fitting curves are shown in Figure 1. A comparison of curves 2 and 3 in Figure 2 shows that addition of 5 mol % LiCl lowers the Tg of 2-methyl-6-heptanol from 158.4 to 153.6 K and broadens the glass-liquid transition temperature region. This is quantified by the decrease in the stretched exponential fit parameter β of eq 1, which is seen as a measure of the distribution of relaxation times, because as β f 0, the spectrum of relaxation times progressively broadens and the glass-liquid transition endotherm becomes stretched out in a temperature plane. As a result of the addition of LiCl to 2-methyl-6-heptanol, β decreases from 0.45 to 0.39, as given in Table 1. Figure 3 shows the normalized DSC data (data points) and the best fitting curves (continuous lines) for two isomeric octanols with sterically more hindered OH groups, namely, pure 2-methyl-3-heptanol (curve 1), pure 4-methyl-3-heptanol (curve 2), and 4-methyl-3-heptanol containing 5 mol % LiCl (curve 3). Again, an endothermic step due to a glass-liquid transition is evident. But contrary to the results shown in curves 2 and 3 in Figure 2 for 2-methyl-6-heptanol, in which the OH group is
sterically less hindered, Tg of 4-methyl-3-heptanol increases upon the addition of LiCl from 153.2 to 158.9 K. Nevertheless, the temperature region for the glass-liquid transition broadens in a manner similar to that for 2-methyl-6-heptanol shown in curves 2 and 3 in Figure 2. This is also quantified by a decrease in β from 0.36 to 0.31, whose values are listed in Table 1. It should be noted that curve 2 was also normalized. But as it has an exothermic dip before the endothermic step, there may be a false impression that the curve was not normalized. This exothermic dip is a reflection of structural relaxation, during rate heating of this sample which was vitrified by rapid cooling (≈1500 K/min) as compared to the cooling rate (20 K/min) used for other octanols. Furthermore, the shape of the curves did not change on changing the sample’s mass. So any thermal conductivity difference amongst the samples did not affect the measurements significantly, an aspect also discussed in an earlier study.21 With the parameters used to fit eqs 1-4 to the DSC data, as summarized in Table 1, we can now address the problem of determining the glass-liquid transition temperature from DSC scans. From a study of inorganic glasses, Pascheto et al.21 have recently shown that the usual procedure for determining the Tg of a sample by drawing tangents to the endothermic step does not give a temperature corresponding to a certain relaxation time. This was examined here further by calculating τ at the Tg of the various octanols by using the parameters listed in Table 1
6804 J. Phys. Chem., Vol. 100, No. 16, 1996
Sartor et al. be used first to obtain the parameters ln A, ∆h*, x, and β and then these parameters be used to calculate the τ of the material as a function of temperature. The temperature for a fixed relaxation time of different materials, instead of the Tg determined by the usual procedure, should then be compared to obtain fundamental information on glass relaxation or to obtain a correlation between a certain property of different liquids. For this purpose, the temperature at which τ ) 20 s was chosen here, and this temperature T at τ ) 20 s, is listed in Table 1. We will henceforth use T at τ ) 20 s instead of Tg for our discussion. Both the Tg obtained from the DSC scans using the line intersection method and the T at τ ) 20 s are marked on each of the 11 curves in Figure 4, the former by a small horizontal line and the latter by a horizontal continuous line. Discussion
Figure 3. Normalized DSC data (data points) and best fitting curves (continuous lines) of (1) pure 2-methyl-3-heptanol, (2) pure 4-methyl3-heptanol, and (3) 4-methyl-3-heptanol containing 5 mol % LiCl. Note that the Cp in curve 2 has indeed been normalized, but the exothermic dip in the scan that appeared at T > 135 K has made part of the normalized curve appear below zero. This is similar to curve 5 in Figure 4 in the paper by Johari et al. (Johari, G. P.; Hallbrucker, A.; Mayer, E. J. Phys. Chem. 1989, 93, 2648) and is a reflection of a significant enthalpy relaxation during rate heating of the sample vitrified by cooling at a high rate (≈1500 K/min).
Figure 4. Structural relaxation time of the isomeric octanols against reciprocal temperature calculated after eq 2: (1) 5-methyl-3-heptanol, (2) 6-methyl-3-heptanol, (3) 3-octanol, (4) 2-methyl-3-heptanol, (5) 4-methyl-3-heptanol with LiCl, (6) 2-methyl-6-heptanol, (7) 2-methyl6-heptanol with LiCl, (8) 4-methyl-3-heptanol, (9) 2-methyl-1-heptanol, (10) 6-methyl-1-heptanol, (11) 4-methyl-1-heptanol.
and eqs 2 and 3. Figure 4 shows plots of the natural logarithm of the structural relaxation time τ, calculated from eq 2, against the reciprocal temperature for all isomeric octanols and the two LiCl solutions in 2-methyl-6-heptanol and 4-methyl-3-heptanol. The values of τ at Tg for different substances are listed in Table 1. A comparison of these values for various octanols shows clearly that these values vary from 12 to 92 s and, contrary to what is expected, are not the same. This means that the Tg of octanols thus derived does not correspond to the same relaxation time. Therefore, it seems necessary that a material’s DSC scans
On the basis of their known dielectric behavior, the nine isomeric octanols listed in Table 1 are divided into two groups: (1) Group 1 is those whose orientational correlation factor, g, is greater than unity and whose (ds/dT)p and (dg/dT)p are negative at temperatures approaching their Tg’s. The molecules of these alcohols associate by intermolecular H bonds to form predominantly linear chainmers. The first seven, 2-methyl-1heptanol to 2-methyl-6-heptanol, listed in Table 1 belong to this group.1,2 (2) Group 2 is those whose g is much less than unity and whose (ds/dT)p and (dg/dT)p are either zero or positive. The molecules of these alcohols associate by intermolecular H bonds to form predominantly nonpolar ring dimers. The last two pure alcohols, 2-methyl-3-heptanol and 4-methyl-3-heptanol, belong to this group.1a Structurally, group 1 and 2 isomers differ in the disposition of the CH3 relative to the OH group on the C-C chain of the molecule. When the C atoms to which the CH3 and the OH groups are attached are separated by at least one C atom, the octanols at low temperatures and high pressures1,2 behave like those in group 1. When the separation is less, that is, when the CH3 and OH groups are attached to the near-neighbor carbon atoms or the same carbon atom, the octanols behave like those in group 2. We first discuss the magnitudes of T at τ ) 20 s and ∆Cp in relation to the disposition of the CH3 and OH groups in the octanol molecule by using the data in Table 1 and the data summarized in Figure 5. T at τ ) 20 s, or T(τ)20s), and ∆Cp values for the first three octanols of group 1 show that, when the OH group is kept at the third C atom of the seven-membered linear chain and the CH3 is moved from the seventh C atom (as in 3-octanol) to the fifth C atom (as in 5-methyl-3-heptanol), T(τ)20s) increases from 164.5 to 169.2 K and ∆Cp increases from 63.0 to 73.9 J K-1 mol-1. (The anomalous behavior of 6-methyl-3-heptanol needs further study). Similar changes in T(τ)20s) occur when the OH group is kept at the terminal or the first C atom and the CH3 group is moved from the sixth C atom (as in 6-methyl-1-heptanol) to the second C atom (as in 2-methyl-1-heptanol), when T(τ)20s) changes from 148.1 to 150.4 K. The increase in ∆Cp, from 34.9 to 81.6 J K-1 mol-1 that occurs now, is much greater than in the former case. The two isomers of group 2, 2-methyl-3-heptanol and 4-methyl-3-heptanol, which are the only ones studied here, do not show the above-mentioned effect, i.e., of the type seen in Figure 5. The magnitudes of their T(τ)20s) and ∆Cp values are found to change even when the proximity of the CH3 and OH groups in the octanol molecule remains the same. When the separation between the CH3 and OH groups in the octanol molecule becomes small enough that the H-bond
Relaxation and H-Bonding in Isomeric Octanols
J. Phys. Chem., Vol. 100, No. 16, 1996 6805 already close to the sum of the entropy contributions from (i) vibrational modes, (ii) sub-Tg relaxation,30,31 and (iii) other unfrozen modes as in a glass, the rate of entropy (and enthalpy) loss on cooling is only slightly more than that of its glassy state, and ∆Cp is low. Conversely, when a liquid’s entropy at T > Tg is much greater than the sum of these contributions listed above, the rate of entropy (and enthalpy) loss on cooling is much higher than that of its glassy state, and ∆Cp is high. Alternatively stated, when the number of configurations accessible to a liquid’s structure decreases slowly on cooling, ∆Cp is small, as for glassy water (∆Cp ≈ 1.6 J K-1 mol-1).32,33 When this number is large, ∆Cp is large, as for H2SO4‚3H2O (∆Cp ) 176.5 J K-1 mol-1).34 Thus, ∆Cp becomes related to the difference between the overall entropy fluctuations in the liquid and the glass states of a substance. When the types of intermolecular motifs, i.e., chainmers and ring dimers, at temperatures near Tg for different octanols are the same, this difference increases when the CH3 and OH groups are brought in closer proximity in the seven-membered C chain for both groups, 1 and 2, of octanols, as is seen in Table 1. Effects of Dissolved Ions
Figure 5. Plots of T(τ)20s) and ∆Cp of several isomeric octanols against the position of the CH3 group in a seven-membered C-C chain. The position of the OH group is given beside the curves.
association into polar chain n-mers becomes less probable than association into presumably nonpolar ring dimers, the behavior of the octanols transforms from that of group 1 to that of group 2, and T(τ)20s) and ∆Cp decrease. This is notable in Table 1, where T(τ)20s) decreases from 169.2 K for 5-methyl-3heptanol to 152.2 K for 4-methyl-3-heptanol and ∆Cp from 73.9 to 55.7 J K-1 mol-1. Thus, it seems that in the structural relaxation of isomeric octanols, there are two factors that determine the magnitudes of their T(τ)20s) and ∆Cp: first, the disposition of CH3 and OH groups relative to each other within the molecule and, second, the type of H-bonded motif formed on intermolecular association. The first increases T(τ)20s) and ∆Cp when the separation between the CH3 and OH groups attached to the C-C chain is decreased in group 1 octanols. The second decreases both T(τ)20s) and ∆Cp when the proximity between CH3 and OH groups causes a change in the H-bonded motifs from chain n-mers to ring dimers. We now discuss the magnitude of ∆Cp of the octanols in terms of configurational changes. In statistical thermodynamic terms, Cp is related to the mean square entropy fluctuation 〈∆S 〉. Hence, ∆Cp, the change in Cp at Tg, is related to 2
〈∆S 〉 by 2
(〈∆S 〉glass - 〈∆S 〉liq) kB 2
∆Cp )
2
(5)
where kB is the Boltzmann constant. In classical thermodynamics, Cp is equal to the change in (dH/dT)p and T(dS/dT)p at Tg. Since the contribution to the terms (dH/dT)p and (dS/dT)p of a glass below Tg is assumed to be mainly vibrational (although sub-Tg relaxations and kinetically unfrozen modes of the main structural relaxation at Tg are also known to contribute30,31), it is generally considered that ∆Cp is a measure of the number of configurations accessible to the structure of a liquid at T infinitesimally above Tg. When a liquid’s entropy at T > Tg is
We now consider how the dissolved Li+ and Cl- ions alter the Tg and ∆Cp of the two groups of octanols. This may occur in at least three manners as discussed below: (i) The electrostatic charge of the ions causes the intermolecular H bonds in the solvent to break. When intermolecular H bonds of long, linear chain motifs are broken and thus short chains and monomers are produced, the specific volume increases (this is similar to the effect of depolymerization), which lowers Tg or T(τ)20s). But when intermolecular H bonds of bulkier ring dimer motifs are broken and linear dimers and/ or monomers are produced, the specific volume decreases, which raises Tg or T(τ)20s). In either case, the number of configurations available to the structure of the liquid increases. This effect is expected thus to increase ∆Cp. (ii) The ion-dipole interactions between the ions and the octanol molecules produce a solvation shell and thus further alter the structure of the liquid. The dipolar, alcohol molecules will arrange themselves such that the oxygen atoms will point toward the cations (Li+) and the hydrogen atoms of the OH groups will point toward the anions (Cl-). This effect is expected to reduce the number of configurations available to the structure and therefore decrease ∆Cp. (iii) When the dielectric constant of the solvent is low and/ or the temperature is low, the concentration of ion pairs increases according to the equation35
( ) ( )
4πNA3 z1z2e2 exp KA ) 3000 askBT
(6)
where KA is the association constant, NA is Avogadro’s number, z1 and z2 are the charge on the cation and anion, e is the electronic charge, a is the ion size parameter, s is the static dielectric permittivity, kB is Boltzmann’s constant, and T is the temperature. So when s is low and/or T is low, there is a greater population of ion pairs, and this population increases with a decrease in the temperature. This may also affect the configurational contribution to the enthalpy and entropy when the concentration of the solution is high. Thus, one expects that the effect of ions on the configurational thermodynamics of a solution will depend also on its concentration. Amongst the three aspects given above, of the effect of ions, the first is due to a change in the liquid’s H-bonded structure, the second is due to ion-molecule interaction, and the third is
6806 J. Phys. Chem., Vol. 100, No. 16, 1996 due to ion-ion interaction. The data summarized in Table 1 show that the addition of LiCl to 2-methyl-6-heptanol, which behaves dielectrically as a highly polar liquid,1 decreases T(τ)20s) from 158.0 to 154.8 K and decreases ∆Cp from 73.4 to 65.3 J K-1 mol-1. In this case, the decrease in T(τ)20s) is consistent with an increase in volume on breaking of intermolecular H bonds of linear chains, as for effect i, but the change in ∆Cp seems to indicate that effect ii dominates. Thus, for octanols in which the OH group is sterically less hindered, ion solvation is more probable and the solvation shell is strongly held to the ions by Coulombic interactions. For 4-methyl-3-heptanol, however, which behaves dielectrically as a nonpolar liquid,1d the opposite occurs, i.e., both T(τ)20s) and ∆Cp increase on addition of LiCl. This decrease in T(τ)20s) is consistent with a decrease in volume on breaking of intermolecular H bonds of bulkier ring dimers, as for effect i, and the change in ∆Cp when this occurs seems to be dominated also by effect i. This is expected in view of the fact that owing to the steric hindrance of the polar OH group by the CH3 group, effect ii, i.e., ion-solvent interactions, may not be pronounced. These results thus seem to support, like a previous study on the dielectric behavior of the isomeric octanols and their electrolyte solution,3 the conclusion of Johari and Dannhauser,1 that isomeric octanols with sterically hindered OH groups, like 4-methyl-3-heptanol, form bulky H-bonded ring dimers. Addition of LiCl breaks the intermolecular H bonds, and the ring dimers are transformed into monomers or short chains. The values of T(τ)20s) of the octanol increases because the short chains are less bulky in comparison to that of the ring dimers and ∆Cp increases because the number of configurations available to a ring structure are expected to be less than that available to monomers or short chains. Interpreted in terms of eq 5, ions increase 〈∆S2〉liq for 4-methyl-3-heptanol, an alcohol that behaves like a nonpolar liquid, and decreases 〈∆S2〉liq for 2-methyl-6-heptanol, an alcohol that behaves like a polar liquid. If there were only one type of intermolecularly H-bonded motif, namely, linear chains, as is postulated by Scaife,8 the changes in both Tg and ∆Cp for 2-methyl-6-heptanol would be qualitatively similar to that for 4-methyl-3-heptanol upon the addition of 5 mol % LiCl. This is not observed here. Although this study is on a relatively simple type of intermolecular association by H bonding in a series of isomeric alcohols, it is instructive to compare these observations with the observations on the effects of LiCl addition on the Tg and ∆Cp of water. Hofer et al.36 reported that addition of LiCl and other electrolytes to water first decreases its Tg and ∆Cp (at Tg) toward a minimum value, and thereafter, a further increase in the concentration increases both Tg and ∆Cp toward the values for the concentrated solutions vitrified by slow cooling. This approach toward a minimum value has been attributed to plasticization of the water’s network structure in the same manner as the plasticization of the SiO2 network structure by the presence of ions.36 For 5.3 mol % LiCl solution in water (Figure 1 in refs 36 and 37), ∆Cp is nearly 3 times as high38 as for pure hyperquenched glassy water.32,39 For 8.33 mol % LiCl solution, which was virtrified by the usual slow cooling in Mayer et al.’s study,38 ∆Cp increased to nearly 11 times the value for the hyperquenched glassy water,32,39 while Tg increased by 2 K and the temperature width of the Tg endotherm decreased38 to less than half the value for hyperquenched glassy water.32,39 In the present study, the effects of LiCl on both the Tg and ∆Cp have been found to depend upon the type of intermolecularly associated H-bonded motifs in the isomeric alcohols, which shows that the effects of ions on the configurational thermodynamics of a liquid depend upon the structure of the liquid
Sartor et al. itself and on any ion-solvent interactions and ion-ion interactions in it. That is, a liquid acting as a solvent no longer has the same structure as in the pure state and any distribution of its structural relaxation times is modified by the presence of ions, in a manner that depends upon the structure of the pure liquid itself. Thus, it seems that the existence of the Tg minimum in LiCl-water solutions is a reflection of a change in the relative effects of the three interactions described above. We conclude that changes in the configurational thermodynamics caused by the presence of ions should be considered also in relations to ion-solvent interactions. It is worth pointing out that these interactions also alter the crystallization kinetics of the solvent, as Mayer et al.38 have discussed. This in turn means that direct comparisons of the crystallization kinetics of a pure liquid and it acting as a solvent, as done for water and LiCl solution by Angell,40 can be misleading. Conclusion A calorimetric study of isomeric octanols in the temperature range of their glass-liquid transition shows that the types of motifs formed by intermolecular H bonds in associated liquids can be distinguished by examining the effects of electrolytes on the features of their Tg endotherm. The Tg is decreased when the motifs are long, linear chains but is increased when the motifs are ring dimers. The distribution of structural relaxation time increases on the addition of an electrolyte when either type of H-bonded motifs exist in the liquid’s structure, but when the intermolecularly H-bonded motifs in the pure liquid are long, linear chains, the distribution of structural relaxation time is generally narrower than when the motifs are ring dimers. We suggest that for studying the enthalpy crossover or memory effects in glasses by DSC, as originally done by Hofer et al.,15 electrolytic solutions are more suitable than pure liquids because of the increased distribution of relaxation times, which is desirable for detection of the enthalpy crossover or memory effects in glasses. When different materials are compared, the calorimetric Tg determined by the usual manner of drawing tangents to an endotherm, does not correspond to their isostructural relaxation time condition. This raises serious doubts on the significance of qualitative correlations on the molecular kinetics deduced by an intercomparison of the Tg values of various substances, as in recent studies.41 It can be avoided by first calculating the structural relaxation times at different temperatures and then seeking for correlations by comparing the behavior of different materials at those temperatures where their relaxation times are the same. References and Notes (1) (a) Dannhauser, W. J. Chem. Phys. 1968, 48, 1911. (b) Johari, G. P.; Dannhauser, W. J. Chem. Phys. 1968, 48, 5114. (c) Johari, G. P.; Dannhauser, W. J. Chem. Phys. 1969, 50, 1862. (d) Johari, G. P.; Dannhauser, W. J. Phys. Chem. 1968, 72, 3273. (2) Johari, G. P.; Dannhauser, W. J. Chem. Phys. 1968, 48, 3407. (3) Hofer, K.; Johari, G. P. J. Chem. Phys. 1991, 95, 2020. (4) Kirkwood, J. G. J. Chem. Phys. 1939, 7, 911. (5) Fro¨hlich, H. Theory of Dielectrics, 1st ed.; Oxford University: New York, 1949. (6) Hill, N. E.; Vaughan, W. E.; Price, A. H.; Davies, M. Dielectric Properties and Molecular BehaViour; van Nostrad Reinhold: London, 1969; pp 262-264. (7) Vij, J. K.; Scaife, W. G.; Calderwood J. H. J. Phys. D: Appl. Phys. 1981, 14, 733. (8) Scaife, W. G. In Energy Transfer Dynamics; Barrett, T. W.; Pohl, H. A., Eds., Springer-Verlag: New York, 1986; pp 96-111. (9) Johari, G. P. J. Mol. Struct. 1991, 250, 351. (10) Johari, G. P.; Ram, S.; Astl, G.; Mayer, E. J. Noncryst. Solids 1990, 116, 282. (11) Ram, S.; Johari, G. P. Philos. Mag. 1990, 61, 299.
Relaxation and H-Bonding in Isomeric Octanols (12) Johari, G. P.; Pascheto, W.; Jones, S. J. J. Chem. Phys. 1994, 100, 4548. (13) Salvetti, G.; Tombari, E. J. Chem. Phys. 1995, 102, 4987. (14) Johari, G. P. Thermochim. Acta, in press. (15) Hofer, K.; Perez, J.; Johari, G. P. Philos. Mag. 1991, 64, 37. (16) Sartor, G.; Mayer, E.; Johari, G. P. Biophys. J. 1994, 66, 149; J. Polym. Sci. B: Polym. Phys. 1994, 32, 683. (17) Green, J. L.; Fan, J.; Angell, C. A. J. Phys. Chem. 1994, 98, 13780. (18) Tool, A. Q. J. Am. Ceram. Soc. 1946, 29, 240. (19) Narayanaswamy, O. S. J. Am. Ceram. Soc. 1971, 54, 491. (20) Moynihan, C. T.; Macedo, P. B.; Montrose, C. J.; Gupta, P. K.; DeBolt, M. A.; Dill, J. F.; Dom, B. E.; Drake, P. W.; Easteal, A. J.; Elterman, P. B.; Moeller, R. A.; Sasabe, H.; Wilder, J. A. Ann. N.Y. Acad. Sci. 1976, 279, 15. (21) Pascheto, W.; Parthun, M. G.; Hallbrucker, A.; Johari, G. P. J. Non. Cryst. Solids 1994, 171, 182. (22) Kovacs, A. J.; Aklonis, J. J.; Hutchinson, J. M. In Structure of Non-Crystalline Materials; Gaskell, P. H., Ed.; Taylor & Francis: London, 1977; p 153. (23) Kovacs, A. J.; Aklonis, J. J.; Hutchinson, J. M.; Ramos, A. R. J. Polym. Sci., Polym. Phys. 1979, 17, 1097. (24) Hodge, I. M. J. Noncryst. Solids 1994, 169, 211. (25) Hodge, I. M. Science 1995, 267, 1945. (26) Hallbrucker, A.; Johari, G. P. Phys. Chem. Glasses 1989, 30, 211. (27) Berens, A. R.; Hodge, I. M. Macromolecules 1982, 15, 756. (28) Hodge, I. M.; Berens, A. R. Macromolecules 1982, 15, 762. (29) It should be noted that there are seven more formalisms that provide an equally appropriate analysis of the DSC data. These are based on the following: (i) configurational entropy model (Scherrer, G. W. J. Am. Ceram. Soc. 1984, 67, 504. Relaxation in Glass and Composites; Wiley: New York, 1986. Hodge, I. M. Macromolecules 1987, 20, 2897); (ii) distribution of relaxation times model (Cumbrera, F. L.; Munoz, A. Thermochim. Acta 1992, 196, 137. Agarwal, A. J. Polym. Sci., Polym. Phys. 1989, 27, 1449); (iii) defect diffusion model (Perez, J. Polymer. 1988, 29, 483. Physique et Mechanique des Polymeres Amorphes; Lavoiser, Tec & Doc: Paris 1992); (iv) distribution of free volume model (Chow, T. S. Macromolecules 1984, 17, 2336); (v) fractal lattice fluctuation model (Chow, T. S. Macromolecules 1992, 25, 440); (vi) two multiparameter models (Kovacs, A. J.; Aklonis, J. J.; Hutchinson, J. M.; Ramos, A. R. J. Polym. Sci., Polym. Phys. 1979, 17, 1097. Rekhson, S. M. J. Noncryst. Solids 1986, 84, 68). With a suitable choice of parameters, all of the seven models listed above seem to give an
J. Phys. Chem., Vol. 100, No. 16, 1996 6807 acceptable simulation of the experimental data. Despite the fact that the procedure used here assumes that Cp of an equilibrium liquid remains constant with changing temperature and that the values of A and ∆h* obtained from the analysis do not seem to be meaningful, we have used this method for its simplicity. We also found that the approximations made in the formalism require that the temperature interval over which the calculations are done should be small, if Tg is low. This interval of 0.2 K seemed sufficiently low for our analysis. However, caution is necessary in deducing molecular level information from such parameter fitting because the equations are based on the assumption that Cp of the material in a thermodynamically equilibrium state at T > Tg remains constant with changing temperature. This is not the case, as Johari and Perez have discussed in their calculations of the internal energy of an equilibrium of a glass at 0 K (Johari, G. P.; Perez, J. Mol. Phys. 1994, 83, 235). It should also be noted that the relaxation function of eq 1 was used by R. W. Douglas (Proc. 4th Int. Cong. on Rheology, ProVidence, RI; Lee, E. H., Ed.; Wiley: New York, 1965; pp 3-27) and (Br. J. Appl. Phys. 1966, 17, 435) for stress relaxation in glasses with time (see also: Majumdar, C. K. Solid State Comm. 1971, 9, 1087) several years before Williams and Watts (Trans. Faraday Soc. 1970, 66, 80) used the β parameter for describing the asymmetry of dielectric perimittivity and loss spectra. (30) Goldstein, M. J. Chem. Phys. 1976, 64, 4767. (31) Johari, G. P. Phil. Mag. 1980, 41, 41. (32) Johari, G. P.; Hallbrucker, A.; Mayer, E. Nature (London) 1987, 330, 552. (33) Johari, G. P. J. Chem. Phys. 1993, 98, 7324. (34) Kunzler, J. E.; Giauque, W. F. J. Am. Chem. Soc. 1952, 74, 797. (35) Davis, C. W. Ion Association; Butterworths: London 1962. (36) Hofer, K.; Hallbrucker, A.; Mayer, E.; Johari, G. P. J. Phys. Chem. 1989, 93, 4657. (37) Hofer, K.; Astl, G.; Mayer, E.; Johari, G. P. J. Phys. Chem. 1991, 95, 10777. (38) Mayer, E.; Hallbrucker, A.; Sartor, G.; Johari, G. P. J. Phys. Chem. 1995, 99, 5165. (39) Hallbrucker, A.; Mayer, E.; Johari, G. P. Philos. Mag. 1989, 60B, 179. (40) Angell, C. A. J. Phys. Chem. 1993, 97, 6339. (41) Bohmer, R.; Ngai, K. L.; Angel, C. A.; Plazek, D. J. J. Chem. Phys. 1993, 99, 4210.
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