Dielectric Relaxation in Monohydroxy Alcohols and Its Connection to

Dielectric Relaxation in Monohydroxy Alcohols and Its Connection to the Glass Transition Process. S. S. N. Murthy ... Citation data is made available ...
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J. Phys. Chem. 1996, 100, 8508-8517

Dielectric Relaxation in Monohydroxy Alcohols and Its Connection to the Glass Transition Process S. S. N. Murthy School of Physical Sciences, Jawaharlal Nehru UniVersity, New Delhi 110 067, India ReceiVed: December 5, 1995; In Final Form: February 12, 1996X

The nature of dielectric relaxation is studied in a number of supercooled monohydroxy alcohols in the frequency range (106-10-3 Hz) at temperatures above 77 K. Differential scanning calorimeter (DSC) measurements are also carried out on all the alcohols above 100 K. The temperature dependence of the relaxation rates and the spectral characteristic of the main relaxation process are critically examined both above and near the glass transition temperature Tg. The measurements clearly indicate that the relaxation rates in the highviscosity regime are non-Arrhenius down to Tg in all the samples and also in most of the cases the dielectric relaxation rate is found to approach the structural relaxation rate in the vicinity of Tg. In the monohydroxy alcohols where the -OH group is easily accessible for hydrogen bonding, the spectral character is nearly Debye down to Tg. In alcohols, where the -OH group is relatively inaccessible for hydrogen bonding, the spectral half-width is significantly higher than that of Debye behavior and this group of liquids is found to be more fragile than the former group of alcohols. Use of scaling law fits (Dixon et al., 1990) indicates that the spectral data over the entire frequency range is perhaps governed by one single mechanism which cannot be described by any of the conventional equations and, hence, the often observed high-frequency deviation of the data from the conventional equations cannot be taken as evidence for one or more processes operative on the higher frequency side. It is also noticed that the monohydroxy systems studied here do not follow the general pattern when the fragility is plotted against the stretching exponential parameter βWW. An attempt has been made to explain this as due to the “decoupling” of dielectric modes in terms of the model suggested by Hassion and Cole (1955). The origin of sub-Tg processes is also briefly discussed.

Introduction In the study of dielectric relaxation in associated liquids, it is often found that multiple hydrogen (H-) bonded liquids exhibit a distribution of relaxation times (non-Debye behavior), while in monohydroxy liquids only a single relaxation time (Debye behavior) is found.1,2 In this context, Litovitz and McDuffie3 made an interesting observation as regarding their dielectricand mechanical-relaxational behavior. They noticed that in the case of monohydroxy liquids, the dielectric relaxation time is larger than the mechanical relaxation time by a factor of a hundred to a few thousands, while in multiple H-bonded liquids, the dielectric relaxation time is larger by a small factor only. As the glass transition temperature Tg approximately corresponds to a structural relaxation time of 100 s (equivalent to a relaxation frequency of 10-3 Hz), one expects an earlier arrest of dielectric modes during the process of supercooling of the liquid, much before Tg is reached. In other words, if one defines the dielectric Tg (or Tg(D)) as the temperature where the dielectric relaxation time (or frequency) is of the order of the experimental time scale of 200 s (or a frequency of 10-3 Hz), one should observe Tg(D) to be greater than Tg for monohydroxy alcohols and Tg(D) to be much closer to Tg in multiple H-bonded liquids. It is also suggested3,4 that the origin of the distribution of relaxation times (or non-Debye behavior) lies in the cooperative character of the structural relaxation and, hence, all liquids should exhibit a non-Arrhenius behavior. However, the model suggested by these authors cannot explain the non-Arrhenius T dependence and the single relaxation time (Debye) behavior of the dielectric relaxation in the lower aliphatic alcohols. After Litovitz and McDuffie’s publication3 a number of alcohols (which consist of mostly the isomeric octanols) were X

Abstract published in AdVance ACS Abstracts, April 1, 1996.

S0022-3654(95)03596-9 CCC: $12.00

investigated by Dannhauser,5 Johari,6,7 and Goldstein,8 in the audio-frequency range. Based on these experiments, Johari and Goldstein7 (JG) made a few observations which are as follows: (a) There is no correlation between the characteristics of the main relaxation (R) process and the T dependence of the relaxation rate. (b) Most of the alcohols show an Arrhenius behavior in the supercooled state. (c) In most of the cases Tg(D) is found to be equal to Tg, but in those cases which show an Arrhenius behavior and Debye character, Tg(D) is less than Tg by a few degrees. On the basis of these observations JG8 questioned the validity of the model of Litovitz and co-workers and suggested that in those cases where Tg(D) is less than Tg, the dielectric relaxation rate fm would fast approach the structural relaxation rate in the vicinity of Tg, so that the dielectric relaxation rate becomes nonArrhenius and, hence, the relaxation character would become non-Debye leading to the identity Tg(D) ) Tg. Recently,9,10 we tested the validity of the above suggestion in a number of lower aliphatic alcohols by extending the frequency to as low as 10-3 Hz, with help of which we measured the relaxation rates down to Tg(D). The T dependence of the dielectric relaxation rate is observed to be strictly, non-Arrhenius in the high-viscosity or low-temperature regime, and the corresponding relaxational characteristic is Debye down to Tg(D). In most cases the measured difference between Tg(D) and Tg is not outside our experimental uncertainity which is about 2 K, and in no case did we find Tg(D) to be less than Tg. Our results invalidate the suggestion of JG8 partially. Before we discuss the implications of this on the glass transition process in alcohols, we wish to make dielectric measurements near Tg in those alcohols which were discussed by JG in their paper8 and critically examine the spectral behavior from the point of view of the conventional fits vs the recent scaling law approach © 1996 American Chemical Society

Dielectric Relaxation in Monohydroxy Alcohols

J. Phys. Chem., Vol. 100, No. 20, 1996 8509

TABLE 1: Details of the Relaxation Processes parameters of (3) substance

Tg (K)

4-methyl-2-pentanol 2-ethyl-1-hexanol 6-methyl-2-heptanol 6-methyl-3-heptanola 5-methyl-3-heptanola 4-methyl-3-heptanol

157.1 148.9 159.0 159.0 159.0 162.8

2-phenyl-1-ethanol (() 1-phenyl-1-propanol

181.4 198.2

a

R R R R R Rb R′ R R

parameters of (4)

T′g

r

log f0,R

142.0 125.0 142.0 143.0 143.0

11.75 14.31 11.70 14.85 15.80

8.09 6.08 7.86 7.93 8.67

150.0 172.5 181.5

11.56 12.77 15.61

9.95 12.02 13.09

Eβ (Kcal/mol)

log f0,β

β β β

3.32 4.58 5.04

9.93 11.02 11.97

β β

3.51 4.49

8.35 10.69

The corresponding values of Tg and fm are taken from refs 5 and 8. b Not well resolved.

of Dixon et al.11 and examine its connection to the fragility12 of the liquid. This is absolutely necessary before speculating about the nature of dielectric relaxation process in the alcohols in general. Also of interest is the origin of the other relaxation processes that are often found in these systems. Experimental Section The samples studied are given in Table 1. For the sake of convenience, hereafter, we designate the samples as S1, S2, etc. according to the numbers given in Table 1. Details of the samples as studied are as follows: S1 (SLR, India; purity 99%), S2 (SD Fine Chem., India; purity 99%), S3, S6, S8 (Aldrich, USA; purity 99%), and S7 (CDH, India; purity 98%). Samples S1, S2, and S7 were distilled twice prior to their use and the samples S3, S6, and S8 were used as received. We have verified the purity of the samples from their boiling temperatures and refractive indices. Three kinds of measurements were made on the samples: (i) differential scanning calorimeter (DSC) measurements using a DuPont 2000 thermal analyzer with a quench cooling accessory, the details of which are given in our earlier publication;13 (ii) dielectric relaxation measurements using HP4284A precision LCR meter in the frequency range 20-106 Hz; and (iii) dielectric absorption current measurements in the time window of 0.36-100 s using Keithley Model No. 617 programmable electrometer. The actual error in the observed absorption current measurement depends on the way the liquid in the dielectric cell is cooled. In case of rapid cooling the liquid may not fill up the gap between the capacitor plates, and the observed current in this case is always lesser then the actual value. However, the corresponding time dependence may be correct. For normal cooling rates, the absolute value of the absorption current can be in error by about 10% in the nanoampere region due to electrical noise. For the other details of the equipment, the dielectric cell, the accuracy, and the temperature control, the reader may refer to our earlier work.9 The DSC transition temperature data given here is an average of five runs. Results The samples that we have chosen for the present work are mostly the ones which were discussed by JG.8 Before starting the dielectric measurements, all the samples were critically examined near Tg for the possibility of an additional glasslike transition as found in some of the lower aliphatic alcohols (see ref 9 for additional details). DSC measurements have not revealed any transition other than the one at Tg. The Tg values are taken as the onset of the steplike change in the DSC trace for a heating rate of 10 K/min. The DSC standard data analysis program supplied by the manufacturer of the DSC instrument has been used for this purpose. Since the value of Tg is known to be affected by the rate of cooling and also in view of the

Figure 1. Variation of tan δ at 1 kHz. Test frequency, with temperature in (1) 4-methyl-2-pentanol (curve is shifted upwards by 0.4 units; (2) 6-methyl-2-heptanol; (3) 4-methyl-3-heptanol; (4) 2-phenyl-1-ethanol; (5) 1-phenyl-1-propanol.

difficulty in making measurements during the process of cooling, the following procedure was adopted to minimize the effect of cooling rate on the measurement of Tg (for a heating rate of 10 K/min). The samples are quench cooled to 100 K, equilibrated, and kept at this temperature isothermally for about 10 min before heating at a rate of 10 K/min for the determination of Tg. The Tg values are found to be reproducible within (0.25 K in the successive runs on the same sample; but for samples with different weights, the data is often reproducible within (0.4 K in most of the cases. To get first hand information about the existence of various relaxation processes, the variation of tan δ at 1 KHz test frequency vs temperature has been plotted in Figure 1 in the case of four samples. There is evidence of sub-Tg processes of much smaller magnitude in these plots in addition to the dominant R-process above Tg. The tan δ variation with temperature is similar in the case of the other two samples as well and hence is not given in Figure 1. The data taken on the LCR bridge in the frequency range of 20-106 Hz is shown in Figures 2-4. The relaxation parameters corresponding to the main relaxation (R-) process are obtained by fitting the real part of the complex dielectric permittivity (*(f)) to the Cole-

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Figure 2. Double logarithmic plot of dielectric loss ′′ vs frequency in 4-methyl-2-pentanol at 194 K (curve 1) and in 6-methyl-2-heptanol at 204.4 K (curve 2). The lower curve of (2) on the lower frequency side corresponds to the dipolar loss (′′ - ′′dc) obtained by subtracting the d.c. loss from the total loss). Note that the Debye equation is valid over 31/2 decades of frequency only and the higher frequency points do not follow Debye equation.

Davidson (CD) equation,14 which is given by

[

]

*(f) - ∞ f ) 1+i 0 - ∞ f0

-βCD

(1)

where βCD is the asymmetric parameter, f0 is the mean relaxation frequency, 0 is the static dielectric constant, and ∞ is the limiting dielectric constant for the process under consideration. The above equation reduces to the Debye form for βCD ) 1. Instead of f0, the peak loss frequency fm is used in all the subsequent analysis as it is found15 to represent the data better than f0. With the help of the identity fm ) f0 tan (π/2(1 + βCD)), the peak loss frequency fm is determined. In the case of samples 1 and 2, the data above Tg can be fitted to the Debye from (βCD ) 1 in eq 1) throughout the temperature range of our bridge measurements, though deviations from the Debye form are noticed at much higher frequencies. Since deviations from Debye form can be seen better in a double logarithmic plot of ′′ vs frequency, the loss data corresponding to samples 1 and 2 have been plotted in Figure 2. In the case of sample 2, i.e., 6-methyl-2-heptanol, there is a considerable contribution of d.c. loss (′′dc ) 1.8 × 1012σDC/f, where σDC is the d.c. conductivity) to the total dielectric loss. This loss was subtracted from the total loss at every frequency to obtain the true dipolar loss (lower curves corresponding to sample 2 in Figure 2). From Figure 2, it is seen that though most part of the data can very well be represented by the Debyde equation there is a considerable deviation of the experimental points from the Debye behavior of the higher frequency side. A CD equation with βCD of approximately 0.97 (with a different ∞ value) is also found to fit the data satisfactorily in the lower and middle frequency regions, but deviations of the experimental points from the CD equation are noticed again on the higher frequency side. In the case of 4-methyl-3-heptanol (Figure 3) the dielectric strength is so small that it is very difficult to get even approximate information about the underlying processes. It appears that the Debye process which was dominant in case of other samples, such as that for example as in Figure 2, appears to be very much suppressed in this case. Though the CC diagram has the inherent weakness of not showing the asymptotic regions clearly, we still prefer to plot the data for this

Figure 3. CC diagrams in 4-methyl-3-heptanol corresponding to the temperatures above Tg. Note that the R process is seen as a small semicircle on the low-frequency side and increases in its magnitude with increase in temperature. The numbers beside the experimental points indicate the corresponding frequency in kHz.

sample in the form of the CC diagram instead of log ′′ vs log f in order to get first-hand information about the various processes that are operational in the frequency window shown in Figure 3 (with our ultra lower frequency measurement setup, we could not detect the processes shown in Figure 3 near Tg as the corresponding absorption current is below the detection level of our experimental setup). A closer examination of Figure 3 reveals that the CC arc has a tendency to approach the real axis in a perpendicular fashion as expected for a Debye (or CD) process, and this Debye-like process appears to be getting suppressed on lowering the temperature. At lower temperatures, for example at 192 K, the entire data can approximately be represented by a CC arc function given by

[

]

*(f) - ∞ f ) 1+i 0 - ∞ f0

RCC-1

(2)

where RCC is the symmetric distribution parameter. However, at higher temperatures above 192 K the entire data cannot be represented by eq 2 alone, but one can describe the data as a superposition of two processes, viz., a high-frequency process which can be approximated by a depressed CC are equation and a Debye process (the latter of which may be identified with the R process) as shown in Figure 3 corresponding to 203.7 K. This procedure allowed estimation of fm values corresponding to the process represented by the CC arc equation, the details of which are given in Table 1. (Since the fm values corresponding to the second or higher frequency process are found to be non-Arrhenius in their T dependence, the second process is designated as a R′ process in Figure 3.) No attempt was made to resolve the lower frequency “Debye-like” process as it is found to involve a lot of uncertainty due to very low magnitude. Since, the origin of the second (or R′) process is not known, we do not wish to discuss it further. In the case of 2-phenyl-1-ethanol (Figure 4), the dielectric loss is found to contain contribution from the d.c. conduction and can be seen as a low-frequency spur (where the corresponding loss is found to vary approximately as 1/f, without any dispersion in the ′ values). Hence, the d.c. loss is subtracted from the total loss to obtain the dipolar loss (Figure 4). From Figure 4, one can see that the dipolar loss in the entire frequency range cannot be described by a single equation, but the lower and middle frequency region can well be represented

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TABLE 2: Details of Tg and Tg(D) and the Nature of r Process and Fragility nature of R process

a

T > Tg

T = Tg

158.0 154.0 158.8 169.2 169.1

nearly Debye nearly Debye nearly Debye nearly Debye nearly Debye

nearly Debye nearly Debye nearly Debye

42.0 27.0 40.1 34.8 37.1

184.0 198.4

strongly non-Debye strongly non-Debye

strongly non-Debye slightly non-Debye

74.0 66.4

substance

Tg (K)

Tg(D) (K)

4-methyl-2-pentanol 2-ethyl-1-hexanol 6-methyl-2-heptanol 6-methyl-3-heptanola 5-methyl-3-heptanola 4-methyl-3-heptanolb 2-phenyl-1-ethanol 1-phenyl-1-propanol

157.1 148.9 159.0 159.0 159.0 162.8 181.4 198.2

fragility m

This follows from Table 1 (the original data8 is not ours). b The corresponding R process is much smaller in magnitude.

Figure 4. Double logarithmic plot of dielectric loss ′′ vs frequency in 2-phenyl-1-ethanol at 209.4 K (curve 1) and 1-phenyl-1-propanol at 220.6 K (curve 2). (In the case of curve 1, the loss contains contribution from d.c. loss and the lower curves on the lower frequency side correspond to the dipolar loss obtained by subtracting the d.c. loss from the total loss.) Note that the loss curves follow eq 1 on the lower and middle frequency region and the corresponding CD distribution parameter βCD is 0.80 and 0.67, respectively. Note the deviation of the experimental data from CD equation on the higher frequency side.

by CD equation. The same trend is seen in the case of 1-phenyl1-propanol (Figure 4). The deviation of the CD equation from the experimental points on the higher frequency side is similar to what is seen in Figure 2. To give an approximate idea to the reader about the change of spectral shape with temperature, the variation of the distribution parameter βCD thus determined is shown in Figure 6, along with the βCD values obtained for temperatures near Tg from time domain measurements. The results of the time domain (dielectric) measurements near Tg are shown in Figure 5 in the form of log iD(t) vs t (where iD(t) is the discharge (dielectric absorption) current); the Debye form of behavior iD(t) R e-t/τ can be seen as a straight line in this plot. The temperature variation of the fm values corresponding to the R process is found to be non-Arrhenius and is well described by the power law (PL) equation15

(

fm,R ) f0,R

)

T - Tg′ Tg′

r

(3)

for all fm values below 106 Hz. In the above equation Tg′ is the limiting glass transition temperature as seen in the dielectric measurements and r is the dynamic exponent. The parameters of eq 3 corresponding to various samples are given in Table 1. In Table 2, the values of Tg(D) and Tg are given along with the spectral characteristics of the (main) R process above and near Tg. The Arrhenius plots corresponding to the other samples are given in Figures 7 and 8.

Figure 5. Semilogarithmic plot of the variation of the discharge current iD(t) with time in the temperature region just above Tg. Note that the Debye process can be seen as a straight line in the above plot. Also note that in 1-phenyl-1-propanol the relaxation current is slightly nonDebye and in 2-phenyl-1-ethanol it is strongly non-Debye.

Figure 6. Variation of βCD with temperature in 2-phenyl-1-ethanol and 1-phenyl-1-propanol.

The spectral shape of β-process is found to obey eq 2 (as is usually the case), and the fm values thus obtained obey the Arrhenius form of equation

fm,β ) f0,β exp(-Eβ/RT)

(4)

where Eβ is the activation energy for the β process. The details of (eq 4) for all the samples are given in Table 1, in those cases where they are resolved. To get some insight into the mechanism of dispersion of R process, the temperature variation of dielectric strength ∆(0 - ∞) (where ∞ is taken as 1.05nD2; nD is the refractive index at the corresponding temperature) is plotted for all the cases in Figure 9. The Fuoss-Kirckwood correlation factor g has also been calculated using the following relation:16

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Figure 7. Arrhenius plots corresponding to the R process in the samples. The solid lines are power law fits for the parameters given in Table 1. The points (.) correspond to the DSC Tg’s (structural relaxation frequency of 10-3 Hz). The curves labeled are (1): 4-methyl2-pentanol, (2) 2-ethyl-1-hexanol, (3) 6-methyl-2-heptanol, (4) 2-phenyl1-ethanol, and (5) 1-phenyl-1-propanol.

(

)

30 ∞ + 2 24ΠNFµ02 0 ) ∞ + g 20 + ∞ 3 3MkT

(5)

In this formulation, 0 is the equilibrium dielectric constant, N is the Avogadro’s number, M is the molecular weight, F is the density, µ0 is the dipole moment of the molecule in vacuum, and kT is the thermal energy. The value of g at each temperature is calculated in all the cases, with the help of the published dipole moments17,18 and also by assuming a linear variation of density F(T) ) F0 - RT (with R approximated as 8.4 × 10-4 gm/(cm3 K) and F0 in the above identity is calculated with help of the density data19 given at 298 K). All these results are plotted in a single figure (Figure 10) for comparison. In Figure 11, the relaxation time 〈τ〉 in seconds ()(2πfm)-1) is plotted against (Tg/T) for the sake of classification of the liquids on the basis of their strength. In view of the recent attempts by researchers in relating the departure from the Debye behavior to fragility, the fragility defined12 is measured as,

m)

d(log〈τ〉) | ′ d(Tg/T) T)Tg

(6)

which in turn can be written with the help of eq 3 as

m)

-d(log fm) rTg(0.36229) |T)Tg ) d(Tg/T) (Tg - Tg′)

(7)

In Figure 12, the fragility m has been plotted against the stretching exponent βWW of the William-Watts decay function. Here, use has been made of the relation20 between the width

Figure 8. Arrhenius plots of 6-methyl-3-heptanol and 5-methyl-3heptanol. The fm values are taken from the work of Dannhauser5 and the Tg’s from ref 8. The solid lines correspond to the power law fits (3) for the parameters given in Table 1. Note that the data points are more consistent with a power law than to an Arrhenius behavior.

parameter βDC of eq 1 and βWW, where

βWW ) 0.021 + 1.39βDC - 0.418βDC2

(8)

In Figure 13, experimental data in the form of the scaling plot has been plotted as suggested by Dixon et al.11 to see whether high-frequency deviation of the experimental points from eq 1 (as shown in Figures 2 and 4) can be argued in favor of some other high-frequency processes. In Figure 13, the normalized width w ) W/WD, where w is the loss width at half-maximum in decades, and WD ) 1.142 is the Debye width. Discussion Conventional Analysis vs Scaling Law. The traditional dielectric data analysis starts with the plotting of the complex plane or Cole-Cole diagram and use of one of the conventional experimental equations such as eq 1 to describe the data from which one gets the distribution parameter and the peak loss frequency fm. However, while dealing with monohydroxy alcohols, one often finds that a Debye form (βCD ) 1 in eq 1) is generally sufficient to describe the data. Deviations are often observed on the higher frequency side as in figure 2 and this has tempted many workers in the past to attribute it to some other higher frequency process and resolve it using superposition principle.9 This analysis often gives rise to one or more processes, and the temperature dependence of the relaxation rates corresponding to the resolved processes often resembled that

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Figure 9. Variation of the dielectric strength (0 - 1.05nD2) with inverse of temperature in the samples studied. The temperature is normalized to the corresponding Tg’s. The curves labeled are (1) 4-methyl-2-pentanol, (2) 6-methyl-2-heptanol, (3) 4-methyl-3-heptanol, (4) 2-ethyl-1-hexanol, (5) 2-phenyl-1-ethanol, and (6) 1-phenyl-1propanol.

of the main (or R1) process (e.g., ref 9). However, no clear justification is given, although it is not totally unreasonable to expect many processes in a complicated system such as H-bonded liquid. Often doubts are raised regarding this kind of analysis, because the origin of the resolved high-frequency processes is not clearly known. If the same data is plotted as suggested by Dixon et al.11 (Figure 13), one can see that the data corresponding to each sample for different temperatures collapses to a single curve which deviates from the Debye behavior on the higher frequency side. This indicates that the data (e.g., Figures 2 and 3) over the entire frequency range is perhaps governed by a single mechanism which is clearly not Debye. In the same figure, one can also see that the data corresponding to all the samples (other than 4-methyl-3-heptanol) collapse to one (nearly) single curve which is similar to the one given by Dixon et al.11 This indicates that a single parameter, namely the normalized width (w), may be sufficient enough to describe the entire data, which is governed by a single mechanism (which obviously cannot be described by any of the conventional equations such as eq 1 or the William-Watts equation) and hence the analysis in terms of a superposition of two or more processes may not be “fully” correct. Since none of the conventional equations describes the data correctly, the results obtained continue to be explained based on eq 1 for the R process, which does not alter the general conclusions to be arrived at. 1. The β Process. The tan δ curves shown in Figure 1 clearly reveal one sub-Tg process (designated as the β-process in Table 1) in addition to the R process above Tg. The β process is found to be symmetrical and can be described by eq 2 with the distribution parameter (Rcc) values in the range of 0.600.72. The characteristics of the β process are found to be very similar to those seen in other alcohols9,10 and van der Waals liquids.21 Our recent study22 of the sub-Tg processes in glasses formed by dipolar solutes in nonpolar glass forming liquids and

Figure 10. Variation of the correlation factor g with temperature in the samples studied. The curves labeled are (1): 4-methyl-2-pentanol; (2) 2-ethyl-1-hexanol; (3) 6-methyl-2-heptanol; (4) 4-methyl-3-heptanol; (5) 2-phenyl-1-ethanol; and (6) 1-phenyl-1-propanol.

also in glasses formed by these dipolar solutes reveals that the sub-Tg processes occurring in pure glasses are due to intramolecular degrees of freedom. Our study also reveals that, when the solute molecule is smaller than the solvent molecule, rotation of the solute molecules can occur in the cages formed by the solvent matrix giving rise to an additional sub-Tg process with much higher activation energy (than the Eβ values shown in Table 1). In addition to this, the Eβ values shown in Table 1 are much larger than the Eβ value (2.0-2.5 Kcal/mol) found for the -OH group rotation in other alcohols.9 Thus it is tempting to attribute the β process shown in Table 1 to segmental motion involving one or two carbon atoms along with the -OH group. However, a pin-pointed explanation as to the exact magnitude of Eβ requires a much more detailed study by extending the measurements to much lower temperatures. The large values of the distribution parameter RCC may be explained as due to a wide range of environments for (the segments of) the molecules which is natural to expect in an amorphous glassy matrix. 2. The R process which is nearly Debye in nature at higher temperatures above Tg (Figure 2) maintains its Debye character down to Tg (Figure 5) in disagreement with the suggestion of JG. 3. The T dependence of the R process is strictly nonArrhenius, (Figure 7) where the power law expression (eq 3) for the T dependence of fm is valid over nine decades of fm. (However, in this connection we wish to point out that one should not expect eq 3 to describe the data at still higher temperatures as T dependence may return to Arrhenius form where the individual characteristics of liquid dominate the

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Figure 11. Modified Arrhenius plot for classification of strong and fragile character of the hydrogen-bonded liquids studied here. Plotted is the logarithm of the average dielectric relaxation time 〈τ〉 ()(2πfm)-1) vs the inverse temperature scaled by Tg ) T (〈τ〉 ) 100 s or fm ) 10-3 Hz). The data for 1-propanol, 1-pentanol, and eugenol are taken from our previous study.10

Figure 12. Fragility m plotted against the William-Watts exponent βWW for many of the glass formers which includes the results of the present study. The solid lines correspond to m ) 250 ( 30 - 320βWW (see ref 12 for complete details on this).

relaxation process13,23). One can also see from Figure 8 that the data of Dannhauser on 6-methyl-3-heptanol and 5-methyl3-heptanol are more consistent with a PL equation (3) rather than the Arrhenius behavior as quoted by JG. It is also clear from the discussion given in point 2 above that the origin of non-Arrhenius character in monohydroxy alcohols, probably,

lies elsewhere and should not be related to the spectral characteristics. 4. In the case of 2-phenyl-1-ethanol, the spectral characteristic is far from Debye with βCD in the range of 0.76-0.82, in the high-temperature region (Figure 6) and its non-Debye character is preserved down to Tg (Figure 5). We have observed

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J. Phys. Chem., Vol. 100, No. 20, 1996 8515

Figure 13. Scaling plot of the data for the liquid studied in this paper (except 4-methyl-3-pentanol). Here (1/w) log(′′fm/fδ) is plotted against (1/w)(1/w + 1) log(f/fm), where ∆ ) 0 - 1.05nD2. The dashed lines correspond to Debye behavior. The curves corresponding to some of the individual samples are shifted vertically for clarity.

that the corresponding dielectric loss current given in Figure 5 varies as exp(-t/τ)βWW with βWW equal to 0.78. This is approximately equivalent20 to a CD expression with βCD = 0.7. It is further noticed that βCD varies smoothly with temperature in a linear fashion down to Tg as shown in Figure 6. Similar T dependence is often observed for van der Waals liquids21,22 and multiple H-bonded liquids.10 In the case of 1-phenyl-1propanol, the βCD variation with temperature does not follow the usual trend as seen, for example, in the case of 2-phenyl1-ethanol (Figure 6). The time domain data for this case is slightly non-Debye in the region of Tg and the corresponding absorption currents as given in Figure 5 can be approximately described with βCD ) 0.97 (see Figure 6). This gives us the suspicion that the loss curve shown in Figure 4 for this sample is actually a result of two competing processes. The process on the lower frequency side is probably Debye in nature, which increases further in its magnitude at the cost of the other, and reveals itself as a Debye process in the region of Tg. It is interesting in this context to note that the correlation factor g (Figure 10) for this sample has a tendency to increase sharply on approaching Tg. 5. Taking into account the “looseness” in the definition of Tg and associated experimental inaccuracies as discussed in the earlier sections, we see in Table 2 that the difference between Tg(D) and Tg is small in most of the alcohols. Such a trend is observed in the case of other alcohols as well.10 This implies that the ratio of dielectric to structural relaxation rates comes down as the liquid approaches Tg as predicted by JG. However, it is surprising that the relaxation spectrum still remains as nearly Debye even though the corresponding liquid viscosity is of the order of 1012 P. This apparent failure of the JG hypothesis, in our view, is probably because the dielectric modes responsible

for the R process are somehow decoupled and are different from the structural modes. 6. The ∆ variation in Figure 9 shows a change in the trend of the T dependence of ∆ in the high-viscosity regime, which otherwise should have a T-1 dependence.25 This behavior can better be understood by plotting the T dependence of the correlation factor g, for parallel alignment of the dipoles, g > 1, and for antiparalleled alignment, g < 1. In alcohols, parallel alignment occurs when the molecules are H bonded in a linear chain and antiparallel alignment occurs when the molecules are H bonded in the form of a ring.5 One striking feature of Figure 10 is that 4-methyl-3-heptanol, which has a value of g closer to 1 on the high-temperature side, has almost a near zero value for g on the low-temperature side which may be attributed to the increasing tendency for ring formation as Tg is approached. This follows from the entropy consideration as in the Dannhauser’s molecular model5 based on H-bond associative equilibria involving both ring dimers and linear chain n-mers. Of the remaining samples, 1-phenyl-1-propanol (with the -OH group sterically blocked by the phenyl ring) has the smallest g value on the low-temperature side followed by 2-phenyl-1ethanol. Liquids like 6-methyl-2-heptanol and 4-methyl-2pentanol, in which the -OH group is relatively accessible for H bonding, tend to form open chains as evident from the larger g values. Thus, except for 4-methyl-3-heptanol, all the liquids appear to have a preference for open chains rather than for ring dimers, which is probably due to the entropy factor associated with the geometry of the molecules as in Dannhauser’s model.5 In the present context it is interesting to note that a drastic change in the g value occurs in the temperature region below 1.25Tg where a number of glass forming liquids show a change in the dynamics.23 It may also be noted that liquids with lower

8516 J. Phys. Chem., Vol. 100, No. 20, 1996 g values are non-Debye in spectral characteristic as can be seen in the case of 1-phenyl-1-propanol and 2-phenyl-1-ethanol. 7. From Figure 11, it is seen that liquids with increasing difficulty in hydrogen bonding and smaller g values are more fragile in nature and, hence, have greater m values. The liquids like 1-propanol,10 and 1-pentanol,10 which have the highest g values and are known to have an easily accessible -OH group for hydrogen bonding, are more Arrhenius and, hence, have lesser m values. Eugenol10 (4-allyl-2-methoxyphenol) which has a g value of =1.1, is the most fragile liquid among the monohydroxy liquids shown in Figure 11 where the corresponding m value is 74. From Figure 12, it is very clear that the monohydroxy alcohols do not follow the general pattern set by the other glass-forming liquids and appear to be an exception to the relation between m and stretching exponent βww, indicating that the mechanism of dielectric relaxation in monohydroxy alcohols is probably different from the rest of the materials and the corresponding dielectric modes are decoupled from the structural modes. From Figures 11 and 12, one gathers that with increase in the accessibility of the -OH group for H bonding (and hence an increase in g value), the fragility decreases and the corresponding dielectric modes get increasingly decoupled. Interestingly, one can also see that the multiple H-bonded liquid, D-sorbitol which is the most fragile (m ) 119) liquid among the liquids shown in Figure 11, has the smallest βww (=0.37). This is not surprisingly because with increase in the number of -OH sites per molecule the coupling between the dielectric and structural modes increases.10 Based on our observations and inferences given in points 1-7 above, the nature of dielectric relaxation in monohydroxy alcohols may be visualized in a manner as follows, which is a synthesis of ideas which have been proposed before.5,7,10,14,26 It is clearly evident by now that the origin of the Debye process lies in the linear chain formation. Since most of the polarization is associated with the R process and also since, the main dipole lies in the -OH group the H-bonding breakage is necessary for dipolar orientation. The breaking and reformation of H bonds are part of the structural relaxation (and hence, the viscous relaxation) and are not part of the dielectric relaxation process. The actual dielectric process starts when the molecule on being liberated tries to orient by a large angle after which the -OH group latches on to an oxygen of another molecule (this is the “-OH flipping process” in the model of Hassion and Cole26). The molecules require sufficient energy for this and also the neighboring molecule (to which it gets latched on after rotation) should be favorably disposed. As the surroundings are also part of the H-bonded structure, the energy of activation for rotation will be influenced by the H-bond energy but may not be equated to it. Favorable disposition of the neighboring (second) molecule may require several makes and breaks of H bonds. Since there is a large positive correlation between neighboring dipoles (g factor substantially greater than unity) the dipole orientation cannot proceed in small steps. The geometry of the linear H-bonded network demands a large concerted reorientation of the reference dipole and its neighbours. Thus, there is a large “waiting time” before the dipolar alignment. Hence, the dielectric relaxation rates are always slower than the structural relaxation rates. This leads to the identity Tg(D) > Tg. So far as the “-OH flipping” is concerned, it occurs in similar surroundings which are part of the H-bonded structure. The flipping of the -OH group and the subsequent rotation of the molecules may be visualized as a rotation in a medium of constant viscosity, influenced only by the surroundings and independent of the rest of the matrix. Thus, we can see that the dielectric modes are not directly coupled to the structural

Murthy modes and this probably gives rise to the Debye behavior for the R process. Since the surroundings act as a medium of constant viscosity and are part of the H-bonded structure, the activation energy E will be influenced greatly by lowering the temperature of the surroundings. Here one notices that the T dependence of the structural relaxation of the surroundings (which is non-Arrhenius) influences the T dependence of the relaxation rate corresponding to the R process. This leads to non-Arrhenius behavior of the R process on the lower temperature range. The above model explains all the experimental observations made above in the case of monohydroxy alcohols. However, it is still not clear as to why in many of the alcohols Tg(D) is not too different from Tg. Dielectric relaxation experiments, especially in the vicinity of Tg with much greater accuracy than the present one, will perhaps be able to answer this question. In 2-phenyl-1-ethanol and 1-phenyl-1-propanol it is interesting to note that the -OH group is sterically blocked by the phenyl ring and the corresponding g factor is also smaller, indicating that extensive polymerization is not taking place at least at temperatures far above Tg. Interestingly, from point 7 above, it is clear that these liquids are more fragile than the alcohols with more open -OH groups, indicating a greater coupling of the dielectric modes to the structural modes as revealed by the larger departures from the Debye behavior, and thus indicating a decrease in the importance of the -OH flipping mechanism in the overall relaxation process. Conclusions By extending the dielectric relaxation measurements down to Tg′ we have critically examined the T dependence of the relaxation rates and also the spectral behavior of the main relaxation process in monohydroxy alcohols. The T dependence of the dielectric relaxation rate is found to be strictly nonArrhenius on the lower temperature side. In most of the cases we have noticed the dielectric Tg (or Tg(D)) to be approximately the same as DSC Tg (within our experimental uncertainity) implying that the dielectric and structural relaxation rates are of nearly the same order near Tg. As far as the spectral shape is concerned, we have identified two groups of liquids. The former consists of liquids with relatively accessible -OH groups and the corresponding spectral characteristic is nearly Debye down to Tg at least in the middle frequency region. The characteristics of this group may be explained qualitatively in terms of the model of Hassion and Cole.24 We have noticed a large deviation from the Debye behavior in the second group of liquids (like 2-phenyl-1-ethanol etc.) which consists of liquids where the -OH group on the molecule is sterically blocked by the bulkier phenyl group and, hence, extensive polymerization is not possible as in the first group of liquids as indicated by the corresponding correlation factors g. Interestingly, all the monohydroxy liquids fall in the same category in the plot of fragility vs stretching exponent βWW and are found to be exceptions to the general behavior observed in a wide variety of glass-forming liquids. In the second group of liquids an increase in the steric hindrance to the -OH group results in smaller g values, greater fragility, and increased deviations from the Debye behavior, indicating that the dielectric relaxation modes in these liquids are increasingly coupled to structural modes and, hence, the spectral behavior moves toward the more general pattern as observed in other ligands. Use of scaling law fits (Dixon et al., 1990) indicate that the spectral data over the entire frequency range is perhaps governed by a single mechanism which cannot be described by any of the conventional equations and hence the often observed high-frequency

Dielectric Relaxation in Monohydroxy Alcohols deviation of the data from the conventional equations cannot be taken as evidence for one or more processes operative on the higher frequency side. Acknowledgment. The author acknowledges the Department of Science and Technology, Government of India, for financial support. The author also thanks the unknown referees for their valuable comments. References and Notes (1) Hill, N. E.; Vaughan, W. E.; Price, A. H.; Davies, M. Dielectric Properties and Molecular BehaVior; Van Nostrand Reinhold: London, 1969. (2) Davidson, D. W.; Cole, R. H. J. Chem. Phys. 1951, 19, 1484. (3) Litovitz, T. A.; McDuffie, G. E., Jr. J. Chem. Phys. 1963, 39, 723. (4) Litovitz, T. A.; Davis, C. M., Physical Acoustics; Mason, W. P., Ed.; Academic Press: New York, 1964, Vol. 2, Chapter 5. (5) Dannhauser, W. J. Chem. Phys. 1968, 48, 1911, 1918. (6) Johari, G. P. Ann. N.Y. Acad. Sci. 1976, 276, 117. (7) Johari, G. P.; Dannhauser, W. J. Chem. Phys. 1969, 50, 1862. (8) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1971, 55, 4245. (9) Murthy, S. S. N.; Nayak, S. K. J. Chem. Phys. 1993, 99, 5362. (10) Murthy, S. S. N. Mol. Phys., in press. (11) Dixon, P. K.; Wu, L.; Nagel, S. R.; Williams, B. D.; Garini, J. P. Phys. ReV. Lett., 1990, 65, 1108. (12) Bohmer, R.; Ngai, K. L.; Angell, C. A.; Plazek, D. J. J. Chem. Phys. 1993, 99, 4201.

J. Phys. Chem., Vol. 100, No. 20, 1996 8517 (13) Murthy, S. S. N.; Gangasharan; Nayak, S. K. J. Chem. Soc., Faraday Trans. 1993, 89, 509. (14) Cole, R. A.; Davidson, D. W. J. Chem. Phys. 1952, 20, 1389. (15) Murthy, S. S. N. J. Chem. Phys. 1990, 92, 2684; J. Chem. Soc., Faraday Trans. 2 1989, 85, 581. (16) Dannhauser, W.; Bahe, L. W. J. Chem. Phys. 1964, 40, 3058. (17) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman & Co.: San Francisco, 1963. (18) Sidwick, N. V.; Hampson, Q. C.; Marsden, R. J. B. A Table of Dipole Moments (Reprinted from Trans. Faraday Soc.); Gurney and Jackson: London, 1934. (19) Weast, R. C.; Astle, M. J. Handbook of Physics and Chemistry, 63rd ed.; CRC: Boca Raton, FL, 1993. (20) Fransson, A.; Backstrom, G. Mol. Phys. 1987, 61, 131. (21) Gangasharn; Murthy, S. S. N. J. Chem. Phys. 1993, 99, 9865. Murthy, S. S. N.; Sobhanadri, J.; Gangasharan. J. Chem. Phys. 1994, 100, 4606. (22) Murthy, S. S. N.; Paikary, A.; Arya, N. J. Chem. Phys. 1995, 102, 8213. (23) Murthy, S. S. N. J. Polym. Sci. Polym. Phys. 1993, 31, 475. (24) Nayak, S. K.; Murthy, S. S. N. J. Chem. Phys. 1993, 98, 1607. (25) Murthy, S. S. N. J. Chem. Phys. 1994, 100, 6102. (26) Hassion, F. X.; Cole, R. H. J. Chem. Phys. 1955, 23, 1756. (27) McDuffie, G.; Litovitz, T. A. J. Chem. Phys. 1962, 37, 239.

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