Dielectric and Calorimetric Study of Orientationally Disordered

2606

J. Phys. Chem. B 2008, 112, 2606-2615

Dielectric and Calorimetric Study of Orientationally Disordered Phases in Two Unusual Two-Component Systems L. P. Singh and S. S. N. Murthy* School of Physical Sciences, Jawaharlal Nehru UniVersity, New Delhi - 110 067, India ReceiVed: September 24, 2007; In Final Form: December 6, 2007

In the present communication, investigations of two interesting (two-component) solid solutions are reported where one is a hydrogen (H-)-bonded pair and the other is a non-H-bonded pair. The former is the twocomponent system cyclooctanol (COOL) + cycloheptanol (CHOL), which forms a simple cubic phase [Rute, M. A.; Salud, J.; Negrier, P.; Lo´pez, D. O.; Tamarit, J. Ll.; Puertas, R.; Barrio, M.; Mondieig, D. J. Phys. Chem. B 2003, 107, 5914]. This solid phase has been investigated at low temperatures and for several concentrations by means of low-frequency dielectric spectroscopy and differential scanning calorimetry (DSC). Depending upon the concentration, this phase reveals a glass transition in the temperature range of 138-172 K and a pronounced relaxation process identifiable with the so-called R process characteristic of a singlecomponent orientationally disordered crystal. The dielectric spectra are found to follow the Havriliak-Negami (HN) equation. The analysis of the various parameters obtained show an isomorphic relationship between the simple cubic phases of both pure components through a continuous change of parameters. In addition, a sub-Tg process, which is Arrhenius, is found. The kinetic freezing of the various dielectric processes has been critically examined in relation to the Tg found in the DSC experiments. The non-H-bonded pair that has been studied is cis-1,2-dimethylcyclohexane (DMCH) and cyclohexylchloride (CHC). The liquid mixture of DMCH and CHC upon lowering the temperature forms a solid solution on the DMCH-rich side, which is an orientationally disordered crystal. This phase demonstrates a pronounced R process in the dielectric measurements that follows the HN equation. The results are discussed in the context of the solid-liquid phase diagram of this binary system. The observed deviations from Arrhenius and Debye behaviors in the solid solutions studied in this paper are shown to follow the “strong-fragility” pattern of Angell.

1. Introduction Liquids consisting of spherically symmetric molecules upon cooling freeze to a plastic crystalline (PC) state where the molecules have translational symmetry but are orientationally disordered (OD).1,2 This OD phase is extremely popular with researchers working on glass transition phenomena since only one degree of freedom is involved. This phase can be supercooled to lower temperatures to reach a kind of glassy state at the so-called glass transition temperature (Tg), which corresponds to the frozen OD phase. Although the OD phase was observed in dielectric measurements by White et al.3,4 in the year 1940, it was not categorized as glass-like phenomena until the work of Huffman et al.5 in 1949 where it became apparent in specific heat measurements as a step-like change. Later research on the OD phase was pursued by many researchers.6-14 Johari15,16 had shown that these materials have many commonalities with glassforming liquids. After these publications15,16 by Johari, many papers were published on this subject.17-19 The relaxation in the supercooled PC phase is found to be very similar in characteristics to supercooled liquids.15,20-45 However, the number of plastic crystalline materials that can be supercooled to reach the glassy state is not large enough20 to get a clear picture about the factors that determine the glass formation in these materials. To study a nonpolar matrix using dielectric spectroscopy, one has to add a dipolar component in a small quantity that is * To whom correspondence should be addressed. E-mail: ssnm0700@ mail.jnu.ac.in.

miscible with the host matrix because the dipolar molecule is expected to rotate cooperatively with the host matrix. If the host matrix is glass forming, then the dipolar component may, in addition, show characteristics of its own through a secondary relaxation process.15-17,46 A similar technique may be extended to the study of nonpolar plastic crystals using a dipolar solute which forms a solid solution. In experimental practice, to some extent, this can be considered as a study of two-component34-37,47 plastic crystalline substances. There appears to be not many research publications on this topic and hence forms the basis for the present study. Among the H-bonded systems, the binary system of cyclooctanol and cycloheptanol is interesting because it forms a solid solution.36 Apart from this, as shown below, the system cis-1,2-dimethylcyclohexane and cyclohexylchloride also forms an interesting system to study. 2. Experimental Section The samples studied here are cyclooctanol or COOL (99% purity), cycloheptanol or CHOL (97%), cis-1,2-dimethylcyclohexane or DMCH (99%), and cyclohexylchloride or CHC (99%), which were obtained from Aldrich Co., U.S.A. They were all used as received without any further purification. Three kinds of measurements were performed on the samples, (i) the differential scanning calorimetry (DSC) measurements using a Perkin-Elmer Sapphire DSC with a quench cooling accessory, the details of which were given in earlier studies,34 (ii) frequency domain dielectric measurements using a HP 4284A precision LCR meter in the frequency range of 20 Hz-1 MHz, and (iii)

10.1021/jp077663o CCC: $40.75 © 2008 American Chemical Society Published on Web 02/07/2008

Dielectric and Calorimetric Study of OD Phases

Figure 1. Behavior of the COOL-CHOL binary system for xm ) 0.25. (a) DSC scan for a heating rate of 10 deg/min (sample size )10.8 mg). Temperature variation of the (b) real and (c) imaginary parts of the complex permittivity at various test frequencies. The phase designated as SI is the solid solution which is simple cubic, and Tsol is the solidus temperature. The step-like rise of dielectric loss above Tliq is mainly due to the dc loss which varies as f-1, where f is the test frequency.

for frequencies in the range of 20-10-3 Hz, the dielectric absorption currents in the time window of 0.01-1000 s were sampled using a digital storage oscilloscope (DSO) card DSO2200 (Link Instruments Inc. USA) in combination with a Keithley Model No. 617 programmable electrometer. The complex permittivity was calculated by taking the discrete Fourier transform (DFT) of the discharging current. For further details of the experimental setup and the measurements, the reader may consult an earlier article34 from this laboratory. 3. Results Results have been discussed under the following subsections for convenience. 3.1. COOL-CHOL Binary System. The pure materials COOL (molecular weight (MW) ) 128.22) and CHOL (MW ) 114.19) were studied individually in detail by earlier workers using calorimetry11,23,32,33,40,48 and dielectric spectroscopy.11,30,31,33 The liquid COOL upon cooling freezes to a plastic crystalline material (phase I), which was reported to be a simple cubic (SC) with the unit cell parameter of 11.96(1) Å at 273 K.36 This phase upon further cooling transforms to phase II, the

J. Phys. Chem. B, Vol. 112, No. 9, 2008 2607

Figure 2. Double logarithmic plot of ′′ versus frequency of (a) pure COOL and (b) the COOL-CHOL binary system with xm ) 0.25 at different temperatures. The dashed-dotted line corresponds to the HN eq 1 for the resolved R process in both panels. The parameters of eq 1 for β and γ processes of COOL in panel (a) are T ) 164.9 K; RCC ) 0.581, 0.756; ∆ ) 0.55, 0.39; and log fm (Hz) ) 0.469, 3.29; at T ) 170.6 K, RCC ) 0.554, 0.687; ∆ ) 0.56, 0.36; and log fm (Hz) )1.08, 3.46, respectively. The β process found in pure COOL is not clearly identifiable in the data of the COOL-CHOL binary system shown in panel (b). Note that the resolved sub-Tg process in panel (b) has been designated as a γ process. The HN parameter corresponding to the resolved processes in the COOL-CHOL system at 175.9 and 165.3 K are, for the R process, RHN ) 0.0431, 0.0659; βHN ) 0.664, 0.705; ∆ ) 20.04, 19.95; and log fm (Hz) ) -0.627, -2.235; and for the γ process (shown by dashed lines), RCC ) 0.728, 0.727; ∆ ) 0.918, 0.412; and log fm (Hz) )4.25, 3.56, respectively. The typical ansatz (HN + CC) fits are also shown by thick lines.

nature of which is not clear23,30,31 and so is the case with yet another phase (III).36 Although the exact crystalline structure of phase II is not known, its symmetry is known to be lower than tetragonal.31 Phase I is clearly an OD phase as it is associated with a large dispersion in dielectric measurements. On the other hand, CHOL has many plastic phases11,23,33 and, hence, many Tg’s,23 although even in this case, controversies exist.33 The X-ray diffraction studies36 indicate that phase I is a simple cubic with the unit cell parameter of 11.54(1) Å at 273 K and phase II is tetragonal with the unit cell parameters of a ) 19.487(2) Å and c ) 11.7805(2) Å at 248.15 K. Because of the similarity in the cell structure and lattice parameters of phase I of COOL and CHOL, the mixtures of these materials form a continuous solid solution in phase I, hereafter designated as SI, which too is simple cubic in structure, exhibiting a linear

2608 J. Phys. Chem. B, Vol. 112, No. 9, 2008

Singh and Murthy

TABLE 1: Details of Various Transitions in the COOL-CHOL Binary Systems sample

nature of transitiona

transition temperature (K) present work

COOL

SI f L SII f SI Tg (I)

291.223 258.223 164.023 172 (D)23 170.9 (D)

COOL-CHOL, xm ) 0.25 COOL-CHOL, xm ) 0.50 COOL-CHOL, xm ) 0.75 CHOL

Tg (II)

148.823

SI f L

285.7 (Tliq)

Tg (I)

160.2 (D)

SI f L

281.1 (Tliq)

Tg (I)

153.8 (D)

SI f L

278.2 (Tliq)

Tg (I)

148.6 (D)

SI f L SII f SI SIII f SII Tg1 (I)

276.623 253.623 225.023 144.523 150.5 (D)23

Tg1 (II)

144.023 147.5 (D)23

enthalpy (∆H) kJ/mol

literature 283.8,40

36

297.1 246.5,40 264.136 14240 145 (MDSC)49 151 (X-ray)49 164 (MDSC)31 151 (AdC)31 16032 144 (MDSC)31 135 (AdC)31 134 (X-ray)31 16032 290.836b (Tliq) 142.3 (MDSC)49b 144.5 (X-ray)49b 285.936b (Tliq) 136 (MDSC)49 140 (X-ray)49 281.836b (Tliq) 130.5 (MDSC)49b 132.3 (X-ray)49b 280.311, 278.336 258.511, 250.436 227.311, 227.936 130 (MDSC)33 128 (X-ray)33 120.5 (MDSC)49 128 (X-ray)49 138 (D)33 143 (X-ray)33 141 (D)33 140 (MDSC)33

present work

literature (refs 36, 40)

2.02 ( 0.05

2.05, 1.97 1.69, 1.97

1.97 ( 0.05

1.92b

1.86 ( 0.05

1.82b

1.80 ( 0.05

1.71b

1.60, 1.51 0.88, 0.78 0.55, 0.45

a S: crystalline solid, L: liquid, AdC: adiabatic calorimetry, MDSC: modulated DSC, D: dielectric. b Interpolated values based on refs 36 or 49.

variation of the lattice parameter with concentration.36,49 This SC-mixed crystal (SI) is orientationally disordered and is the subject of the present study. The nature of the mixed crystals has been examined critically at four concentrations or mole fractions (xm) of CHOL in COOL. The liquid mixtures when slowly cooled at a rate of 1 deg/min collapse to the crystalline phase (SI), which upon subsequent heating, begins to liquefy, which can be seen as a melting endotherm in DSC measurements as shown in Figure 1a. Interestingly, the melting or liquefaction extends by over 1012 degrees, which is typical of a solid solution. This region (shown by vertical dashed lines in Figure 1) corresponds to a mixed phase of liquid and solid. The corresponding dielectric measurements reveal a large dispersion in the crystalline phase SI, as shown in Figure 1b and c. This dispersion moves to much higher frequencies upon melting, which starts at a temperature Tsolidus and is complete at a temperature Tliquidus or Tliq. The above dispersion can also be seen as peaks in the dielectric loss and may be identified as the primary (or R) process. In addition to the above process, there is yet another process designated as the γ process that still continues to exist below Tg(D), the kinetic freezing temperature of the R process. For the measurement of the enthalpy of transition, the samples are annealed at 249 K for 30 min and then at 148 K for 90 min before starting the DSC run from 103 K. They are subsequently heated at a rate of 2 deg/min. For the measurement of the glass transition temperature, a different run with a heating rate of 10

deg/min is employed. The details of various first-order transition temperatures together with the associated enthalpies and glass transition temperatures of the samples used in this study are given in Table 1. The dielectric study on the pure sample CHOL was already reported23 by one of us, and hence, in the present communication, the dielectric spectra of this pure sample is not discussed. The phase I of pure COOL exhibits two sub-Tg processes designated as β and γ relaxations in addition to the R process, whereas in CHOL, only one resolvable sub-Tg process identified as γ relaxation is found. In the two-component system, only one phase (SI) is found, which is very stable against recrystallization to another phase. Only one resolvable sub-Tg process (identified as γ relaxation) is found (Figure 1c), and the β process is hardly detectable in Figure 2b, where the corresponding dielectric spectrum is shown. Dielectric measurement have been performed on pure COOL and two-component cyclic alcohols, that is, COOL-CHOL, at four concentrations, that is, xm )0.075, 0.25, 0.50, and 0.75, where xm is the mole fraction of the second component (CHOL). The relaxation data were analyzed using the Havriliak-Negami (HN) shape function50 given by the equation

( () )

*( f ) - ∞ f ) 1+i 0 - ∞ f0

1-RHN -βHN

(1)

where f0 is the mean relaxation frequency, RHN and βHN are the spectral shape parameters, and 0 and ∞ are the limiting



TABLE 2: Details of Eq 1 in the COOL-CHOL Binary System RHN

βHN

temp (K) 198.0

0.061 0.674 6.17 × 101 8.68 × 101 20.43

206.1 215.5 224.8 237.9 247.1 257.0

0.053 0.038 0.034 0.022 0.012 0.005

193.2

0.108 0.714 6.61 × 101 9.05 × 101 22.65

205.5 213.7 226.9 233.7 240.7 250.5

0.054 0.043 0.033 0.026 0.019 0.008

184.4

0.127 0.743 8.04 × 101 1.07 × 102 22.96

COOL-CHOL xm ) 0.50

COOL-CHOL xm ) 0.75

194.8 207.9 216.9 228.4 238.7 247.1

0.077 0.062 0.044 0.031 0.019 0.009

0.672 0.671 0.683 0.685 0.666 0.625

0.674 0.676 0.685 0.684 0.672 0.631

0.699 0.704 0.697 0.696 0.686 0.671

f0 (Hz)

∆

sample COOL-CHOL xm ) 0.25

3.00 × 102 1.59 × 103 7.96 × 103 4.45 × 104 1.40 × 105 4.29 × 105 6.64 × 102 2.65 × 103 1.79 × 104 4.29 × 104 9.82 × 104 2.97 × 105 3.88 × 3.19 × 103 9.95 × 103 4.39 × 104 1.36 × 105 3.30 × 105 102

fm (Hz)

4.22 × 102 2.22 × 103 1.09 × 104 6.05 × 104 1.94 × 105 6.22 × 105 9.30 × 102 3.69 × 103 2.45 × 104 5.85 × 104 1.35 × 105 4.29 × 105 5.34 × 4.32 × 103 1.35 × 104 5.92 × 104 1.84 × 105 4.53 × 105 102

19.84 18.87 17.98 16.70 15.96 15.54

20.65 19.82 18.51 17.91 17.35 16.76

21.29 20.41 19.56 18.53 17.64 16.80

dielectric constants for the process under consideration. The parameter RHN is a measure of the distribution of relaxation times in the sample, and the parameter βHN is a measure of cooperativity among the molecules. The peak loss frequency (fm) is then calculated from the parameters of eq 1.51 To give the reader an idea of the various relaxation processes, the spectral dependence of the relaxation of a dispersion of pure COOL together with the HN fit is shown in Figure 2a, and that for the COOL-CHOL system for one concentration, xm ) 0.25, with the HN fit is shown in Figure 2b; the behavior was similar to the other samples (with different concentrations). Upon comparison of Figure 2a with 2b, one can notice that the β process is not clearly resolvable in the corresponding binary of COOL with CHOL. The relaxation above Tg of the binary system can be resolved52 into R and γ processes, where the latter can be represented by the Cole-Cole equation (βHN ) 1 in eq 1). The corresponding parameters are given in Table 2. The Arrhenius plot of the samples for all of the concentrations is shown in Figure 3. The R process follows the critical power law23 given by the equation below

fm,R ) f0,R

( ) T - T′g T′g

r

(2)

where f0,R is a constant, T′g is the limiting glass transition temperature at which fm,R ) 0, and r is the dynamic exponent. Alternately, the data can also be described equally well by the Vogel-Fulchers-Tammanns equation53 given by

fm,R ) f0,Re(-B/(T-T0))

in Figure 4 is the variation of various experimental parameters with respect to the mole fraction (xm). Plotted are Tliq and Tg(D) (or dielectric Tg, the temperature at which the fm value is ≈10-3 Hz), the peak loss frequency (fm), and the dielectric strength (∆) at particular temperatures. A continuous change of these physical properties from that of COOL to that of CHOL with xm, according to the following equation55,56

ymix ) y1‚(1 - xm) + y2‚xm + k‚xm‚(1 - xm)

(4)

for T0 ) 0. Tabulated in Table 3 are the results of the fits to eqs 2-4. The relaxation rates and the spectral data shown in Tables 2 and 3 are found to be independent of the sample history, indicating that they indeed correspond to SI. Depicted

(5)

is noteworthy. The above equation is very well discussed in the context of liquid mixtures.55,56 In the above equation, y1 and y2 are the properties of the components and k is the interaction parameter. Interestingly, the R relaxation of this OD phase SI is similar to that of a single-component system. Shown in Figure 5 is the portion of DSC curves in the region of the glass transition temperature Tg, where a step like-change in specific heat flow, indicative of a glass transition event, can be noticed. However, the curves in the glass transition temperatures are so diffuse that it is difficult to clearly find out the value of Tg using the instrument software. To give the reader an idea of comparison of dielectric and thermal events, the corresponding Tg(D) is shown in the figure by an arrow. Figure 5 clearly demonstrate that the diffused step-like event in the DSC curves corresponds to the dielectric R modes which are frozen kinetically at the glass transition (Tg). To establish the relation between the deviations from the Arrhenius equation and the Debye behavior of the R relaxation, the dynamic fragility index (m) defined as25,51,57

(3)

where T0 is the limiting glass transition temperature and f0,R and B are constants. The above equation can also be presented as the Arrhenius equation54

fm ) f0e-(E/RT)

Figure 3. Complete Arrhenius diagram depicting the R and sub-Tg process in the COOL-CHOL binary system. Also included are the fm values of the plastic phase (I) of pure CHOL (Puertas et al.33). The thick line along the R process corresponds to eq 2, and that along the γ process corresponds to eq 4, for the parameters shown in Table 3. The sub-Tg process designated as the β process in COOL is not shown for clarity.

m)

-d(log fm) d(Tg/T)

|T)Tg

(6)

was calculated, and the values of m thus determined are entered in Table 3. 3.2. DMCH-CHC Binary System. In view of the above experience with COOL and CHOL, the materials, namely, DMCH (MW ) 112.22) and CHC (MW ) 118.61) because of their similar molecular shape and size, are expected to show some interesting results, although complete information about the individual crystal structures is lacking.1,5,58 With this in mind,


Singh and Murthy

TABLE 3: Details of the r Process as Well as the Sub-Tg Process in the COOL-CHOL Binary System sub-Tg process (γ process)

R process power law parameters sample

Tg

COOL (ref 23) COOL COOL-CHOL xm ) 0.075 COOL-CHOL xm ) 0.25 COOL-CHOL xm ) 0.50 COOL-CHOL xm ) 0.75 CHOLb (ref 33)

VFT parameters

Arrhenius fit parameters

log f0,R (Hz)

r

Tg′ (K)

log f0,R (Hz)

B (K)

T0 (K)

fragility index (m)

log f0 (Hz)

∆E (kJ/mol)

172.0 170.9 167.3

6.87 7.03 6.92

14.40 13.48 13.14

142.60 143.80 142.46

14.59 13.92 14.12

3690.3 3296.2 3482.7

80.60 84.64 77.95

33.01 32.87 31.67

20.43 18.57 19.89

56.0 49.8 ( 2 57.7

160.2

6.02

14.23

130.72

14.73

4032.6

61.42

28.74

22.19

59.7

153.8

6.09

13.17

130.28

15.33

4640.2

42.68

25.38

12.32

22.0

148.6

5.80

11.96

125.48

13.06

3206.9

60.01

25.95

14.76

27.4

137.6

4.07

14.78

103.35

16.04

5172.8

18.22

21.68

18.69

38.9

(D)a

(K)

Temperature where fm ) 10-3 Hz, calculated from PL parameters. b The data were scanned from Figure 4 (plastic phase I) of Puertas et al. (ref 33) and was analyzed further. a

TABLE 4: Details of Various Transitions in the DMCH-CHC Binary System sample DMCH DMCH-CHC, xm ) 0.125 DMCH-CHC, xm ) 0.249 CHC

transition temperature (Ttr) (K)

enthalpy of transition (∆H) kJ/mol

entropy of transition (∆H/Ttr)c (e u)

SI f L SII f SI Tg (I)b S[A(R)] f L

222.1, 223.25 172.55 107.4,24 935 215.5

1.655 8.265

1.7615 11.4055

1.32 ( 0.05

1.459 ( 0.055

Tg [A(R)]b S[A(R)] f L

211.8

1.27 ( 0.06

1.428 ( 0.067

Tg [A(R)]b SI f L SII f SI SIII f SII Tg (I)

228.7, 229.3,58 229.124) 221.1, 220.4,58 220.624 120.058 116.324

1.67, 2.04,58 1.7824 7.88, 7.93,24 8.0158 0.0558

1.74, 1.851,24 2.12458 7.93, 8.562,24 8.62958 0.09958

nature of transitiona

a S: crystalline solid, L: liquid, A (R): solid solution rich in DMCH. b Outside of the temperature window of the DSC instrument. c 1 eu ) 4.1985 J/deg/mol.

DSC measurements were performed over the complete concentration range in this binary system, and interestingly, the DSC behavior is different for xm < 0.4, where xm is the mole fraction of CHC in the binary system. Pure DMCH and CHC were examined critically by earlier workers5,23,24,55 and both demonstrate the existence of a plastic phase (phase I) that transforms to another phase (II) upon lowering the temperature. [Phase I in CHC is known1 to be face-centered cubic with the unit cell parameter of 9.05 Å at 224 K, but the information about phase II and III is lacking. According to Diky et al.,58 phase I consists of equatorial (e)- and axial-chair conformers, but the phases II and III consist of e-conformers only. Information about phase I of DMCH is lacking, but one may expect it to be a facecentered cubic, as is the case with cyclohexane and some of its derivatives1,2,58]. Realization of phase II in DMCH is difficult with the present experimental techniques as it requires prolonged annealing for at least 7 days,5 and therefore, what is discussed in this paper concerns phase I only, unless specified otherwise. The phase I of DMCH exhibits a Tg at 93 K5 (also see Table 4). In case of CHC, phase I has a Tg of 116 K, but this phase requires much larger cooling rates to form the glassy crystal.24 From the dielectric measurements performed in this laboratory on CHC, it is obvious that phase II is a rigid rotator solid. The same could be the case with phase II of DMCH. The details of the various transitions are given in Table 4. The DSC results on samples with various concentrations are depicted in Figure 6a and b. The DSC curves for xm < 0.4 reveal only one sharp endotherm even after annealing the samples for 48 h at temperatures as low as 125 K (see Figure 7 a). The enthalpy

associated with this endotherm slightly increases upon annealing and is almost of similar magnitude as that of the components (see Table 4). The sample at low temperatures was observed to be a waxy solid. Samples with xm g 0.4 exhibit at least two endotherms, and samples with 0.4 e xm < 0.6 require long annealing of 36 h at 175 K to reveal the lower endotherm designated as “eutectic” in Figure 7b. To get some information about the solid-liquid phase diagram, DSC scans were taken for a heating rate of 2°/min, and the resultant curves were analyzed using the DSC instrument software by determining the onset temperature (Tsol) and end temperature (Tliq) of the endotherms as shown in Figures 6 and 7. The transition temperatures thus determined were plotted as a function of the mole fraction of CHC (xm), as suggested in the literature,56,58-60 to determine the solid-liquid phase diagram. The phase diagram is shown in Figure 8, which, although not clear throughout the concentration range, reveals an eutectic with solid solutions A(R) and B(β) rich in A (i.e., DMCH) and B (i.e., CHC), respectively, on the lower- and higher- concentration sides. To support the interpretation of our DSC results, we have performed the dielectric measurements on the DMCH-CHC binary system for different concentrations, that is, xm ) 0.010, 0.125, 0.249, and 0.501, over a wide frequency range. Shown in Figure 9 is the temperature variation of the real part of the complex permittivity in the DMCH-CHC binary system for xm ) 0.125 at different test frequencies, along with the corresponding DSC curve. Clearly, the endotherm at Tliq corresponds to a small change in the static dielectric constant. Interestingly, there is a dispersion on the lower temperature side



Figure 5. DSC curves in the region of the glass transition temperature taken for a heating rate of 10 deg/min for three concentrations in the range of 0.25 e xm e 0.75. The sample sizes are 10.8 (for xm ) 0.25), 9.10 (for xm ) 0.50), and 12.40 mg (for xm ) 0.75). (The curves are shifted along the y-axis to make the comparison easier.) Also shown are the corresponding Tg(D) values.

Figure 4. Variation of various physical parameters of the COOLCHOL binary system with the mole fraction (xm) of the second component, that is, CHOL: (a) Tliq and Tg(D) [where Tg(D) is the temperature at which the fm value is ≈10-3 Hz]; (b) log fm; and (c) dielectric strength (∆) at three fixed temperatures. The thick lines are fits to eq 5.

which resembles the R process. Unfortunately, the glass transition event could not be seen in DSC as it is located below the lower operational temperature of the DSC. To make obvious the spectral shape of the relaxation, the spectral behavior of the DMCH-CHC system for xm ) 0.1254 is depicted in Figure 10, where the R process can reasonably be explained by eq 1 around the peak frequency region, and the corresponding parameters are given in Table 5. However, within the resolution of the experimental setup, there is no resolvable β process in these samples. Besides this, shown in Figure 11 is the dielectric loss at a 1 kHz test frequency at various concentrations for xm < 0.4, which shows at least another relaxation of much lower magnitude which does not clearly involve the more polar CHC molecules. Shown in Figure 12 is the spectral dependence of the R process of the binary system at a particular temperature for various concentrations of CHC, where one can clearly see the dielectric loss (and hence, the corresponding dispersion) increasing with the concentration of CHC. The spectrum is well represented by eq 1, with small variation of the spectral shape parameters (see the corresponding figure caption). The peak loss frequency at a given temperature decreases with an increase in the concentration of CHC steadily up to xm ) 0.25, beyond which the solid phase below the eutectic temperature exhibits

Figure 6. DSC curves for a heating rate of 2 deg/min in the DMCHCHC binary system (a) for four concentrations in the range of 0.00 e xm e 0.375 [the sample sizes are 8.8 (for xm ) 0.00), 9.6 (for xm ) 0.125), 9.0 (for xm ) 0.249), and 10.4 mg (for xm ) 0.375)], (b) for four concentrations in the range of 0.50 e xm e 0.876 (the sample sizes are 8.9 (for xm ) 0.53), 11.0 (for xm ) 0.625), 11.4 (for xm ) 0.749), and 8.8 mg (for xm ) 0.876)].

relaxation properties that depend on the annealing time, as (also) revealed by the DSC results as a two-phased [A(R) + B(β)] substance (Figures 7 and 8). The relaxation shown in Figures


Singh and Murthy

Figure 7. Effect of annealing in the DSC curves taken for a heating rate of 2 deg/min in the DMCH-CHC binary system for samples (a) with xm ) 0.126 (sample size ) 9.9 mg) and (b) xm ) 0.402 (sample size ) 11.1 mg). The appearance of the endotherm at Teutectic upon annealing may be noted.

Figure 9. DMCH-CHC binary system for xm ) 0.125. (a) DSC scan up to the melting temperature for a heating rate of 2 deg/min. The sample size is 12.2 mg. (b) The corresponding dielectric behavior shown as a variation of the dielectric constant at different frequencies. The nature of the broad diffused endotherm on the lower temperature side is not clear.

Figure 8. The tentative solid-liquid phase diagram of the DMCHCHC binary system obtained from DSC experiments. The upper thick line corresponds to the liquidus points (or Tliq). The phases designated as A(R) and B(β) correspond to the solid solutions rich in DMCH and CHC, respectively. The nature of the phase diagram is not known completely in the region shown by the symbol “?”.

Figure 10. Double logarithmic plot of ′′ versus frequency of the DMCH-CHC binary system with xm ) 0.125 for different temperatures. The thick line corresponds to the HN parameters shown in Table 5.

10 and 12 for concentrations less than xm ) 0.375 corresponds to the A(R) phase. The complete relaxation map of the samples is shown in Figure 13, depicting fm values in the form of an

Arrhenius diagram. The thick lines correspond to the PL fit (i.e., eq 2), as shown in Table 6. Also included in Table 6 are the values of dynamic fragility index m determined from eq 6. From



Figure 11. DMCH-CHC binary system. Variation of log ′′ with temperature at a test frequency of 1 kHz for four different concentrations of CHC. The nature of the smaller processes shown with the mark “?” is not clear.

Figure 12. Double logarithmic plot of ′′ versus frequency of DMCH for different concentrations of CHC at a constant temperature. The thick line corresponds to eq 1 for the given parameters as xm ) 0.00: T ) 114.6 K (RHN ) 0.287, βHN ) 0.513, ∆ ) 0.039, and log fm ) 4.88); xm ) 0.010: T ) 114.3 K (RHN ) 0.092, βHN ) 0.397, ∆ ) 0.128, and log fm ) 4.09); xm ) 0.125: T ) 114.4 K (RHN ) 0.105, βHN ) 0.435, ∆ ) 1.148, and log fm ) 3.54); and for xm ) 0.249: T ) 114.8 K (RHN ) 0.147, βHN ) 0.473, ∆ ) 2.316, and log fm ) 3.05).

TABLE 5: Details of Eq 1 for Samples Shown in Figure 10 sample

temp

DMCH-CHC, 103.9 xm ) 0.125 109.6 111.1 112.7 114.4 116.6 118.6 120.9 123.9 126.5

RHN

βHN

f0 (Hz)

fm (Hz)

∆

0.057 0.386 1.06 × 10-1 2.43 × 10-1 1.126 0.159 0.135 0.111 0.105 0.105 0.095 0.087 0.075 0.061

0.459 0.447 0.431 0.435 0.440 0.439 0.425 0.383 0.295

4.13 × 101 1.45 × 102 4.68 × 102 1.59 × 103 4.82 × 103 1.75 × 104 5.22 × 104 1.55 × 105 3.63 × 105

9.14 × 101 3.18 × 102 1.04 × 103 3.47 × 103 1.04 × 104 3.75 × 104 1.14 × 105 3.66 × 105 1.07 × 106

1.130 1.143 1.147 1.148 1.149 1.150 1.164 1.225 1.248

Table 6, it is interesting to note that the value of the exponent r is approximately 12, as found in many of the supercooled liquids.23,24,34 4. Discussion For the sake of convenience, the results are discussed under the following sections.

Figure 13. Arrhenius diagram for the supercooled phase of the DMCH-CHC binary system. The thick lines correspond to the fit to eq 2 for the parameters shown in Table 6. Shown in the inset is the variation of Tg(D) with xm as per eq 6 given by Tg(mix) ) Tg1‚(1 - xm) + Tg2‚xm + k‚xm‚(1 - xm), where Tg2 ) 116.3 K, Tg1 ) 96.9 K, and the interaction parameter k ) 5.728. In this equation, Tg2 is the Tg of the plastic phase I of CHC given in an earlier publication24 from this lab.

4.1. SI Phase in the COOL-CHOL Binary System. This SI phase is a solid solution (of phase I of the components) and is known to be simple cubic in structure.36 This phase is an OD phase and exhibits a well-pronounced relaxation in dielectric measurements, as shown in Figures 1 and 2. These relaxation characteristics are similar to those of the so-called primary (or R) process seen in many single-component plastic crystals and liquid glass formers. From Figures 3 and 5, one can infer that the glass transition event seen in DSC curves is the same as the one which corresponds to the kinetic freezing of the abovesaid R process. However, because the glass transition event is spread out by about 20 degrees in the DSC curves, it is not apparent whether there are two Tg’s and whether the lower Tg corresponds to the kinetic freezing of the γ process. (For example, the γ process shown in Figure 3 for xm e 0.25 on extrapolation to lower temperatures freezes at about 119-125 K. However, caution should be exercised because of a possible decoupling of dielectric modes from modes of enthalpy relaxation as happens in the case of liquid alcohols61). Salud et al.49 have recently measured the Tg’s for these systems using X-ray data and modulated DSC, which interestingly enough deviate from each other by about 10 degrees and are much lower than the corresponding dielectric Tg or Tg(D) shown in Figure 5. However, what is interesting is the continuous steady variation of the various physical parameters with xm from that of COOL to CHOL, as shown in Figure 4. The curves shown in Figure 4 interestingly follow the mixture rule given by eq 5, as also observed with the lattice parameter.36 The lack of a strong variation of ∆ with xm (Figure 4c) is partly due to the expected similarity in the dipole moments of COOL and CHOL, which are expected to be in the range 1.6-1.9 D (based on the published dipole moments62 of alcohols that are dominated by that of the -OH group). It is also noteworthy that the SI phase does not collapse to a rigid rotational state during the course of the experimental measurements. This binary system shows only one sub-Tg process (see Figures 1-3). However, the interesting observation is that, for xm ) 0.25, this sub Tg process exists near the γ process of pure COOL with almost the same activation energy, that is, 59.7 kJ/mol. This value may be ascribed to the barrier for conversion


Singh and Murthy

TABLE 6: Details of the r Process for Samples Shown in Figure 13 HN parameters sample DMCH (pure) DMCH-CHC xm ) 0.010 DMCH-CHC xm ) 0.125 DMCH-CHC xm ) 0.249 a

Tg(D)a (K)

range of temp (K)

RHN

power law parameters.

βHN

log f0,R (Hz)

r

VFT parameters

Tg′ (K) log f0,R (Hz)

B (K)

fragility T0 (K) index (m)

95.7 98.0

102.0-120.3 0.322-0.090 0.717-0.423 106.8-123.7 0.103-0.087 0.403-0.303

11.47 11.95

11.12 12.78

91.07 91.77

14.20 14.60

951.45 1009.08

69.99 72.32

59.9 65.2

100.6

109.6-126.5 0.135-0.061 0.447-0.295

11.87

12.23

94.82

13.78

870.19

77.70

72.5

102.4

115.7-127.8 0.138-0.043 0.471-0.292

12.14

13.09

95.43

13.58

844.53

79.80

75.6

Temperature where fm ) 10-3 Hz, calculated from PL parameters.

of one conformer to another and is supported by the dielectric study of Davies and Swain63 and may not be associated with another disordered phase.31 With an increase in the concentration of CHOL, that is, for xm ) 0.50 and 0.75, this sub-Tg process gets shifted toward the γ process of pure CHOL with smaller activation energies of 22 and 27.4 kJ/mol, respectively (Table 3). This may probably be due to -OH group relaxation often found at very high frequencies at room temperature.64 4.2. A(R) Phase in the DMCH-CHC Binary System. There are a few reasons to believe that in the mixtures at xm e 0.375, the DMCH molecules form a solid solution with CHC below the solidus temperature (Tsol) (Figure 6a). An external inspection of the samples at temperatures below Tsol indicate them to be solids, and the corresponding DSC curves shown in Figure 6a are so sharp that they appear to correspond to the melting of a simple component crystal, and the difference between the temperatures Tsol and Tliq is not noticeable in the phase diagram shown in Figure 8. Moreover, the liquidus line on the DMCHrich side does not follow the equation for the depression of the freezing point for ideal solutions61 given by

ln(xm) )

(

)

-∆Hf 1 1 R Tliq Tm

(7)

where Tm is the melting temperature, ∆Hf is the enthalpy of melting of DMCH, and Tliq (or Tliquidus) is the freezing (liquidus) temperature. On the basis of eq 5, if one calculates Tliq for xm ) 0.25, it comes out to be 169.5 K, which is much lower than the observed value of 211.8 K. In addition, the enthalpy associated with the curves shown in Figures 6a and 7a is in the range of 1.25-1.35 kJ/mol, which is comparable to the corresponding values of the components DMCH and CHC shown in Table 4. This value is of the magnitude expected if a solid solution was formed of DMCH and CHC (if one overlooks the change in the specific heat of the undercooled liquid). The corresponding entropy of transition if expressed in eu is in the range of 1.43-1.46. According to Timmermanns,2 for a crystal to be plastic, this quantity has to be less than 5 eu, which is the case here. Thus, there is a large frozen entropy in the form of orientational disorder which would also be clear if one took note of the large entropy associated with the transition to the corresponding phase II (Table 4). Both component liquids DMCH and CHC individually and rapidly crystallize to their respective crystalline phases (i.e., phase I), and it is difficult to expect them to undercool partially without complete crystallization to phase I. Therefore, the dispersion shown in Figures 9b, 10, 12, and 13 probably corresponds to a crystalline phase that is rotationally disordered and is a solid solution. The small jump in the (static) dielectric constant shown in Figure 9b at Tliq can be explained as due to an increase in the number of dipoles per unit volume as the liquid freezes to a plastic crystalline state and the molecules are not hindered rotationally.

(The dipole moment “µ” of the DMCH and CHC are 0.08 and 2.09-2.12 D, respectively62). Interestingly, the measured Tg(D) values shown in the inset of Figure 13 follow the mixture rule, and there is a smooth variation of Tg(D) between the corresponding values of the respective (solid) phase I. 4.3. Fragility. It is evident from Figures 2, 10, and 12 and also from Tables 2 and 5 that the relaxation in DMCH (and its binaries with CHC) is broader than that of COOL (and its binaries with CHOL). This is because the value of the asymmetric parameter of eq 1, that is, βHN, is smaller in the former than the latter, with very little change in the value of the symmetric parameter RHN. Similarly, the breadth of relaxation also increases with COOL in the COOL-CHOL binaries (see Table 2). According to Angell and co-workers,25,53,57 departure from Debye behavior can be explained by the kinetic fragility index m given by eq 6, which gives an indication of the extent of deviation of the corresponding R process from Arrhenius behavior. The value of m is higher for DMCH than that for COOL and CHOL, and also within the COOL-CHOL binaries, the fragility index m increases with a decrease of CHOL (Tables 3 and 6). Salud et al.49 have recently measured ∆Cp(Tg) in the COOL + CHOL systems, and hence, their thermodynamic fragility index, which is based on this quantity, also correlates well with the m values. Thus, there is a correlation between the fragility index and the breadth of the relaxation of the R process. An interesting correlation between the William Watts parameter βWW and the fragility index m is given by Bohmer et al.65 as

m ) 250 ( 30 - 320βWW

(8)

The parameter βWW is obtained from the procedure given by Alvarez et al.,66 which is about 0.66-0.68 for COOL-CHOL and 0.47-0.49 for the DMCH-CHC binary system, and these values have been used in eq 8 for calculation of m. The value of m is thus obtained in the range of 68-2 for plastic phase I of the COOL-CHOL binary and 130-63 in case of the plastic phase of the DMCH-CHC system. These values do not compare well with the experimental values of m given in Tables 3 and 6, respectively. This discrepancy is probably due to the fact that eq 8 is meant for liquid glasses rather than plastic crystals. 5. Conclusions The present observations clearly suggest that the relaxation process seen in the plastic phase I of the COOL-CHOL binary system corresponds to the R process, whose kinetic freezing causes the glass transition event, as also reported in glassy crystals23,26,28,31,32,34 such as pure cyclooctanol, cyanoadamantane, pentachloronitrobenzene, and so forth. Interestingly, the various physical parameters determined for this binary vary smoothly between its component values, indicating an isomor-

Dielectric and Calorimetric Study of OD Phases phic relationship between the simple cubic phases of both pure components, as was observed earlier by Rute et al.36 Evidence is presented here to show that the binary of DMCH-CHC on the DMCH-rich side could also be one such example which interestingly behaves like a single-component orientationally disordered phase that demonstrates a glass-like phenomenon. Low-temperature X-ray analysis and calorimetry of these samples are expected to shed more light on the structure and nature of these samples. Another interesting aspect of our study is the observed stability of the plastic phase of COOL and DMCH solutions against a collapse to a more ordered phase, as happens in pure COOL, CHOL, CHC, and DMCH. The suppression of crystallization to a more ordered phase by an addition of a second component can be an interesting theoretical problem. Acknowledgment. One of the authors (L. P. Singh) wishes to thank CSIR, India, for a Senior Research fellowship (SRF). References and Notes (1) Sherwood, J. N., Ed. The Plastically Crystalline State; Wiley/ Interscience: New York, 1979. (2) Timmermans, J. J. Phys. Chem. Solids 1961, 18, 1. (3) White, A. H.; Biggs, B. S.; Morgan, S. O. J. Am. Chem. Soc. 1940, 62, 16. (4) White, A. H.; Bishop, W. S. J. Am. Chem. Soc. 1940, 62, 8. (5) Huffman, H. M.; Todd, S. S.; Oliver, G. D. J. Am. Chem. Soc. 1949, 71, 584. (6) Turney, A. Proc. IEE, II A 1953, 100, 46. (7) Corfield, G.; Davies, M. Trans. Faraday Soc. 1964, 60, 10. (8) Krishnaji Mansingh, A. J. Chem. Phys. 1965, 42, 2503. (9) Aihara, A.; Kitazawa, C.; Nohara, A. Bull. Chem. Soc. Jpn. 1970, 43, 3750. (10) Brot, C.; Darmon, I. J. Chem. Phys. 1970, 53, 2271. (11) Adachi, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Jpn. 1972, 45, 1960. (12) Sorai, M.; Seki, S. Mol. Cryst. Liq. Cryst. 1973, 23, 299. (13) Suga, H.; Seki, S. J. Non-Cryst. Solids 1974, 16, 171. (14) For a review, see: Pethrick, R. A. In The Plastically Crystalline State; Sherwood, J. N., Ed.; Wiley/Interscience: New York, 1979; Chapter 4, p 123. (15) Johari, G. P. Ann. N.Y. Acad. Sci. 1976, 279, 117. (16) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (17) Williams, G. In Dielectric and Related Molecular Processes, Special Periodical Report; Chemical Society: London, 1975; Vol. 2, p 151. (18) Blochowicz, T.; Ro¨ssler, E. Phys. ReV. Lett. 2004, 92, 225701. (19) Capaccioli, S.; Ngai, K. L.; Shinyashiki, N. J. Phys. Chem. B 2007, 111, 8197. (20) Pathmanathan, K.; Johari, G. P. J. Phys. C: Solid State Phys. 1985, 18, 6535. (21) Angell, C. A.; Busse, L. E.; Cooper, E. I.; Kadiyala, R. K.; Dworkin, A.; Ghelfenstein, M.; Szwarc, H.; Vassal, A. J. Chim. Phys. Phys. Chim. Biol. 1985, 82, 267. (22) Benkhof, S.; Kudlik, A.; Blockwicz, T.; Ro¨ssler, E. J. Phys.: Condens. Matter 1998, 10, 8155. (23) Tyagi, M.; Murthy, S. S. N. J. Chem. Phys. 2001, 114, 3640. (24) Murthy, S. S. N. Thermochim. Acta 2000, 359, 143. (25) Angell, C. A. J. Non-Cryst. Solids 1991, 13, 131. (26) Leslie-Pelecky, D. L.; Birge, N. O. Phys. ReV. Lett. 1994, 72, 1232. (27) Fuchs, A. H.; Virlet, J.; Andre, D.; Szwarc, H. J. Chim. Phys. Phys. Chim. Biol. 1985, 82, 293. (28) Leslie-Peleckey, D. L.; Birge, N. O. Phys. ReV. B 1994, 50, 13250.

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Dielectric and Calorimetric Study of Orientationally Disordered

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