Chapter 6

Study of supercooled orientationally disordered binary solid solutions involving cyclohexane derivatives: Evidence for chair-chair transformation, and Johari-Goldstein relaxation

As shown in the previous chapters the OD phase of symmetric molecular liquids1,2 is

interesting to researchers working on glass transition phenomena3- 5 since only one degree

of freedom is involved. The work of Johari6 and later by others7- 38 show that these mate-

rials have many commonalities with glass forming liquids and exhibit chiefly two relaxation

processes. The primary or the so called (a -) process is kinetically arrested at Tg , but the

secondary (or f3 -) process continues to exist even below Tg • The nature of the f3 - process in

frozen OD phase (or glassy crystals) is the subject of exclusive discussion in some papers.36- 45

Arguments are made in favour of both intermolecular (or the so called J ohari-Goldstein (J G-)

relaxation)6,36 and intramolecular origin.39,40,41 The identification of the sub-Tg or f3 -process

with the JG-relaxation is not always easy; for example, liquid alcohols exhibit46- 5o two or

more processes, and the experiments18,,41,45,47,49 have shown that some of these processes

159

might survive in the OD phase.

The study of cyclohexane and its derivatives in their liquid and plastic phase(s) occupy

an important position in this area as these substances exist in more than one isomeric form

in equilibrium and hence, possess intra-molecular degrees of freedom involving chair to boat,

chair (axial) to chair (equatorial) and chair to twisted boat transformation. 51- 6o Based on the

free energy consideration, one may expect that equatorial (e-) confirmer may be preferred at

lower temperatures over the axial (a-) form and hence, in the liquid state one can expect both

the isomers. 59 The conversion from a- to e- confirmer involves an activation energy (E) in the

Arrhenius equation for the relaxation frequency (fm),56-58.61 given by eq. 1.42. The value of

E in the Arrhenius equation (eq. 1.42) was found to be 45 ± 3 kJ Imol in methylcyclohexane

and may increase slightly to 50 ± 8 kJ Imol for chloro- and bromo- cyclohexane.56

Therefore, it is of interest to see how this process would evolve in the supercooled plastic

phase of cyclohexane derivatives. Unfortunately, many of these substances ca:q. not be studied

in their supercooled OD phases because of rapid recrystallization to the more ordered phases.

However, some information is available in,the supercooled plastic phase of cyanocyclohexane

and isocyanocyclohexane.32.36.43.62-65 In these materials, this process (a- to e- confirmer)

would freeze kinetically around 170 K with an approximate E -value of 51 kJ/mo1.32.62.64.65

which is more or less in agreement with E -value quoted above in the context of cyclohexane

derivatives in their liquid state. The recent dielectric measurements on the same substances

by the present authors,36 on methylcyclohexane by Mandanici and coworkers44.51and the

study on cyclohexyl derivatives in glassy polystyrene matrix by Davies and Swain60 have also

confirmed the existence of such a process. Other thaI} these reports not much information

is available in this field.

Cyclohexanol, in its plastic phase I was studied by many research groups16.18.27.28.39-42.47,49 (

but, surprisingly, the chair-chair transformation was not detected in the dielectric spectra,

although its signature was clear in the ultrasonic relaxation studies53 performed in its liquid

160

state. The corresponding relaxation frequency quoted by Karpovich53 is 0.12 MHz at. 305.2

K, and hence, as per eq. 1.42, it is supposed to shift to much lower frequencies as the OD

phase I is supercooled. However, the study of this phase is fraught with collapse to the more

orderly phase II. The collapse to a mor~ ordered phase can be prevented to some extent

by choosing a second component that forms a solid solution for the OD phase.24 ,25,37,66

Although, (two component) solid solutions present significant potentiality in applications

involving energy storage, practical application67,68 of these plastic crystals will then have to

deal with kinetic problem involving supercooling. In view of the above discussion, the present

study of two component plastic crystals could prove to be interesting from an academic

angle as well as applied aspect. As shown below the binary systems of cyclohexanol + neopentanol, and cyanocyclohexane + cyclohexylchloride are interesting for the study of chair-chair transformation and sub-Tg processes as they form· solid solution that can be

supercooled.

6.1: Experiment

The samples studied here are: cyclohexanol, C6 HllOH or CHXOL (99% purity); neopen-

tanol, C5HUOH or NPOL (99%); cyanocyclohexane, C6 HllCN or CNCH (99%) and cyclo-

hexylchloride, C6H llCl or CHC (99%), which were obtained from Aldrich Co., USA. They

are all used as received without any further purification. The samples are critically examined

using dielectric and DSC techniques, the details of which are given in chapters 2 and 3. For

further details of the experimental setup and the measurements the reader may consult an

earlier article36- 38 from this laboratory.

6.2: Results

Results have been discussed under the following subsections for convenience.

161

6.2.1: Pure materials:

The pure materials used in this study, viz. CHXOL [molecular weight (MW) = 100.16],

NPOL (MW = 88.15), CNCH (MW = 109.17) and CHC (MW = 118.61) were studied indi-

vidually in detail by earlier workers using calorimetry4-6,14,24,28,29,40,59,62-65,69-72 and dielectric

spectroscopy.6,14,18,22,28,32,41,42,47,49,73 The details of various first order transition temperatures

together with the associated enthalpies and glass transition temperatures of these samples

are given in Table 6.1. The dielectric study of the plastic phase (I) of the pure samples

CHXOL, NPOL, CNCH and CHC was already reported14,36,41 and hence, in the present

communication only the relevant part of the dielectric spectra concerning the chair-chair

transformation as found in CHXOL will only be discussed. Cyclohexanol is one of the few

substances that has been studied extensively using different techniques. CHXOL on cooling

freezes from the melt into a plastic crystalline phase (phase I) which was reported to be face

centered cubic (fcc), the space group is Fm3m (Z=4), with the unit cell parameter a = 8.809

A 0 at 275 K. 28 This phase on further cooling transforms to either phase II or phase III, de-

pending on the thermal his~ory of the sample. Phase II is produced by annealing phase I or

phase III for a few hours at a temperature (T) 245.2 K < T ::; 265.5 K. The rotational order

prevailing in Phase II is not clear in spite of investigations by a wide variety of techniques 71

while phase III shows X-ray patterns characteristic of an ordered structure. Phase I is

clearly an orientationally disordered (OD) phase as it is associated with a large dispersion

in dielectric measurements. 14 Although this material was studied earlier in detail using di-

electric spectroscopy, 14, 18, 73 none of the reports show the existence of any relaxation process

above Tg that can be attributed to chair-chair transformation, though it was seen clearly in

mechanical relaxation measurements reported by Karpovich. 53 Our dielectric measurements

indicate the existence of higher temperature relaxation process (called a' -process) together

with primary relaxation (a-) process on subtraction of the dc loss from the data. Depicted

in Figure 6.1 is the raw dielectric loss data of the dispersion of the plastic crystalline phase

162

Table 6.1: Details of various transitions in CHXOL-NPOL binary systems.

Transition Sample Nature of temperature Enthalpy (~H)

transition. (K) kl/mole

Present Present Literature work Literature work

SI-L 298.2 299.1 69,297.072 1.73 ± 0.04 1. 7869, 1.6972 CHXOL SII- SI ------- 265.569,263.572 ------------ 8.8369, 8.2072

SIII- SI 245.2 244.869 ------------ 8.6469 Tg (SI) 151.2 150 (AdCfO

147 ± 1 (AdC)4O

SI-L 307.1 1.99 ± 0.02 CHXOL-NPOL, (TJig.)

Xm = 0.25 Tg (SI) 148.7 SI-L 315.3 2.62 ± 0.08

CHXOL-NPOL, (TJiq) Xm = 0.50 Tg (SI) 146.8

SI-L 322.2 3.01 ± 0.06 CHXOL-NPOL, (TJiq)

Xm = 0.75 Tg (SI) 143.6

SI-L 329.7 329.866, 329.3 14 3.86 3.7366

SII- SI 235.1 235.466,236.5 14 ,

4.02 4.1466

NPOL Tg(SI) 139.3 14 135 (D)24 ----- ----------123 (x_ray)24

• S: crystalline solid, L: liquid, AdC: Adiabatic Calorimetry, D: dielectric.

I of CHXOL during cooling (at an approximate rate of 0.5 degjmin.) before it recrystallizes

to phase III. The relaxation data of a- process were analyzed using the Havriliak-Negami

(HN) shape function74 given by the eq. 1.46. The peak loss frequency Um) is then calcu-

lated from the parameters of eq. 1.46.75 The lower frequency side of the spectra in Figure

6.1 shows a shoulder which did not follow eq. 1.46. The shoulder then gets clearly resolved

into another process identifiable as a' -p~ocess after the subtraction of the dc loss from the

raw data. This has been demonstrated in the inset of Figure 6.1 at one temperature i.e.

260.8 K. The spectral shape of the resolved a' -process although not very clear because of

163

w C> o

1.5 ~----~1~.0~~~.============~--------------------------1 '00'6 T=260.8K CHXOL (Supercooled Plastic Phase-I)

1.0

0.5

0.0

-0.5

0.5

'", 0.0 CI

..Q -0.5

-1.0

\, cy

a~V . /'.

234

log f (Hz) 5

r-----u--------,

-1.0 +-______ -L-.,--__ -'--__ -L.-r-__ .L--__ -'---r--L. ___ -. ____ ....,

1 2 3 4 5 6

log f (Hz)

Figure 6.1: Double logarithmic plot of /' vs. frequency at different temperatures in the plastic crystalline phase (I) of Cyclohexanol (CHXOL~: raw data which includes DC contribution. Shown in the inset is the dielectric loss data at T = 260.8 K, before and after subtracting the dc contribution to show the existence of the a' - process on the lower frequency side of the spectrum. The dashed line corresponds to the HN· equation (1.46) for the 0.- process and dotted line (in the inset) corresponds to the CC·function for the resolved a' -process.

lack of enough data can still be approximately fitted to a depressed Cole-Cole arc function61

(obtained from eq. 1.46, by making the parameter f3HN =1). In Figure 6.2, the complete

Arrhenius plot is shown along with the earlier data from this laboratory41and the data of

others. 18,49,53 Interestingly, the mechanical relaxation data in the liquid corresponding to the

a-e confirmer transformation more or less agrees with that of the extrapolated 0/ -process

which has an apparent E value of 51.7 kJ/mol (Figure 6.2). The dielectric strength D.E of

this process at 260.8 k is about 0.56 and increases to 1.0 at 236 K with a large uncertainty.

The other material NPOL (2,2-dimethyl-1-propanol) exhibits two crystalline phases,14,

a high temperature phase (phase I) and a low temperature phase (phase II), where phase

164

Liq. I 1 0 '1E-~·E-E:--CHXOL (Supercooled plastic phase - I)-----~~

N :E: -

8

6

4

2

o

-2

~ I

4 6 8 10

o present work * ultrasonic relaxation (liquid) - ref. 53

o ref. 18

• ref. 49 A ref. 41

12 14

Figure 6.2: Complete Arrhenius diagram depicting the a' -, 0.-, {3'- and (3- processes found in plastic phase (1) of Cyclohexanol (CHXOL). Also included are the data of others for the purpose of comparison. A vertical line is drawn at the melting temperature Tm and the dielectric data above Tm are not shown deliberately to avoid confusion. Also shown are the calorimetric Tg and Tg like events reported by Mizukami et al.40 which approximately correspond to enthalpy relaxation of log fm(Hz) = -2.45 ± 0.45.13 The dashed line along a' - process is the least square fit of Phase I data to eq. 1.42 where the parameter E = 51.7 kJ/mol.

I is clearly orientationally disordered (OD) as shown by Murthy,14 while phase II appears

to be ordered. The X-ray diffraction studies66 indicate that Phase I is face centered cubic

(fcc) with the cell parameter of 8.815 AO at 293 K and phase II is triclinic. The dielectric

relaxation of phase I was already reported by one of the present authors14 and hence, will

not be repeated here.

6.2.2: CHXOL-NPOL binary system.

Because of the similaritY in the cell structure and lattice parameters of phase I of CHXOL

and NPOL, the mixtures of these materials form continuous solid solution in phase I [see Fig-

ure 6.3], which is designated as 8/. The liquid mixtures when cooled at a rate of 1 deg/min.

165

x = 0.25 CHXOL-NPOL (a) -0.2 x = 0.50

X = 0.75 -0.4 -.e>

~ --~ -0.6 0

u::: ..... ro -0.8 Q) :::c

-1.0 0 '0 C W

-1.2 200 220 240 260 280 300 320 340

T (K) 340

(b) CHXOL - NPOL

320

300

- 280 ~ --I-260

240

220

0.0 0.2 0.4 0.6 0.8 1.0

Figure 6.3: Two-component system CHXOL-NPOL. (a) DSC curves for a heating rate of 2 deg.jmin at three concentrations in the range 0.25 :$ Xm :$ 0.75. [The sample size is: 19.3 mg (for Xm = 0.25), 20.15 mg (for Xm = 0.50), 18.6 mg for Xm = 0.75J. Tsol & Tliq are the solidus and liquidus temperatures. (b) The tentative solid-liquid phase diagram deduced from the DSC curves. Note that the low temperature transition to more ordered phases as in the case of pure CHXOL or NPOL start showing up only for Xm :$ 0.10 and for Xm 2: 0.95.

166

1.0

0.5

0.0 -N :c -0.5 ~ T"" -:

W -1.0 C') 0

-1.5

-2.0

CHXOL-NPOL

80 100 120 140 160

o Xm == 0.25 fl. Xm = 0.50 o Xm = 0.75

180 200 220 240 260 280

T (K)

Figure 6.4: Variation of log /' with temperature in the solid phase (S[) of CHXOL-NPOL binary system at a test frequency of 1 kHz, for different concentrations of NPOL. Note the presence of the smaller process designated as a' - process along with the a- and f3- processes. The f3' -process is not clearly resolved in the measurements and hence, the large error bar giving the uncertainty.

collapse to the crystalline phase (S[), which on subsequent heating begin to liquefy.which

can be seen as a melting endotherm in DSC measurements as shown in Figure 6.3( a). The

melting or liquefaction extends by over 5-8 degrees which is characteristic of a solid solution

[Figure 6.3 (b)] and the region between Tlit/uidus (or Tiiq) and Tsolidus (or T sol ) corresponds to a

mixed phase of liquid and solid. For the measurement of enthalpy of transition, the samples

are annealed at 275 K for 15 mins. and then at 254 K for 30 mins. before starting the DSC

run from 103 K. They are subsequently heated at a rate of 2 deg/min. For the measurement

of glass transition temperature, a different run with a heating rate of 10 deg/min. was em-

ployed. These results are entered in Table 6.1. The nature of phase S[ has been examined

critically at three concentrations or mole fractions (xm) of NPOL in CHXOL using dielec-

167

tric spectroscopy. Phase 5[ is orientationally disordered as indieated in Figure 6.4, where

the dielectric. loss at 1 kHz test frequency at various concentrations of NPOL shows clearly

a relaxation behavior typical of a glassy crystal. From Figure 6.4, it is evident that the

magnitude of the higher temperature relaxation process (a' -) decreases with increase in the

concentration of NPOL. The corresponding dielectric behaviour for temperatures above 77

. K is shown in Figures 6.5(b) & 6.5(c). This dominant dispersion [Figure 6.5(b)] mQves to

much higher frequencies upon melting which starts at a temperature Tsolidus and is complete

at a temperature 1'ziquidus or 1'ziq' The above dispersion can also be seen as a peak in the

dielectric loss vs T curve, and may be idel1tified as the primary (or a-,-) process. In addition

to the above said process, there are three other processes designated as: a' - on the higher

temperature side i.e. above primary relaxation process; (3' - & (3- processes that still con-

tinue below Tg (P), the kinetic freezing temperature of the a- process. The (3' - process is

detectable in a very narrow temperature range i.e. between 150-160 K as shown in Figure

6.6(a).

Dielectric measurement have been performed on two-component H-bonded systems i.e.

CHXOL-NPOL, at four concentrations i.e. Xm =0.25, Xm = 0.50, Xm = 0.75 and Xm = 0.95,

where Xm is the mole fraction of second component (NPOL). To give the reader an idea of

the various relaxation processes, the spectral dependence of the relaxation of dispersion of

CHXOL-NPOL system for one concentration Xm = 0.50, with HN-fit (eq. 1.46) is shown

in Figure 6.6, and similar behavior was exhibited in other concentrations. All the processes

other than the a-process, are more or less symmetrical in spectral shape, and can be

represented by Cole-Cole equation (f3HN = 1 in eq. 1.46). To give the reader some idea,

the magnitude (b.E value) of these processes are given in Table 6.2 along with other spectral

details. The Arrhenius plot for all the concentrations is shown in Figure 6.7. The a-process

follows the critical power law34- 38 (eq. 1.59). Alternately, the data can also be described

equally well by the Vogel-Fulchers-Tammanns equation76 (eq. 1.58). Tabulated in Table 6.3

168

o~============================~~ 3

2

o

-1

-2

(c) CHXOL-NPOL, Xm = 0.50 0100/"lz 1!11 KH% ~ 10 KHz 0100 KHz '171 MHz

80 100 120 140 160 180 200 220 240 260 280 300 320

T (K)

Figure 6.5: Behavior of CHXOL-NPOL binary system for Xm = 0.50. (a) DSC scan for a heating rate of 10 deg/min. (sample size =17.56 mg.). Temperature variation of the (b) real and (c) imaginary parts of the complex permittivity at various test frequencies. The phase designated as Sf is the solid solution and Tsol is the solidus temperature. The step-like rise of dielectric loss above Tliq is mainly due to the de loss which varies as j-l, where f is the test frequency.

169

1.5

1.0

0.5

: 0.0 w OJ .2 -0.5

-1.0

-1.5

-2.0

-1.6

-1.8

"w Cl -2.0 o

-2.2

(a) CHXOL - NPOL, Xm = 0.50

/

o 148.4K [!J 156.1 K t:.170.1K (;) 185.3 K v 200.7 K c 220.6 K .t. 240.3 K 'f' 260.7 K

-2 0 2

log f (Hz)

(b) CHXOL - NPOL, Xm = 0.50 0

1.5 2.0 2.5 3.0 3.5

Cl 90.2 K A 95.5 K 'V 100.5 K .t. 105.8 K [!J 110.8 K 0115.8 K (;) 125.2 K

4.0

log f (Hz)

a-process

4 6

~ -process

4.5 5.0 5.5 6.0

Figure 6.6: Double logarithmic plot of €" vs. frequency at different temperatures of CHXOL-NPOL binary system with Xm = 0.50. (a) a' -, a-, & ,,'-processes; (b) {3-process. In panel (a) the dashed dotted line corresponds to the HN- equation (1.46) for the a- process, dashed line corresponds to the CC-function for the resolved {3'-process and solid line corresponds to the CC-function for a'-process. In panel (b) the solid line corresponds to the CC-function for {3-process. The rise in the loss at frequencies above 10 kHz in (a) is due to the {3-process. For the corresponding parameters of fits to eq. 1.46 of various processes, the reader may refer to Table 6.2.

170

Table 6.2: Details of the parameters of Eq. 1.46 for various relaxation processes shown in Figure 6.6, for CHXOL-NPOL, Xm = 0.50

Processes Temp aHN PHN fo(Hz) fm(Hz) M: (K)

a'- process 22'0.6 0.289 1.00 1.87 x 102 1.87x10l 1.109 260.5 0.315 1.00 3.98 x 103 3.98 X 10

3 0.774 148.4 0.032 0.775 1.58 x lO-l 1.95 X lO-l 20.23 156.1 0.039 0.794 2.68 x 10-1 3.25 X 10-

1 20.20

a - process 170.1 0.005 0.718 1.62 x 101 2.11 X 101 19.89

185.3 0.018 0.768 3.98 x 102 4.93 x'102 19.78 200.7 0.008 0.775 3.98 x 103 4.87 X 103 18.49 210.4 0.010 0.791 1.67 x 10

4 2.01 X 104 17.89 220.6 0.011 0.802 5.71 x 104 6.89 X 104 17.27

P' -process 148.4 0.599 1.00 3.98 x 10l 3.98 x 102 0.149 156.1 0.470 1.00 1.77 x103 1.77 x 103 0.188 90.2 0.776 1.00 4.42 x 10l 4.42 X 10k 0.122

~ - process 95.5 0.758 1.00 1.59 x 103 1.59 X 103 0.125

100.5 0.740 1.00 5.31 x103 5.31 x 103 0.126 105.8 0.715 1.00 1.83 x 104 1.83 X 10

4 0.127 110.8 0.711 1.00 6.02 x 104 6.01 X 104 0.137 115.8 0.697 1.00 1.85 x 105 1.85 X 105 0.143 125.2 0.716 1.00 1.48 x 106 1.47 X 106 0.194

are the results of the fits to eqs. 1.42, 1.58, & 1.59. The relaxation rates and the spectral data

shown in Tables 6.2 & 6.3 are found to be similar during cooling and subsequent heating,

indicating that they indeed correspond to 8[. Depicted in Figure 6.8 are the variation of

various experimental parameters with respect to the mole fraction (xm). Plotted are Tg(D)

(or dielectric Tg , the temperature at which the 1m value is ~ 10-3 Hz), the peak loss frequency Um,aJ & dielectric strength of the a-process (~€Q:) at specific temperatures. A continuous

change of these physical properties from that of CHXOL to that of NPOL with X m , according

to the well known Gordon-Taylor eq. 1.3,52 is noteworthy. Figure 6.7 clearly demonstrates

that the kinetic freezing of the (dielectric) a-modes, indeed cause the glass transition event

in D8C at Tg .

To establish the relation between the deviations from Arrhenius equation and the Debye

behavior of the a- relaxation, the dynamic fragility index (m) defined in eq. 1.1575,77 was

calculated and the values of "m" thus determined are entered in Tables 6.3.

171

6

4

-N :::E: -E 2 .... 0 Xm = 0.00 C) .2 A Xm = 0.25

® Xm = 0.50 0 v Xm = 0.75

• Xm = 0.95 I!I Xm = 1.00

-2

4 6 10 12

Figure 6.7: Complete Arrhenius diagram of 8[ in CHXOL-NPOL binary system. The thick line along the 0.'- andi~processes corresponds to eq. 1.59 and that along the /3-process corresponds to eq. 1.42, for the parameters shown in Table 6.3. Note that the uncertainty in /3' - process is very high, and the dashed line along this process is guide to the eye if an arrhenius fit (eq. 1.42) is attempted.

Table 6.3. Details of a- and /3-process corresponding to SI is in CHXOL-NPOL binary system.

Tg (D)· a-process /3-process

Fragility Sample Power law parameters VFT parameters index Arrhenius parameters

(K) (Eq. 1.59 (Eq. 1.58) (m) m,. 1.42) log fo Ep

log fo .• (Hz) r Tg (K) log fo,.(Hz) B (K) To(K) (Hz) (kJ/mol)

CHXOL 149.3 7.14 8.76 140.58 10.83 1628.5 97.77 39.76 14.64 23.6

CHXOL-NPOL 147.3 6.66 9.80 133.42 11.01 1867.6 88.10 34.08 14.68 22.2 Xm =0.25

CHXOL-NPOL 144.4 6.37 10.09 129.12 11.18 2011.9 81.63 32.02 14.80 21.1 xm=0.50

CHXOL-NPOL 141.8 6.25 9.90 126.88 11.06 1975.0 79.47 31.30 14.81 19.8 Xm = 0.75

NPOL 137.6 4.23 14.37 104.56 14.92 4403.2 29.99 22.71 .... --- ----.. (ref. 14)

* Temperature where fm = 10.3 Hz, calculated from PL parameters.

172

j::' -ts .• ..E 01 ,g

j::' -ts II)

Table 6.4. Details of various transitions in the CNCH - CHC binary system.

Sample Nature of Transition Enthalpy of Transition * Temperature transition

(K) (L1H) kJ/mole

S1~L 284.3 3.66 ± 0.07 285.1 62 3.63562

CNCH 281.9 ± 0.863 3.88 ± 0.0463

SII ~ S1 217 ± 3 7.42562

215.062

Tg (S1) 135.6 134.7 ± 0.463 133.5

SI~L 282.5 3.07 ±0.1 CNCH-CHC Tg (SI) 13'2.5

Xm = 0.125 SI~L 276.2 2.77 ± 0.04

CNCH-CHC Tg (SI) 131.2 Xm = 0.25

SI~L 268.8 2.54 ± 0.03 CNCH-CHC

Xm = 0.40 Tg (SI) 129.7 S1~L 228.7 1.67

CHC 229.359 2.0459

229.1 14 1.7814

SII~ SI 221.1 7.88 220.614 7.93 14

220.459 8.0J59

SIII~ SII 120.059 0.0559

Tg(SI) 116.3 14

* S: crystalline solid, L: liquid, T g : glass transition temperature.

6.2.3: CNCH-CHC binary system.

Above results with CHXOL-NPOL, and results from our earlier research work,37 indi-

cated that the mixtures of CNCH (MW = 109.17) and CHC (MW = 118.61) with similar

molecular shape and size may yield interesting results (although complete information about

174

the individual crystal structures is lacking1,59,62). Pure CNCH and CHC were examined crit-

ically earlier36,62-65 and both demonstrate the existence of a plastic phase (phase I) that

transforms to another phase (II) on lowering the temperature. [Phase I in CHC is known59

to be face-centered cubic with the unit cell parameter of 9.05 AO at 224 K, but the informa-

tion about phase II & III is lacking. According to Diky et al. 59 phase I consists of equatorial

(e-), and axial (a-) chair conformers, but the phases II & III consist of e-confirmers only.

Information about the crystal structure of phase I (which is orientationally disordered) of

CNCH is lacking, but one may expect it to be a face centered cubic as is the case with

cyclohexane and some of its derivatives1,59j. Realization of Phase II (which is believed to be

rigid) in CNCH is difficult with the present experimental techniques as it requires prolonged

annealing of at least three weeks62 and therefore, what is discussed in this paper concerns

phase I only. Phase I of CNCH is a non-rigid rotator (plastic) solid as it demonstrates a well

defined a-process associated with the calorimetric Tg at 135 K. 36,48,62,63, In addition, two

more very small step-like changes in specific heat (Cp) were reported at 160-170 K and 55

K. 62,63 The former change corresponds to the kinetic freezing at the interconversion between

the a- and e- conformers with an activation energy of 51 kJ /mo1.36,62-65 and the latter may

correspond to the kinetic freezing of JJ-process36,43 (also see Table 6.4). In case oLCHC,

phase I has a Tg of 116 K, but this phase requires much larger cooling rates to form the

glassy crystal. 14 From the dielectric measurements performed in this laboratory on CHC, it

was obvious that phase II is a rigid rotat.or solid. The details of the various transitions are

given in Table 6.4.

The DSC results on samples with various concentrations of CHC with CNCH are depicted

in Figure 6.9(a) .. The DSC curves for 0.00 ~ Xm < 0.5 reveal only one sharp endotherm even

after annealing the samples at 168 K for three hours. The enthalpy associated with this

endotherm shows a smooth variation with that of the pure components (see Table 6.4). To

get some information about the solid-liquid phase diagram over the entire concentration

175

Figure 6.9: CNCH-CHC binary system. (a) DSC curves for a heating rate of 2 deg./min at three concentrations. [The sample sizes are: 13.13 mg (for Xm = 0.00), 13.45 mg for Xm = 0.25 and 12.63 mg (for Xm = 0.75)J, (b) Tentative solid-liquid phase diagram.

176

range, DSC scans were taken at 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 Figure 6.9(a). The transition

temperatures thus determined were plotted as a function of the mole fraction of CHC (xm ), as

suggested in literature78- 8o to determine the solid-liquid phase diagram. The phase diagram

is presented in Figure 6.9 (b ), which is typical of a solid solution (S I) for 0.00 :S Xm < 0.5,

although the complete phase diagram at still higher concentrations is not clear because of

appearance of time dependent thermal events requiring very prolonged annealing times in

the DSC scans. However, the DSC curves beyond Xm ~ 0.5 show another endothermic

peak at a temperature designated as Ttr as shown in Figure 6.9(a) & 6.9(b) which smoothly

merges with the transition 'temperature Tl of pure CHC [Figure 6.9(b)] below which pure

CHC exists as a rigid phase. The nature of the phase of the samples below Ttr is not clear,

and requires further investigation.

To support the interpretation of our DSC results, we performed dielectric measurements

on CNCH-CHC binary system at concentrations i.e. Xm = 0.125, Xm = 0.25, Xm = 0.40 and

Xm = 0.501, over a wide frequency range. Shown in Figure 6.10 is the temperature variation

of the real [Figure 6.10(b)] and imaginary part [Figure 6.10(c)] of the complex permittivity

in CNCH-CHC binary system for Xm = 0.125 at different test frequencies, along with the

corresponding DSC curve [Figure 6.10(a)]. Clearly, the melting or liquefaction extends by

over 5-8 degrees from Tsol to T"iq (shown within vertical dashed lines in Figure 6.10) as

is the characteristic of a solid solution, and is accompanied by a small change in the static

dielectric constant. Our dielectric measurements on this binary system indicate a well defined

(3- process in addition to the 0;- process [which kinetically freezes to its corresponding Tg]

as shown in Figure 6.10( c). There is also an indication of yet another process designated as

0;' above a temperature Tg,Q" To give the reader an idea about the spectral shape of the

relaxation, the spectral behavior of CNCH-CHC system for Xm = 0.125 has been depicted

177

-C) ~ -~ 0

;;:: .. CO GI ::c

0.0 ~----==~..,..---------:-:--=-=----r"-----' (a)

-0.2

-0.4

-0.6 1 0

-0.8 "0 C W

-1.0

Tg -132.5K j

~ ~Bl • £ .(I.QoI .. :! .0,05

T(K)

I I

Tsol I

-----.......~ I I I I I I I

J

: til C) ,g

1.0~--~----~~~-------------------------------.

(a) CNCH • CHC, Xm = 0.125

0.5

I

0.0

-0.5

-1.0

T = 135.4 K T = 150.5 K T = 165.4 K T = 185.6 K -' ........ -~.-.;n.. a. -process~~. ~, ~~

/&" ~,If'i' , I

I '-1> " ;;> ~£\ '

'k.1 ;;> /~), l

1/ ~~A;t rjl . / Ll-a.'

I 0/' '" . I ". %~~~~1 I . \ I .\

I / I. -1.5 ...L---r----''------r---;.....-~'_r__-~~--_r_...L.)...---~

-2 o 2

log f (Hz)

4 6

-1.2 -r---------------:------------, (b) CNCH • CHC, Xm = 0.125 f3 -process

T = 125.0 K

-1.4

-1.6

-1.8

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

log f (Hz)

Figure 6.11: Double logarithmic plot of /' vs. frequency of CNCH-CHC binary system for different temperatures with Xm = 0.125: (a) a-process and (b) {3- process. The dashed dotted line in panel (a) and solid line in panel (b) corresponds to the HN-parameters shown in Table 6.5. For T = 185.6 K, the solid line represents the typical ansatz (HN + CC) fit to resolve the a' - and a- processes.

in Figure 6.11, where the relaxation process can reasonably be explained by eq. 1.46 around

the peak frequency region, and the corresponding parameters are given in Table 6.5.

179

Table 6.5. Details of parameters of Eq. 1.46 for various relaxation processes for samples shown in Figure 6.11, for CNCH-CHC, Xm = 0.125.

Process Temp (lHN PHN fo (Hz) fm (Hz) At (K)

185.6 0.406 0.943 5.55 x 101 6.07 X 101 1.565

a' 190.1 0.405 1.000 1.99 x 102 1.99 X 102 1.498

195.2 0.355 1.000 5.90 x 102 5.90 X 102 1.355 200.8 0.322 1.000 1.77 x 103 1.77 X 103 1.239

135.4 0.180 0.657 2.25 x 10"'" 3.49 X 10"'" 11.03

a 150.5 0.140 0.586 2.76 x 101 4.66 X 101 11.51

165.4 0.146 0.599 3.98 x 103 6.62 X 103 11.96 185.6 0.045 0.388 1.75 x 105 3.92 X 105 12.56 195.2 0.011 0.299 5.54 x 105 1.49 X 106 13.82

100.8 0.505 0.232 1.93 x 10 1 3.24 X 10'" 0.284

~ 105.5 0.634 0.350 5.17 x 101 8.48 X 102 0.336

110.1 0.680 0.421 2.31 x 102 3.26 X 103 0.389 115.1 0.705 0.501 1.14 x 103 1.14 X 104 0.422 120.4 0.735 0.738 1.59 x 104 4.99 X 104 0.440 125.0 0.759 1.000 1.67 x 105 1.67 X 105 0.481

Similar behaviour was observed for other concentrations in the range O. 00 ~ Xm ~ 0.4.

Shown in Figure 6.12 is the dielectric loss at 1 kHz test frequency at various concentrations

of xm~ 0.4, which clearly shows the existence of two relaxation processes designated as {3-

and 0/, together with primary (or a-) process. In Figure 6.12, it is clearly noticeable, that

with increase in the concentration of second component i.e. CHC, the Tg of this binary

system gets shifted towards the lower temperature side, without any noticeable change in

the position of a' - process. Dielectric measurements for Xm > 0.4 become very complicated

due to the time dependent onset of partial crystallization below Ttr . The complete relaxation

map of the samples is shown in Figure 6.13, depicting 1m values in the form of an Arrhenius diagram. The thick lines correspond to PL-fit (Le. eq. 1.59), as shown in Table 6.6: Also

included in Table 6.6 are the values of dynamic fragility index "m" determined from eq. 1.15.

Interestingly, the exponent "r" is approximately 9-12 (Table 6.6), as also found in many of

the supercooled liquids35,41 and plastic crystals. 13,14,23,34,36-38

180

1.0 CNCH-CHC

0.5 ___ x", = 0.000 -e- x", = 0.125 ~ x", = 0.250

0.0 -e- x", = 0.401

-N J: ~

T'"" -0.5 ---w C>

..Q -1.0

-1.5

-2.0 +----r----.---...... ----.----.----.----,----,----' 80 100 120 140 160 180 200 220 240

T (K)

, Figure 6.12: CNCH-CHC binary system: Variation of log e" with temperature at a test frequency of 1 kHz, for four different concentrations of CHC. Note the presence of two smaller processes designated as a' - and (3- process along with the primary relaxation (0.-) process. The vertical arrows on the curves correspond to the Tg (DSC) shown in Table 6.4.

6.3: Discussion

For the sake of convenience, the results are discussed under the following sections.

6.3.1: a'-process in cyclohexyl derivatives: The main purpose of this present work

is to find out the evolution of a' process. As shown in a number of publications53- 57 the

total strain in the boat confirmation of the molecules of cyclohexyl derivatives, is larger than

that in chair confirmation and consequently the former is less stable than the latter. Within

the chair confirmations, axial to equatorial transformations occur which involve an energy

barrier of 44-50 kJ /mole and the latter confirmation is preferred at lower temperatures.

In Figure 6.1, a process designated as a' process is evident on the lower frequency side of

the dielectric spectra taken for the plastic phase-I of CHXOL. However, the spectral shape

of the resolved a' -process is not clear because of limited frequency used in the present

181

forming a solid solution. An external 'inspection of the samples at temperatures below Tsol

indicate them to be waxy solids, and this is accompanied by only one endothermic peak over

the entire concentration range. The endotherms are slightly broader [Figure 6.3(a)] and the

difference between Tsol and T 1iq is about 5-8 degrees [Figure 6.3(b)], as is the characteristic

of a solid solution. Moreover, the enthalpy associated with the endotherms in Figure 6.3(a)

show smooth variation between the pure component values (Table 6.1). Therefore, the solid

S[ is clearly a solid solution (of phase I of the components) and is (also) face centered cubic in

structure. There is a steady variation of the various physical parameters with Xm from that

of CHXOL to NPOL as shown in Figure 6.8. The curves shown in Figure 6.8 interestingly

follow the Gordon-Taylor rule given by eq. 1.3. The lack of a strong variation of .6.ca with

Xm [Figure 6.8(c)] is partly due to the similarity in the dipole moments of CHXOL & NPOL

which are 1.85 D81 and 1.68 D81 respectively. This solid phase exhibits various relaxation

processes which are discussed in the following subsections.

6.3.2.1: Primary (or (Y-) relaxation: The solid S[ is an OD phase and exhibits a well

pronounced relaxation in dielectric measurements (Figures 6.4-6.6). This relaxation has

similar characteristics to those of the so called primary relaxation process (or (Y - process)

seen in many single component plastic crystals and liquid glass formers. Also the dielectric

spectra can reasonably be described by HN-equation (see Figure 6.6 & Table 6.2). From the

spectral shape, the value of symmetric parameter (YHN is nearly zero and the asymmetric

shape parameter (f3HN) is about 0.72-0.80 (see Table 6.2) indicatingthe spectral shape to

be of the Cole-Davidson type. 61 This value of asymmetric shape parameter is indicative of

cooperative nature of the (Y- relaxation which is also reported by various research groups

using NMR39 and dielectric spectroscopy14,18,41 and in pure cyclohexanol. 14 Similar type of

behaviour was observed at other concentrations as well. This suggests that the binary system

CHXOL-NPOL behaves like a single component as characteristic of a solid solution. From

Figure 6.7 & Table 6.1, one can infer that the glass transition event seen in DSC curves is

184

the same as the one which ~orresponds to the kinetic freezing of the above said a-process.

It is also evident that as the concentration of second component i.e. NPOL increases, the

fragility index decreases (see Table 6.3).

6.3.2.2: Secondary ( {3' - and {3-) relaxation: This binary system shows two sub-Tg

processes designated as {3' - and {3- process similar to those reported by Brand et. al. I8

in case of pure cyclohexanol [see Figures 6.4-6.7]. The clarity of the {3' - process is very

low, while {3- process is clearly resolvable throughout the concentration range (See Figure

6.6). Although the {3' -process has a lot of uncertainty in its resolution, it appears to

be an activated process with an activation energy in the range 36-40 kJ fmole, which is

comparable to other intra-molecular motion(s) associated with chair-boat or chair -twisted

boat transformations. [Interestingly, there is no {3' -process in the other binary system

CNCH-CHC studied here (compare Figure 6.13 with Figure 6.7)]. This high value may not

be due to a simple inter-molecular reorientation as the associated barriers are in the range

20-23 kJ fmol. as shown by us recently.36 The origin of this process can not be speculated

with any certainty. This process on extrapolation towards lower temperatures kinetically

freezes at about 100-120 K, which corresponds to a (one of the small) step like change in

the specific heat (Cp ) vs. temperature curve at 116 ± 2 found by Mizukami et al.40 in their

high precision adiabatic calorimetric measurements on pure cyclohaxanol.

Similarly, the {3- process of pure cydohexanol on extrapolation towards lower temper-

atures, kinetically freezes at about 75-80 K, which corresponds to a small step like change

found by Mizukami et al.40 and Kishimoto et al. 70 The activation energy of {3- process falls

from 23.6 kJ fmol to 19.8 kJ fmol (Table 6.3) as we move from CHXOL to NPOL, where

NPOL is slightly smaller in size. These values are comparable to the {3JC- process of CHC,

CNCH in glassy ortho-terphenyl (OTP)36 and of CNCH36 & iso-CNCH36,43 in their plastic

crystalline phases. Thus, it is tempting to identify the {3- process shown in Figure 6.7 with

{3JC- process.

185

6.3.3: S1 phase in. CNCH-CHC binary system:

There are strong reasons to believe that mixtures of this binary system form solid solution

below the solidus temperature (Tsol ) [Figure 6.9] and the phase behavior is that of a simple

solid solution for 0.00 ~ Xm ~ 0.4 down to the lowest temperatures. An external inspection

of the samples at temperatures below Tsol indicates them to be waxy solids, and the·corre-

sponding DSC curves shown in Figure 6.9(a) reveal only a single endotherm for 0.00 ~ Xm

~ 0.4, and the difference between Tsol and 7liq is about 5-8 degrees [Figure 6.9(b)], which

is a characteristic of a solid solution. In . addition, the enthalpy associated with the curves

shown in Figure 6.9(a), lies between 3.07 to 2.42 kJ/mole and shows a smooth variation

between the pure component values (see Table 6.4). The corresponding entropy of transition

from solid to liquid is in the range 11.1 - 9.2 J/mol K. According to Timmermanns2 for a

crystal to be a rotational solid, this quantity has to be less than 21 J /mol K. which is the

case here. Thus, there is a large frozen entropy in the form of orientational disorder, and

interestingly, this is only a small fraction of the entropy associated with the transition to

the corresponding rigid crystalline state, i.e. to phase II (Table 6.4) of the pure components.

Both the component liquids CNCR & CRC, rapidly crystallize to their respective crystalline

phases (i.e. phase I) and it is difficult to expect the liquid state of their mixtures to under-

cool partially without complete crystallization to phase 1. Therefore, the dispersion evident

in Figures 6.10-6.12 corresponds to S, phase that is orientationally disordered, and is also

a solid solution. This OD phase has three relaxation processes designated as a-, at and

{3- in dielectric measurements, as shown in Figures 6.10-6.13, which are discussed under the

following subsection.

6.3.3.1: Primary (or a-) relaxation: The dipole moment "J-I," of the CNCR and CRC

are 3.79 D62 & 2.09-2.12 D respectively.81 The a- relaxation characteristics are similar to

those of the so-called primary relaxation process seen in the plastic crystalline phase of pure

CNCH36,43 as well as many of the supercooled liquids and plastic crystals. From Figure

186

-N J: ---\t-E

C)

.Q

8~--~~----------------------------~rr=========~

6

4

2

o

-2

3.5 4.5 5.5 6.5 7.5

10001T (K)

~124

120

"6 1121--~--------I1

0.0 0.2 0... 0.6 0.8

o Xm = 0.000 o Xm = 0.125 t::. Xm = 0.250 ® Xm = 0.401 • Xm = 0.500

8.5 9.5

Xm

10.5 11.5

Figure 6.13: Arrhenius Diagram for the supercooled phase (Sr) of CNCH-CHC binary system. The thick lines correspond to the fit to eqs. 1.42 or 1.58, for the parameters shown in Table 6.6. Shown in the inset is the variation of calorimetric Tg

with Xm according to eq. 1.3 given by: Tg(x) = Tg2i::!~~(~'~~~)rm) , where Tg2= 116.3 K, Tgl = 135.2 K and the interaction parameter k = 1.21. In'this equation Tg2 is the Tg of the plastic phase I of CHC (see Table 6.4)

Table 6.6. Details of a- and p-process corresponding to S, is in the samples CNCH-CHC binary system shown in Figure 6.13.

Tg (0)· a-process p-process

Power law parameters VFT parameters Fragility Arrhenius parameters Sample (Eq.I.59 Eq.I.58 index ~Eq. 1.42)

(K) ! (m)

log fo.a(Hz) r Tg (K) log fo.a(Hz) B (K) To(K) log fo(Hz) Ep (kJ/moJ)

CNCH 133.4 8.43 9.96 124.66 11.23 1216.9 95.68 49.5 15.42 23.36

CNCH-CHC, 131.3 8.43 10.87 120.47 12.47 1584.3 85.81 43.65 15.23 24.35 Xm = 0.125

CNCH-CHC, 129.6 8.60 10.21 120.80 11.97 1341.9 89.77 47.60 15.03 23.92 Xm = 0.25

CNCH-CHC, 128.2 8.65 10.21 119.72 12.22 1381.2 88.01 47.60 12.15 19.77 Xm = 0.40

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

investigation, and hence, the estimated 1m values are approximate and should be considered with this approximation in mind. Interestingly, the E value in eq. 1.42, is about 51 kJ fmole

182

(as shown in Figure 6.2) and on extrapolation approximately tallies with the ultrasonic

relaxation frequency value given by Karpovich53 for liquid CHXOL at room temperature with

some discontinuity at the melting temperature. Our earlier calculations,36 using molecular

orbital package (MOPAC) calculations that the difference in the dipole moment between

the axial and equatorial confirmers is not very high and hence, the associated relaxation

from a- to e- transformation will be weak in dielectric measurements appears to be true

in CHXOL (Table 6.1) and its mixtures shown in Figures 6.4-6.6. This transformation is

apparently stronger in mechanical (ultrasonic) relaxation studies of Piercy et. a1. 56,57 and

Mandanici et. a1. 44,51 As shown in Figure 6.4, one can see 'the dilution of this process with

increasing concentrations of NPOL (which does not exhibit chair forms typical of cyclohexyl

derivatives). The a' - process can still be seen up to a concentration of Xm = 0.50 of NPOL

(Figure 6.5 & 6.6) but is hardly detectable at Xm = 0.75 of NPOL (Figures 6.4 & 6.7).

In pure CN CH, the a':.. process associated with axial (a-) to equatorial (e-) confirmer

transformation was largely masked by interfacial polarization36and is hardly resolvable in

dielectric measurements, however the enthalpy relaxation studies62- 65 reveal it as a clear

event. As shown in Figure 6.12, this 0'.'- process is well resolved in the solid solution of

CNCH-CHC system and the analysis of this process at the concentration of Xm = 0.125 of

CHC is presented in Figure 6.1O(c) & 6.11 (It must be remembered that CHC is capable of

a- to e- confirmer transition). Interestingly 0'.'- process has a tendency to be non-Arrhenius

too (Figures 6.7 & 6.13). If we extrapolate this process towards the low temperature side,

it kinetically freezes at about 165-170 K. But, if we assume it to be arrhenious [100 Hz :::;

1m :::; 1 MHz], its apparent activation energy measures to 55.4 ± 1 kJ/mole which is close to that stated in the proposed scenario of Mandanici et. a1.44,51

6.3.2: 81 phase in CHXOL-NPOL binary system:

Both materials CHXOL & NPOL have the same crystal structure as well as almost same

lattice parameter as mentioned in the result section, and hence, their binary is capable of

183

6.10(a) and 6.13, one can conclude that the glass transition event seen in DSC curve is the

same as the one which corresponds to the kinetic freezing of the a-process. Similar is the

case with the other concentrations of this binary system which becomes clearer when Tg(D)

of Table 6.6 is compared with Tg of Table 6.4 (also see Figure 6.13). The Tg values of S1 phase

shown in the inset of Figure 6.13 follow the Gordon-Taylor equation and there is a smooth

variation of Tg between the pure component values of phase 1. Interestingly on extrapolation

towards the higher temperature side, the a- process shown in 'Figure 6.13 smoothly merges

with the 1m value of liquid CNCH82 indicating lesser hindrance to the rotational motion on solidification to phase 1. The spectral characteristic is broader (and asymmetric as shown

in Table 6.5) than CHXOL-NPOL system with a grater fragility index (Table 6.6). Besides

this there is another relaxation process (a') which has been discussed in section 6.3.1.

6.3.3.2: Secondary (or /3-) relaxation: The S1 of this binary system exhibits only one

sub-Tg process. Unlike the usual sub-Tg processes, some amount of asymmetry is observed

in the frequency dependence of the /3- process, due to which we have fitted the data to the

HN-equation to obtain 1m value (Figure 6.11 and Table 6.5). The corresponding activation energy of eq. 1.42 (E,B) is nearly independent of composition, except for larger Xm when

it decreases slightly (Table 6.6). This value is in the range of 20-23 kJ/mol and is more

or less the same as compared to the activation energy of the /3- process of pure CNCH.36

Both the materials CHC and CNCH when dispersed in liquid glassy OTP matrix36exhibit

a secondary or /3- process (besides an a- process above Tg of the solution) whose E,B is in

the same range and is comparable to those of similar sized rigid molecules which have no

internal rotational degrees of freedom. 36 This suggested that the /3- process of this binary

system is intermolecular in nature i.e. JG-type of relaxation process, as reported for pure

CNCH.36,43

187

6.4: Conclusions

The present observations clearly suggest that the relaxation process seen in the plastic phase

I of CHXOL-NPOL binary system corresponds to the a-process, whose kinetic freezing

causes the glass transition event, as also reported in glassy crystals such as pure cyclooc-

tanol, cyclohexanol, cyanoadamantane and pentachloronitrobenzene etc. Interestingly, the

various physical parameters determined for this binary vary smoothly between its compo-

nent values, indicating an isomorphic relationship between the fcc phases of both the pure ,

components. Evidence is presented here to show that binary of CNCH-CHC with Xm in the

range 0.00 :$ Xm :$ 0.4 could also be one such example which interestingly behaves like a sin-

gle component orientationally disordered phase that demonstrates a glass like phenomenon.

The {3- process found in these binary systems .is perhaps intermolecular in nature and hence,

is a {3JG- process. Another process of much smaller magnitude designated as d -process

was found above the glass transition temperature Tg which kinetically freezes around 170

K. This process interestingly, is also non-arrhenius in nature, becomes increasingly weaker

with increase in the second component, and may be identified with (axial) chair- (equator-

ial) chair transformation. Low temperature X-ray analysis of these samples are expected to

throw more light on the structure and nature of these samples.

Another interesting observation of our study is the stability of the plastic phase of

CHXOL-NPOL, CNCH-CHC solutions against a collapse to a more ordered phase as hap-

pens in pure CHXOL, NPOL, and CHC. The suppression of crystallization to a more ordered

phase by the addition of a second component can be a challenging theoretical problem.

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