J. Phys. Chem. B 1999, 103, 4197-4205
4197
Molecular Dynamics and Crystallization Behavior of Chiral Isooctyloxycyanobiphenyl as Studied by Dielectric Relaxation Spectroscopy Maria Massalska-Arodz Institute of Nuclear Physics, 31-342 Krakow, Radzikowskiego 152, Poland
Graham Williams,* Dale K. Thomas, and W. Jeremy Jones Chemistry Department, UniVersity of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.
Roman Dabrowski Military UniVersity of Technology, 01-489 Warzsawa, Kaliskiego 2, Poland ReceiVed: December 2, 1998; In Final Form: March 1, 1999
The complex dielectric permittivity of right-handed isooctyloxycyanobiphenyl (IOOCB) has been studied in the frequency range 10-1-105 Hz and over a wide temperature range. On cooling the isotropic liquid a supercooled liquid is formed that becomes a glass below 220 K. On heating the glass, the material crystallized at about 250 K and remelted at 285 K. The dielectric R-relaxation in the isotropic liquid was found to conform with the Vogel-Fulcher Tamman equation for its average relaxation time and the Kohlrausch-WilliamsWatts function for its spectral line shape. The isothermal crystallization of the supercooled liquid to form a crystalline solid was monitored by dielectric relaxation spectroscopy, and the Avrami exponent was found to be 1.51 at a crystallization temperature of 263 K.
Introduction Molecular motions in glass-forming liquids and amorphous solid polymers may be studied using dielectric relaxation spectroscopy (DRS), dynamic mechanical relaxation (DMR), quasi-elastic light-scattering (QELS), neutron-scattering (QENS), nuclear magnetic resonance (NMR), and fluorescence depolarization (FD) techniques that span an effective frequency range from 10-6-1011 Hz. Such materials exhibit multiple relaxation processes that arise from (i) the microbrownian motions of whole molecules or chain-segments (R and Rβ processes) and (ii) limited, local motions (β process). The R process is associated with the apparent glass-transition temperature Tg that is observable by thermodynamic measurements, e.g., volume, enthalpy, and specific heat, but such measurements have a time scale, which means that measured Tg values depend on nature of the experiment and the rate at which it is conducted. Numerous relaxation studies of amorphous organic and inorganic materials have been made above and below Tg using different techniques over wide ranges of frequency or time. Recent work, together with their theoretical analyses, are to be found in the special publications Relaxations in Complex Systems 1, 2 and 3 (see refs 1-3). It is apparent from these and earlier studies that, for each experimental technique, glassforming systems exhibit common relaxation behavior for the R process in two respects, essentially independent of chemical structure: (i) the relaxation function ΦR(t) (which is a timecorrelation function for molecular motions) is far broader than that for a single relaxation time and resembles a stretchedexponential function of Kohlrausch-Williams-Watts (KWW) type4 and (ii) the average relaxation time 〈τR〉 obeys, at least approximately, the Vogel-Fulcher-Tamman (VFT) equation5 as Tg is approached from high temperatures. There is considerable interest in seeking an understanding of i and ii for both
glass-forming liquids and amorphous polymers, and many approaches are described in the literature. The concepts of freevolume, configurational entropy, and hopping dynamics of molecules in the liquid state above Tg (see, e.g., refs 6, 7, and 8, respectively, for reviews) were introduced to explain the variation of the transport coefficients 〈τR〉 for given observables with temperature, and these have been widely applied.1-3 The observation of a characteristic (KWW) form of ΦR(t) for glassformers, using different experimental methods, has been rationalized by very different models for molecular motion, e.g., controlled random walks, defect-diffusion, hopping on Ising lattices, and hopping in distributed barriers (see refs 9 and 10 for reviews). More recently, mode-mode coupling theories have been introduced to model the R and β processes in amorphous polymers and glass-forming liquids (see refs 1-3 and 11) that extend over the entire frequency/time-range of measurement even down to ultralow frequencies. However there are questions concerning the physical meaning of the memory functions that are explicit in such an approach.12 A new approach was introduced by Schmidt-Rohr and Spiess13 to explain the form of the R relaxation function. Using multidimensional NMR they showed that “dynamic heterogeneities” occurred in amorphous polymers as variations in the local environments of chainsegments and these were a cause of the broadening of the R relaxation function. Further studies of glass-forming liquids by Ediger and co-workers14 using optical techniques, by Bo¨hmer and co-workers15 using NMR and dielectric techniques, by Richert15,16 using Stokes optical-shift techniques, and by Hiwatari and Muranaka17 using molecular dynamics simulations have demonstrated the importance of dynamic heterogeneity in determining the stretched-exponential form for the R relaxations in glass-forming liquids and amorphous polymers.
10.1021/jp9845773 CCC: $18.00 © 1999 American Chemical Society Published on Web 05/05/1999
4198 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Massalska-Arodz et al.
Figure 1. Structure of isooctyloxycyanobiphenyl (IOOCB).
There is a continuing need to obtain detailed and quantitative relaxation data for molecules in glass-forming liquids. In an earlier paper18 we reported a study of the dielectric R-relaxation of chiral isopentylcyanobiphenyl IPCB using DRS. This material supercooled on cooling, with Tg ) 210 K. The supercooled liquid crystallized on heating above 245 K. IPCB has a structure typical of that for a thermotropic liquid crystal (LC) and our DRS data gave indications of LC-formation during the cooling process. In the present work we report DRS data for chiral isooctyloxycyanobiphenyl, IOOCB, during both cooling and heating experiments. On cooling IOOCB forms first a supercooled liquid and then a glass; it crystallizes on heating the supercooled liquid above Tg. We have studied the dielectric R process in supercooled IOOCB and have also used this relaxation feature to monitor the isothermal crystallization of the supercooled liquid above Tg. Experimental Section The structure of IOOCB is shown in Figure 1. A sample of right-handed IOOCB of 97% chemical purity was synthesized by Prof. Dabrowski at the Military University of Technology, Warsaw. Preliminary studies of its phase behavior made using optical microscopy and dsc indicated the following. When the isotropic liquid was cooled from room temperature, a supercooled formed that became a glass below 220 K. When the glass was heated, the liquid phase was recovered but around 250 K this became a crystalline solid which remelted at 284 K. Despite the elongated shape of the molecule, the presence of a terminal dipolar group and a flexible alkoxy tail, no evidence of liquid crystallinity was found. For the DRS measurements the sample was contained between two brass electrodes of effective diameter 15 mm. The distance between the flat top disk and the bottom of the lower cup was kept constant using two PTFE strips of 0.13 mm thickness. The measurements were made with a Novocontrol dielectric spectrometer in the range 10-1-105 Hz as we described previously.18,19 The accuracy of the measurements of complex dielectric permittivity (ν,T) ) ′(ν,T) - i′′(ν,T), where ν is the measuring frequency, obtained using the Solatron SI 1260 frequency response analyzer together with a Chelsea Dielectric Interface, was about 3% for ′ and 5% for ′′. Our observations covered the T range from room temperature to 200 K. Measurements were made at intervals of 5 K both on cooling and on heating the sample, with temperature measured with an accuracy of 0.1 K. During the runs the sample was heated/cooled to the required temperature at a rate of about 5 K/min. A glass was obtained on both fast cooling (10 K/min) and on slow cooling (0.5 K/min) the liquid from room temperature, showing that the crystallization rate was so slow under these conditions that a glass, rather than a crystalline solid, was formed. Temperature was controlled using a Novocontrol Quatro system, which utilized a liquid N2 cryostat. The dielectric measurements were controlled by a central 486 computer with
Figure 2. Frequency dependence of dielectric properties during cooling of IOOCB: (a) ′ vs log(ν/Hz) and (b) ′′ vs log(ν/Hz) at different temperatures: (open circle) 5 °C, (open box) 0 °C, (open diamond) -5 °C, (open up triangle) -10 °C, (open down triangle) -15 °C, (shaded up triangle) -20 °C, (shaded down triangle) -25 °C, (shaded circle) -30 °C, (shaded box) -35 °C, (shaded diamond) -40 °C, (cross) -45 °C, (plus) -50 °C, (times) -55 °C, and (asterisk) -60 °C.
a Novocontrol WINDETA software package that enabled automatic and interactive measurements to be performed.19 Results and Discussion Figure 2a and b show our results for the cooling experiments while Figure 3a and b show the results obtained when heating the sample subsequently. One dielectric process, the R-process, which is due to the large-scale microbrownian motions of the molecules in the isotropic liquid state, is observed in both experiments. It moves to ultralow frequencies as temperature is decreased and shows that a glass forms below ∼220 K. The loss curves are broad and asymmetric (KWW-type) compared with a single relaxation time process, as seen in other glassforming liquids1-3 and in IPCB.18 At 233 K, the full half-width of the loss curve is about 30% greater than that for a single relaxation time process. The curves obtained on heating (Figure 3) are essentially the same as those for cooling (Figure 2) until ∼240 K is reached. On further heating there is a marked decrease in the relaxation strength, because the mobile amorphous material is being replaced by immobile crystalline material. For completeness we show in Figures 4 and 5 threedimensional plots of [′, ′′] vs [log ν, T/K] for the cooling and heating experiments. In Figure 4 the R process is well-separated from the conductivity-related losses at low frequencies and high
Behavior of Chiral Isooctyloxycyanobiphenyl
Figure 3. Frequency dependence of dielectric properties during heating of IOOCB from the glass: (a) ′ vs log(ν/Hz) and (b) ′′ vs log(ν/Hz) at different temperatures. The points in Figure 3b are labeled as in 3a. (open circle) 5 °C, (open box) 0 °C, (open diamond) -5 °C, (open up triangle) -10 °C, (open down triangle) -15 °C, (shaded up triangle) -20 °C, (shaded down triangle) -25 °C, (shaded circle) -30 °C, (shaded box) -35 °C, (shaded diamond) -40 °C, (cross) -45 °C, (plus) -50 °C, (times) -55 °C, and (asterisk) -60 °C.
temperatures. However, in Figure 5, a complex pattern of behavior is observed. In addition to the conductivity-related losses that increase with decreasing frequency for the supercooled liquid (see Figure 5b) the presence of two phases, liquid and crystal, produces Maxwell-Wagner (MW) interfacial polarization losses for T > 240 K. Figure 5b for the crystallizing material shows that plots of ′′ vs T/K for fixed low frequencies exhibit a peak at temperatures higher than the R peak. This is not a relaxation process, since no corresponding peak is seen in plots of ′′ vs log ν in this range, but it is a manifestation of the MW process. Similar observations were made for IPCB in the crystallization range.18 To analyze Figures 2-5, we consider first the plot of ′ vs T/K for a fixed frequency of 10 Hz for cooling and heating experiments (Figure 6). For 240 K < T < 280 K, the ′ values in the cooling experiment are equal to the static permittivity o(T). For T > 280 K the high dc conductivity of the liquid gives ′ values greater than o(T). In the range 280-245 K, o(T) in the cooling experiment is nearly constant (o(T) ∼ 12.5). Dielectric theory for a dipolar liquid predicts20,21 that [o(T) - ∞(T)] is proportional to g(T)µ2/3kT where µ is the molecular dipole moment, g(T) is the Kirkwood factor for orientational correlations between dipoles, and k is the Boltzmann constant. For g(T) constant o(T) is predicted to increase by 13% on cooling from 280 down to 240 K, but the experimental values show a decrease of about 2%. This means
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4199
Figure 4. log(ν/Hz) and T/K dependence of the dielectric properties of IOOCB: (a) ′(log ν,T) and (b) ′′(log ν,T) obtained on cooling the sample in its supercooled liquid state.
that g(T) decreases by about 15% as temperature is lowered in this range which indicates an increase in the antiparallel alignment of dipoles. For IPCB we found that o(T) increased by ca. 7% in the range 300-250 K, whereas if g(T) was constant an increase of 16% would have been obtained. Thus, in common with liquid-crystal-forming alkylcyanobiphenyls22 that have similar structures to IOOCB and IPCB, increasing antiparallel alignment of dipoles occurs with decreasing temperature. For the data at 10 Hz shown in Figure 6 the R relaxation gives the fall in ′ in the range 240-225 K. The curves for the cooling and heating experiments superpose in this range and in the glass (T < 200 K) so the supercooled liquid is sustained in this range for both cooling and heating experiments. Similar behavior was observed for IPCB.18 The low values of ′ for T < 225 K show that molecular motions of IOOCB are suppressed in the glass. When the glass is heated from 212 K, crystallization commences above 240 K; the loss of the supercooled liquid and its replacement by the rigid crystalline material leads to the fall in ′, so above 262 K the material is crystalline. The values of ′ for the solid in the range 262-280 K exceed the values of ′(glass) but this is not evidence of motion in the crystalline material. The ′ values are raised due to the MW process, as seen in Figures 5a and b. If a higher frequencies than 10 Hz are chosen in Figure 6, then the ′ values in the range 260280 K approach the (glass) values. We may define an average relaxation time for the R-process as 〈τ(T)〉 ) [2πνmax(T)]-1 where νmax is the frequency of maximum loss in Figures 1 and 2. The plots of log 〈τ(T)〉 vs T/K for cooling and heating experiments for the isotropic liquid superposed and were strongly curved, as is typical for a glassforming liquid. The data were fitted using the VFT equation5
4200 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Massalska-Arodz et al.
Figure 7. VFT plot of log τ vs (T - To)-1 for IOOCB, points for 〈τ〉 labeled as cross (cooling data) and as open diamond (heating data), points for τKWW labeled as 4 (cooling data) and 3 (heating data).
TABLE 1: βKWW Parameter and Relaxation Times (in 10-4 s) for Right-Handed IOOCB for cooling T [K]
Figure 5. log(ν/Hz) and T/°C dependence of the dielectric properties of IOOCB: (a) ′(log ν,T) and (b) ′′(log ν,T) on heating the sample from the glass at 216 K.
223 228 233 238 243 248 253 258 263
〈τ〉
235 29.7 4.7 1.2 0.3 0.09 0.03
for heating
τ from KWW βKWW 2324.0 186 22.6 3.93 0.88 0.25 0.12
0.73 0.77 0.79 0.82 0.84 0.85 0.76
〈τ〉
τ from KWW βKWW
3400 235 29.7 4.7 1.2 0.3 0.09
45300 3116 199 23.3 4.03 1.01 0.24
Figures 1 and 2 using the KWW function4,23
ΦR(t) ) exp[-(t/τKWW)βKWW]
Figure 6. ′ for IOOCB measured at 10 Hz as a function of temperature on cooling (cross) and subsequent heating (open diamond) of the sample.
〈τ(T)〉 ) A exp Β/(T - To)
(1)
where A, B, and To are material constants. Figure 7 shows the plot of log 〈τ(T)〉 vs (T - To)-1 for To ) 180 K. A good straight line is obtained for the entire range (∆log〈τ〉 ∼ 6.5). The form of the relaxation curves was examined with the aid of the relation23
(ω) - ∞ ) 1 - iωF[ΦR(t)] o - ∞
(2)
where ω ) 2πν and F indicates a one-sided Fourier transform. ΦR(t) is the dielectric relaxation function. We fitted the data of
0.68 0.69 0.76 0.79 0.81 0.81 0.87
(3)
where βKWW is the spread parameter. Table 1 shows the collected results for our cooling/heating experiments, giving 〈τ〉, τKWW, and βKWW at different temperatures. Figure 7 includes the data for τKWW(T), a good straight line being obtained24,25 for To ) 180 K, A ) 5.6 × 10-13 s, and B ) 1200 K. The β values decrease with decreasing temperature, ranging from 0.87 down to 0.68 in this range. These values are similar to those found for the dielectric R-process in cyclooctanol and cyclohexanol, where βKWW ) 0.7526 but are higher than those obtained for o-terphenyl (βKWW ) 0.559) and different amorphous polymers (for which βKWW lies in the range 0.38-0.709,10,27). For IPCB we observed18 a complex behavior for βKWW(T). At higher temperatures βKWW f 1, but on decreasing the temperature βKWW first decreased to 0.58 and then increased again below 235 K to 0.68 at the lowest temperatures studied. In the intermediate range the loss curves became slightly bimodal. In contrast, the loss curves for IOOCB in Figures 1b and b are well-fitted by the KWW function and there is no evidence for bimodal character. As a part of the continuing interest in rationalizing the origins of VFT/KWW behavior for relaxations in glass-forming systems, the concept of fragility, introduced by Angell28,29 has been developed extensively.30-33 A measure of the fragility of the R-relaxation is m ) d[log τ(T)/d(Tg/T)] at T ) Tg where Tg is usually chosen as the temperature at which 〈τ〉 ) 100 s (see, e.g., refs 30 and 32). Analysis of R relaxation data, obtained using different techniques, for about 70 different supercooled liquids,30,33 show that m ranges from the minimum value mmin ) 16 up to m ) 200. If the VFT equation is rewritten as
Behavior of Chiral Isooctyloxycyanobiphenyl
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4201
m ) mmin
Tg 590 ; m ) 16 + Tg - To D
(5a,b)
Figure 8 shows the Angell plot28,29 for our data for IOOCB taking Tg ) 220 K, the temperature at which 〈τ〉 ) 100 s. Our data relate to the range immediately above Tg, so cover only a portion of the entire range. To clarify Figure 8 we write (omitting 〈 〉 for brevity) the VFT equation as
1 - x(T) logτ(T) - logτ(Tg) ) log τ∞ - logτ(Tg) 1 - Rx(T)
(6)
where τ∞ ) τ(T f ∞) and Figure 8. Angell plot of log τ vs (Tg/T) for IOOCB (cooling data). Points are labeled as in Figure 7.
〈τ(T)〉 ) A exp [DTo/(T - To)] then Bo¨hmer writes33
(4)
x(T) ) Tg/T; R ) T0/Tg
(7a,b)
In the work of Angell and co-workers [log τ∞ - logτ(Tg)] ) 16 so writing this quantity as ∆ we derive the slope S(x) ) dlog 〈τ〉/dx as being
Figure 9. Time-dependence of dielectric properties of IOOCB during isothermal crystallization at 263 K: (a) ′′(log(ν/Hz),t) and (b) ′(log(ν/ Hz),t).
4202 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Massalska-Arodz et al.
Figure 10. Plots of (a) ′′ and (b) ′ vs time at different measuring frequencies for isothermal crystallization of IOOCB at 263 K.
S(x) )
∆(1 - R) (1 - Rx)
2
(8)
For high temperatures x f 0 so S(0) ) ∆(1 - R). Thus the plot in Figure 8 is linear for small values of x and would allow R to be determined from data in that range. For T ) Tg, x ) 1 so S(Tg) ) ∆/(1 - R) ) m, again allowing R to be determined. In Figure 8 the continuous line was calculated using ∆ ) 16, Tg ) 220 K, and To ) 180 K so R ) 0.818 and hence m ) 87. Thus IOOCB is a fragile liquid in the Angell sense. For IPCB we found Tg ) 216 K and To ) 172K giving R ) 0.796, so IPCB has a similar fragility to IOOCB. Bo¨hmer et al.30,33 have given data, from different techniques, for about 70 glass-formers in a plot of m against W, the half-width of the R relaxation curve at Tg. A rough correlation between m and W was indicated. As m increased (R increasing toward unity) then W also increased (βKWW decreasing toward zero). For IOOCB we
estimate βKWW ) 0.65 ( 0.03 at Tg ) 220 K so W is calculated to be 1.70 ( 0.10 at Tg (see eq 4 of ref 33). The point [m, W] for IOOCB is thus [87, 1.7] and is found to lie well-above the band of correlation in the Bo¨hmer plot.33 This means that for this value of m the value of W should be 2.1-2.3 for IOOCB in order to lie in the correlation band. It seems unlikely that a correlation between m and βKWW is to be expected for the R process, studied by different techniques, in such diverse systems as linear polymers, polymer networks, alcohols, molten salts, and simple glass-forming liquids. m is determined by the ratio T0/Tg. T0, the temperature at which 〈τR〉 would become infinite, is possibly related to limiting behavior of the configurational entropy of a system,7 so it is a thermodynamic equilibrium property of a material. Tg is chosen to be the temperature at which 〈τR〉 ) 102 s for a particular relaxation experiment (so Tg will have a range of experimental values for each material) so is connected only to the average relaxation time within the
Behavior of Chiral Isooctyloxycyanobiphenyl
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4203
Figure 11. Normalized dielectric data for the isothermal crystallization of IOOCB at 263 K. Plots of (a) ′′(t)/′′(0) and (b) (′(t) - ′∞)/(′(0) ′∞) vs time for different measurement frequencies. Here ′∞ ) ′(t f ∞).
overall distribution of relaxation times. βKWW is a measure of the spread of relaxation times so there is no connection between βKWW and (T0/Tg) from the theoretical viewpoint. A point not commonly noted is that dielectric R relaxation in glass-forming liquids, composed of molecules of short axial ratio, and amorphous solid polymers, composed of flexible polymer chains, may differ in the respect that dipole motions in the polymers will be influenced by the anisotropy of motion of the chain contour giving a correlation function ΦµR(t) (= ΦR(t)) that contains longitudinal and transverse components, as we have explained.34 This would have the effect of increasing W for polymers compared with simple glass-formers such as oterphenyl, di-n-butyl phthalate, and chlorobenzene/decalin mixtures. Anisotropic motions will occur for small molecules that have elongated shapes, e.g., IOOCB and IPCB, but since the dipole moment along the long axis of these molecule greatly exceeds that along the short axis then the contribution of the
longitudinal dipole moment to ΦµR(t) will be far greater than that from the transverse dipole moment. It would be interesting to see for a single class of simple-glass-forming liquids if m and W, determined using a single technique (e.g., dielectric relaxation), are correlated. We saw that βKWW ∼ 0.55 (W ) 2.00) for the dielectric R-relaxation in dipolar-solute/o-terphenyl solutions,9 but W for these systems is much larger than that for IOOCB and IPCB, and this is as yet unexplained. Snapshots taken during a molecular dynamics simulation of o-terphenyl35 showed that different types of angular motions occur and all contribute to the nonexponentiality, and hence to the βKWW value, of the dielectric R-relaxation. The different values obtained for βKWW (dielectric) for simple glass-forming liquids appears to have no simple physical explanation, but it is evident that if different materials have different distributions associated with their dynamic heterogeneity13-15 then βKWW will vary from one material to another. We note that Roland and Ngai36 have
4204 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Massalska-Arodz et al.
considered possible correlations between βKWW values and chemical structure for the R relaxation in polymers. As a part of this study, we have monitored the isothermal crystallization of IOOCB using DRS as we described for IPCB.18 Starting with the glass at 210 K, the temperature was raised to 263 K and [′, ′′] values were accumulated continuously in real-time across the frequency range 1-105 Hz. Figures 9 show the dielectric landscapes during crystallization of IOOCB. The R process is unchanged in (i) its frequency-temperature location and (ii) spectral line shape as crystallization takes place so the material at intermediate times of crystallization corresponds to a mixture of a normal supercooled liquid and a nonmobile, crystalline phase. After on hour, the sample transformed from the isotropic liquid with o ) 12.5 to the solid with o ) 3. In parallel, the loss peak decreased to zero. No broadening of the loss peak was observed so there is no change in the character of the R relaxation, which contrasts with the crystallization process in polymers monitored by DRS, e.g., for poly(ethylene terephthalate), where the motions in the amorphous regions are greatly affected by the presence of crystallites.37-39 In that case, the amorphous material transformed into 100% spherulitic material, but each spherulite was only 50% crystalline with amorphous and crystalline regions in intimate contact, which leads to a marked slowing down in the average rate of dipole motions and to a marked broadening of the R relaxation for the amorphous regions that remain within the spherulites. For IOOCB, and IPCB18 the situation is evidently much simpler. The glass was heated to 263 K to form the liquid which crystallized at that temperature. The crystallization process was monitored through the decrease in ∆′(t) ) [′(t) - ∞]/[ and ′′(t)/′′(0) which are both proportional to the amount of amorphous material at the crystallization time t. The kinetics of crystallization is often expressed by the Avrami equation.40,41
A(t) ) 1 - exp[-(t/τAV)p]
(9)
where A(t) is the volume fraction of new crystalline phase, τAV is a time constant for the crystallization rate, and p is the Avrami exponent that takes on different values for different crystallization processes. A(t) can be expressed as
A(t) ) 1 - [∆′(t)/∆′(0]) ) 1 - [′′(t)/′′(0)]
(10)
thus the crystallization behavior can be monitored using eqs 9 and 10. Figures 10a and b show our data for ′′(t) and ′(t) for crystallization at 263 K for frequencies ranging from 103.2105 Hz in steps of 0.2 in log ν. Figures 11a and b show these data normalized to t ) 0 and t ) ∞. The superposition of data at different frequencies is excellent for both ′′ and ′, showing the spectral line shape for the R process is unchanged as crystallization takes place. Finally, Figures 12a and b show the Avrami plots for the ′′ and ′ data at 263 K for ν ) 105 Hz, giving p ) 1.516 (′′ data) and p ) 1.520 (′ data). The same values were obtained from the equivalent plots at the other frequencies. The Avrami exponents for crystallization in IOOCB (1.52) obtained here and for IPCB18 (1.70) are much lower than p ) 4 and 3 found in calorimetric studies of the transformation between different phases of liquid crystalline mesogens MBBA and 4-4′-di-n-butyloxyazoxybenzene42 and the values of 5 and 6 predicted for predetermined or sporadic growth of spherulites.41 Summary Chiral IOOCB has a monotropic system of phases. On cooling from room temperature, the isotropic liquid supercools and forms
Figure 12. Avrami plots of the dielectric data for IOOCB at 105 Hz. (a) ln [-ln(′′(t)/′′(0)] and (b) ln [-ln [(′(t) - ′∞)/(′(0) - ′∞)] vs ln(t/s) for the sample crystallizing at 263 K.
a glass, while heating from the glass the supercooled liquid crystallizes and then at a higher temperature remelts to reform the isotropic liquid. No evidence of a transition into an anisotropic liquid crystalline phase was observed in our DRS data. The dielectric R relaxation, due to the cooperative reorientational motions of molecules, was characterized by (a) VFT and (b) KWW behavior. A representation of Angell, Bo¨hmer and co-workers was used to describe the behavior of 〈τR〉 with temperature and it was concluded thast IOOCB is a very fragile liquid. The crystallization of IOOCB at 263 K was monitored by ′ and ′′ measurements over the whole frequency range and the data were well-represented by the Avrami equation with parameter p ) 1.52. Acknowledgment. We thank Professor J. Malecki for providing the program for the KWW-fitting procedure and the EPSRC for an award to D.K.T. and for its support for the dielectric spectrometer. G.W. thanks the Leverhulme Trust for a Leverhulm Emeritus Fellowship. The work was supported in part by Grant 2P03B04611 of the Polish Committee for Scientific Research. References and Notes (1) J. Non-Cryst. Solids 1991, 131-133. (2) J. Non-Cryst. Solids 1993, 172-174. (3) J. Non-Cryst. Solids 1998, 235-237. (4) (a) Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80. (b) Williams, G.; Watts, D. C.; Dev, S. B.; North, A. M. Trans. Faraday Soc. 1971, 67, 1323. (c) Kohlrausch, R. Ann. Phys. (Leipzig) 1847, 12, 393. (5) (a) Vogel, H. Phys. Z. 1921, 22, 645. (b) Fulcher, G. S. J. Am. Ceram. Soc. 1923, 8, 339. (c) Cohen, M. H. Grest, G. S. Phys. ReV. B 1979, 20, 1077. (6) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley-Interscience: New York, 1980.
Behavior of Chiral Isooctyloxycyanobiphenyl (7) (a) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139. (b) Matsuoka, S. Relaxation Phenomena in Polymers; Hanser Publishers: Munich, 1992. (c) Angell, C. A. J. Non-Cryst. Solids 1991, 131-133, 13. (8) (a) Dyre, J. C. Phys. ReV. B 1995, 51, 276. (b) Dyre, J. C. Olsen, N. B.; Christensen, T. Phys. ReV. B 1996, 53, 2171. (9) Williams, G. J. Non-Cryst. Solids 1991, 131-133, 1. (10) Williams, G. IEEE Trans. Electron. Insul. 1985, E1-20, 843. (11) (a) So¨jgren, L.; Go¨tze, W. J. Non-Cryst. Solids 1991, 131-133, 153 (b) Go¨tze, W.; Sjogren. L. Rep. Prog. Phys. 1992, 55, 241 (c) Go¨tze, W. In Liquids, Freezing and the Glass Transition; Hansen, J. P., Levesque, D., Zinn-Justin, I., Eds.; North Holland: Amsterdam, Netherlands, 1991; p 287. (12) (a) Williams, G. In Keynote Lectures in Selected Topics in Polymer Science Ed. Riande, E., CSIC Madrid 1995, p 1-39 (ISBN 84-00-074726). (b) Williams, G.; Fournier, J. J. Chem. Phys. 1996, 184, 5690. (13) (a) Schmidt-Rohr, K.; Spiess, H. W. Phys. ReV. Lett. 1991, 66, 3020. (b) Schmidt-Rohr, K.; Spiess, H. W. Multidimensional Solid State NMR and Polymers; Academic Press: London, 1994. (14) (a) Cicerone, M. T.; Ediger, M. D. J. Phys. Chem. 1992, 97, 2156. (b) Cicerone, M. T.; Blackburn, F. R.; Ediger, M. D. J. Chem. Phys. 1995, 102, 471. (c) Cicerone, M. T.; Ediger, M. D., J. Chem. Phys. 1995, 103, 5684. (d) Ediger, M. D. J. Non-Cryst. Solids 1998, 235, 11. (15) (a) Bo¨hmer, R.; Chamberlain, R. V.; Diezemann, G.; Geil, B.; Heuer, A.; Hinze, G.; Kuebler, S. C.; Richert, R.; Schiener, B.; Sillescu, H.; Spiess, H. W.; Tracht, T.; Wilhelm, M. J. Non-Cryst. Solids 1998, 235, 1. (b) Tracht, U.; Heuer, A.; Spiess, H. W. J. Non-Cryst. Solids 1998, 235237, 27. (16) Richert, R. J. Non-Cryst. Solids 1998, 235, 41. (17) Hiwatari, Y.; Muranaka, T. J. Non-Cryst. Solids 1998, 235-237, 19. (18) Massalska-Arodz, M.; Williams, G.; Smith, I. K.; Conolly, C.; Aldridge, G. A.; Dabrowski, R. J. Chem. Soc., Faraday Trans. 1998, 94, 387. (19) Smith, I. K.; Andrews, S. R.; Williams, G.; Holmes, P. A. J. Mater. Chem. 1996, 6, 539. (20) McCrum N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Dover Publishers: New York, 1991. (21) Bo¨ttcher, C. J. F.; Bordewijk, P. Theory of Electric Polarization, Elsevier Scientific: Amsterdam, 1978; Vol. II. (22) Williams, G. In Molecular Dynamics of Liquid Crystals; Luckhurst, G. R., Veracini, C. A., Eds.; NATO ASI Series C, Kluwer Publishers:
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4205 Dordrecht, Holland, 1994. (23) Williams, G. Chem. ReV. 1972, 72, 55. (24) The relaxation times 〈τ〉 and τKWW are related as follows: 〈τ〉 ) τKWW Γ(β-1)/β where β ) βKWW and Γ is the gamma function (see ref 25). (25) Moynihan, C. T.; Boesch, LP.; Laberge, N. L. Phys. Chem. Glasses 1973, 14, 122. (26) Leslie-Pelecky, D. L.; Birge, N. O. Phys. ReV. B 1994, 50, 13250. (27) Williams, G.; Watts, D. C. In Dielectric Properties of Polymers; Karasz, F. E., Ed.; Plenum Press: New York, 1971; p 17. (28) Angell, C. A. In Relaxations in Complex Systems; Ngai, K. L., Wright, G. B., Eds.; National Technology Information Service, U.S. Department of Commerce; Springfield, VA, 1985; p 1. (29) (a) Angell, C. A. J. Non-Cryst. Solids 1991, 131-133, 13. (b) Angell, C. A. Polymer 1997, 38, 6261. (30) Bo¨hmer, R.; Ngai, K. L.; Angel, C. A.; Plazek, D. J. J. Chem. Phys. 1993, 99, 4201. (31) Plazek, D. J.; Ngai, K. L. Macromolecules 1991, 24, 1222. (32) Bo¨hmer, R.; Angell, C. A. Phys. ReV. B 1992, 45, 10091. (33) Bo¨hmer, R. J. Non-Cryst. Solids 1994, 172-174, 628. (34) Williams, G. In Dielectric Spectroscopy of Polymeric Materials; Runt, J. P., Fitzgerald, J. J., Eds.; American Chemical Society Series; American Chemical Society: Washington, DC, 1997; Chapter 1 (see eq 97). (35) Lewis, L. J.; Wahnstro¨m, G. J. Non-Cryst. Solids 1994, 172-174, 69. (36) Roland, C. M.; Ngai, K. L. J. Non-Cryst. Solids 1994, 172-174, 868. (37) Williams, G. AdV. Polym. Sci. 1979, 33, 60. (38) Ezquerra, T. A.; Balta-Calleja, F. J.; Zachmann, H. G. Polymer 1994, 35, 2600. (39) (a) Fukao, K.; Miyamoto, Y. J. Non-Cryst. Solids 1997, 212, 208. (b) Fukao, K.; Miyamoto, Y. J. Non-Cryst. Solids 1998, 235-237, 534. (40) (a) Avrami, M. J. Chem. Phys. 1939, 7, 1103; (b) J. Chem. Phys. 1940, 8, 212 (c) J. Chem. Phys. 1941, 9, 177. (41) (a) Meares, P. Polymers, Structure and Bulk Properties; Van Nostrand: London, 1965. (b) Cowie, J. M. Polymers, Chemistry and Physics of Modern Materials; Blackie: Glasgow, 1991. (42) Bamezai, R. K.; Godlewska, N.; Massalska-Arodz, M.; Sciesinski, J.; Witko, W. Phase Transitions 1990, 27, 113.
