J . Phys. Chem. 1993,97, 11115-1 1121
11115
Kinetics of Isothermal Crystallization of a Smectic Partially Fluorinated Alcohol by 2HNMRl Kenneth J. McGrath' and Richard G. Weiss' Department of Chemistry, Georgetown University, Washington, D.C. 20057 Received: April 29, 1993; In Final Form: August 10, 1993'
The rates of primary and secondary crystallization of F ( C F ~ ) . I C D ( O H ) ( C H ~ )and ~ H F(CF2)7CH(OH)CD2(CH2)7H from their more stable monotropic smectic (Sm2) phase have been measured in situ at a variety of temperatures using a deuterium saturation recovery quadrupole echo NMR technique. Application of the Avrami equation to primary crystallization and the temperature dependence of the associated crystallization time constants provide insights into the mode of nucleation. The deuteron TI spin-lattice relaxation time of F(CF2)7CH(OH)CD2(CH2)7H at 300 K is found to be 141 ms (Sm2) and 77 s (crystalline). A large difference between the TItimes for the initial and final phases and a relatively long phase-to-phase transformation time (10.5h) are necessary to apply this NMR method to other materials. A much more laborious and less precise differential scanning calorimetric method has been used to estimate the time constant (71/2 4 min at 300 K) for conversion of the less stable monotropic smectic (Sml) phase to Sm2.
-
Introduction Previous work in our laboratory has involved synthesis and characterization of the phases formed by perfluoroheptyl octyl carbinol, F ~ ( C H O H ) H BThe . ~ compound was observed qualitatively, by differential scanning calorimetry (DSC), to transform from one monotropic smectic phase to another, and then to a crystalline phase at very different rates (Scheme I). A survey of the literature has revealed very few reports on quantitative measurements of the rate of transformation of monotropic mesophases to more stable (solid) phases. Techniques capable of yielding such information are of fundamental and, perhaps, practical importance since they may be applicable in other areas, such as polymer research, where physical properties are highly dependent upon phase morphology; the ability to measure rates of crystallization is therefore of obvious interest. We anticipated that time-dependent DSC experiments (which allow heats of transition of a mesophase to a higher temperature (isotropic?) phase and of a more stable (solid?) phase to a higher temperature phase to be measured concurrently) could be used to obtain the rates. However, this was not possible with F7(CHOH)Ha and we believe that it probably will not be a viable method for many other liquid-crystallinematerials due to several practical considerations. Consequently, we attempted to use deuteron quadrupole echo NMR spectra, especially with regard to the Av values in selectively deuterated F~(CHOH)HBas a function of incubation time, in order to follow the rates of crystallization. This approach also failed since the 2H NMR spectra of the smectic and crystalline phases were found to be remarkably similar. Their similarity did raise questions about our original attribution of the monotropic phase being smectic rather than a solid.2 Herein, we report NMR methods which provide convincing evidence that our original phase assignmentsare correct and which allow the rates of crystallization of smectic F~(CHOH)HB to be measured in situ at a variety of temperatures. The method relies upon the enormous differencesin TIspin-lattice relaxation values of deuterium nuclei of molecules in liquid-crystalline and solid phases. It should allow for the determination of the rates of crystallization of a wide variety of monotropic phases provided that the transformations are slow compared to the times required to record the appropriate sets of NMR spectra (i.e. 71p 1 0.5 h). The rate data obtained from deuteriated F~(CHOH)HBhave been separated into primary and secondary crystallization *Abstract published in Advance ACS Abstracts. October 1, 1993.
Solid
< - - _ _ _ _ _ _ _ _ -_- _- -_ _ _ -
Sm2
a Broken lines indicate cooling and solid lines indicate heating data. The slow isothermal transitions measured in this paper are indicated by
an asterisk.
components. The primary part, treated according to the Avrami equation describing isothermalcrystallizationkinetics,3+4provides insights into the factors governing the crystallization process.
Experimental Section Nuclear Magnetic Resonance. All NMR experiments were run on a Bruker MSL 300 spectrometer with a static magnetic field of 7.04 T, corresponding to a deuteron Larmor frequency of 46.073 MHz. Temperature was maintained with a precision of *lo using a Bruker variable-temperature controller and is estimated to be accurate to within &lo.Quadrupole echo NMR experimentsg7 were obtained using 90° phase shifted r / 2 pulse widths of 3-ps duration, correspondingto a radio frequency field of 83 kHz and a r refocusing delay of 20 ps. The point of maximum amplitude of the spin echo was obtained by left-shifting of the free induction decay (FID). NMR spin-lattice (TI) relaxation time constants for deuterium in solid and liquidcrystalline phases were determined for subsequent use in quantitative quadrupole echo crystallization rate experiments using this NMR pulse sequence combined with deuteron presaturation. Differential Scanning Calorimetry. DSC thermograms (calibrated with an indium standard) for the two deuteriated partially fluorinated alcohols were run on a Perkin-Elmer DSC 7 Series Thermal Analysis System in the temperature range 30-75
0022-3654/93/2097-11115$04.00/00 1993 American Chemical Society
McGrath and Weiss
11116 The Journal of Physical Chemistry, Vol.97, No. 42, 1993
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Temperature ("C) Figure 1. DSC thermogram of F.I(CHOH)CD~H~ scanned at 2 deg/min: (a) solid
isotropic.
OC and a heating rate of 2 deg min-I. Each heat/cool cycle was repeated (no delay) in order to observe phases formed during the first cooling ramp. Weighed samples (5-10 mg) were sealed in two-piece aluminum pans prior to running. Syntheses. Deuterium labeled liquid-crystalline F(CF2)7CH(OH)CD2(CH2)7H (F7(CHOH)CDzH,) and F(CF2)7CD(OH)(CH2)gH (F7(CDOH)Hg) were synthesized according to previously reported procedures starting from the ketone F(CF2)7CO(CH2)8H.2,8 F.I(CHOH)CD~H.I, mp 64.5-65.0 OC, was obtained by sequential a deuteriation of the ketone by exchange with DzO in monoglymeg and then reduction with LiAlH4 in anhydrous ether. By gas chromatographic (gc) analysis, the alcohol was 99% structurally pure. Previous work has demonstrated that this method leads to -70% deuteriation at the a carbon.8 F7(CDOH)Hg, mp 64.8-65.2 OC, wassynthesized by reduction of the ketone with LiAlD4. After recrystallization from acetonitrile, it was >99% structurally pure (gc analysis) and showed no detectable level of hydrogen at the site of deuteriation by proton NMR.
Results and Discussion
Characterization of Phases by DSC. A thermogram of F7(CHOH)CDzH, is shown in Figure 1. The first heating of the solvent-crystallized material exhibited a single endotherm (96.3 J/g) at a heat-flow maximum of 67.3 OC, corresponding to the solid-isotropic transition (a).2 The first cooling curve included two distinct exotherms, at 60.5 OC (b, -45.3 J/g) from the isotropicSm1 transition and at 53.0 OC (c, -7.7 J/g) corresponding to the S m l S m 2 transition.2 The second heating curve showed a single endotherm at 63.1 OC (d, 59.7 J/g), with no evidence of the solid-isotropic transition (at about 4O higher) of the first heating. This endotherm is attributed to the Sm2isotropic transformation (vide infra). As expected, the second cooling curve was identical to the first and the third heating was identical to the second one. These results are consistent with those reported for the nondeuteriated alcohol.2 The thermal behavior of F~(CDOH)HBwas, as expected, identical within experimental error to that of the a-deuteriated alcohol F7(CHOH)CD2H7. A set of thermograms was also recorded in which temperature was held constant, for varying time intervals, at a point (57.0 "C)
I 70. D
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isotropic, (b) isotropic
-
I
Sml,(c) Sml
+
Sm2, (d) Sm2 +
between the isotropioSm1 and S m l S m 2 transitions in interrupted cooling cycles. Thus, the decreases in the exotherm associated with the S m l S m 2 transition following varying incubation periods at 57 OC can be used to calculate the fraction of Sml which has been converted to Sm2 above the "normal" transition temperature. The magnitude of the exotherm without incubation was -8.2 J/g; when incubated for 2,4, and 8 min, it decreased to -6.6, -4.8, and -1.9 J/g, respectively. Thus, the Sml phase is relatively short-lived at 57 OC, with a half-life of approximately 4 min. Upon being heated, Sm2 does not yield Sml before becoming isotropic. An attempt was also made to measure the rate of crystallization of the longer-lived Sm2 phase by DSC. Thus, we attempted to measure the magnitude of the Sm2-isotropic endotherm after samples had been cooled from the isotropic phase to room temperature and annealed there for various periods. However, the breadth and overlapping nature of the Sm2-isotropic and solid-isotropic endotherms made a quantitative assessment of the individual components extremely difficult. After 24 and 48 h of annealing, the heat of the Sm2-isotropic endotherm was reduced to roughly one-third and one-ninth, respectively, of its value when the sample was cooled to room temperature and reheated immediately. Although the rate of crystallization of Sm2 at room temperature clearly occurs during several hours, the kinetics of the transformation cannot be followed precisely by DSC and the measurements are tedious, requiring that the experiment be restarted to obtain each data point. Deuteron Quadrupole Echo NMR Spectra of F7(CDOH)I& and F7(CHOH)CDJI7 h Their Crystalline and Sm2 Phpses. In an attempt to characterize more quantitatively the kinetics of the Sm2 solid transition, we first considered recording the deuteron quadrupole echo NMR spectra as a function of time with the expectation that significant differences between the Sm2- and crystalline-phasespectra should exist. The quadrupole coupling of deuterium, as determined from the magnitude of splitting between the maxima of a Pake doublet10 in a randomly oriented (powder) sample, is a direct consequenceof the degree of averaging of the electric field gradient." This averaging is, of course, dependent upon motions at the site of the deuterium nucleus in the molecule. F7(CDOH)Hs and F7(CHOH)CD2H7 are identical except for the site of deuteriation. Relativedifferencesin motional averaging
-
Kinetics of Crystallization of a Smectic Alcohol
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The Journal of Physical Chemistry, Vol. 97,No. 42, 1993 11117
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Figure 2. Deuterium quadrupole echo NMR spectra of K(CHOH)CD2H7 at 295 K (a) crystalline phase, (b) Sm2 phase.
TABLE I: Crystallization Time Constants and Avrami Exponents for F7(CHOH)CD&I7 and F7(CDOH)Hs
F7(CHOH)CD2H7 F7(CHOH)CD2H7 F7(CDOH)Hs ("unaligned") F7(CDOH)Hs ("aligned")
315 320 310 310
1.3 1.4 1.3 0.9
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13.8 29.8 34.7 17.1
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Primary crystallization time constant. Secondary crystallization time constant. Approximate duration of primary crystallization in parentheses. (I
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and C-D bond orientation will be reflected in the deuteron NMR spectra of their Sm2 phases and may be contrasted with that of the essentially motionally unaveraged spectrumof their crystalline phase. Figure 2a contains the deuteron NMR quadrupole spectrumof crystalline F,(CHOH)CD2H, at 295 K. The splitting between the singularities (perpendicular C-D orientation with respect to the static magnetic field) is 122.7kHz. This is slightly less than the 125-1 28 kHz expected for a static Pake doublet12 and is most likely a consequenceof small-scale motional averaging. The line shape is consistent with a powder average Pake doublet with very little motional averaging. The deuterium quadrupole echo NMR spectrum of the Sm2 phase of F,(CHOH)CDzH7 at 295 K is shown in Figure 2b. The splitting, 118.4 kHz,isonly4.3 kHzless than that ofthecrystalline phase. The spectrum of the Sm2 phase of F7(CDOH)H* at 295 K (not shown) is very similar in shape to that in Figure 2b, with a splitting of 116.7 kHz. In addition, the line shape of the spectrum differs somewhat from that of the solid phase, but not enough for the two to be distinguished easily. It suggests the presence of a slightly motionally averaged electric field gradient; some degree of long-range C-D bond ordering may also be present in the smectic phase. Spin-Lattice Relaxation in the Sm2 and Solid Phases of Fr (CHOH)CDzH7. The similarity of the Sm2- and the solid-phase spectra forced us to reconsider our original attribution of Sm2 to a smectic phase.2 Could it be a second crystalline phase? To explore this possibility, the T1 spin-lattice relaxation time constants of deuterium in each of the phases of F7(CHOH)CD2H7 were determinedfor each phase using a saturation recovery quadrupoleecho NMR pulse sequence (i.e., a standard quadrupole
-
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5
0
25
50
75
100
125
150
175
200
r h" Figure3. Semilogarithmic plots of deuteron spin echo intensity vs recovery time following saturation in F,(CHOH)CDzH7 at 300 K and linear best fits to data points: crystalline phase (O), upper time scale, TI= 77 s; Sm2 phase (0),lower time scale, TI= 141 ms.
echo pulse sequence which is preceded by a train of five 1712 pulses, each separated by a time delay of 2 ms). This serves to saturate the deuterium spin states in the sample. A variable time delay ( T ) is inserted following saturation to allow for longitudinal relaxation before applying the quadrupole echo sequence and measuring the normalizedmaximum in FID echo intensity, M(7). In measuring TI for the Sm2 phase, the sample was cooled from the isotropic state at 337 K to 300 K and allowed to equilibrate there for 15 min before recording FID intensity data. In this way, interference from the Sml phase could be avoided. The TI of deuterons in the crystalline phase was measured after allowing a sample to remain at room temperature for 6 days. Figure 3 is a semilogarithmic plot of the data at 300 K from which the Tl values were calculated. Assuming an exponential decay of M , T1 is the inverse slope of the line of best fit by linear regression. As a consequence of the lack of motion at the sites of the deuterium nuclei in the crystalline phase, a very low spectral density is expected at short correlation times, including the inverse Larmor precession frequency (46.3 MHz). Since deuterium
McGrath and Weiss
11118 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993
quadrupole and dipole relaxation mechanisms will be most efficient when molecular reorientation occurs in this highfrequency regime,13J4 relatively long TI spin-lattice relaxation time constants in the crystalline phase are expected. Conversely, theSm2 phase should be characterizedby a relatively high spectral density at short correlation times, resulting in efficient relaxation and shorter T I relaxation time constants. Consistent with this expectation and in confirmation of the attribution of Sm2 to a smectic phase, the T I of the deuterons was found to be 141 ms and 77 s in the Sm2 and crystalline phases, respectively, at 300 K. This difference of more than 2 orders of magnitude is interpreted as a consequence of the extent of molecular motion in the Sm2 phase being much greater than that of a solid phase. An additional benefit of the large T1 difference is that it provides a clear means of distinguishing the phases from one another and allows the kinetics of the Sm2 solid phase transformation to be followed in situ. CrystallizationKinetics in F,(CHOH)CD*H7. As mentioned, the velocity and extent of crystallization are important parameters in a variety of systems, including liquid crystals and polymers. Of particular interest are situations in which the rate of transformation to a crystalline state can be monitored quantitatively under isothermal conditions. Such measurements allow the calculation of Avrami crystallization parameters (vide infra), which provide insights regarding crystal growth geometry and nucleation.ls Although many methods are currently being used for the measurement of crystallization isotherms (including calorimetry,l6 dilatometry,I7 light depolarization,18 infrared spectroscopy,19 and small-angle X-ray scattering"), the determination of Avrami parameters from isothermal crystallization investigations has been limited primarily to dilatometry and light depolarization techniques. This is because any satisfactory method of measurement must allow rapid determination of the extent of crystallization relative to the crystallization time constant, high precision so that small increments in crystallinity can be detected, and excellent temperature control. In principle, appropriate NMR techniques should also be capable of satisfying these criteria. A key to developing a suitable NMR technique is the large difference in deuteron TIvalues between the Sm2 and crystalline phases of either F7(CHOH)CD2H7or F7(CDOH)H8. In fact, whenever there is a very large differencein spin-lattice relaxation times between two interconverting phases, the method outlined here should be applicable; it is reasonable to assume that many materials satisfy this condition. The saturation recovery N M R pulse sequence used to determine the TI values takes advantage or these differences, enabling observation of only the shorter T I component from the Sm2 phase: a short time delay (700 ms) following deuteron spin state saturation removes the (crystalline) component with a long deuterium spin-lattice relaxation time constant; the resulting FID contains information only from the (Sm2) componentwithshort T I .Toquantifythedatawithrespect to the amount of remaining Sm2 phase, the maxima in the normalized time domain N M R quadrupole spin echo intensities were recorded as a function of time under isothermal conditions. The intensity of this echo is proportional to the amount of Sm2 phase present. The time required to record each FID (ca. 6.5 min) represents a minuscule fraction of the crystallization periods for the alcohols and, therefore, each data point need not be corrected to a (time) weighted average.21 Figure 4 is a plot of the logarithm of the normalized spin echo intensity as a function of time a t 315 K for F,(CHOH)CDzH7 recorded over a 12-h period. The rate of crystallization for the first 5 h is considerably higher than for times thereafter. An initial higher rate is characteristic of crystallization processes in general and has been designated as primary it is a consequence of the growth of crystallites which are not in direct contact with other crystallization sites and is associated
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Figure 4. Semilogarithmic plot of the deuteron spin echo intensity of Sm2 F,(CHOH)CDzH7 as a function of time at 315 K and best fits to
data points assuming two linear regions.
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Time (hl Figure 5. Semilogarithmic plot of the deuteron spin echo intensity of Sm2 F~(CHOH)CDZH~ as a function of time at 320 K and best fits to
data points assuming two linear regions.
with the incorporation of noncrystalline regions into existing or new crystals. The period of primary crystallization is generally considered to commence when the sample reaches the crystallization temperature and to terminate when large deviations from Avrami kinetics first occur. The rate of primary crystallization is typically highly temperature dependent and has been shown in some cases to vary with molecular weight in polymers.23.24 The ensuing lower rate of crystallization (Figure 4) after approximately 5 h is classified as secondary crystallization; crystallization during this time period is more complex and is restricted primarily to growth within the crystallite boundaries. The time constants (at 3 15 K) were determined from this plot by least-squares analysis (assuming only two growth rates) to be 2.5 h for primary crystallization and 13.8 h for secondary crystallization. A similar plot for F7(CHOH)CDzH7 a t 320 K, recorded over a 39-h period, is shown in Figure 5. Primary crystallization occurs during the first 12 h, more than twice as long as at 315 K. The time constants associated with formation of the solid, during primary and secondary crystallizations, were 6.1 and 29.8 h, respectively. The fact that both the time constant (6.1 h) and period (12 h) of primary growth a t 320 K are longer than a t 3 15 K is consistent with the model of unhindered growth associated with primary crystallization. The time constants for primary crystallization of F7(CHOH)CDzH7, determined over the temperature range 295-325 K, are
Kinetics of Crystallization of a Smectic Alcohol 12
1:
The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11119
1
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(K) Figure6. Timeconstantsfor primary crystallization regionof F7(CHOH)CDzH, as a function of temperature. The curve is included to show the trend and is not intended as an accurate description of the temperature dependence. Temperature
presented in Figure 6 . As temperature is lowered from 310 to 290 K, the rate of formation of the crystalline phase (= r l ) decreases rapidly, primarily due to greater attenuation of molecular mobility in Sm2 (i.e., greater viscosity which inhibits nucleation). As temperature is raised above 315 K, the rate of crystallization also decreases rapidly due to thermal agitation which affects the equilibrium between growth and dissolutionat crystal surfaces. A second run at 3 10 K led to a 7 value virtually indistinguishable from the first. Both data points are included in the figure. The primary crystallization kinetic data obtained at 3 15 and 320 K for F7(CHOH)CD*H7 were fit to the Avrami equation4 (eq 1):
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log (t) Figure 7. Avrami plots of primary crystallization data from Figure 4 (0, n = 1.3) and Figure 5 (0, n = 1.4). 3.5
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where X,(t) is the mass fraction of the crystalline phase formed without experiencing overlapping growth volumes at time t, k is the overall rate constant for crystal growth which embodies both nucleation andgrowth (andshouldnot beconfused with theinverse of the time constants calculated from the slopes of plots of In M ( t ) versus time), and n is the Avrami nucleation parameter which depends upon the geometry and type of nucleation of primary crystal growth. The Avrami parameters are obtained by plotting log[-ln(1 - xc(t))] vs log t, where the slope n can be determined by linear least-squares analyses. Figure 7 contains the Avrami plots from the primary crystallization data of Figures 4 and 5. The Avrami exponents n for crystallization were determined to be 1.3 at 3 15 K and 1.4 at 320 K. While the main focus of the present investigation is to demonstrate that crystallization isotherms and Avrami crystallization parameters can be determined in a facile manner using the NMR technique described here, the magnitude of the nucleation parameters suggeststhat crystal growth occurs primarily in one d i m e n s i ~ n . ~ ~ Crystallization Kinetics of F.I(CDOH)&. Crystallization of F7(CDOH)Hs from its Sm2 phase was also followed using the saturation recovery quadrupole echo NMR procedure. Figure 8 is a plot of the normalized spin echo intensity of the Sm2-phase deuteron signal at 3 10 K over a period of 19 h. The time constant associated with this primary crystallization, 3.5 h, is somewhat longer than the 2.5 h measured at 310 K for F,(CHOH)CDzH7. These differences are most likely attributable to variations in the concentration of nucleation sites between the samples. One set of isothermal crystallization measurements of F7(CD0H)Hg at 310 K resulted in a deuterium NMR spectrum (Figure 9) which suggested more long-range C-D bond ordering
Figure 8. Semilogarithmic plot of the deuteron spin echo intensity of unaligned Sm2 F7(CDOH)H8 as a function of time at 310 K and best fits to data points assuming two linear regions.
(with respect to the applied magnetic field) than had been seen in any of our previous Sm2-phase measurements. Figure 10 is a plot of the time dependence of the normalized deuteron spin echo intensity from this sample (hereafter referred to in relative terms as the "aligned" phase). The time constants for primary and secondary crystallizations were determined to be 4.2 and 17.1 h, respectively. These values differ somewhat from those calculated using data from the same sample (Figure 8) in its "unaligned" or more common state.26 There, the time constants were 3.5 and 34.7 h. The duration of primary crystallization in the aligned sample, 8 h, was approximately 2 h longer than in the unaligned sample. A more conspicuous difference exists in the time constant for secondary crystallization, which is a factor of 2 longer in the unaligned sample. These data suggest that, when crystallization occurs from a phase of higher alignment,the period of primary crystallization may be extended due to less spatial inhibition of crystal growth. Further, once secondary crystallization begins in the aligned sample, the transformation of the remaining Sm2 phase proceeds on a significantly shorter time scale (relative to secondary crystallization in the unaligned sample). However, we note that the fraction of material undergoing primary crystallization in the unaligned and aligned samples is approximately the same (-8&85%). Avrami plots for the aligned and unaligned primary crystallization isotherms at 310 K are shown in Figure 1 1. The Avrami nucleation parameters from the aligned and unaligned sample runs were 0.9 and 1.3, respectively. The value of 1.3 for the
McGrath and Weiss
11120 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993
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Avrami nucleation parameter observed in the aligned sample suggests that the dimensionality of solid crystal growth may be dependent upon the extent of alignment of the medium from which it is formed. Although these data suffer from our inability to reconstitute an "aligned" sample, they are extremely interesting and beg further experimentation with other alignable molecules. Conclusions. The rates associated with the transformation of the monotropic Sml phase of F7(CHOH)Hs to its monotropic Sm2 phase and from Sm2 to the solid phase have been measured qualitatively by differential scanning calorimetry. Due to the tedium and experimental difficulties associated with the DSC method, we have developed a more facile and quantitative technique. 2H NMR spectra of specifically deuteriated F7(CH0H)Hg did not provide the necessary information since they are very similar in the Sm2 and solid phases. However, the greater than 100-fold difference in the T I spin-lattice relaxation times of the deuteriated K(CH0H)Hs molecules in their Sm2 and solid phases confirmsour originalassignmentof Sm2 as a (smectic) mesophase.2 It has provided a convenient means by which the *H NMR signal intensity from the Sm2 component of a neat mixture with some solid phase can be recorded quantitatively and in situ as a function of time and at various temperatures. Simple data manipulation permits the time constants and components of primary and secondary crystallizations to be calculated. Also, application of the Avrami equation to the data has yielded insights into the mechanism of crystallization. The approach described is experimentallyfacile and, although we have no other examples to date, it should be amenable to measuring quantitativelythe rates of crystallization of many liquid crystals and polymers.
0
-0 5
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Fime 11. Avrami plots of primary crystallization region data (Figures 8 and 10) of 'unaligned" (0, c = 1.3) and "aligned" (0,n = 0.9) Sm2 F7(CDOH)Ha at 310 K.
unaligned sample is identical within experimental error to those found for crystallization of F~(CHOH)CD~H.I at 3 15 and 320 K. This is not surprising since the extent of alignment, as evidenced by the deuteron NMR line shapes for each of these samples, was indistinguishable. Particularly noteworthy is that the lower
Acknowledgment. We are indebted to Dr. Patricia Vilalta, who developed many of the synthetic procedures employed, made several key preliminary observations, and shared her expertise. K.J.M. expresseshis gratitude to the Naval Research Laboratory for fellowship support through the Edison Memorial Program and for the use of the NMR facility at NRL to conduct this work. R.G.W. thanks the National Science Foundation for its partial support of this research. References and Notes (1) Part 50 in our series, 'Liquid-Crystalline Solvents as Mechanistic Probes." For part 49, see: Furman, I.; Weiss, R.G. lmngmuir 1993,9,2084. (2) Vilalta, P. M.;Weiss, R.G. Liq. Cryst. 1992, 12, 531. (3) Mandelkern, L. Crystullizotion of Polymers; McGraw Hill: New
York, 1964. (4) Avrami, M . J. Chem. Phys. 1939,7,1103; 1940,8,212; 1941,9,177. ( 5 ) Davis, J. H.; Jeffrey, K. R.;Bloom, J.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1916,42, 390.
Kinetics of Crystallization of a Smectic Alcohol (6) Blinc, R.; Rutar, V.; Seliger, J.; Slak, J.; Smolej, V. Chem. Phys. Lett. 1977, 48, 576. (7) Hentschel, R.; Spiess, H. W. J . Magn.Reson. 1979, 35, 157. (8) Vdalta, P.M.; Hammond,G. S.;Weiss,R. G. Photochem.Photobiol. 1991, 54, 563. (9) Trost, B. M.; House, H. 0. J. Org. Chem. 1965,30, 1341. (10) Pake, G. E. J . Chem. Phys. 1948.16, 327. (11) Abragam. A. The Principles of Nuclear Magnefism;Oxford University Press: Oxford, U.K., 1961. (12) Hentschel, D.;Sellcscu, H.; Spiess, H. W.; Voelkel, R.; Willenberg, B. Magn. Reson. Relat. Phenom., Proc. Congr. Ampere, lPh, 1976. (13) Torchia, D.A.; Szabo, A. J . Magn.Reson. 1982, 49, 107. (14) Spiess, H. W. In NMR-Basic Principles and Progress; Diehl, P., Ruck, E., Kmfeld, R., Eds.;Springer-Verlag: New York, 1978;Vol. 15. (1 5) Wunderlich, B. MacromolecularPhysics, Vol.2, CrystalNucleation, Growth, Annealing; Academic Press: New York, 1976. (16) Mueller, F. H.; Martin, H. J . Polym. Sci. 1964, 6, 83. (17) Bekkedahl, N.Rubber Chem. Technol. 1967, 40, 35.
The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11121 (18) Magill, J. H.Polymer 1961, 2, 221. (19) Cobb, J. H.; Burton, R. L. J . Polym. Sci. 1953, 10, 276. (20) Vignaud, R.; Schultz, J. M.Polymer 1986, 27, 651. (21) Inaddition, deuteron NMRlieshapeanalysisofthefrcquencydomain spectrum potentially provides relevant information regardingmolecular motion and long-range molecular ordering. See, for example: Spiess, H. W.; Sillescu, H. J. Magn. Reson. 1981,42,381. Bloom, M.;Davis, J. H.; MacKay, A. L. Chem. Phys. Lett. 1981,80, 198. (22) Flory, P.J.; Mcintyre, A. D. J. Polym. Sci. 1955, 18, 592. (23) Mandelkern, L.;Fatou, J. G.;Ohno, K. J. Polym. Scf.1968,6B,615. (24) Roussel, S.McElroy, K. L.; Judovits, L. H. Polym. Eng. Sci. 1992, 32, 1300. (25) More detailed discussions on the interpretation of crystallization parameters can be found elsewhere. See, for example: Lauritzen, J. I.; Hoffman, J. D. J. Res. Natl. Bur. Stand., Sect. A 1960, 73, 64. (26) In subsequent experiments we were unable to reproduce the higher levelof algnment;allother deuteronlie shapes werevirtually indistinguishable from that of Figure 2b.