Phase Transitions Phase behavior and nucleation kinetics...

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Phase behavior and nucleation kinetics of OctaphenylcyclotetrasiloxaneGeorge W. Smitha

a Physics Department, General Motors Research Laboratories, Warren, MI

To cite this Article Smith, George W.(1979) 'Phase behavior and nucleation kinetics of Octaphenylcyclotetrasiloxane',Phase Transitions, 1: 2, 107 — 129To link to this Article: DOI: 10.1080/01411597908213195URL: http://dx.doi.org/10.1080/01411597908213195

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Phase Transitions, 1979, Vol. 1, pp. 107-130

@ 1979 Gordon and Breach Science Publishers, Inc. Printed in Great Britain

0141-1 594/79/0102-0107 S04.50/0

Phase Behavior and Nucleation Kinetics of Octap henylcyclotetrasi loxane GEORGE W. SMITH Physics Department, General Motors Research Laboratories, Warren, MI 48090

(Received February 7 , I979; in,finalfi)rm May 8, I979)

Phase behaviour and certain aspects of phase-transformation kinetics for octaphenylcyclotetrasiloxane (OPCTS) have been determined by means of differential scanning calorimetry and optical microscopy. Three solid phases have been observed: 3 (stable at room temperature), 2 (stable above 76.6"C). and I (stable above 1895°C). The 3- and 2-phases are optically anisotropic and mechanically brittle; the 1 -phase is optically isotropic and soft or plastic. Although the 3-phase is thermodynamically unstable above 76.6"C. its transformation to the 2-phase is sufficiently slow that the 3 -, 1 transition can be studied. The transition temperatures (and corresponding latent heats) for the 3 -, 2, 3 + 1, 2 + 1. and melting transitions are: 76.6C (-2.9 KJ/mol), 186.0-C (47.3 KJjmol), 189.6C (43.76 KJ/mol), and 204.9C (1.95 KJ/mol). The entropy of melting (AS,,, = 0.491 R) is one of the lowest measured for any solid. The low- melting entropy, isotropy, and plasticity of the I-phase lead to the conclusion that it is an orientationally-disordered crystal mesophase (plastic crystal).

The kinetic behavior of the 3 -, 2 phase transformation, as determined by DSC, supports a theoretical model taking homogenous nucleation as the rate-determining process.

I INTRODUCTION

Octaphenylcyclotetrasiloxane (OPCTS), [SiO(C6H5)2]4, has been the object of a variety of research for over sixty years (Kipping, 1912, 1914; Hyde et al. 1941, 1945, 1947; Burkhard, 1945; Burkhard, Decker and Harker, 1945; Young, 1948; Brown, Hill and Murphy, 1961; Lopatkina et al., 1973; Keyes and Daniels, 1975; Volino and Dianoux, 1978). It is used as a spectrographic standard (and is thus available in a highly pure state). However, because of the molecule's apparent quasi-spherical shape, it is of considerable interest in developing an understanding of the influence of molecular geometry on mesophase formation (Smith, 1975, 1978). The fact that it is a relatively high

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I08 G. W. SMITH

FIGURE 1 Possible molecular contipration for OPCTS [Black = carbon; white = hydrogen; light grey =silicon: dark grey = oxygen]. Structure shown is consistent with preferred P 2JC (C;,,) space group of Burkhard. (See. for example, A. 1. Kitaigorodskii. Orgunic Chetnicul Crysrullogruphj. Consultants Bureau, New York. 1961. p. 50; and L. E. Sutton, fnteruromic Distances, Chemical Society, London. 1958. p. 20).

molecular weight, but compact, molecule containing eight phenyl groups, makes it an excellent candidate for phase-behavior studies in mixtures with rod-like and planar aromatic molecules-studies designed to test theories of mesophase formation in such systems (Alben, 1974).

Unfortunately, there seems to be little agreement among previous workers as to the phase behavior of OPCTS-perhaps as a result, in the early years, of low purity. However, high-purity material has become available as indicated by the fact that recently-measured values of the melting temperature are several degrees higher than the earliest data.

The first careful study of OPTCS was that of Kipping (1912) who reported apparent polymorphic behavior : he found two different kinds of crystals with “melting points” of about 185°C and 200°C. Much later Hyde, et al. (1945, 1947) published evidence for three crystalline phases: triclinic (I) and monoclinic phases (11) each melting at 200-2Ol0C, and an unstable phase (111) which “melts” at 188°C and slowly converts to I at room temperature.


OPTCS [SiO(C,H,),], NUCLEATION KINETICS I09

They reported lattice constants for the I and I1 phases, each of which contain 4 molecules per unit cell. Earlier Burkhard, et al., (1945) had found only a single phase with a melting point of 201-202°C. Their x-ray data were consistent with a monoclinic structure of density 1.185 g/ml, having 4 molecules per unit cell (this phase was subsequently identified as identical to the I1 phase of Hyde, et al.).

The molecular structure of OPCTS has apparently not been determined, but it is expected to be somewhat globular in shape (Keyes, 1975). A possible molecular configuration is shown in Figure 1.

Keyes and Daniels (1975) have carried out a somewhat abbreviated thermal investigation of solid OPCTS. Using differential thermal analysis (DTA), they found solid-solid phase transitions at 76°C and 188"C, followed by melting at 205°C. They did not report latent heats or entropies of transition but estimated that the entropy change at 188°C is some 22 times greater than the entropy of melting.? This fact, plus the optical isotropy of the high- temperature solid phase, led them to suggest that OPCTS is a "plastic crystal " (an orientationally-disordered crystal mesophase) (Smith, 1975, 1978). With a molecular weight of 793.2, OPCTS is several times heavier than other plastic crystals.

The findings of previous workers are summarized in Table I. It is apparent that the phase behavior of OPCTS is incompletely understood. We have undertaken a detailed investigation employing both differential scanning calorimetry (DSC)$ and optical microscopy (McCrone, 1957), in an effort to throw additional light on the situation. We have found evidence for three solid phases(label1ed 3,2, and 1) with that at highest temperature (the 1 phase) exhibiting several characteristics of a plastic crystal, in agreement with the suggestion of Keyes and Daniels. In fact, we find the entropy of melting AS,,, to be one of the lowest yet measured for any crystalline species (AS,,,/R = 0.491).§ The solid phase stable at room temperature (the 3-phase) demonstrates sufficiently slow conversion to the intermediate-temperature phase (2-phase) that it is possible to measure both 3 + 1 and 2 -, 1 transition temperatures (T31 x 186"C, T2, x 189S"C) and entropies. Indeed, the 3 --f 2 transformation is so sluggish that its equilibrium transition temperature (T32 zz 77°C) was observable on only a few occasions by calorimetric means.

The latent heats of the 3 -+ 2, 3 + 1, 2 -, 1, and melting transition (LJZ, L31, Lzl , and L,) are reported here for the first time, as is a study of the kinetics of the 3 -, 2 phase formation.

t The transition at 76°C seemed to have small associated entropy. A Perkin-Elmer DSC-2 instrument was used in this study. AS, for OPCTS is comparable to the values for 2.2-dimethylbutane ( A S , / R = 0.402) and

cyclopentane (AS,,,/R = 0.407), where R is the gas constant. See Timmermans (1950.1965).


110 G. W. SMITH

TABLE I

Summary of OPCTS phase data of previous workers.

Reference" Observed solid phases and reported propertiesb

Kipping T,,, = 200-201°C (I91 2. 1914) triclinic.

plates Hyde er a/.

(1945, 1947) triclinic.'

flat rectangular

I : T . = 201°C'

plates. converts to

111 at 100°C or on cooling from melt.

Stable at room temp.

Burkhard ( 1945)

Keyes T,,, = 205°C (1975) isotropic

p of high-temp. phase greater

than of lower temp. phase.

E d

11: T, = 201°C' monoclinic.' rapid conversion needles. converts to

111: T,,, = 188°C

to I at room temp.

I11 on cooling from melt.

Stable at room temp.

T,,, = 201 -202°C monoclinic.' p = 1.185g/ml. 4 mols/cell

T, = 188°C ASJAS,,, t 22

T, = 76°C

Citations are from reference list at end of text. Nomenclature: T,,, = melting temp., T, = transition temp.; AS,,, = melting entropy,

AS, = transition entropy; p = density; I, 11, I11 designations are those of Hyde er af. Kipping reports a substance with well-defined rhomboidal crystals, melting at 184-186°C.

He ascribed this to a mixture of OPCTS with hexaphenylcyclotrisiloxane. Kipping reports that the crystals with T,,, = 201" become opaque below 100°C. Hyde reports that I and I1 form mixtures which melt at 200-201 "C. X-ray crystallographic data reported.

II EXPERIMENTAL ASPECTS

A Samples

Octaphenylcyclotetrasiloxane was purchased from a commercial source (Eastman Organic Chemicals, Rochester, N.Y .) and was studied without purification. It is supplied as an atomic absorption standard and is therefore assumed to be of high purity. This assumption is confirmed by the fact that the melting temperature T,,, is high (-205°C) and the measured melting and transition temperature ranges are narrow ( 5 1 "C). Microscopic examination of the crystals of OPCTS reveals them to be irregularly-shaped truncated cylinders of various sizes up to ~ 0 . 0 5 cm on a side (see Figure 2).


OPTCS [SiO(C,H,),], NUCLEATION KINETICS 1 1 1

FIGURE 2 Crystals of OPTCS as received (microscopic view x 72). .

The samples were studied in two different states of preparation: (1) as- received (virgin samples) and (2) previously-melted or transformed to a high-temperature crystalline phase (heat-treated samples). As we shall see, the thermal data are quite sensitive to prior history of the sample. One virgin sample was dried under a desiccant in order to ascertain the possible presence of any water which might influence the calorimetric behavior. (No evidence for such an influence was found.)

The virgin sample material had been stored in a closed container at room temperature for several years prior to study. Thus it seems likely that stresses introduced during synthesis would have had ample time to relax.

B Scanning calorimetry

Seven samples of OPCTS weighing from 1.60 to 3.1 1 mg were hermetically sealed in aluminium capsules for calorimetric study. We estimated that a typical DSC sample (weighing -2 mg, with particle size distribution like that shown in Figure 2) contained some 100 to 200 crystallites as initially prepared.

Temperature calibration of the DSC instrument was performed using indium and zinc standards (melting temperatures T, = 156.7"C and 419.6"C). Indium (latent heat of melting, L, = 3.27 KJ/mol) was the standard for energy calibration. Latent heats of transition were determined by


1 I2 G . W. SMITH

planimeter integration of DSC peak areas using the baseline correction of Smith (1977). Transition temperatures were determined from the positions of peak maxima, a procedure which has been shown to be adequate for all but the narrowest transitions (Perkin-Elmer, 1974).

The estimated error in determination of peak areas is less than 1 %. However, the experimental scatter in latent heats is a little larger, ranging from 2 to 4%. The accuracy in the temperature measurement is certainly better than 1 "C; indeed, the discrepancy between transition temperatures determined calorimetrically and the more accurate values found from microscopy is only of the order of 0.5"C.

Calorimetric data for both virgin and heat-treated samples were obtained at temperature scan rate settings, s, ranging from 0.3 l"C/min. to S.O"C/min. As will be seen below (Section 111) the thermal behavior of the virgin samples depended crjtically on scan rate, whereas the results for heat-treated samples were insensitive to scan rate.

C Thermal microscopy

Phase transitions and crystal growth behavior of OPCTS were observed using a polarizing microscope at magnifications of the order of 50X-70X (Leitz Dialux-Pol, E. Leitz, Wetzlar, Germany) and a precision microfurnace (Mettler FP-52 + FP-5 microfurnace and controller, Mettler Instrument Corp., Princeton, N.J.). Previous experience (Smith, 1973) had shown that the temperature accuracy of the microfurnace is of the order of _+O.l"C. About ten samples, placed between glass microscope slides and glass cover slips, were examined in both virgin and heat-treated states. Crystal transformations were most easily followed using previously-melted samples, since reflections and sample thickness made observations on crystals like those of Figure 2 difficult. In microscopy, transition temperatures were determined from the point of coexistence of two phases (estimated at very slow or zero temperature scan rate).

111 CALORIMETRY RESULTS

A Virgin samples

1. T 6 177°C. No evidence for phase transitions between 27°C and approximately 177°C was found by DSC for any of the virgin samples. At first consideration this seems surprising in view of previous work (Keyes, 1975) indicating a low-entropy transition at about 76°C. However, as we shall see below, it appears that nucleation of the 2-phase occurs more slowly in virgin samples than in heat-treated ones.


OPCTS [SiO(C,H,)2], NUCLEATION KINETICS

A

113

183 184 186 186 187 188 189 190 Temperature (OC)

FIGURE 3 DSC tracing showing 3 -, 1 and 2 -+ 1 transitions (virgin sample, scan rate = I .25"C/min). Temperatures shown are nominal values; corrected values are reported in text.

2. 177°C < T < 195°C. Calorimetric behavior in this temperature regime was quite sensitive to temperature scan rate. The seven virgin samples were subjected to roughly similar thermal histories in warming from 27°C to 177°C: warmup times varied from - 13 to - 17 minutes. Although apparently slow, this warmup was actually rapid enough to preserve the virgin samples in the 3-phase, as demonstrated by subsequent thermal behavior in the transition region above 177°C.

For some samples warmed from 177°C at slow scan rates (0.31 to 1.25"C/min.) there was evidence for weak, broad endotherms (of the order of instrumental sensitivity) at temperatures around 178 to 181°C. This suggests that if enough time was allowed, some 3 + 2 conversion occurred just below the phase transitions at and above 185°C. For a faster scan (5OC/min.), no endotherms indicating 3 -, 2 conversion were seen between 177°C and 185"C, although an undetectable amount of conversion probably did take place.

In Figure 3 is shown a typical DSC tracing for a virgin sample in the temperature range 183°C to 190°C. (Temperatures given in the figure are only nominal, uncorrected for scan rate; values corrected by referencing against a standard at the same scan rate are reported in the tables below.) The two peaks, labeled A and B, correspond to the 3 + 1 and 2 + 1 transitions. As previously indicated, the 3-phase is thermodynamically unstable in this temperature range, but calorimetric and microscopic evidence shows that it can persist long enough in virgin samples for the 3 + 1 transition


I I4 G . W. SMITH

TABLE I I

Scan rate dependence of L , . L, , L , + L, . r., . and T,

Sample mass Scan rate L , Ln LA + Lo T , TI3

1.64mg 5"Cmin 46.61 K J mol 0.83 K J mol 47.44 KJ,'rnol 186.0"C - 189°C I .60 5 45.6 I 1.34 46.95 185.8 188.7 2.35 2.5 34.14 11.76 45.90 185.7 189.1 1.79 I .25 21.30 24.89 46.19 185.4 188.8 2.19 I .25 18.07 26.07 44.14 185.5 189.0 2.06 0.62 15.15 29.12 44.27 185.3 188.7 3.11 0.31 8.28 35 35 43.63 185.1 188.6

I I I I I

I

I I I I 0 1 2 3 4 5

Scan Rate (OC/Min)

FIGURE 4 data; curves are best fits of theory.

LA, L,. and L., + LB as a function of scan rate, s, for virgin samples. Points are


OPTCS [SiO(C,H,),], NUCLEATION KINETICS I15

40-

30 - a ? a 4

20 -

10 -

0 10 20 30 40 50

L B (kJ/MOL)

FIGURE 5 LA versus LB for virgin samples at different scan rates. The curve is a best-fit straight line (see text). Intercepts on ordinate and abscissa correspond to L 3 , and L 2 , , respectively.

to be observed at about 185°C. The slightly negative (exothermic) excursion at temperatures above A, probably corresponds to a very slow 1 + 2 conversion (to be discussed below in Section V). The measured heats of transition, LA and Lg , for the A- and B-peaks are quite sensitive to the rate of scan, s, through the transition region. (We define LA to include the contribution of the small negative excursion). The values of LA, Lg, LA + L g ,

and the corrected peak temperatures TA and T,,, are listed in Table 11. The transition heats and their sum are plotted in Figure 4. The functional relationship of LA and Lg is given in Figure 5. The theoretical curves of the two figures will be discussed in Section V.B. High values of LA and low values of LB in Figure 5 correspond to higher scan rates. The intercepts (as we shall see) are equal to L , , and L 2 , , the latent heats of the 3 -+ 1 and 2 -+ 1 transitions.


I16 G . W. SMITH

t

I I I 1 I I I I I 200 202 204 206 208

Temperature (OC)

FIGURE 6 sensitivity is about 5 x that in Figure 3). Temperature values shown are nominal.

DSC tracing showing melting transition (scan rate = S"C/min: instrument

The temperatures TA and TB are taken as measures of transition temperatures T,, and T,, . It is seen in Table I1 that, whereas TB is independent of scan-rate, TA shows a slight scan-rate dependence, the source of which is unknown.

3. T > 195°C. The melting behavior of OPCTS is independent of sample treatment. Both virgin and previously-melted samples yield a melting peak at 204.3 k 0.2"C with latent heat of melting L, = 1.95 & 0.10 KJ/mol. A typical DSC melting peak is given in Figure 6.

B Heat -Treated samples

1. T 5 177°C. For the sake of completeness, several high-sensitivity DSC scans were run from temperatures as low as - 53°C to search for additional phase transitions. None was found between - 53°C and 76°C.


OPCTS [SiO(C,H,),], NUCLEATION KINETICS 117

3 73 75 77 79 81 83

Temperature (“C)

FIGURE 7 DSC tracing showing 3 -, 2 transition (previously melted sample, scan rate = I0”Clmin: instrument sensitivity approximately equals that of Figure 3). Temperature values shown are nominal.

Although virgin samples yielded no peaks corresponding to the low- temperature transition of Keyes and Daniels, previously-melted specimens showed a phase transition at 76.6 f 0.5”C on four occasions (see Figure 7). The latent heat from integrated peak areas varied appreciably among the runs but never exceeded 2.9 KJ/mol. Although the conditions under which the transition could be observed are not readily apparent from the meagre data, it does appear that ample “soak time” at or below room temperature may be a factor. It also seems, from the difficulty in obtaining the 3 -, 2 DSC peak and the wide variation in observed latent heat, that nucleation of the 2 phase is, at best, difficult.

2. T > 177°C. Although nucleation of the 2-phase is usually slow in the vicinity of the 3 + 2 transition temperature, it apparently occurs rapidly enough, for heat-treated samples, over the interval 76” to 185”C, that essentially all the OPCTS has transformed below T3 1 . This is evident from Figure 8, in which we see only a very small “bump” at T31 but a large peak at T Z 1 . Integration of the large peak (for a number of runs and different samples) gives a value of LZl (43.76 f 0.79 KJ/mol) in agreement with that derived from the abscissa intercept of Figure 5 .

As already mentioned, the melting behavior of heat-treated samples is indistinguishable from that of virgin samples. A typical scan showing the


I18 G . W. SMITH

1 1 I I I I I 184 185 186 187 188 189 1 9 0

Temperature ( O C )

FIGURE 8 DSC tracing showing large 2 + I transition plus small residual 3 - 1 transition (heat-treated sample, scan rate = 1.25"C/min; instrument sensitivity is about 1/2 that in Figure 3). Temperature values are nominal. (cf. Figure 3).

remnant 3 .+ 1 peak, the 2 + 1 transition, and the melting peak is seen in Figure 9.

3. Supercooling behavior. Very little supercooling of OPCTS from the melt was observed. At a scan rate of - S"C/min, solidification to the 1-phase (as identified from the magnitude of the latent heat) occured at about 199"C, only 5°C below the melting point.

On the other hand, it was possible to supercool the I-phase (at - 10"C/min. scan rate) to roughly 130"C, some 60" below T2,. Transition to the lower- temperature phase [apparently the 2-phase as indicated by the magnitude of the accompanying latent heat, (-42.7 KJ/mol)] occurred in two or three steps over the range 134°C to 121°C.

TABLE 111

Summary of calorimetric data for OPCTS.

Transition Entropy Transition Temperature Latent Heat (L) (AWRY

3 + 2 76.6 f 0.5"c(Tjz) - 2.9 KJ/mol(L,,) -0.99 3 - 1 185.6 k o.4(T3,) 47.3 f 0.7(L,,)b 12.4 f 0.18

Melting ( 1 - I)' 204.3 f O.3(Tm) 1.95 k 0. IqL,,,) 0.491 f 0.025 2 - I 189.1 k 0.5(T,,) 43.76 f 0.79(L~,) 11.39 f 0.21

a Transition entropy is expressed as a unitless quantity by dividing by the gas constant R. Value of L,, determined from ordinate intercept of Figure 5. Melting transition is also indicated as transition from solid I state to liquid ( I ) at the

melting temperature T,,, = TI,.


OPCTS [SiO(H,H,),], NUCLEATION KINETICS 1 I9

t

Temperature ("C)

FIGURE 9 DSC tracing showing remnant 3 --t 1 transition ( - 185"C), 2 + 1 transition (- 189"C), and melting (-204°C) (scan rate = 5"C/min; instrument sensitivity is about 1/2 that in Figure 3). Temperature values are nominal.

C Summary of calorimetric data

From our calorimetric studies of both virgin and heat-treated samples we compile the summary given in Table 111. The value of L31 shown is obtained from the ordinate intercept of the curve (a best linear fit) in Figure 5, a procedure which is justified below (Section V.B). Errors in Table 111 for all quantities except (and thus AS3,) are standard deviations; that for L31 (and AS31) is the 95% confidence limit obtained from the linear fit of Figure 5. The value of L32 (which may be regarded as approximately correct) is reasonable since it is of the order of L3 - Lz .

IV MICROSCOPY RESULTS

Thermal microscopy studies were performed on both virgin and heat- treated samples. The examination of the microscopic crystal textures


I20 G. W. SMITH

(appearance) aided in the identification of the various phases and determination of their transition temperatures. In addition a brief study of crystal transformation kinetics assisted in the unraveling of the scan-rate dependent DSC results for virgin samples.

A Virgin samples

As is evident from Figure 2, microscopic studies of virgin samples were difficult because of reflections, sample thickness, and sample shape. However, it was possible to estimate roughly the fraction ofa polycrystalline specimen in an anisotropic solid phase, the isotropic solid phase, or the liquid phase. For neither virgin nor heat-treated samples was it possible to detect, through the microscope, the 3 + 2 transition at about 76.6"C. There did, however, seem to be some appearance of rather gradual structural changes as the temperature was increased above - 165"C, in accord with DSC evidence.

The microscopic studies (of both virgin and heat-treated specimens) made it clear that the high-temperature I-phase is optically isotropic (and thus cubic). The two lower-temperature phases are optically anisotropic. Further- more, a low pressure (exerted by a pair of tweezers) on the cover glass easily deformed the soft I-phase. (Virgin crystallites retained their shape upon warming to the I-phase unless pressure was exerted on the cover glass). On the other hand, the same pressure treatment shattered an anisotropic sample. Thus, the I-phase may be regarded as "plastic" whereas the anisotropic crystals are apparently "brittle."

Although both the 1-phase and the liquid are optically isotropic, it was not difficult to observe the 1 + I transition (melting) microscopically. This was accomplished simply by rotating the microscope analyzer slightly to brighten the field and make visible the crystallite edges (for virgin samples) or grain boundaries (for previously-melted ones).

Scan-rate dependent microscopic behavior was seen upon warming virgin samples through the vicinity of the 186"( T 3 ] ) and 189"C(T2,) transitions. At faster scan rates (e.g. 3"C/min) most crystallites converted to the isotropic phase at T31. As scan rate decreased, the fraction of sample remaining anisotropic up to T, increased markedly, in agreement with DSC behavior. Thus for s = O.TC/min, only about 207, became isotropic a t T , ] , the remainder converting at T, , . Furthermore, for slow scan rates, smaller crystallites were more likely to become isotropic at the lower transition temperature, T,, (i.e., not convert to 2-phase). These observations are consistent with the view that the probability of nucleation of the 2-phase within the 3-phase decreased as crystallite volume decreased, but increased as longer times were allowed for conversion. Although all material within a


OPTCS [SiO(C,H,),]4 NUCLEATION KINETICS 121

(c) (d? FIGURE 10 Microscopic textures of previously melted OPCTS. (a) Coexistence of 3-phase (fan-like columnar structure) and 2-phase (plate-like mosaic) at 30°C. (b) Growth of 2-phase plates in 3-phase at 162.6”C. (c) Coexistence of 2-phase and I-phase (isotropic) at 187.I”C. Remnant 3-phase had converted to 1-phase at 1858°C. Parallelogram-shaped crystallite of 2-phase in lower center is slowly growing in isotropic solid. (d) Coexistence of 2-phase and 1- phase at 187.1°C, photograph taken 10 minutes after c). Note growth of crystallite in lower center.

given crystallite frequently converted to the isotropic phase almost simul- taneously (at either T3 or T2 occasionally portions of crystals transformed at T31 and the remainder at T 2 1 . The rapidity with which 3 + 1 and 2 -P 1 transformation, once begun, occurred within a crystallite suggests that nucleation is the controlling factor. The sluggishness of 3 + 2 conversion indicates that this, too, is nucleation-controlled.

B Heat-treated samples

A sample which had been warmed above T21 without melting showed essentially the same transition temperatures as one which had been melted. Since microscopic observations of samples which have melted, flowed and then solidified were easier and more informative than those of crystallites like the ones of Figure 2, we shall confine our attention to the former. It


I22 G . W. SMITH

should first be reiterated that we did not observe microscopically the phase transition at T32 . Thus the only data for this transition were obtained calorimetrically.

It was possible to observe, at room temperature and above, two anisotropic crystal textures corresponding to phases 3 and 2 (see Figure 10). These phases were identified by observing their transition temperatures to the isotropic 1-phase. In Figure 10, the mosaic or plate-like regions correspond to the 2-phase and the fan-like columnar structures are regions of 3-phase. As the temperature is raised, the plate-like 2-phase regions grow slowly at the expense of the 3-phase (Figure 10a and lob). At T,, = 1856°C any remnant 3-phase converts to isotropic 1-phase. For T3 < T < T, the 2-phase grows slowly in the 1-phase (Figure 1Oc and 10d). Raising the temperature to T21 = 189.5"C permits the 2-phase regions to convert to 1-phase, leaving the entire sample in the isotropic high-temperature solid phase which subsequently melts at about 204.9"C.

Crystallization kinetic behavior can be roughly calculated from the time dependence of a picture sequence such as that of Figure 10. The transformation processes are quite slow, taking minutes to hours. A crude estimate indicates that 3 -, 2 conversion at 162.6"C occurs with a velocity of the order of 2 x cm/sec, whereas 1 -, 2 conversion at 187.1"C is some 10 times slower.

C Summary of microscopy results

In Table IV are collected the various temperature, texture, and mechanical data obtained from these microscopic studies. The temperature values from microscopy are about 0.5"C higher than those from DSC. Since the microscopy definition of transition temperature is less arbitary than that of DSC, we believe that the temperature values of Table IV are more correct thermodynamically than those of Table 111. Errors cited in Table IV indicate the observed limits of the transition ranges.

V DISCUSSION OF PHASE AND KINETIC BEHAVIOR

A Phase behavior

A careful integration of the calorimetric and microscopic data yields a consistent phase diagram for OPCTS. We visualize the phase behavior by means of a schematic diagram of Gibbs function G versus temperature (Figure 11). (For a discussion of such Gibbs function plots see, for example, Turnbull, 1956; McCrone, 1965; Verma and Krishna, 1966; Sears and Salinger, 1975).


OPCTS [SiO(C,H,)J4 NUCLEATION KINETICS

TABLE IV

Summary of microscopy data for OPCTS.

I23

Transition Temperature’ 3 - 2 Not observed 3 + 1 186.2 + 0.3”C (V)

185.8 0.3 (M) 2 - 1 189.7 f 0.2 (V)

189.4 f 0.3 (M)

204.9 f 0.2 (M) melting ( 1 + 4 204.8 f 0.2 (V) - Phase Microscopic Texture Mechunieul Behavior

Brittle Plastic

3 Anisotropic columnar 2 Anisotropic plates I Isotropic

a V = virgin sample: M = previously-melted sample.

In view of the inconsistency of phase data of early workers, it is difficult to correlate present solid-phase assignments with previous ones. Since Hyde’s structures for his phases I and I1 are non-cubic, it would appear that neither one could be equated with the present 1-phase which, on the basis of its optical isotropy, is cubic. The fact that Hyde describes his 111-phase as “melting” at 188°C arouses the suspicion that the transition to the high- temperature isotropic solid phase may have been mistaken for melting. Furthermore, it may be that Hyde’s I and I1 phases are, in fact, the present 2- and 3-phases, which, as we have seen, readily coexist at low temperatures. Another possible cause of discrepancy which cannot be ruled out is, of course, the influence of impurities. Indeed, Keyes and Daniels suggest that impurities may have “suppressed” the high-temperature phase in early work.

The fact that Keyes and Daniels did not detect the virgin-sample scan-rate effect may possibly be due to lack of temperature resolution, rapid scan rates in their DTA experiment, or perhaps use of previously-melted sample.7

6

The scan-rate dependence of the DSC behavior for virgin samples provides an opportunity to examine the kinetics of the 3 -, 2 phase conversion. As McCrone (1965) states, “more work should . . . be carried out on rate of [phase] transformation, and, in particular, the rate of nucleation should be

Kinetics of 3 + 2 transformation

t Unfortunately, Keyes and Daniels do not state their temperature scan rate or sample condition. Also their AT peak for the transition region around 188°C is off-scale. Thus it is impossible to determine which of these possibilities (if any) is correct.


124 G . W. SMITH

Temperature (OC)

FIGURE 1 1 Schematic plot of Gibbs function G for solid phases 3, 2, and 1 and liquid I of OPCTS. Thermodynamically stable phases (those with lowest G ) are indicated by solid lines, unstable phases by dashed lines. The quantities Xand Zrefer to the mole fractions of 3 converted to 2 below T, , and 1 converted to 2 above T, , respectively. as discussed in Section V.

differentiated from the rate of transformation.” The formation of crystal nuclei is, in general, not understood with any degree of certainty (Mullin, 1972).

The evidence of both DSC and microscopy supports the view that most 3 -P 2 conversion in virgin samples occurs just a few degrees below T 3 1 . If this were not so, one would expect a smaller A-peak due to the occurrence of 3 -P 2 conversion during the rather leisurely warmup from 27°C (- 13-17 minutes); thus, the relative A- and B- peak areas would then be expected to much less sensitive to scan rate in the immediate vicinity of T, and T2 .

The scan-rate dependence of Table I1 and Figure 4 can be interpreted rather well in terms of a model taking homogeneous nucleation as the rate- controlling mechanism (Kantrowitz, 1951 ; Frenkel, 1955 ; Turnbull, 1956; Fine, 1964). We assume that once a critical-sized nucleus (Mullin, 1972) of 2-phase has been created within a crystallite of 3-phase, conversion of the entire crystallite to 3-phase occurs rapidly. For a virgin sample, the total amount of material converted is, of course, controlled by the number of crystallites (> 100 for a DSC sample), the volume of each crystallite, and


OPTCS [SiO(C6HS)2]4 NUCLEATION KINETICS 125

the time allowed for conversion (i.e. the temperature scan rate). For previously-melted material, nucleation is assisted by heterogeneous sites at sample/container interfaces and by stresses and defects generated during volume changes at the transition temperatures ; furthermore, volume available for growth, once nucleation has occurred, is less restricted in previously- melted specimens than in samples consisting of numerous crystallites. Even for a sample which has not been melted (but which has been heat treated by warming through T3 and T2 stresses and defects will enhance 3 4 2 nucleation in subsequent runs. Thus, it is entirely reasonable that heat- treated samples show a very small A-peak and a large B-peak, independent of scan rate.

The latent heats of transition, LA and LB, measured for the A- and B-peaks of virgin samples, can be expressed quite simply in terms of X, the mole fraction of 2-phase transformed from 3-phase below T 3 1 , and Z, the mole fraction of 2-phase transformed from I-phase in the temperature range between T3 and Tz (see Figure 11). As mentioned previously (Section III.A.2.) we include the exothermic 1 -, 2 contribution in LA. Thus,

(1) LA = (1 - X)L31 - ZL21

Equation 3 is a parametric straight-line representation of the data in Figure 5 , and we are therefore justified in taking the ordinate intercept of the figure to equal L3, . (The value of L3 given in Table 111 was determined in this manner). The abscissa intercept of the best-fit straight line (43.1 k 2 KJ/mol) agrees well with the directly-measured value of Lzl (43.76 & 0.79 KJ/mol).

From the model for homogeneous nucleation the number of critical-sized nuclei of 2-phase in 3-phase is proportional to exp(-t/t), where t is time and t is the time-constant. (Of course, a complete discussion of nucleation would take account of other factors such as temperature, crystallite volume, etc.). Since growth within a given crystallite occurs rapidly once a critical nucleus has formed, the total mole fraction X of 2-phase which has formed up to temperature T31 should be governed by the same time dependence.? Thus,

(4) x = exp( - :) where r is now the total time elapsed since nucleation was initiated.

t A completediscussion ofthe kinetics of nucleation in the DSC experiment should include the detailed effects of the linear temperature scan as given by Prime (1970) and Norwist (1978). However, since we are addressing only gross features, we shall not include this refinement.


I26 G . W. SMITH

We take the zero of time to occur at some temperature To (To < T31) during the scan upward through the transition region. We also assume that, once nucleation has begun, it proceeds at a more-or-less temperature- independent rate since the temperature scan range is narrow (only a few degrees). Because temperature varies linearly with time, the total time elapsed up to the transition temperature (and hence the total time available for 3 -, 2 conversion before 3 -, 1 transformation occurs) is

T31 - TO AT t = -- -

S S

where, as before, s = scan rate. Hence, the mole fraction converted below T3 is

where a is proportional to the time constant for 3 -, 2 nucleation. The co- efficient of the right-hand side of Eq. 6) is unity since X -, 1 ass + 0 ( t .-+ 00).

We assume that above T3 a similar scan-rate dependence governs Z, the total mole fraction of 1 -phase converted to 2-phase :

z = Z, exp - = (1 - X)e-Bs ( 2) (7)

where r', AT' (=TZl - T,,) , and /3 are appropriate constants for the 1 -, 2 conversion process. Equation (7) has been normalized to give the proper relation of Z to A'.

Substitution of Eqs. (6) and (7) into Eqs. ( I ) to (3) now yields

LA = ( 1 - e-as)(L31 - e-BSL21)

LB = [e-" + ( 1 - e-as)e-@S]L21

(8)

(9)

(10) LA + LB = (1 - e-"")L31 + e-"LZ1

A simplex minimization process (Nelder and Mead, 1965) yields a best fitofEq.(8)tothedataofTableIIfora = 0.513min/"Cand/3 = 122min/"C. The large value ofb leads to the conclusion that the Z-terms in Eqs. (8) and (9) are small, indicating that 1 + 2 conversion is slow (as noted from optical microscopy) and that the resulting exothermic contribution to the A-peak is negligible.

Thus

LA = (1 - e-")LJ1 (1 1)

LB = e-"SL21 (12)


OPTCS [SiO(C6HS)2]4 NUCLEATION KINETICS 127

The curves of Figure 4 are plots of Eqs. (lo), (ll), and (12). The fit is reasonably good.

VI CONCLUDING REMARKS

From the two techniques-DSC and optical microscopy-we have extracted a reasonable understanding of the phase behaviour of OPCTS and a plausible interpretation of the kinetics of the 3 + 2 phase conversion process. However, we feel that much more can be learned by further studies of this system. Crystal and molecular structural information obtained from modern X-ray and neutron techniques are clearly needed, as are molecular dynamics data obtainable from nuclear magnetic resonance and various scattering methods.

Recently Volino and Dianoux (1978), on the basis of powder neutron diffraction spectra, have proposed that, in spite of the compact molecular structure of OPCTS, and the optical isotropy of the high-temperature phase (1-phase in our notation), this phase may resemble a smectic A phase rather than a “plastic crystal.” In support of this interpretation, they point out that they observe only two diffraction peaks- behavior suggestive of long-range order in one dimension only. On the other hand, it should be mentioned that diffraction data of plastic crystals are also characterized by relatively few peaks (Dunning, 1961 ; Staveley, 1962). For instance, the high- temperature crystal form of cyclobutane shows only two reflections. Al- though cyclobutane has a very low entropy of melting (Timmermans, 1950, 1965) (AS J R = 0.718), the high-temperature phase of OPCTS is even more disordered (AS,,,/R = 0.491 from Table 111) and therefore might be expected to exhibit as few (or fewer) diffraction peaks. Furthermore, the latent heat of melting of OPCTS (1.95 KJ/mol) is considerably less than the lower limit (2.9 KJ/mol) of latent heats for 93 smectic A-to-isotropic transitions reported by Marzotko and Demus (1975). In addition, the large values of ASJ1 and ASz1 suggest that some configurational as well as orientational disordering may be occurring at TJ1 and T,, . This configurational disordering might be expected to result in a “smoothing” of the shape en- velope of the molecule, a view that is consistent with a plasticcrystal interpretation of the 1-phase.

It appears that more evidence is needed before a clear-cut choice can be made between the proposed plasticcrystal and smectic interpretations of the 1-phase. Nuclear magnetic resonance studies of the 1-phase would be particularly valuable‘ in making this choice.

Further studies of the kinetics of the solid-solid phase transformations of OPCTS would also be of value. Investigations of the influence of sample


128 G. W. SMITH

preparation and thermal history may yield greater understanding of the nucleation and growth processes.

Note added in proof

T. C. Moore and C. G. Wade (private communication) have performed proton magnetic resonance studies on OPCTS. In the 1-phase they observe a single narrow line (width 50.02 G) showing that both general molecular reorientation and self diffusion are occurring. This result is consistent with the view that the 1-phase of OPCTS is a plastic crystal (Smith, 1978). At higher temperatures in the 1-phase, further line narrowing reveals indica- tions of a chemical shift (6 - 0.7 x The chemically shifted lines (intensity ratio - 2/3) are clearly observable in the liquid phase. The chemical shift and relative intensities indicate that all 12 meta protons on the six phenyl groups are magnetically equivalent, as are the 18 ortho and para protons.

Acknowledgement

The author thanks Dr. J. G. Gay for several valuable discussions and for performing the simplex calculations. He also thanks Professor R. Rudman (Adelphi University) for pointing out the work of Volino and Dianoux. and Dr. M. Kaplit. who wrote the simplex computer program based on the method of Nelder and Mead.

References

Alben. R. (1974). Possible phase diagrams for mixtures of "positive" and "negative" nematic liquid crystals. In J . 1. Johnson and R. S . Porter (Eds). Liyuid Crysrals und Ordered Fluids, 2. Plenum Press, New York, pp. 81-84.

Brown, G. P., J. A. Hill, and C. B. Murphy (1961). Differential thermal analysis of silicones. J . Polymer Sci.. 55,419.

Burkhard, C. A. (1945). Hydrolysis of diphenyldichlorosilane. J. Am. Chem. SOC.. 67,2173. Burkhard, C. A.. B. F. Decker, and D. Harker (1945). Octaphenykyclotetrdsiloxane. J . Am.

Dunning, W. J . (1961). Crystallographic studies ofplastic crystals. J . P h p . Chem. Solids. 18,21. Fine. M. E. (1964). Phase TransJiormofions in Condensed S.vsfems. MacMillan, New York.

Frenkel. J. (1955). Kineric Theor,. of l iyuids . Dover, New York, pp. 390400. Hyde. J . F. and R. C. deLong (1941). Condensation products of the organo-silane diols. J . Am.

Hyde, J. F. (1945). Condensation products of the organo-silane diols. C h m . and Ind.. p. 270. Hyde, J. F., L. K. Frevel, H. S. Nutting, P. S. Petrie. and M. A. Purcell (1947). Cyclo-diphenyl-

Kantrowitz. A. (1951). Nucleation in very rapid vapor expansions. J . Chem. Phw.. 19. 1097. KK);cs. P. H. and W. B. Daniels ( 1975). Oc~aphenylcyclotetrasiloxan~ (OPTCS): ;I new high-

Kipping. F. S. (1912). Organic derivatives of silicon. Part XVII. Some condensation products of

Chem. SOC. 67,2 174.

pp. 11-15.

Chem. SOC., 63, 1194.

siloxanes. J. Am. Chem. Soc., 69. 488.

temperature plastic crystal. J . Chem. Phjs.. 105.484.

diphenylsilicanediol. J . Chem. Sor.. 101. 2125.


OPCTS [SiO(C6H5)2]4 NUCLEATION KINETICS I29

Kipping, F. S. and R. Robison (1914). Organic derivatives of silicon. Part XXI. The conden-

Lopatkina, I. L., L. A. Kucherskaya, A. G. Kuznetsova, and Yu. Kh. Shaulov (1973). Vapor

Marzotko. D. and D. Demus (1975). Calorimetric investigation of liquid crystals. Pramana,

McCrone, W. C. (1957). Fusion Methods in Chemical Microscopy, Interscience, New York. McCrone, W. C. (1965). Polymorphism. In D. Fox, M. M. Labes, and A. Weissberger (Eds.),

Physics and Chemistry of the Organic Solid Stare, Vol. 2, Interscience, New York, pp. 725-767. Mullin, J. W. (1972). Crystallization, CRC Press, Cleveland, pp. 137-146. Nelder, J. A. and R. Mead (1965). A simplex method for function minimization. Comp. J., 7 ,

308. Norwisz, J. (1978). The kinetic equation under linear temperature increase conditions. Thermo-

chim. Acta. 25, 123. Perkin-Elmer (1974). Instructions, Model DSC-2 differential scanning calorimeter. Perkin-

Elmer Cop. . Norwalk, CT. Prime, R. B. (1970). Dynamic cure analysis of thermosetting polymers. In R. S. Porter and J. F.

Johnson (Eds.). Analvtical Calorimetry. 2. pp. 201-210. Sears, F. W. and G. L. Salinger (1975). Thermodynamics, Kinetic Theory, and Statistical Mech-

anics, Addison-Wesley, Reading MA, pp. 186192. Smith, G. W. and Z. G. Gardlund (1973). Liquid crystalline phases in a doubly homologous

series of benzylideneanilines- textures and scanning calorimetry. J. Chem. Phys., 59,3214. Smith, G. W. (1975). Plastic crystals, liquid crystals, and the melting phenomenon. The im-

portance of order. In G. H. Brown (Ed.), Advances in Liquid Crystals, 1, pp. 189-266. Smith, G. W. (1977). Baseline construction for determination of transition enthalpies by

differential scanning calorimetry. Thermochim. Acta. 21.431. Smith, G . W. (1978). Orientational order and melting. Comments Solid State Phys., 9 ,21 . Staveley, L. A. K. (1962). Phase transitions in plastic crystals. Ann. Rev. Phys. Chem., 13,351. Timmermans. J. (I950 and 1965). Physico-Chemical Constants of Pure Organic Compounds,

Turnbull, D. (1956). Phase changes. In F. Seitz and D. Turnbull (Eds.), Solid State Physics, 3.

Verma, A. R. and P. Krishna (1966). Polymorphism and Polytypism in Crystals, Wiley, New

Volino, F. and A. J. Dianoux (1978). Octaphenylcyclotetrasiloxane (OPCTS): a new kind of

Walton, A. G. (1964). Nucleation in liquidsand solutions. In A. C. Zettlemoyer (Ed), Nucleation,

Young, C. W . , P. C. Servais, C. C. Currie, and M. J. Hunter (1948). Organosilicon polymers.

sation products of diphenylsilicanediol. J. Chem. SOC., 105, 484.

pressure of some cyclosiloxanes. Zh. Fiz. Khim.. 47.2900.

SUPPI. NO. I , pp. 189-213.

Vols. 1 and 2, Elsevier, Amsterdam.

Academic Press, New York, pp. 225-306.

York, pp. 7-44.

mesophase? Ann. Phys., 3, 151.

Dekker, New York, pp. 28-32.

IV. Infrared studies on cyclic disubstituted siloxanes. J. Am. Chem. Soc., 70, 3758.


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