Makromol. Chem. 190,613 - 621 (1989) 613

Small-angle X-ray diffraction study of the monoclinic modification of poly(3,3-dimethyloxetane)

Ernesto Perez*, Antonio Bello, JosP G . Fatou

Instituto de Plasticos y Caucho, Juan de la Cierva 3, 28006-Madrid, Spain

Jose A, Rausell-CoIorn

Instituto de Ciencia de Materiales, Serrano 1 15-B, 28006-Madrid, Spain

(Date of receipt: April 1 1 , 1988)

SUMMARY: The long spacings of several samples of poly(3,3-dimethyloxetane) (PDMO) were determined

by small-angle X-ray diffraction as a function of molecular weight and crystallization tempera- ture, in the interval where only the monoclinic modification is produced. The equilibrium melting temperature and the basal interfacial free energy of the mature crystals were determined from the correlation between long spacings and melting temperatures. Finally, an estimation of the critical sizes of the nuclei was made from nucleation theory, and the results were compared with the actual sizes of the crystallites, assuming a two-phase model. Our results show that both the nuclei and the mature crystals have rather small sizes, which is attributed to the high under- coolings involved in the crystallization of PDMO.

Introduction

Small-angle X-ray diffraction (SAXD) of polymers gives information on crystallite sizes, and, when measurements are made for different crystallization conditions, two important parameters relating to crystallization kinetics can be estimated as well. These parameters are the equilibrium melting temperature, q , defined as the melting temperature of a perfect crystal of infinite size, and the interfacial free energy associated to the basal plane, o,, , of the mature crystal, i. e., the actual crystal that has experienced a thickening process, and that, in principle, should be thicker than the nucleus from which it has been formed's2). The temperature q can also be obtained by alternative methods, involving the measurement of the melting tempera- ture, T,,, , as a function of the crystallization temperature, T, , for low levels of crys- tallinity.

Poly(3,3-dimethyloxetane) (PDMO) with structural formula A is an interesting

cH2-c-cn,-o ::,: in A

0025-1 16X/89/$03.00

614 E. Perez, A. Bello, J. G. Fatou, J. A. Rausell-Colom

polymer because it presents three crystalline modifications3). Two of these can be obtained by crystallization from the melt4). At temperatures higher than about 16 "C, only a monoclinic modification is obtained while an orthorhombic form is the only one obtained at T, below 0 "C, and both modifications coexist at intermediate crystal- lization temperatures4-'). The melting behaviour of these two modifications has been previously studied", and the value of E was determined from extrapolation of T,,, as a function of T, . The third crystal modification of PDMO is unstable, and is obtained only under stretching, disappearing when the tension is released3).

The crystallization kinetics of the high-temperature monoclinic modification of PDMO has been previously studied by measuring both the overall crystallization rate') and the spherulitic growth rate"), from which the temperature coefficient of the process was determined.

The purpose of this work is to correlate the long spacings of the monoclinic modification of PDMO with molecular weight and crystallization temperature, and to compare the deduced values of and interfacial free energies with the values previously reported, bearing in mind the basic difference of nucleus and mature crystal. In addition, the experimentally determined crystallite sizes are compared with the values obtained from nucleation theory.

Experimental part

PDMO was prepared by ring-opening polymerization in methylene chloride solution of the monomer, using triethyloxonium hexafluoroantimonate as catalyst ' I ) . The bulk sample was fractionated by precipitation with cyclohexane/ethanol at 30 "C. The molecular weights of the five fractions selected for this work were determined in a Mechrolab 502 membrane osmometer from cyclohexane solutions at 25 OC, and are given in Tab. 1 .

For the small-angle diffraction measurements, a 12 kW rotary anode Rotaflex RU-200 generator was used as X-ray source, working at 40 kV, 200 mA. Ni-filtered CuK, radiation was used. A goniometer of the horizontal axis type was modified to contain a slit collimating system consisting of a set of Soller vertical slits, a divergence slit of 1/30" aperture placed next to the X-ray window, and a second slit of adjustable aperture incorporated just before the goniometer axis, at 240 mm distance from the target. The detector was a LET1 linear position proportional counter placed perpendicular to the X-ray beam direction, at 420 mm distance from the goniometer axis. Its linear resolution was better than 120 pm. A vacuum path and a beam stopper at 2 8 = 0 were incorporated. Background intensitks near the direct beam are suffi- ciently low to allow recordings down to s = 2,s . A - ' , at point intervals of As =

Samples were prepared in aluminium holders by moulding the molten polymer into windows of 15 x 4 x 1 mm and then crystallizing at the pertinent T, . The sample was placed at the goniometer axis perpendicularly to the incident X-ray beam. Diffraction is thus recorded in the transmission mode. In order to approach point collimation conditions and minimize distortion of the intensity

profile by the umbrella effect, the effective length of the slit collimated beam was reduced to 1 mm by vertical lead screens of that width placed just before the specimen holder. Thus, the beam cross-section was I mm x 0,l mm at the goniometer axis. In addition, the window on the detector was screened all along its length to have a 1 mm width apperture.

Fig. 1 shows a typical SAXD profile for a PDMO sample. Intensities were corrected for the Lorentz polarization factor, and the long spacing was obtained from the maximum of the corrected profile.

2 , 1 3 . 1 0 - ~ A - I .

Small-angle X-ray diffraction study of the monoclinic modification of

VI 9000-

9

a

m

L 01

rn 6000 1

c 3 0 u

3000

615

- ......

-

Fig. 1 . SAXD profile as a function of the para- meter s = 2 . sin B/I for the fraction of PDMO with M,, = 130000, crys- tallized at 36 "C. Accumu- lation time of 1000 s. CuK, radiation

............. .... ............ .................. ......I.

0 15 25 103.s

The melting temperatures were determined with a Mettler TA-3000 differential scanning calorimeter, at a heating rate of 10 K/min. The instrument was calibrated with different standards. The peak in the endotherm was taken as the melting temperature.

Results and discussion

Molecular weights, M,, and long spacings, L , for a series of five fractions of PDMO, slowly crystallized from the melt at room temperature, are given in Tab. 1, together with the crystallinity, a, deduced from dilatometric measurements9). If a two-phase model is assumed, i.e., a crystalline region plus an amorphous region, of sizes I, and I,, respectively, then:

and:

lc = a L (2)

Tab. I . crystal sizes, I , , for five fractions of PDMO crystallized at room temperature

Number-average molecular weights, a,, , long spacings, L, crystallinities, a, and

- M" L / A a I , /A

I30 000 1 I4 67 500 109 55 000 106 31 000 102 18 500 101

0,622 70,9 0,625 68.1 0,627 66,s 0,630 64,3 0,635 64.1

616 E. Perez, A. Bello, J. G . Fatou, J . A. Rausell-Colom

: 120 1 : 120 -

110 -

100 -

90 -

I

100 200 300 RA'2/(g.mol-')'/2

Fig. 2. Variation of the long spacing, L, with the square root of the molecular weight, for the different fractions of PDMO crystallized at room tem- perature

The values of I, from the above expressions are also given in Tab. 1 . The first observation to be made is that both the long spacings and crystallite sizes

are rather small. Considering that the c axis of the monoclinic unit cell3) of PDMO is 8,35 A, with f i = 97,9", then the I, values in Tab. 1 would correspond to crystallites of 8 or 9 unit cells only. This fact should be explained by the high undercoolings for the crystallization of these samples, i. e., about 50 K. It would appear that higher sizes could be attained by raising the crystallization temperature. However, it has been s h o ~ n ~ . ' ~ ) that the rate of crystallization of PDMO is very slow at any temperature, so that even for undercoolings of the order of 30 K, the times required for the completion of crystallization would be unreasonably long.

The second observation from Tab. 1 is that for the samples crystallized at room temperature, long spacings are correlated to molecular weights. The existence of an empirical relationship between the long period of polymers and the square root of their molecular weight has already been suggestedl2, 1 3 ) . This relationship was tested here for PDMO, for the range of available molecular weights. The result is shown in Fig. 2, and, in fact, the straight line of Eq. (3):

L / A = 92 + 0,062MA'2 (R = 0,98) (3)

fits the experimental values. Considering that the uncertainty in the experimental determination of the long period is estimated to be about 2 A, any conclusions from this linear relationship are rather speculative. We present it here only for the purpose of comparison. The slope appears to be very small compared with other cases like PE or PET'2v13), but the intercept for PDMO lies between those for the other two polymers.

The relationship between crystallization temperature and long spacings for PDMO was investigated here for the two higher-molecular-weight fractions. The data are given in Tab. 2, together with the values for the crystal size, I,, calculated from Eq. (2), and for their melting temperatures, T,,, . The range of crystallization temperatures was restricted to 293 to 313 K, because at lower T, some amount of the orthorhombic modification may be formed, and at higher T, crystallization cannot be attained in a

Small-angle X-ray diffraction study of the monoclinic modification o f . . . 617

Tab. 2. Melting temperatures, T,,, , long spacings, L, and crystal sizes, I , , as a function of crystallization temperature, T, , for two fractions of PDMO

T, /K L / A I , /A T , /K

(a)M, = I ~ O O O O ~ . ~ O I - ' : 293 106 297 110 301 116 305 121 309 125 313 133

(b)M, = 67500g.mol-': 293 1 02 297 104 301 112 305 116 309 120 313 125

65,9 68,4 72,l 75,3 77,8 82,7

63,7 65,O 70,O 72,5 75,O 78,l

320.4 321,5 322,8 324,2 326,l -

319,s 320,7 321,8 323,3 325,4 -

reasonable time9+l0). All the results in Tab. 2 correspond to samples crystallized at completion, except for T, = 3 13 K, where the time required for complete crystalliza- tion is unreasonably long.

It is clear again that even the highest long spacing in Tab. 2, 133 A, is rather small because of the high undercoolings involved; again the crystal size is just 9 or 10 unit cells (two monomeric units are contained along the c-axis dimension3)).

For polymers of high molecular weight, the relationship existing between crystal size and melting temperature is given by the expression:

where Afu (T,) is the free energy of fusion at the temperature of melting and Q,, the basal interfacial free energy of the mature crystal. In this equation the value for the free energy of fusion is uncertain because its variation with temperature is not usually known. As a first approximation, the enthalpy of fusion is assumed to be constant with temperature, and the value for the free energy can be taken from:

where AHu is the enthalpy of fusion of the 100% crystalline polymer. Thus, from Eqs. (2), (4) and ( 5 ) , the depression of the melting temperature of a crystal of a given finite size is:

618 E. Perez, A. Bello, J. G. Fatou, J. A. Rausell-Colom

I

from which the inverse of the crystal size is linearly related to the actual melting tem- perature, allowing to obtain 7", from the intercept and om from the slope of the line, provided that the enthalpy of fusion is known. For the two fractions of PDMO, Fig. 3 shows a plot of T , versus 1/L, since L is the variable which was actually measured in the experiment. A mean-square fitting to a straight line yields:

(7) T, = 353.4 - 3,474. lo3 . I /L (R = 0,971

with T, in K and L in A. Thus, taking the enthalpy for the monoclinic modification of PDM08) as 1 1 1 . lo6 J/m3 (2200 cal/mol) and assuming the crystallinities in Tab. 1 to be constant with T, , one gets 7", = 353 K and oec = 34-

Theoretically, a linear dependence of T, with I, as per Eq. (6) holds best for low undercoolings, as in the case of PE, where the actual melting temperatures are close to 2 . For high undercoolings, as for the case of PDMO, and in the absence of accu- rate data on the variation of AHu with temperature, an alternative approximation has been proposedI4) which may fit the experimental data mor accurately. Thus, taking for the variation of the free energy of fusion with temperature the expression:

J/mZ.

I 0 5 10

Fig. 3. Relationship between melting temperatures, T, , and long spacings, L, for the two higher-molecular-weight frac- tions of PDMO, crystallized at different T , . (0): T, vs. 1/L; ( 0 ) : T, vs. 1/(L . T,)

Small-angle X-ray diffraction study of the monoclinic modification of . . . 619

then Eq. (6) takes the form:

showing T, to be inversely related to the product T, I , . Thus, in Fig. 3 the data of T, are also plotted versus l / ( T , L ) as per Eq. (9) and, indeed, the points fit a straight line of equation:

T, = 350,8 - 1,027. l o6 . I/(T,,,L) (R = 0,97) (10)

with T, in K and L in A. The regression coefficient R of Eq. (10) is as good as in the case of the plot versus 1/L.

From the intercept and the slope, respectively, the values of c = 351 K and oec = 29. J/m2 are now obtained.

This value of compares very well with the one previously reported*) from extrapolation of the data of melting temperatures as a function of crystallization tem- perature, for samples with low levels of crystallinity. That value was 348 K. The difference of 3 K , among other po~sibilities'~), may be attributed to the extrapolation to a point far away from the experimental data. Such a small difference should not have much effect on crystallization analysis, because the actual range of available Tc comprises undercoolings always higher than 33 - 36 K.

It is worth comparing the value obtained for oec with that of the basal interfacial free energy of the nucleus, bearing in mind that both magnitudes do not have to be identical necessarily'). Thus, a temperature coefficient of 381 K was foundlo) from the growth rates of several fractions of PDMO crystallized in the monoclinic form. This coefficient is defined by nucleation theory as:

4 *en a u n K g = R AHu

where uen and B,, are the basal and lateral interfacial free energies of the nucleus, respectively.

To estimate the value of den, the usual procedure is to approximate D,, by the expression:

aun = 0,l AH,

When applied to the case of PDMO, this approximation leads to B,, = 920 J/mol and to B,, = 7890 J/mol. The conversion to area units can be made by considering the unit cell parameters of PDMO)), giving B,, = 36.

This value of B,, is significantly close to the value of oec determined in this work from the long spacings. In fact, the difference lies within the limits obtained when considering the different approximations for the free energy of melting. It seems, therefore, that the interfacial free energy of the nucleus is not very different from that for the mature crystal. Besides, the approximation Eq. (12) is rather arbitrary, and the value found for B,, depends on the accuracy of that approximation.

J/m2.

620 E. PCrez, A. Bello, J. G. Fatou, J. A. Rausell-Colom

To test the validity of this approximation, one may calculate the critical size of the nucleus, (*, obtained at a given crystallization temperature. Again, from nucleation theory:

valid for high molecular weights. Taking for Af, (T,) the value from Eq. (7), it takes the final form:

allowing the sizes of the critical nuclei to be calculated as a function of crystallization temperature. The results of this calculation, taking om = 36 * J/m*, are shown in Tab. 3 for the two values of c obtained by the two different extrapolation methods. Tab. 3, too, gives the calculated sizes corresponding to the crystallization temperatures used in this work, together with a size calculated for a T, of 333 K, only for comparative purposes, since it is experimentally unfeasible to crystallize PDMO at that temperature.

It may be seen from Tab. 3 that the 1: values calculated in this way are just slightly smaller than the sizes of the mature crystals given in Tab. 2. This means that for the high undercoolings involved, the thickening process has not proceeded too far, as expected. This also points to the conclusion that despite the low value obtained for oun , which should be a consequence of the small enthalpy of fusion of PDMO, the approximation from Eq. (1 2) appears to be valid in this case.

does not affect too much the values of I$ The reason is, again, the high undercooling. Regarding the hypothetical case of T, = 333 K (last row in Tab. 3), where the undercooling is only 17 - 20 K, the difference between the two calculated values of (*is quite significant, considerably dependent on the value chosen for 7", . For those values of &*, one would obtain long spacings as large as 200- 250 A, even without considering crystal thickening, which may be quite considerable at that undercooling. Such spacings would be comparable

It is also evident that a three degrees difference for

Tab. 3. Calculated critical sizes for the nuclei, I;, as a function of crystallization temperature, T, , for PDMO (c : equilibrium melting temp.)

T, /K l:/A

(c = 348 K) (g = 351 K)

293 297 301 305 309 313

333

48,7 51,9 5 5 3 59,9 65,2 71,7

157,3

47,O 4 9 3 53,l 57,O 61,6 67,2

133,3

Small-angle X-ray diffraction study of the monoclinic modification of. . . 62 I

to those for other polymers, but, unfortunately, crystallization of PDMO is impracticable at that temperature.

In summary, the SAXD analysis of several fractions of PDMO shows that long spacings and crystallite sizes produced in the Crystallization of this polymer from the melt are rather small due to the high undercoolings necessary for reasonable crystalli- zation times. On the other hand, the critical sizes of the nuclei predicted by nculeation theory are just slightly smaller than the actual crystallite sizes, which points t o the fact that isothermal thickening processes do not proceed too far at high undercoolings.

The financial support of the Comision Asesora de Investigacion Cientifica y TPcnica, project number 568, is gratefully acknowledged.

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