Polymer Spherulites II. Crystallization Kinetics J. M. Marentette and G. R. &own1
McGill University, 801 Sherbrooke St. W., Montreal, PQ, Canada The crystallization of small molecules generally occurs too rapidly to permit evaluation of the kinetics of the process; however, an interesting kinetic study can be carried out using polymers. Although the study of the crystallization kinetics and morphology of polymer sphemlites is a current area of research that has seen marked progress during the past decade, many of the important aspects are still the subject of heated debate. The historical development of crystallization theory, from the Turnbull-Fisher treatment ( I ) , to modern ideas of regime transitions (2) offers a means of giving students a perspective of the natural sequence of scientific thought. (For a detailed review, see ref. 3.) Radial growth rates of polymer spherulites grown in thin section can be measured with the aid of a polarized light microscope equipped with a hot stage, via time-lapse photomicroscopy or videomicroscopy, Two other features of polymer crystallization discussed in the preceding paper (41, birefringence and morphology, can be monitored eoncurrently. Kinetic Theory The growth rate of polymer spherulites, G, has been described by the classical Turnbull-Fisher equation (1)
a Gaussian-like function shown in Figure 1,where Gorepresents a preexponential factor, A E d , the activation free energy of transport of a crystallizing segment across the melt-crystal interface, A@, the activation free energy required to form a nucleus of critical size, T., qstallization temperature, and k, Boltzmann's constant. Thus, the first
exponential term often is referred to as the "transport* term while the second describes the "nucleation" behavior. The crystallization temperature influences the manner in which the macromolecular segments fold and pack together. Changes in packing lead to significant variation of the radial growth rate of spherulites as well as changes in morphology The isothermal radial growth rate of sphemlites usually is linear, a t a given T,. As the crystallization temperature is decreased below the melting temperature, T,, the rate of crystallization is nucleation-controlledand increases due to a decrease in the movement of macromolecules in the melt and an increase in the driving force. After attaining a maximum about midway between (Tm10 K) and (Tg+ 30 K), where Tgis the glass transition temperature of the polymer, the growth rate decreases with decreasing crystallization temperature due to a decrease in molecular motion; that is, the growth rate becomes diffusion-controlled. Relation of eq 1 to experimental data requires further definition of the parameters A E d and A@. The first activation energy term is similar in form to the definition of the Williams-Landel-Ferry (WLF) activation energy for viscous flow of a polymer (51,and depends on the temperature difference (T. -Tg) and two empirical constants, CI and Cz, which are approximately 1.72 x lo4 J.mo1-' and 51.6 K, respectively, for many polymers (2) where R is the ideal gas constant. If spherulite growth is assumed to proceed via twodimensional secondary surface nucleation, t h a t is, new crystalline material is deposited on the surface of the growing spherulite, the second activation energy term can he expressed as A@lkTc= KBT,'IT&T
(3)
where Tmois the equilibrium melting temperature of the polymer, and ATis the supercooling, T,'- T,. The constant Kg, defined by Kg= nb.ooJkAHv
(4)
is related to the thickness of a growth layer (i.e., stem thickness), b,; the lateral surface interfacial free energy and fold surface interfacial free energy of a polymer chain in the sphemlite, o and c&, respectively; the enthalpy of fusion per mole of repeat units of the polymer, AH,; Boltzmann's constant, k; and a parameter, n, that depends on the "regime" of crystallization. Substitution of eqs 2-4 into eq 1, followed by taking the natural logarithm of the ' resultant equation yields
In G = In Go- CIIR(Cz+ T, - Tg)- nb.oaeTm0lkAHvT&T( 5 ) Accordingly, a plot of in G + C11R(C2+ To- TJ as a function of l/TcATshould yield a straight line from which the interfacial free energies can be derived. The constants CI Figure 1. Theoretical radial growth rate of polymer spherulites, G,as a functionof crystallization temperature T,.
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539
and Cz generally are considered to be adjustable parameters that are varied to obtain the best fit (6, 7). Regime Transitions
More careful examination of the plot of the growth rate as a function of the crystallization temperature indicates that, for a number of polymers, irregularities occur a t temperatures between T', and the temperature of maximum growth rate. ~ecently,Hoffman (8j identified three "repimes" of crvstallization kinetics that OCCUPY different res o n s of the-growth rate-temperature curve, as shown in Figure 2a. In regimes I and 111, n = 4, and in regime 11, n = 2, so that a plot of in G as a function of VT,AT should resemble the plot in Figure 2b, where the ratio of the equivalent slopes of the regime I and 111segments to the slope of the regime I1 segment is 2:l. If b, and AH, are known from X-ray diffraction and calorimetry measurements, respectively, determination of the slopes of the linear segments, nb.oo.Tmo/kAH,, permits determination of the product ooe for a specific polymer and regime. The fundamental difference among the regimes is the rate a t which polymer chain sements are deposited on the crystal surfack. I" some cases, ihese regime [ransitions appear to be related to observable chan~esin morpholopv. In the highest temperature regime, regime I, afte;depo&ion of the first crystalline stem on an exposed surface, other
1fr&T (degm2) Figure 2. Theoretical plots of (a) In Gas a function of T,, and (b) [In G + C,IR(C2 + T, - Tg)]as a function of I I T d T , showing regions corresponding to regimes I, I I and I l l of nucleation theory. 540
Journal of Chemical Education
stems from the same or other macromolecules are deposited adjacent to the surface nucleus until a new layer completely covers the available surface area. As undercooling is increased. that is as T. is decreased. the rate of nucleation becomes greater than the rate of crystallization of each molecule so that multinle surface nuclei develou. and regime I1 is observed. ~ e & m e111 appears when tl;; distance between neighboring nucleation sites on a given lamella, the so-called niche separation, in regime I1 approaches the width of a stem. Strictly, regime 111is defined to apply only to temperatures as low as the temperature corresponding to the maximum growth rate. For certain polymers, a reversion from regime I to regime I1 gmwth has been observed a t very low undercoolings (9,101. Several explanations have be& proposed for such areversion (10-14): however a t present, there is insufficient experimental data to test tGese hypotheses rigorously. Thus. nucleation theorv shows that the erowth rate curve does not exhibit a simple Gaussian-like shape as originally thought. The data can be examined for the incidence of regime transitions by plotting in G as a function of T,, as in Figure 2a. A discontinuity in the slope of such a plot may indicate a regime transition. A plot of in G as a function of 1/T&T (as in Fig. 2b) provides a more rigorous test ofthe existence of regime transitions. Difficulties arise in the interpretation of these plots. For example, experimental error may lead to slopk ratios + 2:l foi an adual regime transition in the latter plot. On the other hand, a slope ratio of -2:l is not irrefutable evidence of a regime transition. Examination of spherulite morphology in the light of current nucleation theory reveals an even more complex picture. The relationship between regimes and morphology is the subject of much debate in the literature (see refs. 9,1O, 15, and 16, for example).Regime transitions have been observed in selected p&mers;and in some cases, they have been linked with morphological transitions. Studies of samples such as ci~-~&isoprene(10) and poly(ethy1ene oxide) (PEO) (9) have indicated a direct relationship; whereas, studies involving isotactic polypropylene (15) and poly(pheny1ene sulfide) (16) have yielded no evidence for such a relationship in the samples examined. As an example, the characteristics of the regime IYIII transition of PEO are discussed further below.
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A Case Study: PEO The crystallization kinetics of PEO have been studied extensivdy (see for example, refs. 9, 17-19) due to its relatively low nucleation density, measurable sphemlite growth rates and experimentafiy accessible crystallization temperature range. The feature that stands out in the case of high molecular weight PEO is the drastic increase in organization of spherulitic structure from T , = 55.0 OC to T , = 40.0 'C. Figures 3a and 3b are photographs of spherulites formed with high molecular weight PEO (MW = 5 x lo5, a fractionated Union Carbide sample) nucleated a t 40.0 ' C and subsequently crvstallized a t T,50.0 and 55.0 'C. res~ectivelv.The spkerulite centeis are similar i n texture to those of spherulites grown a t 40.0 'C (Fig. 1,Part I of this series ( 4 ) ) .The distinctly different textures of the peripheries of the spherulites arise mainly from differences in the degree of branching of the radially growing fibrils. For both of these samples, when the temperature was increased from 40.0 'C to their respective crystallization temperatures, the morphologies began to change, so that the growth habit is indeed strongly temperaturedependent. Spherulites grown a t the highest T, (55.0 'C) are highly mixed, and do not exhibit a definite Maltese cross extinction pattern characteristic of polymer spher-
tomicroscopy or videomicroscopy. The latter two methods are preferable, if available, because they provide permanent records of experiments and demand less of the vision of the observer. In order to study isothermal crystallization, samples are premelted and crystallized as described in Part I of this series. A microscope hot stage such as a Mettler FP-52 (see ref. 20 for alternatives) is required to ensure precise temperature control during crystallization. In the case of time-lapse photomicroscopy, photographs of one or more spherulites in the viewlield are obtained as the spherulites grow. In addition, a microscope stage micrometer must be photographed for calibration of the radius measurements. The radial growth rate of a given spherulite is, in general, linear in time so that it can be calculated as the slope of a plot of spherulite radius as a function of time. Isothermal growth rates measured at different temperatures can then be used to construct a plot of G as a function of T,.The properties of many crystalline polymers, including PEO, permit exploration of only a small portion of the growth rate curve; however, polymers such as isotactic polystyrene UPS) allow construction of the entire curve (6). Part 1. lsotactic Polystyrene
Isotactic polystyrene, a highly crystalline polymer that crystallizes solely in the trigonal unit cell, is readily available, and in a limited temperature range crystallizes as regular, negatively birefringent spherulites with slow, easily measured growth rates. A sample of polystyrene that is 60% isotactic (40% atactic, MW 1.78 x lo6, available from Polysciences, Inc., Warrington, PA, with worldwide distributors) can be fractionated to yield purely isotactic material. The commercial product is dissolved in methylene chloride to form a 5% solution ( d v o l ) . This solution is then added slowly to boiling methyl ethyl ketone (10% Figure 3. Spherulitesof PEO (a) T, = 50.0 'C; (b) T, = 55.0 'C vovvol). The isotactic material precipitates, while the atactic fraction remains in solution. Solvent is then removed ulites: whereas.soheru1iteserownatanintermediatetemfrom the iPS by redissolution in benzene and freeze drying, perat~re(50.0~~;rxhibitdi~orderedrnixedpatternsanda followed by heating a t 100 'C and -lo3 torr for 24 h. h i n t Maltese cross. The amearanceofs~herulitesmown Samples of iPS (T, 240 'C) are premelted at 270 'C for a t 50.0 'Cis intermediatibetween the &stinctly regular 10 min before woling to a suitable T,.Further details of birefringence of lower temperature spherulites and the sample preparation are provided in Part I of this series (4). steplike birefringence pattern of higher temperature The induction time of spherulite nucleation of iPS is typispherulites. callv several minutes. Analysis of the crystallization kinetics data of this samPhotographs of growing spherulites are obtained at varple of PEO indicates the incidence of a r e h e II/III transiious T, between -120 and 200 "C with crossed oolars and iion at approximately 50 'C. The transition from regular to withnit any compensators. At least six photogr~phsof one steplike bircfnn~encethat occurs in this series of photoor more soherulites should be taken a t wnvenient time ingraphs appears to reflect a morphological transitioi and tervals a t each T,.Amicroscope stage micrometer must be coincides with the regime I H I I transition, a correlation photomaphed a t the same ma&cation as the spherulites that supports the description of the growth process in reon ev&ifilm. lnconsistencie; in the developing process gimes I1 and 111 presented above. ks the niche separation may cause the scale to vary from film to film. on the crystal substrate approaches the width of a stem in To minimize the time required for data acquisition, four regime 11, the irregular texture of the spherulite should radius measurements can be performed on each spheruappear coarse or highly branched, until the increasing lite; a larger number (2&30) may be obtained if greater proximity of neighboring fibrils leads to a structure that is accuracy is desired. Care must be exercised in the selection so highly branched, with stems that are packed together of spherulites for radial growth rate measurements. very tightly on the growth surfaces, that the macroscopic Spherulites growing in the proximity of the edge of the structure appears to be very fine. I t is clear that in the case melt or other spherulites tend to exhibit irregular growth of PEO, this kinetic regime transition is accompanied by a rates that are significantly less than those of isolated transition in spherulite morphology spherulites growing near the center of the melt. Only Sample Experiment spherulites in the latter category should be wnsidered. Unlike the very rapid, almost instantaneous crystallizaRadius plotted as a function of time a t each T,should tion rates of many low molecular weight organic and inoryield a straight line with slope G. The growth rate of iPS ganic compounds, the isothermal radial growth rates of s~herulitesranees from -1 x lo4 to 2 x lo-' um min-'. If polymer spherulites are much slower and can, in general, a'sufficient amount of data is collected over'the trrnperabe measured directly using a microscope equipped with an ture range of interest, a plot of C; as a function of '/'.should ocular micrometer, or indirectly using time-lapse phoyield a b h s h a p e d c&&.
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Volume 70 Number 7 July 1993
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Par12. Poly(ethy1ene oxide)
Only part of the growth rate curve of PEO is readily accessible. At high T,(50'C), the nucleation rate is too slow to cause sphemlite formation, even after the sample has been at T,for several days. At lower T,(< 40 'C), nucleation oceurs very rapidly, and may begin before the sample has been cooled completely to T,;that is, crystallizatiou occurs nonisothermally. The T,range 45-54 'C merits study, though, because the regime 111111transition described above occurs within this range. Samples of PEO are premelted at 100 'C for 10 min before cooling to a selected T,.The induction time for PEO spherulites in this temperature range can be a few minutes to a few hours, depending on the purity of the polymer. To minimize experiment time, samples crystallized above 47 'C may be nucleated at 45 T,then allowed to equilibrate at the desired T,before taking photographs of the growing sphemlites. Growth rates in this T,range span several orders of magnitude, from -10 pm s-' at 45 'C to 0.1pm s-' at 54 OC, for high molecular weight PEO. The existence of a regime transition near 50 'C can be tested superficially by plotting In G as a function of T,.The variation of spherulite birefringence and morphology with T,also should be noted. The experiments described in Parts 1 and 2 would both be appropriate for an undergraduate research project and certainly would require more than a single three-hour laboratory period.
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Conclusion
The discussion of polymer crystallization from the melt lends itself to a highly visual presentation. For many observers, the most intriguing aspect of spherulite growth from the melt is the resultant morphology and birefringence. Polymers crystallize in an assortment of general
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Journal of Chemical Education
sphemlitic forms, the precise crystalline structure being determined mainlv bv the nature of the crvstallizine ~ o"l v mer and the crystkill~ationtemperature. ?he crystallization of ~olvmers~hemlitesis even more comdex than the nonspher&tic e ~ ~ s t a l l i z a t i oofn many low molecular weight species, but the former occurs at a rate that is readily ohservahle, especially in the case of iPS. Detailed inv~stixationof the crystallization kinetics of polymer sphemhtrs can lead to the observation of the phenomena known as rekme transitions, which may be related to visible changes-in morpholo&and birefringence in certain polymers. A commonplace polarized light microscope equipped with a hot stage examination of cryst& lization kinetics in addition to morphology and birefrinpence., three facets of ~olvmer crvstailizatzn that are inti" " mately related and are of current interest in polymer science and engineering and related fields.
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Literature Cited 1. TumbulLD.; Fisher, J. C. J Chem.Phys. 1846,17,71-73, 2. Hoffman, J. D.; Lauritzen, J . I . J. Ilrs. Natl. Bur. Sfd. 1961, A65,297. 3. Sperting, L. H.lnfmducflon f o P h y s l d Polymr S c i i i ; Wiley: New York, 1986: pp 1M-22.3 4. Mmntelfe, J. M.; Brawn, G. R. J. Chem Edue. 189S,70. XX&. 5 . Williams, M. L.; Landel, R. F.; Ferry, J. D . JACS 1955, 77,37013707. 6. Kennedy, M, h; ntm,G.; Bmwn, G. R.; %.-Pieire, L. E. J . Polym. Sci., Polym. Phys Edn. 1985.21.1403-1413. 7. Male=, R. 0. In X'lom-Induced CrysfaNimfion;Oardon and Breach Great Britain. 1979; pp 31-55. 8. Hoffman. J. 0.Poly-r 1985.24.346, 9. Cheng, S.Z. D.;Chen, J.;Jsnimak, J . J P o l y m r I s s O , 3 1 , 1018-1024. 10. Phillips, P. J.;Vatansever,N.MaemmalPeules 1857.20,2138-2146. 11. Hoffman, J. D.; Miller, R. L.Mocmm&cules 1 9 6 8 , 2 1 , 3 0 ~ 0 5 1 . 12, Sadler, D. M Palymr 1987,28,144CL1454. 13. Hoffman. J. D.Poly-r 1985,26,803410. 14. Goldenfeld,N. Polym. Commun. 1884.25.41-48. 15. Cheng, S . Z. 0.;Janimak, J. J.; 2hang.A. Mocmmoleeules 1960,23,298302. 16. Loving-, A J.; Davip,D. D.;Padden, F, P., J r P o l y m r l S S S , 26, 1595-1604. 17. Bewh, D. R.; Bmth, C.; Hillier, I. H.; FiekleeEur Polym. J . 1812.8, 799-807. 18. Hay, J N.;Sabir,M.Pdymr 1969,IO. 187-202. h e , F P J. P h y ~ C h , l961.65,174%1718. 19. Bamea, W J.; Luetzel, W 0.; . Hondbwk of Chemlml Micmsmpy, 4th ed,Wiley: New Yo&, 1983; pp 20. Mason, C. W 189-199.
