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Crystallization studies of isotactic polystyrene
Crystallization studies of isotactic polystyrene B. C. Edwards and P. J. Phillips Department of Materials, Queen Mary College, London E1 4NS, UK (Received 9 November 1973; revised 17 January 1974) The kinetics of lamellar crystallization in thin films of isotactic polystyrene have been determined using transmission electron microscopy. The morphological changes accompanying crystallization have also been investigated as a function of solvent, supercooling and strain prior to crystallization. Crystallization temperatures have been attained by both cooling from the melt and warming from the glass. Similar growth rates were obtained in both cases. The nucleation density of spherulites is difficult to control when warming from the glass but does depend on the solvent used in preparing the thin film. The rate of lamellar growth follows a 'bell' shaped curve versus crystallization temperature and the kinetics were analysed using the secondary nucleation theory of Hoffman and Lauritzen. The end surface free energy, ~e, of the lamellar crystals was determined using the variation of lamellar thickness with supercooling. INTRODUCTION The crystallization kinetics of polymers are commonly studied using microscopic measurements on bulk material. Techniques such as calorimetry, X-ray diffraction and thermal analysis are employed from which the degree of conversion to a new phase is obtained. These methods yield no knowledge of the fundamental physical processes involved in the nucleation and growth. A more definitive treatment of the kinetics is obtained using thin film optical microscopy which enables spherulitic growth rates to be measured. It is well established 1 that the growth of a spherulite is a cooperative process involving growth of lamellar crystals, diffusional segregation of molecular species and nucleation of new lamellar crystals. Hence, the optical measurement of spherulitic growth rate may not equal the actual growth rate of individual lamellar crystals, Direct measurements of the rate of lamellar growth were first made by Andrews et al.2 on stained films of
cis-polyisoprene, In this work the thin film technique has been extended to a linear polymer which is not a member of the polyene family. The electron microscope methods adopted provide the necessary resolution for simultaneous measurement of growth rate and lamellar thickness as a function of crystallization temperature. From these measurements the parameters governing growth may be determined. Isotactic polystyrene (iPS) was chosen for this study because of its low rate of crystallization which allows quenching to the glassy state without appreciable crystallization occurring. It is therefore possible to determine the parameters governing the lamellar crystallization from the glass as well as from the melt. One further objective was to show that the results of investigations on natural rubber are equally applicable to 'non-rubbery' polymers, EXPERIMENTAL
Materials Isotactic polystyrene (My=2.1 × 106) was supplied by the Dow Chemical Company. Prior to use the powder
was extracted for 24h using methyl ethyl ketone in a Soxhlet tube, in order to remove atactic material, and then dried.
Preparation of thin films Homogenized solutions (2 ~ by wt) of the polymer were prepared using benzene, xylene or dichlorobenzene. Thin films (80-100nm) were cast from the solutions onto water, ethylene glycol or mica surfaces, the thickness being judged by the interference colours. The films were then either: (a) crystallized from the glass at a predetermined temperature in a silicone oil bath, or (b) crystallized from the melt after a prior heat treatment of 30 min at 250°C. The effect of strain prior to crystallization was investigated by applying known extension ratios to polymer films cast onto ethylene glycol at temperatures above the glass transition temperature (90°C). The extension was applied by separation of parallel needles placed in contact with its upper surface, as described by Andrews 3. Results obtained confirm that high strains were retained by this method, presumably because of the very high molecular weight. Electron microscope studies were carried out using a JEM 7 microscope operated at 100 kV. RESULTS AND DISCUSSION
Morphology Representative electron micrographs of the morphologies obtained by crystallization from the glass and the melt are shown in Figures la and b respectively. Spherulites formed on crystallizing from the glassy state are nucleated in very high densities and are evenly distributed throughout the film. Crystallization from the melt results in spherulites which are randomly distributed and a low nucleation density is obtained. The morphologies present in Figure 1 represent different stages of spherulitic growth. The initial stage of growth of a spherulite is the formation of a single lamella crystal as shown in
POLYMER, 1974, Vol 157 June
351
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips
Figure 2. The growth of this crystal perturbs the surrounding melt so as to facilitate the nucleation of further lamellar crystals and a 'sheaf-like' bundle of lamellae is formed, as discussed later. A significant observation of the present investigation was that in unstrained films the lamellar crystals usually nucleate in the 'edge-on' orientation. This orientation is normally associated with strained films and hence it seems likely that nucleation occurs at points of stress concentration or localized strain. A similar effect was observed in thin films of natural rubber by Owen 4. In certain areas, (A, Figure 2) crystals nucleated in the 'side-on' position
"~-.. ~ ~ ~ -~
Film thickness
Figure 3 Diagrammatic representation of the 'side-on' and 'edge-on' orientations of the lamellar crystals, with respect to the electron beam
are present. A diagrammatic representation of the 'side-on' and 'edge-on' orientations is shown in
Figure 3.
Figure 1 Specimens crystallized from (a) the glass and (b) the melt at200°Cfor60min
Figure2 Specimen crystallized from the glass at 180°C for 1 min
352
P O L Y M E R , 1974, Vol 15, d u n e
The space filling mechanism of spherulitic growth is often referred to as 'branching'1. However, an inspection of high resolution micrographs (Figure 2) shows that no physical branching of the lamellae is involved but instead a new lamella crystal is nucleated some distance (up to 40nm) away from a growing lamella. Similar observations have been reported in stained films of natural rubber 4 and gutta percha 15 and the description of 'spawning' used by Owen will be adopted here. The 'branch-like' appearance of spherulites in some micrographs of this paper, e.g. Figure lb, is due to the heating effect of the electron beam producing deformation of the lamellar crystals. Figures 4a and b are micrographs obtained by: (a) focusing on an adjacent area and photographing using a low beam intensity and long exposure time, and (b) focusing on the area itself, the micrograph being taken 30 sec after the impingement of the electron beam. Irradiation by the electron beam produces deformation of the lamellar crystals and loss of resolution. Polystyrene is known to be highly resistant to radiation damage in the amorphous phase 5 and the crystalline phase is expected to be even more resistant by comparison with polyethylene. The observed effects are probably thermal caused by different coefficients of expansion of the amorphous and crystalline phases; however, other effects cannot be ruled out. Similar observations of the deformation of structure have been reported by Andrews6 for the electron irradiation of natural rubber where, however, crosslinking is the predominant product of irradiation. Spawning of new lamellar crystals is probably a general feature of all high molecular weight crystallizing polymers (this work) and lightly crosslinked 4, z5 crystallizing polymers and is a fundamental process of spherulitic growth. The growth of a spherulite from its inception as a single lamellar crystal can be described as a spawning phenomenon. It is important to emphasize at this point that the observation of spawning is critically dependent upon the lamellar orientation in the film and that thin film electron microscopy is ideally suited to study this phenomenon since nucleation of lamellar crystals usually occurs in the 'edge-on' orientation. Spawning may be explained4 as resulting from entanglements in the melt. As molecules are 'reeled in' to the
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips The non-crystallized region between the spawned and the parent crystal may be considered as a segregation of non-crystallizable species which have been rejected during crystallization. A related feature is the presence of non-crystallizable material between impinging spherulites. This may be explained as due to the segregation of low molecular weight species, which possess sufficient mobility in the melt to diffuse away radially in advance of the growing spherulite 1. This segregation may also explain the breakdown of the linear lamellar growth rate at long times as shown in Figure 7. As the spherulites approach impingement the growth rate decreases owing to increasing impurity concentration at the growth front.
a
Figure 4 (a) Area photographed immediately after focusing on an adjacent area, taken using low beam intensity; (b) same area as (a) but photographed after 30see in the beam, with increased beam intensity
b
C Figue 6 Schematic representation of the different stages of spherulitic growth, as viewed using thin film electron microscopy. (a) Single lamellar crystal; (b) spawning of new lamellar crystals; (c), (d) formation of radial spherulite by spawning mechanism
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growth front of a lamellar crystal, entanglements cause neighbouring molecules to become aligned in a direction normal to the parent lamella. These molecules can then act as nucleating sites for new lamellar crystals, as shown diagrammatically in Figure 5. The different stages of spherulitic growth are shown in Figure 6. The curved profile of the spawned crystals may be due to a concentration gradient of crystallizable material 1.
/ ~
/ , , 20 40 60 Crystallization time (rain) Figure 7 kamellar growth rate at 140°C on crystallizing from the glassy state O
POLYMER, 1974, Vol 15, June
353
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips In the case of iPS-benzene solutions, the substrate was at a temperature above the boiling point of benzene and hence more disorder would be expected in the thin film. Lamellar growth rates. Lamellar growth rates were determined as a function of crystallization temperature. The growth rate was difficult to determine using benzene as a solvent, as impingement of the spherulites occurred after short crystallization times (e.g. 20min at 140°C; 5min at 180°C). Casting above the glass transition temperature onto ethylene glycol had the desirable effect of reducing the nucleation density and hence, the growth rate could be determined over a longer time period. No difference in the growth rate was found by casting above or below the glass transition temperature although the nucleation density was significantly Table I
Nucleation densities of spherulites crystallized from the
glass
Condition
Nucleation density of spherulites cast at 21°C x 10-12(m-2)
Nucleation density of spherulites cast at 120°C x 10-~2(m-2)
~2.0 ~1.9 ~0.40
1.1-1.6 0.2 0-90
iPS-benzene iPS-xylene iPS-dichlorobenzene
o x ~ I-0 Figure 8 Specimen strained to (a) I00~/oand (b) 200~ extension
prior to crystallizationat 140°C for 15rain
Pre-straining of the films results in the production of aligned row nucleated structures similar to those reported by Andrews 3 for natural rubber. Figure 8a is a micrograph of a film strained 100 ~o prior to crystallization. Row nucleated lamellar crystals are present with an 'edge-on' orientation normal to the strain direction. On increasing the strain to 2 0 0 ~ prior to crystallization (Figure 8b) the density of lamellar crystals increases. The selected area diffraction pattern is a fibre pattern with the e-axis aligned parallel to the strain direction. The nature of strain induced crystallization will be discussed in detail in a future publication,
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Kinetics of crystallization Primary nucleation. The differences in the nucleation densities of films crystallized from the glass and from the melt were described in the previous section. The nucleation density of spherulites in films crystallized from the glass is independent of crystallization temperature over the range studied but somewhat surprisingly is dependent on the solvent from which the film was cast, the results are shown in Table 1. The difference in nucleation density of films cast at room temperature does not appear to be caused by residual solvent as evacuation for 24 h prior to crystallization had no effect. This effect could be due to differing amorphous densities, structures or strains caused by different rates of solvent evaporation. Casting the film onto a substrate above the glass transition temperature had the effect of reducing the nucleation density. These results are given in Table 1.
3,54 POLYMER, 1974, Vol 15, dune
I |
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' 120
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' ' ' 16(3 2(90 Crystallization temperature leE)
'
Graph of log growth rate, G vs. crystallization temperature. O, Present study; x, Boon et al.7; O, Suzuki and Kovacs s Figure 9
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips affected. Similarly, the solvent used had no influence on the growth rate but affected the nucleation density. A plot of the log radial growth rate versus crystallization temperature for samples crystallized from the glass is shown in Figure 9, together with the growth rates for samples crystallized from the melt obtained using optical microscopy by Boon et al. 7 and Suzuki and Kovacs s. The general features of the log G versus T graph suggest that the lamellar growth rate obeys the HoffmanLauritzen 9 secondary nucleation theory which may be expressed as: ~ ( - AF*/ [ - 4b0~(reTm/ ° = ° ° e x p I R T lexPtkTAHzATJ
CtT
(1)
x
~-
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,-
G
\
x
\
8-c
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~
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~, < 4-
o, __a° 6<
~
~
(2)
where C1 and C2 are constants generally made equal to 17.24kJ/mol and 51.6K respectively; Tg is the glass transition temperature. Substituting in equation (1) we obtain: _ AFwLr . ~ 4bocr(reTm og(./+2.303 RT = l ° g ° ° - 2 . 3 0 3 k l " A H f A T
10.0
Q:
where b0 is the monomolecular thickness, cr and (re are the side and end interfacial energies respectively between the nucleus and the melt, A H I is the heat of fusion per unit volume, Tra is the equilibrium melting point and AT is the supercooling, Hoffman and Weeks 10 equated the transport term AF* to the activation energy for viscous flow, which has a temperature dependence derived from the WLF equation of: AF* = AFwLF = C2 + T ~ Tg
x/ [
(3)
To ascertain if the lamellar growth rate of iPS can be described using the above approximation, the quantity log G+(AFwLF/2.303RT) is plotted against TIn~TAT. If the growth rate can be described by equation (3) then the plot is a straight line with a slope of -(4bo(r(re/ 2.303kAHf). Such a plot is shown in Figure 10. With C2=51"6K it was not possible to fit the growth rate data to the above equation. However, if (72 is chosen to be 81K, as found by calorimetry measurements 1~, a reasonable straight line is obtained. From the slope of the line, with b0=0.55nm, A H =91.1 x 106J/m 3, ~(re was calculated to be 153.0× 10-rJ2/m4, by taking b0 as the distance between adjacent molecular layers in the [110] direction. This plot yields a value of 4.7 × 10s /~m/h for Go. Using the plot suggested by Suzuki and Kovacs s, l o g G + ( 3 4 5 - 2 / T - T ~ o ) versus Tm/TAT, with Too= 333"5K, Tm=515"2K; an approximate linear relationship was obtained from which a value of (r(re= 140x 10-rJ2/m 4 was obtained; however, the data do not fit this plot at high and low values of ATas well they do the HoffmanWeeks equation, The lamellar growth rates of specimens crystallized from the melt were found to be in good agreement with those obtained from the glassy state. This indicates that the growth rate is independent of the thermal history and depends only on the crystallization temperature. A similar result has been found by Magil112 using optical microscopy, for poly(tetramethyl-p-silphenylene) siloxane,
4.~
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Tm/TATxIO2(K-I}
40
Figure I0 Graph of log G+AFwLF/2.303RT versus Tm/TAT. x, C2=51"6K; ©, C~=81-0K
Lamellar thickness. One of the predictions of secondary nucleation theory is that lamellar thickness,/, should be inversely proportional to the supercooling. This has now been shown to be the case for a number of polymers including natural rubber 2 and polyethylene 13. The variation of lamellar thickness of isotactic polystyrene with reciprocal supercooling is shown in Figure 11 together with the variation of X-ray long period by Blais and Manley ~4. A value of (re of 28"8 × 10-3J/m 2 has been calculated from the slope using the equation I=2creTm/AHAT and values of Tm=515"2K and AH=91-1 × 106J/m 3. Combining this value with the earlier derived values of the product or(re, values of 5.3 × 10-3 and 4.9 × 10-3 J/m 2 have been calculated for or. (Values of (re of 32.0× 10 -3 and 26.6× 10-3J/m 2 were obtained by Suzuki and Kovacs assuming (r=4.16× 10-3 and 5-0×10-3J/m 2 respectively). It is useful to compare these values of ~ and (r~ with the values for other polymeric systems (Table 2). It is important to emphasize that the values of (re quoted in this Table were calculated from the measured lamellar thickness, using transmission electron microscopy 2, ~5 or from X-ray long period 16. These values of (r and (re are based on experimental measurements and do not rely on any empirical formulation of (r. An approximately linear relationship between (r and (re was found (Figure 12) with the ratio (re/(r equal to 5.8 + 0.8. The values for natural rubber calculated were for (110) and (120) growth faces. POLYMER, 1974, Vol 15, dune
355
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips 12 x~ 24.0
~e 8
b 4 A
20.0
x I
O
15
I
I
30 (:re X 103(j/m 2)
I
45
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x
x
xx
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80
,
0
,
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4'0
6"0
A 7"-I x IO2{ K "1 ) Figure 11 Graph of lamellar thickness vs. reciprocal supercooling. x , long period of Blais and Manley14;O, present study
Table 2 Surface free energies obtained from investigations of growth rates and lamellar thicknesses qxl02O a
Polymer
(dS/m4)
Isotactic polystyrene (present study) Natural rubber s assuming (120)
153 140 300 251
growth face Gutta percha15: low melting form
247
high melting form
Polyethylene z6
492
540
(d/m s) (d/m s) 28.8 28.8 35.2
5"3
35.2
7.13
43.5
7.0
58.0
0.06
4.9 8.5
(m 2)
fold)
of natural rubber and gutta percha (low melting form) are lower than that for polyethylene presumably owing to a less constrained system resulting from a larger number of bonds in the loop. The high value of q is obtained for iPS due to the steric hindrance of the phenyl groups causing a highly constrained system. Assuming the same number of monomer units/fold (i.e. 2) for both crystal structures of gutta percha, the high melting form ( H M F ) has the larger value of q because the larger value of a0 produces a more constrained chain, where a0 is the monomolecular width. (Gutta percha LMF: ao=O'426nm, bo=O.437nm; HMF: ao= 0.479 nm, b0 = 0.493 nm.) From the above analysis it may be inferred that
q/2Ao¢
is n e a r l y c o n s t a n t a n d e q u a l t o 4.8 + 0.8. T h i s
in itself is not unreasonable since the factors (q/2Ao) and ~r will both be determined by the molecular structure of the chain involved. Since all of the polymers considered are n o n - p o l a r the p r o p e r t i e s d e t e r m i n i n g these p a r a m e t e r s will be those o f simple van d e r W a a l ' s forces a n d steric hindrance. To a first a p p r o x i m a t i o n it is, therefore, possible to o b t a i n a value for ere f r o m kinetic d a t a b y substituting ~ / 5 . 8 for ~ e in the
Hoffman-Lauritzen expression.
70.5 70.5
3.32 3.37
27.69
1.48
27.69
1.55
ACKNOWLEDGEMENTS
20.15
1.47
We are grateful to Professor E. H. Andrews for many valuable discussions and to the SRC for support through a Research Grant.
9.7
23.59
2.27
0"009
18.3
1.85
REFERENCES
The value of the surface free energy ~e of a folded chain nucleus is related to the work required t o f o r m a f°ldX7" ere= ere0+ 2 0
where q is the work required to form a fold, A0 is the cross-sectional area of the polymer molecule and ere0 is the c o n t r i b u t i o n to ~e due t o factors other than folding. To a reasonable approximation ~e0 can be equated to or. • •"
ere= 1 4- q_ ~ "-2A0~
(4)
Values of q obtained using this relationship are shown in Table 2. q contains an important contribution from the internal rotational potential of a t o m s o r groups in the loop and the trends obtained are consistent with the trends in the molecular structure. The values of q
356
POLYMER, 1974, Vol 15, dune
1 Keith, H. D. and Padden, F. J. Jr,/. ,4ppl. Phys. 1964, 35, 1270 2 Andrews, E. H., et al. Proc. R. Soc. (.4) 1971, 324, 79 3 Andrews, E. H. Proe. R. Soc. (.4) 1964, 277, 562 4 0 w e n , P. J. PhD Thesis University of London, 1970 5 Charlesby, A. 'Atomic Radiation and Polymers', Pergamon, New York, 1960 6 Andrews, E. H. Proc. R. Soc. (A) 1962, 270, 232 7 Boon, J., et al. J. Polym. Sci. (.4-2) 1968, 6, 1791 8 Suzuki, T. and Kovacs, A. J. Polym. J. 1970, 1, 82 9 Lauritzen, J. I. and Hoffman, J. D. J. Res. Nat. Bur. Stand.
1960, 64A, 1 10 11 12 13 14
Hoffman, J. D. and Weeks, J. J. J. Chem. Phys. 1962, 37, 1723 Karasz, F. E., et al. J. Phys. Chem. 1965, 69, 2657 Magill, J. H. J..4ppl. Phys. 1964, 35, 3249 Kavesh, S. and Schultz, J. M. J. Polym. Sci. (A-2) 1971, 9, 85 Blais, J. J. B. P. and Manley, R. St John. J. MacromoL Sci.
(B) 1967, 1, 525
15 Ong Eng Long, PhD Thesis, University of London, 1973 16~Gornick, F. and Hoffman, J. D. lnd. Eng. Chem. 1966, 58, 41 17 Hoffman, J. D. and Lauritzen, J. L Jr J. Res. Nat. Bur. Stand.
1961, 65A, 297
cis-polyisoprene, In this work the thin film technique has been extended to a linear polymer which is not a member of the polyene family. The electron microscope methods adopted provide the necessary resolution for simultaneous measurement of growth rate and lamellar thickness as a function of crystallization temperature. From these measurements the parameters governing growth may be determined. Isotactic polystyrene (iPS) was chosen for this study because of its low rate of crystallization which allows quenching to the glassy state without appreciable crystallization occurring. It is therefore possible to determine the parameters governing the lamellar crystallization from the glass as well as from the melt. One further objective was to show that the results of investigations on natural rubber are equally applicable to 'non-rubbery' polymers, EXPERIMENTAL
Materials Isotactic polystyrene (My=2.1 × 106) was supplied by the Dow Chemical Company. Prior to use the powder
was extracted for 24h using methyl ethyl ketone in a Soxhlet tube, in order to remove atactic material, and then dried.
Preparation of thin films Homogenized solutions (2 ~ by wt) of the polymer were prepared using benzene, xylene or dichlorobenzene. Thin films (80-100nm) were cast from the solutions onto water, ethylene glycol or mica surfaces, the thickness being judged by the interference colours. The films were then either: (a) crystallized from the glass at a predetermined temperature in a silicone oil bath, or (b) crystallized from the melt after a prior heat treatment of 30 min at 250°C. The effect of strain prior to crystallization was investigated by applying known extension ratios to polymer films cast onto ethylene glycol at temperatures above the glass transition temperature (90°C). The extension was applied by separation of parallel needles placed in contact with its upper surface, as described by Andrews 3. Results obtained confirm that high strains were retained by this method, presumably because of the very high molecular weight. Electron microscope studies were carried out using a JEM 7 microscope operated at 100 kV. RESULTS AND DISCUSSION
Morphology Representative electron micrographs of the morphologies obtained by crystallization from the glass and the melt are shown in Figures la and b respectively. Spherulites formed on crystallizing from the glassy state are nucleated in very high densities and are evenly distributed throughout the film. Crystallization from the melt results in spherulites which are randomly distributed and a low nucleation density is obtained. The morphologies present in Figure 1 represent different stages of spherulitic growth. The initial stage of growth of a spherulite is the formation of a single lamella crystal as shown in
POLYMER, 1974, Vol 157 June
351
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips
Figure 2. The growth of this crystal perturbs the surrounding melt so as to facilitate the nucleation of further lamellar crystals and a 'sheaf-like' bundle of lamellae is formed, as discussed later. A significant observation of the present investigation was that in unstrained films the lamellar crystals usually nucleate in the 'edge-on' orientation. This orientation is normally associated with strained films and hence it seems likely that nucleation occurs at points of stress concentration or localized strain. A similar effect was observed in thin films of natural rubber by Owen 4. In certain areas, (A, Figure 2) crystals nucleated in the 'side-on' position
"~-.. ~ ~ ~ -~
Film thickness
Figure 3 Diagrammatic representation of the 'side-on' and 'edge-on' orientations of the lamellar crystals, with respect to the electron beam
are present. A diagrammatic representation of the 'side-on' and 'edge-on' orientations is shown in
Figure 3.
Figure 1 Specimens crystallized from (a) the glass and (b) the melt at200°Cfor60min
Figure2 Specimen crystallized from the glass at 180°C for 1 min
352
P O L Y M E R , 1974, Vol 15, d u n e
The space filling mechanism of spherulitic growth is often referred to as 'branching'1. However, an inspection of high resolution micrographs (Figure 2) shows that no physical branching of the lamellae is involved but instead a new lamella crystal is nucleated some distance (up to 40nm) away from a growing lamella. Similar observations have been reported in stained films of natural rubber 4 and gutta percha 15 and the description of 'spawning' used by Owen will be adopted here. The 'branch-like' appearance of spherulites in some micrographs of this paper, e.g. Figure lb, is due to the heating effect of the electron beam producing deformation of the lamellar crystals. Figures 4a and b are micrographs obtained by: (a) focusing on an adjacent area and photographing using a low beam intensity and long exposure time, and (b) focusing on the area itself, the micrograph being taken 30 sec after the impingement of the electron beam. Irradiation by the electron beam produces deformation of the lamellar crystals and loss of resolution. Polystyrene is known to be highly resistant to radiation damage in the amorphous phase 5 and the crystalline phase is expected to be even more resistant by comparison with polyethylene. The observed effects are probably thermal caused by different coefficients of expansion of the amorphous and crystalline phases; however, other effects cannot be ruled out. Similar observations of the deformation of structure have been reported by Andrews6 for the electron irradiation of natural rubber where, however, crosslinking is the predominant product of irradiation. Spawning of new lamellar crystals is probably a general feature of all high molecular weight crystallizing polymers (this work) and lightly crosslinked 4, z5 crystallizing polymers and is a fundamental process of spherulitic growth. The growth of a spherulite from its inception as a single lamellar crystal can be described as a spawning phenomenon. It is important to emphasize at this point that the observation of spawning is critically dependent upon the lamellar orientation in the film and that thin film electron microscopy is ideally suited to study this phenomenon since nucleation of lamellar crystals usually occurs in the 'edge-on' orientation. Spawning may be explained4 as resulting from entanglements in the melt. As molecules are 'reeled in' to the
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips The non-crystallized region between the spawned and the parent crystal may be considered as a segregation of non-crystallizable species which have been rejected during crystallization. A related feature is the presence of non-crystallizable material between impinging spherulites. This may be explained as due to the segregation of low molecular weight species, which possess sufficient mobility in the melt to diffuse away radially in advance of the growing spherulite 1. This segregation may also explain the breakdown of the linear lamellar growth rate at long times as shown in Figure 7. As the spherulites approach impingement the growth rate decreases owing to increasing impurity concentration at the growth front.
a
Figure 4 (a) Area photographed immediately after focusing on an adjacent area, taken using low beam intensity; (b) same area as (a) but photographed after 30see in the beam, with increased beam intensity
b
C Figue 6 Schematic representation of the different stages of spherulitic growth, as viewed using thin film electron microscopy. (a) Single lamellar crystal; (b) spawning of new lamellar crystals; (c), (d) formation of radial spherulite by spawning mechanism
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/
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X
growth front of a lamellar crystal, entanglements cause neighbouring molecules to become aligned in a direction normal to the parent lamella. These molecules can then act as nucleating sites for new lamellar crystals, as shown diagrammatically in Figure 5. The different stages of spherulitic growth are shown in Figure 6. The curved profile of the spawned crystals may be due to a concentration gradient of crystallizable material 1.
/ ~
/ , , 20 40 60 Crystallization time (rain) Figure 7 kamellar growth rate at 140°C on crystallizing from the glassy state O
POLYMER, 1974, Vol 15, June
353
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips In the case of iPS-benzene solutions, the substrate was at a temperature above the boiling point of benzene and hence more disorder would be expected in the thin film. Lamellar growth rates. Lamellar growth rates were determined as a function of crystallization temperature. The growth rate was difficult to determine using benzene as a solvent, as impingement of the spherulites occurred after short crystallization times (e.g. 20min at 140°C; 5min at 180°C). Casting above the glass transition temperature onto ethylene glycol had the desirable effect of reducing the nucleation density and hence, the growth rate could be determined over a longer time period. No difference in the growth rate was found by casting above or below the glass transition temperature although the nucleation density was significantly Table I
Nucleation densities of spherulites crystallized from the
glass
Condition
Nucleation density of spherulites cast at 21°C x 10-12(m-2)
Nucleation density of spherulites cast at 120°C x 10-~2(m-2)
~2.0 ~1.9 ~0.40
1.1-1.6 0.2 0-90
iPS-benzene iPS-xylene iPS-dichlorobenzene
o x ~ I-0 Figure 8 Specimen strained to (a) I00~/oand (b) 200~ extension
prior to crystallizationat 140°C for 15rain
Pre-straining of the films results in the production of aligned row nucleated structures similar to those reported by Andrews 3 for natural rubber. Figure 8a is a micrograph of a film strained 100 ~o prior to crystallization. Row nucleated lamellar crystals are present with an 'edge-on' orientation normal to the strain direction. On increasing the strain to 2 0 0 ~ prior to crystallization (Figure 8b) the density of lamellar crystals increases. The selected area diffraction pattern is a fibre pattern with the e-axis aligned parallel to the strain direction. The nature of strain induced crystallization will be discussed in detail in a future publication,
o.5 lid
[ O.(
×
/
/,
A
i
~E o, o,-0.5
• |
Kinetics of crystallization Primary nucleation. The differences in the nucleation densities of films crystallized from the glass and from the melt were described in the previous section. The nucleation density of spherulites in films crystallized from the glass is independent of crystallization temperature over the range studied but somewhat surprisingly is dependent on the solvent from which the film was cast, the results are shown in Table 1. The difference in nucleation density of films cast at room temperature does not appear to be caused by residual solvent as evacuation for 24 h prior to crystallization had no effect. This effect could be due to differing amorphous densities, structures or strains caused by different rates of solvent evaporation. Casting the film onto a substrate above the glass transition temperature had the effect of reducing the nucleation density. These results are given in Table 1.
3,54 POLYMER, 1974, Vol 15, dune
I |
x I o
-I.O
o
-I. 5 o -2.0 80
'
' 120
'
' ' ' 16(3 2(90 Crystallization temperature leE)
'
Graph of log growth rate, G vs. crystallization temperature. O, Present study; x, Boon et al.7; O, Suzuki and Kovacs s Figure 9
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips affected. Similarly, the solvent used had no influence on the growth rate but affected the nucleation density. A plot of the log radial growth rate versus crystallization temperature for samples crystallized from the glass is shown in Figure 9, together with the growth rates for samples crystallized from the melt obtained using optical microscopy by Boon et al. 7 and Suzuki and Kovacs s. The general features of the log G versus T graph suggest that the lamellar growth rate obeys the HoffmanLauritzen 9 secondary nucleation theory which may be expressed as: ~ ( - AF*/ [ - 4b0~(reTm/ ° = ° ° e x p I R T lexPtkTAHzATJ
CtT
(1)
x
~-
\
,-
G
\
x
\
8-c
\ \
~
\
~, < 4-
o, __a° 6<
~
~
(2)
where C1 and C2 are constants generally made equal to 17.24kJ/mol and 51.6K respectively; Tg is the glass transition temperature. Substituting in equation (1) we obtain: _ AFwLr . ~ 4bocr(reTm og(./+2.303 RT = l ° g ° ° - 2 . 3 0 3 k l " A H f A T
10.0
Q:
where b0 is the monomolecular thickness, cr and (re are the side and end interfacial energies respectively between the nucleus and the melt, A H I is the heat of fusion per unit volume, Tra is the equilibrium melting point and AT is the supercooling, Hoffman and Weeks 10 equated the transport term AF* to the activation energy for viscous flow, which has a temperature dependence derived from the WLF equation of: AF* = AFwLF = C2 + T ~ Tg
x/ [
(3)
To ascertain if the lamellar growth rate of iPS can be described using the above approximation, the quantity log G+(AFwLF/2.303RT) is plotted against TIn~TAT. If the growth rate can be described by equation (3) then the plot is a straight line with a slope of -(4bo(r(re/ 2.303kAHf). Such a plot is shown in Figure 10. With C2=51"6K it was not possible to fit the growth rate data to the above equation. However, if (72 is chosen to be 81K, as found by calorimetry measurements 1~, a reasonable straight line is obtained. From the slope of the line, with b0=0.55nm, A H =91.1 x 106J/m 3, ~(re was calculated to be 153.0× 10-rJ2/m4, by taking b0 as the distance between adjacent molecular layers in the [110] direction. This plot yields a value of 4.7 × 10s /~m/h for Go. Using the plot suggested by Suzuki and Kovacs s, l o g G + ( 3 4 5 - 2 / T - T ~ o ) versus Tm/TAT, with Too= 333"5K, Tm=515"2K; an approximate linear relationship was obtained from which a value of (r(re= 140x 10-rJ2/m 4 was obtained; however, the data do not fit this plot at high and low values of ATas well they do the HoffmanWeeks equation, The lamellar growth rates of specimens crystallized from the melt were found to be in good agreement with those obtained from the glassy state. This indicates that the growth rate is independent of the thermal history and depends only on the crystallization temperature. A similar result has been found by Magil112 using optical microscopy, for poly(tetramethyl-p-silphenylene) siloxane,
4.~
o
'
'
2o
'
Tm/TATxIO2(K-I}
40
Figure I0 Graph of log G+AFwLF/2.303RT versus Tm/TAT. x, C2=51"6K; ©, C~=81-0K
Lamellar thickness. One of the predictions of secondary nucleation theory is that lamellar thickness,/, should be inversely proportional to the supercooling. This has now been shown to be the case for a number of polymers including natural rubber 2 and polyethylene 13. The variation of lamellar thickness of isotactic polystyrene with reciprocal supercooling is shown in Figure 11 together with the variation of X-ray long period by Blais and Manley ~4. A value of (re of 28"8 × 10-3J/m 2 has been calculated from the slope using the equation I=2creTm/AHAT and values of Tm=515"2K and AH=91-1 × 106J/m 3. Combining this value with the earlier derived values of the product or(re, values of 5.3 × 10-3 and 4.9 × 10-3 J/m 2 have been calculated for or. (Values of (re of 32.0× 10 -3 and 26.6× 10-3J/m 2 were obtained by Suzuki and Kovacs assuming (r=4.16× 10-3 and 5-0×10-3J/m 2 respectively). It is useful to compare these values of ~ and (r~ with the values for other polymeric systems (Table 2). It is important to emphasize that the values of (re quoted in this Table were calculated from the measured lamellar thickness, using transmission electron microscopy 2, ~5 or from X-ray long period 16. These values of (r and (re are based on experimental measurements and do not rely on any empirical formulation of (r. An approximately linear relationship between (r and (re was found (Figure 12) with the ratio (re/(r equal to 5.8 + 0.8. The values for natural rubber calculated were for (110) and (120) growth faces. POLYMER, 1974, Vol 15, dune
355
Crystallization studies of isotactic polystyrene: B. C. Edwards and P. J. Phillips 12 x~ 24.0
~e 8
b 4 A
20.0
x I
O
15
I
I
30 (:re X 103(j/m 2)
I
45
I
I
I
60
,t'-
-~ ~E .~
_~
I
16"0
"~ e o "
t
Figure 12 Graph of surface free energy ~ versus end surface free energy oe
x
x
xx
12"O
80
,
0
,
,
,
2.0
,
4'0
6"0
A 7"-I x IO2{ K "1 ) Figure 11 Graph of lamellar thickness vs. reciprocal supercooling. x , long period of Blais and Manley14;O, present study
Table 2 Surface free energies obtained from investigations of growth rates and lamellar thicknesses qxl02O a
Polymer
(dS/m4)
Isotactic polystyrene (present study) Natural rubber s assuming (120)
153 140 300 251
growth face Gutta percha15: low melting form
247
high melting form
Polyethylene z6
492
540
(d/m s) (d/m s) 28.8 28.8 35.2
5"3
35.2
7.13
43.5
7.0
58.0
0.06
4.9 8.5
(m 2)
fold)
of natural rubber and gutta percha (low melting form) are lower than that for polyethylene presumably owing to a less constrained system resulting from a larger number of bonds in the loop. The high value of q is obtained for iPS due to the steric hindrance of the phenyl groups causing a highly constrained system. Assuming the same number of monomer units/fold (i.e. 2) for both crystal structures of gutta percha, the high melting form ( H M F ) has the larger value of q because the larger value of a0 produces a more constrained chain, where a0 is the monomolecular width. (Gutta percha LMF: ao=O'426nm, bo=O.437nm; HMF: ao= 0.479 nm, b0 = 0.493 nm.) From the above analysis it may be inferred that
q/2Ao¢
is n e a r l y c o n s t a n t a n d e q u a l t o 4.8 + 0.8. T h i s
in itself is not unreasonable since the factors (q/2Ao) and ~r will both be determined by the molecular structure of the chain involved. Since all of the polymers considered are n o n - p o l a r the p r o p e r t i e s d e t e r m i n i n g these p a r a m e t e r s will be those o f simple van d e r W a a l ' s forces a n d steric hindrance. To a first a p p r o x i m a t i o n it is, therefore, possible to o b t a i n a value for ere f r o m kinetic d a t a b y substituting ~ / 5 . 8 for ~ e in the
Hoffman-Lauritzen expression.
70.5 70.5
3.32 3.37
27.69
1.48
27.69
1.55
ACKNOWLEDGEMENTS
20.15
1.47
We are grateful to Professor E. H. Andrews for many valuable discussions and to the SRC for support through a Research Grant.
9.7
23.59
2.27
0"009
18.3
1.85
REFERENCES
The value of the surface free energy ~e of a folded chain nucleus is related to the work required t o f o r m a f°ldX7" ere= ere0+ 2 0
where q is the work required to form a fold, A0 is the cross-sectional area of the polymer molecule and ere0 is the c o n t r i b u t i o n to ~e due t o factors other than folding. To a reasonable approximation ~e0 can be equated to or. • •"
ere= 1 4- q_ ~ "-2A0~
(4)
Values of q obtained using this relationship are shown in Table 2. q contains an important contribution from the internal rotational potential of a t o m s o r groups in the loop and the trends obtained are consistent with the trends in the molecular structure. The values of q
356
POLYMER, 1974, Vol 15, dune
1 Keith, H. D. and Padden, F. J. Jr,/. ,4ppl. Phys. 1964, 35, 1270 2 Andrews, E. H., et al. Proc. R. Soc. (.4) 1971, 324, 79 3 Andrews, E. H. Proe. R. Soc. (.4) 1964, 277, 562 4 0 w e n , P. J. PhD Thesis University of London, 1970 5 Charlesby, A. 'Atomic Radiation and Polymers', Pergamon, New York, 1960 6 Andrews, E. H. Proc. R. Soc. (A) 1962, 270, 232 7 Boon, J., et al. J. Polym. Sci. (.4-2) 1968, 6, 1791 8 Suzuki, T. and Kovacs, A. J. Polym. J. 1970, 1, 82 9 Lauritzen, J. I. and Hoffman, J. D. J. Res. Nat. Bur. Stand.
1960, 64A, 1 10 11 12 13 14
Hoffman, J. D. and Weeks, J. J. J. Chem. Phys. 1962, 37, 1723 Karasz, F. E., et al. J. Phys. Chem. 1965, 69, 2657 Magill, J. H. J..4ppl. Phys. 1964, 35, 3249 Kavesh, S. and Schultz, J. M. J. Polym. Sci. (A-2) 1971, 9, 85 Blais, J. J. B. P. and Manley, R. St John. J. MacromoL Sci.
(B) 1967, 1, 525
15 Ong Eng Long, PhD Thesis, University of London, 1973 16~Gornick, F. and Hoffman, J. D. lnd. Eng. Chem. 1966, 58, 41 17 Hoffman, J. D. and Lauritzen, J. L Jr J. Res. Nat. Bur. Stand.
1961, 65A, 297