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The crystallization of polydecamethylene terephthalate
The
Crystallization of Polydecamethylene Terephthalate A. SnARPLES and F. L. SwiwroN*
A study has been made o[ the crystallization o[ polydecamethylene terephthalate at various temperatures. The interpretation of the results is uncomplicated by tile presence of any detectable secondary stage but the process nevertheless shows several unusual [eatures. First, although the majority o[ the crystallization con[orms to an Avrami relation, the values of the exponent, n, are [factional, whereas current theory requires integral values. Secondly, an additional process intervenes towards the end o[ the crystallization to cause a decrease in the normal rate. It is possible that this is related to an observed decrease in the nucleation rate. Finally, a pronounced change in behaviour takes place about 15°C below the melting point causing a 30 per cent decrease in the density change during crystallization to occur Jor a temperature lowering o[ only 0"5°C. The kinetic behaviour also changes on passing through this point.
IN GENERAL,the crystallization of high polymers is considered to involve the formation of nuclei in the supercooled melt, followed by the growth of these centres to form rods, discs or spheres. The decrease in volume of the system resulting from the formation of the more dense, crystalline phase, can be related to time by an equation of the form 1-a (V, - Voo)/(Vo - V,,~) = exp ( - zt") (1) where V, is the volume of the system at time t, z is constant for a given temperature, and n is an integer having a value of 1, 2, 3 or 4. Usually a process referred to as secondary crystallization* intervenes to complicate the interpretation of the data, and although methods have been proposed to allow for this effect5, it was considered desirable to study the behaviour of a polymer where it is absent, especially in view of the fact that recent results on polyethylene5 have indicated that the integral values of n predicted by existing theory are not always obtained. Polydecamethylene terephthalate shows no detect~ible secondary crystallization, and an account of its behaviour is given below. EXPERIMENTAL
Materials
The polymer was prepared by the method of Flory, Bedon and Keefe#. The equilibrium melting temperature obtained by dilatometry using slow (1°C/24 h) rates of heating was found to be 137-5°C, in good agreement with Flory's value of 138°C, although the values of 0"968~ cm3/g for the specific volume of the liquid polymer at 150°C is in rather poor agreement with that of 0.956 cm 3/g quoted by Flory. The melt viscosity of the liquid polymer was measured at 255°C and was found to be 740 poise. According to Flory et aL e this indicates that the number average molecular weight is greater than 10 000, and that the true equilibrium melting point will not be depressed to any extent by the number of chain ends present in the melt. *Present address: Chemistry Department, Royal College of Science and Technology,
119
Glasgow, C.l.
A. SHARPLES and F. L. SWINTON
Dilatometry Molten polydecamethylene terephthalate has the property of wetting glass, so that when the temperature is lowered and the polymer crystallized, the resultant volume contraction invariably shatters the containing tube if this is made of glass. The dilatometers used in the present study were consequently constructed with stainless steel bodies, connected to the measuring capillaries through flanged joints, which were lightly greased with high melting silicone grease to render them vacuum-tight. The measuring capillaries were made of 2 mm internal diameter precision-bore Veridia tubing, The dilatometers were filled with weighed amounts of polymer and mercury in the usual way, under Vacuum 4. Approximately 10g of dried polymer was used for each dilatometer, and the height of the mercury column as a function of time and temperature was measured to + 0-01 mm using a 1 m cathetometer manufactured by the Precision Tool and Instrument Co. The crystallizations were carried out in an oil thermostat of conventional design, the temperature control of which was +0'03°C at the experimental temperatures. Before each crystallization run, the sample was melted at 180 ° to 190°C for 30min, As an indication of the extent of the volume change measured, the specific volume of the polymer at 120'00°C before crystallization is 0"9527o cm 3/g, while after crystallization at this temperature the value is 0-91136 cm ~/g.
Microscopy Measurements of nucleation and growth rates were made using a 10× micrometer eyepiece and a ~ in. objective. Temperature control was effected with a Ktifler hot-stage, thermostatted to + 0" 1 °C. Films of polymer approximately 10~t thick were prepared by pressing the molten material between glass slides and cover slips, but even when precautions were taken to avoid degradation, the resultant nucleation densities were very variable, and often were so high that an unresolvable birefringent mass was formed 7. The results reported were obtained using a sample with resolvable spherulitic structure prepared under similar conditions to those involved in the dilatometry. Approximately 1 mg was heated on an open glass slide in vacuo at 170°C for 15 min. The sample was then cooled, a cover slip was placed in position, and the slide was reheated to 2000C prior to pressing to form a suitable film. Subsequent measurements were made by first melting at 160°C for 5 min and then lowering the temperature to that required for crystallization. Prior melting at 140°C and 300"C produced identical results. The mean thickness of the specimen was determined from the known weight and the measured area. Variation in thickness across the specimen was assessed by differential focusing under high magnification, and was found to be less than 20 per cent. This was considerably less than the variation in nucleation density observed to occur from one sample to another. RESULTS
Dilatometry Relative values of the volume change occurring in a crystallizing polymer can in practice be determined from dilatometric heights, so that equation (1) can be written (h,-h,o)/(ho - hoo)= exp (-ztO (2) 120
THE CRYSTALLIZATION OF POLYDECAMETHYLENE TEREPHTHALATE
~ 00
211111 ,
50(
-
45C101
122,95
-
10 2
10 3
t rain Figure 1--Cryst~tllization of polydecamethylene terephthalate at various temperatures. Dilatometric height versus log (time) where ht is the dilatometric height at time t. Results for ht obtained during the crystallization of polydecamethylene terephthalate at various temperatures, are plotted 3 in Figure 1 against log t and it is immediately apparent that, for example at 118°C, the final value, i.e. k,~, is constant (to within 0' 1 per cent of the total change, h 0 - h~) for a period of time one order greater than that involving the primary crystallization. Thus, secondary crystallization', which involves a continual, slow decrease in volume after the completion of the primary stage, is effectively absent from this polymer. The unexpected feature of the results is the anomalous volume change which takes place at ca. 122'8°C. This can be seen more readily in Figure 2, where the change in dilatometer height occurring during crystallization is plotted as a function of crystallization temperature: Above 122"95°C and below 122-50°C the volume change increases with decreasing temperature, as is to be expected from the different expansion coefficients of liquid and ~5oI E E
Figure 2--Volume change occurring during crystallization, plotted as a function of to temperature ~: 0
I
I
I
120
I
I
Temperature
121
~
I
1
I
125 °C
A. SHARPLES and F. L. SWINTON
~. 600 E E
Figure 3--I.ntervention of pro-
55O
cess causing decrease in crystallization rate--122.00°C. B and C: experimental plots. A: theoretical plot, assuming continuation of early stages of B and C according to equation (2)
500
c
101
102 t
rain
solid phases. Between these two temperatures, however, there is a displacement of about 30 per cent. No obvious explanation or precedent is available to account for this effect, but it immediately raises the question of whether the kinetics are also affected on passing through this transition. In the first instance it was noted that an obvious discontinuity is present at all temperatures in the crystallization plots. This is illustrated by the results for 122"00°C (Figure 3). Deviations from the extrapolated curve A are apparent in two successive experiments, B and C, and it is evident that some process intervenes in an irreproducible manner to slow down the normal course of crystallization. In most of the isotherms the discontinuity does not occur until the crystallization is about 80 per cent complete as t
min
102
103
7%
. /.
100
123.7 °cV 80% ! •
conformity to equation (2) for majority of crystallization
I
! I
Figure 4--Avrami plots showing
J
I 4 1
I
!
!
i
I
I
/"
120.95oc
I
101 t
102 rain
122
THE CRYSTALLIZATION OF POLYDECAMETHYLENE TEREPHTHALATE Table 1. Crystallization rate parameters for polydecamethylene terephthalate Crystallization temperature oc
n
125"00 123"75 123"40 122"95 122"80 122"50 122"00 120'95 120"00 118"00
3-76 _+0"05 3"79 3"87 3"60 3"74 3"59 3"97 3"49 3"08 2"66
z
Range ot
(time, rain)
agreement per cent
7"00× 10 -11 1.00X 10-9 1,13X 10-9 1'25 X 1 0 - s 8.04X 10-9 5'65 × 10- s 3'44X 10 - 8 1.40x 10-~ 3"23 × 1O- 5 1 "35 × 1 0 - z
97 98 97 94 57 90 and 59 80 75 80
can be seen from T a b l e 1 and in fact the slight deviations observed for the results at 122"95°C and above only occur in the last 2 to 3 per cent of the crystallization and are barely outside the limits of experimental error. Before this discontinuity occurs, the results at all temperatures accurately fit the version of the Avrami relation given in equation (2). Two typical sets of data are plotted in Figure 4 in the form of log { - l o g [ ( h t - h ~ ) / ( h o - h,~)]} versus log t. For the results at 123-75°C, agreement is found for 97 per cent of the crystallization, while at 120"95°C the discontinuity occurs after 80 per cent crystallization. The values of the Avrami exponent n, however (equation 2), frequently differ signficantly from the integral values required by theory, as can be seen in T a b l e 1. A similar effect has been reported for the crystallization of polyethylene5 where the values of n were found to range from 2"0 to 4 0 . For the temperatures covered in the present study, the range is from 2-7 to 4.0 ( T a b l e 1). The temperature dependence of the crystallization rate has been shown by Mandelkern 3 and others to take the form log z = A - 4 B / A T 2
(3)
where A and B are constants, and AT is the difference between melting and crystallization temperatures. In the case where n varies with temperature it has been proposed 5 that this should be modified to log z = A - n B / A T 2
(4)
and in F i g u r e 5 the results from T a b l e 1 are plotted on this basis. The agreement with equation (4) is good, confirming that the observed variations in n are real, and require to be accounted for s. Alternative plots (e.g. equation 3) which do not allow for changing n, show very poor agreement. The parameter B, which is a measure of the critical free energy involved in secondary nucleation 3, decreases on passing through the temperature at which the crystaUinity changes (122-80°C, Figure 2) indicating a transition in the nature of the growing surface. This, however, is the only aspect of the kinetics which can be considered unambiguously to change on passing through the transition temperature. 123
A. SHARPLESand F. L. SWlNTON
1(]
Figure 5--Temperature dependence of crystallizationrate (dilatometryexperiments). • Results for 122-80°(2 and above. 0 Results for 122"50°C and below
0
'6
,
I
10
1~5
n/A72x 103
2tO
z5
Microscopy The dilatometric method yields information only on the combined effect of nucleation and growth during crystallization. The microscopy experiments were designed to determine whether the behaviour reported in the previous section could be accounted for in terms of anomalies in the separately observed nucleation and growth rates. A major difficulty was encountered, however, in that the nucleation density was found to vary from sample to sample, an effect which has previously been observed for polyethylenC. As with this latter polymer, the nucleation density is frequently so great as to produce a birefringent structure which is not resolvable microscopically at any stage during its growth. The particular sample studied was chosen because it yielded resolvable nuclei and because the method of preparation-(given in the experimental section) is not likely to have caused any degradation. The absolute values of the nucleation rate, however, are subject to an unknown error. The appearance of the spherulitic structures formed during crystallization is similar to that for the spherulitic aggregates observed in nylons, and remains constant over the measurable temperature range of 120.0"C to 126-0"C. Apart from the effect discussed later, both nucleation and radial growth rates (N and G) are also constant at a given temperature, and the values obtained are given in Table 2. It has previously been shown that for sporadic nucleation and spherulitic growth, as is observed here, the constant z in equation (2) is related to G and N by z = ~rp~NG3/ 3p~,~
(5)
where pz and pc are the densities of the liquid and crystalline phases and X,~ is the weight fraction of crystalline material within the spherulites. The derivation of this equation, however, also leads to a value of n = 4 in equation (2), and consequently the deviations from this value observed in the present case (Table 1) indicate that one of the assumptions involved 124
THE CRYSTALLIZATION OF POLYDECAMETHYLENE TEREPHTHALATE Table 2. Microscopy data for polydeeamerhylene terephthalate Temperature o¢ crystallization
126"0 125"0 123"9 123"7 123-0 121"9 121"0 120"0
G X 10 ~ cm / min
N x 10- ~/cmS/rain
t8 (rain)
t½ (rain) from dilatometry
127 88 82 52 23 16 10
457 241 210 143 70 45 25
0-246 0"800 1"90
1"53
3"73 6"55 6"60 9"50 15-4 20-7 33 "2
1"86
3"33 11"0 22"6 54"6
(possibly the one implying that the density of growing spherulites is constant) is not valid. Consequently a comparison of the values of z obtained dilatometrically from equation (2), and microscopically from equation (5) is not justifiable on an absolute basis, although the relative changes with temperature m a y be comparable. In Figure 6, values of z from microscopy data are plotted for various temperatures on the basis of equation (3). The solid fines ropresent the dilatometric data from Figure 5, and it can be seen that the change in behaviour at 122"8°C is confirmed, although the absolute values are displaced by a factor of 200 to 300 per cent. This displacement may be due to the arbitrary nature of the nucleation rate, or to the unknown factor causing n to be less than its predicted value of 4. A feature of the nucleation process which has previously been reported ~ is that although the rate is constant for a considerable period of time, it eventually decreases and finally falls to zero, leaving a fixed number of nuclei which is determined by the temperature of crystallization. The time at which nucleation stops t, is well within the time scale of the overall crystallization process as can be seen from T a b l e 2 where the observed values of t, are compared with those calculated for the half-life, t,, from 12
10 Temperature dependence of crystallization rate (microscopy experiments). • Results for 123"0°C and above. 0 Resuits for 121"9°0 and below. Solid line indicates dilatometric plot from Figure 5 Figure
6 --
t, o ' 8
/ /o 1=5
2to 41& T 2 x 10
125
3
215
310
A, SHARPLES and F. L. SWINTON
dilatometry data. Owing to the arbitrary nature of the nucleation experiments, the absolute values of t, are likely to have a considerable error attached to them. Relatively, however, the change with temperature follows that of t~ very closely, and again indicates a change in behaviour at ca. 122"8°C. DISCUSSION
In spite of the absence of any complicating secondary process, the crystallization of polydecamethylene terephthalate nevertheless shows several unusual features. First, fractional values of the Avrami exponent n (equation 2) which have previously been observed for polyethylene5, are also found in the present Case (Table 1), and as existing theory2'3 requires integral values of 1, 2, 3 or 4, it is evident that some aspect of the present mechanism requires modification. It is possible that more careful analyses of existing data for other polymers, where the presence of secondary crystallization in general renders interpretation more difficult, may reveal that integral values of n are the exception rather than the rule. No detailed explanation can be proposed to account for this behaviour, but the microscopy data suggest that the usual picture of sporadic nucleation followed by spherulitic growth at a constant radial rate may be basically correct, and that some process is superimposed to reduce n from its expected value of 4 for this system. One likely possibility5 is that the density of the growing spherulites is not constant with time, as is normally assumed. Secondly, there is evidence from the dilatometry experiments that the crystallization is interrupted by some process which causes a slowing down of the normal rate. It is important to note, however, that this effect does xmt prevent the attainment of the expected value for the final density, as the data for the earlier stage of crystallization conform to an Avrami plot (equation 2) best if the experimentally observed value of h~ is used. It would seem at first sight that this effect is explicable in terms of the stopping of nucleation, which is observable microscopically, and which is naturally expected to lead to a decrease in rate. Comparison of the observed time of stopping with the time at which the decrease in rate occurs in the dilatometric experiments is unfortunately not justifiable owing to the arbitrary nature of the nucleation data, so that this obvious test is not possible. The quantitative form of the dilatometric rate plots is informative, however, and is such that the decrease in rate (Figure 3) is much too sharp to be accounted for solely by cessation of nucleation. Consequently, although these two effects may be related (and obviously, as is noted above, some decrease in overall rate is bound to occur if the reduction in nucleation rate takes place within the time scale of the bulk crystallization), some additional factor must also be operative. Thirdly, in the region of 122"80°C, a pronounced change occurs in the density of the crystallized product (Figure 2). For example, the density increase resulting from crystallization is ca. 30 per cent greater at 122"95°C than at 122.50" C. At the same time the temperature dependence parameter for the rate of crystallization (Figure 5) also changes indicating an alteration in the nature of the growing spherulites. No difference is detectable in the qualitative appearance of the spherulites above and below this 126
THE CRYSTALLIZATION OF POLYDECAMETHYLENETEREPHTHALATE temperature, but the change is reflected quantitatively in the microscopically observed rate constant (Figure 6). Changes in kinetic behaviour on decreasing the crystallization temperature have previously been observed for polyethylene terephthalate 10, and explained on the assumption that sporadic and predetermined nucleation occur simultaneously to varying extents, depending both on temperature of crystallization, and on time and temperature of melting. However, the existence of two simultaneously occurring Avrami processes, each with a different value of n, such as would be expected if nuclei are formed both sporadically and from pre-existing sites, leads to a changing value of n, whereas in the present case, n, although fractional, is also constant. The most pronounced change is not that occurring in the kinetics but in the value for the final density of the crystallized product. In general this effect (Figure 2) could arise from one of three causes; incomplete crystallization, a modification of crystal form, or a change in the fraction of crystalline material within the spherulite. Incomplete crystallization is unlikely because it would require that the value of h.o~(equation 2) to give the best fit for the data should be less than the observed value. In fact, as is noted above, the experimentally observed value gives the optimum agreement. Simple modification of crystal form is also unlikely to account for the large effect observed, but the following explanation proposed by Morgan 11 is a possibility. This assumes that crystallization at higher temperatures involves only the polar groups in the chain, and that it is not until temperatures below 122.8°C are reached that the ten-carbon paraffinic segments take part in the process, imposing more restrictive conditions that result in a reduced extent of crystallization within the growing spherulite. This hypothesis would also predict a change in the nature of the growing surface on passing through the transition temperature, and this is consistent with the observed change in the temperature dependence parameter 3, B (equation 4, Figure 5). It suffers, however, from one serious objection, in that at the higher temperatures where the density change on crystallization is at a maximum, this change should still be less than, for example, in polyethylene terephthalate where the entire chain is presumably capable of being involved in crystallization. In fact, at 122-95°C the density increase on crystallization is 5-I per cent, whereas the maximum figure observed for polyethylene terephthalate 1° is 2'6 per cent. The effects discussed above, and the results reported recently for polyethylene~, suggest that the existing picture of polymer crystallization may require modification. The postulate of nucleation and spherulitic (or occasionally rodlike) growth may be generally correct, but the additional assumptions that the growth and nucleation rates are constant, and that the density of the growing crystalline regions is similarly independent of time, require to be examined in greater detail than has previously been the case.
Arthur D. Little Reseatvh Institute, lnveresk, Musselburgh, Midlothian (Received July 1962) 127
A. SHARPLES and F. L. SWINTON REFERENCES J-AVRAMI,M. J. chem. Phys. 1940, 8, 212 2 MORGAN,L. B. Phil. Trans. 1954, 247, 13 8 Mg~DELKF~N, L. Growth and Perfection of Crystals, pp 467-497. Chapman and Hall: London, 1958 4 Kov^cs, A. J. Ric. sci.A, 1955, 25~ 666 s BANKS, W., GORDON, M., ROE, R.-J. and StlARpI~S, A. Polymer, Lond. 1963, 4, 61 e FLORY, P. J., BEDON, H. D. and Ke~l~Xt, E. H. J. Polym. Sci. 1958, 28, 151 BANKS, W., HAY, J. N., StIARPXJBS,A. and THOMSON, G. Nature, Lond. 1962, 194, 542 s I~ouRY, F. J. Polym. Sci. 1958, 33, 389 * SHARPLES, A. Polymer, Lond. 1962, 3, 250 10 HARTLEY, F. D., LOP.D, F. W. and MOROAN, L. B. Phil. Trans. 1954, 247, 23 11 MORGAN, L. B. Conference on Physics of High Polymers, University of Bristol, 1961
128
Crystallization of Polydecamethylene Terephthalate A. SnARPLES and F. L. SwiwroN*
A study has been made o[ the crystallization o[ polydecamethylene terephthalate at various temperatures. The interpretation of the results is uncomplicated by tile presence of any detectable secondary stage but the process nevertheless shows several unusual [eatures. First, although the majority o[ the crystallization con[orms to an Avrami relation, the values of the exponent, n, are [factional, whereas current theory requires integral values. Secondly, an additional process intervenes towards the end o[ the crystallization to cause a decrease in the normal rate. It is possible that this is related to an observed decrease in the nucleation rate. Finally, a pronounced change in behaviour takes place about 15°C below the melting point causing a 30 per cent decrease in the density change during crystallization to occur Jor a temperature lowering o[ only 0"5°C. The kinetic behaviour also changes on passing through this point.
IN GENERAL,the crystallization of high polymers is considered to involve the formation of nuclei in the supercooled melt, followed by the growth of these centres to form rods, discs or spheres. The decrease in volume of the system resulting from the formation of the more dense, crystalline phase, can be related to time by an equation of the form 1-a (V, - Voo)/(Vo - V,,~) = exp ( - zt") (1) where V, is the volume of the system at time t, z is constant for a given temperature, and n is an integer having a value of 1, 2, 3 or 4. Usually a process referred to as secondary crystallization* intervenes to complicate the interpretation of the data, and although methods have been proposed to allow for this effect5, it was considered desirable to study the behaviour of a polymer where it is absent, especially in view of the fact that recent results on polyethylene5 have indicated that the integral values of n predicted by existing theory are not always obtained. Polydecamethylene terephthalate shows no detect~ible secondary crystallization, and an account of its behaviour is given below. EXPERIMENTAL
Materials
The polymer was prepared by the method of Flory, Bedon and Keefe#. The equilibrium melting temperature obtained by dilatometry using slow (1°C/24 h) rates of heating was found to be 137-5°C, in good agreement with Flory's value of 138°C, although the values of 0"968~ cm3/g for the specific volume of the liquid polymer at 150°C is in rather poor agreement with that of 0.956 cm 3/g quoted by Flory. The melt viscosity of the liquid polymer was measured at 255°C and was found to be 740 poise. According to Flory et aL e this indicates that the number average molecular weight is greater than 10 000, and that the true equilibrium melting point will not be depressed to any extent by the number of chain ends present in the melt. *Present address: Chemistry Department, Royal College of Science and Technology,
119
Glasgow, C.l.
A. SHARPLES and F. L. SWINTON
Dilatometry Molten polydecamethylene terephthalate has the property of wetting glass, so that when the temperature is lowered and the polymer crystallized, the resultant volume contraction invariably shatters the containing tube if this is made of glass. The dilatometers used in the present study were consequently constructed with stainless steel bodies, connected to the measuring capillaries through flanged joints, which were lightly greased with high melting silicone grease to render them vacuum-tight. The measuring capillaries were made of 2 mm internal diameter precision-bore Veridia tubing, The dilatometers were filled with weighed amounts of polymer and mercury in the usual way, under Vacuum 4. Approximately 10g of dried polymer was used for each dilatometer, and the height of the mercury column as a function of time and temperature was measured to + 0-01 mm using a 1 m cathetometer manufactured by the Precision Tool and Instrument Co. The crystallizations were carried out in an oil thermostat of conventional design, the temperature control of which was +0'03°C at the experimental temperatures. Before each crystallization run, the sample was melted at 180 ° to 190°C for 30min, As an indication of the extent of the volume change measured, the specific volume of the polymer at 120'00°C before crystallization is 0"9527o cm 3/g, while after crystallization at this temperature the value is 0-91136 cm ~/g.
Microscopy Measurements of nucleation and growth rates were made using a 10× micrometer eyepiece and a ~ in. objective. Temperature control was effected with a Ktifler hot-stage, thermostatted to + 0" 1 °C. Films of polymer approximately 10~t thick were prepared by pressing the molten material between glass slides and cover slips, but even when precautions were taken to avoid degradation, the resultant nucleation densities were very variable, and often were so high that an unresolvable birefringent mass was formed 7. The results reported were obtained using a sample with resolvable spherulitic structure prepared under similar conditions to those involved in the dilatometry. Approximately 1 mg was heated on an open glass slide in vacuo at 170°C for 15 min. The sample was then cooled, a cover slip was placed in position, and the slide was reheated to 2000C prior to pressing to form a suitable film. Subsequent measurements were made by first melting at 160°C for 5 min and then lowering the temperature to that required for crystallization. Prior melting at 140°C and 300"C produced identical results. The mean thickness of the specimen was determined from the known weight and the measured area. Variation in thickness across the specimen was assessed by differential focusing under high magnification, and was found to be less than 20 per cent. This was considerably less than the variation in nucleation density observed to occur from one sample to another. RESULTS
Dilatometry Relative values of the volume change occurring in a crystallizing polymer can in practice be determined from dilatometric heights, so that equation (1) can be written (h,-h,o)/(ho - hoo)= exp (-ztO (2) 120
THE CRYSTALLIZATION OF POLYDECAMETHYLENE TEREPHTHALATE
~ 00
211111 ,
50(
-
45C101
122,95
-
10 2
10 3
t rain Figure 1--Cryst~tllization of polydecamethylene terephthalate at various temperatures. Dilatometric height versus log (time) where ht is the dilatometric height at time t. Results for ht obtained during the crystallization of polydecamethylene terephthalate at various temperatures, are plotted 3 in Figure 1 against log t and it is immediately apparent that, for example at 118°C, the final value, i.e. k,~, is constant (to within 0' 1 per cent of the total change, h 0 - h~) for a period of time one order greater than that involving the primary crystallization. Thus, secondary crystallization', which involves a continual, slow decrease in volume after the completion of the primary stage, is effectively absent from this polymer. The unexpected feature of the results is the anomalous volume change which takes place at ca. 122'8°C. This can be seen more readily in Figure 2, where the change in dilatometer height occurring during crystallization is plotted as a function of crystallization temperature: Above 122"95°C and below 122-50°C the volume change increases with decreasing temperature, as is to be expected from the different expansion coefficients of liquid and ~5oI E E
Figure 2--Volume change occurring during crystallization, plotted as a function of to temperature ~: 0
I
I
I
120
I
I
Temperature
121
~
I
1
I
125 °C
A. SHARPLES and F. L. SWINTON
~. 600 E E
Figure 3--I.ntervention of pro-
55O
cess causing decrease in crystallization rate--122.00°C. B and C: experimental plots. A: theoretical plot, assuming continuation of early stages of B and C according to equation (2)
500
c
101
102 t
rain
solid phases. Between these two temperatures, however, there is a displacement of about 30 per cent. No obvious explanation or precedent is available to account for this effect, but it immediately raises the question of whether the kinetics are also affected on passing through this transition. In the first instance it was noted that an obvious discontinuity is present at all temperatures in the crystallization plots. This is illustrated by the results for 122"00°C (Figure 3). Deviations from the extrapolated curve A are apparent in two successive experiments, B and C, and it is evident that some process intervenes in an irreproducible manner to slow down the normal course of crystallization. In most of the isotherms the discontinuity does not occur until the crystallization is about 80 per cent complete as t
min
102
103
7%
. /.
100
123.7 °cV 80% ! •
conformity to equation (2) for majority of crystallization
I
! I
Figure 4--Avrami plots showing
J
I 4 1
I
!
!
i
I
I
/"
120.95oc
I
101 t
102 rain
122
THE CRYSTALLIZATION OF POLYDECAMETHYLENE TEREPHTHALATE Table 1. Crystallization rate parameters for polydecamethylene terephthalate Crystallization temperature oc
n
125"00 123"75 123"40 122"95 122"80 122"50 122"00 120'95 120"00 118"00
3-76 _+0"05 3"79 3"87 3"60 3"74 3"59 3"97 3"49 3"08 2"66
z
Range ot
(time, rain)
agreement per cent
7"00× 10 -11 1.00X 10-9 1,13X 10-9 1'25 X 1 0 - s 8.04X 10-9 5'65 × 10- s 3'44X 10 - 8 1.40x 10-~ 3"23 × 1O- 5 1 "35 × 1 0 - z
97 98 97 94 57 90 and 59 80 75 80
can be seen from T a b l e 1 and in fact the slight deviations observed for the results at 122"95°C and above only occur in the last 2 to 3 per cent of the crystallization and are barely outside the limits of experimental error. Before this discontinuity occurs, the results at all temperatures accurately fit the version of the Avrami relation given in equation (2). Two typical sets of data are plotted in Figure 4 in the form of log { - l o g [ ( h t - h ~ ) / ( h o - h,~)]} versus log t. For the results at 123-75°C, agreement is found for 97 per cent of the crystallization, while at 120"95°C the discontinuity occurs after 80 per cent crystallization. The values of the Avrami exponent n, however (equation 2), frequently differ signficantly from the integral values required by theory, as can be seen in T a b l e 1. A similar effect has been reported for the crystallization of polyethylene5 where the values of n were found to range from 2"0 to 4 0 . For the temperatures covered in the present study, the range is from 2-7 to 4.0 ( T a b l e 1). The temperature dependence of the crystallization rate has been shown by Mandelkern 3 and others to take the form log z = A - 4 B / A T 2
(3)
where A and B are constants, and AT is the difference between melting and crystallization temperatures. In the case where n varies with temperature it has been proposed 5 that this should be modified to log z = A - n B / A T 2
(4)
and in F i g u r e 5 the results from T a b l e 1 are plotted on this basis. The agreement with equation (4) is good, confirming that the observed variations in n are real, and require to be accounted for s. Alternative plots (e.g. equation 3) which do not allow for changing n, show very poor agreement. The parameter B, which is a measure of the critical free energy involved in secondary nucleation 3, decreases on passing through the temperature at which the crystaUinity changes (122-80°C, Figure 2) indicating a transition in the nature of the growing surface. This, however, is the only aspect of the kinetics which can be considered unambiguously to change on passing through the transition temperature. 123
A. SHARPLESand F. L. SWlNTON
1(]
Figure 5--Temperature dependence of crystallizationrate (dilatometryexperiments). • Results for 122-80°(2 and above. 0 Results for 122"50°C and below
0
'6
,
I
10
1~5
n/A72x 103
2tO
z5
Microscopy The dilatometric method yields information only on the combined effect of nucleation and growth during crystallization. The microscopy experiments were designed to determine whether the behaviour reported in the previous section could be accounted for in terms of anomalies in the separately observed nucleation and growth rates. A major difficulty was encountered, however, in that the nucleation density was found to vary from sample to sample, an effect which has previously been observed for polyethylenC. As with this latter polymer, the nucleation density is frequently so great as to produce a birefringent structure which is not resolvable microscopically at any stage during its growth. The particular sample studied was chosen because it yielded resolvable nuclei and because the method of preparation-(given in the experimental section) is not likely to have caused any degradation. The absolute values of the nucleation rate, however, are subject to an unknown error. The appearance of the spherulitic structures formed during crystallization is similar to that for the spherulitic aggregates observed in nylons, and remains constant over the measurable temperature range of 120.0"C to 126-0"C. Apart from the effect discussed later, both nucleation and radial growth rates (N and G) are also constant at a given temperature, and the values obtained are given in Table 2. It has previously been shown that for sporadic nucleation and spherulitic growth, as is observed here, the constant z in equation (2) is related to G and N by z = ~rp~NG3/ 3p~,~
(5)
where pz and pc are the densities of the liquid and crystalline phases and X,~ is the weight fraction of crystalline material within the spherulites. The derivation of this equation, however, also leads to a value of n = 4 in equation (2), and consequently the deviations from this value observed in the present case (Table 1) indicate that one of the assumptions involved 124
THE CRYSTALLIZATION OF POLYDECAMETHYLENE TEREPHTHALATE Table 2. Microscopy data for polydeeamerhylene terephthalate Temperature o¢ crystallization
126"0 125"0 123"9 123"7 123-0 121"9 121"0 120"0
G X 10 ~ cm / min
N x 10- ~/cmS/rain
t8 (rain)
t½ (rain) from dilatometry
127 88 82 52 23 16 10
457 241 210 143 70 45 25
0-246 0"800 1"90
1"53
3"73 6"55 6"60 9"50 15-4 20-7 33 "2
1"86
3"33 11"0 22"6 54"6
(possibly the one implying that the density of growing spherulites is constant) is not valid. Consequently a comparison of the values of z obtained dilatometrically from equation (2), and microscopically from equation (5) is not justifiable on an absolute basis, although the relative changes with temperature m a y be comparable. In Figure 6, values of z from microscopy data are plotted for various temperatures on the basis of equation (3). The solid fines ropresent the dilatometric data from Figure 5, and it can be seen that the change in behaviour at 122"8°C is confirmed, although the absolute values are displaced by a factor of 200 to 300 per cent. This displacement may be due to the arbitrary nature of the nucleation rate, or to the unknown factor causing n to be less than its predicted value of 4. A feature of the nucleation process which has previously been reported ~ is that although the rate is constant for a considerable period of time, it eventually decreases and finally falls to zero, leaving a fixed number of nuclei which is determined by the temperature of crystallization. The time at which nucleation stops t, is well within the time scale of the overall crystallization process as can be seen from T a b l e 2 where the observed values of t, are compared with those calculated for the half-life, t,, from 12
10 Temperature dependence of crystallization rate (microscopy experiments). • Results for 123"0°C and above. 0 Resuits for 121"9°0 and below. Solid line indicates dilatometric plot from Figure 5 Figure
6 --
t, o ' 8
/ /o 1=5
2to 41& T 2 x 10
125
3
215
310
A, SHARPLES and F. L. SWINTON
dilatometry data. Owing to the arbitrary nature of the nucleation experiments, the absolute values of t, are likely to have a considerable error attached to them. Relatively, however, the change with temperature follows that of t~ very closely, and again indicates a change in behaviour at ca. 122"8°C. DISCUSSION
In spite of the absence of any complicating secondary process, the crystallization of polydecamethylene terephthalate nevertheless shows several unusual features. First, fractional values of the Avrami exponent n (equation 2) which have previously been observed for polyethylene5, are also found in the present Case (Table 1), and as existing theory2'3 requires integral values of 1, 2, 3 or 4, it is evident that some aspect of the present mechanism requires modification. It is possible that more careful analyses of existing data for other polymers, where the presence of secondary crystallization in general renders interpretation more difficult, may reveal that integral values of n are the exception rather than the rule. No detailed explanation can be proposed to account for this behaviour, but the microscopy data suggest that the usual picture of sporadic nucleation followed by spherulitic growth at a constant radial rate may be basically correct, and that some process is superimposed to reduce n from its expected value of 4 for this system. One likely possibility5 is that the density of the growing spherulites is not constant with time, as is normally assumed. Secondly, there is evidence from the dilatometry experiments that the crystallization is interrupted by some process which causes a slowing down of the normal rate. It is important to note, however, that this effect does xmt prevent the attainment of the expected value for the final density, as the data for the earlier stage of crystallization conform to an Avrami plot (equation 2) best if the experimentally observed value of h~ is used. It would seem at first sight that this effect is explicable in terms of the stopping of nucleation, which is observable microscopically, and which is naturally expected to lead to a decrease in rate. Comparison of the observed time of stopping with the time at which the decrease in rate occurs in the dilatometric experiments is unfortunately not justifiable owing to the arbitrary nature of the nucleation data, so that this obvious test is not possible. The quantitative form of the dilatometric rate plots is informative, however, and is such that the decrease in rate (Figure 3) is much too sharp to be accounted for solely by cessation of nucleation. Consequently, although these two effects may be related (and obviously, as is noted above, some decrease in overall rate is bound to occur if the reduction in nucleation rate takes place within the time scale of the bulk crystallization), some additional factor must also be operative. Thirdly, in the region of 122"80°C, a pronounced change occurs in the density of the crystallized product (Figure 2). For example, the density increase resulting from crystallization is ca. 30 per cent greater at 122"95°C than at 122.50" C. At the same time the temperature dependence parameter for the rate of crystallization (Figure 5) also changes indicating an alteration in the nature of the growing spherulites. No difference is detectable in the qualitative appearance of the spherulites above and below this 126
THE CRYSTALLIZATION OF POLYDECAMETHYLENETEREPHTHALATE temperature, but the change is reflected quantitatively in the microscopically observed rate constant (Figure 6). Changes in kinetic behaviour on decreasing the crystallization temperature have previously been observed for polyethylene terephthalate 10, and explained on the assumption that sporadic and predetermined nucleation occur simultaneously to varying extents, depending both on temperature of crystallization, and on time and temperature of melting. However, the existence of two simultaneously occurring Avrami processes, each with a different value of n, such as would be expected if nuclei are formed both sporadically and from pre-existing sites, leads to a changing value of n, whereas in the present case, n, although fractional, is also constant. The most pronounced change is not that occurring in the kinetics but in the value for the final density of the crystallized product. In general this effect (Figure 2) could arise from one of three causes; incomplete crystallization, a modification of crystal form, or a change in the fraction of crystalline material within the spherulite. Incomplete crystallization is unlikely because it would require that the value of h.o~(equation 2) to give the best fit for the data should be less than the observed value. In fact, as is noted above, the experimentally observed value gives the optimum agreement. Simple modification of crystal form is also unlikely to account for the large effect observed, but the following explanation proposed by Morgan 11 is a possibility. This assumes that crystallization at higher temperatures involves only the polar groups in the chain, and that it is not until temperatures below 122.8°C are reached that the ten-carbon paraffinic segments take part in the process, imposing more restrictive conditions that result in a reduced extent of crystallization within the growing spherulite. This hypothesis would also predict a change in the nature of the growing surface on passing through the transition temperature, and this is consistent with the observed change in the temperature dependence parameter 3, B (equation 4, Figure 5). It suffers, however, from one serious objection, in that at the higher temperatures where the density change on crystallization is at a maximum, this change should still be less than, for example, in polyethylene terephthalate where the entire chain is presumably capable of being involved in crystallization. In fact, at 122-95°C the density increase on crystallization is 5-I per cent, whereas the maximum figure observed for polyethylene terephthalate 1° is 2'6 per cent. The effects discussed above, and the results reported recently for polyethylene~, suggest that the existing picture of polymer crystallization may require modification. The postulate of nucleation and spherulitic (or occasionally rodlike) growth may be generally correct, but the additional assumptions that the growth and nucleation rates are constant, and that the density of the growing crystalline regions is similarly independent of time, require to be examined in greater detail than has previously been the case.
Arthur D. Little Reseatvh Institute, lnveresk, Musselburgh, Midlothian (Received July 1962) 127
A. SHARPLES and F. L. SWINTON REFERENCES J-AVRAMI,M. J. chem. Phys. 1940, 8, 212 2 MORGAN,L. B. Phil. Trans. 1954, 247, 13 8 Mg~DELKF~N, L. Growth and Perfection of Crystals, pp 467-497. Chapman and Hall: London, 1958 4 Kov^cs, A. J. Ric. sci.A, 1955, 25~ 666 s BANKS, W., GORDON, M., ROE, R.-J. and StlARpI~S, A. Polymer, Lond. 1963, 4, 61 e FLORY, P. J., BEDON, H. D. and Ke~l~Xt, E. H. J. Polym. Sci. 1958, 28, 151 BANKS, W., HAY, J. N., StIARPXJBS,A. and THOMSON, G. Nature, Lond. 1962, 194, 542 s I~ouRY, F. J. Polym. Sci. 1958, 33, 389 * SHARPLES, A. Polymer, Lond. 1962, 3, 250 10 HARTLEY, F. D., LOP.D, F. W. and MOROAN, L. B. Phil. Trans. 1954, 247, 23 11 MORGAN, L. B. Conference on Physics of High Polymers, University of Bristol, 1961
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