546 J. F. JACKSON
AND
L. MANDELKERN
Mucromolecules
Solubility of Crystalline Polymers. 11. Polyethylene Fractions Crystallized from Dilute Solutions' J. F. Jackson and L. Mandelkern Dejxirtnient of' Clieinistrj~wid Institute of' Moleculur Biopliysics, Floridrr State Unirersitj., Tcrllcihassee, Florida. 32306. Receiced JLI!).11. I968
ABSTRACT: The relations between the dissolution temperature, or melting temperature in dilute solution, the crystallite thickness and the crystallization temperature of linear polyethylene fractions crystallized from dilute solution have been investigated. The range of crystallite sizes has been extended over other studies and the limits for isothermal crystallization have been established. The data are analyzed using previous independently determined equilibrium dissolution temperatures. It is found that the interfacial free energy. associated with the 001 basal plane, characteristic of the mature crystallites, differs from that involved in nucleation. From the most general considerations of nucleation theory, it is concluded that the interfacial structure of the nucleus is different from that of the mature crystallite that develops from it. Analysis of data for crystals formed from different solvents firmly establishes that the crystallite thickness is nucleation controlled although details of the nucleation process itself and of the chain structure within the nucleus cannot be uniquely specified.
wen
stallized from dilute solution, long chain molecules cry of regular structure form characteristic lamellalike crystalswhichextendfor several microns in the lateral directions. T h e lamella thickness, depending ypon the crystallization conditions, is the order of 100 A . ? , ~T h e chains are preferentially oriented normal to the wide faces of the lamella so that each chain clearly must traverse a crystallite many times. A n interesting and important set of questions and problems has developed in regard t o the nature and properties of such crystals. These questions center about the details of the interfacial structure, the concentration and kind of internal defects present and the underlying basis and mechanism for the formation 0' such crystals. Crystals of the kind described are naturally amenable t o analysis by the theory applicable t o the melting of crystals of finite size. Appropriate data must be available, including the equilibrium melting temperature at a given polymer composition. Equilibrium dissolution temperature data, the melting temperature in a dilute solution, have now been obtained from independent studies of the solubility properties of bulk crystallized molecular weight fractions of linear polyethylene. These quantities, which had previously only been estimated, are of fundamental importance in analyzing many aspects of the crystallization process from dilute solution including the solubility of the crystallites formed and the energetics of the kinetics involved. With this background, the present report is primarily concerned with the relations between the dissolution temperature, the crystallite thickness and the crystallization temperature of linear polyethylene fractions crystallized from dilute solution. A major effort has been made t o extend the range of data available and t o analyze the results from as general a viewpoint as possible. (1) This work was supported by a contract between the United States Air Force, Systems Engineering Group, and Florida State University. (2) A . Keller, Phil. Mag., [SI 2, 1171 (1957). (3) E. W. Fischer, Z . Naturforsch., 12A, 753 (1957). (4) J. F. Jackson, L. Mandelkern, and 0. C. Long, Macronzokcules, 1, 218 (1968).
Experimental Section
The dilute solution crystals were prepared at polymer concentrations of 0.08 % from doubly distilled xylene with n-phenyl-P-naphthylamine being added as an antioxidant. Two molecular weight fractions of linear polyethylene. M,, = 2.00 X 10: and 1.95 X lo4,were utilized for most of this work. but in a special set of experiments a fraction M,>= 3.5 X 10"was used. The methods of preparation and characterization of the fractions have already been reported in detail.6 The crystallization procedures adopted in this work were similar to those outlined previously.6 The polymer sample was added to a small aliquot of solvent, dissolved at 140'. and then maintained at 1 IO" for 15-30 min. The temperature of a large aliquot of the pure solvent was so adjusted in a thermostat that upon mixing of the two liquids the desired crystallization temperature was achieved. The polymer concentration in the small aliquot was 0.4%, and that in the final solution was 0.08 %. The nominal range of crystallization temperatures, T,, was from 50 to 95". It is important i n these experiments to assess whether the crystallizations were actually carried out isothermally. particularly at the lower range of temperatures. For this purpose the crystallization process can conveniently be divided into the following portions: (i) the first appearance of cloudiness, (ii) the formation of the first flakes. (iii) the termination of the crystallization. For a simple type of transfer experiment, where an 0.08 solution is transferred from a thermostat at 110" to another one at the desired T,. the measured temperature changes during the course of crystallization are summarized i n Table I. In this table. T, represents the nominal crystallization temperature and T the measured temperature in the crystallizing mixture at the time t . The data in the table are for the transfer type of crystallization procedure. It becomes evident from the data that below about 80' the crystallization process is not isothermal. The crystallization process becomes virtually complete before thermal equilibrium is established. In the actual mixing process used here, the crystallization rates were greatly enhanced. Thus, although thermal equilibrium was established rapidly upon mixing, it is extremely doubtful that the nominal crystallization tempera(5) J. G . Fatou and L . Mandelkern, J. Phys. Chern., 69, 417 11965) \____,.
(6) J . F. Jackson and L. Mandelkcrn, J . P d ~ mSci.,Part E , 5, 557 (1967).
CRYSTALLINE POLYMERS 547
Vol. I , No. 6, November-December 1968
TABLEI MEASURED TEWPERATURE DURING THE COURSE OF CRYSTALLIZATION IN TRANSFER EXPERIMEAT
-
-I--
T,., 'C
t , min
T. T
60
2 0.5
50
0.3
76 78 73
80 70
-Il------.
...
-Il-
min
I,
80
3 I
0.3
T, 'C
I,
80 75 75 73
min
T. T
13
80
5 2 I
72 66.5 68
TABLE 11 TIME FOR COMPLETION OF CRYSTALLIZATION T,. C
Time
95 92.5
1 month 2 weeks 2 . 2 hr 3 min 3 sec
90
85 80
ture was reached before crystallization occurred for temperatures below 80'. 111 fact, in this temperature range. crystallization was observed to take place at the point of contact of the solution and solvent before complete mixing took place. Fischer and Lorenzi used a similar technique for crystallization by adding the small aliquot of polymer solution to a large aliquot of solvent at the crystallization temperature. At low temperatures they used dropwise addition to attempt to gain rapid thermal equilibrium. However, their results for the crystallite thickness are essentially identical with those obtained in this study. as well as those obtained by the method of transfer of the crystallizing solution.* I t is highly probable, therefore, that none of the techniques described allows for thermal equilibrium to be established below 80" before crystallization takes place. This conclusion is further substantiated by the experimental results to be given su bsequeii tl y. For the mixing technique of crystallization that was adopted here. the approximate times for the completion of the process, for high molecular weights, are listed in Table 11. Molecular weight fractions in the range above 45,000 show no discernible difference i n rate. For a fraction of 19.500 molecular weight, crystallization at 90' took approximately twice as long as for a fraction of 200,000 molecular weight. The data in this table reflect the well-known very strong negative temperature dependence of the crystallization rate.g,lo The practical limitations to the accessible range of temperatures for isothermal crystallization are also indicated. At the higher temperatures the time required for the crystallization process becomes unduly long. while for the lower temperatures. as has been indicated above. the rates are much too rapid to allow attainment of thermal equilibrium. The self-nucleation technique described by Blundell, Keller. and Kovacs" reduces the time scale for the crystallization process by a factor of about 0.5. However. even this procedure does not allow complete crystallization to occur above 95' i n a reasonable length of time for this system. Dissolution temperatures were determined visually by placing the crystallization tube, with crystals still in the mother liquor, directly into a 110' thermostat and simultaneously recording the temperature of the solution and the (7) E. W . Fischer and R . Lorenz, Kolloid-Z., 189, 97 (1963). (8) L. Mandelkern, A. L. Allou, Jr., and M. R . Gopalan, J . Ph.1.s. Chem., 72, 309 (1968). (9) L. Mandelkern, PO!, mer, 5, 637 (1964). (IO) L. Mandelkern, "Crystallization of Polymers," McGrawHill Book Co., Inc., Ne\\; York, N . Y., 1964. ( 1 1 ) D. J . Blundell, A . Keller, and A. J. Kovacs, J . P O l ) ' f l 7 . Sci., Part B, 4, 481 (1966).
disappearance of the crystals. The time required for the dissolution of the crystals was of the order of 0.4-0.8 min. The reproducibility of this method was found to be f l " for crystallization conditions which are comparable (see below). The results obtained in this work agree very well with those reported by others. I 2 - l 6 For the determination of the crystallite size by low-angle X-ray diffraction, the crystals were separated from the mother liquor by slow filtration. In initial experiments, at 85 and 90", samples were filtered at the crystallization temperature to establish times for completion of the crystallization. I n the other experiments the samples were filtered at room temperature and dried mats prepared.' Preliminary attempts to obtain dissolution temperatures on the dried samples yielded irreproducible results. Therefore, undried crystals were used in the experiments. The thickness of the crystallites was obtained from the low-angle scattering maxima of the dried mats using a Rigaku-Denki camera. The well-defined maxima were converted into linear dimensions by means of Bragg's law with an experimental uncertainty estimated to be +t4 A.
Results The main experimental results that were obtained from this study are summarized in Figures 1 and 2 as plots of the crystallite size, i-,in ingstroms, and the dissolution temperature, T., as functions of the crystallization temperature T,. It has previously been demonstrated6 that both the low-angle X-ray diffraction maxima and the dissolution temperature remain invariant with time during the complete period of the isothermal crystallization and during storage for long time periods under the crystallization conditions. Hence in analyzing and discussing the data in Figures 1 and 2 it is not necessary t o be concerned with any time changes in these properties during the crystallization process. The general character of the plot in Figure 1 agrees very well with that previously reported. 17, 18a The range of crystallization temperatures has, however, been extended t o 95". As a consequence a significant increase has been observed in :he size of the crystallites formed. The spacing of 190 A. obtained after crystallization at 95", for crystals formed by our technique, agrees exactly with that reported by Blundell, Keller, and Kovacsll by their "self-nucleation" method at the same crystallization temperature. T h e invariance of the results for the two molecular weight fractions studied here agrees with other reports over a comparable molecular weight range. lifi1,I h , (12) J . B. Jackson, P. J . Florq, and R. Chiang, Trans. Faraday Soc., 59, 1906(1963). (13) A . Peterlin and
G .1Meinel, J . Poli,m. Sci., Part B, 2, 751 (1964). (14) D. A . Blackadder and H . M. Schleinitz, Polj.mer, 7, 603 (1966). (15) V. F. Holland, J . Appl. Phj s., 35. 59 (1964). (16) (a) A. Nakajima, F. Hamada, S. Hayashi, and T . Sumida, Kolloid-Z., 222, 10 (1968); A . Nakajima, S . Hayashi, T. Korenaga, and T. Sumida, ibid., 222, 124 (1968); (b) B. Wunderlich, P. Sullivan, T. Arakawa, A. B. Dicyan, and J. F. Flood, J . P0lj.m. Sci., Parr A - 1 , 1, 3581 (1963). (17) (a) V. F. Holland and P. Lindenmeyer, ibid., 57, 589 (1962); (b) F. P . Price, J . Chem. Phys., 35, 1884 (1961). (18) (a) A. Keller and A . O'Connor, Polymer, 1, 163 (1960); (b) B. Wunderlich, E. A . James, and T. Shu, J . Polj,m. Sci., Part A , 2, 2759 (1964). (19) It is not necessarily implied, nor should it be construed that if the range of study was extended to lower and to higher molecular weight fractions that the invariance of crystallite sizes with chain length a t a given crystallization temperature would still be obtained.
548 J. F. JACKSON AND L. MANDELKERN
COhlPILATION OF
Ref
TABLE It1 DISSOLUTION TEMPERATURE MEASUREMENTS FOR DILUTE SOLUTION CRYSTALS OF LINEAR POLYETHYLENE
Technique
Present work
Visual Light scattering
13 14
DTA
16
Visual
Macromolecules
Polymer
Solvent
Fraction M , = 200,000 Fortiflex
Xylene
85
93 f 1 96 i 1 92.7 k 1
Tc, "C
T,, "C
Xylene
90 85
601500 M , = 55,000 Rigidex 50 M , = 104,000
Xylene
85
92.6-93.1
Fraction
Xylene
89.1
96.3 i 1
Toluene
86
93.7
Xylene Tetralin
84 YO 50
93 96.5 93.5
Tetralin
90
97.5
M , = 20,000
16
Fraction
Visual
M,
15
20,000
Fraction
Electron microscopy Visual
12
=
M,,
=
135,000
Fraction M , = 50,000
Fraction
Visual
12
M,> = 50,000
The extension of the range of crystallite*sizes now available from a previous high of about 150 A obtaine? after crystallization at 90" to the present high of 190 A demonstrates the existence of two distinctly different positions t o the plot in Figure 1. There is a very definite change in the slope of this plot which occurs at a crystallization temperature in the vicinity of 80". This phenomenon was not apparent in previous compilations of comparable datalo which, however, were restricted t o crystallization temperatures (in xylene) of 90" or below. These new observations, therefore, necessitate a reexamination and reanalysis of the data. The data presented earlier relating the crystallization times to the times required to attain thermal equilibrium suggest rather strongly that the relatively small change of that is observed in the range T, 50-80" is a consequence of nonisothermal crystallization. A major portion of the crystallization in these circumstances occurs by necessity in the range 70-80". The solubility temperatures, illustrated in Figure 2, show a trend with the crystallization temperature which is very similar t o that just discussed. For To of 80" and higher all the dissolution takes place within n o more
than a 1 " range, and there is a very definite monotonic increase of the dissolution temperature with the crystallization temperature. Below 80", however, the temperature range for the disappearance of the crystals is greatly increased as is indicated by the vertical bars in the figure. There is a n invariance of the end point with T, in the range 50-80" and the data are identical for crystallization conducted at nominal temperatures of 50 and 60". These results, together with those cited above, give very strong indication that the crystallization below 80" is not isothermal. This is a n important factor in the analysis of the data so that consequently in the subsequent discussion we will restrict consideration to the data obtained over the crystallization temperature interval 80-95". As is indicated in the compilation in Table 111, the results obtained here in the range 80-90" agree well with those obtained by others, using various crystallization and measure-
I
2oot-
L
i
T,CTI
Figure 1. Lamella thickness as a function of crystallization temperature, determined by low-angle X-ray diffraction. Molecular weight fractions: 0 , 200,000; X, 19,500.
Figure 2. Thermodynamic stability of polyethylene crystallized from dilute xylene solution. Plot of dissolution temperature against crystallization temperature. Molecular weight fraction M , = 200,000. The right-hand ordinate represents TsO values, corresponding to extrapolations to the left-hand ordinate.
CKYWALLINE POLYMERS 549
Vol. I , No. 6, Nocenzber-Deceniber I968
ment techniqueis. T h e increased crystallite sizes that have now been obtained result in dissolution temperatures which are much greater than have been reported heretofore. For example, after crystallization at 90" from xylene, the dissolution temperature of t h e crystals formed is 96 i 1 ". When crystallized at 95", however, 1". the dissolution temperature is increased to 100 One might anticipate, therefore, that these new results could alter the previous analysis and parameters deduced. One of the niajor reasons for determining T , is t o relate this quantity t o the properties of the actual crystals formed at To. As the data in Figure 2 and Table I11 indicate, T , is substantially greater than To. It therefore becomes important t o ascertain whether any changes occur in the structure or morphology during the heating process required t o establish T,. To examine this matter a suspension of crystals formed at 90" was placed in a bath at 94" (a temperature just below the observed T.) for 1 min. T h e resulting lowangle X-ray pattern gave a spacing of 151 A which is the expected value for crystallization at 90". We can conclude therefore that no significant melting or structural changes occur during the time span of performing the dissolution temperature measurements. This result confirms previous reports of Peterlin and Meinell3 and of Blackadder and Schleinitz,14 who have shown independently that no reorganization of the crystallites occurs when the heating rates are greater than about 2.5 "/min.
/
60-
20 496 2700
-
*
D'scussion Relation between ( and Dissolution Temperature. F o r the lamellalike crystals formed from high molecular weight chains in dilute solution, where each chain is restricted t o participate in only one crystallite, it is easily shown that
Here T.0 is t h e equilibrium dissolution temperature (or equilibrium melting temperature in a dilute solution) for a macroscopically perfect crystal of infinite molecular weight, T , is the observed dissolution temperature for crystals whose size in t h e chain direction is j-, A H , is t h e enthalpy of fusion per repeating unit and ueeis the excess free energy or interfacial free energy characteristic of each crystalline sequence which emerges from the 001 basal plane of the mature crystallite. I n this high molecular weight approximation, eq 1 is of t h e general form applicable t o the melting of crystals of finite size. In the derivation of this equation no restriction is made as t o the molecular nature of the interfacial region. Thus it is not required that the interface be regularly structured although of course this latter case fits ihe general category t o which eq 1 is applicable. 2o This term becomes relatively small for < of the order of 500-1000 CH2 units. It is, however, (20) (a) For the situation where a single chain is not restricted to participate v i r t ~ ~ a l lcompletely y in one crystallite, as for example in bulk crystallized polymer, an additional term R/CAH, In c?, where 02 is the effective polymer concentration in the dilute solution, appears on the right side of eq 1 ; 4 (b) P. J. Flory, J . Chem. Ph.1 s., 17, 223 (1949).
I
IO0
-1,o
L/
* 5 5c L d 2 --L d 15 0 4 08 I2 I6 20 2 4 2 8 I/(Tr
X
5J'8
Figure 3. Comparison of stability of dilute solution crystals and bulk crystallized fractions. Dilute solution molecular weight fraction: 0 : 200,000 (this work); 0 , data of Nakajima, et al.;16 A, bulk crystallized fractions 20,OO0-570,000. The right-hand ordinate representes TSovalues corresponding to extrapolations to the left-hand ordinate. included as a small correction to l/T, for the bulk crystallized polyethylene data plotted in Figure 3. According to the suggestion of eq 1, the data from Figures 1 and 2 are plotted in Figure 3 as l/T, against l/Ta{ with { being in Bngstrom units. Included in this plot are the data of Nakajima, et al.,16a for the same system. However, the largest crystallite size and di%solution temperature that they report are only 152 A and 96.3 ", respectively. For comparative purposes the previously reported results for high molecular weight bulk crystallized polyethylene, M = 3.8 X l o 4 to 5.7 X lo5, are also plotted in Figure 3.4 T h e crystallite thickness for ;he latter type of specimens ranges from 820 t o 1050 A . 2 1 T h e reason for including these data is that the ultimate extrapolated value for T,O must be independent of the mode of crystallization, the morphological nature of the crystallites and their interfacial structure. As drawn in Figure 3, the bulk crystallized specimens yield a n extrapolated value of 118.6 i 2 " for T,O.* The value for the thermodynamic interaction parameter x1 for the polyethylene-xylene system is found to be 0.41 from two independent investigations. 4 , 1 6 a 9 2 2 This has enabled a calculation to be made of T S ofrom T,O, the equilibrium melting temperature of bulk crystallized material. 4 This latter 1 the theoretical exquantity is taken to be 145.5 pectation given by Flory and V ~ i j and , ~ ~in agreement with the extrapolated result of 146.0 i 0.5" obtained from experimental observations on the dependence of the melting temperature on the crystallization temperature and molecular weight.Y4 T,O is then found to be 118.6".* We can conclude, therefore, that the set T,O = 118.6 =t 2" in xylene and Tn,O = 145.5 2" are theoretically and experimentally consistent with one another. We note, however, that if the deduced
*
O,
*
(21) L. Mandelkern, J. M . Price, M. Gopalan, and J. G. Fatou, J . P o l j m . Sci., Part A-2, 4, 385 (1966). (22) A . Nakajima, H. Fujiwara, and F. Hamada, ibid., Part A-2, 4, SO7 (1966). (23) P . J. Flory and A . Vrij, J . Amer. Chem. SOC.,85, 3548 (1963). (24) M. R . Gopalan and L. Mandelkern, J. Phys. Chem., 71, 3833 (1967).
550 J. F. JACKSONAND L. MANDELKERN
value of x1 was reduced from 0.42 to 0.31, a T,O of 114" would be consistent with TO , = 145.5". The analysis and extrapolation of the data for the dilute solution crystals, solely by themselves, yield a large uncertainty in T,O. This is a consequence of the restricted range of small crystallite sizes that can be developed by this mode of crystallization and the experimental uncertainty in the determination of the solubility temperature. F o r example, Nakajima, et report a n extrapolated T,O of 109.4" based solely on their four experimental points. When all the dilute solution crystal data in xylene are considered, Tq0 is found to be in the range 114-119". The requirement for consistency with the bulk crystallized specimen reduces this range of uncertainty and leads t o the straight line that is drawn. This line is compatible with the actual results obtained with the dilute solution crystals and leads to a Tao in the range 116-119'. The true value for T,O is extremely important in the analysis of the dilute solution data. Therefore, the basis for the selection and the uncertainty that exists in this quantity must be clearly delineated. The slopes of the two straight lines drawn in Figure 3 differ by a factor of about 2.6. This clearly indicates that the interfacial free energy of mature crystallites a i d consequently the molecular structure of the interfacial regions are quite different in these two cases. This conclusion is reached irrespective of the exact value assigned to T.0. It then becomes apparent that in attempts t o extrapolate to the equilibrium solubility temperature or to the bulk equilibrium melting temperature o n the basis of crystallite size, samples of different morphologies and interfacial structures must be considered separately.*j From the slope of the straight line representing the dilute solution crystallized samples, uecis found to be 3400 c a l h o l of sequence, or 125 ergs/cm2.2j" If T,O is reduced to 116" the deduced interfacial energy is correspondingly lowered to 2900 calimol. It is of interest to compare this result with the corresponding quantity found for linear polyethylene crystallized in the bulk at low undercoolings.4i 2 1 , 2 6 , 2i F o r bulk crystallized specimens uccdepends on chain length for lower molecular weights because of the variation in the ratio of the crystallite size to extended chain length 2 6 and reaches a n asymptotic value at higher molecular weights. A value of upcof 3400 calhnol is found in the molecular weight range of 5-8 X l o 3 for a bulk crystallized sample. In this molecular weight range it is well established that extended chain crystals i.e., the aforementioned ratio is of are formed,21~z7~?* the order of unity, This does not imply, however, that molecular crystals of the kind formed by the monomeric n-hydrocarbons exist. If a correlation can be made between interfacial structure and the values of the interfacial free energy, the crystals formed from a dilute solution would by analogy possess a mildly disordered interface. This conclusion is in accordance with a (25) (a) I
