J. Phys. Chem. 1984, 88, 6587-6595
6587
Thermodynamic and Structural Properties of Copolymers of Ethylene Rufina Alamo, Roman Domszy, and Leo Mandelkern* Department of Chemistry and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306 (Received: June I , 1984; In Final Form: August 2, 1984)
Thermodynamic and structural properties of a series of compositional fractions of copolymers of ethylene were investigated. The copolymers studied included hydrogenated polybutadienes, ethylene-vinyl acetate, diazoalkane-prepared copolymers containing n-propyl side groups, and ethylene-butene-1and ethylene-octene-1copolymers prepared by Ziegler type polymerization. For those cases where random sequence distribution was established by carbon-13 NMR the melting temperatures were found to be independent of the chemical nature of the side group except for copolymers with directly bonded methyl groups. In this case it was reaffirmed that the methyl groups enter the lattice on an equilibrium basis. However, there are examples where, for the same chemical side groups, different melting temperature-composition relations are observed. This result can be attributed to small differences in the sequence distributions. Other properties such as density, enthalpy of fusion, and crystallite thickness were found to be very dependent on co-unit concentration but essentially independent of co-unit type. The relative interfacial content, as determined from an analysis of the Raman internal modes, increases very rapidly with increasing co-unit content. This quantity is also found to be independent of the chemical nature of the co-unit or branch group.
Introduction The analysis of the crystallization and melting of copolymers represents a general problem in phase equilibrium involving more than one species. In such problems, irrespective of whether small molecules or polymers are involved, an a priori decision must be made with respect to the distribution of the species (repeating units) between the phases.' When considering the equilibrium between the liquid and crystalline phases, one must decide whether the co-unit enters the crystal lattice, Le., whether cocrystallization of the species takes place or whether it is restricted to the liquid state. The second species either can enter the lattice as an equilibrium requirement, akin to compound formation in monomeric systems, or can manifest itself as an internal defect within the crystalline state. These latter two situations are quite different. They require different analytical treatments which yield different results. A general theory for the melting of copolymers has been developed by Flory on the basis of phase equilibrium theory, under the assumption that the minor co-unit does not enter the crystal l a t t i ~ e . ~(It . ~ has often been misconstrued that the exclusion of the co-units from the lattice is a deduction of the theory rather than an assumption. It is always necessary that an assumption of this type be made in order for any theoretical development to be accomplished.) According to this equilibrium theory, the melting temperature of the copolymer T,, relative to that of the homopolymer Tmo,can be expressed as2v3
Here AH, represents the enthalpy of fusion per repeating unit and p is the probability that if the crystallizing unit is selected at random it is succeeded by another such unit. Thus, the melting temperature of a copolymer does not depend directly on composition but rather on the sequence distribution. An alternative derivation of eq 1 relates the parameter p to the number of ways the sequences can be arranged along the chain.4 This term makes a contribution to the entropy of fusion which results in the melting point depression. For an ordered or block copolymer,p approaches unity. Hence, there is virtually no melting point depression with copolymerization. For a random copolymer the parameter p can be identified with the mole fraction of crystallizing units. The (1) Wilson, A. H. "Thermodynamics and Statistical Mechanics"; Cambridge University Press: Cambridge, England, 1960; pp 402 ff. (2) Flory, P. J. J . Chem. Phys. 1949, 17, 223. (3) Flory, P. J. Trans. Faraday SOC.1955, 51, 848. (4) Baker, C. H.; Mandelkern, L. Polymer 1966, 7 , 7 .
0022-3654/84/2088-6587S01.50/0 I
,
major implication of eq 1, the relation between sequency distribution and melting temperature, has been amply verified by experiment.5 Equation 1 also implies that the specific chemical nature of the noncrystallizing co-unit should not play any significant role in the crystallization behavior of copolymers as long as it is excluded from the lattice. This important conclusion has also been verified by e ~ p e r i m e n t . ~ There are, however, some serious shortcomings in the quantitative application of eq 1 to actual experimental data. These problems have been related primarily to the difficulty in actually achieving the required equilibrium condition and to the participation, on occasion, of a specific co-unit in the crystallization process. In very early studies involving random copolyesters and copolyamides it was found that although the functional form of eq 1 was obeyed, the values deduced for AH, were significantly lower than those obtained by other method^.^-^ This discrepancy can be attributed to the difficulty in crystallizing a sufficient concentration of the very long sequences that are required to satisfy the equilibrium conditions.2 Since very thin lamellae are the usual crystallite habit in such copolymers, there is a contribution to the melting point depression from this cause. In addition, there will be a perturbation of the equilibrium sequence distribution between the two phases. Foreign units contained within the crystal lattice, which behave as internal defects, will also depress the melting temperature. (Attempts have been made to calculate the effect of internal defects on the melting temperature.*-I0 These calculations have all assumed a regular folded-chain lamellar structure. The co-unit, or defect, was treated as though it were an isolated, classical impurity. It was not recognized that the crucial matter in this problem is the sequence distribution within the lattice as compared to the distribution in the noncrystalline region.) A correct modification of eq 1, which satisfies the attainable experimental conditions, has proven to be very elusive. In the present work we recognize the limitations of eq 1, which have been well documented, so that this matter is not of current concern. In contrast our interest is focused primarily on the question of the influence, if any, of specific chemical type side groups on the thermodynamic and structural properties of ethylene copolymers. Although the melting behavior of ethylene copolymers (5) Mandelkern, L. "Crystallization of Polymers"; McGraw-Hill: New York, 1964, pp 74 ff. (6) Evans, R. D.; Mighton, H. R.; Flory, P. J. J . A m . Chem. SOC.1950, 72, 2018. ( 7 ) Flory, P. J.; Mandelkern, L.; Hall, H. K. J. Am. Chem. SOC1951, 73, 2532. (8) Eby, R. K. J . Appl. Phys. 1963, 34, 2442. (9) Colson, J. P.; Eby, R. K. J . Appl. Phys. 1966, 37, 3511. (10) Sanchez, I. C.; Eby, R. K. J. Res. Natl. Bur. Stand., Secr. A 1973, 77A. 3 5 3 .
0 1984 American Chemical Societv
Alamo et al.
6588 The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 TABLE I: Molecular Characteristics of Copolymers of Ethylene [side group], mol % "C N M R Ethylene-Butene- 1 1.7 0.42 1.15 1.60 3.43 4.10 1.15 2.64 2.80 4.22
fractionation temp, OC EB EB 1 EB2 EB3 EB4 EB5 EB6 EB6a EB7 EOA EOAl EOA2 EOA3 EOB EOB 1 EOB2 EVA-A EVA-A 1 EVA-B EVA-B 1 EVA-B2 EVA-C EVA-C 1 EVA-D EVA-Dl EVA-E EVA-El EVA-F EVA-Fl
82 66 54 0 0 67 20 25
83 54 71 70 64
IR
Ethylene-Octene- 1 1.37 0.69 1.49 1.01 1.7 1.40 1.45 1.54
Ethylene-Vinyl Acetate 1.43 71.5 1.12 2.20 51.6 2.12 23 2.67 2.58 23 2.73 3.90 23 4.14 5.40 4 5.70 6.16 6.60 4
M,
14
M, 1.96
7.31
3.08
10.65
2.72
5.35
2.06
5.08
2.81
7.14 8.29 6.03 7.64
1.63 1.57 2.35 1.53
9.77 10.74
1.59 1.40
6.66
2.59
P108 HPBD4 HPBD5 HPBD7 HPBD6 HPBD 12 HPBD 1 1 a By
has been extensively studied, the major concern has been on the limitations of eq 1 and the question of internal defects."-'9 It is appropriate to note at this point that the widely observed a-axis expansion of the orthorhombic unit cell and the concomitant decrease in crystallite thickness, with increasing branching concentration, have been interpreted as meaning that the branches are included within the Since a reduced crystallite thickness is a natural consequence of a nonordered sequence distribution, B ~ n suggested n ~ ~ that a a-axis expansion could be caused by strain at the interface of the thin crystallites and the congregation of co-units in this region. Hence, the lattice expansion is not necessarily a reflection of internal defects.
Experimental Section Materials and Fractionation Procedure. Because of our main interest it was essential that compositional fractions be used in the present work. Hence, we shall describe in some detail the fractionation procedures that were used and the characterization of the copolymer samples. A fractionation procedure combining solvent extraction and preferential crystallization from dilute solution was developed for (11) Wunderlich, B.; Poland, D. J . Polym. Sci. Pur? A 1963, I , 357. (1 2) Jackson, J. F. J. Polym. Sci., Pur? A 1963, I , 2 19. (13) Casey, K.; Elston, C. T.; Phibbs, M. K. J . Polym. Sci., Polym. Let?. Ed. 1964, 2, 1053. (14) Bastien, I. J.; Ford, R. W.; Mark, H. D. J . Polym. Sci., Polym. Lett. Ed. 1966, 4, 147. (15) Bodily, D.; Wunderlich, B. J . Polym. Sci., Pur? A-2 1966, 4, 25. (16) Shida, M.; Ficker, H. K.; Stone, I. C. J . Polym. Sci., Polym. Let?. Ed. 1966, 4, 347. (17) Griskey, R. G.; Foster, G. N. J . Polym. Sci., Part A-1 1970,8, 1623. (18) Ver Strate, G.; Wilchinsky, Z. W. J . Polym. Sci., Pur? A-2 1970, 9, 177 __ . (19) Vonk, C. G. J . Polym. Sci., Part C 1972,38, 429. (20) Walter, E. R.; Reding, F. P. J . Polym. Sci. 1956, 22, 501. (21) Eichhorn, R. M. J . Polym. Sci. 1958, 31, 197. (22) Swan, P. R. J . Polym. Sco. 1962, 56, 409. (23) Baker, C. H.; Mandelkern, L. Polymer 1966, 7, 71. (24) Bum, C. W. In "Polyethylene"; Renfew, A.; Morgan, P., Eds.; Illife:
London; Chapter 5.
TABLE 11: Molecular Characteristics of Hydrogenated Polsbutadienes [ethyl side group]," mol % 2.2 f 0.3 3.2 f 0.3 4.5 f 0.5 4.4 f 0.3 5.75 f 0.5 5.50 f 0.3 7.25 f 0.3
M, 108 000 160 000 180000
MwIMn 1.3 1.05 1.05
150 000 103 000 71 000
1.05
"C NMR.
the ethylene-butene-1 and ethylene-octene-1 copolymers studied here. These copolymers were prepared by Ziegler type polymerization. The ethylene-butene- 1 whole polymer (EB) was first extracted with a series of solvents with increasingly higher boiling point. Selected extracts were then further fractionated by crystallization from dilute p-xylene solution (0.3-0.4% w/v) for 1-4 days. In selected cases the fractionation procedure was repeated until single-peaked endotherms were obtained, by differential scanning calorimetry on quenched samples. The crystallizations were conducted (in the presence of antioxidant) in a sealed tube fitted with a central fritted disk. This device allowed the separation of the crystals at the predetermined crystallization temperature. The solution was crystallized at a sufficiently high temperature so that the linear chains and those with low co-unit content precipitated from the total distribution. The suspension was then filtered and the supernatant crystallized at a second lower temperature, with the resultant suspension being collected. Fractions EB4 and EB7 were obtained from the hexane extracts. The cyclohexane extracts served as the precursors for fractions EB3 and EB6. The remaining fractions EB1 and EB2 were derived from the insoluble residue and heptane extract, respectively. The fractionation temperatures and sample characteristics are given in Table I. An ethylene-butene-1 whole polymer yielded a set of fractions whose composition ranged from 0.4 to 4 mol % ethyl side groups. The ethylene-octene- 1 copolymer series, labeled EO, were fractionated following a similar scheme. For example, for EOA, the fraction EOAl was derived from the insoluble residue of the extraction procedure while fractions EOA2 and EOA3 were obtained from the heptane extract. The whole copolymer EOB was not solvent extracted owing to its apparent high compositional homogeniety. A fractionation scheme utilizing a series of crystallizations from dilute toluene solution was used in this case. For example, EOB2 is the supernatant from the third crystallization of the whole polymer, the supernatant from each stage being used in the next crystallization. The fractionation temperature and the characteristics of this set of fractions are also given in Table I. It is clear that for these hexyl-branched copolymers each parent polymer does not yield a set of fractions which encompass a broad composition range. This result is in marked contrast to the results for the ethylene-butene- 1 copolymer. Conventional, free-radical polymerized ethylene-vinyl acetate copolymers were obtained from Scientific Polymer Products. A given whole polymer was crystallized from toluene (0.5-1% w/v) (with added antioxidant). The crystallization temperature was chosen so that the precipitate forms slowly over a period of 3-7 days. After separation at the crystallization temperature the remaining supernatant was crystallized at 23 "C. The detailed characteristics of the whole polymers, and the fractions derived from them, are also given in Table I. In general, fractionation by this procedure indicated a fairly narrow compositional distribution of acetate co-units. The properties of the hydrogenated polybutadiene polymers that were used in this work are also summarized in Table 11. Sample P108 was purchased from the Phillips Chemical Co. The other copolymers were supplied by Dr. William Graessely; their synthesis and properties have been given p r e v i o ~ s l y . ~ ~ , ~ ~ , ' ~ (25) Rachapudy, H.; Smith, G. G.; Raju, V. R.; Graessley, W. W. J . Polym. Sci., Polym. Phys. Ed. 1979, 17, 1211.
Copolymers of Ethylene
The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 6589
The copolymers containing propyl side groups were prepared TABLE III: Carbon-13 Characteristics of Ethylene-Vinyl Acetate by the copolymerization of the appropriate diazoalkanes. These Fractions samples are identical with those studied by Richardson, Jackson, re1 int MD and Flory in their pioneering work in this field.27*74 In the triad calcd obsd obsd Bernoullian preparation of these samples the copolymerization was only alEVA-Cl, 2.73 f 0.3 mol % Acetate Side Group lowed to proceed to low conversion. It can thus be presumed that EVE 0.933 0.860 93 96 they possess a narrow composition distribution. It is also well0.140 VVE 0.067 known that diazoalkane homopolymers and copolymers have very high molecular weights, Le., in the range of several m i l l i ~ n . ~ ~ , ~ ~ EVA-Fl, 6.60 0.3 mol o/c Acetate Side Group Two unfractionated ethylene-propylene copolymers were also EVE 0.774 0.691 88 studied here for certain very specific purposes. The properties VVE 0.211 0.278 83 VVV 0.014 0.0303 of these samples have been described p r e v i ~ u s l y . ~ ~ Analysis and Characterization. The determination of the at 69 and 73 ppm by for head-to-head vinyl acetate copolymer side-group content and sequence distribution is of placements, due to vinyl acetate inversion, were not observed. paramount importance in analyzing problems concerned with Tail-to-tail vinyl acetate sequences would be difficult to detect.38 copolymer crystallization. Carbon-13 N M R is clearly the method The normalized observed relative intensities, those calculated of choice for this analysis for the copolymers of interest here. by assuming a Bernoullian triad distribution model, as well as the However, because of the amount of sample that is currently needed monomer dispersity factor (MD) defined as34 to effectively apply this technique, complementary infrared absorption spectroscopic analysis was also carried out. The carbon-13 MD = [(EVE) + OS(VVE)]/(V) N M R resonances are distinguishable from one another up to the length of the pendant hexyl side Assignments to are given in Table 111. A MD value of 100 indicates that the resonances originating from the distribution of sequences are vinyl acetate units are isolated. The observed MD values are known for hydrogenated p ~ l y b u t a d i e n e and , ~ ~ the ethylene-butgenerally slightly lower than calculated. This is indicative of a ene- 134 and ethylene-hexene- 135copolymers. Graessely et a1.26 biased incorporation of the comonomer. Similar results, utilizing have reported that the hydrogenated polybutadiene samples have the same methods, have been reported for the hydrogenated poessentially a random distribution of ethyl side groups at low co-unit lyb~tadienes.~~,~~ content. There is, however, a slight tendency to develop a more The infrared method of analysis is based on the measurement ordered sequence distribution a t higher co-unit content. of the absorption coefficient of the 1378-cm-' methyl deformation The proton-decoupled carbon-1 3 N M R spectra were recorded band.40 Both fractionated and unfractionated copolymers, whose at 67.89 MHz with a pulse angle of 90' and a pulse delay of 30 compositions were accurately determined by carbon-1 3 NMR, s in a solution containing 10% w/v of polymer. Measurements were used to obtain a calibration for this absorption band. In the were made either in deuteriochloroform at 5 5 OC or in tripresent work calibration curves for the ethyl- and hexyl-branched chlorobenzene at 120 OC, depending on the dissolution temperature copolymers were determined. A separate calibration procedure and hence branch content. In the latter case the magnet was is necessary for copolymers containing different alkyl pendant sufficiently stable for use without a lock solvent. Intensities were groups since the absorption coefficient of the methyl group depends measured by peak area integration. The ethylene-butene-1 on the length of the branch. The values for propyl and longer samples were analyzed by the method developed by branches are, however, the ~ a r n e . ~ This ' , ~ ~method assumes that For the ethylene-octene- 1 copolymers, assignments based on the contribution from the terminal methyl end groups of the isolated hexyl branches were used.32 The intensities measured backbone is small. This is a reasonable assumption for the from the ethylene-vinyl acetate spectra were analyzed by using polymers studied here since M , is always greater than 5 X lo3. literature assignment^.^^,^' The ethylenevinyl acetate copolymers In the spectral region of interest (1400-1200 cm-I) the intencontained between 0.8 and 1.8 mol % butyl branches, irrespective sities of the 1365- and 1350-cm-' bands, associated with the of co-unit content. In the subsequent discussion of the properties deformation of the methylene units, are known to depend on the of these copolymers the total branch content was taken into accrystallinity of the, sample.43 They also interfere with the 1378count. cm-' band. It has been stated43that the absorption coefficient An analysis of the sequence distribution was carried out for for the 1378-cm-' band depends only on the temperature and not two ethylene-vinyl acetate fractions which contained 2.73 and on the crystallinity level. However, in the present study a de6.60 mol% side groups, respectively. On the basis of the relative pendence on the crystallinity was also found. These problems were intensities of the calculated and observed triads in the methine circumvented by recording spectra of molten samples and comcarbon r e g i ~ n , ~ a measure ~J~ of the randomness was calculated pensating for the methylene bands by obtaining difference spectra from the 13CNMR spectra. The resonance centered at 74.6 ppm utilizing a high molecular weight linear polyethylene fraction. corresponding to the EVE sequences and those at 71.5 and 70.4 Although a more accurate calibration is achieved by using molten ppm corresponding to the two forms of the comonomer triads film samples, those with a high branch content are prone to E(VV) meso and E(VV) racemic are well resolved under our oxidation. experimental conditions. Methine carbon chemical shifts predicted Uniform polymer films (0.10-0.15 mm thick) were prepared by melt quenching in air. The area per unit mass and the density were measured at 23 O C . The films were cut into 2.5 cm diameter (26) Krigas, T. M.; Carella, J. M.; Struglinski, M. J.; Crist, B.; Graessley, disks and placed on one side of a sodium chloride plate before W . W.; Schilling, F. C. J . Polym. Sci. Polym. Phys. Ed., in press. (27) Richardson, M. J.; Flory, P. J.; Jackson, J. B. Polymer 1963, 4, 221. being mounted in a Perkin-Elmer heated cell which was con(28) Fatou, J. G.; Mandelkern, L. J . Phys. Chem. 1965, 69, 417. trollable to f 2 OC. Spectra were recorded at 23 and 140 OC by (29) Axelson, D. E.; Mandelkern, L.; Popli, R.; Mathieu, P. J. Polym. Sci., using a Perkin-Elmer 983 grating spectrometer equipped with a Polym. Phys. Ed. 1983, 21, 2319.
*
(30) Dorman, D. E.; Otocka, E. P.; Bovey, F. A. Macromolecules 1972, 5. 574.
(31) Randall, J. C. J . Polym. Sci., Polym. Phys. Ed. 1973, 11, 275. (32) Axelson, D. E.; Mandelkern, L.; Levy, G. C. Macromolecules 1977, 10, 557. (33) Randall, J. C. J . Polym. Sci., Polym. Phys. Ed. 1975, 13, 1975. (34) Hsieh, E. T.; Randall, J. C. Macromolecules 1982, 15, 353. (35) Hsieh, E. T.; Randall, J. C. Macromolecules 1982, 15, 1402. (36) Wu, T. K.; Ovenall, D. W. J. Polym. Sci., Polym. Phys. Ed. 1974, 12, 901. (37) Sung, H. N.; Noggle, J. H. J . Polym. Sci., Polym. Phys. Ed. 1981, 19, 1593.
(38) Randall, J. C. "Polymer Sequence Determination. Carbon-1 3 NMR Method"; Academic Press: New York, 1977. (39) Domszy, R. C.; Alamo, R.; Mathieu, P. J. M.; Mandelkern, L. J. Polym. Sci., Polym. Phys. Ed. 1984, 22, 1727. (40) Willbourn, A. H. J . Polym. Sci. 1959, 34, 569. (41) Reding, F. P.; Lovell, C. M. J . Polym. Sci. 1956, 21, 157. (42) Freche, P.; Grenier-Loustalot, M.; Cascoin, A. Makromol. Chem. 1982, 183, 883. (43) Cross, L. H.; Richards, R. B.; Willis, H. A. Discuss. Faraday SOC. 1950, 9, 235.
6590 The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 100-
I
I
I
I
Alamo et al. The weight- and number-average molecular weights were obtained from gel permeation chromatography following conventional
I
procedure^.^^ L
80-
W V
$60-
tai
m
-
0
%
i40-
-
2ot MOLE PERCENT SIDE-GROUP
Figure 1. Infrared calibration of side-group concentration. Plot of spe-
cific absorbance at 1378 cm-I against side-group concentration determined by means of high-resolution carbon-13 NMR: Ethyl branches: (0) 23 and ( 0 ) 140 O C . Hexyl branches: (A) 140 OC. data station. A resolution of 1.O cm and a scan time of 13 min were used. A spectra of linear polyethylene ( M , = 225000), recorded at the appropriate temperature and after being suitably scaled, was digitally subtracted from the copolymer spectra, leaving the 1378-cm-l absorption as a symmetrical undistorted band for most samples. The specific absorption coefficient ( K ) was determined from
mr) = - 4 r ) 1% U O / l )
(2)
where A is the area per unit mass (cm2 g-l) of the sample at temperature T and log (Z,,/l) is the absorbance obtained from peak height measurement of the deconvoluted 1378-cm-' band. In order to determine K(140 "C) a correction to the measured area per unit mass is required. The correction was made according to eq 3 by assuming isotropic expansion and accounting for the latent A(140 "C)
A(23 "C)[1
+ d((1 - X)AV, + AV,)]2/3
(3)
volume change. Here d is the density of the polymer at 23 "C, 1 - X is the volume crystallinity at 23 OC, AVl is the volume change from perfect crystal to the melt (at 23 "C, 0.172 34 cm3 gl),and AV, is the volume change of the melt from 23 to 140 "C (0.10296 cm3 g-I). The specific absorbance measurements at 140 O C for both types of branching are plotted in Figure 1 together with data measured at 23 OC for the ethyl-branched copolymers. At 140 OC the data for each of the copolymers are linear but have different slopes. Hence, a separate calibration is clearly necessary. The data for the ethyl-branched copolymer at 23 O C are also apparently linear but with a greater slope than the high-temperature data. They are thus more sensitive to copolymer compositional changes. However, at this temperature the results are also sensitive to crystallinity. For example, for the hydrogenated polybutadiene sample P108, a 7% increase in crystallinity results in a 19% increase for the value of K at 23 "C.
Crystallization and Melting Procedures. Crystallizations were conducted from the melt under two extreme sets of conditions. For those fractions where sufficient material was available (P108, HPBD7, EVA-B2, EVA-Fl), crystallization and fusion were studied by standard dilatometric methods. Conventional dilatometer~:~with sample weights ranging from 0.2 to 1.0 g, were employed. In order to minimize the volume of mercury required, a spacer, about 1 mm less than the internal diameter of the dilatometer bulb, was used. The crystallization procedures were similar to those used by Richardson, Flory, and Jackson.27 Samples sealed in the dilatometer were completely melted by heating at 150 "C for 1 h. They were then quickly brought to a bath controlled at a temperature 2 "C below the melting temperature (measured by differential scanning calorimetry (DSC) or by fast melting of the sample in the dilatometer), this temperature being maintained for 7-10 days. Under these conditions only about 2-10% crystallinity is developed. The temperature was subsequently reduced approximately 1 OC every 5 h. When the temperature was about 20 "C below the melting temperature, the sample was allowed to crystallize slowly by turning the oil bath off (it normally took about 10-12 h to cool to room temperature). Although this procedure involved a somewhat shorter crystallization period than that used by Richardson, Flory, and Jackson,27 the final results were about the same. Subsequent to crystallization, the samples were heated at a rate of 10 "C/h until a temperature of about 40 "C below the melting temperature was reached. The heating rate was then decreased to about 1-2 OC/h until about 15 "C below the melting temperature. Subsequently, the temperature was increased at about 1 OC/day until melting. The total time involved in the fusion process was about 15-20 days. Fractions which were not available in amounts large enough for dilatometry were quenched rapidly from the melt to -35 "C, and the fusion process was followed by DSC. This crystallization procedure was adopted to ensure as similar as possible morphological and crystallite structure between the different copolymers. A Perkin-Elmer DSC-2B instrument was used with a heating rate of 20 "C/min. Melting points were identified with the maximum in the endothermic peak.46 In order to avoid differences in this melting temperature caused by variations in sample weight, the mass of sample was limited to approximately 2 mg in all experiment~.~~~~~ The enthalpies of fusion determined from the DSC thermograms were converted to degrees of crystallinity by using the enthalpy of fusion AH, of a perfect polyethylene crystal at the melting point of the copolymer. AH,, at T," was taken to be 69 cal/g and ACp = 0.0713 ~ a l / g . ~ ~ The densities of the samples quenched from the melt to -70 "C were measured at 23 OC in a 2-propanol-water density gradient column calibrated with standard glass floats.28 These density values, with the exception of those for the ethylene-vinyl acetate copolymers, were converted to degree of crystallinity by the specific volume relationship given by Chiang and F10ry.~~This relation has been shown to be applicable to ethylene c o p o l y r n e r ~ . ~ ~ The Raman spectra in the internal mode region were obtained by using instrumentation that has been previously described, as has the detailed method of data a n a l y ~ i s . ~The ~ - ~laser ~ power (44) Westerman, L.; Clark, J. C . J . Polym. Sci., Polym. Phys. Ed. 1973, 11, 559. (45) Ergoz, E.; Fatou, J. G.; Mandelkern, L. Macromolecules 1972,5, 147. (46) Mandelkern, L.; Stack, G. M.; Mathieu, P. J. M. Anal. Calorim. 1984, 5, 223. (47) Harrison, I. R ' Varnell, W. D. J . Therm. Anal. 1982, 25, 391. (48) Flory, P. J.; V&, A. J . Am. Chem. SOC.1963, 85, 3548. (49) Chiang, R.; Flory, P.J. J . Am. Chem. SOC.1961, 83, 2057. (50) Glotin, M.; Mandelkern, L. Colloid Polym. Sci. 1982, 260, 182. (51) Glotin, M.; Domszy, R.; Mandelkern, L. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 285. ( 5 2 ) Strobl, G. R.; Hagedorn, W. J . Polym. Sci., Polym. Phys. Ed. 1978, 16, 1181.
The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 6591
Copolymers of Ethylene
6ot 0
I
1
I
I
I
I
I
1
2 3 4 5 6 7 MOLE PERCENT BRANCHES
\ i I
8
I
9
Figur Dilatometric-determinedmelting temperatures, T,, of ethylene copolymers plotted against mole percent branches. Dashed line represents equilibrium theory for random copolymer as calculated from ref 2. Experimental results: diazoalkane copolymers from ref 27 methyl branch (0);ethyl branch (0); propyl branch (A). Present work hydrogenated polybutadiene (A); ethylene-vinyl acetate ( 0 ) .
was limited to 100 mW to avoid heating the samples. To remove the interference originating from the acetate side group in the ethylene-vinyl acetate copolymers, the carbonyl stretching band near 1740 cm-' was used as the intensity standard to subtract the spectrum of poly(viny1 acetate) from that of the copolymer^.^^ The instrument and methods used to obtain the low-frequency Raman longitudinal acoustical mode (LAM) have also been previously described in detai1.53*54,59 The laser power was again limited to 50-100 mW to avoid heating the sample. The raw LAM data were corrected for the temperature and frequency dependence and transformed into a distribution of ordered sequence lengths by using methods developed by Snyder et a1.55956 The value for Young's modulus in the chain direction was taken to be 2.9 X 10l2 N m-2.57
Results and Discussion Melting Temperatures. We first examine the influence of the concentration and chemical nature of the side groups on the melting temperatures determined by dilatometric methods. These results are summarized in Figure 2. Also plotted in this figure are the results of Richardson, Flory, and Jackson27for the random diazoalkane copolymers containing either methyl, ethyl, or n-propyl side groups. These earlier results had clearly shown that the copolymers containing the directly bonded methyl groups had significantly higher melting temperatures than those with longer alkyl type side groups. These results must reflect the fact that the methyl groups enter the lattice on an equilibrium baskz7 A more detailed study has shown that there is actually a maximum, at low co-unit content, in the melting temperature-composition relation for this type of copolymer.23 In contrast, co-units entering the crystal lattice as nonequilibrium defects will invariably cause a lowering of the melting temperature. The melting temperatures of the ethyl- and propyl-branched diazoalkane copolymers have the same concentration dependence. These melting temperatures are substantially less than those of (53) Glotin, M.; Mandelkern, L. J . Polym. Sci., Polym. Phys. Ed. 1983,
the methyl-branched samples of corresponding compositions. The dashed line in the figure represents the expectation from equilibrium theory for a random copolymer as calculated from eq 1 with Tmo= 418.5 K and AH,, = 970 cal/mol. The reasons for the major discrepancy between experiment and equilibrium theory have already been discussed in the Introduction and amply described in the As far as the original results for the diazoalkane copolymers are concerned all but one of the pints on the lower curve in Figure 2 represent samples containing n-propyl side groups. The other point represents an ethyl-branched copolymer. These results caused some doubt to be raised as to the validity of the conclusion that side groups larger than methyl all follow the same melting temperature relation.I6 We have therefore expanded this type of study by measuring the melting temperatures of compositional fractions of two hydrogenated polybutadienes and two ethylenevinyl acetate copolymers. As has been indicated earlier the NMR analysis indicates essentially a random sequence co-unit distribution at the lower branching content for these copolymers. The dilatometrically determined melting temperatures for these samples are also given in Figure 2. The melting temperatures of these four new copolymer samples fall on the same curve as those for the propyl and ethyl side group diazoalkane copolymers. We can conclude, therefore, that copolymers which contain side groups larger than methyl, Le., ethyl, propyl, vinyl acetate, and larger, must behave in a very similar way with respect to incorporation into the crystal lattice. Because of the large size variation in these side groups they cannot enter the lattice to any meaningful extent in bulk crystallized systems. A similar conclusion has been reached from selective oxidation studies of both ethylene-butene cop o l y m e r ~ and ~ ~ conventional high-pressure branched polyethylene.59 On the other hand, from low-angle neutron and X-ray scattering studies of chlorinated polyethylene, Fisher has concluded that there is a substantial chlorine content within the lattice.6G Vonk61 has suggested that relatively small side groups, such as methyl, chlorine, and oxygen, enter the lattice, while the larger groups are excluded. Except for the methyl branch, it still remains to be determined whether the included species enter the lattice under equilibrium requirements. The major conclusion to be drawn from the melting point data of Figure 2 is that, except for the methyl side group copolymers, the melting temperatures are independent of the chemical nature of the co-unit when random sequence distribution is established beforehand. They depend only on the co-unit content. Hence, the much earlier conclusion of Flory, Richardson, and Jackson27is clearly substantiated. Dilatometric studies of fractions suffer from the restraint of the relatively large amount of material needed. Hence, more extensive melting point measurements were carried out by differential scanning calorimetry. In these experiments in order to eliminate the influence of crystallite size, as well as other aspects of morphology, very rapid crystallization and heating rates were used. Although these procedures are clearly far from equilibrium, they are quite adequate for comparative type experiments. All of the copolymer types studied dilatometrically, and described in Figure 2, were also studied by this procedure. In addition, the melting temperatures of the fractions of ethylene-butene- 1 and ethylene-octene- 1 copolymers were also obtained. The endothermic peaks were found to broaden considerably with increasing co-unit content as would be expected theoreti~ally.~J The fusion process takes place over an increasingly wider temperature range because of the restriction imposed to the longitudinal development of the crystallite^.^^^,^ The position of the endothermic peak is also systematically lowered with increasing co-unit content. The melting temperatures determined by differential scanning calorimetry are plotted against the mole percent of branches in
21, 29.
(54) Glotin, M.; Mandelkern, L. J . Polym. Sci., Polym. Left. Ed. 1983, 21, 807. (55) Snyder, R. G.; Krause, S. J.; Scherer, J. R. J . Polym. Sci., Polym. Phys. Ed. 1978, 16, 1593. (56) Snyder, R . G.; Scherer, J. R. J . Polym. Sci., Polym. Phys. Ed. 1980, 18, 1421. (57) Strobl, G. R.; Eckel, R. J. Polym. Sci., Polym. Phys. Ed. 1976, 14, 913.
(58) Cutler, D. J.; Hendra, P. J.; Cudby, M. E. A,; Willis, H. A. Polymer 1977, 18, 1005.
(59) Bowmer, T. N.; O'Donnell, J. H. Polymer 1977, 18, 1032. (60) Kalepky, U.; Fischer, E. W.; Herchenriider, P.; Schellen, J.; Lieser, G.; Wegner, G. J . Polym. Sci., Polym. Phys. Ed. 1979, 17, 21 11. (61) Vonk, C. G. "Polyethylene Golden Jubilee Conference"; Plastics and Rubber Institute: London, 1983; Vol. D2.1.
6592
The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 I
4
I
I
O
I
I
I
a
I
I
(62) Mandelkern, L.; Posner, A. S.; DiOrio, A. F.; Roberts, D. E. J . Appl. Phys. 1961, 32, 1509. (63) Fischer, E. W.; Schmidt, G . F. Angew. Chem., Int. Ed. Engl. 1962, I , 488. (64) Grubb, D. T.; Liu, J. J. H.; Caffney, M.; Bilderback, D. H. J . Polym. Sci., Polym. Phys. Ed. 1984, 22, 361. ( 6 5 ) Alamo, R.; Mandelkern, L., to be submitted for publication.
Alamo et al. position relation as they did in the dilatometric studies. Since these copolymers have close to random sequence distribution, concordance in their melting temperatures is expected. Most interesting is the fact that the hexyl-branched copolymers (ethylenmtene-1) follow the same melting temperature relation, while very different results are obtained with the fractions from the ethylene-butene-1 copolymer. The melting temperatures of these particular ethylene-butene fractions, in this composition range, are significantly higher than those of the other copolymers studied. These differences are about 5 “ C for 0.5 mol % side groups and increase to 10 O C at about 3 mol %. These differences in melting temperature cannot be attributed to the chemical nature of the side groups since a direct comparison can be made with the hydrogenated polybutadienes which contain ethyl side groups and are thus chemically identi~al.’~ On the basis of eq 1 we then conclude that the melting point differences are a result of different sequence distributions between the ethylbutene- 1 copolymer and the others, including the ethyl-octene- 1 polymer. The difference in sequence distribution could be caused by different polymerization procedures as well as different comonomer reactivity ratios for the same general polymerization method. In the composition range of interest in the present work, Le., the order of a few mole percent co-unit, only very small differences in the sequence propagation parameter p can cause melting point differences of the magnitude observed here. For example, for a random sequency copolymer, like hydrogenated polybutadiene, p = 0.980 for 2 mol % side group content. If we assume that the contributions to the deviation from equilibrium are the same for both types of polymers, then from the melting temperature determined for the 2 mol % ethylene-butene copolymer, the calculated value o f p = 0.9875. A similar conclusion is reached in the analysis of the higher co-unit content samples (see below). Therefore, for the data under present discussion the differences in melting temperature between the ethylene-butene and ethylene-octene copolymer are not directly due to the difference in the chemical nature of the side groups. Rather, there must be small differences in sequence distribution between the two cases. It is clearly conceivable that varying copolymerization conditions, with a change in reactivity ratios, could alter the situation and conceivably reverse matters. As theory teaches, except for the very specific situation of cocrystallization, neither the chemical nature of the co-unit not its nominal composition directly determines the melting temperature. The melting temperatures of the higher co-unit copolymers studied here do not give as simple a result as in the lower concentration. However, there are still several important features in this set of data. For purposes of discussion it is convenient to take the results for the hydrogenated polybutadienes as reference. The diazoalkane copolymers follow the same melting temperature pattern as the hydrogenated polybutadienes. The melting temperatures of the ethylene-butene-1 fractions are still quite definitely about 10 OC higher. Thus, the differences in the sequence distribution of co-units are still maintained. On the other hand, the melting temperatures of the ethylene-vinyl acetate copolymers are beginning to deviate from the results for the other random copolymers. Their melting temperatures are now 10-15 OC higher with increasing co-unit content. This pattern of the melting point composition relation indicates a tendency for the ethylene-vinyl acetate copolymers to deviate from random sequence and to develop a more ordered distribution. As was indicated previously such a trend is consistent with the currently available NMR analysis. Degree of Crystallinity. It is well established that for linear polyethylene,66 as well as other homopolymer^,^^ the level of crystallinity is very dependent on the molecular weight. Crystallinity decreases with an increase in molecular weight. However, for fractions of conventional, high-pressure, branched polyethylene, as well as for hydrogenated polybutadiene it has been shown that (66) Mandelkern, L. “20th Army Materials Research Conference”; Syracuse University Press: Syracuse, NY, 1975; pp 369. (67) Mandelkern, L.; Allen, R. C., to be submitted for publication.
Copolymers of Ethylene
The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 6593
.60
v
MOLE PERCENT BRANCHES
Figure 4. Plot of degree of crystallinity calculated from enthalpy of fusion measurements, (1 - A ) M , against mole percent branches: hydrogenated polybutadiene (A);ethylene-vinyl acetate ( 0 ) ;diazoalkane copolymer with propyl side groups (A);ethylene-butene copolymer (0);
ethylene-octene copolymer (H). the level of crystallinity is dependent primarily on the co-unit ~ o n t e n t . ~It~is, ~essentially ~ independent of molecular weight except in the extreme limits of chain length.68 With this background, we examine in Figure 4 the influence of co-unit content on the level of crystallinity for the copolymers studied. The degree of crystallinity, as derived from the enthalpy of fusion, (1 - A,) is plotted against the side-group content for samples rapidly crystallized from the melt. The propyl-branched copolymers give somewhat smaller, but significantly different, values for (1 - A), as compared to the other copolymers. This difference can be attributed to the very high molecular weights of the diazoalkane copolymers. The molecular weights for all the other copolymer fractions are in the range between 5.0 X lo4 and 2.0 X lo5. The introduction of noncrystallizing co-units into the chain leads to a very rapid and continuing decrease in (1 - A), with increasing side-group content. The chemical nature of the side group has virtually no influence on the values of (1 - A), for these samples. The level of crystallinity varies from about 0.50 to less than 0.10. This steady decrease in the degree of crystallinity and thus the enthalpy of fusion, with co-unit content, is a natural consequence of copolymer crystallization. Since the side group is excluded from the lattice, the concentration of sequences of crystallizing units that can participate in the crystallization process becomes severely restricted as the concentration of randomly introduced co-units is increased. For this reason the detailed chemical nature of a co-unit should not be very important. As can be seen from the data in Figure 4,we have found that the chemical nature of the side group has virtually no influence on (1 - A)Aw The results described above are surprising in one respect. The differences in melting temperatures between the ethylene-butene and the other copolymers were attributed to small differences in the parameter p . Yet we find that the degree of crystallinity, as derived from the enthalpy of fusion, is the same for all the polymers at a given co-unit content. This apparent contradiction can be explained by examining some of the details of equilibrium theory.*J Theoretically, in the range of interest here, small differences in the value of p will only significantly influence the level of crystallinity in the fusion range. At lower temperaturs, comparable to the rapid crystallization conditions employed here, the differences in the level of crystallinity over the range of p values of (68) Mandelkern, L.; Glotin, M.; Benson, R.A. Macromolecules 1981,14, 22. (69) Glotin, M.; Mandelkern, L. Macromolecules 1981, 14, 1394.
I
2o0
2
3
5
4
6
MOLE PERCENT BRANCHES
Figure 5. Plot of degree of crystallinity calculated from density measurements, (1 - A)d, against mole percent branches: hydrogenated polybutadiene (A);ethylene-butene copolymer ( 0 ) ;ethylene-octene copolymer (H). ,601
I
I
I
I
I
,20t ,lot
/
/'
/ .IO .30 SO
0
.40
.20
.50
(I-h)d
Figure 6. Plot of (1 - A),
against (1 - A)d: hydrogenated polybutadiene (A);ethylene-butene copolymer (0);ethylene-octene copolymer (W).
interest are very small even under equilibrium conditions. For the actual nonequilibrium situation these differences should actually be even less. The levels of crystallinity were also determined from the density measurements for the hydrogenated polybutadienes, and the ethylene-butene- 1 and ethylene-octene- 1 copolymers. These results are given in Figure 5 and are again found to be independent of the chemical nature of the co-unit. The degree of crystallinity determined from the density depends on the co-unit content in a very similar manner as was found for the enthalpy of fusion. For a very wide variety of bulk and solution crystallized linear polyethylenes, and ethylene copolymers, it has been found that the density always yields about a 10%greater value for the degree of crystallinity than does the enthalpy of f ~ s i o n . ~ The ~ * ~ ~ * ~ ~ ~ results with the copolymers studied here follow a very similar pattern as is illustrated in Figure 6. The degrees of crystallinity (70) Maxfield, J.; Mandelkern, L. Macromolecules 1977, 10, 1141.
6594
The Journal of Physical Chemistry, Vol. 88, No. 26, 1984 I
0.lt
0
I
0 .
I
I
I
I
I
Alamo et al.
I
/
1
I
I
I
I
I
2
3
4
5
6
7
8
MOLE PERCENT BRANCHES
Figure 7. Plot of interfacial content q ainst mole percent branches: hydrogenated polybutadiene (A);ethylene-vinyl acetate (0)f diazoalkane copolymer with propyl side groups (A);ethylene-butene copolymer (0); ethylene-octenecopolymer (m); ethylene-propylene copolymer (0). Solid curves indicate data trends.
determined from densities are about 10%greater than the enthalpy of fusion values. It has been suggested that the difference between (1 - A)d and ~ ~ density (1 - A), is due to contributions from the i n t e r f a ~ e .The measurements include a contribution from the interface. The interfacial content of the polyethylene can be obtained from an analysis of the Raman internal mode^.^^^^* It is to be expected that copolymers would possess a more extensive interfacial region because of the rejection of co-units from the lattice and their high concentration, relative to the nominal one, at the crystallite interfce. The interfacial content, ab,determined from the Raman internal modes, is plotted in Figure 7 for the rapidly crystallized copolymers studied here. Also plotted are the results for two unfractionated ethylene-propylene samples.29 Except for the diazoalkane propyl-branched copolymers, the results for all the other samples follow the same general pattern. For these copolymers the values of ab range from about 5% to 25% as the branching content increases from 0.5 to 6 mol %. Comparison of these data with previous results obtained with other ethylene copolymers shows good agreement.29*50*71 There is a virtual coincidence of all the available data. Thus, the chemical nature of the specific side group does not influence the relative interfacial content. The results for the two ethylene-propylene copolymers fall into the same grouping. As was pointed out eariler a substantial concentration of the directly bonded methyl groups are incorporated into the crystal lattice. However, within the current limits of experiment this fact does not disturb the proposed Raman a n a l y ~ i s . ~Put ~ *another ~~ way, the co-units incorporated into the lattice do not disturb the deduction of the interfacial content from the Raman spectrum. The propyl-branched copolymers clearly give higher values for the interfacial content. This result is not a consequence of the chemical nature of the branched species. Rather it reflects the very high molecular weight, characteristic of this series of copolymers. These results parallel the findings for the linear polyethylenes. For bulk crystallized linear polyethylene the interfacial content is known to increase substantially in the high molecular weight range, with a corresponding influence on certain
proper tie^.^^^^' The degree of crystallinity, ac,as calculated from the Raman internal model,50352 depends on the co-unit content in a very similar (see Figures 4 and 5). manner as does (1 - A), and (1 - A), However, differences of the order of 5-10% have been previously found between a, and (1 - A)AH, for both bulk and solution crystallized copolymers of ethylene at any given co-unit content. (71) Popli, R.; Glotin, M.; Mandelkern, L.; Benson, R. S. J . Polym. Sci., Polym. Phys. Ed. 1984, 22, 407.
(I-x)d
Figure 8. Plot of aF
+ ab,determined from Raman internal modes
against (1 - A)d: hydrogenated polybutadiene copolymer (0); ethylene-octene copolymer (m).
ethylene-butene
(A),
I
20
'0
I 2 3 4 5 6 MOLE PERCENT BRANCHES
/
Figure 9. Plot of most probable ordered sequence length LR,as determined from Raman LAM, against mole percent branches, for samples quenched to -78 "C: hydrogenated polybutadiene (A); ethylene-butene copolymer (0); ethylene-octene copolymer (m); ethylene-propylene copolymer (A);linear polyethylene, M , = 1.05 X lo5 (0).
A similar difference is manifested in the present work. These small differences can be attributed to the fact that, because of the very broad melting range, (1 - ,A) includes a contribution to the enthalpy of fusion from crystallinity which disappears at room temperature. On the other hand, the Raman-determined a, only measure the crystallinity at the ambient temperature. Consistent with the premise that the density measurements include a contribution from the interfacial region, while a, only measure the core thickness, it was previously found that for bulk crystallized polyethylene a, ab = (1 - A)& A similar situation holds for the present data as is shown in Figure 8. Crystallite Thickness. It has previously been demonstrated that the analysis of the low-frequency Raman longitudinal mode (LAM) is a very effective method for determining the distribution of ordered sequence lengths in all types of polyethylene^.^^^^^ When these data are corrected for the tilt angle, this measurement yields the crystallite thickness. Typical examples of the spectra that can be obtained from bulk crystallized, branched polyethylenes as well
+
J . Phys. Chem. 1984,88, 6595-6605 as from ethylene copolymers have already been given.71 Very good spectra can also be obtained from solution crystals of ethylene copolymer^.^^ Hence, this analytical method presents no difficulties when applied to copolymers. The ordered sequence lengths which correspond to the peak height in the distribution, the most probable value, are given in Figure 9 for the rapidly crystallized copolymer fractions studied here. With the exception of the methyl-branched copolymers, all of the other copolymers display essentially the same behavior, irrespective of the specific chemical nature of the side group. If we take the rapidly crystallized linear polyethylene as a reference point, a very precipitous decrease in the ordered sequence length takes place with the initial random introduction of co-units. The most probable size has been reduced by more than a factor of 2 when 3 mol % of side groups have been introduced. However, as the branching content increases to 6 mol %, the most probable value, as well as the total size distribution, does not change very much. We can recall, however, from Figures 4 and 5 that the level of crystallinity that is attained continuously decreases with increasing co-unit content. An insight into this apparent contradication can again be obtained by recourse to theory. The minimum sequence length necessary for incipient crystallization can be calculated on an equilibrium basis. It is found to be about 50 8, for ethylene copolymers and is independent of copolymer composition at low temperatures. On the other hand, the level of crystallinity that can be attained depends on the concentration of suitable sequences. This quantity continually decreases with increasing co-unit content. The results shown in Figure 9 for the two ethylene-propylene copolymers are clearly quite different. They obviously do not behave as random copolymers with co-units excluded from the crystal lattice. The much larger crystallite size, for a given co-unit content, which is in fact very close to that found for the linear homopolymer, reflects the less severe restriction on the availability of crystallizable sequences. These results could be anticipated from the melting point studies where it was established that the methyl groups enter the crystal lattice on an equilibrium basis.27 Crystallite structure and properties would thus be expected to be
6595
closer to that of homopolymers rather than the random copolymers. This expectation is found in many properties, including the present crystallite size measurements, and recent studies of mechanical behavior.72 In summary, the study of the compositional fractions of ethylene copolymers has substantiated certain general principles. Except for the copolymers containing directly bonded methyl groups, the observed melting temperatures, under extremes in crystallization conditions, are independent of the chemical nature of the side groups, or co-units, as long as a random sequence distribution is maintained. However, the observed melting temperatures are shown to be very sensitive to small changes in the sequence distributions. Hence, a discussion and comparison of melting temperatures cannot be made solely on the basis of chemical composition. Other properties such as crystallite thickness, degree of crystallinity, and interfacial content, except for the methylbranched samples, do not depend on the chemical nature of the side group. They are, however, very sensitive to the copolymer composition. The behavior and properties of the methyl-branched copolymers are very similar to that of the homopolymers.
Acknowledgment. The support of this work by the Exxon Chemical Corp. is gratefully acknowledged. R.A. acknowledges support provided by Comisidn Asesora de Investigacidn Cientifica y Ticnica, CAICYT (Spain). Registry No. (Ethylene).(butene-I) (copolymer), 25087-34-7; (ethylene).(cctene-1) (copolymer),26221-73-8;(ethylene).(vinylacetate) (copolymer), 24937-78-8; (ethylene).(propylene)(copolymer),9010-79-1. (72) Capaccio, G.; Ward, I. M. J. Polym. Sci., Polym. Phys. Ed. 1984, 22, 475. (73) We sincerely thank Dr. Graessely for his kindness in supplying us with these samples and for many helpful discussions with regard to their properties. (74) We thank Professor P. J. Flory for kindly furnishing us with these
samples. (75) The melting temperature recently reported by Graessely et al. for the hyrogenated polybutadienes are about 10 O C higher than those reported here.26 These differences can be attributed to the selection of different portions of the endotherms in the two studies.
Equilibrium Copolymerization as a Critical Phenomenon Stephen J. Kennedy+and John C. Wheeler* Department of Chemistry, University of California, San Diego, La Jolla, California 92093 (Received: June I, 1984)
A lattice model for equilibrium copolymerization is introduced. An extended model is also presented, with a qualitative application to sulfur-selenium copolymerization, where the “monomer” consists of more than one A or B type subunit. The models are solved for the limiting case of long copolymer chains. In both cases a trace over the Ising-like variables A,-B is performed first, followed by a mapping onto an underlying n 0 vector model. The n 0 vector model incorporates the polymer excluded volume.
-
I. Introduction In this paper we will present a model for a particular type of copolymerization, that is, equilibrium copolymerization. In equilibrium copolymerization the chain propagation step is reversible and involves more than one type of monomer. The polymerization is incomplete and copolymer chains and monomer units are in thermodynamic equilibrium. The extent of polymerization and the length, composition, and sequence distribution of the copolymer chains are temperature dependent. The properties of the system are not determined by rates of reaction as is the case in a large number of copolymerizations. Some examples Present address: Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139.
0022-3654/84/2088-6595$01.50/0
-
of systems that undergo equilibrium copolymerization are the thermal copolymerization of sulfur and selenium, copolymerization by a “living” polymer mechanism,’ and copolymerization of vinyl compounds near their ceiling temperatures. The model we present here is a lattice model. The volume of the system is divided into cells on a regular lattice where each cell will contain either an A or B unit which can be either a monomer or part of a polymer chain. A statistical weight will be assigned to the monomer and to the copolymer chains. The statistical weight of a particular copolymer chain will depend upon (1) (a) Szwarc, M. “Carbanions, Living Polymers, and Electron Transfer Processes”; Wiley: New York, 1968. (b) Lowry, G. G. J. Polym. Sci. 1960, 42, 463.
0 1984 American Chemical Society
