Copolymerization with Ziegler-Natta catalysts—II. Monomer reactivity ratios for several olefin pairs

Copolymerization with Ziegler-Natta catalysts—II. Monomer reactivity ratios for several olefin pairs

European Polymer Journal. 1967, Vol. 3, pp. 161-170. Pergamon Press Ltd. COPOLYMERIZATION Printed in England. WITH ZIEGLER-NATTA CATALYSTS 4II. M ...

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European Polymer Journal. 1967, Vol. 3, pp. 161-170. Pergamon Press Ltd.

COPOLYMERIZATION

Printed in England.

WITH ZIEGLER-NATTA

CATALYSTS 4II. M O N O M E R R E A C T I V I T Y R A T I O S F O R S E V E R A L O L E F I N PAIRS

I. H. ANDERSON,* G. M. BUgNETTand W. C. GEDDESt Department of Chemistry, University of Aberdeen, Old Aberdeen, Scotland (Received 7 January 1967)

Alntraet--The study of copolymerizations of styrene with a-olefins, using a Ziegler-Natta catalyst composed of aluminium triethyl and a-titanium trichloride in toluene, has been extended to hex-l-ene, hept-l-ene, and 4-methylhex-l-ene. These results, together with those from a similar study of 4-methylpent-l-ene reveal a pattern of reactivity which is governed by a combination of steric and electronic factors. Determination of reactivity ratios gave the values: styrene/hex-1-ene, r~ffi0"19+ 0.04, r2 = 9"75+ 0-81 ; styrene/hept-l-ene, rl--0"61+0-01, r2=5"70+0"15; styrene/4-methylhex-l-ene, rl--1"80+0"04, r2-- 1"30+0"06. These values were found to be independent of temperature, catalyst ratio and catalyst concentration but subject to the nature of the TIC13sample. The styrene/hex-l-ene and styrene/hept-l-ene copolymers were isolated as rubbers but the styrene/4methylbex-l-ene copolymers gave crystalline X-ray patterns, which indicate mixtures of block copolymers (cf. styrene/4-methylpent-l-ene copolymers). THE COPOLYMERIZATIONSof styrene with 4-methylpent-l-ene and with 5-methylhex-1ene have been described in previous papers. (1,2) Since the products of the m o n o m e r reactivity ratios obtained were greater than unity in each case, the work has been extended to the study of a series of a-olefins copolymerized with a c o m m o n monomer. A study of such a series, using identical reaction conditions, is of value in establishing an order of reactivity which can be compared with the order of reactivity obtained from overall rates, and should illustrate the relative importance of steric and electronic factors. In heterogeneous catalyst systems, active sites of variable reactivity invalidate the assumption that the reactivity ratios are the same throughout the system. When using Ziegler-Natta catalysts (3) therefore, it must be remembered that such things as crystal size, method of preparation of the catalyst, rate of stirring and dispersion may profoundly influence the values obtained for reactivity ratios. Since the copolymerization of two m o n o m e r pairs t1'2) has given rise to polymers which are heterogeneous in character, the effect of several experimental variables on the values of the m o n o m e r reactivity ratios has been studied in more detail, and the values found to be remarkably constant. * Present address: Heriot-Watt University, Edinburgh, Scotland. t Present address: Rubber and Plastics Research Association of Great Britain, Shawbury, Shrewsbury, England. II 161

162

I . H . ANDERSON, G. M. BURNETI" and W. C. G E D D E S

MATERIALS AND EXPERIMENTAL TECHNIQUE Hex-l-ene This monomer, ex B. Newton Maine Ltd., was dried over sodium sulphate and fractionally distilled at atmospheric pressure. The fraction boiling at 63.5--64.0 ° (n2°= 1-3883) was collected. Hept-l-ene This monomer, ex B. Newton Maine Ltd., was fractionally distilled as above, the fraction boiling at 93.0-94.0 ° (n~° = 1.4005) being collected. 4-Methylhex-l-ene This olefm, exB. Newton Maine Ltd., was 99 per cent pure, boiling point 87.0 °, (n~°--- 1.4020). The sample showed no optical activity and it was assumed that it was a racemic mixture. Immediately before use, the a-oleflns were dried over Linde Molecular Sieves, type 4A, in a storage reservoir of a high vacuum system. The dilatometric technique used to follow the course of the copolymerizations, and the purification of solvents and catalyst components are described in the previous paper. ¢z)

RESULTS A spectrophotometric method was used to analyse the copolymers and so determine their composition, as in the determination of the styrene content of butadiene-styrene random copolymers<4' and methylmethacrylate-styrene block copolymers.~s) The optical density of solutions of copolymers in "Analar" chloroform, 0.2 g/1. for high styrene content to 1.0 g/1. for low styrene content, was measured at 260 m/~ using a Unicam spectrophotometer. The presence of both styrene and the comonomer in the reaction product was also shown by these studies, but the results did not give any proof of copolymerization since the same spectra were obtained from physical mixtures of homopolymers. Extraction of copolymer samples with hexane yielded two fractions (Tables 1-3). The insoluble fraction contained more styrene than the bulk polymer, but nevertheless TABLE 1. S ~ / I - m X - l - ~

COPOLYME~: ~XANE ~x'rRAc'noNs

% Styrene in copolymer

~o Copolymer soluble in hexane

% Styrene in soluble fraction

5 8 13 22 47

99 99 97 92 61

3 5 11 13 19

also contained appreciable quantities of comonomer. The soluble portion was relatively enriched in the comonomer, although the styrene content could be quite high. Pure polystyrene was completely insoluble in hexane under our experimental conditions. The poly 0~-olefinprepared in this way is completely soluble in hexane, whereas higher molecular weight material has been shown to be insoluble.(6) The soluble styrene in the copolymer samples cannot be present as homopolymer and must be incorporated in a copolymer chain. This was taken as sufficient proof of copolymerization. In order to determine the monomer reactivity ratios r~ and r2, the following technique was adopted. All copolymerizations were carried out at 35 ° with an aluminium/ titanium ratio of 3.0, the ,,-titanium trichloride concentration varying between 0-04

Copolymerization with Ziegler-Natta Catalysts---H TAsus2. STYRZNB/HEPT-I-eNECOPOLYM~RS:I c s x & ~

163

~TRXCnoNs

Styrene in copolymer

% Copolymer soluble in hexane

% Styrene in soluble fraction

8 10

97 98

8 10

17 29 59

91 85 51

15 21 33

Txst~ 3. S~/4-MEm'/LHSX-I-e~CS COPOLYMeP.S:HEXANE EXTRACTIONB Styrene in copolymer

~ Copolymer soluble in hexane

~ Styrene in soluble fraction

29 35 40 60 65 73 77 78

63 63 61 50 41 39 31 33

27 26 27 42 48 53 54 55

85

25

75

and 0.15 mole/l. The total monomer concentration was maintained in the region of 2.5 mole/1, which is about a 30% solution by volume. The results are shown in Tables 4-6. The reactivity ratios were determined by the method o f Fineman and Ross. (7) To apply this method the copolymer composition equation is rearranged as: f1(1 - 2F1) r- -~ [ f~(F, - 1) 1 (1 ffi z~- L( 1

-fl)rl

_fl)2FiJrl

where f l is the mole fraction o f one monomer in the feed a n d / ' 1 the mole fraction of the same monomer in the copolymer. A n example of this procedure is shown in Fig. 1. in

Y

"-I0

I

-8

,

-6

i

-4 X

I

2

FIo. I. Fineman-Ross plot for styrene (Ml)/hept-l-ene (M2), Slope (rt)ffi0-61 +0.01. Intercept (r2)-ffi5.70+ 0-15.

164

I . H . ANDERSON, G. M. BURNETr and W. C. GEDDES

which the l e f t - h a n d side o f the e q u a t i o n is Y a n d the b r a c k e t e d t e r m o n r i g h t - h a n d side is X. T h e c o p o l y m e r c o m p o s i t i o n curves are s h o w n in Fig. 2, the line d r a w n t h r o u g h the p o i n t s being in each case the best theoretical fir. P r o b a b l e errors in r 1 a n d r 2 were calculated f r o m the F i n e m a n - R o s s plots using the m e t h o d o f least squares, a n d the values listed in T a b l e 7. I-O

g g .s

i0-o 8

=Y 0-5 Mole fraction styrene in feed

t-O

FIG. 2. Copolymer composition curves, x Styrene/hex-l-ene. o Styrene/hept-l-ene. • Styrene/4-methylhex-l-ene. TABLE 4.

STC~NE/HEX-I-ENE

COPOLYMER

COMIK~ITION

['fiCl3] (mole/L)

Mole fraction styrene in feed

Mole fraction styrene in copolymer

0.042 0.042 0-042 0.043 0.042 0.092

0-2O 0.35 0.40 0.50 0-65 0.80

0.03 0.05 0-06 0.10 0.18 0.34

TgeL~

5.

ST'~ZNE/tmFr-I-ENE

COPOLYMER

C.,OMPOSI~ONS

[TiCI3] (mole/L)

Mole fraction styrene in feed

Mole fraction styrene in copolymer

0.047 0"050 0-052 0-056 0-102 0-131

0-25 0"35 0.45 0"50 0"65 0-80

0.07 0.10 0"16 0-20 0"34 0.58

Copolymerization with Ziegler-Natta Catalysts--H

165

TAeI~ 6. STYRE~/4-MZmYLt~X-I-E~ COIN3LYMER COMPO~rrIONS

[TiCI3] (mole/L)

Mole fraction styrene in feed

Mole fraction styrene in copolymer

0.114 0.119 0.119 0"119 0.112

0.35 0.50 0-65 0-65 0.80

0-34 0"59 0.71 0"73 0.85

TABLE7. REACTIVITYRATIOSOF STYRENEANDa-OLEFINS Comonomer

rl (styrene)

Hex-l-ene hept-l-ene 4-methylhex-l-ene 4.methylpent.l.enetL 2) 5-methylhex-l-ene(1. 2)

r2

0.19+_0.04 0-61 +_0-01 1.80+_0.04 0-89+ 0.06 0.59+_0.06

9.75+_0.81 5.70+_0.15 1.30_+0.06 3.67 +_0.22 4.00+_0.28

r 1r 2 1.85 3.48 2.34 3.26 2.36

Stability of monomer reactivity ratios These reactions are quite different f r o m the n o r m a l polymerization processes in that they are heterogeneous and the p o l y m e r f o r m e d is precipitated. The system styrene/ 4-methylpent-l-ene was therefore studied in m o r e detail to ascertain the effect o f catalyst concentration, AI/Ti ratio and temperature on the reactivity ratios. I n order to determine the effect o f the catalyst concentration o n the values o f the reactivity ratios, a series o f copolymerizations was carried o u t at 45 °. The titanium trichloride concentration was varied f r o m 0.05--0.14 mole/l, while the aluminium/ titanium ratio was maintained at 3.0. The p o l y m e r was isolated in the usual way and analysed by u.v. absorption in c h l o r o f o r m solution. The results in Table 8 show that for two different m o n o m e r feed compositions (mole fraction styrene in f e e d = 0 . 6 5 o r TAeLe 8. S3Tt~/4-~'Tm~Z~1~rr-l-~'~ COPOLYMER COMPOflI~ON WITH VARYING CATALYST CONCENTRATION

[TiCl3] (mole/L)

Mole fraction styrene in feed

Mole fraction styrene in copolymer

0-054 0.080 0.117 0.138 0"083 0"117

~65 0-65 (~65 0.65 0.35 0.35

0.52 0.49

0.47 0.50 0.21 0-20

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I . H . A N D E R S O N , G. M. B U R N E T T and W. C. G E D D E S

0.35), varying the titanium trichloride concentration has no effect on the copolymer composition--that is, the reactivity ratios are not dependent on the catalyst concentration. TABLE 9. STYP.~/4-~mYLPL3~rr-I-~

COr~LYMERCOm,osmos wrm vAR~,3 Al/Ti RATIO

AI/Ti ratio

Mole fraction styrene in feed

Mole fraction styrene in copolymer

1"5 3.0 6"0 7.5

0"35 0-35 0 35 0"35

0-18 0.18 0"21 0"19

The influence of the aluminium/titanium ratio on the copolymer composition was investigated by carrying out a series of polymerizations at 45 ° in which the concentration of titanium trichloride was kept constant (0"085 mole/L) while the aluminium triethyl concentration was increased to give a variation in the ratio of aluminium/titaniumfrom 1.5 to 7-5. It can be seen fromTable 9 that the composition of the copolymer is virtually unaffected by this variation of the catalyst components. The effect of temperature on the copolymer composition was determined by copolymerizing a monomer mixture for which the mole fraction of styrene was 0.80, at a series of temperatures ranging from 30° to 55°, using a catalyst concentration of 0.116 mole/1, and an aluminium/titanium ratio of 3"0. A monomer feed containing this high proportion of styrene was chosen because the presence of a large amount of 4-methylpent-l-ene would have rendered high temperature experiments dit~cult, since vapour bubbles form very readily in the dilatometer capillary. Table 10 shows that, while there is a certain spread of results, there is no dependence of the copolymer composition on temperature. TXeLE 10. S T Y ~ / 4 - ~ ' T H Y L P E ~ r r - I - ~ COPOLYMERCOMPOSITIONWITH VARYING~ T U R E

Temp. (°C)

Mole fraction styrene in feed

Mole fraction styrene in copolymer

30 35 45 45 50 55

0.80 0.80 0.80 0.80 0"80 0"80

0.70 0"68 0"71 0-70 0"76 0.67

In contrast to the results quoted above, the reactivity ratios were found to change considerably when the catalyst itself was altered. The preparation of a series of styrene/ 4-methylhex-l-ene copolymers was repeated using a different sample of the main catalyst component, titanium trichloride.

Copolymerization with Ziegler-Natta Catalysts---II

167

The results of Table 11, which may be compared with those in Table 6, show that the copolymer composition has been changed considerably by the use of a different sample of ,,-titanium trichloride. The effect on the reactivity ratios is shown more dearly in Fig. 3. TXBI.E 11. COPOLYMERIZATIONOF STYI~NE/4METHYLHr.X-I-E~ USINGTiCl3 (SAMPL~s)

[TiCI3]

(mole/L) 0.115 0.121 0.138 0"140 0. I 12

Mole fraction Molefraction styrenein styrene in feed copolymer 0.15 0.28 0.45 0.60 0.65

0.28 0.40 0.63 0-77 0-78

I'G

g

O:

o

=E

I

0-5 Mole fraction styrene in feed

I'0

Fro. 3. Copolymer composition curves for styrene/4-methylhcx-l-cne, x TiCI3 sample A. © TIC13 sample B.

The pronounced difference in the reactivity ratio values demonstrates the extreme sensitivity of reactivity to the catalyst in this type of polymerization system,o,s,9) From X-ray studies(2) on styrene/4-methylpent-l-ene and styrene/5-methylhex-l-ene copolymers it was concluded that these materials were probably mixtures of block copolymers. Styrene/4-methylhex-1-ene copolymers appear to have a similar structure. The powdered crystalline samples of poly-g-methylhex-l-ene and its copolymers with styrene gave well defined diffraction patterns. Typical diffraction patterns from copolymer samples are shown in Fig. 4. Up to almost 30 per cent styrene content the copolymer diffraction pattern shows no peaks attributable to polystyrene, whose main peaks should appear at 20= 18.3° and 8-0°. These peaks become evident in diagram C and, as the styrene content increases, their intensities increase at the expense of the 4-methylhex-l-ene peaks at 8"9° and 16-2°, although the decrease in the latter is not so noticeable since it is supplemented by the polystyrene peak at 16.25°.

168

I. H. ANDERSON, G. M. BURNETI" and W. C. GEDDES D

I

E

C

F

I0

15

;:'0

I

I

I

7'.5

I0

20

I

I

15

!

I

20

I

I

25

20 Fro.4. X-ray diffraction patterns for styrene-4-methylhex-l-ene. Mole % styrene in polymer: A---O; B---29; C--40; D--75; E--85; F--100. At 85 per cent styrene content there are still traces of the methylhexene structure although the peak at 8.9 ° is slightly obscured by the polystyrene atactic peak. The main observation from these diffraction patterns is that there is a gradual change from one structure to another as the styrene content increases, and that the two structures co-exist. N o new structures are formed. Hexane extracted samples give much the same picture, with the relative amounts of the two crystal structures depending on the amount of styrene present. The copolymers of hexene and heptene with styrene are rubbery when isolated. X-ray diffraction showed only one crystal structure, that of polystyrene. DISCUSSION The values of the reactivity ratios are of considerable interest. In ionic polymerization the charge on the propagating centre is approximately the same for different terminal units, hence the relative reactivities for different monomers should be nearly independent of the terminal unit and the polarity of the monomer assumes greater importance. Since the terminal unit does not affect the addition of monomer kll/k12=k21/k22, where k is propagation rate constant, i.e. rl r2 1. As can be seen from Table 7 the product rl r2 in each case is greater than unity, and in the case of 4-methylhex-l-ene both rx and r2 are greater than one. The reason for this departure from the ideal condition of rl r2 = 1 is probably due in part to the heterogeneity of the system. Not only is a mixture of polymer produced, but the activity of the individual catalyst sites is far from uniform. It is quite possible that the product of rl and r2 approaches the ideal for each site, but the actual values of rl and r 2 differ from site to site giving an overall picture which is not a true reflection of the reactivities. -----

Copolymerization with Ziegler-Natta Catalysts---II

169

Since extraction a n d X - r a y diffraction studies indicate that the copolymers have a block structure and are heterogeneous in character, it is perhaps surprising that the reaction variables have no effect on the reactivity ratio values. The insensitivity o f these values to changes in titanium trichloride concentration, the aluminium/titanium ratio and temperature agree with the results o f N a t t a and his colleagues o ° - m w h o f o u n d that in the f o r m a t i o n o f h o m o g e n e o u s copolymers o f ethylene and propylene using Ziegler type catalysts based o n titanium and v a n a d i u m halides, the concentration o f catalyst did n o t influence the p o l y m e r composition. Operating at high catalyst concentrations they did find that some variation in composition occurred, but this was a physical effect due to the loss o f equilibrium conditions in the reaction vessel. These workers also f o u n d that a variation o f the aluminium/titanium ratio f r o m 1.0 to 4.0 had

no effecton the copolymer when titanium trichloride or dichloride was used as the main catalyst component. W h e n titanium tctrachloridc was used in place of the trichloride, the composition of the copolymer was influenced by the aluminium/titanium ratio when the ratio was greater than 4.0. This is probably related to the limiting activity in the homopolymerization of propylcne using titanium tetrachloride and aluminium alkyls at a ratio of 4.0. It is apparent from the foregoing discussion that there are few concrete conclusions which can be reached. The fact that the reactivity ratios lead to products substantially greater than unity, is possibly indicative of block formation, and this is borne out to some extent by X-ray diffraction evidence. Thus, contrary to expectation, study of copolymerization, at least for the systems described here, will not provide additional information which will be of assistance in deciding the mechanism of the isotactic process.

REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

I. H. Anderson, G. M. Burnett and P. J. T. Tait, Proc. Chem. Soc. 225 (1960). I. H. Anderson, G. M. Burnett and P. J. T. Tait, J. Polym. Sci..56, 391 (1962). G. Natta, G. M~zT~uti, A. Valvassori, G. Sartori and A. Barbagallo, J'. Polym. Sci. 51,429 (1961). E. J. Meechan,3".Polym. Sci. 1, 175 (1946). A. S. Dunn; B. D. Stead and H. W. Melville, Trans. Faraday Soc..50, 279 (1954). Monsanto Chemical Company, Private communication. M. Fineman and G. D. Ross, 3". Polym. Sci. 5, 259 (1950). W. L. Carrick, F. K. Karol, G. L. Karapinka and J. J. Smith, 3.. Am. chem. Soc. 82, 1502 (1960). F. J. Karol and W. L. Carrick, 3.. Am. chem. Soc. 83, 2654 (1961). G. Natta, G. M~77~uti, A. Valvassori and G. Pajaro, Chimica Ind., Milano 39, 733 (1957). G. Natta, G. Ma77~nti, A. Valvassori and G. Pajaro, Chimica Ind., Milano 39, 825 (1957). G. Natta, G. M~-7~ti, A. Valvassori and G. Sartori, Chimica Ind., Milano 40, 717 (1958). G. Natta, G. Ma77arxti, A. Valvassori and G. Sartori, Chimica Ind., Milano 40, 896 (1958).

R,~sum~--L'~tude de la copolymtrisation du styrene avec les a-oltfmes, amorc~e par un catalyseur Ziegler-Natta, compos~ de tritthylaluminium et de trichlorure de titane-a en solution darts le tolu~'ne, a ~t6 poursuivie avec rhex~ne-l, l'hept~ne-1 et le mtthyl-4-hex~e. Les r~sultats de ce travail ainsi clue les r~-ultats d'une ~tude semblable avec le m~thyl-4-pent~ne-1 r~vtlent que les rapports de r~activit~ sont d~ermin& ~ la fois par des facteurs st~riques et 61ectroniques. Les valeurs suivantes ont ~t~ trouv~es pour les rapports de r~activit~: styNme/hex~ne-1, riffi0,19+0,04 r2ffi9,75+081; styrt~'ne/hept~ne-1, rl--0,61+0,01, r2ffi5,70+0,15; styr~ne/m~thyl4-hex~e, rl ~ 1,80 + 0,04, r2 ~ 1,30 + 0,06. Ces valeurs 6talent indtpendantes de la teml~rature, du rapport des catalyseurs et de leur concentration mais d~pendaient de la nature de l'~hantillon de TiCI3.

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I.H. ANDERSON, G. M. BURNETT and W. C. GEDDES

Les copolym~res styr6ne/hex6ne-1 et styr6ne/hept6ne-I 6taient caoutchoutiques, tandis que les copolym6res styr6ne/m6thyl-4-hex6ne-a donnaient des diagrammes de rayons X cristallins ce qui indique qu'il s'agissait de m61anges de copolym6res s6quenc~s (of. les copolym6res styr6ne/m6thyl-4pent6ne-1). Sommario--Lo studio della copolimer/77a=ione dello stirene con a-olefine, usando un catalizzatore Ziegler-Natta composto di alluminiotrietile e tricloruro di titanio czin toluene, 6 stato esteso alresene-1, eptene-1 e 4-metilesene-l. Questi risuRati insieme a quelli ottenuti da uno studio simile sul 4-metilpentene-1 indicano che randamento della reattivit/t dipende sia da fattori sterici che da fattori elettronici. La determinazione dei rapporti di reattivit~t d~ i seguenti valori: stirene/esene-1 r]=0-19_+0"04, re ffi9.75 _+0"81 ; stirene/eptene-1 rl ffi0. 61 _+0"01,re-- 5"70_+0"15; stirene/4-metilesene-1 r~ = 1"80-+0"04, r2ffi 1"30+(~06. Si 6 visto che questi valori sono indipendentidalla temperatura, dalrapporto catalitico e dalla concentrazione de1 catalizzatore mentre variano con la natura de1 campione di TIC13. I copolimeri stirene/esene-1 e stirene/eptene-I vengono isolati come gomme, mentre i copolimeri stirene/4-metilesene-1 danno ai raggi X spettri cristallini che indicano la presenza di miscele di copolimeri a blocchi (copolimeri stirene/4-metilpentene-1). Zusammeafatmng---Die Untersuchung der Copolymerisation yon Styrol mit a-Olefinen, unter Verwendung Ones Ziegler-Natta Katalysators ans AluminiumtrilRhylund a-Titantrichloridin Toluol, wurde auch auf Hex-l-en, Hept-l-en und 4-Methylhex-l-en ausgedehnt. Diese Resultate zeigen, in Verbindung mit denen einer ghnlichen Untersuchung von 4-Methylpent-l-en,ein Reaktivititsschema, dns dutch eine Kombination sterischer und elektronischer Faktoren bestimmt wird. Bei der Ik~'-timmungder ReaktivitiRsverl~ltnisse wurden folgende Werte erhalten: Styrol/Hex-l-en, rl =0-19__.0"04, rz--9"75 +0"81 ; Styrol/Hept-l-en, rl--0"61 _+0"01, rzffi 5.70_+0.15; Styrol/4-Methylhex-1-en, rl ffi 1"80_+0.04, r2-- 1-30+ 0.06. Diese Werte erwiesen sich als unabhiingig yon der Temperatur, dem Katalysatorverhiltnis und der Katalysatorkonzentration,aber abhitngig yon der Beschaffenheit der TIC13Probe. Die Styrol/Hcx-l-en und Styrol/Hept-l-en Copolymeren wurden als Gummi isoliert, abet die Styrol/4-Methylhex-l-en Copolymeren gaben kristalline R6ntgendiagramme, die auf Mischungen yon Block-Copolymeren hinweisen (cf. Styrol/4-Methylpent-l-enCopolymere).