the optical-configuration parameter for ethene-propene copolymers

Makromol. Chem. 188,2185 -2192 (1987) 2185

The optical-configuration parameter for ethene-propene copolymers

Enrique Saiz*

Departamento de Quimica Fisica, Universidad de Alcala de Henares, Madrid, Spain

J. E. Mark

Department of Chemistry and the Polymer Research Center, The University of Cincinnati, Cincinnati, Ohio 45221, USA

(Date of receipt: November 29, 1986)

SUMMARY: Rotational isomeric state theory is used to predict values of the optical-configuration para-

meter Aa for ethene-propene copolymers as a function of chemical composition, chemical sequence distribution, and stereochemical structure of the propylene sequences. The calculations are based on information available for ethene and propene homopolymers, and on the model used to interpret the unperturbed dimensions of these copolymers. Values of Aa were generally found to decrease significantly with increase in the fraction of propylene units, but to be relatively insensitive to chemical sequence distribution and stereochemical structure. The extent of their agreement with experiment is consistent with comparisons previously reported for a variety of homopolymers. It is intermediate to the poor agreement generally obtained for symmetric chains (such as polyethylene) and the satisfactory agreement generally obtained for asymmetric chains (such as polypropylene).

Introduction

There is a wide variety of properties that have been used to characterize the spatial configurations of polymer In general, experimental values of such properties are well interpreted by rotational isomeric state theory1), and such comparisons provide information which can be used t o predict other configuration-dependent properties of the chains being investigated. The one area in which the agreement between theory and experiment is frequently very unsatisfactory involves the birefring- ence An, and in particular the closely related optical-configuration parameter2g6- 14)

Aa. There have now been enough optical property studies of this type t o discern the

following very interesting trend. In general, rotational isomeric state calculations on symmetric chains give values of Au very much smaller than e ~ p e r i m e n t ~ * ~ - ~ ) , frequently by an order of magnitude or more. On the other hand, in the case of asymmetric chains the agreement between theory and experiment is generally quite satis- factoryi0-- 14).

The present investigation further explores this relationship by focusing on ethene- propene (EP) copolymers, which of course consist of both symmetric (E) and asymmetric (P) repeating units. Results of rotational isomeric state calculations based on a modelI5) employing information on polyethylene'. (6) and polypropylenei* 17)

0025-1 16X/87/$03.00

2186 E. Saiz, J. E. Mark

homopolymers are compared with published experimental resultst8) to gauge the extent to which theory agrees with experiment when both types of units are present in the same chain.

Theory

Geometry and conformational energies

These characteristics of the ethene-propene (EP) chain were the same as those used previous- if5) for the interpretation of the unperturbed dimensions (s), of these chains. Specifically. bond lengths were taken to be 1 3 3 A, bond angles to be 112'. and rotational isomeric state locations to be 0" (trans, t), 120" (gauche positive, g + ), and - 120" (gauche negative, g- ).

The conformational energies were I$ = 0, & = 0,SO (2,09), and I& = 2,OO kcal . mol- I

(8,37 kJ . mol-' ), and were used to calculate statistical weights (Boltmann factors) for tem- peratures of 20, 25, and 30°C. The resulting values were used to construct statistical weight matrices in the usual manner'.

Generation of representative chains

The Monte Car10 scheme employed was the same as that used in the earlier EP studyts). One set of random numbers in the interval 0,O- 1 ,O was used to construct chains with a given chemical composition (governed by a chosen value of the fraction& of propylene units), and a second independent set to generate the stereochemical structure of the propylene units (repre- sented by the replication probability 4 ) . Each chain generated was checked and rejected if its actual values of either & o r q differed in more than 0,Ol from the desired values. All the results to be presented (except in the case of & = 0, which is pure polyethylene) are averages of the values obtained from five independent chains. The two values of ha required to evaluate the variation of Aa with the various parameters of importance were obtained with the same chains. For example, in the evaluation of dAa/dT, the value of Aa was calculated at 20°C as an average of the results obtained with five chains for a given pair of values of& andp, ; then, the value of Aa was obtained at 30°C with the same five chains used at 20°C.

The computational program was successfully checked by reproducing the calculated results for the unperturbed dimensions reported for these copolymers '3. Then the optical sections of the program were successfully checked by calculating the known (trivial) values of Aa for short all-trans EP sequences.

Anisotropic part of the polarizability tensors

The chains was generated as CH3(CHR-CH2),- ,CHA2R, with R being H (ethylene units) or CH, (propylene units), as shown in Fig. 1. The quantity a, represents the anisotropic part of the polarizability tensor due to skeletal bond i (joining skeletal atoms i - 1 and i ) plus the two side bonds meeting at the i - 1 skeletal a toy.

Ethylene units: In this case, all the a tensors represent -CH2-C< groups. In order to simplify their formulation, a fictitious C-H bond is added in the direction of the i - 1 skeletal bond when formulating the 4 tensor, thus transforming the -CH2- C- < group into a symmetri- cal CH,-C< group. This fictitious C-H bond is subtracted when the g. tensor is formulated. Disregarding the small distortions from tetrahedral symmetry and taking 8(CH3) = - &(CH), one obtains

4 = 8(CH3-C) - 8(C-H) = 8(C-C) - 28(C-H) (1)

The 8(C-H) which is subtracted in this equation is that of the fictitious C-H bond that will be added when transforming CH2-C< into CH,-C< for the &+, tensor.

The optical-configuration parameter for ethene-propene copolymers 2187

irl

Fig. I . ment of two propylene units

Sketch of parts of an ethene-propene chain. The labelled part shows an isotactic place-

The &, tensor representing the first bond of the chain is also given by this expression. It corresponds to an actual CH,-C< group minus a fictitious C-H bond which will be added in 4. However, & (which represents the last bond of the chain) i,” zero since with this scheme it represents a CH,-H group (i.e., a CH, molecule), for which a = 0.

This method amounts to generation of a chtin T t h degree of folymerization x by joining 2x - 1 molecules of CH,-CH, , zach having a = a(C-C) - 2a(C-H) with elimination of 2x - 2 molecules of CH, having a = 0.

The 4 tensor can also be written

4. = &(C-C) - 2&(C-H) = ( A q c - 2 A q H ) J = rcc J (2)

with J = diag(2/3, - 1/3, - 1/3) andI9) rcc = 0,53. 10-% cm3.

situation is the same as that in the ethylene units and therefore, 4 = fcc J .

replace it by a $C-CH, group. The tensor can then be formulated as

Propylene units: For bonds such as i in Fig. 1 (including the first bond of the chain) the

In the case of bonds such as i + 1 in Fig. 1 one needs to remove one of the C-H bonds and

i,, = k(C-C) - 2k(C-H) + T[k(C-C) - 2k(C-H)1 TT = f & [J + T J T T I (3)

where T represents the matrix required to bring the coordinate system referred to the lateral CH, group into coincidence with that of skeletal bond i + 1 .

The T matrix, (and therefore the resulting Q, I tensor) depends on the configuration of the tertiary carbon atom. For d configurations the result is

1 0,2312 -0,0808 0,1392 -0,0808 -0,2335 -0,2064

0,1392 -0,2064 0,0028 (4)

The tensor for I configurations can be obtained by reversing the signs of the third row and third column of 4, , (d) , noting that this transformation leaves unchanged the 3,3 element of the tensor.

The tensor for the last bond of the chain is & = rccTJTT and can be formulated as

-0,1222 -0,0808 0,1392 -0,0808 -0,0568 -0,2064

0,1392 -0,2064 0,1790

A A

for a d configuration.

(1) First bond of the chain (-CH,-C<): Summary: The above results can be summarized in detail as follows:

.̂, = diag(0,3533, -0,1766, -0,1766)

2188 E. Saiz, J . E. Mark

(2)Bonds such as i + l(-CHR-C<): a) Ethylene units:

G+, = diag(0,3533, -0,1766, -0,1766)

b) Propylene units: See Eq. (4) (3) Bonds such as i (-CH2-C<):

4 = diag(O,3533, -0,1766, -0,1766)

(4) Last bond of the chain (-CHR-H): a) Ethylene unit:

(7)

& = O (9)

b) Propylene unit: See Eq. (5)

The above information was used in standard matrix multiplication techniques to calculate the desired values of ha.

Results and discussion

Some exploratory calculations were carried out to determine the variation of Aa with the degree of polymerization x of the chains. They showed that Aa increases with x for low values of x but then reaches an asymptotic value for 70 6 x < 80. Typical differences between the values of Aa calculated for x = 100 and those extrapolated to x + 09 are of the order of 1 to 2%. All the results presented below were therefore computed for x = 100.

Figs. 2,3, and 4 show the results of Aa as functions of the chemical composition& for the three stereochemical structures pr = 0,05 (highly syndiotactic), p, = 0,50 (atactic), andp, = 0,95 (highly isotactic), respectively. Solid, dashed and dot-dashed lines in these Figures represent the values obtained for reactivity ratios r, * r, = 100, 1, and 0,01, respectively. Typical values of the standard errors are shown, as illustra- tion, only in one of the lines. All these calculations were performed for 25 “C with the “standard set” of energies, E,, = 0, E, = 0,5 (2,09), and E, = 2,O kcal mol-I (8,37 kJ emol-’). These results for Aa are very similar to those reported for the unperturbed dimension^'^), particularly in the case of the highly isotactic polymer.

As the Figures indicate, Aa decreases with increasing& (Aa for pure polyethylene is roughly twice that for pure polypropylene). This behavior is quite easy to explain. In the case of ethylene units, all the anisotropy lies along the backbone; in the case of the propylene units, however, the anisotropy of the laterally located CH, group acts against that of the backbone. (Compare the values of the 4+, tensor for ethylene and propylene units). This situation also explains why Aa is more sensitive to rcc in the case of & = 0 than in the case of& = 1 (see below). In this case, modification of rcc changes the anisotropy of both the backbone and the lateral groups. In the ethene- propene copolymers, the positive contribution to Aa produced by the backbone dominates the negative contribution of the lateral groups and, consequently, Aa for the whole chain is positive. When the anisotropy of the lateral groups dominates that


Fig. 2. Dependence of the optical-configuration parameter Au on the fraction pz of propylene units in the chain of ethene- propene copolymers for the case in which these units are highly syndiotactic in stereochemical structure (replication proba- bilityp, = 0,05). The solid, dashed, and dot- dashed lines correspond to results for chains generated using reactivity ratio products of 100, 1 , and

2.0 -

1.5 -

0,01, resp., and a temperature of 25 "C 1.0

0 0.2 0.4 0.6 0.8 1.0 P2

r

Fig. 3. As Fig. 2 but: dependence of Au on pz for atactic propylene sequences (p, = 0,50) 1.0 1

0 0.2 0.4 0.6 0.8 1.0 PZ

of the backbone, however, Aa is negative; this is for example the case for poly(methy1 acry1ate)lO) or poly(viny1 acetate)l').

The coefficient Au is rather insensitive to the values of r, * r j and even to the stereochemical structure of the propylene units; only in the case of highly isotactic chains is there a substantial dependence. The explanation for this is similar to the one


6 I

p,:0.95

1.5 0 0.2 0.1 0.6 0.8 1.0

P2

Fig. 4. 035)

As Fig. 2 but: dependence of ha on 4 for highly isotactic propylene sequences @, =

given foris) ( 3 >o. For long helical sequences, the values of ^a add along the axis of the helix and therefore rT ̂ ar increases faster than r * r; consequently, Aa increases with increase in r, * r, .

0,6 < p~ < 0,7 are roughly one-third the experimental results"). The extent of agreement thus lies between the case of symmetric chains (in which the theoretical values are about one order of magnitude smaller than the experimental onesz.6-9)), and the case of asymmetric chains (in which there is a reasonable agreement between theory and experiment10- 14). Intermolecular inductive effects are presumably the origin of the disagreement, but it is not known why such effects could be larger in symmetric chains.

Tabs. 1, 2, and 3 show the variation of Aa with the parameters used in the calcula- tion. All these results were calculated for chains of x = 100, r, r, = 1, T = 25 "C, rcc = 0,53cm3,E, = O,E, = 0,5(2,09),andE, = 2,0kcal.mol-' (8,37 J*mol - I ) as the standard input.

Tab. 1 summarizes the values of the temperature coefficient of Au. The coefficient is negative, in good agreement with experimentI8), although the absolute value is much smaller than the experimental. However, the variations in the calculated quanti- ties are small and they fall very close to the standard errors of the averages.

The variation of Aa with r,, is shown in Tab. 2. It increases with r,, although the effect is, in general, smaller at high values of p~ because of the partial cancellation between the anisotropies of the backbone and the lateral groups explained above. Tab. 3 summarizes the variation of ha with the three conformational energies.

The absolute values of Aa at 25 "C, p, = 0,50, 0,l 6 r, - r, < l , O , andfs,


Tab. 1. Temperature coefficient dAa/dT of the optical-configuration parameter h a for ethene-propene copolymers as a function of the fraction 4 of propylene units and the stereochemical replication probability p,

4 - (1 02' . dAa/dT)/(cm3 . K - ' ) for I \ pr = 0,05 = 030 = 0,95

A

4,84 3,75 2,73 2,oo 1,53 2,29

4,84 3,76 2,91 2924 I ,76 1,41

4,84 3,87 3,20 3,24 4,67 8,37

Tab. 2. Variation of the coefficient dAa/N,, of the optical-configuration parameter h a with the anisotropy parameter f,, for ethene-propene copolymers as a function of the fraction& of propylene units and the stereochemical replication probability p,

4 dAa/Ncc r > p, = 0,05 = 030 = 0,95

A

2,85 2946 2,08 1,76 1,49 1,37

2,85 2,43 2,11 1,83 1 3 5 1,32

2,85 2,47 2,18 1,96 1,93 2,16

Tab. 3. Variation of the optical-configuration parameter ha with the conformational energies E,, , E, , and E, for ethene-propene copolymers as a function of the fraction h of propylene units and the stereochemical replication probability pr

4 - dAa/dE,, a)

cm3 . mol . kcal- ' for 7 pr=0,05 =0,50 =0,95

0,o 2,60 2,60 2,60 0,2 2,38 2,32 ,2,24 0,4 2,22 2,Ol 1,82 0,6 2,l I 1,71 1,37 0,8 2,08 1,34 0,80 l,o 2,l I 1,02 0,09

a) In SI units 1 kJ = 4,184 kcal.

1 024 dAa/dE, a)

an3 . mol . kcal-' for -

p, =0,05 =0,50 =0,95

2,80 2,80 2,80 2,02 1,96 2,04 1,35 1,39 1,50 0.87 0,94 1,06 0,49 0,50 0,73 0,24 0,lO 0,41

10DdAa/dE, a)

cm3 . mol . kcal - ' for

p,=O,O5 =0,50 =0,95

0,09 0,09 0,09 0,08 0,09 0,09 0,08 0,09 0,12 0,08 0,11 0,20 0,lO 0,12 0,44 0,27 0,16 1,17

A variation of roughly two units in either r,, , 4 , or E, (or any equivalent combi- nation of simultaneous variations of the three parameters) would be required t o bring


agreement between theoretical and experimental results for Aa. None of these variations is compatible with previous analyses of other conformation-dependent properties. Basic problems in interpreting the optical properties of symmetric polymer chains are thus confirmed, and really must be solved before the configurational analyses of such chains can be considered in a satisfactory state of completion.

JEM wishes to acknowledge the financial support provided by the National Science Foundation under grant DMR-8415082 (Polymers Program, Division of Materials Research).

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1969

( 1984)

(1985)

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the optical-configuration parameter for ethene-propene copolymers

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