1390
HERBERTA. POHL AND HOWARD H. ZABUSKY
Since the size and shape of toluene and a,a,atrifluorotoluene are very nearly the same, a direct comparison of these two systems seems valid. The former with a high electron density forms a compound, the latter of low density does not.
Vol. 66
Acknowledgment.-The authors gratefully acknowledge the support given this project by the National Science Foundation. We also wish to thank A h . Frank W. Tsien, who assisted vith the freezing point measurements.
STEREOSPECIFICITY ,4ND DIELECTRIC PROPERTIES OF POLAR POLYMERS BYHERBXRT A. POHLAND HOWARD H. ZABUSKY Princeton University Plastics Laboratory, Princeton University, Princeton, N . J . RGcGzVGd January 6, 1968
A method of determining stereoregularity in polar high polymers by dilute solution dielectric measurements is investigated on polyvinyl isobutyl ethers, polyethyl acrylates, and poly-p-chlorostyrenes of differing steric forms. I n all cases no significant differences were found in the dielectric constants or di ole moments of the different steric forms of the same polymer. This was generally true of the relaxation times and distriiution of relaxation times of the polymers also. The results are compared to those on polymethyl methacr lates where differences were found, and it is concluded that the degree of hindrance to rotation about the carbon-carbon%onds of the main chain and the degree of steric repulsion to ositioning of side groups are the determining factors as t o whether differences in dielectric properties will be observed. simple and approximate method of predicting relative polarizations and dipole moments of stereospecific vinyl polymers based on dipole-dipole and repulsion energies is presented. It is concluded that the method of determining stereoregularity in polar polymers by dilute solution dielectric measurements is not generally applicable, but the method is a valuable tool for gaining insight into the flexibility of polar polymer chains.
Introduction The object of the present study was t o determine if the dielectric behavior of stereoregular polar polymers in dilute solutions is a function of the steric order of the polymer molecule. If it were so, then the dielectric constant or average dipole moment of the polymer in solution could be used as a measure of stereoregularity. This method has been used in the past on small organic molecules differing in steric configuration, especially on diastereomers, molecules containing pairs of asymmetric carbon atoms. Differences in the apparent dipole moment were found between the optically compensated meso form and the uncompensated d-d or 1-1 forms. Extrapolating this to polymers, the meso form would correspond to a syndiotactic polymer and the uncompensated optically active d-d or 1-1 form would correspond t o an isotactic polymer. The atactic polymer may be thought of as containing random blocks of these two. Bacskai and Poh14 applied this method to isotactic, atactic, and syndiotactic polymethyl methacrylate, and found differences in the dipole moments of the three forms in the order isotactic > atactic > syndiotactic, indicating greater freedom of rotation in the isotactic form. The results were further substantiated by relaxation studies which showed an increase in mean relaxation time and in the distribution of relaxation times in going from the isotactic to the syndiotactic form. I n the present study three polymers were studied with regard to dipole moment and dielectric relaxation-polyvinyl isobutyl ether, polyethyl acryl(1) A. Weissberger, J . Oru. Chem., 2, 248 (1937-1938); J . Am, Chem. SOC.,67, 778 (1945). (2) 6. Winstein and R. E. Wood, zbzd., 63, 548 (1940). (3) V. Ramakrishnan, Kollozd-Z., 182, 30 (1953). (4) R. Bacskai and H. A. Pohl, "Stereospecificity and Electiic Polarization in High Polymers," Princeton University Plastics Laboratorv Report No. 55A, Oct. 1, 1939: J . P o l y n e i Scz., 42, 151 (1960).
ate, and poly-p-chlorostyrene. The polymers each were synthesized in a t least two different steric forms. The dielectric properties were measured at a single temperature and at several frequencies. I n addition, brief studies were made of polymethyl methacrylates at differing temperatures. A simple and approximate method was used to try to predict the relative polarizations and dipole moments of the stereospecific polymers. The method consists of considering the monomer units pair by pair as they may lie in space. Each pair can be shown to exist in 18 most probable conformations. Among these 18 conformations the probability and moment of each is calculated. The relative average polarization then is calculated from the weighted average of the pair moments. Experimental Polymer Preparations .-Polyvinyl Isobutyl Ethers .-The niethods of Schildlmecht, et u L . , ~ were used. Rubber-like Atactic Polyvinyl Isobutyl Ether.-To 100 ml. of pentane was added 15.4 g. (0.154 mole) of vinyl isobutyl ether (Carbon and Carbide Chemicals Co.) freshly distilled from CaH2. The mixture was cooled to - 65' in a Dry Iceacetone bath. BFa(Matheson Coleman &. Bell) was bubbled into 20 ml. of pentane so that the concentration of BFI was greater than 0.0170 that of the monomer. The cooled catalyst mixture was added rapidly to the monomer-pentane mixture, causing a rapid increase in the solution viscosity. Eighty ml. more of pentane was added, the solution was filtered, then precipitated in 10 volumes of methanol. The white, rubbery product was dried under vacuum, giving 10.4 g. (67y0yield). Crystalline, Isotactic Polyvinyl Isobutyl Ether. Vinyl isobutyl ether (15.4 g.), distilled from CaH2, was added to 80 ml. of pentane, and a small amount of crushed Dry Ice, and cooled to about -70" in a Dry Ice-methanol bath. Exercising care to exclude moisture, 0.22 g. of (C*H6)20BFB complex with 4770 BFa (Matheson Coleman &. Bell) was added at the rate of one drop every 10 sec., giving a catalyst concentration of 0.657,. Some instantaneous polymerization resulted and the mixture was allowed to sit 6 hr. The gel formed was dissolved by adding 500 ml. of toluene ( 5 ) C. I?. Schildknecht, 8.T. Gross, H. R . Davidson, ,J. 11. Lam. bert,, a n d A. E . Zoss, I n d . Zng. Chem., 40, 2104 (1948).
August, 1062
STEREOSPECIFICITY AND DIELECTRIC PROPERTIES OF POLAR POLYMERS
and this mixture precipitated in 10 volumes of methanol. The polymer"was washed with additional methanol and dried in vacuo 24 .hr., giving 12.0 g. (78y0yield) of white fibrous non-tacky product. Polyethyl acrylates were prepared by methods of Garrett, et al.6 Sy.ndiotactic Polyethyl Acrylate (or what is now believed to be this modification).-Benzoin (0.13 g.) was added to 24 g. of ethyl acrylate (Eastman Chemicals) which had been distilled from CaH2. The mixture was degassed by vacuum refreezing and sealed in a tube, then placed in a bed of Dry Ice and subjected to ultraviolet radiation for 2 hr. The product was a clear solid gel. This was dissolved in 750 ml. of warm toluene and precipitated in 4000 ml. of petroleum ether. The product was a high molecular weight, white, elastomeric polymer, 22.2 g. (92'% yield). Atactic l?olyethyl Acrylate.-Ethylacrylate (30.3 g.) freshly distilled from CaHp, 67.5 ml. of benzene, and 0.1 g. of benzoyl ,peroxide (Matheson Coleman I% Bell) were refluxed under nitrogen for 30 min. and precipitated in 1000 ml. of petroleum ether. The vacuum-dried product (657, yield) was clear, tacky, and elastomeric. Isotactic :Poly-p-ch1orostyrene.-Monomer (Borden NIonomer-Polymer Laboratories), vacuum distilled from CaC12, was #dissolvedin benzene which had been freshly distilled over sodium1 metal. Under a dry nitrogen atmosphere, 5.59 g. of p-chlorostyrene, 0.19 g. of TiC14,0.34 g. of Al(CZH5)3, and 12 ml. of benzene were mixed. The mixture was degassed by vacuum refreezing and sealed in a glass tube, then shaken at 70" for 94 hr.7 The product wa8 precipitated. in 350 ml. of methanol, filtered, washed with methanol, and vacuum dried. The polymer was reprecipitated from benzene using methanol, and again vacuum dried. The polymer was obttined in 4oyO yield as a white powder melting at 125-l30 . Atactic Poly-p-chlorostyrene .-To 14.3 g. of the purified monomer a?: above was added 0.10 g. of azobisisobutyronitrile (Brothers Chemical). The mixture, after degassing with the aid of vacuum refreezing, was sealed in glass and agitated 37 hr. a t 70". The reaction mixture then was diluted with1 10 ml. of benzene and t'he polymer precipitated with 200 ml. of methanol, filtered, washed with methanol, and dried. The polymer was redissolved in benzene, reprecipitated with methanol, and vacuum dried; 5.3 g. (37% yield) was obtained. Polymethyl Methacrylates .-Samples of atactic, isotactic, and Eiyndiotactic material were those described earlier in the work of Pohl, et Dielectric Polarization Measurements. -The polymers were examined in dilute benzene solution in apparatus and using techniques described earlier . e Dielectric constant, dielectric loss, density, infrared spectra, and X-ray measurementJswere made as described earlier.8
Results The values of the polarization measurements made a t low frequency are given for polyvinyl isobutyl ether (PVIBE), polyethyl acrylate (PEA), and poly-p-chlorostyrene (PCS) in Table I. These results show no significant variation with steric form in any of t'hese polymers. The da'ta obtained from the high frequency measurements are shown in Table 11. Here a' =: dc'/bc and a" = d r " / b ~ .I~n these measurements the tmo forms of the vinyl ethers and of the ohlorostyrenes give identical result's, but there is considerable variation in the polyethyl acrylates. At the very high frequency (10 cm.) the at,actic (6) ti. Y. Garrett, W. E. Goode, S. Gratcli, J. F. Kincaid, C , I,. Levesque, 4.Spell. J. D. Btroupe, a n d W. H. Watanabe, J . Am. Chem. Soc., 811, 1007 (1959). (7) G. Natta, F. Drtnusao, a n d D. Sianesi, iMakromo2. Cham., 26, 253
(1958).
(8) H. A. I'obl. R. Bacskai, and W. P. Purcell, "Steric Order and Dielectric Behavior in Methyl Methacrylates." Princeton Univ. Plastics Laboratory Report No. 57A, April 1, 1960; J . Phgs. Chem., 64, 1701 (1960). (Q) D. A. Pitt a n d C. P. S m y t h , ibid., 63, 582 (1969).
1391
TABLE I AVERAGEMOLARPOLARIZATIOXS AND DIPOLEMOMEXTS PER MONOMER UNIT FOR DILUTESOLUTIOXS OF POLYMERS AT 30" IN BENZESE h A€/ P8PP Polymer Steric form X IO3 g PZ PO X 1018 PVIBE Atactic 2.67 1.07 48.56 19.2 0.976 PVIBE Atactic 4.37 1.09 48.86 1 9 . 5 ,983 PVIBE Isotactic 2.34 1.09 48.86 19.5 ,983 4.49 1 . 1 0 49.00 19.6 .987 PVIBE Isotactic PEA PEA PEA PEA
Atactic Atactic Syndiotactic Syndiotactic
3.17 1.74 1.28 5.35
3.12 3.09 3.13 3.09
45.88 45.44 46.03 45.44
21.2 20.7 21.3 20.7
1.025 1.015 1,029 1.015
PCS
Atactic Atactic Isotactic Isotactic Isotactic
1.06 1.81 0.93 1.72 0.88
3.16 3.14 3.14 3.16 3.11
78.47 78.18 78.18 78.47 77.74
30.3 30.0 30.0 30.3 29.5
1.227 1.221 1.221 1.227 1.211
PCS PCS PCS PCS
form has a higher dielectric constant than the syndiotact'ic, while the reverse is true a t lower frequencies. TABLE I1 RESULTS OF MICROWAVE MEASUREMENTS Polymer PVIBE PVIBE PEA PEA PCS PCS
Steric form
7-10 om.-
Atactic Isotactic Atactic Syndiotactic Atactic Isotactic
a'
-25 a'
om:a,,
0.31 0.15 0.38 0.19 0.31 .12 0.39 .l9 1.18 .59 2.39 .68 0.51 .49 2.66 .54 1.13 .09 1 . 4 7 .21 1.08 . l 2 1.48 .25
em.a" 0 . 4 6 0.24 0.49 .22 2.47 .62 2.79 .5l 1.85 . 2 7 .29 1.85
-50
Static
a'
aa
1.08 1.09 3.10 3.11 3.15 3.14
The data shown in Table I1 are shown in Fig. 1 in the form of Cole-Cole plots. From these plots are obtained the most probable relaxation time T ~ the , critical wave length A,, the distribution parameter a, and the upper and lower limits of the relaxation distribution T~ and 7 2 . These results are given in Table 111. REL.4XATIOX
TABLEI11 DATAOBTAINED FROM COLE-COLE PLOTS TO
A,
Polymer
Sterlc form
em
PVIBE PVIBE PEA PEA PCS PCS
Btactic Isotactic Atactic Syndiot:rctic Atactic Isotactic
113 1 120.6 20 7 80 2 63 1 60 3
x
10'0,
see.
72
TI
a
X 10'0
X
1010
6 0 0 33 0 55 65 5 6 4 33 59 69 8 I 1 29 07 76 7 1 ti 29 11 24 3 3 3 69 006 1797 1 3 2 67 009 1168 1
These results show no significant dependence of relaxatioii on the steric form for polyvinyl isobutyl ether and poly-p-chlorostyrene, but do show a considerable difference in relaxation time htweerr the two polyethyl acrylates. Low frequency measurements were made on three samples of polymethyl methacrylates at 30 and 60' to observe the effect of temperature on the apparent dipole moment. The results of these nieasurements are given in Table IV. The X-ray spectra for films of the polyvinyl ethers were examined. The spectrum of the iso-
HERBERT A. POHL AND HOWARD H. ZABUSKY
1392
Vol. 66
os I SOT A C T IC
1.2
0.4-
1.6
2.0
2.4
2.8
3.2
ATACT I C
Fig. IC.--Cole-Cole
Fig. la.-Cole-Cole
plot for isotactic poly-p-chlorostyrene.
plots for polyvinyl isobutyl ethers.
t
SYNDIOTACTC
0
0.4 0.8
Y' t
ATACTIC
Fig. Id.-Cole-Cole
plot for atactic poly-p-chloroEtyrene.
isotactic and atactic spectra of polyvinyl isobuty ether or between the atactic and syndiotactic spectra of polyethyl acrylate. In the poly-p-chloro2.0 2.4 28 32 0 styrene spectra the following differences are observed: at 3.3 p the isotactic absorption is twice that of the atactic, there is a small peak at 9.7 p in the isotactic which is not evident in the atactic, Fig. 1b.-Cole-Cole plots for polyethyl acrylates. and there is a large broad absorption at about 14.8 p in the isotactic which is about three times as large TABLEIV as that observed for the atactic. MOLAR POLARIZATIOX AND DIPOLEMO~UENT OF The X-ray spectra of the polyvinyl isobutyl ethers POLYMETHYL METHACRYLATES AT 30 A N D 60" indicate differences between the forms, the infrared Steric Temp., Pl I" spectra indicate differences between the poly-pform Ar/fe Pz Po X 10Bo X 10l8 chlorostyrenes, but there is no such evidence for Atactic 30 2.58 61.07 36.6 1.820 1.349 differences between the polyethyl acrylates. 60 2.46 59.31 34.8 1.902 1.379 Atactic Syndiotactic 30 2.48 59.60 35.1 1.745 1.321 Discussion Syndiotactic 60 2 ' 3 5 57'69 33'2 814 1'347 Briefly summarizing the experimental results, Isotactic 30 2 89 65.63 41.1 2.044 1.429 2 , 8 3 64.75 4 0 , 2 2.197 1,482 there are no significant differences in the molas Isotactic Dolarixation or average dipole moments per monotactic polymer shows many peaks indicating crys- mer unit, in the mean reiaxatioii times,-or in the tallinity, while the atactic polymer is void of any distributioii of relaxation times between the different steric forms of polyvinyl isobutyl ether and evidence of crystallinity. The infrared spectra of the polymers also were poly-p-chlorostyrene. Polyethyl acrylate shows used to distinguish differences between the forms. differences in dielectric constant between the two There are no significant differences between the forms a t high frequencies but not at low frequency.
d
^ I
O C .
August, 11962
STEREOSPECIFICITY AND DIELECTRIC PROPERTIES OF POLAR POLYMERS
There are also significant differences between the relaxation times of the two forms of polyethyl acrylate. The polyethyl acrylates and the polyp-chlorostyrenes have been shown previously to be non-crysGallizable in any f ~ r m and , ~ ~the~ polyvinyl isobutyl ether is shown to be crystalline in the isotactic form but not in the atactic form. I t is possible to interpret these results by comparing them to the results obtained on polymethyl methacrylate by Bacskai and Poh14 and Pohl, Bacskai, and Purcell,s where differences among the various steric forms were observed. The differences observed in the polymethyl methacrylates were explained in terms of hindrance : hindrance to rotation about main chain bonds and hindrance to positioning of chain-attached side groups. Greater hindrance to rotation about the main chain bonds in the syndiotactic polymethyl methacrylate than in the isotactic explains the longer relaxation time and the broader range of relaxation times observed. Differences in steric repulsions to positioning of side groups account for the observed differences in average moments. IJnder the influence of an alternating electric field the polar molecules of a system tend to align themselves in the direction of the field. I n the case of a polymer the whole molecule does not follow the elect,ric field, but rather we find segmental rotation and alignmeiit with the alternating field. Since the rotating segments may be of different sizes and may be in different environments, the reactions to the field of different segments mill vary. This gives rise to a distribution of relaxation times. I t is not surprising, therefore, that hindered rotation about the carbon-carbon bonds will effect the relaxation process. It is apparent from looking a t molecular models and from other .\yorklo,ll tha,t rotation about the C-C bond in the polymers studied isi hindered. The fact that the most probable relaxation time and the distribution of relaxation times do not vary between steric forms of polyvinyl isobutyl ether and poly-p-chlorostyrene leads to the conclusion that the relative location of the bulky side group, Le., cis or trans, on adjacent mer units does not affect the degree of freedom of rotation about the carbon-carbon bond. That the situation is different for polymethyl methacrylate possibly could be due to the fact that there are two side groups per mer unit on the main chain of the methacrylate and only one on the other polymew. The addition of the methyl group causes enough additional hindrance so that interactions between ,Adjacent mers take place and the relative positions of the two groups become important. As for the molar polarizations, the same conclusions can be drawn with regard to specific steric repulsion to positioning of side groups. In the case of polyvinyl isobutyl ether, polyethyl acrylate, and poly-p-chlorostyrene, whether the large side groups are cis or trans to each other on adjacent mer units does not significantly affect the conformations in which the syndiotactic and isotactic (10) R. hl. Fuoss and J. G. IZirkwood, J . A m . Chem. Soc., 63, 391 (1941). (11) J. Marohal and C. Lapp, J . Polymer Sca., 27, 571 (1958).
1393
forms may lie. I n the case of polymethyl methacrylate the additional methyl group is large enough to affect the degree of steric repulsion and change the probability of a given conformation from the isotactic to the syndiotactic form. The fact that differences in molar polarization are indicated at high frequencies but not a t low frequencies, and that there are differences in the relaxation times but not in the distribution parameter for the different polyethyl acrylates cannot be explained adequately at this time. From the results on the polymethyl methacrylates where the differences between the syndiotactic and atactic forms were very slight, there is reason to expect less difference between the syndiotactic and atactic polyethyl acrylates than between the ot,her polymers where an isotactic and atactic form were compared. Atactic polymethyl methacrylate has been shown6,I2to be largely syndiotactic, but this may not be true in the case of polyethyl acrylate. With regard to the molar polarization and steric repulsion to positioning, Pohl, Bacskai, and PurcelP presented a simple and approximate method of predicting the average moments of polymers by using molecular models and considering successive monomer units pair by pair as they lie in space. Each pair can exist in 18 most probable conformations. Probabilities between 0 and 1 were assigned to each conformation and the moment of the paired monomers calculated. The average polarization of the chain then was calculated from a weighted average of the pair moments. This method, while approximate, gave good results in predicting the observed results on polymethyl methacrylates. This method was applied independently and without knowing the experimental results to polyvinyl isobutyl ether and polyethyl acrylate in the isotactic and syndiotactic forms. While in both cases the absolute value of the moment may have been uncertain, the method predicted that there would be no significant relative differences in the dipole moments of the two forms of the polymer. This was confirmed by experiment. The fact that certain conformations are more probable than others and that rotation is restricted indicates an energy barrier to rotation. As the temperature is raised, that is, more energy is put into the system, more and more molecules transcend the barrier and the system tends to overcome the steric hindrance. Table IV shows the effect of changing the temperature from 30 to 60' on the polymethyl methacrylates. I n all cases the molar polarization decreased with an increase in temperature. The greater freedom of rotation at the higher temperature would lead to a higher molar polarization, but this is offset by an increase in randomness which results from an increase in temperature. To observe the effect of hindrance only, it is necessary to look a t the dipole moment or the square of the dipole moment which is otherwise independent of temperature. I n all cases the square of the moment increased slightly with temperature. As the temperature is increased, one would expect, that the dipole moments of the two forms mould approacli each other. At a temperature where (12) F. -4.Bovey and G. V. D. Tiers, %bad.,44, 173 (1960).
1394
HERBERT d.P O H L
AND
enough energy was being added to the system to overcome all steric hindrance, the moments of the two forms would be expected t o be equal. The temperature range investigated was not great enough t o show any significant change in the ratio of the moments of the two forms. A theoretical investigation considering the repulsion and dipoledipole energies which leads to the same conclusions is given in the Appendix. Some support of the discussion of relaxation phenomena is given by Saito and Nakajarna,l3 who found an increase in the relaxation time and a corresponding decrease in the glass transition temperature in vinyl chloride-vinylidene chloride copolymers with an increase in vinylidene chloride content, and by Borisova and M i k h a i l ~ v 'who ~ found a decrease in the relaxation time of methacrylate-styrene copolymers with an increase in styrene content. I n both cases the molecule with the bulkier side group causes an increase in the relaxation time due to the additional hindrance which it provides. Finally, it is necessary t o conclude that the proposed method of determining stereoregularity of polar polymers from dilute solution dielectric measurements is not generally applicable because sufficient steric hindrance to dipole rotation is not always present. There is sufficient hindrance in the case of polymethyl methacrylate but not in the case of polyvinyl isobutyl ether, polyethyl acrylate, or poly-pchlorostyrene to produce ascertainable differences in the average dipole moments, the relaxation times, or the distribution of relaxation times. The method does, however, offer considerable insight into the flexibility of polar polymer chains. The above computations show that the major source of differing chain flexibility lies in the presence of crowded groups attached to the main chain. This is confirmed by observations on the glass transition temperature, T,, of the isotactic, syndiotactic, and atactic forms of various polymers. Those polymers with little crowding of groups along the main chain show near identity of Tg among their differingstereospecific forms. Polypropylene, poly1-butene, polystyrene, poly-1-pentene, and polyvinyl isobutyl ether are examples of this. On the other hand, a polymer such as polymethyl methacrylate having crowded side groups on the main chain shows T , to vary strongly among its stereospecific forms, the isotactic form exhibiting T , = 4 5 O , the syndiotactic, 1 1 5 O , and the atactic about 90O.15 Appendix The Estimation of Average Moment in Stereospecific Vinyl Polymers.-In the following, a simple and approximate method is used to try to predict the relative polarizations and dipole moments of stereospecific vinyl polymers. The method consists essentially of considering the monomer units pair by pair as they may lie in space. Each pair can be shown to exist in 18 most probable conformations.
HOWARD H. ZABUSKY
Vol. 66
Among these 18 conformations the probability and moment of each is calculated. The relative average polarization of the chain then is calculated from the weighted average of the pair moments. In the specific case of polymethyl methacrylate, the configurations of the isotactic and syndiotactio forms may be written
0-CHE CHI
I
C=O -C*2-C-CH2-L I
CH3
I -CH2-C-CHz-CL o I
I c=.o I
I
CH,
O-CHs A-CH, dd-configuration
CH,
I I
C=O
0-CH, lbconfiguration
As a more complete spatial representation one may refer to Fig. 2, ref. 8. The shorthand method shown in Fig. 3, ref. 8, is adopted for representing the 18 different interlapping conformations of the two asymmetric carbon tetrahedron assemblies. Conformations other than the gauche, in which the direct overlapping of groups attached to the tetrahedral corners is present, are regarded a priori as too improbable to include in the calculation. As was shown earlier8 the moment of the monomer pair, Pp,
1s
Pp = 2PLl
cos (8/2)
(-4-1)
where po is the moment of the monomer molecule and 6 is the angle between the average moments of the monomer units as directed along the asymmetric carbon-carboxyl carbon bond. To evaluate the average polarization of the whole polymer, we assume as a good approximation that the average moment, pLsv,per monomer unit of the ensemble of monomer pairs in the polymer chain is the root mean square of the weighted moments of the pairs
5 - 5 cos2 (8i/2) 4 2fi 5 fiPi2
=
Po2
fi
i
(A4
fi
where n is the number of differing conformations possible in the given polymer species (e.g., 9 for either the isotactic or the syndiotactic species), p L is the moment of the ith pair, andf, is the probability of the individual pair conformations of p L as shown in shorthand form in Fig. 3 . Necessarily, n
Cf,= 1. a
The evaluation of the .fl's was made using statistical mechanical methods based on reasonable values for dipole-dipole energies and H-H repulsion energies for the separate conformitions. The energy above an arbitrary zero of each dimer conformation, E,, was considered to consist principally of the dipole-dipole interaction energy of the ester group dipoles, E D , and of the repulsion energy ER, arising from the tight placement of the various molecular groups.
Ei
=
ED
+ ER
(-4-3)
The dipole-dipole energy for non-polarizable dipoles is -3(?&*S)(WS) ED =
SS
C"l't!Z
+s" (A-4)
PO
- _ (cos 8 -
- 3 cob p cos 7)
5.3
(13) S.Saito and T. Nakajama, J . Polymer Sci., 37, 229 (1959). (14) T. I. Borisova a n d G. P. Mikhailov, Vysokomolekzll~Soedkn.,1, 56.7 (1959); J . Polymer Sci.. 40, 285 (1969). (1.5) N. G. Gaylord and H. P. Mark, "Linear a n d Stereoregular Addition Polymers," Interscience Publishers, Kew York, K. Y., 1969, pp. 71, 322.
where w1 and pc2are the moment vectors of dipoles 1 and 2, po is the absolute value of the moment of the vectors p1 and ,us, s is the distance vector expressing the distance detwwn dipole centers, and 8, 7,and 6 are the angles of the bipole conformation (see F 2).
STEREOSPECIFICITY AND DIELECTRIC PROPERTIES OF POLAR PoLYmris
August, 1962
1395
For po = 1.69 D., chosen as for a similar simple ester, methyl propionate,lBand for s = 1 A., 6 = 0", 5, = go", we obtain
Eno =
(1.69)"(3.33) 2( 10-30) (4T)( 1 0 - - 9 / 3 ~(io-i0)3 ~)
coul. m. * COUI.
volt-m.
m.
= 29.4 X 10-20joules
Fig. 2.-Georiietry
of dipoles.
= 42.6 kcal./mole and eq. A 4 becomes
(A-5) where s is in A. To obtain the potential energy values for repulsion a t various distances between non-bonding hydrogen atoms, the following equations from the valence-bond method can be applied
where Q ~ , H and J h , h are the coulomb interaction energy and the exchange energy, respectively, for the pair of orbitals of the two H atoms. Hirschfelder and 1 h 1 m t tshowed ~~ that &a,n arid J h , h may be obtained from R(I2) and E( %) for the singlet and triplet u orbitals
,
,
10
L.7;, -.-
. .
DISTANCE I K T V E K N C
.-+.
Y
Ill
, , 2 0 ,i energy ss s funct'ion of interatomic distmce. 16
Fig. 3.-Repulsion
911 conformations in Table V. The ~al~uIat('(l values of ER, XI,, Ei,fi, ttndfi cos*(&/2) are given in Table VI. V
'rABLE
Figure 3, taken from a private meniorsnduni of Ih. Keniti Higasi, is the result of this estimation. The values of the repulsive energy E R = E H , Hare given as a function of the interatomic distance, d n , ~in , three different scales. Adrian1* made a similar calculation for the distance range 1.3 to 3.5 A. The values for EDand E R used in the present study were calculated d t e r determining the appropriate constants for the 18 conformations. The repulsion energy E R WIIS calculated using the above relation, E R = EH.H,and values of dH,Hwere obtained from the conformations using
(A-7) where do = 2.1 A., a nominal internuclear distance for close approach of non-bonding hydrogen atoms, A, = overlap distance of hydrogen atoms in the conformation. The values of the angles 8, 7 , and 6, and the distances s and A were determined for each conformation by calculations checked by measurement on molecular models (Fisher Taylor-Hirschfelder). From these parameters, values of EDand E R were calculated and used to evaluate Ei. The probability of each state, f i , is given by f
- p oe -Ei/RT
~ ~ I~WI , ~MOI~ECCIAR . ~ ~ COSPORMATIONS
~IIGASUIIIW \ , 7 ( 'oiiforrnu tion
B
Y
c,
s
(A.,
A
(A.,
dH.H
(A.,
Isotactic
I
TI
120" 60 105 105
I11
135
Iv
v
VI VI1 VI11
IS
120 180 150 130 !IO 1OU
10 50
--
75 20
80 90 70
70' 40 150 110 110 100 I60 00 45
3.8 3.5 6.3 6.8 5.5 7.0
1x5 20
(iti
0.3
.o .8
.6 .2 .6 .6
6.i 3.4 4.7
.:3 .8
1.8 2.1 1.3 1.5 1.9 1.5 1.5 1.8 1 .:3
Syndiotact,ic.
I
v
1;KI 90 90 160 180
VI
130
VI1
110 110 120
I1 111
IV
VI11 IS
80
100 60 55 60
60 60
55 115 120 100 53
90
55
0
140
3 7 4 5 6 7 5.7 6 2 4 7 3 8 6 8
0 3 1 8 6 1 1 0 0 7 0 0 1 0
18 2 0 13 1 5 2 0 I 1 1 4 2 I I 1
For isotactic polynipthyl niethacrylate, QO = 11.17 at 30" and 8.415 at 60". For syndiotactic polymethyl methacrylate, PO = 6.73 at 30" and 5.12 a t 60".
Thc valucs of The measured values of B, 7 , 6, s, A, and d u , are ~ given for (16) C. P. Smyth, "Dielectric Uohavior and Structure," M c G r a a Hill Book Co., New York, N. Y.,1955, pp. 303-304. (17) .T. 0. ITirschfrldcr and .J. K. L i n n e t t , .I. C h m . Phgs., 18, 130
f l cos2 ( 6 , / 2 )obtained were a
isotactic --30"--0.7417 isotactic -60°-0.7321 syndiotactic --30°--0.6219 syndiotactic .-60'-0.6123
HERBERT A. POHLAND HOWARD H. ZABUSKY
139G
Vol. 66
TABLE VI CALCULATED VALUES FOR MOLAR CONFORMATIONS Conformation
BR, kcal.
ED. kcal.
Ei. kcal.
Isotactic I I1 111 IV V VI 1'1I VI11 IX
3 .0 1.1 15 8.4 2.2 8.4 8.4 3.0 15
0.85 . 56 * 21
3.85 1.66 15.21 8.48 2.31 8.56 8.50 3.54 15.38
.08 .I1 .I6 * 10 .54 .36
Total
0.0186 .710 0 0 .239 0 0 .0313 0
0.0248 .681 0 0 .255 0
0.999
0.0125 .627 0 0 .OB7 0 0 .0235 0
0.0166 ,6020
1.000
0.7417
0.7321
0.0345 ,1270 0
0.0421 .1376 0
0 0062 ,1330
0
0
0,0051 .1228 0 0 ,0800
0 ,0398 0
n n .0838 0 0 ,0297 0
Syndiotactic
I I1
3.0 1.6 15 8.4 1.6
I11 IV V VI VI I VI11 IX
0.17 * 79 ,117 .17 .23 .21 .45 44 - .IO
30 11 1.1
3.17 2.39 15.27 8.57 1 .83 30.21 11.45 1.54 29.90
#
30
Total
.3200 0 0 $5225 0 1.004
the polymcr spccics as, for cxamplc piSo,3p =
__
l.(j!1d.7417
=;
1.457
Calculated and observed values are coinparcd in Table VII.
TABLE VI1
.3220 0 0 ,4984 0
1.000
0 0
I
0 0 ,0805 0 0
,4140 0
.39%6
0.6219
O.Gl23
0
An alternative, vrry qualitative, calculation of the average moment of the polymcr can bc madc by assuming that each momomer loses one degree of rotatiorial frcmlom on being in the chain. Ignoring special orientation of thc moments within the chain, we have
COMPARISON OF CAI,CvI.ATED A N D O B S E R V E D M O M E N T S F O R
PMMA Temp., "C.
Steric furrn
F~~
(theor.)
A
L
(obsd.) ~ ~
Isotxtic 30 1,457 1,429 I s o t ,tic ~~ (io 1.410 1.482 Syndiotactic 30 1 ,333 1.321 Syndiotactic GO 1.323 1.347 Atactic 30 ... 1.349 1.379 Atactic GO ... The theory is examined by comparing ratios predicted and observed in Table VIII. C o & r p A I i I s o s s OF T I I E O R E T I C A I , A N D OBSERVE]) 1tATIos
h f O M U S T S F01t
(pm/pa
PhfM.4
for thc ntaatic \vas obxerved t o be 1.023 f 0.05)
Tlw agrcerncnt is considcred quitc sstisfactory. The 1;rrgor errors for measurements a t highcr tcmperatures :ire due in p a r t to the volatility of the solvent. A concentration error of pcrhaps -2 to - 4 7 c was observable. Tlie average momcnt calculated for the two forms when ut "infinite temperature," that is, a temperature high enough to overcome all restrictions t o rotation and to positioning, is found by settingfi = 1 for all conformations. On doing this one obtains
d.4807= 1.173 psyn = ].GO d .XCZ = 1.202 piso =
1.G9
It may be noted that the theory predicts and the experiment confirms that little change in the average moment occurs in the experimental 30" temperature interval. This is a. consequence of having rcJ1:atively small "activation energies" for the rotation hindering process. A large energy of activation could produce large changes with small tempcrature increments. In the limit of free rotation, the calculation indicates that the syndiotactie form would havc a slight1 larger niomcnt than the isotclvtic form (1.202us. 1.173). &e would expect exact equivalence instead of the small diffcrencc indictrtcd in the calculation. This mav reflect small cumulative crrors in the assignment of the a i values. OF In summary, it may be said that: 1. The RVerage moments calculated for the isotactic and nyndiotactic polymer species are in reasonable ngrecmcnt with those observed (Table VII). 2. The temperature coefficients of the moments calculated A 0.05 ngrcc closcly with those observed (Ttible VIII). 3 . The calculated ratios of thc average moments of the isotactic and syndiotactie polymer spcxics ngrcc closely with those observed. 4. The method of considerin$ the average moment of a polar polymer to arise from paired monomer units having enumerable conformations and preassigncd degecs of freedom (based on dipole-dipole and repulsion cnergieu) gives 5 reasonably satisfactory rcprcseritation of the complex problem of polar polymer moments in polymethyl methacrylates. ll,las A c ~ o w l e d g m e n t . - ~ portion of this supported by Signal Corps Contract No. D-36-039sc-78105; DA Project 3-99-1548; ONR 356-375; WADD Project 7371, for which the authors wish to express their appreciation.
