The Unperturbed Dimensions of Polypropylene and Polyethylene1

H. INAGAKI, T. MIYAMOTO, AND S. OHTA

3420

The Unperturbed Dimensions of Polypropylene and Polyethylene1

by Hiroshi Inagaki, Institute for Chemical Research, Kyoto University, Kyoto, Japan

Takeaki Miyamoto, and Shigeyasu Ohta Ube-Nitto Chemical Industry Go., Ltd., Yaesu, Tokyo, Japan

(Received March 7, 1966)

~

~

~

_

_

The unperturbed dimensions for propylene polymers with different stereospecificities are compared with those for polyethylene. Two types of syndiotactic polypropylene have been prepared at -78" with the catalytic system VCl4-anisol-A1(C2H5)&1 by using toluene and n-heptane as solvents for polymerization, respectively. Tacticities of these polymers range from 0.8 to 1.5 as determined by the relative absorption intensity at 867 cm-l (infrared index). Determination of molecular weights, M , of six fractions having an infrared index of ca. 0.8 was made in heptane by the Archibald ultracentrifugal method and by light scattering. Intrinsic viscosities [q] of these fractions were determined in different solvents. Isoamyl acetate is found to be a 8 solvent for the syndiotactic polymer and the 8 temperature is elevated from 34" to over 70" with an increase in the infrared index from 0 to 1.5. Relationships between [q] and M obtained by various authors for polypropylene fractions, including our own data for the syndiotactic polymer, are analyzed using our recent semiempirical equation and the Stockmayer-Fixman equation for estimating the unperturbed dimensions. The unperturbed dimensions of propylene polymers are greatly influenced by temperature, showing a negative temperature coefficient, but are only evaluated slightly influenced by the choice of solvent. The characteristic ratios (R2)o/nZ2 with the proper data at 135" in decalin, assuming that the Flory constant cB0 is02.87 X cgs, average about 5.0, 4.3, and 4.7 for atactic, isotactic, and syndiotactic polypropylene, respectively. These ratios evaluated with the proper data at room temperature in different solvents converge around 5.9 and 6.1 for the atactic and syndiotactic polymer, respectively. The latter ratios are explicable in terms of a theoretical prediction recently made by Flory, Mark, and Abe. According to these results, it is concluded that the characteristic ratio obtained at 135" in decalin for polyethylene, 6.1, is significantly higher than those for polypropylene with any stereospecificity. In connection with this conclusion, a qualitative discussion is made on the correspondence of molecular conformations assumed in the solid state to those in solution.

Introduction The mean dimension of the polymethylene chain has been discussed on the basis of various molecular conformation calculations for lower n-alkane homologs.2p Thus the characteristic ratios, (R2)o/n12,and the temperature coefficients d In (R2)o/dT observed for polyethylene have been interpreted fairly well in terms of the above calculations.4~5 Here (R2)0 is the unperturbed mean square of the end-to-end distance R of the chain averaged over all of its configurations, and n is the numThe Journal of Physical Chemistry

ber of bonds of length I in the chain. However, if the interdependent-rotation model6 used for calculations is (1) A part of this work has been presented at the 14th Polymer Symposium held in Kyoto, Japan, Oct 1965. (2)C. A. J. Hoeve, J . Chem. Phys., 35, 1266 (1961). (3) K. Nagai and T. Ishikawa, ibid., 37, 496 (1962). (4)A. Ciferri, C. A. J. Hoeve, and P. J. Flory, J . A m . Chem. SOC., 83, 1015 (1961); P. J. Flory, A. Ciferri, and R. Chiang, ibid., 83, 1023 (1961). (5) (a) R. Chiang, J . Phys. Chem., 69, 1645 (1965); (b) C. J. Stacy and R. L. Arnett, ibid., 69, 3109 (1965).

_

_

_

THEUNPERTURBED DIMENSIONS OF POLYPROPYLENE AND POLYETHYLENE

applied to stereoregular vinyl polymers bearing substituents R on alternate carbon atoms, -(CH2--CHR),-, it follows that tlheir characteristic ratios should be much larger than that of p~lyethylene.~This result is the contrary to the observations of some other workers.8 This discrepancy between calculation and experiment might be partly attributable to uncertainties associated with the estimate of the unperturbed dimensions. There has been no sure method to making these estimates for this purpose since they were based on viscosity [71] and molecular weight, M , alone,gs10and especially since the 0 solvent could not be determined for a given system. Recently, however, Inagaki, et al., have proposed a tentative method for estimating the unperturbed dimensions from viscosity data obtained for extremely good solvent systems, especially those in which the expansion factor a is larger than 1.4." Here a is defined by ((R2)/(R2)O)'/2, ( R 2 )being the mean square of the endto-end distance perturbed by long-range interactions between segments. Moreover, they have proved that the Stockmayer-Fixman method for the same purpose12 is applicable if 1 < a < 1.4." Thus if, corresponding to the magnitude of a of a given system, one of these two methods is alternatively used, the characteristic ratios ((R2)o/nZ2)may be determined irrespective of thermodynamic properties of the solvent used. The purpose of the present paper is to visualize the effect of substituted methyl groups upon the unperturbed dimension of the polymethylene chain by applying the methods mentioned above to data of [ q ] and M obtained by different authors for polypropylene fractions in various solvents. The unperturbed dimensions of atactic and isotactic polypropylene are estimated by referring to the relationships between [T] and M reKinsinger and hug he^,^^^'^ ported by Danusso, et aZ.,l3>'4 and Parrini, el al.,17respectively. That of the syndiotactic polypropylene is estimated by using our new viscosity data. Two types of syndiotactic propylene polymers are prepared at -78" with a catalytic system proposed by Natta, et aE.,18in toluene and in heptane, respectively. Thus the characteristic ratios (R2)o/n12 of these polymers with different stereospecificities are discussed in comparison with those reported recently for polyethylene.

Experimental and Results Preparation and Fractirmatirm of Syndiotactic Polypropylene. Syndiotactic propylene polymers were prepared using a catalytic system of vanadium tetrachloride-anisol-diethylaluminum monochloride, which has been described by Natta, et aE.18 Two different series of polymerizates were obtained using toluene and heptane, respectively, as the solvent for polymerization.

3421

The catalytic solution was obtained by treating mole of vanadium tetrachloride and mole of anisol with 5 X mole of diethylaluminum monochloride in 200 ml of one of the solvents at room temperature for about 1 hr. Then 3 moles of liquid propylene was introduced into the catalytic solution and the polymAfter 24 hr, erization mixture was kept at -78". the mixture was poured into a large amount of methanol which was slightly acidified with hydrochloric acid, thus recovering the polypropylene as a precipitate. The precipitated polymer was pulverized in a blender and washed several times with the acidified methanol until the green color of the polymer disappeared. A very small amount of the polymer prepared with toluene as solvent was insoluble in boiling diethyl ether, and the removal of this insoluble portion was made by means of an extraction with boiling ether for 24 hr. The portion soluble in ether was recovered and its intrinsic viscosity in decalin at 135" was 204 ml/g. This fraction will hereafter be designated SP-T. One the other hand, the polymer prepared with heptane as solvent was almost completely dissolved in boiling heptane except for a small portion which existed in a gel form. After removing this gel portion, the fraction easily soluble in boiling heptane (SP-H) was further divided into two portions with boiling ether, i.e., into boiling ethersoluble and -insoluble portions (SP-HE and SP-HI). The [ q ]values in decalin at 135" were 64 and 78 ml/g, respectively, and the weight fractions of SP-HE and SP-HI were 0.35 and 0.65, respectively. The polymer sample SP-T was fractionated into eight ~

~~

~

(6) T. M. Birshtein and 0. B. Ptitsyn, Zh. Tekhn. Fiz., 29, 1048 (1959); S. J. Lifson, J . Chem. Phys., 30, 964 (1959); K. Nagai, ibid., 31, 1169 (1959); C. A. J. Hoeve, ibid., 32, 888 (1960); P. J. Flory and R. L. Jernigan, ibid., 42, 3509 (1965). (7) P. J. Flory, J. E. Mark, and A. Abe, J. Polyner Sci., B3, 973 (1965); report presented a t the Joint U. %-Japan Seminar in Polymer Physics, Kyoto, Oct 1965. (8) A. Kotera, report presented at the 13th Annual Meeting of the Society of Polymer Science of Japan, Kyoto, June 1965. (9) G. C.Berry and T. G Fox, J . Am. Chem. SOC.,86,3540 (1964). (10) H. Inagaki, H. Suzuki, M. Fujii, and T. Matsuo, J. Phys. Chem., 7 0 , 1718 (1966). (11) H. Inagaki, H. Suzuki, and M. Kurata, report presented at the Joint U. S.-Japan Seminar in Polymer Physics, Kyoto, Oct 1965; J . Polyner Sci., in press. (12) W.H.Stockmayer and M. Fixman, ibid., C1, 137 (1963). (13) F. Danusso and G . Moraglio, Rend. Accad. Nasl. Limei, (8j 2 5 , 509 (1958). (14) F. Danusso and G. Moraglio, M a k r m l . Chem., 28, 250 (1958). (15) J. B. Kinsinger and R. E. Hughes, J . Phys. Chem., 63, 2002 (1959). (16) J. B. Kinsinger and R. E. Hughes, ibid., 67, 1922 (1963). (17) P. Parrini, F. Sebastiano, and G. Messina, M a k r m l . Chen., 38, 27 (1960). (18) G.Natta, I. Pasquon, and A. Zambelli, J . Am. Chem. Soc., 84, 1488 (1962).

Volume 70,Number 11 November 1966


3422

Table I : Characterization of Syndiotactic Polypropylene Samples

hl, ml/g Iioamyl MP,

code

Infrared index

SP-T" SP-Tz SP-Ta SP-TI SP-Ts SP-Ta SP-T,

0.85 0.79 0.75 0.85 0.80 0.81 0.85

83-94

SP-HE" SP-HEzs6

1.20

96-104

SP-HI"

1.50

Polymer

Arohibald

L.S.

135*

Heptane, 30°

422 (0.32) 209(0.74) 151 (0.93) 118 (1.24) 88 (1.14) 54(1.41)

452 (0.64) 228(0.83) 154(0.95) 122b(0.99) 94 (1.04)

204 370 209 5 154.5 130 99 72.8

320 185 142.3 120.7 95.4 71 .I)

--Ma

OC

X 10-1 and At X IO+

Deoalin,

I

...

Toluene, 30°

aoetats, 450

264 155 121 102 84 61

125 87 73 64.5 56 42

64 83. 3d

a Unfractionsted polymers. mined in isoamyl acetate.

2

78

130-132

' M, = 117,000 in isoamyl acetate.

3

4

6

6

Mixture of fractions SP-HE*, SP-HEs, and SP-HE4.

8

7

9

10

12

11

Deter-

13

Wavelength, p .

Figure 1. Infrared spectrum of syndiotactic polypropylene prepared in this study.

fractions by usual fractionation-precipitation techniques with a system of n-octane and n-propyl alcohol at 30". Using the same procedure, the polymer sample SP-HE was fractionated into six fractions. Results of the characterization of these fractions are seen in Table I. On the other hand, because of the instability of the n-octane solution of SP-HI, a sand column fractionation technique using decalin and butyl carbitol as the elution agent at the boiling point of toluene was applied to this sample. As will be described later, the fractions obtained from SP-HI had high stereoregularities, and one of these fractions was used for the @-pointdetermination in isoamyl acetate. Infrared Spectra. The 2-15-p spectra were taken on a Shimadzu AR-275 113 spectrometer. Polypropylene films (thickness of 80 p ) for the memurement The Journal of Physical Chenzktry

were prepared from trichloroethylene solution. According to Natta, et uZ.,'~ syndiotactic polypropylene shows a characteristic absorption band at 11.53 p (867 cm-I). The spectra obtained for all of the present samples were found to have this characteristic band, M is illustrated in Figure 1. To indicate the syndiotacticity of sample, an infrared index first proposed by Nattale WM used. This index I , is given by

1,

E

+

'YIl.6?,/(1/2)(?'2.82

728.5)

where the 7's are the optical absorptions at 11.53, 2.32, and 2.35 p. The base line for the 11.53-p band was the (19) G. Natta, Iriah Patent Application 430/60 (filed June 1960); E-J-Addink and J. Beinterns, Polymer, 2 , 186 (1901); M. Okamoto, K. Miyamichi, and 0. Ishizuka, Chem. HGh Polymers Japan, 21, 218 (1964).


IU

-

LU

29

Figure 2. X-Ray diffraction spectrum of syndiotactic polypropylene corresponding to Figure 1.

straight line drawn tangentially between the absorption minima near 11.3 and 11.7 p, while that for the 2.32- and 2.35-p bands was the straight line drawn tangentially between the absorption minima near 2.2 and 2.7 p. The infrared indices of our samples were found to range from 0.8 to 1.5. The results are given in Table I together with the other data. The samples used showed the same X-ray spectrum characteristic of syndiotactic polypropylene as was obsellred by Natta, et al.ls (See Figure 2.) Melting Points. The melting point determinations were made only for the whole polymers with a Chiyoda polarization microscope equipped with a thermostage. The rate of temperature elevation was adjusted to 0.25"/min. Melting points observed for these samples were in a range between 83 and 132" and parallel to the increases of the infrared indices (see Table I). Molecular Weight Determinations. All solution measurements were made in n-heptane unless otherwise stated. The Archibald ultracentrifugal procedureZ0 was applied for the molecular weight determination of the fractions of the SP-T series. The measurements were carried out at 30 f 0.1" using a Phywe analytical ultracentrifuge. Apparent molecular weight data obtained as a function of the initial concentration co were analyzed according to the following semiempirical equation to yield the weight-averaged molecular weight Mw21

In (l/Mapp) = In (l/Mw)

+ 2A2Mwco

where A , is the osmotic second virial coefficient appear-

3423

ing in the well-known lighbscattering equation. For the partial specific volume 8, we assumed that 8 was equal to the apparent specific volume 8*, which was found for this system to be 1.127 ml/g at 30" in the concentration range from 0 to 1 g/dl. For the density of n-heptane, we used a literature value of 0.6753 g/ml at 30". The values of M , and AZare included in Table I. For unknown reasons, the A2 value found for the highest molecular weight sample SP-TS was abnormally low, and therefore we rechecked all of these data by light scattering. The calibration and use of the light-scattering photometer was described previously.1° The refractive index increment for this system was found to be 0.1077 ml/g at 30" for 436 mp. The required values of Kc/Ro, where K is the well-known light-scattering factor and ROthe reduced intensity of the scattered light at zero angle, were obtained by the usual extrapolation according to Zimm.22 The values of M , and A z are given in Table I. Except for the result of SP-T2, these are in fairly good agreement with those obtained by the Archibald method, although M , values obtained by light scattering are always higher by a few per cent. The double logarithmic plot between [ q ]obtained in heptane at 30" (see next section) and M , determined by light scattering gives the equation [q]30 (ml/g) =

3.12 X 10-2M,0.71

In a preliminary experiment we found that isoamyl acetate which is known as a 6 solvent for atactic polypropylene (6 = 34")12 could dissolve our syndiotactic samples as well. Thus the scattered-light intensities in isoamyl acetate were determined once more for three fractions, SP-Tb, SP-HE234,23 and SP-HI3 a t various temperatures ranging from 45 to 70". The value of A2 at each temperature was computed by plotting Kc/Ro us. c. Subsequently, Az was plotted against T to find by extrapolation the temperature at which A z vanishes (see Figure 3). Thus the temperatures for SP-T and SP-HE series were determined to be approximately 41 and 43.5, respectively. Details of the data obtained are given in Table 11. However, the 8 point for SP-HI3 could not be confirmed; the solution exhibited a transition into a turbid, gel-like state as soon as the temperature dropped below 70". For this crystalline polymer, therefore, we may only suppose that the 6 point, if it exists, would be somewhat lower than 70". (20) H.Fujita, H.Inagaki, T. Kotaka, and H. Utiyama, J. Phy8. Chem., 66, 4 (1962). (21) H. Inagaki, Makromol. Chem., 64, 196 (1964); H. Inagaki and 5. Kawai, ibid., 79, 42 (1964). (22) B. H.Zimm, J . Chem.Phys., 16, 1099 (1948). (23) See footnote c of Table I.

Volunzs 70. Number 11

Nonember 1966

H. INAGAKI, T.MIYAMOTO, AND S. OHTA

3424

Table ILI: Temperature Dependence of Intrinsic Viscosity

6(P In

rl

0

TeC) Temperature dependences of A2 for SP-TS and Figure 3. SP-HEaa4 studied by light scattering. The approximate estimates of e temperatures are 41 and 43.5' for the former and latter sample, respectively.

I n any event, the close parallel correlation found between 8 temperature and infrared index as a relative measure of syndiotacticity should be interesting. This finding will be discussed later.

Discussion Estimate of Unperturbed Dimensions. To estimate the unperturbed dimensions using relationships between [v] and M alone, a need for an appropriate equation describing the excluded-volume effect upon the hydrodynamic radius of polymer chains is apparent. As will be discussed later, however, no complete cognizance has yet been taken of any equations available to date for this purpose. Recently, we have proposed a tentative procedure based on combining the Ptitsyn equationz4 a2 = 0.786 4- [(I

Table 11: Light-Scattering Data for Syndiotactic Polypropylene in Isoamyl Acetate

Polymer

SP-Tb

SP-HEW

SP-HI3

Mv

x

Temp,

lo-'

117

83.5

..

o c

A~

x

8,

104

46.5 52.0 67.0 52.0 60.0

0.80 1.64 4.0 1.37 2.57

67.0

3.52

...

...

O C

+ 9.36~*M'/~)~'/~/4.68](1)

with a semiempirical relation between two expansion factors a,,and CY for the hydrodynamic radius and the end-to-end distance, respectively, i.e.

42

43.5

Equation 2 was first suggested by Yamakawa and Kurata.z6 Here z* is defined by Z* =

70"

" The e point lies somewhat below 70".

0.330BA-3

with A' = (Rz)o/M

Viscosity Measurement. Viscosity measurements were made in a Ubbelohde viscometer with a flow time of 105 sec for n-heptane at 30". The kinetic energy correction of [ q ] was determined to be less than 0.2%. The sample of the highest molecular weight was examined in a variableshear viscometer and was found to exhibit Newtonian flow. The intrinsic viscosities of all of the fractions in decalin were determined at 135" under a nitrogen atmosphere with 2,Pdi-t-butyl-p-cresol added to the solution in order to avoid the oxidative degradation of the polymers. I n addition, the measurements in toluene (30") and isoamyl acetate at different temperatures near the 8 points relevant to each sample series were made on some selected fractions. The latter data will be used to derive the temperature coefficient of the unperturbed dimension and are listed in Table 111. The Journal of Phyaieal Chemistry

(3)

B

=

p/msZ

(4) (5)

p and m, being the binary cluster intergral between segments and the molar weight of a segment, respectively. If aq3is replaced, according to its definition, by the familiar Flory-Fox equation26 aq3= [ q ] / K M 1 / 2

(6)

with

K

=

@oA3

(7)

and unity appearing in the second term in eq 1 is neglected, the combination of eq 1 and 2 yields (24) 0.B. Ptitsyn, Vyaokomolekul. Soedin., 3, 1673 (1961). (25) H.Yamakawa and M. Kurata, J . Phya. SOC.Japan, 13, 78 (1958). (26) P. J. Flow and T.G Fox, J . Am. Chem. SOC.,7 3 , 1904 (1951).


( [7]/M1/')'/' = 0.786K'/s

+ 0.950K''sz*''3M'~a (8)

Here (Po is the universal constant of Flory at the 8 point. 27 In our prevjous work,ll the validity of eq 8 has been tested with [q]-M relationships established for polystyrene and poly(methy1 methacrylate) fractions in good solvents, respectively, and no serious inconsistencies between K values thus obtained and those in 0 solvents have been found. This does not mean, however, that the unperturbed dimension can be evaluated with certainty according to eq 8, since the theoretical value of (Po has not yet been established2'" and, on the other hand, it has been found to depend on the polymer and a bit on the solvent.27b At the present, we believe that eq 8 may yield correct K values, thus allowing one to make, at least, relative estimates of the unperturbed dimensions for different polymer chains. The Ptitsyn equation (1) and the Stockmayer-Fixman equation12

[ ~ ~ ] / M= "'K

3425

+ 0.51@,$M1"

(9)

are essentially in agreement at low values of a. However, when CY drops lower than 1.4, eq 8 becomes only the asymptote for eq 1 as the result of the mathematical simplification introduced on its derivation. Thus eq 9 will be used in the low CY region for the sake of simplicity of treatment. Atactic and Isotactic Polypropylene. Figure 4 shows plots of eq 8 with relationships between intrinsic viscosity and number-average molecular weight Mu reported by Danusso and Moraglio for atactic polypropylene fractions. l 3 The viscosity numbers are determined in decalin at 135", and in cyclohexane, toluene, and benzene at 30', and the values of M , by osmotic measurements. For the system in decalin the [q]-M, and -M, data obtained by Kinsinger and Hughe@ (half-filled and filled circles, respectively) are plotted simultaneously with those of Danusso and M ~ r a g l i o(open ~~ circles). Disagreement between these two series of data is remarkable, especially in the region of the higher molecular weights. However, two data points for the lowest and the second from the lowest molecular weight obtained by the former authors fall on a line passing through those of the latter authors. Taking such a circumstance into consideration, an extrapolation of the plot to M'Ia-+ 0 was made. The intercept on the ordinate was found to be 0.144, which yields K = 12.0 X in accordance with eq 8. This K value is thus in excellent agreement with that estimated by Kinsinger and Hughes using a 8 solvent, diphenyl ether, at 153",16 but remarkably lower than the value of 16.8 X 10-2 obtained by Danusso and Moraglio using another 8 solvent, isoamyl acetate, at 340.13 This dif€erence may

Q

0.71

\

0.6

0.5

-.-----. $ ! 0.4

s

G

0.3

isoamyl acetate

0.2

34'C

r O*'t

I

I

2

4

I

I

6

M? *lo-' Figure 4. Plots of eq 8 with [q]-M. relationships reported by various authors for atactic polypropylene in different solvents. The lower and upper chain lines indicate the limits of application of eq 8 for the system in decalin a t 135" and for the other solvent systems, respectively. The circles @ and 0 show data of Kinsinger and Hughes for decalin, while the circles e and 0 show data of Danusso and hloraglio for cyclohexane and the other solvents, respectively. For details, see text.

be attributable to a negative temperature coefficient of the unperturbed dimension of this polymer. However, such an interpretation seems to be opposed to some observations of Kinsinger and Hughes made at other 8 temperatures;16 they have found higher K values than 16.8 X at higher 8 temperatures, e.g., 74 and 92' (see Table IV). What we note will be the effect of molecular weight heterogeneity on the K value, for the (27) (a) P. L. Auer and C. S. Gardner, J. C h m . Phys., 23, 1545, 1546 (1955); B. H. Zimm, ibid., 24, 269 (1956); J. E. Hearst, ibid., 37, 2547 (1962); and C. W. Phun and M. Fixman, ibid., 42, 3838 (1965). The theoretical values of 10-2arPo (cgs) obtained by these authors are 2.87, 2.84, 2.82, and 2.68, respectively. By refining mathematical approximations introduced into those calculations, the (Po value may be expected to be slightly smaller than 2.68 (M. Kurata private communication). (b) Experimental determination of rP made by Baumann shows that this value is cu. 2.4 as an average o diiTerent determinations: F. H. Baumann, J. Polymer Sci., B3, 106 (1965).



3426

Table IV: Polypropylene a t the Ideal States ( e ) Configuration

Solvent

Isoamyl acetateb Cyclohexaneb Benzeneb Tolueneb l-Chloronaphthalenee Cyclohexanonec Decalinb

34 (e) 30 30 30 74 (e) 92 (e) 135

16.5 15.9 15.3 15.3 18.2 17.2 12.0

831 820 81 1 81 1

4 9.05 2.30 4.12

1.75 1.73 1.71 1.71

6.12 5.96 5.83 5.83

748

8.11

1.57

4.96

Syndiotactic

Isoamyl acetated Toluened Heptaned Decalind

45 (-e) 30 30 135

17.2 16.4 16.4 11.2

843 830 830 731

-0 3.37 5.13 8.70

1.77 1.75 1.75 1.54

6.30 6.11 6.11 4.74

Isotactic

Tetralin" DecalinC a-Chloronaphthalene' Diphenyl etherc

135 135 145 145 (e)

9.55 9.55 8.95 13.2

693 693 678

4.85 9.52 1.84

1.46 1.46 1.43

4.26 4.26 4.07

Atactic

Calculated assuming (PO = 2.87 X loaacgs. of the present work. ' Data of Parrini, et d.17

Data of Danusso and Moraglio.1%14

' Data of Kinsinger and Hughes.1b816

Data

present treatment is made on the basis of numberaveraged molecular weights. This effect may be corrected by introducing a factor qn2' defined by .Q

=

=

r(h

[ v ] e / ~ ~ , 1 / 2

+ i.5)/hr(h + 1)

+

where (h l)/h = M,/M, and I' represents the I' function. The last form results from the Schulz distribution. This correction is quite large if polymers are poorly fractionated, but this amounts only to 1.09 if h = 4. Moreover, our main icterest consists not in the K value itself but in the quantity A , which is proportional only to KIIa,as is seen in eq 7. Thus differences in the characteristic ratios among polymers may be discussed without taking into consideration the averaged nature of the molecular weight. I n connection with the above problem, the K values estimated in other good solvents should be discussed. Chain lines drawn parallel to the abscissa in Figure 4 indicate the limit for application of eq 8, which is described by

[?7]/KM1/2 > 2.2 (10) corresponding to a > 1.4. The lower chain line indicates the limit for decalin, while the upper indicates that for the other solvents. Data points below this limit should pass through a little higher point on the ordinate, which corresponds to Kb/'rather than 0.786 X K4l6. Thus below this limit, eq 8 is the asymptote of eq 1 and hence is inapplicable to data points for toluene and benzene, but is applicable for decalin and cyclohexane.I3 Therefore, for these series of data points we The Journal of Physical Chemistry

30 -

isoamyl acetate 3 ~ ' c 10'

0

2

4

6

M?.lO* Figure 5. Stockmayer-Fixman plots with the same data as shown in Figure 4.

use the Stockmayer-Fixman equation (9). Figure 5 shows plots of eq 9 with the data for toluene, benzene, and isoamyl acetate. The data points for the highest and the second from the highest molecular weight with toluene as solvent deviate downward slightly from the most reasonable extrapolation line. However, such (28) M. Kurata and W. H. Stockmayer, Fortschr. Hochpolyner. Forsch., 3. 196 (1963).


deviations should occur as expected from a values of these samples (see Figure 4). With the aid of the Stockmayer-Fixman plot we get nearly the same K value 15.3 X 10-2 for both toluene and benzene. To establish further the K values obtained above, we use the original equation of Ptitsyn. This is (a2

- 0.786)"'

=

0.099

+ 0.305BA-3M'/'

I

3427

I

I

1

1

W I

'decalin 1135' C

I

(11)

where a is computed from = [7]4/s/K4/tM'/b

(12) The above equation may permit the justification of whether a value of K assumed for calculating a was reasonable. If a wrong K value is assumed, the plot of eq 11 should not pass through the theoretical value 0.099 on the ordinate. For applying this procedure to the present problem, we assumed K values relevant to each system. Figure 6 shows plots of eq 11. Straight lines for each system are obtained and meet at ca. 0.10 on the ordinate. This finding clearly indicates that the assumed K values were correct and, at the same time, that the unperturbed dimension of this polymer decreases with increasing temperature almost independent of solvent used. On the other hand, the B value for each system may be easily evaluated from the slope of each straight line. Using this B value and referring to eq 8 we may draw the asymptote for each system. These asymptotes are shown in Figure 4 by dotted lines. Each dotted line appears to give a natural asymptote for each series of the data points. Thus we may conclude that the lo2 X K values 12.0 and 16.8 found at 135 and 34", respectively, are consistent with each other and a negative temperature coefficient of the unperturbed dimension is expected. The same procedure for estimating the unperturbed dimension is applied to [7] and M , data reported by different authors for isotactic polypropylene in decalin,15 tetralin at 135", and a-chloronaphthalene at 145",17 These plots are demonstrated in Figure 7 together with the limit for application of this procedure indicated by chain line. According to Figure 7, we see that all of the data points for decalin and tetralin lie beyond the chain line. Thus a direct extrapolation to M,''a --t 0 should be permissible to obtain correct K values. Dotted lines indicate such extrapolations for each system and appear to have a common intercept on the ordinate at 0.120, which leads to K = 9.55 x irrespective of the solvent used. This lo2 X K value is considerably lower than the 13.2 estimated by Kinsinger and Hughes from 8 point viscosity data in diphenyl ether at 145°,15but in good agreement with 9.4 reported by Kotera, et al., for the same system as mentioned a2

I

I

1

I

I

I

I

1

2

3

4

5

6

7

1

M? -16' Figure 6. Plots of the original Ptitsyn equation (11) with the same data shown in Figure 4 for justifying the K values estimated according to eq 8.

0.7

-

0.6 -

0

2

6

4

8

M? ,10"

Figure 7. PloeS of eq 8 with [q]-Mw relationships for isotactic polypropylene in different solvents. For details, see text.

above.* In this connection it should be noted that if eq 9 is applied to the same data shown in Figure 7, higher K values, approximately 13 X (11 X for a-chloronaphthalene), are obtainable. However, Volume YO, Number 11

November 1066


3428

/

heptane 3dC

/ O

*-.-.-.-*-* isoamyl acetate 45" C

isoamyl acetate 450 c

~

2

I

I

2

4 Md/3.10-'

6

6

4 M:-10

8

Figure 9. Plots of eq 9 with the same data as shown in Figure 8.

Figure 8. Plots of eq 8 with our own data for fractions of SP-T series with infrared index of ca. 0.8'in various solvents. Lower and upper chain lines indicate the limits of application of eq 8 for decalin and for the other solvents, respectively.

taking into consideration the fact that the solvents used are extremely good for this polymer, these values may be overestimated. This is unavoidably associated with the application of eq 9. Syndiotactic Polypropylene. For estimating the unperturbed dimension of syndiotactic polymer we use our own data of [q] and M , obtained in decalin (135"), heptane and toluene (30°),and isoamyl acetate (45"). Figure 8 shows plots of eq 8 for SP-T series having infrared indices of ca. 0.8. As is indicated by two chain lines in the figure, only data points for decalin may be treated in accordance with eq 8, while the others should be treated with eq 9. Figure 9 shows the results of the latter treatment. From this figure we see that isoamyl acetate is a 8 solvent for the syndiotactic polymer as well as for the atactic. K values estimated using eq 8 and 9 alternatively are given in Table IV. Tests of these K values according to eq 11 are shown in Figure 10. The mathematical requirement of eq 11 seems to be fulfilled with these K values. As pointed out previously, the unperturbed dimensions of propylene polymers are influenced much more by temperature than by the solvents used. Thus to discuss the dependence of the K value on stereospeciThe Journal of Phyaiea2 Chemistry

W OD

6

Nl

-6

v

I

I

I

I

I

I

I

t

1

2

3

4

5

6

7

Figure 10. Plots of eq 11for the same systems given in Figure 8, using K values estimated according to eq 8 and/or 9.

ficity, we choose the data obtained in decalin at 135". The values of lo2 X K for the atactic and syndiotactic samples are nearly the same, ie., 12.0 and 11.2, respectively, whereas they differ considerably from 9.6 found for the isotactic. However, this finding supports previous observations that the unperturbed dimension

3429


generally depends little on s t e r e o r e g ~ l a r i t y .3o~ ~ ~ ~ ~ : Especially, the fact that the unperturbed dimensions of propylene polymers are almost independent of stereospecificity may be well interpreted in terms of the theoretical prediction made by Flory, et al., taking the existence of heterotactic units in the polymer chain into consideration.' In addition, the characteristic ratios evaluated experimentally converge at about 6.0. This also is in agreement with calculations by Flory, et al.' (See Table IV.) I n connection with the above finding, it is interesting to note the following facts. The atactic and syndiotactic polymers have a common 6 solvent, isoamyl acetate. The 8 temperature of the latter polymer increases proportionately to its stereoregularity, changing from 34" (or somewhat lower) for the former to ca. 70" (or somewhat lower than 70") for the latter with an infrared index of 1.5 (see Table 11). I n accordance with Figure 11. Plots of eq 13 with data obtained for syndiotactic the conclusion drawn by Kinsinger and Wessling, 31a polypropylene in isoamyl acetate. these observations imply that the atactic and syndiotactic polypropylene may be identified as a family in which only the microsyndiotacticity differs from the one direct comparison with those of the other polymers. to the other. Such an idea may be well supported by However, the fact that this value lies between those the finding of Woodbrey that a polypropylene sample, for polyethylene and polyi~obutylene~ might be exwhich has been regarded as atactic because of the abplained in terms of the effect of the methyl group on sence of its optical absorption at 867 cm-', could be the steric hindrance of bond rotations. highly syndiotactic from the viewpoint of nmr study131b Comparison of Polypropylene with Polyethylene. and also by a recent infrared study of Grant and Recently, a number of authors have been engaged in Ward.31c establishing [q]-M relationships for polyethylene in Last to be mentioned in this section is the temperdifferent solvents. Thus K values reported by difature coefficient of syndiotactic polypropylene d In ferent authors now give an identical value within exper(R*)o/dT. Starting from the Kurata-Yamakawa perimental e r r ~ r . ~ , ~ ~ example, Figure 12 shows a As an turbation theory of intrinsic v i ~ c o s i t y we , ~ ~arrived at plot of eq 8 with Chiang's data of [q] and M , for the (d In [q]/dT)e = (d In (R2)o/dT)e kM'/* (13) system polyethylene-decalin at 135°.5a A reasonable extrapolation of this plot to M'/* -t 0 affords 30.6 X where k is a constant independent of T and M and the for its K value, which is almost identical with the subscript 6 means that the quantities referred to are value of 30.0 X estimated using eq 9. These those at the 8 point.1° Thus the temperature coeffi102 X K values are also in excellent agreement with the cients evaluated with eq 13 should differ from those 29.5 and 31.6 obtained in diphenyl ether at values of with other methods by a change due to temperature 6 point (161.4")5a and in dodecanol-1 at its 6 point its variation of appearing in eq 7. Since In [ q ] changes (138"),6b respectively. linearly with T in the vicinity of the 6 point,l0the value

+

of its temperature derivative a t e is obtainable with good accuracy. In Figure 11, values of (d In [q]/dT), obtained with the system syndiotactic polypropyleneisoamyl acetate are plotted against M,'" (see Table 111). Extrapolation of this plot to Mwl/*+ 0 yields - (d In [v J/dT)e = 1.1 X deg-l, which corresponds to -(d(R2)o/dT)e = 0.7 X

deg-l

Because of a lack of experimental data this value is somewhat inaccurate and might be inadequate for

(29)W. R. Krigbaum, D. K. Carpenter, and S. Newman, J . Phys. Chem., 62, 1586 (1958);W. R.Krigbaum, J. E. Kurz, and P. Smith, ibid., 65, 1984 (1961). (30)I. Sakurada, A. Nakajima, 0. Yoshiaaki, and K. Nakamae, Kolloi&Z., 186, 41 (1962); G. V. Schulz, W. Wunderlich, and R. Kirste, Makromol. Chem., 75, 22 (1964). (31) (a) J. B. Kinsinger and R. A. Wessling, J . Am. Chem. SOC..81, 2908 (1959); (b) J. C. Woodbrey, J. P o l m r Sci., 8 2 , 315 (1964); (0) I. J. Grant and I. M. Ward, Polymer, 6, 223 (1965). (32) M.Kurata and H. Yamakawa, J. Chem. Phys., 29, 311 (1958); M. Kurata, H. Yamakawa, and H. Utiyama, Makromol. Chem., 34, 139 (1959). (33) L. H.Tung, J . Polymer Sci., 24,333 (1957).

Volume 70,Number 1 1

November 1966


3430

1

t

Table V: Summary of the Characteristic Ratios and the Steric Factors Obtained for Polypropylene in Decalin a t 135' and Comparison with Polyethylene ConPolymer

figuration

Polypropylene

Atactic Syndiotactic Isotactic

Polyethylene

r

u

1.57" 1.54" 1.46" 1.75"

a Calculated assuming Qio = 2.87 assuming Qio = 2.4 X lodz3.

Figure 12. Plots of eq 8 with [v]-M, relationships obtained by Chiang for polyethylene in decalin and phenyl ether (e solvent). The same plot for isotactic polypropylene in decalin a t 135" is given for comparison by dotted line.

Now we compare the characteristic ratios or the steric factors u for polyethylene with those for polypropylene. The steric factor is defined by

(14)

(A2/A2p

u =

with

A2r = (d2/M)(1

+

COS

8)(1-

COS S)-l

(15)

for polymer chains consisting of only one kind of bond. Here 8 is the supplement of the valence bond angle. Thus the characteristic ratio is related to u by

(R2)o/nZ2= d ( 1

+

COS

8)(1 -

COS

8)-l

(16)

For the purpose of eliminating the effects of temperature and solvent upon the unperturbed dimension, we may conveniently use K values obtained in a common solvent a t a common temperature. Fortunately, we have such data, those for decalin at 135". The available data to date, summarized in Table V, indicate clearly that the characteristic ratios or the u values for polypropylene, irrespective of its stereospecificity, never exceed that of polyethylene. This result presents a sharp contrast to that of the calculation of Allegra, et u E . , ~ ~ and also with that of Flory, et al., in which the interdependent-rotation model6 was applied to strictly stereoregular poly-a-olefins.' I n spite of this discrepancy between calculation and experiment, the order of magnitudes found for the u The Journal of Physical Chemistry

-(Rl)a/nl2-

-

1.67b 1 . 64b 1.55b 1.86b

x

4.96" 4.74" 4.26" 6.14"

10-23.

5.60b 5 . 36b 4.81b 6.9h

Calculated

values is fortuitously consistent with the fact that in the crystalline state, polyethylene chains take the most extended conformation tttt. . . . . . . , while syndiotactic and isotactic polypropylene chains take the more contracted conformations ttgg. . . . . and tgtg. . . . , respect i ~ e l y . Here ~ ~ t denotes the trans form and g the g a u c h e form. A similar interpretation has been presented by K0tera.l Thus a simple question arises as to how far the chain conformations preferred in crystalline state are retained still in solution. There exist several cases, e.g., for p ~ l y e t h y l e n e , polyisobutylene,36 ~,~ and polyethylene oxide,37 in which calculation achieved good agreement with experiments made on solutions. This would be an answer to the question just raised above. However, the solvent effect on the unperturbed dimension, hence on the chain conformation, has only been studied very little from experimental as well as theoretical viewpoints, 38 although a formulation of this effect was proposed.39 Perhaps owing to the average torque induced by solvent molecules upon the internal rotations,39 original conformations of polymer chains would only partly be retained fluctuating about their preferred positions. Thus an original conformation could be modified to another one after the polymer is isolated in solution.40 In fact, Tadokoro, et al., ob(34)G. Allegra, P. Ganis, and P. Corradini, Makromol. Chem., 61, 225 (1963). (35) (a) C . W.Bunn and D. R. Holmes, Discussions Faraday Soc., 25, 95 (1958); (b) S. Mieushima and T. Shimanouchi, J . Am. Chem. SOC.,86, 3521 (1964). (36) M. V. Volkenstein, "Configurational Statistics of Polymer Chains," translated by S. N. Timasheff and M. J. Timasheff, Interscience Publishers, Inc., New York, N. Y., 1963,Chapter 6. (37) J. E.Mark and P. J. Flory, J . Am. Chem. SOC.,87, 1415 (1965). (38)The solvent effect on the unperturbed dimension has been studied somewhat systematically by Elias, et al. [Makromol. Chem., 89, 12,228 (1965)land by Abe and Fujita [ J . Phys. Chem., 69,3263 (1965)l. (39) 5. Lifson and I. Oppenheim, J. Chem. Phys., 33, 109 (1960). (40) H.Tadokoro, report presented at the 13th Polymer Symposium held in Tokyo, Nov 1964.


servad by infrared studies that syndiotactic polypropylene dissolved in CSz indicated the absorption bands a t 831, 964, and 1131 cm-l characteristic of the planar zigzag more distinctly than the solid did, whereas the band at 867 cm-l characteristic of the original helical conformation almost d i ~ a p p e a r e d . ~ ~ ? ~ ~ On the other hand, there is little doubt that, for instance, the planar zigzag is the minimum energy conformation for an isolated polyethylene chain. Thus we think of a polyethylene chain with all the linkages fluctuating around their favorable positions. This picture differs somewhat from the usual one that a small fraction of the linkages departs from the trans position and ~t number of “planar zigzag” is connected by gauche linkages. In general, the pattern of the conformation fluctuation may be related to the nature of nonbonded interactions between neighboring substit uents, or between substituents and chain atoms. I n isotactic chains of -(CH2-CHR),- type, where R means any alkyl group, the conformation fluctuation could be affected dominantly by the molecular volume of R, since the repulsions between nonbonded atoms are not symmetrical about the 120” position. Upon increasing the volume of R the conformation fluctuation would tend to be diminished, bringing the chain to a more extended form. Taking the experimental result of Tadokoro, et u Z . , ~ O into consideration, however, the pattern of the fluctuation in polyethylene chains should not be noticeably different from that in polypropylene chains, and the original conformations of these polymer chains could be retained in solution to nearly the same extent. This situation may allow one to compare the u values of these polymers solely on the basis of the original conformations. However, this trend no more holds for isotactic poly(pentene-1) probably because of its bulky side group; the u value is found to be far larger than that of polyethylene At present, we believe that the u value may be described essentially in terms of a balance between the following two factors: the type of the original conformation and the degree of the conformation fluctuation or the retention of the Conformation. Thus to achieve good agreement between calculated and observed unperturbed dimensions, one might have to invoke whole profiles of potential curves of internal rotations, in addition to energy dif-

3431

ference between rotational isomerisms. It may be worthwhile to notice that the agreements between calculation and experiment reported to date have been limited to chain polymers having either no substitsubstituent^.^^ u e n t ~ ~ or ~ 4two ~ ~equal ’ Last to be mentioned here is the u value of atactic polypropylene. This u value has been computed on the basis of the number-averaged molecular weight, and this must be corrected for the polydispersity to compare directly with the other data. Since this correction factor will amount to only a few per cent, it is probable that the atactic polymer has a u value close to that of the syndiotactic polymer. On the other hand, no finite figure has been given to the atactic polymer extracted with ether from the heptane-soluble fraction obtained in the isotactic p~lymerization.~~ However, the magnitude of this u value implies that the atactic polypropylene is very similar to the syndiotactic with respect to its stereochemical structure. Such a figure is consistent not only with the results of nmr31b and infrared31c141 but also with our finding that these polymers have the common 0 solvent, isoamyl acetate. However, our preliminary experiment shows that isoamyl acetate is quite likely to be a 8 solvent even for isotactic fractions of polypropylene unless their tacticities exceed ca. 40%. This study is in progress in our laboratory. Acknowledgment. The authors wish to thank Professor M. Horio of Kyoto University for his interest and encouragement, and also Professor H. Tadokoro of Osaka University, Dr. K. Nagai of the Government Research Institute for Industry, Osaka, and Professor M. Kurata of this Institute for helpful discussions and suggestions, especially concerning the contents of the last section. (41) This observation seems to be related closely to our recent finding that single crystals of syndiotactic polypropylene can be obtained from its dilute solution without any strict conditioning, as likely as those of polyethylene, and the crystalline forms cannot be explained in terms of the original 81 helix (Inagaki and Miyamoto, Makromol. Chem., in press). (42) G. Moraglio and J. Brezzinski, J . Polymer Sci., B2, 1106 (1964); J. E. Mark and P. J. Flory, J. Am. Chem. Soc., 87, 1423 (1965).

(43) V. L. Folt, J. J. Shipman, and S. Krimm, J. Polymer Sci., 61, 920 (1962).


The Unperturbed Dimensions of Polypropylene and Polyethylene1

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