Macromolecules 1986,19, 2572-2575
2572
Concluding Remarks The critical interpretation of the configuration-dependent properties of poly(oxyneopentyleneoxyadipoy1) suggests the following: 1. The dipole moment ratio of the chains is strongly dependent on the conformational energy Ed associated with gauche states about C(CH3)2-CH2bonds of the glycol residue. In order to obtain agreement between theory and experiment an extra stabilization energy of about -0.40 kcal mol-' must be postulated for these states. 2. The temperature coefficient of the unperturbed dimensions shows a significant dependence on the conformational energy associated with gauche states about CH,-C* bonds. Good agreement between the theoretical and the experimental results is only obtained by assuming that the value of E, is zero or lower. Therefore, the results reported by Moravie and C ~ r s e twhich , ~ suggest that the C=O/C-C eclipsed form is more stable than the C= O/C-H eclipsed form, are not supported by the present study. Acknowledgment. This work was supported by the CAICYT through Grant No. 513/83. Registry No. PNA (SRU),28039-87-4; (neopentyl glycol). (adipic acid) (copolymer), 103439-11-8; 2,4-bis(p-isocyanatobenzy1)phenyl isocyanate, 4326-63-0.
References and Notes (1) Riande, E.; Guzmin, J.; de la Campa, J.; de Abajo, J. Macromolecules 1985, 18, 1583. (2) Dirlikov, S.; Stokr, J.; Schneider, B. Collect. Czech. Chem. Commun. 1971,36, 3028. (3) Moravie, R. M.; Corset, J. Chem. Phys. Lett. 1974,26,210; J . Mol. Struct. 1975, 24, 91. (4) Bowles, A. J.; George, W. 0.; Cunliffe-Jones, D. B. Chem. Commun. 1970, 103. George, W. 0.; Hassid, D. V.; Madams,
W. F. J . Chem. SOC.,Perkin Trans. 1972,2, 1029. (5) Abe, A. J. Am. Chem SOC.1984, 106, 14. (6) CRC Handbook of Chemistry and Physics, 52nd ed.; CRC: Cleveland, 1971-1972. (7) Riddick, J. A.; Bunger, W. B. Organic Soluents. Physical Properties and Methods of Purification; 1970; Vol. 11. (8) Mark, J. E.; Flory, P. J. J. Appl. Phys. 1966, 37, 4635. (9) Mark, J. E.; Rahalkar, R. R.; Sullivan, J. L. J. Chem. Phys. 1979, 70, 1794. (10) Riande, E. J . Polym. Sci., Polym. Phys. Ed. 1976, 14, 2231. (11) Guggenheim, E. A. Trans. Faraday SOC.1949,45, 714; 1951, 47, 543. (12) Smith, J. W. Trans. Faraday SOC.1950, 46, 394. (13) Abe, A.; Mark, J. E. J . Am. Chem. SOC.1976, 98, 6468. (14) McClellan, A. L. Tables ofErperimenta1 Dipole Moments; W. H. Freeman: San Francisco, 1974; Vol. I. Zbid., Rahara Enterprises: El Cerrito, CA, 1974; Vol. 11. (15) Saiz, E.; Hummel, J. P.; Flory, P. J.; Plavsic, M. J. Phys. Chem. 1981,85, 3211. (16) Treloar, L. R. G. The Physics of Elasticity; Clarendon: Oxford, 1975. Mark, J. E. Rubber Chem. Technol. 1975,48,495. (17) Mark, J. E. Adu. Polym. Sci. 1982, 44, 1. (18) Flory, P. J.; Ciferri, A.; Hoeve, C. A. J. J. Polym. Sci. 1960,45, 235. (19) Flory, P. J.; Hoeve, C. A. J.; Ciferri, A. J. Polym. Sci. 1959,34, 337. (20) Mark, J. E. Rubber Chem. Technol. 1973,46, 593. (21) Yoon, D. Y.; Suter, U. W.; Sundararajan, P. R.; Flory, P. J. Macromolecules 1975, 8, 784. (22) Flory, P. J. Statistical Mechanics of Chain Molecules;WileyInterscience: New York, 1969. (23) Pitzer, K. Adu. Chem. Phys. 1959, 2, 49. (24) Abe, A,; Jernigan, R. L.; Flory, P. J. J. Am. Chem. SOC.1966, 88, 631. (25) Riande, E.; Guzmin, J.; Tarazona, M. P.; Saiz, E. J. Polym. Sci., Polym. Phys. Ed. 1984, 22, 2165. (26) . . Saiz. E.: Riande., E.:, Guzmin., J.:, de Abaio. " , J. J . Chem. Phvs. 1980, 73, 958. (27) Garrido. L.: Riande. E.: Guzmln. J. J . Polvmn. Sci.. Polvm. Phys. Ed. 1982,20, 3378. (28) Flow, P. J. Macromolecules 1974, 7, 381. (29) The-calculations were performed for a chain of 284 skeletal bonds with two hydroxyl terminal groups.
Conformation of Polybutadiene in the Network State by Small-Angle Neutron Scattering A. M. Fernandez, L. H. Sperling,*+and G. D. Wignallr Polymer Science and Engineering Program, Materials Research Center No. 32, Lehigh University, Bethlehem, Pennsylvania 18015. Received December 9, 1985
ABSTRACT: Deuterated polybutadiene (D6)was blended with protonated polybutadiene (He), cross-linked, and swollen in toluene. All three cases were studied by small-angle neutron scattering (SANS). The deuterated polybutadiene had M , = 37 300, with R, = 90 A. Cross-linking does not appreciably affect the molecular dimensions. The molecular deformation induced by swelling agrees with that predicted by the phantom network model but is much lower than that predicted by the affine deformation model. Introduction The reactive forces in elastomers arise through conformational changes of the chains themselves. To the surprise of the polymer community, several small-angle neutron scattering experiments showed that the radius of gyration of network chains increases much more slowly on stretching or swelling than the predictions of the affine model.l+ The most critical experiments were done by Beltzung et a1.,7,8who found that poly(dimethylsi1oxane) network chains swelled according to the predictions of the 'Department of Chemical Engineering, Lehigh University, Bethlehem, PA 18015. *NationalCenter for Small Angle Scattering Research, Oak Ridge National Laboratory, Oak Ridge, TN 37830.
de Gennes C* theorem? with relatively modest changes in molecular dimensions. This paper will present a set of experiments on the molecular dimensions of polybutadiene (PB) in the linear, cross-linked, and swollen states. The networks were randomly cross-linked with peroxide so as to approximate those used in many studies as well as practical applications.
Theory The theory of small-angle neutron scattering has been described in numerous papers and two recent reviews,lOJ1 and details of the application to scattering from polymer solutions have been given by King et a1.12 In brief, the differential scattering cross section, dZ/dQ, per unit volume of sample in units of cm-' is related to the polymer-
0024-9297/86/2219-2572$01.50/00 1986 American Chemical Society
Macromolecules, Vol. 19, No. 10, 1986 ization index, n, and number of polymer molecules per unit volume, Np,by dZ
-(K) d0
= ((YH - a D ) 2 x ( 1 - x)Npn2s,(K) +
Conformation of Polybutadiene by SANS 2573 Table I Molecular Characterization of Deuterated and Protonated Polybutadiene M," M," MJM," M,b samde desk 37 300 1.23 40 000 PB(D6) 30 160 244 300 2.36 182 000 PB(H6) 103400 ~
[(Y$
+ (1- x)(YH - (YiI2Npn2St(K)(1)
where CYD and (YH are t h e scattering lengths of deuterated (labeled) and protonated monomers a n d CY: is t h e scattering length of a solvent molecule normalized t o t h e volume of a monomer unit.12 T h e quantity S, is t h e single-chain structure factor normalized to unity at K = 0 and S,(K) is the total scattering structure factor,12where K = 47rX-lsin (0/2), X is the neutron wavelength, 0 is t h e angle of scatter, a n d x is t h e volume fraction of t h e deuterated portion.
Experimental Section Materials. 1,3-Deuterated butadiene (Merck, Sharp and Dohme, Ltd.) was distilled at -10 "C into a bottle containing granular CaHz (Fisher Scientific)of 4-40 mesh, occasionally stirred and kept at 0 "C overnight, and then distilled again into a polymerization bottle. The catalyst, n-butyllithium (1.6 M in hexane, Fisher Scientific)was used as received. Hexane (Fisher Scientific) was dried over 4-A molecular sieves and purified by a chromatographic column using neutral alumina (Fisher Scientific). Commercial high cis-polybutadiene(PB(IQ) (Diene 35 NFA/AC, Firestone Co.) was purified by dissolving in tetrahydrofuran (THF) and precipitating with methanol, washed several times with methanol, and dried. Dicumyl peroxide (dicup) (K and K Laboratories, Inc.) was used as received. Deuterated Polybutadiene Synthesis. The deuterated polybutadiene (PB(D,)) polymerization was carried out in a glovebox under a dry argon atmosphere. The reactor was a 20-mL bottle fitted with a rubber-linked covered plastic cap and an aluminum disk. The bottle, containing an appropriate amount of hexane, was filled with deuterated butadiene. Then the catalyst was added by means of a hypodermic syringe, and the solution was stirred for about 10 h at 50 f 3 "C. The polymerization was terminated by adding methanol containing 0.3% of antioxidant (Ionol, Shell Co.) based on polymer, and the polymer was precipitated by further methanol addition, washed, and dried under vacuum at room temperature for 1week. Infrared analysis showed the sample was 69% cis-l,4 17% trans-1,4, and 14% 1,2. The sample was frozen under vacuum until use. Polybutadiene Networks. Randomly cross-linked PB networks containing 0.16 volume fraction of PB(Ds) in 0.84 volume fraction of PB(H6)matrix were made by dissolving the polymers in tetrahydrofuran (THF), mixed with the appropriate amount of dicup, and the solvent was evaporated. The material was partially cured in a compression-moldingoperation at 120 OC at a pressure of 45 psi for 20 min and then placed in a nitrogenatmosphere chamber for 4 h at 130 OC. Sample Designation. Several kinds of materials were investigated: sample 1, an un-cross-linked homopolymer blend, consisting of 16% PB(Ds) chains mutually dissolved in PB(H6); sample 2, a dry homopolymer network poly(cross-butadiene)made from sample 1by cross-linking with 0.1% (w/w) dicup; and sample 3, a swollen homopolymer network, consisting of a piece of the previously characterized sample 2, swollen to equilibrium with protonated toluene (swelling ratio Q = 4.67). The swollen gel was placed between 1-mm-thick quartz plates. Polymer Characterization. Molecular Weight Characterization. Gel permeation chromatography (GPC)experiments were carried out on a Waters 440 chromatograph. Analyses were performed on both PB(Ds) and PB(H6),using THF as the carrier solvent. Instrument calibration was made by using narrow molecular weight distribution standard polystyrenes (Waters). In addition, measurements of molecular weights by small-angle light scattering (SALS) were performed on both polymers. SALS experiments were carried out on a Chromatic KMX-6 spectrometer. SANS Experiments. The scattering experiments were performed at the 10-m SANS spectrometer at the Oak Ridge Re-
~~
From GPC. From SALS. search Reactor, using neutrons of X = 4.75 8, and a fixed sample-to-detector distance of 4.65 m. For solid amorphous polymer samples the contribution from the second term in eq 1is negligible as S,(K) z 0 in the bulk,"-13 and hence the single-chain structure factor, S,(K), may be extracted directly from the measured s~attering.~~.'~ For polymer solutions the contribution of the total scattering term containing S,(K) is finite, and the simplest procedure to extract S,(K) is to choose a value of x , the fraction of labeled polymer, such that the prefactor of the second term in eq 1is zero. For polybutadiene in toluene this balance condition occurs for x = 0.22, and thus for the samples run in these experiments a small contribution may be expected from the second term as the fraction of labeled polymer ( x = 0.16) does not ensure exact cancellation. An estimate of the residual scattering may be made from the known prefacton and the ratio of S,(K) to S,(K). In general, this ratio is dependent on both K and the polymer concentration and is of the order 50 for linear polymer solutions in the K range covered in this experiment.12 For polymer networks the ratio S,(K)/S,(K) is smaller and reflects network heterogeneities of the correlation hole effect.15 For the range of concentration and K used in this experimenP the ratio S,(K)/S,(K) is -0.1 and thus by calculating the prefactors of the respective terms in eq 1we can show that the error introduced by not having the exact balance condition is less than 0.5%. This approximation was tested by comparing the molecular weights calculated from dZ(O)/dQfor both swollen and unswollen samples. The difference (3%) was within the statistical errors of the measurements. To correct for background and incoherent scattering contributions due to protons several blanks utilized. The blank specimens used were as follows: sample 1, protonated polybutadiene; sample 2, poly(cross-butadiene)(H6)with 0.1 % (w/w) dicup; sample 3, poly(cross-butadiene) (H6) with 0.1% (w/w) dicup, swollen to equilibrium with protonated toluene. The measurements were converted into absolute differential scattering cross sections of units cm-' by comparison with wellcharacterized precalibrated secondary standards."
Results A. Polymer Characterization via GPC and SALS Experiments. For t h e GPC experiments, values of K = 1.56 X d L / g a n d a = 0.80 were used for [ q ] = KM" for polybutadiene.18 The molecular weights determined from the GPC and SALS experiments are summarized in Table I. Since t h e molecular weight determination is referred to a polystyrene calibration, the major benefit was t o check the polydispersity indices of t h e polymers. Only t h e M , values determined from SALS experiments were used to correct molecular weight mismatch in the SANS results. B. Swelling Characterization. On swelling t h e poly(cross-butadiene) sample with toluene, we obtained a Q value of 4.67. Application of t h e Flory-Rehner equation yielded a M , = 5930. C. SANS Experiments. T h e SANS experiments were performed on all three samples. The molecular weight, M,, a n d t h e radius of gyration, R,, were calculated from t h e intercept a n d t h e slope, respectively, of Zimm plots in t h e Guinier region. In general, t h e Zimm results were higher t h a n those derived from t h e Debye results because part of the data was taken at K values for which PR,2 > 1. After correction factors developed by Ullmanlg were applied for this effect, t h e Debye a n d Zimm results were consistent and t h e average values of M, and R, derived by both approaches differed by -3%. T h e following
2574 Fernandez et al.
Macromolecules, Vol. 19, No. 10, 1986
lm K21041”
K 2 10‘
Figure 1. Zimm and Debye form factor plots: un-cross-linked (PB(D6)/PB(H6))polymer blend (sample 1).
r2
Figure 2. Zimm and Debye form factor plots: dry homopolymer network (PB(D6)/PB(H6))poly(cross-butadiene)(sample 2).
Table I1 Characterization of PB(D,)/PB(H,) Polymers via SANS Experiments av of Zimm and Debyeb Zimm plota Debye fit values sample code M, R,, 8, M , R,, M, R,, 8, 1 (un-cross-linked) 37 100 89.6 35 300 86.1 31 700 82.2 2 (cross-linked) 44 500 85.7 43 600 84.1 38 550 79.5 42000 103.5 40600 109.3 36100 99.6 3 (swollen) a 1.18 1.28 1.23
h
lo[
Corrected for effects of finite angular range by methods of ref 15. Corrected for effects of mismatch between the polymerization indices of the H and molecules by methods of ref 16.
Figure 3. Zimm and Debye form factor plots: swollen homopolymer network (PB(D6)/PB(H,)) poly(cross-butadiene)(sample
discussion emphasizes the Zimm results. I t should be noted that the coherent scattering cross section [dX(k)/dQ] has been multiplied by the constant, CN,to obtain absolute values of the molecular weights directly from the Zimm plots. Figures 1-3 show the Zimm and the Debye form factor plots for samples 1-3, respectively. Table I1 summarizes the molecular weights evaluated from the Zimm plots after corrections for mismatch in molecular weights (correction factor = 0.873) by methods developed by Bou6 et a1.20 The quantity a defines the increase in the radius of gyration due to sample swelling, a = R,*/R, (see Table 111). The experimental value of a of 1.23 most closely fits the phantom network theoretical value.
cross-link junctions deform affinely with macroscopic swelling, the expected value of Rg*is given bya
Discussion Table I1 shows that the values of M, and R, obtained from the Zimm plot of samples 1and 2 are the same within experimental error. This indicates that the cross-linking reaction does not significantly affect the molecular dimensions. Comparing the experimental R,‘s of samples 1and 2 with that measured for sample 3, one finds that an increase in molecular dimensions is apparent after swelling to 4.67 times its original volume, but the increase is less than classically expected. Models. Three deformation models, chain affine, junction affine deformation, and phantom network, were used to determine the theoretical relationship between the molecular and the macroscopic deformation. If the deformation is chain affine
R,* = RgQ113 (2) For the junction affine deformation, in which only the
3).
(3) For tetrafunctional networks (f = 4), Pearson21derived the following expression for the phantom network model: Q2/3
Rg* = R‘(
+3
‘1’
7) (4)
More recent calculations by Ullman,22 which assume multi-cross-links, show that Rg* may be higher than Pearson’s result by about 20% for this model. Table I11 illustrates that the a’s calculated from the chain affine and junction models are too large. The experimental average a is just below that of the phantom network model. Relationship between R, and M,. The coherent scattering intensity data have been fitted to the Debye form factor for a Gaussian random coil. Examination of Figures 1-3 reveals that the Debye form factor fits the experimental data remarkably well for all of the materials, indicating that a Gaussian random coil conformation is still present for the elastic chains under the variety of states studied. SANS experiments yield the z-average radius of gyration. The weight-average value of R,, RgW,can be estimated from the PB(D,) molecular weights determined from GPC experiments. Since R, is proportional to the molecular weight to the 0.5 power for its respective molecular weight average, RgWhas the value
Table I11 Experimental and Calculated Molecular Parameters a
R,, A dry
linear polymer cross-linked polymer
82.2 79.5
swollen
99.6
exptl
affine
calcd junction affine
phantom networks
1.23
1.67
1.37
1.20
Conformation of Polybutadiene by SANS 2575
Macromolecules, Vol. 19, No. 10, 1986 RgWSANS = (M~/M~)&!R:SANS
(5)
After corrections for the molecular weight ratios between protio- and deuteriopolybutadiene and the finite angular range employed, a value of Rgw/Mw1/2 = 0.35 A g-'I2 mo1'I2 was obtained. Intrinsic viscosity data's,23yield 0.34-0.42 8, g-'I2 mo1'I2, increasing with trans content.
Conclusions Deuterated polybutadiene was mutually dissolved in protonated polybutadiene to form linear and cross-linked blends. These materials were studied by SANS in the dry and swollen states. Important conclusions are as follows: 1. Every sample was observed to fit the Debye form factor for random coil molecules, demonstrating that the chains exhibit Gaussian conformations in the linear, cross-linked, and swollen states. 2. Chemical cross-linking does not affect the molecular dimensions as measured by R,. 3. The R, of the elastic chains in the swollen network is about 23% larger than in the dry network, even after the network is swollen to 4.67 times its original volume. 4. The R, measured after swelling agrees better with that predicted by the theoretical phantom network model than with that predicted by the affine deformation model. Acknowledgment. We acknowledge financial support through the Polymers Program of the National Science Foundation, Grant No. DMR-8106892. The SANS experiments were performed at NCSASR, funded by NSF Grant No. DMR-77-24458through Interagency Agreement No. 40-637-77 with the U S . Department of Energy under Contract DE-AC05-840R 21400 with Martin Marietta Energy Systems, Inc. We also thank Dr. D. Nagy of Air Products and Chemicals, Inc., for help with the light scattering experiments. Registry No. Neutron, 12586-31-1.
References and Notes Benoit, H.; Decker, D.; Duplessix, R.; Picot, C.; Rempp, P.; Cotton, J. P.; Farnoux, B.; Jannink, G.; Ober, R. J. Polym. Sci., Polym. Phys. Ed. 1976, 14, 2119. Ullman, R. In Elastomers and Rubber Elasticity; Mark, J. E.,
Lal, J., Eds.; American Chemical Society: Washington, DC, 1982; ACS Symp. Ser. No. 193. Hinkley, J. A.; Han, C. C.; Mozer, B.; Yu, H. Macromolecules 1978, 11, 836.
Clough, S.;Maconnachie, A.; Allen, G. Macromolecules 1980, 13, 774.
Bastide, J.; Picot, C.; Candau, S. J.Macromol. Sei., Phys. 1981, B19(1), 13.
Candau, S.; Bastide, J.; Delsanti, M. In Adu. Polym. Sci. 1982, 44.
Beltzung, M.; Pi,cot, C.; Rempp, P.; Herz, J. Macromolecules 1982, 15, 1594.
Beltzung, M.; Herz, J.; Picot, C. Macromolecules 1983,16,580. de Gennes, P.-G. Scaling Concepts in Polymer Physics; Corne11 University: Ithaca, NY, 1979. Sperling, L. H. Polym. Eng. Sci. 1984, 24, 1. Wignall, G. D. In Encyclopedia of Polymer Science and Engineering, 2nd Ed.; Grayson, M., Kroschwitz, J. I., Eds.; Wiley: New York, 1985. King, J. S.; Boyer, W.; Wignall, G. D.; Ullman, R. Macromolecules 1985,15, 709.
Wienall. G. D.: Hendricks. R. W.: Koehler. W. C.: Lin. J. S.: W z , M.'P.; Thomas, E. L.'T.; Stein, R. S. Polymer 1981,22; 886.
The single-chain form factor S,(K) used in ref 12 is equivalent to P(K) used in ref 13. The function S,(K) used in ref 12 is equivalent to P + NQ(K) used in ref 13. Tsay, H. M.; Summerfield, G. C.; Ullman, R. Polym. Prepr. (Am. Chem. SOC.,Diu. Polym. Chem. 1986, 27(1), 87. Tsay, H. M.; Ullman, R., private communication. Hayashi, H.; Flory, P. J.; Wignall, G. D. Macromolecules 1983, 16, 1328.
Brandrup, J.; Immergut, E. H., Eds. Polymer Handbook, 2nd ed.; Wiley: New York, 1975; p IV-34. Ullman, R. J . Polym. Sci., Polym. Lett. Ed. 1983, 21, 521. Bo&, F.; Nierlich, M.; Leiber, L. Polymer 1982, 23, 29. Pearson, D. S. Macromolecules 1977,10,696. Ullman, R. Macromolecules 1982, 15, 1395. Abe, M.; Murakami, Y.; Fujita, H. J. Appl. Polym. Sei. 1965, 9, 2549.
