Macromolecules 1986,19, 2651-2653
Cohen-Addad, J. P. J. Chem. Phys. 1974,60,2440. Vega, A. J.; English, A. D. Macromolecules 1980,13, 1635. Spiess, H.W. Adv. Polym. Sei. 1985,66, 23ff. English, A. D. Macromolecules 1985,18, 178. English, A. D.Macromolecules 1984,17, 2182. English, A. D.;Zoller, P. Anal. Chin. Acta, in press. Schreiber, L. B.; Vaughan, R. W. J. Catal. 1975,40, 226. Eichhoff, U.;Zachmann, H. G. Ber. Bunsenges. Phys. Chem. 1970,74, 919. Cohen, M. H.;Turnbull, D. J. Chem. Phys. 1959,31, 1164. Zoller, P., In Polymer Handbook, in press. Zoller, P.; Bolli, P. J. Macromol. Sei., Phys. 1980,B18(3),555. Zoller, P., unpublished results. Axelson, D. E.; Mandelkern, L. J. Polym. Sei., Polym. Phys. Ed. 1978,16, 1135. Mandelkern, L.Pure Appl. Chem. 1982,54(3),611. Brandrup, J.; Immergut, E. H., Eds. Polymer Handbook, 2nd ed.; Wiley: New York, 1975;p V-66. Starkweather. H. W.: Zoller. P.: Jones. G. A. J. Polvm. Sci.. Polym. Phys.'Ed. 1983,21, 295.' McCrum, N.B.; Read, B. E.; Williams, G. "Anelastic and Dielectric Effects in Polymeric Solids"; Wiley: New York, 1967.
Small-Angle Neutron Scattering of Perfluorosulfonated Ionomers in Solution PIERRE ALDEBERT,*f BERNARD DREYFUS, and MICHEL PINERI
2651
2ol
+++
+
+
+
+
+
+
+
+
+
+
+
++
++
100
+*++*
+++++
Figure 1. Corrected and normalized SANS spectra, intensity vs. Q, of aqueous H+Nafion 1100 solutions: volume fraction concentrations of polymer are 16.9% (29w%) and 2.6% (5w%) for the upper and the lower spectra respectively; 0.0510 and 0.018 A-1 are the respective Q values at the maximum of the broad peak.
20;oj ++
+++ ++ + +
++
+
+
I
I
Centre d'Etudes Nucleaires de Grenoble, Departement de Recherche Fondamentale, Service de Physique, Goupe Physico-Chimie Moleculaire, 85X-38041 Grenoble Cedex, France. Received February 19, 1986
I. Introduction Numerous studies have been devoted to the structure of perfluorinated ionomer membranes such as Nafions (E. I. du Pont de Nemours, Inc.)lP2because of their practical importance as cation-exchange membranes in brine electrolysis cells.3 The chemical formulation and properties of these sulfonic ionomers have been extensively de~ c r i b e d . ~Recently, .~ methods for obtaining solutions of high equivalent weight (EW 1 1000) or low exchange capacity Nafions have been reported;- solutions of 1100EW Ndion are now commercially available. Nevertheless, little is known about the nature and structure of these solutions! We have therefore undertaken a SANS study of these solutions in water and ethanol over a wide range of concentrations. 11. Experimental Section Dissolution of 117 Nafion (EW 11005)has been achieved by swelling small pieces of acidic membrane in a 50/50 water-ethanol mixture and heating for 1 h at 250 "C under pressure!,' The ether formed during the dissolution process and residual ethanol were removed by slow evaporation around 80 "C. By adding progressively small amounts of water, ethanol- and ether-freesolutions were obtained that contained 0.5-29 w t % polymer. In a similar way, ethanol solutions almost free of water were prepared by adding ad-hoc quantities of ethanol during the evaporation process. Solutions containing 0.5-23% polymer were thus obtained. The concentrations of the solutions were determined by weighing the dry polymer after evaporation of the solvent around 110-120 "C. The solutions were examined with the SANS spectrometer PACE (Orphee Reactor of the L h n Brillouin Laboratory, Saclay, France) over a wide range of momentum transfer Q (5 x 5 Q I lo-' A-') by using two wavelengths associated with two sample-detector distances d (7A with d = 2.5 m and 12 A with d = 4.75 m). Sample containers were quartz disks separated with 1-mm-thickspacers, hermetically closed when fmed in the metallic C.N.R.S., Grenoble
0024-9297/86/2219-2651$01.50/0
.T'
100
+
Figure 2. SANS spectra of H+Ndion 1100 solutions in different solvents for similar volume fraction concentrations of polymer: (upper spectrum) in water with a concentration of 9.9% (18.1w%, Q at the maximum 0.0395 A-1); (lower spectrum) in ethanol with a concentration of 9.7% (21.5w%, Q at the maximum 0.058 A-l). holder. The scattering curves exhibited a more or less pronounced broad peak, which became undetectable a t concentrations less than 1%.Typical curves (Figure 1)show that the peak intensity depends upon the polymer concentration. Figure 2 shows that both shape and intensity of the peak are affected by the nature of the solvent at nearly equal polymer concentrations. In this paper we focus mainly on the shift of the position of the peak with dilution and ita relationship to the structure of the solution.
111. Results and Discussion Data on the scattering peak are reported in Table I. For each sample we give the volume fraction of polymer &. deduced from the weight percentage assuming constant bulk densities for both solvents (pwabr = 1, p e h o l = 0.785,and ppolper = 2); volume fractions are more significant for comparisons between solvents. In the second column d = 27r 8' (A) is given, Q being the position of the maximum of the broad peak. We make the usual assumption that the peak is associated with an interference between the scattering objects, d being related to their separation. Figure 3 shows log d vs. log bV. It is important to note that in all cases d and vary simultaneously; a phase separation leading to a constant-density phase, i.e., a constant d , can therefore be ruled out. Such a phase separation would occur if the interaction potential of the scattering objects through the solvent exhibited a m i n i m ~ m .Thus ~ we assume that the scattering objects are repelling each other because of electrostatic repulsions and occupy
1986 American Chemical Society
Macromolecules, Vol. 19, No. 10, 1986
2652 Notes
Table I Experimental Data on Acidic Solutions of Nafion (EW = 1100) in Water and Ethanol (First Two Columns (See Text)) and Several Characteristic Values of the Basic Colloidal Object Calculated according to the Structural Model Chosena rods fcc lattice hexagonal array cubic array 2r, A L, A L, A &, % d = 2r/Q, A (spheres) n 2r, A (n = 1) 2r, A (n = 1) a/& A Nafion 1100 H+/Water 16.9 123 92 2.46 61 56 33 195 61.5 9.9 159 100 3.11 61 57 33 199 79.5 111 4.29 64 51 35 176 97 7.5 194 111 4.36 61 57 33 196 109.5 5.3 219 3.6 266 119 5.30 61 56 33 196 133 2.6 349 140 8.65 68 45 37 157 174.5 10.5 9.7 6.8 3 2.1 0.4
109 108 135 194 217 350
Nafion 1100 H+/Ethanol 1.06 43 115 0.96 41 127 1.31 43 116 1.71 41 127 1.68 38 145 1.34 27 293
70 67 75 82 81 75
23 22 23 22 20 14
399 440 402 441 504 1016
54.5 54 67.5 97 108.5 175
a n is the number of polymeric chains, 2r is the diameter of the spheres or cylinders, L is the length of the rods, and a is the cell parameter of the cubic phase of rods (Figure 4 from de Gennes et al.''). B Log d 6-
-1 \+
- 0 5-
\ +\
\
\
-
0 33%' 2 --&
+\
5-
+,
\
-0
+, '00
G
,
I
\
\ I
*
B F i g u r e 4. Cubic phase of mutally orthogonal rods A, B, and C (from de Gennes et al.lO). 1. Three-Dimensional fcc Lattice. Electrostatic repulsions between identical charged objects in a solution usually lead to an hcp or fcc lattice, although a bcc lattice cannot be excluded. The choice of an fcc lattice is only a guide; the results in Table I would be the same for an hcp lattice and only slightly changed for a bcc lattice. The distance D between nearest neighbors is related to d (the Bragg distance deduced from the position of the peak) by the relation D = (3/2)%, and the volume of the primitive cell is 2-'l2D3;from the known volume fraction of polymer for each sample, we deduce the volume of the scattering object. The results are listed in Table I, either as 2r, the diameter of a compact sphere of bulk polymer, or as n, the number of polymeric chains ( M 2 X lo5) that correspond to each object, which could be a compact sphere, ellipsoid, or coil. We can see that n varies significantly. Furthermore, while in solutions in ethanol n is roughly 1, in aqueous solutions n is of the order of several units. It is difficult to conceive that in one case all the chains are disentangled, while in the other case from 3 to 5 chains are needed to constitute the basic scattering object. The lack of constancy of n together with this latter argument lead us to conclude that this model is unrealistic. 2. Two-Dimensional Hexagonal Array of Rods. In this case the distance D between parallel rods is given by D = 2(3)-'/*d. The volume for one rod of length H is 2(3)-1/2H~,d2,and comparison with the volume of one polymeric chain ( V = 1.66 X lo5 A3) leads to an effective length Lher covered by one chain (n = 1) along the rod (Lhex= 3ll2V/(2&,d2)). With the supplementary assumption that the rod is a cylinder of constant density ( p = 2) a diameter (2r)hexcan be deduced (Table I). It must be noticed that Lhex is independent of any assumption about the nature of the rod (compact cylinder or coil); the only assumption used to
-
2653
Macromolecules 1986, 19, 2653-2656
calculate Lhexis that the different chains do not overlap along the rod. This seems reasonable since if it was not true, the chains would make entangled fibers, a result which is not supported by the behavior of the solution. On the other hand, (2r)hexdepends upon the assumption of compact cylinders. From Table I it can be seen that Lhex is almost constant for both solutions if one discards the lowest concentrations, especially with ethanol. However, the absolute values of Lhex and (2r)hexraise a serious problem. Lhexand (2r)hexare almost equal for water and of the same order of magnitude for ethanol; the cylinders look rather like spheres than like rods. The value of Lhex in water is smaller than the distance D between nearest neighbors, and this is also true, although less pronounced, for ethanol. There is a contradiction between the shortness of the individual rods and their tendency to arrange end to end along lines with a separation D generally much greater than For this reason, although Lhex is rather constant, we think that its small value argues against the hexagonal lattice. 3. Cubic Phase of Rods. In this case, Figure 41°, the cubic lattice has a parameter a = d = 2 n / Q . The closest approach between orthogonal lines is a / 2 . The volume of the primitive cell is a3 and it contains a total length 3a of lines or rods. The volume of each rod within the primitive cell is given by d4z3/3 (a, or d). If one compares this volume with the volume V of one polymeric chain, one gets the length Lab covered by one chain ( n = 1) along the rod. The calculation is straightforward and the result can be expressed in terms of Lhex: Lcub = 2(3)'/' Lhel = 3.46Lhe1. As for the hexagonal lattice, Lab is independent on any assumption about the nature of the rod and supposes no rod overlapping; similarly, with the supplementary assumption of compacity, one can calculate the diameter of the cylinder (2r),b = (31/2/6)'/2(2r)hex = 0.54(2r),,, (Table I). This model keeps L constant throughout dilution except for the lowest concentrations, but gives absolute values of L that are much larger than the diameter, and thus compatible with a rod shape. It must also be noticed that L is larger than a / 2 over the entire concentration range except for the lowest concentration in water. So, among the three models, this model appears best. Comparison between the two sets of samples shows that the individual rod lengths are increased in going from water to ethanol from about 192 to 437 A, a factor of 2.28. Since the dielectric constants of water and ethanol are respectively 80 and 24, the results is not qualitatively surprising. In ethanol the electrostatic repulsion between charges is stronger than in water, and one expects the system to be more elongated; in these systems with no coions the Debye screening length is longer than L.l0 The ratio of rod lengths, 2.28, is presumably related to the ratio of the dielectric constants. A complete theory is still lacking; the condensation of the cations, the electrostatic interactions between the anions through both the solvent and the polymer, and the finite radius of the cylinder must also be taken into account. Here we provide a crude analysis based on what has been done on po1yelectrolytes."J2 If the force opposing elongation is the elasticity of chains, which varies as L2, the optimization of the sum of such a term added €-'I3 and to an electrostatic contribution l / t L would lead to L in the present case to a ratio of elongation Lethol/Lwater= (24/80)-'13 = 1.49, much smaller than the observed one. In these compounds, which have a rather low charge content and strong phobicity to solvents, one may also think that the term opposing electrostatic repulsion is the unfavorable enthalpy of interaction between solvent molecules and polymer. In other words, an elongation of the rod increases the surface of contact 2nrL between the solvent and the polymer. If one calls y the interfacial energy and notes that for a compact cylinder of constant L-'I2, one has to add to the electrostatic energy a density r surface energy expressed by yL1l2. Optimization leads to L Unfortunately, y is a quantity to which we have no direct access. In principle, y could be estimated from the Hildebrand parameters of the solvents and the p ~ l y m e r . ' ~However, the simultaneous presence of different kinds of physical interactions (van der Waals, dipolar, dipolar induced, etc.) makes any such deduction rather speculative. In the absence of data we take the same y for both solvents and determine the ratio of the elongations to be 2.23, a value close to the experimental value 2.28. Although this agreement relies upon a hypothetical constancy of y, we
-
-
-
0024-9297/86/2219-2653$01.50/0
believe that ow resulta favor the compact cylinder model, in which the solvent-polymer contact is at the surface of the "micelle", rather than the open coil model, in which the solvent-polymer contact is maintained all along the chain.
Acknowledgment. We acknowledge the LBon Brillouin Laboratory (Saclay, France) for providing neutron facilities and are especially grateful to Dr. J. P. Cotton and Dr. J. Teixera, staff of this laboratory, for their help i n the SANS experiments and data reduction. Registry No. Neutron, 12586-31-1; Nafion 117, 66796-30-3. References and Notes Roche. E. J Pineri. M.: Dudessix. R.: Levelut. A. M. J.Polvm. Sci., Polym. Phys: Ed: 1 9 h , 19,'l. ' Gierke, T. D.: Munn, G. E.: Wilson, F. C. J . Polym. Sci., Polym. Phys. Ed. 1981,' 19, 1687. Grot, W. G.; Munn, G. E.; Wamsley, P. N. Paper 154 presented at the Electrochemical Society Meeting, Houston, TX, May 7-11, 1972. Eisenberg, A.; Yeager, H. L., Eds. ACS Symp. Ser. 1982, No. 180.
E. I. du Pont de Nemours, Inc. Nafion Perfluorinated Membranes (product literature), Feb 1, 1984. Grot, W. G.; Chadds, F. European Patent 0066369, 1982. Martin. C. R.: Rhoades. T. A,: Fereuson. J. A. Anal. Chem. 1982,54, 1641. Covitch. M. J. American Chemical Societv Meeting. Philadelphia,' PA, Aug 1984. Ise, N.; Okubo, T.; Kunugi, S.; Matsuoka, H.; Yamamoto, K.; Ishii, Y. J. Chem. Phys. 1984,81, 3294. Matsuoka, H.; Ise, N.; Okubo, T.; Kunugi, S.; Tomiyama, H.; Yoshikawa, Y. J. Chem. Phys. 1985, 83, $78. de Gennes, P.-G.; Pincus, P.; Velasco, R. M.; Brochard, F. J. Phys. (Paris) 1976, 37, 1461. Manning, G. S. J. Chem. Phys. 1969., 51, 924. Katchalsky, A. Pure Appl. Chem. 1971,26, 327. Barton, A. F. M. Chem. Rev. 1975, 75, 731. I
I
Elastic Modulus of Isotactic Polypropylene in the Crystal Chain Direction As Measured by X-ray Diffraction CHIE SAWATARI and MASARU MATSUO* Department of Clothing Science, Faculty of Home Economics, Nara Women's University, Nara 630, Japan. Received May 6, 1986
The ultimate value of the Young's modulus of polymeric materials is well-known to be equivalent to the crystal lattice modulus in the direction of the polymer chain axes. The s t u d y of crystal lattice moduli has concentrated on polyethylene, and the values have been reported as measured b y X - r a y diffraction (235 GPa),' Raman spectroscopy (290 GPa),2 and inelastic neutron scattering (329 GPa).3 The Raman and neutron values are significantly higher than that obtained b y X-ray diffraction. T h i s difference m a y be due to the essential problem of determining the crystal lattice modulus by Raman spectroscopy and inelastic neutron scattering; i.e., i n addition to the difficulty i n estimating lamellar length b y small-angle X - r a y scattering, both methods contain an unavoidable assumption concerning the frequencies of absorption bands i n a polymeric system. X-ray diffraction measurements were carried out by Sakurada et al.' using several kinds of oriented polyethylene samples having different crystallinities and molecular weights, which were prepared by elongation of
* To whom correspondence should be addressed. 1986 American Chemical Society
