Macromolecules 1986, 19, 2639-2643
Conclusion
Although the structural study of the crystalline phase of 3T and 5T nylons is not yet completed, it can be assumed from the study of the model compounds in conjunction with the IR study, the conformational analysis, and the value of the fiber repeat as measured by X-ray diffraction of oriented films of 3T and 5T nylons that (1) the 7 torsion angles between the amide group and the aliphatic chain does not adopt the trans conformation and (2) the presence of a gauche angle in the aliphatic chain is highly probable. %o conformations are retained 89 possible solutions for the 3T One Of which is 'lose to that Of 3DBN, its model compound. Because of the similarities of the X-ray diffraction patterns it is expected that 3T nylon and 5T have 'Omparable structures* The confirmation will however have to wait for the final Structure determination using the X-ray data and possibly electron diffraction data.
We are grateful to the Science and Engineering Research Council of Canada for financial support. Registry No. BDBN, 10239-34-6; BDBN, 41640-76-0; 3T nylon (copolymer), 103691-99-2; 3T nylon (SRU), 35483-54-6; 5T nylon (copolymer), 32761-06-1; 5 T nylon (SRU), 32985-25-4. Supplementary Material Available: Anisotropic temperature factors for 3DBN and 5DBN (3 Pages); structure fador tables for BDBN and BDBN (21 pages). Ordering information is given on any current masthead page. References and Notes (1) Shashoua, V. E.; Eareckson, W. M. J. Polym. Sci., Polym. Phys. Ed. 1971, 9, 2081. (2) Livingstone, H. K.; Gregory, R. L. J. Polym. Sci., Polym. Phys. Ed. 1971, 9, 2081. (3) Palmer, A.; Brisse, F. Acta Crystallogr., Sect. B 1980,36, 1447. (4) Harkema, S.; van Hummel, G. J.; Gaymans, R. J. Acta Crystallogr., Sect. B 1980, 36, 3182. (5) Brisson, J.; Brisse, F. Acta Crystallogr., Sect. B 1982,38, 2663.
2639
(6) Pineault, C.; Brisse, F. Acta Crystallogr., Sect. C 1983, 39, 1434. (7) Pineault, C.; Brisse, F. Acta Crystallogr., Sect. C 1983, 39, 1437. (8) Pineault, C. MSc. Thesis, UniversitB de MontrBal, 1982. (9) Brisson, J.; Brisse, F. Can. J. Chem. 1985, 63, 3390. (10) Ahmed, F. R.; Hall, S. R.; Pippy, M. E.; Huber, C . P. J . Appl. Crystallogr. 1973, 6, 309. Accession Nos. 133-147. (11) Main, P.; Hull, S. E.; Lessinger, L.; Germain, G.; Declercq, J.; Woolfson, M. M. A System of Computer Programs for the Automatic Solution of Crystal Structures from X-Ray Diffraction Data, MULTAN 78; Universities of York, England, and Louvain, Belgium, 1978. (12) Doedens, R. J.; Ibers, J. A. Inorg. Chem. 1967, 6, 204. (13) Johnson, C. K. ORTEP, Report ORNL-3794, Oak Ridge National Laboratory, Oak Ridge, TN, 1965. (14) Sarko, A. CRYSP, 1979, Crystallographic packing program, modified by S. Pdrez and N. Tran, 1982, CERMAV, Grenoble. (15) Cromer, D. T.; Mann, J. B. Acta Crystallogr., Sect. A 1968,24, (16) rdwart, R. F.; Davidson, E. R.; Simpson, W. T. J. Chem. Phys. 1965, 42, 3175. (17) Benedetti, E.; Ciajolo, M. R.; Corradini, M. Eur. Polym. J. 1974, 10, 1201. (18) Ciajolo, M. R.; Pavone, V.; Benedetti, E. Acta Crystallogr., Sect. B 1977, 33, 1295. (19) Kakida, H.; Chatani, Y.; Tadokoro, H. J. Polym. Sci., Polym. Phys. Ed. 1976, 14, 427. (20) Poulin-Dandurand, S.; PBrez, S.; Revol, J.-F.; Brisse, F. Polymer 1979,20,419. (21) Arimoto, H. J . Polym. Sci., Part A 1964, 2, 2283. (22) Sandeman, I.; Keller, A. J. Polym. Sci. 1956, 19, 401. (23) Matsubara, J.; Magill, J. H. J. Polym. Sci., Polym. Phys. Ed. 1973, 11, 1173. (24) Schneider, B.; Schmidt, P.; Wichterle, 0. Collect. Czech. Chem. Commun. 1962,27,1749. (25) Miyake, A. J. polym. sei, 1960, 44, 223. (26) Ward, I. M.; Wilding, M. A. Polymer 1977, 18, 327. (27) Koenig, J. L.; Lin, S. B. J. Polym. Sci., Polym. Phys. Ed. 1983, 21, 2067. (28) Palmer, A.; Poulin-Dandurand, S.; Revol, J. F.; Brisse, F. Eur. Polym. J . 1984,20, 783. (29) Bellamy, C. IR Spectroscopy of Complex Molecules; Chapman and Hall: London, 1975. (30) The programs used in this work are modified versions of NRC-2, data reduction, NRC-IO, bond distances and angles, NRC-22, mean planes;" FORDAP, Fourier and Patterson maps (A. Zalkin); MULTAN, multisolution programs;" NUCLS, least-squares refinement;'* ORTEP, stereo drawing^;'^ and CRYSP, conformational analy~is.'~
Notes Linking Phenomena in the Amorphous Phase of Semicrystalline Polymerst R. C. LACHER,* J. L. BRYANT, L. N. HOWARD, and D. W. SUMNERS Department of Computer Science, Florida S t a t e University, Tallahassee, Florida 32306. Received February 27, 1986
Introduction The amorphous phase of a long-chain semicrystalline polymer has recently been the subject of much experimental and theoretical investigation. (See, e.g., ref 1-3.) According to results of Flory et al.,' polymer chains emerging from the face of a lamella into the region between lamellar crystals, which is normally 50-200 A in thickness, pass through an interphase, ca. 10-12 A thick, before reaching a fully disordered or isotropic state, the l i q u i d phase. In the interphase approximately 70% of the chains ?Thisresearch was supported by ONR Grant "14-84-K-0761.
0024-9297/86/2219-2639$01.50/0
undergo complete reversal, so that only (about) 3 0 % proceed to the liquid phase. Assuming a completely isotropic amorphous phase, Guttman et a1.,2 model the distribution of chains in the amorphous region as a random walk on a cubical lattice. Using as a unit between adjacent lattice points the statistical unit for the polymer ~ h a i n , l which ,~ for poly(methylene) is about 3.5 monomers,' they consider a chain emanating from a crystalline face into the region between parallel lamellar faces M units apart as being described by a random walk on the lattice, starting at a lattice point one unit from the face. The walk is continued on the lattice, with probability 1/6 of proceeding to any one of the six possible adjacent lattice points, until one of the two faces is reached. A simplifying assumption is that the molecular weight of the chain is sufficient to guarantee that one of the faces will eventually be hit. (That this occurs with finite expectation may be seen in Feller.? The chains are thus broken up into two classes: loops, i.e. chains that return to the face from which they emerged, and bridges 0 1986 American Chemical Society
2640 Notes
Macromolecules, Vol. 19, No. 10, 1986
or ties, i.e. chains that proceed to the opposite face. Using Gambler’s Ruin statistics, Guttman et a1.2 compute the theoretical distribution PL of loops and PT of ties as
PL = (M - 1 ) / M
Ami
and
PT = 1 / M and the average length of a loop (I,)or tie (2’)as
( L ) = 2M and
(T)=
W
w
Thus, the average length of a chain is
PL(L)+ PT(T)= 3M - 2 This implies that the density of chains in the amorphous region is three times the (planar) density of sites in the lamellar faces from which chains emerge. It is consistent with the results of Flory et al.’ to consider the random walk model as a model of the liquid region between the interphases. Given that chains emerging from only about 30% of the sites on a lamellar face proceed into the liquid phase, the random walk on a cubical lattice model would then predict that the density of chains in this region would be less than or equal to the density of chains in the lamella. The purpose of this paper is to report a phenomenon that occurs in a random walk on a cubical lattice, which may give new insight on the structure of the amorphous region of a semicrystalline polymer. Specifically, we have discovered through computer simulation that a strong form of topological entanglement, known as homological liking, occurs between loops based on one face of a lamellar crystal and loops based on the opposite face. It is found that the incidence of linking, which depends to some extent on the distance between lamellae, is significant in the range of distances observed in many semicrystalline polymers, such as polyethylene. In particular, the evidence suggests that the percentage of loops based on one face of a lamella that link at least one loop based on the opposite face remains constant as the thickness of the liquid region increases and exceeds the percentage of ties for distances greater than 20 statistical units. Thus, it may not be, as is often supposed,7 that the ultimate strength of a semicrystalline polymer depends on the percentage of ties, which decreases with the distance between lamellae. On the contrary, “entanglements involving chains that reenter the same crystalline a form of which we have sought to quantify here, may contribute at least as much to the interconnection of crystal lamella in some polymers. Moreover, the evidence seems to indicate that the total linking number between a loop from one surface and all loops from the other increases with the distance between lamellae. As of yet we have not found a theoretical argument that would explain these phenomena, but the data we have obtained so far from our computer simulations are compelling. We thank Leo Mandelkern for his encouragement and many enlightening conversations concerning this project. Topological Linking By a closed curue in Euclidean 3-space, R3, we shall mean the image of a smooth or piecewise linear map of the unit circle S’ into R3. Two disjoint curves A and B are topologically unlinked if there is a topological transfor-
Figure 1. (Top) Homologically linked curves: lk (A,B,) = 1. (Middle)B is homotopically linked to A, but A is not homotopically linked to B. lk (A,B) = 0. (Bottom) A and B are topologically linked, but each is homotopically unlinked from the other. lk (A,B) = 0.
-
mation (homeomorphism) of R3 onto itself, h: R3 R3, such that h(A) and h(B) are separated by a 2-dimensional plane. A curve A, given by a function f: S’ R3, is said to be homotopically unlinked from a curve B if A can be “continuously shrunk to a point” in the complement of B, that is, iff extends to a continuous function F: B2 R3\B of the unit 2-disk into the complement of B in R3. Finally, a curve A is said to be homologically unlinked from a curve B if A bounds an orientable surface that misses B. Of the three ways in which curves may be linked, generally only the first and third are symmetric. They are related as follows: A and B are homologically linked * A is homotopically linked to B A and B are topologically linked. Thus, of the three types of linking that may occur, homological linking is the strongest, and it is also the easiest to detect. Figure 1gives examples of some of the various possibilities that may arise.
-
-
-
Homological Linking Fix an orientation on the unit circle S’. Given disjoint smooth curves A and B, there is the Gauss linking number of A and B defined by the integral lk (A,B) = (1/4n)$ l(Ir1-3)r.(drAXdrB) where rAand r g are vector fields defining A and B, respectively, and r = rA- rB Note that lk (A,B) = lk (B,A). This number is an integer, which remains unchanged under all sufficiently small perturbations of A and B. It also follows that lk (A,B) = 0 if and only if A and B are homologically unlinked. (See ref 9 for a comprehensive discussion of linking invariants.) A useful method for calculating lk (A,B) is the “signed undercrossing method”. (See ref 9.) In order to use this method, it is more convenient to assume that the curves are piecewise linear-that is, each is the union of a finite number of straight line segments. Choose an orthogonal projection of the curves into a plane so as not to identify a vertex of A with any point of B or vice versa. Almost all projections have this property. An (oriented) segment from A and one from B whose projections intersect determine a crossing as viewed along the projection. Using
Macromolecules, Vol. 19, No. 10, 1986
0
Notes 2641
tA, 1
+1
I
-1
Figure 2. Signed crossings. The sign is determined by the right-hand rule.
the additional information that the segment from A crosses over or under the segment from B, we associate to the crossing a number +1 or -1 according to whether the crossing is positive or negative as determined by the right-hand rule. (See Figure 2.) The sum of these numbers over all undercrossings of A with B is then lk (A,B). Random Walk Model Following Guttman et a1.,2 we use as a model of the liquid region between two lamellae in a semicrystalline polymer random walk on a cubical lattice in X Y Z space, R3, between the planes Y = 0 and Y = M. The unit distance between adjacent lattice points is interpreted as a statistical unit for the polymer being represented. Walks are not considered to be self-avoiding, since the various techniques used to produce self-avoidingwalks do not seem to generate significantly different statistical data. (See ref 2, 5, and 10.) The applicability of this model is discussed extensively in ref 1-3. A chain emerging from the plane Y = 0 is modeled as a walk in the lattice starting from a point (Xl,l,Zl) and continuing with probability of passing from a lattice point to any one of the six adjacent points until some point ( X N , Y N , Z N ) satisfies Y N = 0 or Y N = M . If YN= 0, the chain is called a loop; if Y N = M , the chain is called a tie. Similarly, a chain emerging from the plane Y = M is modeled as a walk starting from a point (Xl,M-l,ZJ. A loop based at the plane Y = 0 is a lefthand loop and one based at Y = M is a right-hand loop. Although we do not require that a walk be self-avoiding, in order to compute the linking number of a right-hand loop and a left-hand loop, we must require that two such loops be disjoint. Otherwise, their linking number is not defined. We accomplish this by offsetting each of the coordinates of the lattice on which walks from the right emerge by -lI2. Thus a right-hand loop is based at the plane Y = M - lI2. We close up a loop by adding to it an arbitrary path (e.g., a straight line segment) in the plane at which it is based joining its initial and terminal points. (See Figure 3.) The linking number of a left-handed and right-handed loop may now be computed by the signed undercrossing method applied to the projection of the loops into the X Y plane. Since the paths added to the loops do not contribute to the linking number, the linking number as computed above between a right-hand and a left-hand loop is well-defined. Simulations We now describe the computer simulations carried out to observe the possibility of linking between loops based at opposite faces of the amorphous region between two lamellar crystals. The details of the algorithms developed for this purpose are given by Lacher in ref 11. A game is set up by generating a family of random walks from the plane Y = M (from the right) into the region 0 5 Y 5 M . Walks from the right start at points with X Y Z coordinates 5 M , 121 5 M , and Y = M - 1. A walk is satisfing terminated when its coordinate ( X N , Y N , Z N ) satisfies Y N = 0 or YN= M . The density of starts from the right is set at lI6 because of the density considerations discussed above. (Although it can be argued that changes in starting density affect statistical results proportionately, reducing
1x1
G”0
Figure 3. (Top) lk (A,B) = 0. (Bottom) lk (A,B) = -3.
the density allows for experimentation with the patterns of starts and decreases run time by a factor of almost 6 ) . The resulting density generated by walks from the right is then approximately 1/2, thus simulating a density of 1 when walks from both sides are considered. The distribution of starting sites may be selected in two different ways, randomly and uniformly. Simulations have been carried out by both methods. The pseudo-random number generator used here is the Lag Fibanacci L(R,S) recommended by Marsaglia (see ref 12 and also Knuth.13) Once the family of walks from the right has been set up, a trial is performed by generating a walk from the left into the region starting at the point (O,l,O). The coordinates of the walks from the right are then changed by -1/2 so as to be disjoint from a trial walk from the left. Each random walk is then considered to be a piecewise linear path whose edges are the segments of length one joining adjacent lattice points in the walk; the initial segment is, of course, the unit segment joining the starting point of the walk and the plane from which it emerges. If the walk from the left is a loop, then the paths are projected into the X Y plane, and from this projection the signed undercrossing method is used to compute the linking number of this loop with all loops resulting from the walks generated from the right. The following data are recorded from a trial: (1)the type of walk generated from the left (loop or tie); (2) if the walk from the left is a loop, (a) whether it links (i.e., has a nonzero linking number with) some loop from the right, (b) the number of such loops from the right, (c) the sum of the absolute values of these linking numbers (the total linking number, and (d) the sum of the squares of these linking numbers. A game is completed by performing a number of trials with the given setup of walks from the right, and the following data are recorded: (3) the number of trials, (4) the number of ties generated from the left, (5) the number of loops generated from the left, ( 6 ) the number of those loops that link a loop from the right, (7) the mean and standard deviation of the number of loops linked, and (8) the mean and standard deviation of the total linking number over all trials. A r u n consists of a number of games. Although the linking data may vary significantly from game to game, it tends to stabilize at the run level. A typical run of 50 games, each with 200 trials, is shown in TabIe I. By comparison, Table I1 shows the results of 20 runs of 50 such games each. The simulations were develope6 md run on a Zenith 2-100for 2 5 M 5 12 and on DEC 1 50 and 2
Macromolecules, Vol. 19,No. 10,1986
2642 Notes
Table I" Results from a Typical R u n of 50 Games, with Uniform Starting Distribution and M = 12, R u n on a Zenith 2-100 Microcomputer distance between planes: 12 no. of trials per game: 200 no. of games: 50 loops generated: 9131 loops with linking: 50 ties generated: 869
reach 1 2
3 4 5 6 I 8 9 10 11 all
count 4929 1691 838 477 358 237 167 137 122 106 69 9131
total linking density: mean = 0.09, std dev = 0.52 total tie no.: mean = 0.09. std dev = 0.28 breadth linking density mean std dev total mean std dev 0.96 0 0.00 0.00 1.00 7 0.00 0.06 2.40 1.38 26 0.03 0.20 3.64 1.83 0.29 2.41 34 0.07 5.04 54 0.15 0.43 6.16 2.76 3.46 77 0.32 0.62 7.39 0.79 3.28 71 0.43 1.87 143 1.04 1.21 9.95 4.24 189 1.55 1.62 11.29 4.73 11.42 4.49 168 1.58 1.83 181 2.62 2.09 12.80 5.50 3.19 950 0.10 0.54 2.69
total 0 7 23 32 47 65 57 117 145 143 146 782
loops linked mean 0.00 0.00 0.03 0.07 0.13 0.27 0.34 0.85 1.19 1.35 2.12 0.43
std dev 0.00 0.06 0.17 0.27 0.35 0.50 0.58 0.97 1.09 1.51 1.72 0.43
'From Lacher.'l In the table reach = maximum Y coordinate of a walk from the left; breadth = larger of maximum X coordinate and maximum Z coordinate of a walk from the left in absolute value. Table 11" Results from 20 R u n s of 50 Games Each, with Uniform Starting Distribution a n d M = 12, R u n on a Zenith 2-100 Microcommter distance between planes: 12 no. of trials per game: 200 no. of games per run: 50 no. of runs: 20 total linking density: mean = 0.09, std dev = 0.01 tie density: mean = 0.08, std dev = 0.00 left linking density: mean = 0.05, std dev = 0.01 right linking density: mean = 0.08, std dev = 0.01 right linking breadth linking density density reach mean std dev mean std dev mean std dev 0.00 0.00 0.00 0.00 1 1.00 0.01 0.01 0.01 0.01 0.01 2 2.38 0.04 0.03 0.01 0.03 0.01 3 3.57 0.07 0.07 0.02 4 4.75 0.08 0.08 0.02 0.03 0.15 0.03 0.15 0.17 5 5.93 0.05 0.06 0.27 0.32 6 7.03 0.20 0.06 0.08 0.43 7 8.23 0.29 0.51 0.83 0.11 0.69 0.08 8 9.38 0.34 0.15 0.97 0.12 0.57 1.19 9 10.69 0.13 0.18 1.42 10 11.84 0.51 1.76 11 0.65 2.46 0.31 2.02 0.24 13.14 0.09 0.01 all 2.65 0.03 0.10 0.01
M 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Table 111" Summary of Results for 2 I M I 24 Using Distribution of Starts left linking right linking density density tie densitv mean std dev mean std dev 0.50 0.02 0.01 0.02 0.01 0.04 0.01 0.04 0.01 0.33 0.25 0.04 0.00 0.04 0.01 0.01 0.05 0.01 0.20 0.05 0.17 0.05 0.01 0.05 0.01 0.14 0.05 0.01 0.06 0.01 0.13 0.05 0.01 0.06 0.01 0.11 0.05 0.01 0.06 0.01 0.01 0.10 0.05 0.07 0.01 0.09 0.05 0.00 0.07 0.01 0.08 0.05 0.01 0.08 0.01 0.08 0.05 0.08 0.01 0.01 0.07 0.05 0.00 0.08 0.01 0.07 0.05 0.01 0.08 0.01 0.06 0.05 0.08 0.01 0.00 0.06 0.05 0.01 0.08 0.01 0.06 0.05 0.01 0.08 0.01 0.05 0.05 0.00 0.08 0.01 0.05 0.05 0.00 0.09 0.01 0.05 0.05 0.00 0.09 0.01 0.05 0.05 0.00 0.09 0.01 0.04 0.04 0.00 0.09 0.01 0.04 0.05 0.00 0.09 0.01
a Random total linking density mean std dev 0.02 0.01 0.04 0.01 0.04 0.01 0.06 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.07 0.01 0.08 0.01 0.08 0.01 0.09 0.01 0.09 0.01 0.10 0.01 0.10 0.01 0.10 0.01 0.10 0.01 0.11 0.01 0.11 0.01 0.01 0.11 0.12 0.01 0.01 0.12 0.12 0.01 0.13 0.01
"From Lacher." Right linking density = proportion of loops from the right that are linked by some loop from the left, and total linking density = total linking number divided by number of trials.
aFrom Lacher." For each value of M the statistics were obtained from 20 runs of 50 games each with 200 trials per game.
780 machines for 12 IM 5 24. (Run time is O ( W )and approaches 12 h of CPU time when A4 = 24.) In Table I11 statistics are given for the simulation of the liquid region between interphases ranging from 2 to 24 statistical units thick. For each distance M the statistics were obtained from 20 runs of 50 games each with 200 trials per game. Note that the density of loops from the left that link at least one loop from the right appears to become constant, 0.05, once the distance between planes is 5 units. On the other hand, the density of loops from the right that are linked by a loop from the left (right linking density) appears to increase with the distance between planes as does the total linking density. The
graph in Figure 4 shows the relation of these densities with the density of ties. It is not clear to what extent the excess of right linking density or total linking density over left linking density contributes to the strength of a semicrystalline polymer (assuming that these phenomena actually occur in the polymer). Other forms of topological linking that may occur between loops With linking number zero are more subtle and are not as easily detected. There is virtually nothing known about the density of such linking although it is suspected that it is marginal as compared to homological linking. It is possible, however, that recent work of Pohll4 or des Cloizeaux and BalIl5 may help to explain the ho-
2643
Macromolecules 1986, 19, 2643-2644
Table I Dipole Moments ( M ~ (D2) ) and Molar K e r r Constants ,K (X10-'2 cm-' SC2mol-') per Repeat Unit x for E-V Copolymers
---
...-... Ties Left-hand loops that link Right-hand loops linked Total linking number
~~
J
~ t 12 . ' ~ I8. ~ ' 24 . ~M ~ ' Distance Between Planes Figure 4. Density of ties plotted against various linking densities (data from Table 111). o
~
~
6"
mological linking phenomena that we have observed. References and Notes (1) Flory, P. J.; Yoon, D. Y.; Dill, K. A. Macromolecules 1984,17, 862. (2) Guttman, C. M.; DiMarzio, E. A,; Hoffman, J. D. Polymer 1981,22, 1466. (3) Guttman, C. M.; DiMarzio, E. A. Macromolecules 1982, 15, 525. (4) Mandelkern, L. Acc. Chem. Res. 1976,9,81. (5) Mansfield, M. L. Macromolecules 1983, 16, 914. (6) Feller, W. An Introduction to Probability Theory and Its Applications, 3rd ed.; Wiley: New York, 1968; Vol. 1. (7) Blackman, D. K.; De Vries, K. L. J. Polym. Sci., Part A-1 1979, 7, 2125. (8) Flory, P. J.; Yoon, D. Y. Nature (London) 1978, 272, 226. (9) Rolfsen, D. Knots and Links; Publish or Perish, Inc.: Berkeley, CA, 1976; Mathematics Lecture Series, Vol. 7. (10) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience: New York, 1969. (11) Lacher, R. C. The CROSSWALK Simulation: Design, Development, Verification, Analysis, and Data, Technical Report; Florida State University, Tallahassee, FL, 1986. (12) Marsaglia, G. Keynote Address, Computer Science and Statistics, XVI Symposium on the Interface, Atlanta, GA, 1984. (13) Knuth, D. E. The Art of Computer Programming, 2nd ed.; Addison-Wesley: Reading, MA, 1981; Vol. 2. (14) Pohl, W. F. International Symposium in honor of N. H. Kuiper, Utrecht, 1980; Lecture Notes in Mathematics; SpringerVerlag: Berlin, Heidelberg, New York, 1981. (15) des Cloizeaux,J.; Ball, R. Commun. Math. Phys. 1981,80,543.
Kerr Effect and Dielectric Study of Ethylene-Vinyl Chloride Copolymers A. E. TONELLI* and M. VALENCIANO+ AT&T Bell Laboratories, Murray Hill, New Jersey 07974. Received April 11, 1986
A series of ethylene-vinyl chloride (E-V) copolymers were obtained recently1 by reductive dechlorination of poly(viny1 chloride) (PVC) with tri-n-butyltin hydride [(n-Bu),SnH]. Their microstructures (comonomer composition, sequence distribution, and stereosequence) were determined by NMR analysis, and GPC measurements indicated that all E-V copolymers have the same chain length ( x = lo00 repeat units) as the PVC from which they were made. AT&T Bell Laboratories Summer Research Program Participant. Current address: Merck and Co., Inc., Rahway, NJ.
0024-9297/86/2219-2643$01.50/0
"
E-V PVC E-V-85 E-V-71 E-V-61 E-V-50 E-V-46 E-V-35 E-V-21 E-V-14 E-V-2 .PE ~ ~
P, 0.44 0.42 0.40 0.38 0.36 0.34 0.26 0.19 0.15 0.08
'
"
a 2.6 4.2 2.5 2.5 2.2 1.4 1.3
~
b 3.7 3.3 2.8 2.4 2.0 1.9 1.6 0.9 0.6 0.1 0.0
c 3.7 3.5 3.1 2.7 2.6 2.2 1.7 1.0 0.7 0.1 0.0
a -14 9 20 34 23
b
-4 6 15 16 18 16 13 7 4 1.5 1.5
C
-4 5 15 21 30d 27 22 11 6 1.5 1.5
a Measured. *Random with P, = 0.44 calculation. Triad simulation calculation. d , K / x = 31 and 30 when averaged over 10 and 20 chains, respectively. Values of ,K/x ranged from 26 to 42 when calculated for the set of 20 Monte Carlo generated chains.
We are currently studying the physical properties of this well-characterized set of E-V copolymers. To date, we have determined their densities and thermal propertiesz (T, and T,,,), studied the compatibilities of their blend^,^ and completely assigned their IR spectra: all in the solid state. It has been demonstrated both by and by calculations6J0that the molar Kerr constant (,K) as obtained from the electrical birefringence measured on its dilute solutions is one of the properties of a polymer most sensitive to its conformational and configurational characteristics. In this note we describe the results of dielectric (dipole moment) and electrical birefringence (Kerr effect) measurements performed on dilute E-V copolymer solutions. The synthesis and microstructures of the E-V copolymers were presented earlier.' The Kerr effect and dielectric apparatus along with the experimental techniques have been previously described.6 Kerr effect and dipole moment measurements were performed at 25 OC in p-dioxane. E-V copolymers rich in E units are insoluble in p-dioxane, thereby limiting our study to those copolymers with at least 35 mol % V units. Molar Kerr constants and dipole moments were calculated according to the methods detailed in ref 9 and 11. The polarizability tensor and dipole moment for the C-C1 bond are the same as presented in our study of PVC and its model compounds,S and treatment of the polarizability tensors for the E-V copolymers is also described there. Mark's12 conformational model of E-V copolymers was used to perform the appropriate average1' over all conformations. E-V copolymer chains of 200 repeat units ( x ) were generated by Monte Carlo methods in two different ways. In the first method E and V units were randomly added one at a time with adjacent V units (VV diads) incorporated with P,,, = 0.44, i.e., 44% meso (m)and 56% racemic (r) VV diads, corresponding to the P, = 0.44 of the parent PVC.l The second procedure took cognizance of the detailed E-V microstructure as determined by our 13C NMR study.' For each E-V copolymer we have knowledge of the triad comonomer sequence distribution and the VV diad stereosequence. Consequently, we generated each E-V copolymer chain a triad at a time in a way t~ produce an E-V copolymer with the same microstructure (comonomer composition and stereosequence) as observedl by 13C NMR. We generated 20 Monte Carlo chains for each E-V 0 1986 American Chemical Society
