RANDOM MONOMER DISTRIBUTIONS IN COPOLYMERS
1975
Random Monomer Distributions in Copolymers. Copolymerizations of Ethylene-Vinyl Chloride and Ethylene-Vinyl Acetate
by Jacob Schaefer Monsanto Company, Central Research Department, St. Louis, Miasouri
(Received January 22, 1966)
The high-resolution single and multiple proton resonance spectra of ethylene-vinyl chloride and ethylene-vinyl acetate copolymers prepared by free-radical copolymerization and covering a wide composition range have been obtained a t 100 Mc/sec and 125'. The spectra are interpreted in terms of the monomer distribution in the chain, which is conclusively shown to be zeroth-order Markoffian (Bernoullian) for both copolymers. The spin-decoupled spectra are fit by computer in order to obtain estimates of areas of overlapping peaks using an idealized line shape and a least-squares approach, whose applicability is discussed. The significance of reactivity ratios, obtained from nmr data, for several low-conversion, emulsion ethylene-vinyl chloride copolymers is studied.
Introduction The high-resolution proton magnetic resonance spectra of vinyl homopolymers with only a single a substituent, (-CH2CHX-),, are severely complicated by a-p spin-spin interaction and the relatively poor resolution characteristic of polymer backbone spectra. The presence of a second type of monomer unit, also containing a and p protons, to form a copolymer hinders analysis of the single resonance spectra still further. The use of proton-proton spin-spin decoupling to aid in the interpretation of homopolymer spectra has been demon~trated.'-~ This paper reports the use of decoupling techniques in the interpretation and analysis of spectra of two vinyl copolymers, ethylene-vinyl chloride (E-VC1) and ethylene-vinyl acetate (E-VA), in terms of the monomer distribution in the copolymer backbone.
Monomer Distribution Formulas for Zeroth-, First-, and Second-Order MarkofRan Copolymerization Processes The description of the monomer distribution in a copolymer resulting from a free-radical copolymerization may be given by the statistics of Markoffian processes.' Alternative descriptions given by non-Markoffian statistics6 (which may be necessary for anionic polymerizations, for example) will not be explicitly considered here.
Theoretical descriptions of diastereosequence distributions in homopolymers and monomer distributions in copolymers have been given in terms of Makoffian processes of zeroth, first, and second order where, respectively, the reactivity of the growing polymer chain is independent of the past history of the chain (Bernoullian process), depends on the terminal radical, and depends on the terminal radical and also on the next monomer unit in the chain once removed from the reaction site, the penultimate unit. For copolymers the second-order description uses addition prob= abilities defined in the following m ~ n n e r :PBAA ~ probability that a growing polymer chain ending in BA will add an A monomer unit, when the chain grows left to right. A and B are the two different monomer species. PAAB, PBBA,PABBare defined in an analogous manner. These addition probabilities are independent. They do not explicitly contain kinetic mechanistic information and are dependent on the relative concentrations of monomers A and B in the feed. The relative numbers of dyads and triads (sequences of two or three monomer units) in the com(1) F. A. Bovey, E. W. Anderson, and D . C. Douglass, J . Chem. Phya., 39, 1199 (1963). (2) S. Satoh, J . Polymer Sci., 2A, 5221 (1964). (3) K. C. Ramey and N. D. Field, Polyner Letters, 3, 69 (1965). (4) F. P. Price, J . Chem. Phys., 36, 209 (1962). (5) B. D. Coleman and T. G Fox, J . Polymer Sci., l A , 3183 (1963).
Volume 70,Number 6 June 1966
JACOBSCHAEFER
1976
pleted, linear chain of infinite length may be expressed in terms of these addition pr~babilities.~
(1)
V B B = CZW
VBBB VABB
=
VABA
CXy
= c ~ ( 1- Y)W
VBBA =
czyw
TAAB
=
= C Z Y ( ~ - W)
vBAB
= C Z ~ (-I X)
VBAA
= CZyX
VAAA
= ~ ( 1 Z)~X
(2)
Further, the first-order Markoffian description reduces to zeroth order if the next subscript is ignored, and only one independent addition probability is required as in eq 9
-
= P(B)A = P(A)A =
w
where
(3) The V’S are dyad and triad concentrations; c is an effective normalization constant. The numberaverage sequence lengths of A and B in the copolymer chain are given by
(A) = 1
(B)
= 1
+
Z/Z
+ w/y
(4)
The final composition of the chain may also be given by the addition probabilities M B / M A =
z(y
+
W)/V(X
+
Z)
(5)
and M A are the mole fractions of A and B. The reactivity ratios are defined as M B
RBB=
~BBB/~BBA
RAB=
~ABA/~ABB
RBA=
kBAB/kBAA
RAA=
kAAA/kAAB
\”/
where the k’s are pseudo-first-order rate constants for the reactions indicated by the subscripts, and if
MA(‘)
= mole fraction of
A in monomer feed
MB(‘)
= mole fraction of
B in monomer feed
where the superscript c indicates the charge concentration, then
+1 +1
I/Y =
RBBMB(~)/MA(~)
l/w =
R . ~ ~ M A ( ~ ) / M ~ ( ~ )
(7)
A second-order Markoffian description reduces to a first-order Markoffian description if the first subscript is ignored. For example, in first order only two independent addition probabilities are required. Equation 8 shows the two relations which connect x, y, z, and The Journal o j Physical Chemistrg
The subscripts in
= cy2
VBA = V A B
VAA
w in the first-order description. parentheses are ignored.
=
1- y =
P(B)B
x
=
=
1-z
P(A)B =
z
(9)
High-resolution proton multiple magnetic resonance provides a means of experimentally obtaining addition probabilities from proton resonances characterized as dyad or triad. Then, not only are quantities such as (A) and (B) determined, but the question of how the monomer distribution in the chain may best be described can be approached. With present magnetic field strengths only dyads and triads are nmr observables. Homopolymerizations require one or two independent parameters to describe the diastereosequence distribution in a firstor second-order Markoffian description, respectively.4 (A zeroth-order hlarkoffian distribution for honiopolymers corresponds to a completely random or “atactic” distribution since the addition probability is independent of chain history and the monomer charge ratio is unity.) For copolymers, the monomer distribution requires one, two, or four independent parameters for zeroth-, first-, or second-order Markoffian descriptions, respectively. Since there are two independent observables for homopolymers (syndio-, iso-, and heterotactic triads, normalized) and there are, ideally, five independent nmr observables for copolymers (the six triads), nmr analysis can only definitely establish the existence of Markoffian first-order or lower homo- and copolymerization processes by eq 2, 8, and 9 without reference to the possibility of any non-Markoffian process. For example, the five copolymer nmr observables are sufficient to evaluate the four parameters of a second-order Markoffian distribution but not all the parameters of any higher order so that an unambiguous check of four unequal second-order parameters is not possible. The experimental diastereosequence distribution resulting from free-radical homopolymerizations of methyl methacrylate,6 vinyl acetate, and vinyl chloridel.2 have been successfully described by a single parameter, and in these cases the Markoffian naturg of (6) F. A. Bovey and G. D. V. Tiers, J. PoEymer Sci.. 44, 173 (1960).
RANDOM MONOMER DISTRIBUTIONS IN COPOLYMERS
1977
the process is clear. Non-Markoffian processes are indicated in some instances as mentioned earlier. Some copolymer monomer distributions have been reported, most notably styrene-methyl methacylate.’ These distributions have been determined by nnir and various chemical means8 but not completely enough SO that the nature of the statistics could be definitely established. If the monomer distribution is second or lower order Markoffian, a study of, say, l / y as a function of charge ratio will allow the determination of the reactivity ratio RBBif the charge ratio is known (constant) throughout the copolymerization (low conversion).
peak, and let k be the number of peaks. The model is then given by
Experimental Section E-VC1 copolymers were prepared by free-radical, emulsion copolymerization of ethylene and vinyl chloride. E-VA copolymers were prepared by freeradical, emulsion (high ethylene content) or solution (high vinyl acetate content) copolymerization of ethylene and vinyl acetate. Several low-conversion, freeradical, emulsion E-VC1 copolymers were made by blowing out the emulsion and rapidly venting the monomers at the first sign of polymerization; any significant postpolymerization was eliminated. Solution viscosities indicated that molecular weights of all copolymers were high. Chemical compositions of the final copolymers were determined by elemental H and C analysis. All nmr samples were prepared by dissolving 1 g of copolymer in 10 ml of o-dichlorobenzene (unless otherwise noted) containing 1% by volume of hexamethyldisiloxane (7 9.94) as internal reference, pipetting a portion of this solution to a 5-mm 0.d. thin-walled precision tube, flushing with nitrogen, and firmly capping. All spectra were obtained from a Varian HR-100 spectrometer with an operating probe temperature of 125”. Multiple resonance field sweep spectra were obtained by the technique described by J o h n ~ o n using ,~ one or two irradiating frequencies in order to obtain maximum decoupling. Each spectrum was calibrated in the usual way by side-ba,nd modulation. Xeasurements of signal intensities were performed in two ways. First, the observed spectrum was copied, cut out, and weighed with all overlap of adjacent peaks visually estimated. Second, the observed spin-spin decoupled spectrum was assumed to arise from chemically unique, noninteracting protoris and was fitted by a computer using a least-squares approach and an idealized line shape in the following manner. Let zt denote the ith value for the abscissa (calibrated magnetic field) and let y, denote the ith observed value for the ordinate (resonance pattern). Let p, be the assumed location of the center of the j t h
where yt is the computed ordinate for the ith point; c,, T,, and pi are regression coefficients; and the vertical lines denote absolute value. The regression coefficients were estimated by a nonlinear regression program based on the Gauss-Newton iterative process. lo Initial values for the coefficients were obtained by assuming that the peaks are nonoverlapping, reading three points from each peak, and solving a set of three simultaneous equations for the associated values of c,, T,, and p,. Convergence was usually obtained in 8-10 iterations of the Gauss-Newton process. About 100 yc values were used for each spectrum. The area under the j t h peak is given by
The areas were determined by using an integration subroutine which is based on the Romberg algorithm.” Approximate standard deviations for the areas were obtained from
where $(A,) is the approximate standard deviation of the area of thejth peak and where s(c,), s(T,), and ~ ( p , ) are, respectively, the standard deviations of the coT,), etc., are the coefficients c,, Ti, and pi. The variance of c, and T,, etc. The various derivatives appearing in expression 12 were evaluated numerically. The computed spectra were plotted automatically.
s(~,,
Results and Analysis
I. Ethylene-Vinyl Chloride. The single and multiple resonance spectra of typical E-VC1 copolymers are presented in Figures 1 4 . I n the a-p decoupled multiple (7) F. A. Bovey, J. Polymer Sci., 62, 197 (1962); H.J. Harwood and W. Ritchey, Polyner Letters, 3 , 419 (1965). (8) H.J. Harwood, Angew. Chem., 77, 405 (1965); 77,1124 (1965), and references contained therein. (9) L. F. Johnson, Varian Associates Technical Information Bulletin, 1962,No. 3,p 5,Vol. 111. (10) H. 0. Hartley, Technometrics, 3 , 269 (1961). (11) P. Henrici, “Elementary Numerical Analysis,” John Wiley and Sons, Inc., New York, N. Y.,1964.
Volume 70, Number 6 June 1966
JACOB SCHAEFER
1978
1'
I
' .
50 CPS
.
-1k-
.
so CPS
Figure 1. 100-Mc/sec spectra of a region of E-VC1 sample M (a) single resonance and (b) double resonance in which CI region is decoupled revealing a-region lines 1-6. Magnetic field increases left to right.
?l
5ocps
50 CPS
a .
* .
.
. : CPB 50
Figure 2. lOO-Mc/sec double resonance spectra of a region of typical E-VC1 copolymers (a) A, (b) C, (c) S, and (d) V in order of increasing VCl content. Magnetic field increases left to right. The left-hand marker is always centered under line 1. Occasionally a line is obscured by overlap from a large neighboring line. Thus line 3 is not observed in samples A and C. Line 6 is too weak to be observed in samples S and V. Recorder gains are not all equal.
resonance spectra, the low-field CY region consists of six lines, arising from methine protons, and the high-field p region consists of five lines, arising from methylene The Journal of Physkal Chemistry
dk-
so CPS
-1 T-
L.
.. i 1
50 CPS
+I+
Figure 3. lOC-Mc/sec double resonance spectra of p region of typical E-T'Cl copolymers (a) A, (b) C, (c) 31,and (d) V in order of increasing VCl content. Sample C shows the five p-region lines 7-11. Magnetic field increases left to right. Lines 10 and 11 are too weak to be observed in sample V. Left-hand marker indicates line 7.
+I--
~
SOCPS
so CPS
I t Figure 4. lOO-Mc/sec double resonance spectra of a region of three similar E-VCI copolymers (a) L, (b) N, and (c) T. Left-hand marker indicates line 1.
protons. The positions of these lines, from sample to sample, are remarkably constant. I n order of increasing magnetic field, the positions and assignments are given in Table I. These assignments were made by comparison of all spectra ranging from final composition mole fraction M A = 0 to 0.7. (A will always represent ethylene, and B will always represent vinyl chloride or vinyl acetate.) Examination of Figures 1-4 and Table I reveals the following information. (a) There are no resonances a t lower fields than those observed for pure poly(viny1 ch1oride)I (PVC),
RANDOM MONOMER DISTRIBUTIONS IN COPOLYMERS
1979
Table I: Line Positions and Assignments in E-VC1 Copolymer Nmr Spectra in Order of Increasing Magnetic Field Cps from
Nmr line
1
2 3 4 5 6 7 8 9
10 11
Proton
Sequence
CHzCHClCHzCHClCHzCHCl
CH&HClCHzCHClCHzCHz CHzCHzCHzCHClCH2CHz CHzCHClCHzCHCl CHzCHClCHzCH2CH&HCl CHzCHClCHzCHz CHzCHClCHzCH2CHzCHz CHzCHzCHzCHzCHzCHz CHiCHzCHzCHzCHzCHCl
{
BBB BBB BBB BBA,ABB BBA,ABB ABA BB BB BAB BA,m BAA, AAB
Tacticity
Syndiotactic Heterotactic Isotactic Racemic Meso Meso Racemic
HMDS at 100 Mc/sec
446 435 423 411 396 374 218 198 167 145 124
' Since backward VCl addition is not present (see Results), these methylene protons in either AB or BA sequences cannot have a next nearest neighbor CHCl group, and so the resonance is characterized as dyad rather than triad. * BAA does not contain a proton of this type. I n triads only resonances from protons of the central monomer unit are considered in order to avoid double counting. The BAA proton corresponding to CH2CH2CH&H2CH2CHC1is not in the central monomer unit. If the chain is considered to grow right to left, opposite to the direction considered in the text, and with only frontward addition of B units, then BAA contains this proton and AAB does not. Using an arrow on the last unit in the chain to symbolize the direction of growth, AAB: +CH2CH2CH2CH2CHClCHz and BAA: +CHClCH2CHzCHZCH&Ht. Because of the symmetry of eq 2, eq 13 is unaffected by the choice of growth direction.
thus eliminating the possibility of any head-to-head vinyl chloride additions, -CH2CHClCHClCH2-, and allowing line assignments 1-3. (b) Lines 4 and 5 are assigned to racemic and meso BBA (ABB) triads, respectively, and the highest field CY resonance, line 6, is assigned to ABA triads. (c) Lines 7 and 8 in the fl region correspond to dyad resonances observed in pure PVC which arise from methylene protons with two CHCl group nearest neighbors. (d) Line 9 allows the introduction of an ethylene unit and arises from p protons with only one CHCl nearest neighbor or two CHCl next nearest neighbors. (e) Line 10 arises from fl protons with no CHCl nearest nejghbor and only one CHCl next nearest neighbor. (f) Line 11 arises from /3 protons with only CH2 nearest and next nearest neighbors. There are no complications in these line assignments due to the possibility of vinyl chloride adding to the polymer chain, which grows from left to right, in two ways, that is, normally (-CH&HCl-) to form a B unit, or backwards (-CHClCH2-) to form a B* unit. If such a possibility existed, then resonances which are typical of dyads or triads containing BB* or AB* sequences should be observed. BB* resonances are not observed as noted in (a) above. AB* sequences
are also not observed as can be seen from the following argument involving the /3-region data. If AB* sequences did occur, as well as AB sequences, then the methylene proton resonances could still be definitely classified according to nearest and next nearest neighbors: thus, starting from the highest field 0 CHCl nearest neighresonance, line 1 1 , O and 0 ( k , bors and 0 CHCl next nearest neighbors); line 10, 0 and 1; line 9, 1 and 0 (and perhaps 0 and 2); and the average of lines 7 and 8,2 and 0. If line 11 is taken as reference, the positions of lines 10,9, and the average of 7 and 8 are 21, 43, and 84 cps at 100 Mc/sec, respectively, t o lower field. Thus it appears that in the /3 region the deshielding effect of a CHCl nearest neighbor is approximately twice that of a CHCl next nearest neighbor, the latter of which lowers a methylene resonance about 0.21 ppm. If AB* sequences existed, however, then triads such as BAR* would give rise to /3 lines having the neighbor classification of 1 and 1. These lines would appear at about 0.60-0.65 ppm below line 11. Although some overlap usually occurs between lines 8 and 9 in this region (see Figure 3c), inspection of E-VC1 spectra shows the presence of no significant amounts of BAB* sequences. By a similar argument about the relative shielding effects of CHCl and CH2 nearest and next nearest neighbors in the CY region, the spectra of E-VC1 coVolume 70,Number 6 June 1966
1980
JACOBSCHAEFER
polymers with M B > 0.5 show that B*BA, B*BB, and AB*B are not present in significant amounts. The existence of B* units in a few particular sequences (e.g., . . .AAB*AB.. .) cannot be eliminated by inspection of the spectra. However, such sequences would cause line 9 to show a complicated dependence on M B since no B*AB protons are in line 9 and all BAB protons are and since, further, B*AB could only form after runs of two A units. This complication is not observed. (See Discussion.) Finally, B* units might exist in sequences which, in the triad-counting process, are indistinguishable from those containing no B* (e.g., . . .AAB*AA.. ., . . .AAB*B*AA. , . , and . . .AAB*AB*AA. . .). Hence, in the remainder of this paper VC1 can be assumed to add to a growing chain in only one way. The possibility of any sizable effects arising from branching is neglected. Branching was evaluated by reduction of E-VC1 to polyethylene and infrared determination of the CHsCHt ratio and was found to be one branched carbon per 100. Using these line assignments and the relative dyad and triad concentrations from eq 2 and 3 and considering the number of protons giving rise to resonance in each unit, the observed signal intensities are related to dyad and triad concentrations by eq 13.
I,i
=
Ii
+ 1 2 + 1 3 = CZW(1 - y)
I,z
=
I4
f 15 = 2cxwy
Ia3
=
16
=
I84
= 17 f
CZ(1
- W)y
Is
c’xw
=
(13)
185 =
Ips
=
I10
+ In
- s) + 2 4 = C’zy(3 - s) = c’(2zyz + 2zy(l - 2 ) = c’(yz(1
=
c’sy(2
+
+ zyzj
2)
The primes act as a reminder that usually the (Y and p parts of the spectrum were obtained under different experimental conditions (radiofrequency power, recorder gain) and that, for convenience, the two parts are normalized separately. I n determining the monomer distribution in a copolymer, tactic information is ignored; thus Ial is considered as a single signal intensity from BBB triads and contains syndio-, hetero-, and isotactic BBB triad signal intensities; Ia2 and Ia3 are intensities corresponding to BBA (ABB) and ABA triads. I n all E-VC1 spectra line 9 of the P region was well resolved, symmetrical, and comparatively narrow; it was fitted with a Gaussian line shape whose center, height, and half-width a t half-height were assumed to be independent of adjacent peaks. I n this way the total P region of the spectrum was divided into three parts. The nonlinear multiple regression computer program described earlier was used to fit the CY region of the spin-spin decoupled spectra. Examples of the final fit are shown in Figures 5 and 6, and the areas and approximate standard deviations are given in Tables I1 and 111. No attempt was made to use the computer program to fit the P region because of the often serious overlapping of peaks. The error associated with the observed signal in-
Figure 5. Least-square-fitted crregion double resonance spectra of E-VCl samples (a) C, (b) M, (c) S, and (d) V. Computed spectra were plotted automatically.
T h Journal of Physkcd Chemistry
I9
1981
RANDOM MONOMER DISTRIBUTIONS IN COPOLYMERS
~~
Table I1 : Signal Intensities from Least-Squares Fit of Typical Spin-Spin Decoupled Spectra Line no.
Area
Std dev
F
1 2 3
0.034 0.445 0.520
0.012 0.025 0.020
0.015 0.025 0.033 0.042 0.014
H
1 2 3
0.247 0.527 0.226
0.025 0.038 0.017
0.012 0.019 0.047 0.013 0.015
J
1 2 3
0.401 0.465 0.134
0.039 0.065 0.038
E-VC1 sample
Line no.
Area
Std dev
E-VA sample
C
1 2 4 5 6
0.076 0.094 0.488 0.120 0.221
0.016 0.018 0.036 0.012 0.020
S
1 2 3 4 5
0.241 0.413 0.163 0.156 0,027
V
1 2 3 4 5
0.258 0.345 0.302 0.041 0.054
Table I11 : Parameters for Least-Squares Fit of Spin-Spin Decoupled Ethylene-Vinyl Chloride Nmr Spectra Sample
Line
Area
Std dev
T
L
1 2 3 4 5 6
0.224 0.241 0.143 0.179 0.174 0,039
0.007 0,008 0.012 0.012 0.015 0.007
AI
1 2 3 4 5 6
0.180 0.246 0.270 0.113 0.148 0.043
N
1 2 3 4 5 6
T
1 2 3 4 5
C
P
4.52432 6.38870 2.91628 7.34133 3.63423 5.23860
2.29551 2.64989 1.64027 1.68381 1.60790 0.39876
2.83928 4.05893 5.37787 2.58156 2.44923 3.23680
0.013 0.014 0,037 0,011 0.017 0.010
5.57506 7.02506 5.30082 11.3312 5.56117 13.0070
1,47338 2.09585 1.64987 0.92683 1.21933 0.30781
3.10493 3.63777 1.80000 3.17549 3,24368 2.36817
0.260 0.267 0.093 0.198 0.156 0.026
0.010 0.009 0,011 0.012 0.017 0.007
4.80383 6.41685 5.40448 7.79367 3.85255 7.29308
2.02927 2.39900 0.82145 1.62113 1.19815 0.23371
2.17519 3.63919 3.46752 2,78244 2,41626 3.62150
0.274 0.372 0.201 0.055 0,098
0.011 0.019 0.041 0.014 0,019
5.94560 5.63478 3.19794 6.21553 2.16198
1.67676 2.52593 1.27814 0.38032 0.68347
2.30311 3.37284 2,73648 3.55043 3.72709
tensities is in all cases taken as I t , (a and ,8 normalized separately) f 0.03; i = a , j = 1, 3; i = p , j = 4, 6. This value for the error was arrived at by comparison of visually fit (Tables IV and V) and computer-fit (examples in Tables I1 and 111) spectra. The two methods are always in agreement if this error is as-
sumed. Also, when both up- and downfield sweeps of a given spectrum under the same decoupling conditions were considered, reproducibility of the visuallyfit and of the computer-fit signal intensities suggested this value as a reasonable estimate for the error. It is not necessarily an upper or lower bound. Volume YO, Number 6 June 1066
JACOBSCHAEFER
1982
Figure 6. Least-square-fitted a-region double resonance spectra of E-S'Cl samples (a) L, (b) N, and ( c ) T. Computed spectra were plotted automatically.
From eq 14 y and ZL' can be determined independently
9
8
from the a-region data; x and x can be determined from 0-region signal intensities, y , tu, and eq 5. A number of other schemes may be used to evaluate the monomer distribution parameters. (See Discussion.) Approximate errors in the evaluations of these addition probabilities are determined from the errors in the I values. Table IV and Figures 7 and 8 contain the parameters for E-VCI. The single and double resonance spectra of the /3 region of pure PVC (Opalon 660, 1 g in 10 ml of a 50-50 mixture of benzaldehyde and o-dichlorobenzene) are shown in Figure 9. II. Ethylene-Vinyl Acetate. The single and double resonance spectra of poly(viny1 acetate) (PVA) and typical E-VA copolymers are shown in Figures 10-12; line positions and assignments are given in Table VI. Figure 10 shows the importance of a proper choice of solvent. I n CCl, the p protons of PVA and those /3 protons of E-VA with two acetate nearest neighbors are considerably upfield from the acetate methyl resonance, which is a triplet corresponding to syndio-, hetero-, and isotactic located 192.5, 190.6, 188.6 f 0.5 cps, respectively, from hexamethyldisiloxane (HilIDS) at 100 Mc/sec. However, in odichlorobenzene the acetate methyl has merged to a singlet (189.6 f 0.5 cps) and the p protons are shifted downfield where they provide less interference to any 0 protons with fewer than two acetate nearest neighbors. The appearance, interpretation, and analysis of the fl region of E-VA are identical with those of the E-VC1 0 region except for the neglect of the VA dyad The Journal of Physical Chemistry
7
6
5
CYCP
0
hlva In ElVCt
Figure 7 . Vinyl chloride number-average sequence length in E-VC1 as a function of final composition. Estimated errors are indicated by vertical brackets.
resonances, partially obscured by the acetate methyl, and for the somewhat different positions and shapes of the lines due to differences in the shielding character-
RANDOM MONOMER DISTRIBUTIONS IN COPOLYMERS
1983
Q
Volume 70,Number 6 June 1966
JACOBSCHAEFER
1984
ME In E/VCI Figure 8. Ethylene number-average sequence length in E-VCI as a function of final composition. SOCPS
Figure 10. 100-Mc/sec spectra of poly(viny1 acetate) a t 125': single resonance of p region (a) CCla as a solvent and (b) o-dichlorobenzene as solvent. CY region, o-dichlorobenzene as solvent: (c) single resonance and (d) double resonance. Magnetic field increases left to right.
IO CPS
+I+
IO CPS
4I-
10 CPS
4b
Figure 11. lOO-Mc/sec double resonance spectra of CY region of E-VA samples ( a ) F, (b) H, and (c) J in order of increasing VA content and showing or-region lines 1-3. Magnetic field increases left to right. Left-hand marker indicates line 2. Figure 9. lOO-hIc/sec spectra of region of poly(viny1 chloride) a t 125": ( a ) single resonance; (b) double resonance. Magnetic field increases left to right. An equal volume mixture of benzaldehyde and o-dichlorobenzene is the solvent.
istics of the acetate and chlorine groups. Monomer distribution parameters may be found in Table V and Figures 13 and 14. The errors associated with the observed signal intensities are the same as for E V C I . When M B > 0.5, this may lead to an underestimate for The JOUTW~ of Physical Chemistry
some of the I , values since a realistic separation of the overlapping signals becomes increasingly difficult. The a region of PVA in o-dichlorobenzene shows a single resonance quintuplet, 500 cps from HMDS at 100 Mc/sec, which on double resonance collapses to a singlet with no indication of extra lines due to different diastereosequences. Since the various triads in the E-VA have a-proton resonances which are closely spaced, the absence of any tactic information simplifies the a-region interpretation, which is otherwise identical
1985
RANDOM MONOMER DISTRIBUTIONS I N COPOLYMERS
8 ,
Table VI : Line Positions and Assignments in E-VA Nmr Copolymer Spectra in Order of Increasing Magnetic Field (x = VA)
c PS from
N mr line
1 2 3 4
6
Proton
Sequence
CHZCHXCHZCHXCH~CHX BBB CHZCHXCH~CHXCHZCHZ BBA,BBA ABA CHzCHzCHzCHxCHzCHz CHzCHxCHzCH&HzCHx CHzCHxCHzCHz BAA, AAB CHzCHxCHzCHzCHzCHz CH&HzCHzCHzCHzCHz CHZCHZCH&HZCH~CHX
HMDS at 100 Mc/sec
500 493 483 189 141
120
BAA does not, contain a proton of this type.
0
.
.
.I
.2
.3
.4
.S
.6
.7
.e
.9
1.0
MVA In E/VA Figure 13. Vinyl acetate number-average sequence length in E-VA as a function of final composition.
analysis of the low-conversion E-VC1 spectra is identical with that of the high-conversion spectra. Data and parameters from the a-region analysis are given in Table VI1 and Figure 16.
Discussion I . Monomer Distribution in Copolymers. The monomer distributions in both the E-VCI and E-VA free-
--It-
-Ik
Figure 12. 100-Mc/sec single resonance spectra of p region of E-VA samples ( a ) H and (b) J in order of increasing VA content and showing p-region lines 4-6. Magnetic field increases left to right. Left-hand marker is centered under line 5. VA methylene dyad protons, partially buried under line 4, make an accurate estimate of the intensity of line 5 increasingly more difficult with increasing VA content.
with that of E-VCI. Typical computer-fitted spectra are shown in Figure 15. I I I . Low-Conversion Ethylene-Vinyl Chloride. The
radical copolymerized systems may be described by zeroth-order Markoffian statistics since eq 9 is satisfied within experimental error. (See Tables IV, V, and VII.) y and w were evaluated using eq 14 and found to satisfy eq 8. To avoid combining a- and 0region data in evaluating z and z, the relation z = 1 - z was assumed to be true. Then z was evaluated in two ways, first using a-region data alone and eq 5, 8, and 15 and, secondly, using 0-region data alone and eq 13 and 16. z = yMB/(1 z = 1/(1
- MB)
+ Ii3e/Igd
(15) (16)
The validity of the assumption z = 1 - z was then checked by comparing the two values for z, which were found to be in agreement within experimental error. Because of the severe overlap in the p region of both Volume 70,Number 6 June 1966
JACOB SCHAEFER
1986
Table VI1 : Low-Conversion Ethylene-Vinyl Chloride Signal Intensities and Monomer Distribution Parameters E-VCI
(LC) sample
Iul
A B
0.58 0.61 0.64 0.74 0.83
C D E
la1
Ius
Y
0.39 0.36 0.35 0.25 0.17
0.03 0.04 0.01 0.01 0
0.25 f 0.03 0.23 f 0.03 0.21 f 0.03 0.14 f 0.02 0.09 f 0.02
0.85 f 0.10 0.84 f 0.10 0.94 f 0.10 0.92 iz 0.20 1.0 f 0 . 3 0
0.450 0,675 1.00 1.83 3.08
4.0 f0.4 4.4 f 0.5 4.8 iz 0 . 6 7.1 f1 11 f 2
1.05 1.01 1.03 1.00 1.00
S 0
8
6
I
4
3
Figure 15. Least-square-fitted double resonance spectra of E-VA samples (a) F, (b) H, and (c) J. 2
I
0
Figure 14. Ethylene number-average sequence length in E-VA as a function of final composition. Brackets indicate ranges of values obtained from B region alone. Circles indicate values (without ranges) obtained from (Y region alone. 0'
E-VC1 and E-VA spectra, there may be plausible pline assignments other than those given in Tables I and VI and eq 13, but all are in substantially worse agreement with a-region and composition data within a zeroth-order Markoffisn description. For example, if E-VC1 IBs were assigned only to CH2CHdX32CH2CHzCHz and CHzCHzCH2CHzCHzCHClwhile CHzCHXCHzCHzCH2CHzwere included in the ID5assignment, then typical values for z are 0.43 (sample C) and 0.58 (sample 0) compared to 0.63 and 0.77 by the assignment in Table I and 0.61 and 0.82 from a-region and composition data. Of course, if incorrect line assignments are made, the resulting values for the addiThe Journal of Physical Chemistry
0
M
;
I
2
, 4,
3
I
6
'/u
4
i
A B
Io
h
i2
ib
Figure 16. Vinyl chloride number-average sequence length, l / y , in low-conversion, free-radical, emulsion E-VCl as a function of bulk charge ratio.
tion probabilities may be inconsistent. What is done, actually, is to test any plausible line assignment for consistency within the framework of the simplest possible statistics and, if no line assignment is consistent, then move to the next highest order statistics. For the E V C l copolymer system a partial internal check on the line assignments is available regardless
RANDOM MONOMER DISTRIBUTIONS IN COPOLYMERS
of the order of the statistical distribution and regardless of the fact that not all six triad concentrations are distinguishable. 184, which counts BB dyads, can be used to check Ial and Iat, which count BBB and BBA triads. Considering the number of methylene protons with CHCl nearest neighbors contained in BBB and BBA (ABB) triads compared to BB dyads (4 to 1) and the ratio of total number of p to a protons [2(2 - MB)/MB to M B ] , the CY- and ®ion signals are related by
I,I
+
Ia2
= (2
- MB)I~~/MB
(17)
Equation 17 is found to be valid for all E-VCl samples within experimental error. The fact that .c = y for E-VA and E-VC1 within experimental error means that the product RBBRAA= 1, which is easily seen from eq 6 when only the single subscript of the zeroth-order description is used. Burkhart and Zutty12 have reported the product of reactivity ratios equal to unity for free-radical, bulk, and solution prepared E-VA and E-VCl copolymers from composition data alone without knowledge of the actual monomer distribution. I I . Least-Squares Fit of Spectra, Signal Intensities, and Determination of Tacticity. The nonlinear regression analyses of the spin-spin decoupled spectra provide reasonably good fits, signal intensities, and approximate errors. However, if a peak is incompletely resolved or asymmetrically distorted owing to significant residual spin-spin coupling and is partially obscured owing to overlap with neighbors, then the Lorentzian-like model is not appropriate even though the use of three parameters for each peak was designed to allow for some variation in line shape due to different decoupling conditions. Although the fit may be close in a least-squares sense, the values for the resulting areas and associated error estimates may not be meaningful because of the uncertainty introduced by overlap with distortion. The a-region spectra of E-VC1 samples L, AI, N, and T provide an illustrative example. The spectra are presented in Figures 1 and 4 along with the computer fits in Figures 5 and 6; the least-squares analysis data are contained in Table 111. The spectra of these four samples are similar, but identical experimental conditions, including identical degrees of decoupling and sweep speeds, are not realized. A weaker, more poorly resolved line immediately adjacent to a stronger, well-resolved line tends to be ignored in the least-squares fitting procedure, in part due to the presence of fewer data points, resulting in the weaker line appearing as a shoulder (rather than as an incompletely decoupled line, distorted, and with perhaps substantial area beneath the larger peak). This
1987
effect can be seen, for example, in line 1 of sample M compared to line 1 of samples L, N, and T and in line 3 of samples M and T compared to line 3 of samples L and N and reduces the confidence that can be placed in the calculated relative intensities of such lines. Fitting these spectra by eliminating one of the parameters ( p = 2) was not successful since the calculated spectra were not as well resolved as the observed spectra. A lower limit of 1.8 was placed on the exponent p in eq 10 in order to prevent convergence to flat lines with sharp peaks. The limit improved the situation but is not a solution. The inability to judge accurately overlapping, distorted, non-Lorentzian line shapes and signal intensities is inherent in any visual cutting-weighing method to an even greater extent. Thus, least-squares fitting of spectra of this type gives the best possible estimate of signal intensities but, unfortunately, does not provide reliable estimates of the associated errors. When signal overlap is a less serious problem, as it is in determining the monomer distribution in which two or three signals are considered as one, then both the leastsquares-fitted and visually fitted lines and areas are more reliable because exact shapes can be accurately judged even for distorted lines. It is not possible to remove completely distortion in lines caused by residual spin-spin coupling for five or six chemically unique protons with just one or two irradiating frequencies when these protons are coupled to polymer backbone protons poorly defined within patterns spread over a total of around 60 cps. Concentrating on only one line at a time to obtain maximum resolution in either field or frequency sweep multiple resonance experiments does not solve this problem since distortion and overlap are still present from neighboring lines (and now not necessarily just nearest neighbor lines). This total decoupling problem is less severe for E-VA than for E-VC1 since the /3 protons in E-VA are more sharply defined with a narrower spread apparently due to the less potent effect of the acetate function in deshielding the /3 protons. Because of the uncertainty in estimating overlap and occasionally of detecting very weak signals from one of the monomers present in small amounts, no attempt was made to investigate quantitatively the tacticity of BBB arid BBA triads in E-VC1. The errors involved would be a t least twice as large as in the monomer distribution determination and so would probably be unacceptable. Qualitatively, despite changes in reaction conditions, ail E-VC1 samples investigated (12) R. D. Burkhart and N. L. Zutty, J. PoZymer Sci., A l , 1137 (1963).
Volume 70,Number 6 June 1966
JACOB SCHAEFER
1988
showed approximately the same triad tacticity ; that is, for BBB: hetero- > syndioisotactic; and for BBA: racemic meso. III. P Protons of PVC. From a study of the pregion triad distribution in PVC samples prepared at different temperatures2 and from the available X-ray diffraction analysis,13 it appears that the triad tactic assignments made by previous authors and used in this study are probably correct. To be consistent then, the P-region tactic assignments are determined : meso dyads (isotactic) at lower field and racemic dyads (syndiotactic) at higher field. Now the asymmetry of the p-region spectrum in PVC, clearly seen at 100 Mc/ sec, has been attributed somewhat unconvincingly to nonequivalence of meso protons,14 the presence of tetrad proton resonance^,'^ and branching in the carbon backbone. l6 The double resonance spectrum of this region shows three lines, two of the three close together and upfield from the third, and is only consistent with, but not necessarily proof for, the last two explanations. This result shows that the meso dyad protons under present resolution and solvent conditions may be classed in the “coincidentally equivalent” category and that the observed high-field asymmetry is not caused by their nonequivalence.’’ I V . Reactivity Ratios. The large deviation from ) the straight-line plot of l / y against M B ( ‘ ) / M A ( ~from eq 7 shown by the low-conversion free-radical, emulsion E-VC1 samples is a quantitative measure of the difference between monomer charge ratio in the bulk
>
The Journal of Physical Chemistry
and charge ratio at the reactive site. I n this particular emulsion copolymerization, the reactive site, whose exact environment is left unspecified, is richer in vinyl chloride than the bulk. Still, the copolymerization is described by a zeroth-order Markoffian process. Clearly, more than a simple reactivity ratio, obtained from the straight-line plot of Figure 16, is necessary to characterize emulsion copolymerizations at a given monomer charge ratio. How the bulk and reactive site ratios are related over the entire composition range and how this relationship may fluctuate during the course of the copolymerization must be known before final compositions can be obtained in any way other than trial and error.
Acknowledgment. The author wishes to acknowledge the assistance of Dr. Allan W. Dickinson, Central Research Department, who performed the nonlinear regression analysis, and the helpful criticisms of Dr. James C. Woodbrey, also of Central Research Department, Monsanto Co. (13)G.Natta and P. Corrandi, J . Polymer Sci., 20, 251 (1956). (14) W.C. Tincher, ibid., 62, 5148 (1962). (15) T. Yoshino and J. Komiyama, Polymer Letters, 3 , 311 (1965). (16) W.C. Tincher, MalcromoZ. Chem., 85, 20 (1965). (17) If the PVC triad assignments were reversed, that is, in order of
increasing magnetic field, is-, hetero-, and syndiotactic, then the E-VC1 BBB and BBA triad and BB dyad tactic assignments would be reversed, and the 0-region double resonance experiment would be in agreement with all three explanations. The monomer distribution in E-VC1 is, of course, unaffected.
