408
Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 408-412
ation is too complex, especially when tartaric acid is present, to be adequately analyzed. The effect of cations on compressive strength, with one exception, follows the sequence: Sn(I1) > Zn > Mg > A1 (Table VI), a sequence similar to that found for rate of set. The exception, mentioned above, occurs in the cements formed from G-247 where MgFz produces the strongest cement, although probably not significantly stronger than that where SnF, is used. In general, stannous fluoride, in conjunction with tartaric acid, is the most effective accelerating salt across the whole range of glasses. Why this should be so is difficult to ascertain. Conclusions
Cement formation between certain glasses which react only slowly with a poly(a1kenoic acid) can be accelerated considerably by some metal salts, an effect enhanced by the presence of tartaric acid and, indeed, some nonreactive glasses can be induced to form cements by this means. The salts serve to provide cations for gel formation, and tartaric acid aids the release of ions from the glass. The effective cations, with the exception of Ag(I), are multivalent and all are known to be bound to specific sites on the polyanion chains. Sodium and calcium salts are ineffective, probably because their cations are not site bound. Although metal salts can initiate or accelerate cement formation they do not necessarily improve hydrolytic stability. However, the combination of metal salts and tartaric acid is much more effective in this respect.
by permission of the controller of Her Majesty's Stationery Office, holder of Crown Copyright. Literature Cited Begala, A. J., Thesis, Rutgers University, 1971. Bovis, S. C., Harrington, E., Wilson, H. J., Br. Dent. J., 131, 352 (1971). Casson, D., Rembaum, A., J. Polym. Sci., BE, 773 (1970). Crisp, S.,Wilson, A. D., J. Dent. Res., 53, 1408 (1974a). Crisp, S.,Wilson, A. D., J. Dent. Res., 53, 1420 (1974b). Crisp, S.,Wilson, A. D., J. Dent. Res., 55, 1023 (1976). Crisp, S.,Wilson, A. D., British Patent 1484454 (1977). Crisp, S., Prosser, H. J., Wilson, A. D., J. Mater. Sci., 11, 36 (1976). Crisp, S.,Pringuer, M. A., Wardleworth, D., Wilson, A. D., J. Dent. Res., 53, 1414 (1974). Crisp, S.,Wilson, A. D., Elliott, J. H., Hornsey, P. R., J. Appl. Chem. Biotechno/., 27, 369 (1977). Crisp, S.,Wilson, A. D., British Patents 1 532 954; 1 532 955 (1978). Crisp, S.,Ferner, A. J., Kent, B. E., Lewis, B. G., Wilson, A. D., J . Dent. Res., to be published, 1980. Giilmore, Q. A., "Practical Treatlse on Limes, Hydraulic Cements, and Mortars", New York, 1864. Gregor, H. P., Luttinger, L. B., Loebl, E. M., J. Phys. Chem., 59, 990 (1955a). Gregor, H. P., Luttinger, L. B., Loebl, E. M., J . phys. Chem., 59, 34 (1955b). Hodd, K. A., Reader, A. E., Br. Polym. J., 8, 131 (1976). Kent, B. E., Lewis, B. G., Wilson, A. D., J. Dent. Res., 58, 1607 (1979). McLean, J. W., Wilson, A. D., Aust. Dent. J., 22, 31 (1977a). McLean, J. W., Wilson, A. D., Aust. Dent. J.. 22, 120 (1977b). McLean, J. W., Wilson, A. D., Aust. Dent. J., 22, 190 (1977~). Mandei, M., Leyte, J. C., J. Polym. Sci., A2, 2883 (1964). Potter, W. D., Barciay, A. C., Dunning, R., Parry, R. J., U.S. Patent 4043327 (1977). Ruehrwein, R. A., Ward, D. W., Soil Sci., 73, 485 (1952). Smith, D. C., British Patent 1 139430 (1969). Wilson, A. D., Crisp, S., Br. Polym. J., 7, 279 (1975). Wilson, A. D., Crisp, S.,British Patent 1422337 (1976). Wilson, A. D., Crisp, S.,"Organollthic Macromolecular Materials", Applied Science Publications, London, Chapter IV, 1977. Wilson, A. D., Kent, B. E., British Patent 1316 129 (1973). Wilson, A. D., Crisp, S.,Ferner, A. J., J. Dent. Res., 55, 489 (1976).
Acknowledgment
The authors thank the Government Chemist, Dr. H. Egan, for permission to contribute this paper. Reproduced
Received for reuiew February 19, 1980 Accepted May 6, 1980
Refractory Concrete for Graphitizing Furnaces Rudolph W. Wallouch' and Frank V. Fair Technical Department, Airco Carbon, Niagara Falls, New York 14302
Ferrochromium and chromium silicide slag have been utilized as the aggregate to provide a refractory concrete of improved strength. The graded slags were admixed with calcium silicate or calcium aluminate cement as a hydraulic bond material. The resulting concrete materials were subsequently fired in 100 O C increments to 1200 O C and the fired compressive strengths determined. The concrete grog of graded ferrochromium slag and calcium aluminate cement developed above 700 O C a fired ceramic-type bond of increased strength as compared to refractory products based upon conventional blast furnace slag. The practical implications of this study are discussed.
Background
The usefulness of concrete made with common Portland cement is limited to temperatures up to about 650 "C. When Portland cement-type (structural) concrete is heated above 700 OC, the cement becomes dehydrated and loses its strength and structural integrity. In many important applications of these materials, however, structural integrity a t elevated temperatures is of paramount significance as has been discussed in more detail by Coss and Kent (1932) and McGrue (1937). For example, durability of the material being utilized is perhaps the single most important characteristic of an acceptable sideblock in an Acheson type furnace for graphitizing carbon products. Not only are replacement costs of conventional concrete 0196-4321/80/1219-0408$01 .OO/O
sideblocks extremely high, but, in addition, an early breakdown of sideblocks has a direct bearing on the operating cost of graphitizer units. If sideblocks rupture a t top graphitizing temperatures, insulating mix will run through the gap in the sidewall and cause temporary problems in operating the graphitizer. The life cycle of sideblocks is especially short in graphitizing units where the blocks are exposed to above-average temperatures (of the order of 1000 to 1200 "C) when making premium graphite electrodes. In the past, concrete for high-temperature applications (refractory concrete) has been prepared from refractory aggregates, such as crushed firebrick, and high-temperature cement. The usual high-temperature cement thus em@ 1980 American Chemical Society
Ind. Eng. Chern. Prod. Res. Dev., Vol. 19, No. 3, 1980
ployed is a calcium aluminate cement, such as the cements of the type known to the industry under the trade name Luminate, or under such specific product designations as Alcoa CA-25. An excellent account of the application of high alumina cement iin the steel industry has been given by Pole and Moore (1946). The formulation and properties of hydraulic refractory concretes have been studied by Giles (1939) and Arnould (1953). A typical such calcium aluminate cement thus includes the following components: A1203,79.0% (wt), CaO, 18.0%, Si02, 0.1%, MgO, 0.4%, and Fe203, 0.3%. These calcium-aluminate cements start to form a fired bond with the refractory aggregate at about 700 "C, thereby making such material superior to Portland cement-type structural concrete. The object of the present investigation was to provide a refractory concrete which possesses a high-fired strength at temperatures of the order of 800 "C and which in specified formulations possesses improved strength up to at least 1000 "C. The results obtained with blast furnace slag, ferrochromium slag, and chromium silicide slag as aggregate and the two cements, calcium aluminate cement and calcium silicate cement (Portland cement), are discussed.
Concrete Mixing and Sample Preparation Refractory products comprising calcium aluminate cement and ferrochromium slag were prepared and compared to refractory products based upon blast furnace slag. The use of blast furnace slag instead of sand in concrete formulations has been reported by Fedynin and Krivosudor (1968). The blast furnace slag was comprised of the following components: CaO, 4040% (wt), Si02,30-40%, and A1203,8-18%. The ferrochromium slags utilized as the refractory aggregate were derived from production of socalled high-carbon ferrochrome and from production of ferrochrome silicon alloy. The said aggregate, depending upon the specific metallurgical process from which it is derived, has a typical composition range of MgO, 25-4070 (wt), S O z , 20-5070, and Alz03, 10-40%, together with less than about 15% by weight of such constituents as Cr, Cr203,CaO, FeO, C, and S. The ferrochromium slags were obtained from Airco Alloys and Carbide Division of Airco, Inc., Niagara Falls, N.Y., and Charleston, S.C. All aggregates were crushed and sized to form a graded grog as recommended by Taylor (1965) and combined with Alcoa CA-25 calcium aluminate cement or Portland Cement Type IIIA as hydraulic bond material. The aggregate used in all instances to prepare the experimental mixes was well graded from coarse to fines and contained at least 50% of sized slag which would pass through a 14 mesh screen (Tyler series). The cement-toaggregate ratio in the mix was 1:4 and the water-to-cement ratio, W/C, was equal to 0.60. Generally, 0.8 ft3 batches were prepared. After mixing, the concrete batch was cast into four logs (6 in. diameter X 1 2 .in.) using standard concrete test molds. The molded logs were cured for 24 days at room temperature, and core drilled in the direction of the log axis using a 2-in. diameter core drill. The 12-in. core samples, cut on a diamond saw into 2 in. long sections, yielded a total of 24 test plugs (2 in, diameter x 2 in.) per batch. The 2 in. diameter sample plugs were used to study the effect of temperature 011 the strength of the experimental concretes. For this purpose, 22 plugs representative of an experimental batch were dried for 48 h a t 125 "C and subsequently exposed to elevated temperatures in a globar muffle furnace. The furnace temperature was increased in 100 "C increments every 2 days up to a maximum tem-
n
I
I +I
I
409
/
/ I I-
Figure 1. High-temperature compressive strength testing assembly.
perature of 1200 "C. After every 2-day hold at temperature, two sample plugs were removed from the furnace for rapid cooling. The weight loss in percent of the samples was determined from the weight change before and after each of the incremental heat treating steps. The roomtemperature compressive strength was determined on one of the samples. The other sample was placed in a hightemperature press, brought to the same temperature it experienced for the 2-day temperature run, and had its elevated temperature compressive strength measured. Test Procedure The cold compressive strength of test plugs was determined according to the standard ASTM method (ASTM, 1971). In order to measure the high-temperature compressive strength, a test rig was set up in which concrete test specimens could be subjected t o high temperatures under load. The assembly used is shown schematically in Figure 1. The apparatus consists of a hydraulic press (1)with ram (2) and an induction furnace. The high-temperature furnace is comprised of a steel table (3) to hold the lampblack sample base (4) and concrete sample (5) with inserted chromel-alumel thermocouple (6). The sample is placed in a graphite susceptor ( 7 ) and is surrounded by carbon black insulation (8), a quartz furnace shell (9), and the induction coil (10). Resting on the sample is a graphite plunger (11) which is separated from the water-cooled hydraulic ram (12) by a 10000 lb load cell (13). Mechanically connected to the top plunger (11) is a differential transformer (14) which registers the displacement of the plunger due to shrinkage of the concrete sample when under load. The signal from the differential transformer is recorded on the x axis by an x-y recorder of the test specimen. The as dimensional change (a) signal from the load cell is recorded along the y axis. The resulting recording is a load deflection curve (15) of the concrete sample as a function of the test temperature. Results and Discussion Room Temperature Load Test. Table I shows how the room temperature compressive strength of six different refractory concretes is affected after sustained exposure for 2 days at service temperatures as high as 1200 "C. Mix 1 through mix 3 are representative of Portland cement-
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 3, 1980
410
Table I. Room-Temperature Compressive Strength (psi) of Six Sideblock Materials Which Have Been Heat-Treated up to 1200 C in 100 C Increments with 2-Dav Hold Periodsa compressive strength, psi heat treatment temp, " C accum days RT 125 200 300 400 500 600 7 00 800 900 1000 1100 1200
(cure ) 2 4 6 8 10 12 14 16 18 20 22 24
Portland IIIA cement
alumina CA-25 cement
mix 1
mix 2
mix 3
mix 4
mix 5
mix 6
5716 4803 3907 3636 4258 2190 27 05 1592 501 613 137 245
5370 6066 4749 3902 5161 3389 2781 1474 742 290 133 162 774
5886 6818 6438 4295 5125 5059 4047 1808 1123 409 182 136 212
4207 4349 2830 2813 3431 2737 1731 2134 1828 1907 1754 1713
8235 4514 4869 4417 4808 4256 4582 4447 3313 2712 2503 2470 3069
7878 6490 6493 4978 6110 5630 4827 4814 4159 2740 2825 2321 3659
__
a Legend to mixes: mix 1 : graded blast furnace slag; Portland cement Type IIIA; mix 4: same as mix 1 ; calcium aluminate CA-25 cement; mix 2: ferrochromium slag from production of high carbon ferrochrome (composition approximately 25-35% MgO, 20-35% SiO,, 20-40% A1,0,); Portland cement Type IIIA; mix 5: same as mix 2 ; calcium aluminate CA-25 cement; mix 3: ferrochromium slag from production of ferrochrome silicon alloy (composition approximately 30-40% MgO, 30-50% SiO,; 10-25% A1,0,); Portland cement Type IIIA; mix 6: same as mix 3; calcium aluminate CA-25 cement.
-z -
t
7000-
7000
I
6000-
z
I
t
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E ~
I-
5000-
JIY
w
?
a,
4000W
a
0
3000V
n
d
2000-
1
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- 4
I
S
I l . . " ' ~ ' ~ ~ I
I
I
I 2 3 4 5 6 7 8 9 IO I I +FIRING TEMPERATURE,*C x IO-*COLD FACE c SIDEBLOCK THICKNESS, INCHES-
I
121314
I 2 HOT FACE
Figure 2. Cold fired strength of blast furnace slag concrete;Portland cement (1) vs. alumina cement (2); mix 1 vs. mix 4 in Table I.
type concrete compositions using as aggregate, blast furnace slag (mix l),ferrochromium slag from production of high-carbon ferrochrome (mix 2), and slag from production of ferrochrome silicon alloy (mix 3). Mix 4 through mix 6 are of the same composition as mix 1 through mix 3 except that calcium aluminate cement Type CA-25 is substituted as binder for Portland cement Type IIIA. As illustrated by mix 1 through mix 3 in Table I, any concrete using Portland cement Type IIIA retains its high cold strength up to 700 "C maximum. By firing the Portland cement-based concretes above 700 "C, the strength of the sideblock materials deteriorates rapidly. In other words, the useful life of sideblocks made with Portland cement is limited to temperatures below 700 OC. This holds regardless of the type of aggregate used. By comparing mixes 4 , 5 , and 6 with mixes 1, 2, and 3 listed in Table I, it is evident that calcium aluminate cement CA-25 is superior to Portland cement Type IIIA as the binder for refractory concrete whether blast furnace slag or ferrochromium slag is used as the aggregate. By comparing mix 4 with mix 5 and mix 6 it will be noted that
3 4
5
6
7
8
- FIRING TEMPERATURE, COLD FACE - SIDEBLOCK THICKNESS ,
91011 C x IO-*
-
121314
--
HOT FACE
INCHES
Figure 3. Cold fired strength of concrete consisting of slag from production of high-carbon ferrochrome; Portland cement (1) vs. alumina cement (2); mix 2 vs. mix 5 in Table I.
ferrochromium slags in combination with CA-25 cement outperform blast furnace slag as the aggregate. Blast furnace slag has a high concentration of sulfur compounds which are apt to react at elevated temperature with the cement binder and therefore are believed detrimental. The cold strength data listed in Table I are presented graphically in Figures 2, 3, and 4. The plots show the effect of alumina cement CA-25 vs. Portland cement on the fired strength of refractory concrete mixtures consisting of graded blast furnace slag (Figure 2), graded ferrochromium slag from production of high-carbon ferrochrome (Figure 3), and from production of ferrochrome silicon alloy (Figure 4).
Included in Figure 2 is a curve typical for both cured concrete formulations, showing the weight percent change with temperature due to the decomposition of the hydrated cements. It will be noted that upon heating, combined water is being expelled up to 500 "C whereupon the weight loss tapers off. This results in a steady decrease in bonding
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 3, 1980 411 8000
1
Table 11. High-Temperature Compressive Strength (psi) of Experimental Refractory Concretesa compressive strength, psi
K
temp, "C
blast furnace slag mix 4
800 900 1000 1100 1200
2907b 2340 964 1362 810
ferrochromium slag mix 5 3230d 3183d 2730
(2134)c (1829) (1907) (1754) (1734)
(3313)c (2712) (2503) (247 0) (3069)
_-
2730
a Legend to mixes: mix 4 and mix 5: for composition Roomsee Table I. b High-temperature strength. temperature strength. d Sample did not break a t 3200 psi maximum load.
n
I 3000 0
' I
'Oo0 c STRENGTH ZONE
-FIRING COLD FACE
TEMPERATURE ,
- SIDEBLOCK
THICKNESS
3500 -
0
c
a 10'-
, INCHES-
HQLE4€E
Figure 4. Cold fired strength of concrete consisting of slag from production of ferrochrome silicon alloy; Portland cement (1) vs. alumina cement (2); mix 3 vs. mix 6 in Table I.
ln
2
2000
k ln
t
1500
strength for both types of cement. However, the alumina cement is capable of holding the mass intact to higher temperatures than is the Portland cement, apparently due to the capability of the alumina cement to start forming a fired bond a t about 700 "C. Consequently, the 900 "C prefired Portland cement-type material mix 1 has a cold strength of only 501 psi, while the alumina cement concrete mix 4 has a strength of' 1828 psi. Referring to Figures 3 and 4, a similar function of the alumina cement is noticed in concrete consisting of graded ferrochromium slag aggregate. The x axis in Figures 3 and 4 represents the thickness and corresponding hypothetical temperature gradient of a 12 in. thick sideblock. The graphitizer sidleblock made of graded ferrochromium slags and alumina cement CA-25 and heated only on one side at 1200 "C has three distinct cold strength zones: Strength Zone I is a section starting at the heated face and penetrating a short distance depending on the exposed temperature where fired bond has developed. Strength Zone I1 is a section at the cold face and extends into the concrete for some distance where good hydraulic strength still exists. Strength Zone I11 is an intermediate or low-strength section, where the temperature has not been high enough to develop a fired bond but has been sufficiently high to des1,roy a considerable portion of the hydraulic bond of the alumina cement. High-TemperatureLoad Test. Load deflection curves were obtained for two of the most promising experimental sideblock materials (mix. 4 and mix 5 listed in Table I and illustrated by curve 2 in both Figure 2 and Figure 3). Both compositions were made with calcium aluminate cement CA-25. No high-temperature testing was possible on materials made with Portland cement since the fired strength of the samples was less than 100 psi as illustrated by curve 1 in Figure 2 through Figure 4. For the high-temperature measurements, 2 in. diameter X 2 in. high refractory concrete plugs were fired to 800-1200 "C in a muffle furnace over a period of 24 days. Subsequently, the prefired samples were transferred into the high-temperature test rig (Figure 1) and refired inductively. The crushing strength of the concrete plugs was determined after attaining temperature equilibrium. The
1000
500
1
2
3
4
5
6
STRAIN AL / L o
I
7 10
8
9
*
Figure 5. Load deflection curves at several temperatures of graded blast furnace slag and CA-25 cement-type concrete; mix 4 in Table I.
3500
- 3000
t
z 2500 J
-
I
v)
2000 K
I-
v)
I500
t 2
3
4
5
7
6
STRAIN ; A L / L o
I
8
9
10
IO-*
Figure 6. Load deflection curves at several temperatures of concrete consisting of slag from production of high-carbon ferrochrome and CA-25 cement-type concrete; mix 5 in Table I.
compressive strengths of the test materials at elevated temperatures are listed in Table 11. The stress (pounds curves of the optimum per square inch) vs. strain (AL/L) sideblock formulations a t 800 to 1200 "C are shown in Figures 5 and 6. For the sake of comparison, the room temperature strength data of the fired concrete samples are included in Table 11.
412
Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 412-415
The relatively low room-temperature strength of mix 4 listed in Table I and Table I1 and illustrated in Figure 2 by curve 1 is reflected in poor strength properties at high temperatures. When the concrete sample of mix 4 is stressed at 800 "C with an increasing force, a stress-strain diagram of the shape shown in Figure 5 is obtained. It can be seen that up to the maximum load before the concrete approaches catastrophic failure, the deformation of the material is apparently elastic. For the material of mix 4, consisting of blast furnace slag and aluminate cement, the maximum load before failure drops off rapidly with temperature and is less than 800 psi at 1200 "C as listed in Table IT and illustrated in Figure 5. A t 1200 "C a gradual increase of the load above 500 psi produces plastic flow and a considerable deformation of the piece. Figure 6 illustrates load deflection curves at various temperatures of concrete utilizing slag from production of high-carbon ferrochrome and alumina CA-25 cement. It will be noted in Table I1 and Figure 6 that the samples of mix 5 did not fracture up to 900 "C under a pressure of 3200 psi (the maximum load attainable) and did not show plastic flow up to 1200 "C. Thus, the incorporation of ferrochromium slag into the mix configuration improved considerably the high-temperature properties of the concrete as compared to a formulation using blast furnace slag as the aggregate. Summary and Conclusions Concrete made with Portland cement retains its initial strength up to 650 "C maximum. At and above 700 "C the strength of the block deteriorates rapidly. In other words, the useful life of concrete made with Portland cement is limited to temperatures up to 700 "C. This holds regardless of the type of aggregate used. Calcium aluminate cement, CA-25, is superior to Portland cement Type IIIA as hydraulic binder for refractory concrete since the aluminate cement is capable of producing a strong room temperature bond. Further, CA-25 cement starts to form
at 700 "C a fired bond with the aggregate. Based on room temperature strength of fired bodies, graded ferrochromium and chromium silicide slag, in combination with alumina cement CA-25, outperform graded blast furnace slag as the aggregate. In addition, at temperatures above 800 "C, and under load, blast furnace slag-type concrete shows plastic deformation. Based on strength measurements, the optimum composition for high-temperature graphitizers is a concrete mix consisting of graded ferrochromium slag and calcium aluminate cement (Wallouch, 1974). The entire aggregate must be well graded from coarse to fines and contain at least 50% of sized slag which should pass through a 14 mesh screen (Tyler series). The cement-to-aggregate ratio in the mix is (1:4) and the water-to-cement ratio W/C = 0.60. The above-optimum sideblock material for graphitizing furnaces has outstanding nonspalling and noncracking characteristics after repeated heating to 1200 "C and subsequent cooling. Acknowledgment The authors wish to thank Airco Carbon management for permission to publish the results of this project. Literature Cited Arnould, J., Chim. Ind., 70(6) 1081-1085 (1953). ASTM Method, C-133-55 (1971). Coss, H. T., Kent, N. J., Ceram. Age, 20(6) 212-14, 241 (1932). Fedynin, N. I., Krivosudor, Iu. S., Beton ZhelezobetOn(Moscow)14(7), 14-16 (1968). Giles, R. T., Bull. Am. Ceram. SOC., 18(9) 326-32 (1939). McGrue, W. M., Blast furn. Steel Rant, 25(6) 624-27 (1937). Pole, G. R., Moore, D. G., J . Am. Ceram. SOC., 29(1) 20-24 (1946). Taylor, W. H., "Concrete Technology and Practice", 3rd ed, American Elsevler Publishing Co., New York, 1965, Chapter 29, pp 409-415. Wallouch, R. W., US. Patent 3 7 9 8 0 4 3 (1974).
Received for review December 17, 1979 Accepted April 22, 1980 This paper was presented a t the 14th Biennial Conference on Carbon, The Pennsylvania State University, June 25-29,1979.
Improved Analysis of Copolymerization Involving Participation of Comonomer Complexes Rudolf E. Cais, Ronald G. Farmer, David J. T. Hill, James H. O'Donnell," and Paul W. O'Sulllvan Department of Chemistry, University of Queensland, Brisbane, Australia 4067
Interaction between comonomers may lead to formation of an association dimer or donor-acceptor complex, which may participate in copolymerization. Probability theory has been used to derive equations relating the copolymer composition and sequence distribution for a particular comonomer composition to the equilibrium constant for complex formation and six reactivity ratios. A multidimensional, least squares, minimization procedure is described for deriving "best estimates" of these parameters, without recourse to approximations. Measurements of sequence distributions, for example by 13C NMR, provide a method to confirm the involvement of comonomer complexes. Physical and mechanical properties of copolymers are influenced by sequence distribution and hence by complex participation in the copolymerization.
Introduction The usual mechanism of copolymerization between two monomers comprises four propagation reactions involving addition of each monomer molecule to a propagating chain having either monomer as the terminal unit. These re0196-4321/80/1219-0412$01.00/0
actions, 1-4, for two monomers represented by 0 and 1are -o+o--0 (1) -0 1 -1 (2) -1 0 -0 (3)
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0 1980 American Chemical Society
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