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 3798043 (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)
+ +
0 1980 American Chemical Society
+
+
Ind. Eng. Chem. Prod. Res.
-
.-I+ 1 -1 (4) The familiar copolymerization equation which relates the copolymer and comonomer compositions for this mechanism was derived by Mayo and Lewis (1944) and Alfrey and Goldfinger (1944). Most copolymerizations can be described by eq 1-4, but there are some systems which show systematic discrepancies. An alternative mechanism, which includes second-order, or penultimate-unit, effects on the reactivities of the chain propagating species, has been shown to describe some copolymerizations (Ham, 1964). Copolymers with equimolar compositions are formed from some comonomer pairs and the possibility of effective homopolymerization of a 1:l comonomer complex has been considered for many years. The formation of comonomer complexes has been clearly demonstrated in many systems. In fact, some form of interaction is likely for most monomers. Thus, the development of a yellow coloration on mixing two monomers sometimes provides visual evidence for the formation of a charge-transfer complex. The presence and composition of a complex can also be revealed by Job’s method of continuous variation. Measurements of equilibrium constants for complex formation have been made by UV (Booth et al., 1959) and NMR spectroscopy (Cais and O’Donnell, 1975). However, the existence of comonomer complexes does not prove their participation in the copolymerization. Alternating copolymerization may be equally explained by alternative addition of the separate monomers, favored by polarity or steric factors. The equilibrium constant for complex formation and/or the reactivity of the complex may be sufficiently high for the copolymerizationto be essentially homopolymerization of the complex. In this case the copolymer will have a composition close to equimolar, will not vary markedly with comonomer composition, and the sequence distribution will be close to alternating. We are particularly concerned with the general case when the comonomer complex and both monomers contribute significantly to the formation of the copolymer. The complex usually results from a 1:l interaction between the comonomers, but it may have a different composition, e.g. 2:1, in some systems. This usually results from one monomer complexing to the other at two different sites, e.g. a t a double bond and at a polar substituent, in which case a 1:l combination of the two monomers may still be incorporaited into the copolymer. Theory If we consider the case of 1:l complex addition, the comonomer pair may add in either direction and hence, four further, propagation reactions, 5-8, must be considered. -0+5--0 (5) -0+m+-1 (6) -1 + lo- -0 (7) -1+oi--l (8) Appropriate reactivity ratios may be defined according t o eq 9. r1 = kll/klO ro = k,//zol;
PO = koiji/koiij; so = koi6/i’vo1;
P1 = klE/klE
s1 =
(9)
kliji/klO
Our kinetic-probabilistic treatment (Cais et al., 1979) leads to equations expressing the probability (pl(ln))of finding a sequence of 1 units of any particular length in the polymer chain. These expressions allow derivation of
Dev.,Vol. 19, No. 3, 1980 413
B
2 0! 1
\ 1 OODO
-5.0
0.100
5
0
+
5.0
SO
Figure 1. Typical two-dimensional topography of the hypersurface in the region of the minimum for (A) rl, and (B)SO using the “goodness-of-fit” parameter, T, and the search program of Chandler. The parameter range a-b corresponds to values of T 4 27 at the minimum, where T = (Y(l)exp- Y ( l ) d c ) z .Note the difference in abscissa scales for rl and sg.
the equations for the number fraction of sequences of any desired length for each monomer (eq 10).
NA1”) = P,(ln)/
5P1(lrn)
m=l
(10)
Equations for the mole fraction composition of the copolymers Y1 (11)and the triad fractions (12) can also be obtained. Yl = [(I - P,)(PlO + PllO) + (1- PlO)(POl + P00l)l/ [ P l O + Pll0)(2 - Po1 - POO) + (Po1 + P,,)(2 -p 11 P10)I (11) F(010) = [P1(ll)(l- Pll)zl/[Pl(llH1 - P11I2+ P1(12)(2- P1l)l (12) The transition probabilities for the state space of events given by eq 1-8 are represented by P,, POI,PIO, PII,PO^, PG, P l ~and , Pliji, respectively, and are related to the reactivity ratios and the concentrations of the monomers and complex. Results Since the equations for copolymer composition (10) or sequence distributions (11/12) are functions of the six reactivity ratios and the equilibrium constant, they can be used to compute “best estimates” for these parameters, provided sufficient experimental data are available over the full range of feed composition. This can be done by defining a “goodness-of-fit’’ parameter, 7 , which specifies a multi-dimensional hypersurface, for which the “best values” of the reactivity ratios and equilibrium constant (based on the experimental data) correspond to the global minimum in the surface. We have used the direct search Q.C.P.E. program of Chandler (1976) to locate this minimum. The topography of the hypersurface defines the reliability of the calculated parameters. The sharpness of the minimum in any coordinate gives a measure of the reliability of the best estimate of that coordinate. Thus, in Figure 1,a relatively sharp minimum in rl and a shallower minimum in so are shown for calculations on the methyl acrylate-diphenylethylene system (Cais et al., 1979). Despite the mathematical generality of this approach, few systems have been studied in sufficient detail and with
414
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 3, 1980
1.o
1 .o
B .
c
‘
I
10.2
c 0
\
I
0:2
0’4
x,
016
0.8
,lo
\
4 \
0.’2
016
0:4 XI
0:8
!:
Figure 2. Analysis of alternative mechanisms for copolymerization of styrene and maleic anhydride in bulk a t 60 O C : A, copolymer composition; B, number fractions of 010 sequences: ---, penultimate model; -, complex model (unconstrained); - - -, complex model (constrained to single maleic anhydride sequences); Yl = mole fraction of styrene in copolymer; XI = mole fraction of styrene in feed.
sufficient accuracy to allow complete, simultaneous relaxation of all seven parameters. In those cases where insufficient data points are available for a full treatment, and where there is good reason to believe that some of the reactivity ratios approach zero (e.g., one monomer does not homopolymerize), these parameters may be set equal to zero in the minimization. This constraint reduces the dimensionality of the hypersurface and may make unambiguous determination of the global minimum possible. Styrene-Maleic Anhydride. We present an evaluation of the bulk copolymerization of styrene and maleic anhydride as an illustration of our procedure to derive “best estimates” of reactivity ratios and the equilibrium constant. Here the copolymer composition data of Dodgson and Ebdon (1977) was used, and then the number fractions of sequences were calculated from the computed parameters (Farmer et al., 1980). The complex participation model provides a better fit to the copolymer compositions, as shown in Figure 2A, than the penultimate model, which had been proposed by Dodgson and Ebdon to explain the deviations from the terminal model. The sequence distributions calculated for the complex participation and penultimate models differ markedly over most of the comonomer composition range, as shown in Figure 2B, and therefore provide a more definite discrimination between the mechanisms. Moreover, there are significant differences between alternative complex participation models which do, or do not, permit reactions 1 and 6. Discussion Seiner and Litt (1971) developed the first mathematical treatment of the complex participation model, which was an important factor in reviving interest in this mechanism. However, the mathematical procedures described by Seiner and Litt were limited to copolymer systems for which the equilibrium constant was relatively small ( K I 0.01), and in which one of the two monomers formed only single unit sequences in the polymer. By contrast, the present treatment, besides being unconstrained in these ways, also enabled the formulation of expressions for the number fractions of sequences in the copolymer by using a probabilistic approach. Types of Comonomer Complex. Interaction between different molecules must be considered normal, rather than unusual, and some type of comonomer “complex” will frequently be formed, however “loose” this association may be. Complex formation may be usefully classified into (i)
donor-acceptor complexes, which include charge-transfer, Lewis acid-Lewis base, and ion-pair complexes, (ii) hydrogen-bonded complexes, and (iii) association complexes involving van der Waals forces of attraction. The strength of the interaction within the complexes decreases from (i) to (iii) and their importance in copolymerization can be expected to follow the same order. Complexation with Propagating Chains. Apart from the addition of 1:l comonomer complexes as considered in our treatment, interaction may be expected to occur between monomer molecules and the propagating chains, which would be influenced by concentration, solvent, etc., and also by the formation of comonomer complexes. Thus, the comonomer complex may have a significant effect without actually adding to the chain. Solvent Effects. Monomers containing double bonds will interact readily with many solvents via electronic effects, and “inert” solvents are difficult to find. These solvent effects operate in various ways: (i) The solvent molecules compete with the formation of M1-M2 complexes by formation of S-M1 complexes, thus reducing the concentration of the comonomer complex and hence its participation in copolymerization. (ii) The formation of the S-M1 complex may change the reactivity of the monomer M1, thus affecting the copolymerization. (iii) The solvent may enhance the formation and the reactivity of the comonomer complex by interaction to form the complex S-M1-M2. (iv) The solvent may affect the behavior of the propagating chain due to its good or poor solvent power for the polymer, which may produce a steric effect on propagation or termination. Temperature Effects. Temperature is an important experimental variable and can greatly affect complex participation. It will affect (i) the rate constants of individual propagation reactions, and hence the reactivity ratios, according to the usual Arrhenius activation energy relationships, and (ii) the equilibrium constant for complex formation, a reaction which is usually exothermic and also involves a decrease in entropy. Consequently, the equilibrium constant will increase with decreasing temperature, and low polymerization temperatures should enhance complex participation. This has been demonstrated by Seymour and Garner (1978), who have shown that the copolymer composition changed from alternating to random with increasing temperature for the copolymerization of maleic anhydride with styrene, vinyl acetate, acrylonitrile, and a-methylstyrene. Pressure Effects. Pressure is a variable with a potential comparable to temperature for influencing chemical reactions. Rates of individual propagation steps will be increased or decreased depending on the sign and magnitude of the volume of activation. However, the most significant effect in copolymerization is likely to be on the equilibrium constant for complex formation, which should increase with increasing pressure. This is a relatively unexplored field, although Kellou and Jenner (1979) have reported that increasing pressure increased the alternation of the monomers in several maleic anhydride copolymers without distinguishing complex participation. Complex Activation. Initiation of copolymerization by activation of a comonomer complex by UV light or other means is well known for systems where the comonomers form donor-acceptor complexes. However, the participation of the comonomer complexes in propagation reactions should also be capable of activation, but this is a t present an unexplored field.
Conclusions There are many copolymerizations in which charge-
Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 415-421
transfer complexes or association dimers are formed between the two comonomer species. Frequently, a significant tendency toward equimolar incorporation of the two monomers in the copo:lymer is observed, which may result from involvement of the comonomer complex in the copolymerization. The patterned search procedure outlined above enables best estimates of reactivity ratios and the equilibrium constant to be obtained for a general complex-participation mechanism based on copolymer compositions. The equations for sequence distributions can be utilized to give discriminatory tests between possible mechanisms, which may be evaluated by recently developed experimental techniques such as 13C NMR. The material properties of copolymers depend on the overall composition, lbut are also quite sensitive to the comonomer sequence distribution. Future developments in this field are likely to include (i) compilation of more extensive data on copolymerizations to enable reliable evaluation of different mechanisms, (ii) utilization of 13C NMR and other techniques to determine comonomer sequence distributions in many more copolymers, and (iii) selection of polymerization conditions, including temperature and pressure, to maximize the participation of co-
415
monomer complexes and hence control the sequence distributions in copolymers.
Acknowledgment The authors wish to thank the Australian Research Grants Committee and the Australian Institute of Nuclear Science and Engineering for supporting their research.
Literature Cited Alfrey, T., Goldfinger, G., J . Chem. fhys., 12, 205 (1944). Booth, D., Dainton, F. S., Ivin, K. J., Trans. Faraday SOC.,55, 1293 (1959). Cais, R . E., O'Donnell, J. H., Eur. folym. J., 11, 749 (1975). Cais, R. E., Farmer, R. G., Hill, D. J. T., O'Donnell, J. H., Macromolecules, 12, 835 (1979). Chandler, J. P., "Quantum Chemical Program Exchange", 1976, No. 11, p 307. Dodgson, K., Ebdon, R., Eur. folym. J., 13, 791 (1977). Farmer, R . G., Hill, D. J. T., O'Donnell, J. H., J. Macromol. Sci. Chem., A14, 51 (1980). Ham, G. E., in "Copolymerlzation", G. E. Ham Ed., Interscience, New York, 1984, p 10. Kellou, M., Jenner, G..Makromol. Chem., 180, 1687 (1979). Mayo, F. R., Lewis, F. M.. J . Am. Chem. Soc., 86, 1594 (1944). Seiner, J. A., Li, M., Macromolecules, 4, 308 (1971). Seymour, R . B., Garner, D. P., Polym. News, 4, 209 (1978).
Received for review April 21, 1980 Accepted April 28, 1980
Dye Sensitization and Surface Structures of Semiconductor Electrodes Mlchio Matsumura, Shigeyuki Matsudaira, and Hiroshi Tsubomura' Department of Chemistty, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, 560, Japan
Masasuke Takata and Hiroaki Yanagida Department of Chemistry, Faculty of Engineering, University of Tokyo, Tokyo, 113, Japan
The dye-sensitization effects on the ZnO, CdS, and TiO, electrodes in electrochemical photocells were investigated for anionic, cationic, and zwitterionic dyes. The most efficient dye-sensitized photocell was achieved by using an aluminurndoped porous ZnO sinter electrode dyed with rose bengal (an anionic dye), the energy conversion efficiency being i!.5% for incident light of 562 nm. The effect of aluminum doping was attributed to the increase of the porosity (or surface area) of the sinter and the decrease of the electrical resistance. The effect of pH and the added salts in the solution as well as the effect of crystal face were extensively investigated. It turned out that these effects mainly influence the adsorptivity of the electrode surfaces for the sensitizing dyes, not the intrinsic current quantum efficiency. From these results, the structures of the dyes on the semiconductor surfaces were discussed in relation with the mechanism of photoinjection of electrons. The merits of dye-sensitized photoelectrodes as a photoenergy converter were discussed.
Introduction The electrochemicad photocells composed of semiconductor photoelectrodes, metal counterelectrodes, and aqueous solutions of redox systems and supporting electrolytes have been attracting wide attention in recent years from the viewpoint of solar energy conversion. Functionally, the electrochemical photocells are divided into two types-those producing electrical power in the presence of regenerative redox systems and those producing fuels, e.g., hydrogen from water. In either of these two types, however, the semiconductor electrode of an efficient solar energy converter should have 0196-4321/80/1219-0415$01 .OO/O
the following properties, in addition to the fundamental requisite of a good semiconducting material: (1)a band gap (I$)small enough to absorb the main part of the solar radiation lying in the visible region, and (2) sufficient resistivity against corrosion or dissolution. These two requirements seem to be somewhat dilemmatic, for it has been recognized that most materials having narrow band gaps are rather corrosive, e.g., in the case of silicon, gallium phosphide, and cadmium chalcogenides, while relatively stable semiconductors, e.g., titanium oxide and some metal titanates, have band gaps higher than 3 eV and work only with ultraviolet light which
0 1980 American Chemical
Society
