J . Phys. Chem. 1990, 94, 5029-5033
5029
Kinetics of Ethane Oxidation on Vanadium Oxide S. Ted Oyama,* Departments of Chemical Engineering and Chemistry, Clarkson University, Potsdam, New York 13676
Ann M. Middlebrook, and Gabor A. Somorjai Department of Chemistry, University of California, Berkeley, Berkeley, California 94720 (Received: August 31, 1989; I n Final Form: January 29, 1990)
The oxidation of ethane with molecular oxygen on a well-characterized V205/Si02catalyst produced ethylene and acetaldehyde as the only selective oxidation products. The effects of partial pressures of ethane, oxygen, and water were investigated at 841 K, and it was found that only water had a strong influence on the overall selectivity. The results were described by a simple sequence of steps. Ethylene was the major product, and its oxidation was studied further to determine whether its secondary reaction affected the kinetic results. A first-order analysis of the reaction network indicated that the oxidation of ethylene and acetaldehyde contributed significantly to the observed kinetics.
Introduction The selective oxidation of alkanes has been receiving increasing attention because of the potential benefits of using these relatively plentiful and inexpensive raw materials to produce chemicals. In studies of the conversion of higher alkanes like propane, butane, and pentanes the main objective has been to replace more expensive olefin feedstocks. In the production of maleic anhydride the use of butane is already a well-established commercial rea1ity.l-j In the production of C3 allylic oxidation products, investigating the use of propane instead of propylene is an active area of investigation.@ For lower alkanes, notably methane, the research is driven by the existence of vast quantities of natural gas, whose energy content approaches that of petroleum reserves.’ Among the alkanes, the catalytic oxidation of ethane has received the least attention, principally because of the existence of an attractive route to ethylene by nonoxidative cracking.* However, ethane is an abundant component in natural gas and is the primary product of methane conversion by oxidative couling.^ Thus, development of alternative conversion routes is desirable. In this investigation of ethane oxidation vanadium oxide was chosen for study because it is a principal component of many alkane activation catalysts. For example, butane oxidation catalysts are composed of oxides of vanadium and phosph~rusl-~ and propane oxidation catalysts contain oxides of vanadium, molybdenum, and boron.@ Methane oxidation with N 2 0 as the oxidant is catalyzed by vanadium oxide.’0*” A limited amount of work has been already reported on the oxidation of ethane. Catalysts composed of mixed oxides of vanadium and molybdenum have been extensively studied for the oxidative dehydrogenation to ethylene using molecular oxygen,I2 while vanadium oxide itself has been studied using N2O.I3 We find in this study that ethylene was the most abundant product of ethane oxidation. In order to investigate the ethane oxidation kinetics more fully, a limited study of ethylene oxidation was also carried out. An approximate analysis of the ethane reaction network showed that the further oxidation of the products, acetaldehyde and ethylene, was significant and probably limited the achievable selectivity. Experimental Section The catalysts employed in this study were the same ones employed in the companion paper in this j0urna1.I~ The characterization techniques, flow reactor system, gas chromatographic analytical method, reactant gases, and experimental procedures were likewise the same. The additional reactant used in this study, ethylene, was a certified purity grade (Matheson, 99.8%). As with ethane, it was purified from possible sulfur impurities by passage * T o whom correspondence should be addressed.
0022-3654190/2094-5029$02.50/0
through a bed of reduced Ni/Si02 catalyst. The standard conditions for ethane oxidation employed earlier = were used again. Partial pressures of reactants were PCHjCH3 13 kPa, Po, = 28 kPa, PH2O = 10 kPa, and PHe = 50 kPa. Expressed as mole fractions these are Y C H ~ C H=~ 0.13, yo, = 0.28, y H Z O= 0.10, and y H e= 0.49. In the case of ethylene oxidation the partial pressures of reactants were PcH2cH2= 2.9 kPa, Pol = 32 kPa, PHlo= 9.3 kPa, and PHe= 57 kPa. The ethane contained a 0.5% ethylene impurity whose presence was taken into consideration in the rate measurements. The partial pressures were chosen so as to be outside the flammability limits of the hydroc a r b o n ~ . ’Again, ~ in all experiments the total flow rate was 73-74 Fmol s-I and the total pressure was 101 kPa. (Flow rates in pmol SKI may be converted to cm3 (NTP) min-l by multiplying by 1.5.) The same amounts of catalysts as employed previously were used. For each experiment weights of catalyst amounting to 7.0 mg of V,05 were loaded, with the total sample weight adjusted to 500 mg with Si02diluent to form a bed of volume 3.1 cm3. Rates were expressed as turnover rates based on surface sites measured by oxygen chemisorption as described earlier. Care was used to ensure that the catalysts were stable at the reaction conditions. The catalysts were pretreated before every run in the 02-H20-He flow mixture without hydrocarbons for 1 h at the highest temperature of reaction. The temperature was then lowered, and the hydrocarbon reactant was added. After having reached the maximum temperature, at the end of each run, a point at lower temperature was taken to verify that catalyst deactivation did not occur. In the case of the partial-pressure
(1) Wohlfahrt, K.; Emig, G. Hydrocarbon Process. 1980, 6, 83. (2) Chem. Eng. News 1987 (Feb 9), 24.
(3) Miyamoto, K.; Nitadori, T.; Mizuno, N.; Okuhara, T.; Misono, M. Chem. Lett. 1988, 303. (4) Ai, M. J . Cata1.*1986, 101, 389. (5) Cavani, F.; Centi, G.; Riva, A.; Trifiro, F. Catal. Today 1987, 1, 17. (6) Komatsu, T.; Uragami, Y.; Otsuka, K. Chem. Lett. 1988, 1903. (7) Saint-Just, J.; Garat, A. Rev.Energ. 1986 (Aug/Sept), 3. (8) Satterfield, C. N . Heterogeneous Catalysis in Practice; McGraw-Hill: New York, 1980. (9) Lee, J . S.; Oyama, S. T. Catol. Rev.-Sci. Eng. 1988, 30, 249. (IO) Zhen, K. J.; Khan, M. M.; Mak, C. H.; Lewis, K. B.; Somorjai, G. A. J . Catal. 1985, 94, 501. (1 1) Iwamoto, M. Japan Kokai Tokkyo Koho 5892630, 1983. (12) Thorsteinson, E. M.; Wilson, T. P.; Young, F. G.; Kasai, P. H. J . Carol. 1978. 52, 116. (13) Iwamatsu, E.; Aika, K.; Onishi, T. Bull. Chem. SOC.Jpn. 1986, 56, 1655. (14) Oyama. S. T.; Somorjai, G . A. J . Phys. Chem., preceding paper in this issue. (15) Coward, H. F.; Jones, G. W. Bulletin 503 US. Bureau of Mines: Limits of Flammability of Gases and Vapors, US. Government Printing Office: Washington, DC, 1952.
0 1990 American Chemical Society
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700
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990
800 Temperature i K
YO0
Oyama et ai.
1 3
11
1
l o 3 i-
Figure 1. Conversion,selectivity,and Arrhenius plots in ethane oxidation: X, conversion; 0, acetaldehyde; 0, ethylene, V, carbon monoxide; A, carbon dioxide.
x Converslaq
0.01k 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1
I
1
I
i
&.i
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
Figure 3. Arrhenius plots in ethylene oxidation: V, 1.4% V20,/Si02; 0.3.5% V,O,/SiO,; X , 1.7% V205/Si02. TABLE 11: Representative Conversion and Selectivity Values in Ethylene Oxidation
T=710K Temperature
1
SiO, I .4% V,05/Si0,
K
Figure 2. Conversion and selectivity in ethylene oxidation: X, conversion; 0,acetaldehyde: V,carbon monoxide; A,carbon dioxide. (a) SO,; (b) I .4% V205/Si02;(c) 3.5% V205/Si02;(d) 7.7% Vz05/Si02.
3.5% V205/SiOz 7.7% VzO,/SiOz
SO2 TABLE I: Representative Conversion and Selectivity Values in Ethane Oxidation
8 3 8 2
I .4% V205/Si0, 3.5% VzOs/SiO, 7.1% V20s/SiOz
2 1 1
T = 169 K 28 5 22 37 14
2 1
4 2
5
11
100 98 99 93
2.5 1.1
95 94 97 84
8.6 16 8.1
1.1
T = 800 K
SiO,
T = 710 K
SOl
7.7% V20J/Si0,
0 0
Si02 7.7% V,0s/Si02
0 0.2
1.4% V,O,/SiO, 3.5% V205/SiOz 7.7%) V20s/Si02
T = 769 K 12
68
3
17
1.0
1.4% V205/Si02 3.5% V205/Si02
T = 800 K
Si02 7.7% V20s/Si02
0 0.9
SO2
0.3 4.5
9
65
6
20
3.8
T = 841 K 7.7% V,Os/SiO,
100
1
SiO,
54
12
27
19.5
studies, measurements taken at the beginning of a series were repeated at the end. Carbon and oxygen mass balances of 100 f 5% were always achieved. Partial-pressure dependencies of the reaction rates were measured by varying the flow rate of one reactant, while keeping all the others except helium constant. The helium flow rate was adjusted to maintain a constant total flow rate. As with the rate measurements, each point required 1-2 h for steady state. No deactivation was observed in the course of 16-24-h runs. Results Conversion and selectivity in ethane oxidation and corresponding Arrhenius plots are reproduced in Figure 1. They show that at low temperatures ethylene is the predominant product followed
1.1%V,O,/SiO,
32 31 46 23 20 50 45 41
93 90 93 19
1
3 2 6
1
5 15
T = 841 K 1
IS IS
82 80 84 58
17
5 4 10
11
15 12 32
I5 18 22
TABLE 111: Summary of Activation Energies (kJ mol-') in Ethylene Oxidation ECH~CHO HT E m 130 141 121 34 158
samvle LT 1.4% V,0s/Si02 134 3.5% V205/Si02 127 7 7T V205/S102
~ EC02_ LT
HT
_ E, _
LT
~
146 142 152
~
12 22 14
144 149 160
HT 54 24 62
by carbon dioxide, acetaldehyde, and carbon monoxide. At higher temperatures ethylene and acetaldehyde formation decrease, and carbon monoxide and dioxide formation increase. Values of conversion, selectivity, and turnover rate are summarized in Table I. Conversion and selectivity values in ethylene oxidation in the same temperature region are summarized for Si02and a series of supported samples (Figure 2). As in the previous study, points were taken after the highest temperature was reached, and these
_
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 5031
Kinetics of Ethane Oxidation on Vanadium Oxide
TABLE IV: Kinetics of Ethane Oxidation on 7.7% V,0s/Si02 Experimental Results L'CH2CH2 = kPCH~CH: 96p010073pH204 47 L'CHlCHO
=
L'CO
Uco, = kH2CH2
=
kPCH3CH3' 'spO: 'OPH2O4
kPCHICHll
"Po10 "PH20-'
kPCH1CH3'
29
23p07013P~20-' 23
Rate Expressions = k3(CH3CH20*)
-- k2k3(k3 + k4)-1K11'2PC"CH,P0,''2 [ 1 + Ks-1~2Kl'/4P~,'~4PH2~1/2] k 'PcH~cH,~o~"~PH~o-''~ 0.01
0.1
1
0.1
0.01
UCH~CHO
1
Figure 4. Ethane partial-pressure effect in ethane oxidation: 0, acetaldehyde; 0,ethylene; V, carbon monoxide; A, carbon dioxide.
I
01
0 01
1
N
+ k4)-'KIPCH3CHjP02 [ 1 + KS-1/2KI'/4P021/4PHZ01/2]2 k "Pc H lcH jPo21 l2P H 20-' k2k4(k3
Discussion
i
i
= k4(CH3CH20*)(0*)
--
CH3CH3 Mole Fraction
01
0.01
1
O2 Mole Fraction
Figure 5. Oxygen partial-pressure effect in ethane oxidation: 0,acet-
aldehyde; 0,ethylene; V, carbon monoxide; A, carbon dioxide.
Ethane Oxidation Kinetics. Concentration in this investigation was placed on the 7.7% V205/Si02sample because it is representative of the high-loading supported samples studied earlier. Oxygen chemisorption uptakes and laser Raman spectroscopy indicate that the sample consists of small V 2 0 5 crystallites of size less than 4 nm.I6 The kinetic studies of ethane oxidation were conducted at 841 K where the conversion was 4.5%. This conversion value was sufficiently high so that partial-pressure variations around the standard conditions reported earlier could be easily carried out. The results of the partial-pressure effect experiments (Figures 4-6) are summarized on the top panel of Table IV. The turnover rates for the formation of the various products are given as power rate law expressions. It must be remembered that considerable scatter occurred in the measurements, especially for the ethane and oxygen experiments. Errors of &20% are estimated for these, while for water &lo% is estimated. A reaction sequence that accounts for the observed kinetics is described below: 02
K + 2* 2 20*
-
+ 2 0 * CH3CH20* + HO* C H 3 C H 2 0 *+ O* -kCH2CHz+ HO* + O* CH3CH20* + O* 5 C H 3 C H 0 + HO* + * CH3CH3
0 0 01.
1
10 1 0
.
11
0.01 :
'
'
0.1 '
'
'
'I
1
H20 Mole Fraction
Figure 6. Water partial-pressure effect in ethane oxidation: 0, acet-
aldehyde; 0,ethylene; V, carbon monoxide; A, carbon dioxide. are indicated by arrows and filled symbols. Unlike for the oxidation of ethanol and ethane, in the case of ethylene oxidation deactivation occurred, and the extra points show lower conversions and altered selectivity. Arrhenius plots for the total rate and the formation of C 0 2 , CO, and acetaldehyde are shown in Figure 3. A break in slope occurs at 1 / T = 1.3 X K-I ( T = 769 K). Values of conversion, selectivity, and turnover rate are summarized in Table 11. Activation energies are reported in the low-temperature (LT) and high-temperature (HT) regimes in Table 111. Partial pressure effects for ethane, oxygen, and water vapor in the formation of all products were measured (Figures 4-6). The effect of ethane was positive and of order approximately 1 for all products. The effect of oxygen was also positive, but of order approximately 0.1 for all products. The effect of water was negative and varied for all the products. The actual power rate exponents are reported in the top of Table IV. Because of the difficulty in adjusting the flow rates with the rotometers, considerable scatter was observed, particularly for the measurements of the ethane and oxygen partial pressure effects (Figures 4-6). In these cases the measurements were repeated with fresh samples which are indicated by the symbol variations in each figure.
(1)
k2
K
2HO* & H 2 0 + O* +
(2) (3) (4)
*
(5) We wish to attach no particular significance to the details of the sequence above. The steps simply represent the adsorption and reaction of the reactant ethane, the fast reoxidation of the reduced sites by gas-phase oxygen, and the adsorption of water vapor. The sequence above consists of steps that are all second order in surface species and thus can be solved analytically. Step 3 has been expressed in second-order form, with O* on both sides, as a mathematical convenience. Although possible, we do not present a mechanistic rationale in order to emphasize that the details of the steps are immaterial. There is insufficient data to warrant such close scrutiny. The derived rate expressions are given in the bottom panel of Table IV. They were obtained assuming that the surface oxidation steps 3 and 4 were rate-limiting and that HO* adsorbs competitively. Limiting expressions in power rate form at high coverages of HO* are also given. These equations give reasonable approximations to the experimental expressions: exponents of the order of unity for the hydrocarbons, small exponents for oxygen, and negative exponents for water. The agreement suggests that the sequence above describes the essential (16) Oyama, S. T.; Went, G. T.; Lewis, K. B.; Bell, A. T.; Somorjai, G. A. J . Phys. Chem. 1989, 93, 6786.
5032 The Journal of Physical Chemistry, Vol. 94, No. 12, 1990
features of the reaction steps. Detailed agreement is not expected as the sequence does not incorporate subsequent total oxidation steps which will be shown to be important in the last section of the paper. In this study considerable effort was expended to control the partial pressure of water vapor. This is an important variable in any partial-oxidation investigation because water is one of the products of reaction. As can be seen from the last equilibrium, water vapor partial pressure will have a strong effect on the identity of surface species. Water partial pressure was found not to have an effect at low values comparable to those produced by reaction (Figure 6). The partial-pressure studies were carried out to better understand the mechanism of oxidation of ethane and to determine conditions for higher selectivity. From the summary of the studies (Table IV) it can be seen that ethane and oxygen partial pressures had limited influence on the selectivity. In comparison, the exponents for the effect of water vapor varied considerably from product to product, thus offering a means of controlling the selectivity. Increasing the water vapor partial pressure increased the relative formation of ethylene and acetaldehyde over COX. The trade-off was a decrease in rate. The reason for the decrease in rate can be understood qualitatively from the reaction sequence. At higher H 2 0 partial pressures equilibrium (5) is shifted to the left which consumes 0" and produces HO*. This in turn leaves less O* sites available for ethane adsorption. It must be recognized that the increase in selectivity with water partial pressure is due in part to a decrease in conversion. However, the influence of HzO on all products is not uniform and its primary effect is probably related to its control of surface coverage by O*. Water vapor is expected to have a beneficial effect on selectivity through its depressing action on the surface O*/HO* ratio. This is because total oxidation entails a higher molecularity in O* than partial oxidation and therefore should be suppressed as the O*/HO* ratio decreases. This helps explain the H,O partial-pressure exponents of the various products. The magnitudes of the exponents are small for ethylene, intermediate for acetaldehyde, and large for CO and COz. Thus, they track with the number of oxygen atoms involved in the formation of each product. Ethylene Oxidation. The study of the oxidation of ethylene was undertaken as part of this investigation because ethylene was the most important product of ethane oxidation. It was also desired to check the structure sensitivity of the reaction. It was found that the catalysts deactivated in the course of the reaction, probably starting at 769 K, where the break in slope occurs for the Arrhenius plots. The breaks in slope are not due to the onset of mass-transfer limitations. The decrease in the rate of reaction is evident from the points marked by arrows and dark symbols taken at the end of each run (Figure 2). If mass transport limitations were involved, the activation energies would have dropped only by a factor of about 2 , not 3-10 (Table 111). The deactivation is likely to have been due to the excessive heat released in the reaction. Compared to ethanol or ethane oxidation, ethylene oxidation produced much greater amounts of unselective products with high heats of reaction. At 769 K, ethylene conversion was 14% and, from the product distribution, the heat released in the 3.1-cm3 bed was 0.35 J s-l. Above 769 K much more heat was released. For ethanol oxidation no heat-transfer limitations were found even at 90% conversion at 620 K where heat released was 0.01 1 J SKI. In the case of ethane oxidation, at the highest temperature investigated, 870 K, conversion was 15% and heat liberated was only 0.083 J s-l. In the calculations above heat released has purposefully been expressed extensively in J s - I , not J mol-' s-l, because the partial pressures of reactants were different for each case. It is clear that for the ethylene oxidation the combination of heat released, temperature, and hydrothermal conditions contributed to the deactivation. For ethylene oxidation in the region below 769 K, unfortunately conclusions cannot be drawn about the structure sensitivity either. For this reaction the blank due to the silica support was excessive
Oyama et al.
CH
Figure 7. Reaction network in the oxidation of ethane.
TABLE V: Kinetic Network for the Oxidation of Ethane
d[CH2CH21= kb[CH3CH3]- k,[CH2CH2] - k,[CH2CH2] dr d [CH,CHO] = ka[CH3CH3] + kc[CH2CH,] - k,[CH,CHO] r-. lr I d[Coxl 2 di
- kd[CH3CH3]ik,[CH2CH2]+ k,[CH,CHO]
[COX1 = I 2 [CH3CH3I0 I
[cH3CH 31
[CH&Hd [CH3CH3I0 [CH3CH3l0
and dominated the reaction on the catalyst (Figure 2, Table 11). The high activity of the silica may have been due to its ability to hydrate ethylene to the even more reactive ethanol. Approximate Analysis of the Reaction Network. From the results above it is clear that the rate of ethylene oxidation is high and produces mostly COz and that this oxidation occurs to a significant extent on the SiOz support. A critical question is, what are the contributions of ethylene and acetaldehyde oxidation to the overall selectivity in the ethane oxidation studies? To answer this question, a first-order kinetic analysis of the network was carried out. Figure 7 shows the reaction network, and Table V shows the model and its analytical solution. It must be recognized that this is a very simple model used only to gain a perspective on the magnitude of the contributions of ethane and ethylene to the reaction products. Linear models such as these must be treated with caution as they do not take into account competitive adsorption by different species. However, at the conditions of this analysis, 841 K, the conversion is only 4.5% and surface converages should be low. The rate expressions discussed earlier indicate that the surface is predominantly covered by HO* at these conditions, and thus competitive adsorption effects may be small. Rate parameters, k,-k,, were evaluated by using the available kinetic data at 841 K (Table V). For the case of ethylene, where deactivation occurred, rate data were extrapolated from the
J . Phys. Chem. 1990, 94, 5033-5040 TABLE VI: Kinetic Data at 841 K for the Ethane Reaction Network reaction vi, ks-l rate parameter, cm3 s-I CHXH, -+ CHaCHO 1.4' k . = 1.2 X CHiCH; CH;CH2 10.5' kb = 4.3 X CH2CH2 CH3CH0 2.4b k, = 3.4 x 10-21 CH3CH3 2C0, 7.6" kd = 6.0 X CH2CH2 -+ 2C0, 576 k, = 8.0 X CH3CHO 2C0, 200c k , = 5.1 x 1049
--
-
+
From Table I, using the reported selectivities. Extrapolated from the low-temperature region of the ethylene oxidation data. CApproximatedby ethanol oxidation data (ref 14) extrapolated to the conditions of this study. TABLE VII: Sources of CHICHOand COXCalculated from the Model in Table IV % oroduct originated from
product CH3CHO COX
CHJCHi
CHZCH2
CHJCHO
97 25
3 41
34
low-temperature region. For the ethylene reaction the rate parameters were obtained directly from vi = kiC2 where vi is the turnover rate for product i formation, ki is the rate constant, and C2 is the number density of ethylene (7.1 X l o i 7 cm-j, for PCHICHl = 2.9 kPa). For the ethane reaction the rate parameters were obtained by solving the model equations (Table IV) using the number density of ethane (3.2 X IO1* for PCH,CH, = 13 kPa). For the acetaldehyde reaction the rate parameter kf was estimated to be that of the ethanol oxidation reaction by using previously reported rate data and activation e n e r g i e ~ . 'This ~ is a gross estimate justified because the entire analysis is only approximate. From these rate parameters and the model it becomes possible to determine what the contribution of the further oxidation of
5033
acetaldehyde and ethylene was to the overall selectivity (Table VI). It can be seen that, for the production of acetaldehyde at 841 K, 97% came from ethane and 3% from ethylene. For the production of COX,25% came from ethane, 41% from ethylene, and 34% from acetaldehyde. Thus, it appears that the further oxidation of the intermediate products contributes substantially to the final product distribution. This is surprising, considering that the conversion is only 4.5%. However, this analysis indicates that considerable care must be placed in the interpretation of kinetic data where highly reactive products are produced, such as in selective oxidation reactions. This caveat applies to the results presented in the first part of this paper, and it is for this reason that the results were not given detailed interpretations.
Conclusions 1. In ethane oxidation a simple sequence of steps accounts for the partial-pressure exponents measured in this study. 2. Variation of the water vapor partial pressure offers the greatest means of control of product selectivity. 3. Studies of the oxidation of ethylene on supported vanadium oxide catalysts were hampered by the high activity of the silica support and by deactivation of the catalysts at high temperatures. 4. Extrapolation of the low-temperature data for ethylene oxidation allowed the use of a kinetic model of the ethane oxidation network. The model indicates that at the conditions of this study a substantial amount of overoxidation of products occurs. Acknowledgment. The experimental work was carried out at U.C. Berkeley with support from the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U S . Department of Energy, under Contract DE-AC03-76SF00098. The paper was written at Clarkson University with support from the Director, Division for Chemical and Thermal Systems of the National Science Foundation, under Grant CTS-890998 1. Registry No. V 2 0 5 , 13 14-62-1 ; CH3CH3, 74-84-0.
Adsorption of Random Copolymers from Solution B. van Lent? and J. M. H. M. Scheutjens* Department of Physical and Colloid Chemistry, Wageningen Agricultural University, Dreijenplein 6, 6703HB Wageningen, The Netherlands (Received: October 13, 1989; In Final Form: February 2, 1990)
In this paper a theory for the adsorption of random copolymers of uniform chain length is presented. The self-consistent-field model of Evers for adsorption of copolymers with a given order of segments within the chains is extended so that the polymer may consist of a statistically determined mixture of molecules which differ in primary structure. The sequence distribution of random copolymers is determined by the average fraction of each segment type in the polymer and by the sequence correlation factors (blockiness). For a fully random copolymer, Le., when the correlation in segment order is absent, the model reduces to a variation of the two-state model of Bjorling et al. for adsorption of PEO, in which the segments assume two energetically different states. For this case, expressions for the average adsorption energy and solvent quality are obtained. Results are given for random copolymers with two different segment types. Chains with a higher than average content of adsorbing segments are preferentially adsorbed from the bulk solution. Only in the beginning of the segment density profile is the fraction of adsorbing segments higher than average. In the remainder of the profile the segment composition is the same as in the bulk solution. The adsorption behavior of random copolymers is remarkably different from that of diblock copolymers. Much higher adsorbed amounts are found for diblock copolymers than for random copolymers with the same average fraction of adsorbing segments. The adsorption of random copolymers is usually less than that of a homopolymer of equal length and consisting of the same type of adsorbing segments. Only for very high adsorption energies are the adsorbed amounts essentially the same. The influence of blockiness and interaction parameters is studied.
Introduction In many colloidal dispersions, copolymers are used as stabilizing agents. In recent years much attention has been paid to the 'To whom all correspondence should be addressed. 'Present address: Bayer AG, Zentrale Forschung-TPF 1 , Bayerwerk, D5090 Leverkusen, FRG.
0022-3654/90/2094-5033$02.50/0
adsorption behavior of block copolymers, both e~perimentallyl-~ and thmreticallY.3-'0 In Practice, copolymers often have a random ( I ) Tadros, Th. F.; Vincent, 9. J . Phys. Chem. 1980, 84, 1575. (2) Kayes, J. 9.; Rawlins, D.A. Colloid Polym. Sei. 1979, 257, 622. (3) Hadziioannou, G.;Patel, S.; Granick, S.; Tirrell, M. J . Am. Chem. Soc. 1986, 108, 1869.
0 1990 American Chemical Society
