2473
Kinetics of Two Simultaneous Second-Order Reactions
Conclusion cyclic voltammetry has proven to be a quick, easy method for qualitatively testing electrolytes as to their suitability for electrolytically doping silicon. The incorporation of cathodically lithium or arsenic into the electrode - deposited material is characterized by a broadening of the reoxidation peak or its resolution into two peaks, as compared to the dissolution from an essentially inert electrode material such as platinum. The more anodic dissolution peak which arises from the incorporated metal is enhanced by slower voltage sweep rates. Both lithium and arsenic showed a high reversibility of the primary incorporation which, at least in the case of lithium, is partly of a direct electrochemical nature. A secondary chemical reaction between deposited surface metal and the electrode material also leads to alloying. Direct electrochemical incorporation of arsenic into silicon could not be detected. From the dissolution current strengths under similar conditions of concentration, electrode area, and voltage sweep rate it can be estimated that the rate of alloy formation between lithium and silicon is about an order of magnitude larger than that of arsenic with silicon. The validity of the method was subsequently tested by electrolytically doping silicon with lithium and arsenic from the solutions examined here. The penetration of the metal ions from solution into the electrode material was verified by means of secondary ions mass spectroscopy1 and electric resistance measurements.13
Cyclic voltammetry cannot however absolutely exclude that alloying will take place. A very low rate or extent of alloying fails to give rise to.the above mentioned characteristic features in a cyclic voltammogram. The deposition of lithium on Platinum demonstrates this. Acknowledgments. The authors are indebted to Professor Dr. H. P. Fritz of the Institute for Inorganic Chemistry of the Technical University of Munich for the use of laboratory facilities and to Dr. J. 0. Besenhard of the same institute for many useful discussions. Thanks are due to the company Wacker-Chemie, Burghausen, Germany, for providing the silicon material.
References and Notes (1) J. Antula and G. Staudenmair, to be submitted for publication. (2) J. C. Larue, Phys. Status SolidiA, 6, 143 (1971). (3) W. Harth, “Haibleitertechnologle”, 8. G. Teubner, Stuttgart, 1972. (4) A. K. Vljh, “Electrochemistry of Metals and Semiconductors”, Marcel Dekker, New York, N.Y., 1973. (5) A. N. Dey, J. Electrochem. Soc., 118, 1547 (1971). (6) M. M. Nicholson, J. Nectrochem. SOC.,121, 734 (1974). (7) B.N. Kababov, Elektrokhimiya, 10, 765 (1974). (8) J. 0. Besenhardand H. P.Fritz, J. Nectroanal. Chem., 53, 329 (1974). (9) J. 0. Besenhard and H. P. Fritz, Nectrochim. Acta, 20, 513 (1975). (IO) L. Svob, Solidstate Nectron., 10, 991 (1967). (11) M.Shaw and A. H. Remanick, US Report No. 66-37 286 (1966). (12) R. N. Adams, “Electrochemistry at Solid Electrodes”, Marcel Dekker, New York, N.Y., 1969. (13) J. Antula, to be submitted for publication.
Kinetics of Two Simultaneous Second-Order Reactions Occurring in Different Zones Malcolm Dole,* Chang S. Hsu, V. M. Patel, and G. N. Patel Department of Chemistry, Bay/or University, Waco, Texas 76703 (Recelved January 30, 1975; Revised Manuscript Received August 20, 1975) Publication costs assisted by Eaylor University
Equations have been derived for the case of free radicals recombining according to the second-order kinetics with or without diffusion control under the conditions that there are two simultaneous spatially separated recombination reactions but that only the overall free-radical concentration can be observed. The properties of these equations are discussed and methods for determining the three independent parameters in the first case and five in the second developed. The resulting equations have been applied to the interpretation of data obtained in studying the decay of allyl chain free radicals in irradiated extended chain crystalline polyethylene.
1. Introduction Some years ago’ Dole and Inokuti drived the conditions for first- or second-order kinetics of reactions in which the reacting species were isolated in multiple reaction zones, the reaction rate constant being the same in each zone. They did not consider the case where the reaction rate qonstant was different in different zones. In this paper we wish to look into the mathematical consequences of having two reaction zones with different reaction rate constants, but
under the condition that only the overall concentration of the reacting species can be measured. Such a situation would exist, for example, in a second-order recombination reaction between allylic type chain free radicals in the crystalline or amorphous phases of an irradiated polymer such as polyethylene. In the case of the decay of alkyl type free radicals in irradiated polyethylene, Johnson, Wen, and Dole2 demonstrated that the data could be quantitatively interpreted in terms of two simultaneous first-order reac-
2474
M. Dole, C. S. Hsu, V. M.Patel, and G. N. Patel
tions. In the latter case the overall decay was first order in radiation dose, i.e., initial alkyl radical concentration, but not in time. Such reactions have been called composite first order by French and Willard.3 However, the decay of allyl type free radicals, such as -CHpCHCH=CHp, in irradiated polyethylene is neither pure first order nor composite first order. As shown by Wen, Johnson, and Dole4 the decay of the allyl free radicals in irradiated single crystalline samples of polyethylene can be interpreted in terms of a homogeneous, i.e., single zone, second-order decay reaction with diffusion control. However, as will be shown below in other types of polyethylene (PE) such as extended chain crystals of polyethylene, it has not been possible to interpret the data in the same way as in the case of the single crystalline PE. Instead it is necessary to invoke the concept of two second-order reactions separated spatially but occurring simultaneously. It is the purpose of this paper to show how the theory of such reactions can be developed with or without diffusion control and applied to the data. Recently Shimada and Kashiwabara5 have proposed a two phase second-order decay of alkyl free radicals in irradiated single crystalline polyethylene and have assumed that the decay is diffusion controlled. However, their data might possibly be interpreted in terms of two simultaneous first-order reactions as was done by Johnson et a1.2 for alkyl radicals. The possibility of allyl free-radical decay reactions occurring at different rdtes in the amorphous and crystalline phases of irradiated polyethylene has also been suggested by Moshkovskii et aL6 The latter authors did not develop the kinetics of two simultaneous second-order decay reactions. 2. Two Simultaneous Second-Order Decay Reactions without Diffusion Control
Consider two reaction zones whose second-order reaction constants are k f for a fast decay in one zone and k , for a slow decay in the second zone. We assume that the zones are isolated so that there is no interdiffusion of reacting species from one zone to another. If diffusion occurred rapidly between zones so that the system could be considered homogeneous, the overall reaction would be simple second order with reaction rate constant equal to k f + k,. With the above boundary condition of no exchange between zones, we can immediately write the following equations
C
=
1
+
where xf and x s are the mole fractions of the fast and slowly decaying radicals at zero time, respectively; e.g., x f = co,f/ co.
Equation 6 can be rearranged to
making use of the fact that
Before developing methods for determining the unknown constants of eq 7 , let us investigate its properties. First, it is interesting to see what eq 7 reduces to if k , > 1, the slope approaches the value
er, and is defined as the free-radical separation distance within which they react and outside of which the potential of an unreacted radical is independent of position). Combining 20 and 21 we obtain
The slope of a Waite-type4 plot at zero time is given by where p can be defined as a "reduced" reaction rate constant. Remembering that Q - l equals the ordinary second-order rate constant in simple second-order kinetics, it is interesting to point out that for the kinetics developed here d(l/Q)/dt = d{(A
+
Bt)/(l
+
Kt)}/dt = ( B - AK)/(1
+
Kt)2
and inasmuch as ( B - A K ) can be shown to be equal to
-
C+fXs(X$f
- X,I,)'
(25)
Inasmuch as in all the examples studied by us the term involving the intercepts in eq 25 is about three orders of magnitude smaller than the other terms on the right-hand side of (25) we can neglect it and write the initial slope as being equal to X P K ~ x S 2 ~ which , is the same as that found for the nondiffusion controlled case, eq 18. A t long times the slope approaches the ratio KfKg/(Kf K , ) again similar to that found fnr the nondiffusion controlled case. Also on setting the intercepts equal to zero in eq 24 we recover the nondiffusion controlled case, eq 7. The limiting intercept of the Waite plot at zero time is easily shown to be x?If + xe2IS.
+
+
- XsKsI2
-CoXfX,[XfKf
2 X, K,
Xf'K,
which is always negative, 1/Q must always decrease with increase of t . Therefore, in the case of two simultaneous spatially separated second-order reactions, the reaction rate constant for the overall reaction must always decrease with time; in other words the curve of llc vs. t can never be concave upward (although the curve of the Waite-type plot, Figure 2, can be concave upward over certain time ranges). Mathematical methods for determining the three unknown parameters, A , B , and K , from the data, are given below. However before considering this problem, let us investigate the extent to which the above equations are modified if either or both of the recombination reactions become diffusion controlled. 3. Two SimultaneousSecond-Order Reactions with Diffusion Control Assuming again the same conditions as above, that is, two spatially separated second-order reactions in which only the overall concentration of the reacting species can be measured, but with the rate of the reactions controlled by diffusion within the spatially separated zones, the derived equations are more complicated. Instead of (3) and (4) we now have
4. Methods for Determining the Unknown Parameters of the Equations Inasmuch as the compact expression for Q , eq 15, is not a simple linear equation, the usual method of solving for the constants by the method of least squares cannot be applied. However, it is possible to solve this problem in several ways as outlined below. First, rearrange eq 15 into the form
Q =
L i + (K - B Q ) ~ ~ / A
(26)
If measurements of the overall concentration c are made at equal increments of time At as is easy to do, for example, by means of a minicomputer interfaced with an ESR spectrometer in the case of free-radical decay reactions, we can rewrite (26) for the measurement after the first time interval Q
+
AQ
[I
+
( K - B{Q
+
AQ})(~+
A ~ W A(27)
Subtracting (26) from (27) we find
9-
A t - A
- B[Q
A
+
AQ((t
-t-
At)/At}l
(28)
or where K and I are the slope and intercept of the Waite equation4,7 K
I =
=
4TV$
2?',K/(7fD)i'2
(22) (23)
In eq 22 and 23 D is the sum of the diffusion coefficients of the two reacting species and ro is the radius of the reaction cage (the reaction cage radius is of the order of 10-8 cm while the spatially separated zones containing the fast and slowly reacting species are considered to be very much larg-
K B A-Q/At = - - - Y A A where Y is the quantity in brackets on the right-hand side of (28). The applicability of (28) to the data may be tested graphically by plotting AQlAt vs. Y , and the constants KIA and BIA obtained by a least-squares analysis of the data. To obtain A eq 26 was summed over all values of Q and t and A then calculated from K
I''
A = n ZQi - - E t , + - Z Q i t , A [ A where n is the total number of experimental observations. The Journal of Physical Chemistry, Vol. 79, No.23, 1975
2476
M. Dole, C. S.Hsu, V. M. Patel, and G. N. Patel
Computer routines were developed for all of these calculations. From the definitions of A , B, and K plus the relation, xf x, = 1, it is possible to determine the four constants, xf, xs, kf, and k,, in the following way. Rewrite the definition of A , eq 12, in the form
+
where the subscripts 1 and 2 have been written for f and s (the equations are symmetrical with respect to f and s). Replacing ~ 1 x by 2 its value in (14)
Similarly from (13)
so that the following quadratic equation can be obtained:
The two roots of this equation are x l k l and x2k2. Solving for xlkl, x2k2 is readily found from (32) or vice versa and from (30) (34) Once x 1 has' been determined, x2, k l , and k2 are readily calculated. Having obtained x ~ x, ~ k,l , and k 2 we arbitrarily assign the higher of k l and k2 to kf; this determines also the assignment of x 1 and x2 to x f and x,. In case data are not taken at equal time intervals, the constants A , B, and K of eq 26 can be determined exactly by the following method (which is a general method). Rewrite eq 26 in the form (as written for one measurement QL a t a specific time, t,)
Qr =
Ci
+ czti + COI
(35)
where c1 is A-l, c2 is KA-I, c3 is -BA-l, and y L is t,Q,. Then finding the variation of Zr[Qr,calcd - QL,obsd]2with respect to each of the constants c1, c2, and c g and setting the variation equal to zero, it is possible to derive the equations CQi =
+
VZC~
CzZtt
+
~3CQiti
+ czZti2 + ~3CQiti' + c z C Q i t i2 + c ~ C
CIiQt = c i C t , C&t2ti = c i C Q i t t
(36) (37) Q(38) ~
in which n is the total number of data points used in the least-squares calculation. The three eq 36, 37, and 38 contain three unknown constants c1, c2, and c3 which are easily found by suitable algebraic manipulations, and from these constants it is easy to calculate A, B, and K. Computer routines were developed for these calculations. Alternatively, the constants of eq 35 can be found by the use of matrix algebra (eq 39). Equation 39 can also be writ-
ten AC = B. A is a symmetric coefficient matrix. The column vector C is obtained from C = A-IB by finding the inverse matrix of A. Using computer programs for the soluThe Journal of Physical Chemistry, Vol. 79, No. 23, 1975
tion of matrices, the constants CI, c2, and c3 can be found and printed out and from them the desired quantities A, B, and K readily follow. Although considerably more complicated, the constants of eq 24 can also be estimated by the least-squares method described above. The required equations will not be given here because they were not applicable to the data given in the Experimental Section.
5. Application to Experimental Data Although the major application\ of the above equations will be reserved for later publications we give here one example of the application of experimental data to the equations for two simultaneous second-order spatially separated free-radical recombination reactions without and with diffusion control. A sample of extended chain polyethylene8 was used. Its density was 0.993 at 25'; it was irradiated to 7.6 Mrads a t 77 K, and then heated to room temperature or higher to remove all chain alkyl radicals, -CH&HCH2-, before studying the kinetics of the chain allyl radical decay. In contrast to earlier studies4 of allyl decay on single crystalline PE there was no significant allyl decay until temperatures above 90' were reached. Allyl free-radical concentrations were measured by means of a Varian E-4 EPR spectrometer coupled to a 620/i mini-computer SpectroSystem-100 interface system as previously de~cribed.~ The t ~ computer could be programmed to read ESR peak heights after equal increments of time. Reciprocal allyl radical concentrations are plotted in Figure 1 according to simple second-order kinetics where the pronounced curvature of the data especially at times less than 50 min is readily seen. Parenthetically, it can be noted that the approximately linear section of the curve at long times does not extrapolate to a value of co/c equal to 2 a t zero time as found by Bart19 in his study of the decay kinetics of free radicals in vacuum-irradiated polyvinyl chloride. The curvature of the plot of Figure 1 a t short times suggests the possibility of a diffusion-controlled secondorder recombination r e a ~ t i o nFigure .~ 2 illustrates a Waite plot of the decay data where if the reaction were a simple second-order diffusion-controlled reaction, the curve should be linear with a finite value of (l/c - 1/co)/t1/2 a t zero time.4 Again a pronounced curvature is seen. Attempts to interpret the data in terms of two simultaneous first-order decay reactions2 were equally unsuccessful. ~ With ~ ~the~failure of simple second-order or diffusion-controlled second-order kinetics to agree with the data, we then made a large scale plot of Q vs. time, and from this smoothed plot values of AQlAt were calculated a t equal time intervals and used in eq 29 to determine the constants of eq 7 as described above. We also calculated the constants by means of the set of eq 36,37, and 38 and by means of the matrix method, eq 39. The last two calculations yielded identical results as expected. The constants obtained are listed in Table I along with the standard deviation of the calculated allyl concentration values as compared to the observed defined by the equation
where n is the number of concentration measurements, 61 in this particular case. The standard deviation divided by the initial concentra-
2477
Kinetics of Two Simultaneous Second-Order Reactions
TABLE I: Constants Used in the Calculations Involvine Ea 7. 15. and 24a
2.00 ALLYL DECAY E C 120. 7 . 6 MRAD
Eq 7 and 15 Method
A B K x,
I 150
100
200
Figure 1. Second-order plot of the decay at 120' of chain allyl free radicals in irradiated polyethylene. Solid line calculated by means of eq 6 using constants of Table I as calculated from eq 29.
Eq 36-39
Eq 24
1.241 X lomzo 1.159 X 1.339 X 1.072 X 6.07 X 5.086 X l o m z 0.121 0.134 0.879 0.866 7.27 X 5.60 X 2.21 X 2.12 X
0.10 0.90 k , o r K~ 7.27 X lomi9 k, or K , 2.00 X If 9.59 x 10-20 I, 0.52 x std dev 2.65 X loi5 2.48 X 1015 2.70 X loi5 a For all calculations, co = 7.814 X lo1' spins cm-3; A , k, and K in X*
50
Eq 29
units of cm3 spins-1 min-1; I in units of cm3 spins-1 min-1 in units of cm3 spins-* min-2; and K in units of min-1.
2; B
ALLYL DECAY E C 120.
(
1 4
8
12
9
)
t
x lo-2o
Figure 3. Test of eq 26 using constants of Table I as calculated from eq 36, 37, and 38. Solid line drawn with unit slope as required by theory. c in units of spins ~ m - ~t i n. minutes.
16
Figure 2. Waite-type plot4 of the data of Figure 1. Solid line calculated using c values from eq 6 and constants of Table 1. Dotted line calculated from eq 24 using constants of Table l. c in units of spins ~ m - ~t i n. minutes.
tion in percentage units is 0.32%in the case of the calculations based on eq 36-39; 0.34%in the case of eq 29. This error calculation shows that determination of the parameters A, B, and K by any of the above methods gives results identical within the experimental uncertainty of the data. In Figures 1and 2 the solid line represents the theoretically calculated values for the nondiffusion controlled case. The agreement with the data is excellent in Figure 1,but in the case of the more sensitive Waite-type plot, Figure 2, the trend of the data at times less than about 60 min seems to be slightly different from the calculated trend. The deviation of the experimental values from those calculated theoretically a t short times can also be seen in Figure 3 where the experimental values of the Q function are plotted ac-
cording to the linear relation, eq 26. The A, B, and K constants used in this calculation were those determined from eq 36, 37, and 38. The straight line of Figure 3 has been drawn with unit slope as required by theory. Again the data a t very short times deviate from the theory. A more sensitive plot is obtained by plotting the Q function as a function of the square root of the time as illustrated in Figure 4. The simple Waite equation for a one component system: namely
where I is the intercept and k the slope of curves of the type of Figure 2, can be rearranged to
The Journal of Physical Chemistry, Vol. 79, No. 23, 1975
2478
M. Dole, C. S.Hsu, V. M. Patel, and G. N. Patel
EC
PE
ALLYL
both of the slow and fast decay reactions, If/I,= (Kf/Ks)ll2. Based on this assumption we then found If and I , equal to 9.59 X and 0.52 X cm3 spins-l min-Il2, respectively, using the values for k f and k , obtained from eq 3639, see Table I. A t this point we should explain that an attempt was made to determine the six constants of eq 24, xf, x s , Kf, K,, If,and I,, by the exact methods described above for the nondiffusion limited case. The mathematical equations derived were considerably more complicated and will not be given here. Unfortunately, the constants so determined were physically unrealistic; that is, negative values for some of the constants resulted. Apparently, in order to produce the smallest net sum of the square of the deviations, the calculation pays more stress to the many points collected at long times than to those at short times. Having obtained If and I , we then readjusted the constants xf, x , , and K, slightly to obtain the best agreement of eq 24 with the data. These constants are also given in Table
120. DECAY
I.
Figure 4. Q as a function of the square root of the time. Solid circles, experimental points; solid and dotted lines, calculated from eq 24 and 15 respectively using the constants of Table I. c in units of spins ~ m - t~ in. minutes.
TABLE 11: Constants of the Waite Equation for Diffusion Controlled Two Simultaneous and Spatially Separated Second-Order Reactionsa
If only the lowest 16 Q values of Figure 4 are considered, the standard deviation of the data from eq 24 is 1.56 X 1Ol5, less than any of the standard deviation values of Table I. Using the equations4 Yo = [(1/4)*(1/K)l"3
D = K/(4T'Yo) we next calculated the values given in Table I1 of ro and D for the slow and fast reactions. If the above diffusion-controlled kinetic theory for the yo, f yo, s D, D, two simultaneous but spatially separated second-order reactions is physically reasonable, then the values of r and D 9.25 x lo-* 9.45 x 1.04 x lomi4 2.8 x lo-'? should be within physically possible limits. This is true for Reaction in Amorphous Phase Only the data of Table 11, but it should be pointed out that the 1.42 x lom8 3.01 x lo-* 2.43 x lo-'' 2.85 x close agreement between rO,f and ro,, is a consequence of our assumption that If = Is(Kf1'2/Ks1'2). In our previous4 apAssuming 10% Melted at 120" plication of diffusion-controlled kinetic theory we pointed 2.21 x 4.70 x 5.93 X 10"' 6.90 x lomi8 out that if all of the decay reaction occurred in the amora ro values in cm, D values in cm2 sec-1. phous zones, the initial concentration was increased by the factor aV-l where a,, is the volume fraction of the amorphous phase. This means that in this case the rO,f and ro,, which shows that at zero time, Q should extrapolate to zero. This dlso follows for the case of two simultaneous secvalues would be reduced by the factor and ond-order reactions with diffusion control as can be shown ( ~ , a , , )and ~ / ~Df and D, values by the factor fa,,)^/^ and by a suitable rearrangement of eq 24. Thus a plot of Q vs. ( ~ ~ a , , respectively. )~/~, In the sample of PE used in this t1I2is very revealing in that if Q extrapolates to a finite work a,, was 0.036 at 25'. Table I1 contains ro and D values *nonzero value, the reactions. are not diffusion controlled, calculated assuming that all of the decay reaction occurred but if Q approaches zero at zero time, the reactions are difin this small amorphous volume fraction. However, the refusion controlled. The two lines of Figure 4 represent theoaction occurred at 120° where the PE had probably meltretical values of Q; the dotted line was drawn from values edlo about 10% raising av to 0.136. Therefore, we have also of Q calculated from eq 15 using the A, B, and K constants included ro and D values calculated for this volume fracof Table I for the nondiffusion case (constants derived tion. from eq 36-39) while the solid line was calculated theoretiIn conclusion we can state that the assumption of two cally from c values obtained from eq 24 using the constants spatially separated diffusion-controlled second-order reacof Table I obtained as described below. The data agree bettions gives the best interpretation of the experimental data. ter with the diffusion-controlled theory than with the nonAcknowledgments. This research was supported by the diffusion-controlled case. It is obvious that to obtain a clear U.S. Atomic Energy Commission and by income from the differentiation between these two possibilities accurate exchair in chemistry endowed at Baylor University by The perimental data at very short times are required. Robert A. Welch Foundation. We thank D. Turner of the To determine the constants of the diffusion-controlled Mathematics Department of Baylor University for helpful eq 24 we proceeded in the following way. suggestions. First we estimated from Figure 2 that the value of x$If xg21y,the limiting intercept, was equal to 0.54 X cm3 References and Notes spins-' mini/2. According to eq 22 and 23, I = 4 r 0 ~ ~ ~ (1) ~ ~M. 'Dole ~ and ; M.Inokuti, J. Chem. Phys., 39,310 (1963). ( 2 ) D. R. Johnson, W. Y. Wen, and M. Dole, J. Phys. Chem., 77, 2174 hence if ro, the size of the reaction cage, is the same for
+
The Journal of Physical Chemistry, Vol. 79,No. 23, 1975
2479
Electronic Spectra of Trapped Electrons (1973). (3) W. G. French and J. E. Willard, J. Phys. Chem., 72, 4604 (1968). (4) W. Y. Wen, 0. R . Johnson, and M. Dole, J. Phys. Chem., 78, 1798 (1974). (5) S. Shirnada and H. Kashiwabara, Polym. J.,8, 448 (1974). (6) A. S. Moshkovskii, V. V. Panasenko, E. G. Yarmilko, and A. M. Kab-
akchi, Sov. Prog. Chem., 37, 60 (1971). (7) T. R. Waite, Phys. Rev., 107, 463 (1957). (8) Kindly donated by Professor B. Wunderlich of Rensselaer Polytechnic Institute. (9) A. Bartl, Makromol. Chem., 134, 169 (1970). (10) B. Wunderlich. Thermochim. Acta, 4, 175 (1972).
Electronic Spectra of Trapped Electrons in y-Irradiated Organic-Mixture Glasses at 77 K 1.Ito, N. Ujlkawa, and K. Fuekl' Department of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Nagoya, Japan
(Received May 29, 1975)
Publication costs assisted by Nagoya Universiiy
An optical absorption study has been made of trapped electrons produced in y-irradiated organic-mixture glasses at 77 K. Electronic spectra were observed for trapped electrons in a variety of binary-mixture glasses which consist of solvents with various polarity. Optical parameters obtained from the observed spectra are reported. The spectra of trapped electrons have the only one absorption maximum in all of the mixture glasses studied except for 2-propanol-3-methylpentaneglass. The absorption maximum in the spectrum of trapped electrons in a mixed solvent is located a t a wavelength between those in pure component solvents, the wavelength depending on the mixture composition. There are two absorption maxima in the spectrum of trapped electrons in 2-propanol-3-methylpentaneglass, each maximum corresponding to that in its component spectrum. Changes in the trapped-electron spectra with composition of the mixtures are interpreted in terms of the polarity and structure effects.
Introduction In the last decade extensive studies have been made of electronic spectra of trapped electrons in organic glasses a t low temperat~res.l-~ Optical studies of trapped electrons provide valuable information on the nature and properties of the ground and excited states of trapped electrons and often complement magnetic studies of trapped electrons in the interpretation of their structure. In the present work we have made an optical absorption study of trapped electrons produced in y-irradiated organic-mixture glasses at 77 K. Electronic spectra were observed for trapped electrons in a variety of binary mixture glasses: 1,2-propanediamine (1,2-PDA)-triethylamine (TEA), see-butylamine (s-BuA)-TEA, 2-methyltetrahydrofuran (MTHF)-TEA, ethanol-TEA, s -BuA-ethanol, diisopropylamine (D1PA)-ethanol, s-BuA-3-methylpentane (3-MP), MTHF-3-MP, and 2-propanol-3-MP. Optical parameters of trapped electrons were obtained from the observed spectra. Changes in the spectra with composition of the mixtures are interpreted in terms of the polarity effectthe polarity of matrix molecules influences significantly the optical properties of trapped electrons-and of the structure effect-the molecular structure of matrix molecules affects the trapped-electron spectra. Experimental Section 1,2-PDA, s-BuA, DIPA, and TEA were Tokyo Kasei guaranteed reagents and purified as previously described.4 Aldrich MTHF and 3-MP were purified by passage through a column of activated silica gel followed by distilla-
tion and were dried with a freshly prepared sodium mirror. 2-Propanol was a Kishida Chemicals guaranteed reagent and used after distillation. Ethanol was Hayashi Pure Chemicals purest grade and used as received. Samples were degassed and transferred to quartz optical absorption cells (optical path length 5 mm) and irradiated by 6oCo y rays at 77 K in the dark. The dose given to the samples was 2.6 X 10lS eV g-l. Optical absorption measurements were carried out with a Hitachi Model 323 spectrophotometer. Spectra of trapped electrons were obtained as the difference between the spectra observed before and after photobleaching of y-irradiated samples.
Results The experimental results are given in Figures 1-9 and Tables 1-111. Mixtures Containing TEA. Figure 1 shows electronic spectra of trapped electrons in 1,2-PDA-TEA mixtures. Curves a, b, c, d, and e represent, respectively, the spectra for pure 1,2-PDA, 75 1,2-PDA-25 TEA, 50 1,2-PDA-50 TEA, 25 1,2-PDA-75 TEA, and pure TEA. Here and in what follows, the fraction of a mixture component indicated by a number is given in units of mol 96. It can be seen in Figure 1 that there is the only one absorption maximum in all of the spectra, which shift to longer wavelengths with increasing fraction of TEA. The wavelength A,, at the absorption maximum is 980 nm for pure 1,2-PDA, is 1680 nm for pure TEA, and lies between these two wavelengths for the mixtures. It is also seen that there is a large spectral shift between curves b and c, i.e., between a 75 1,2-PDA-25 TEA mixture and a 50 1,2-PDA-50 TEA mixture. In Table The Journal of Phys/ca/Chemistry, Vol. 79, No. 23, 1975
