J . Phys. Chem. 1991, 95, 3376-3379
3376
Hy molecular weight is seen. This could not be explained by the theoretical model.
Acknowledgment. We are grateful to Drs. Bengt Jonsson, Svante Nilsson, and Mikael Bjorling for fruitful discussions. Ingegerd Lind is acknowledged for skillful technical assistance
and for drawing most of the figures and Ingela Hillgng, Pharmacia AB, for performing the molecular weight determinations. This work was financially supported by Pharmacia AB. Registry No. NaHy, 9067-32-7; C,,TAB, 2082-84-0 DTAB, 1 1 1994-4; C,,TAB, 1 1 19-97-7.
Turbidity Measurements of Binary Polystyrene Solutions Near Critical Solution Points Weiguo Shen, Careth R. Smith,+Charles M. Knobler, and Robert L. Scott* Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024 (Received: August 27, 1990) Correlation lengths ( I ) and susceptibilities( x ) for three binary mixtures of methylcyclohexane + polystyrene (M,= 13OO0, 23 OOO, and 29 OOO) at various temperatures near the upper critical solution points have been determined by a series of turbidity measurements at various wavelengths and temperatures. The critical exponents v and y have been determined from the temperature dependences of ( and x and are in a reasonably good agreement with the theoretical predictions. The prefactors p and xo, which have been determined by two methods, are uncertain by more than 20%, but their ratio has been determined more precisely.
Extensive investigations of light scattering in the critical region for binary mixtures of cyclohexane with polystyrene samples of different molecular weights were first carried out by Debye et al.’-3 in order to determine the “molecular force range”. More recent light-scattering studies of the same systems4s5were used to determine the behavior of the correlation length ( and the susceptibility x in the critical region, where they are expected to diverge according to
t = t O [ ( T- Tc)/Tcl-”
(1)
x = x O [ ( T -Tc)/Tcl-T (2) The prefactors Fo and xo and the critical exponents v and y are constants, and T, is the critical temperature. The susceptibility and correlation length can be obtained from measurements of the angular dependence of the scattered light or from studies of the turbidity as a function of temperature. This latter method was employed by Puglielli and Ford6 in an investigation of gas-liquid critical phenomena and, more recently, by Jacobs and co-workers’~*in studies of binary mixtures. The relation between the turbidity T , t, and x may be expressed by an integrated form of the Ornstein-Zernike equation6s9 T = (n3/ Ao4) (8n2/84)’kBTXf(~) (3) where A,, is the wavelength of light in a vacuum, kBis Boltzmann’s constant, n is the refractive index of the solution, and I$ is the order parameter. The correlation length enters through the function
with a = 2(2nn(/A#. Jacobs et ala8made a series of measurements of turbidity versus temperature at a fixed wavelength for the mixture polystyrene diethyl malonate. They found it necessary to introduce a background parameter in order to fit the experimental data to eqs 1-4. The fits are sensitive to this extra scattering, and it was found that both prefactors and exponents could not be determined. The least-squares analysis was therefore carried out with y and v fixed at their theoretical values. The parameter a can be varied by changing the wavelength, allowing the susceptibility and correlation length to be determined
+
‘Present address: British Gas Corp., Bristol, England.
from turbidity measurements at a fixed temperature. This is the procedure that we have employed to study binary mixtures of polystyrene samples of three different molecular weights with methylcyclohexane. The critical behavior of such mixtures was previously investigated by Dobashi et a1.I0 and by Shinozaki et al.” Our interest in them arises from their connection to the three-phase equilibria’2 in bimodal mixtures of polystyrene with methylcyclohexane and the character of tricritical points in such ternary polymer + solvent systems.I3
Experimental Section Materials. Methylcyclohexane (>99%) obtained from Aldrich Chemical Co. was dried and stored over sodium wire. Polystyrene samples with weight-average molecular weights 13 000,23 000, and 29000 were purchased from Pressure Chemical Co. The ratias of the weight-average to the number-average molecular weights were reported to be 51.06. The polymer samples were dried in a vacuum desiccator over Pz05for 24 h before use. Preparation of Mixtures. The critical compositions of the mixtures were approached by adjusting the proportions of the two components in order to achieve equal volumes of the two phases. Mixtures were first prepared in 10 mm i.d. glass tubes provided with Ace-Thred connections, which allowed them to be sealed with Teflon caps. Each sample contained about 2 g of polymer. The loading composition was determined by weight and was reproducible to 0.1%. Samples were mixed by continuous end-over-end rotation of the tubes for 72 h while they were simultaneously heated with (1) Debye, P.; Coll, H.; Woermann, D. J . Chem. Phys. 1968,33, 1746. (2) Debye, P.; Woermann, D.; Chu, B. J Chem. Phys. 1962, 36, 851. (3) Debye, P.; Chu, B.; Woermann, D. J . Chem. Phys. 1962. 36, 1803. (4) Kuwahara, N.; Fenby, D. V.; Tamsky, M.; Chu, B. J . Chem. Phys. 1971, 55, 1146. (5) Kojima, J.; Kuwahara, N.; Kaneko, M. J. Chem. Phys. 1975,63,333. (6) Puglielli, V.; Ford, N. C., Jr. Phys. Reo. Lefr. 1970, 25, 143. (7) Jacobs, D. T. Phys. Reo. A 1986.33, 2605. (8) Stafford, S.G.;Ploplis, A. C.; Jacobs, D. T. Macromolecules 1990, 23, 470. (9) Omstein, L. S.;Zernike. F. Proc. K.Ned. Akod. Wer. 1914,17,793. (IO) Dobashi, T.; Nakata, M.; Kaneko, M. J. Chem. Phys. 1980,72,6685, 6692. (1 1) Shinozaki. K.; Hamada, T.; Nose, T. J. Chem. Phys. 1982,77,4734. (12) Dobashi, T.; Nakata, M. J . Chem. Phys. 1986, 84, 5775. (13) Shen, W.; Smith, G. R.; Knobler, C. M.; Scott, R. L. J. Phys. Chem. 1990, 94, 7943.
0022-365419112095-3376%02.50/0 0 1991 American Chemical Society
Turbidity Measurements of Binary Polystyrene Solutions
7'he Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3311
'-
I
I S
IT-Tc1 /Tc
Figure 1. Schematic diagram of apparatus: XE,xenon arc lamp; BS, beam splitter; C, optical cells; WB,water bath; FW,filter wheel; PMT, photomultiplier; PA, preamplifier; AD, A-D converter; SC, shutter controller: M,motor to position cells; SI and S2,shutters.
Figure 2. log 4 as a function of log [(T - T,)/T,]for three polystyrene methylcyclohexane mixtures: 0 , system 1 (M,= 13000); 0, system 2 (M,= 23 OOO); A,system 3 (M,= 29000). The lints are calculated from eq 1 with the parameters given in Table 111.
TABLE I: Critical Values for Methylcyclohexane + Polystyreme Mixtures system tJ0C we system tJ0C we 1 18.190 0.238 3 32.947 0.184 2 29.118 0.197
beam splitter (BS) into two beams, the transmitted beam, which passed through the optical cell, and the reference beam. The intensity of the transmitted beam was always measured with respect to that of the reference beam to minimize the effects of fluctuations in the lamp. Two sample cells (C), one containing the mixture and the other only solvent, were clamped in the cell holder, which could be moved vertically by a screw system. The intensities of the light transmitted through the solvent and sample cells were measured alternately by moving the cells into the beam with a motorized stage. Eight narrow-band-pass filters with wavelengths a t maximum of 3820,3990,4195,4505,5005,5504,6360, transmission ,A, and 6405 A were mounted in a filter wheel (FW), which was placed in front of the photomultiplier tube (PMT). Two shutters (Sl, S2) activated by solenoids were used to control the beam paths. The output of the PMT was fed into a preamplifier (PA), passed through a low-pass filter [(F), Krohn-Hite, Model 33421 set at 6 H z to block high-frequency noise, and fed to a microcomputer via an A-D converter. The computer controlled the sequence of shutter operations and the motor that moved the cell. The angle of acceptance of the optical system was less than 1.7 X lo4 rad. The effect of forward scattering was estimated to be negligible. Two types of measurements were made a t each wavelength: (1) With the solvent cell in the light path, the photomultiplier signal was recorded with both shutters closed, with only S1 open, and with only S2 open, thereby allowing the dark signal Vd and the intensities of the reference beam VI and the transmitted beam Voto be measured. These measurements were repeated 10 times, and an average value of &, [=(Vo- Vd)/( VI - Vd)] was obtained. (2)The same series of measurements was performed with the sample cell in the transmitted beam, and the average of R, [=(V, - Vd)/( Vo- Vd), where V, is the intensity of the beam transmitted through the sample] was obtained. The ratio R (=R,/Ro)was then calculated. Several determinations of R were made, and the average value and the uncertainty were calculated. The precision of the determination of R was usually about 0.5%. The critical temperature of each mixture was rechecked before turbidity measurements were carried out. The turbidity was calculated from
an infrared lamp to keep the mixture in the one-phase region. The tubes were then placed into a water bath in which the temperature could be controlled to within f2 mK and could be measured with a digital platinum resistance thermometer with a reported accuracy of f0.03 OC. The tubes were rotated again for a few hours after the bath temperature was stable. From 12 to 24 h was usually required for the phases to settle and clarify. After phase equilibrium had been reached, the height of each phase was measured at several temperatures with a cathetometer and the height fractions (approximately equal to volume fractions) were calculated. The critical composition was then estimated from the volume fractions, and a new sample was prepared and studied. This procedure was repeated until approximately equal volumes of the two phases were obtained. A sample of critical composition was then prepared in a 5 mm path length optical cell for system 2 (polystyrene M , = 23 000) and in 2 mm path length cells for systems 1 ( M , = 13 OOO) and 3 ( M , = 29000). The cells for systems 1 and 3 were sealed by flaming; that for system 2 was sealed by a threaded Teflon cap. The temperature of phase separation, which was taken as the critical temperature, was carefully determined for each system. The precision of this measurement was 3 mK for systems 1 and 3, but samples made up to the same compositions underwent phase separation at temperatures that differed by as much as 0.1-0.2 K. Such differences can very likely be attributed to uncontrolled amounts of moisture introduced during the sample preparation. System 2, which was sealed with a Teflon cap, showed a 1 mK upward shift in temperature after each remixing that could have been caused by a slow extraction of impurities from the cap. Such shifts were taken into account in the calculation of T - T,. The approximate critical compositions and temperatures for the three systems are given in Table I, in which w, is the mass fraction of polystyrene. Coupling Consrant ( a t ? / & f ~ )The ~ . coupling constant (&?/ad)* and the refractive index of the solution must be known in order to determine the susceptibility and the correlation length from eq 3. The mass fraction of polymer has been discovered to be a good order parameter in these mixt~res.'~ The relations between refractive index, mass fraction of polymer, temperature, and wavelength were obtained from a series of measurements on mixtures of known composition. These calibrations were used to calculate the refractive indices and coupling constants for the particular mixtures studied. Turbidity Measurement. The optical system is shown schematically in Figure I . Light from a 75-W xenon high-pressure arc lamp (XE)passed through a collimator and was split by the
+
T
= (-In R ) / L - T~
(5)
where L is the cell path length. The background turbidity Tb was determined by measurements of R a t temperatures far from T, ( T - T, = 25 K).
Results and Discussion Values of the turbidity a t various temperatures for the three mixtures are listed in Table 11. The total uncertainty in T , including the random uncertainty in the measurement and the nonlinearity of the PMT, is about 0.1 cm-'. The wavelength
3378 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
Shen et al.
TABLE 11: Turbidity (s/cm-’) of Mixtures of Metbylcyclohexane + Polystyrene at a Series of Temperatures and Wavelengths
AIA 1 0 4 ( ~ - T,)/T,
3820
3990
1.064 1.613 2.162 3.673 5.1 14 7.723
16.60 14.50 13.09 10.61 8.49 7.00
14.01 12.24 10.84 8.66 7.06 5.55
4195
4505 System 1 (M,= 13 000) 9.59 11.95 10.43 8.82 9.35 7.45 5.91 7.55 5.88 4.67 4.84 3.78
5005
5504
6360
6405
6.91 5.87 5.30 4.16 3.40 2.62
5.12 4.46 3.86 3.04 2.42 1.83
3.44 2.86 2.52 2.00
1.41
3.47 2.80 2.60 2.05 1.54 1.25
5.68 4.21 3.40 3.00 2.44 1.71 1.36 1.10 0.7 1 0.63 0.46
4.19 3.05 2.46 2.18 1.72 1.19 0.92 0.7 1 0.49 0.40 0.29
2.71 1.95 1.54 1.31 1.05 0.66 0.52 0.37 0.27 0.21 0.13
2.71 1.98 1.50 1.30 1.04 0.69 0.54 0.45 0.27 0.24 0.17
5.97 4.45 3.54 2.82 2.23 1.73 1.41 0.93 0.69
4.35 3.28 2.57 2.00 1.57 I .21 0.98 0.59 0.47
2.85 2.08 1.60 1.18 0.93 0.76 0.43 0.31 0.21
2.81 2.10 1.62 1.25 0.93 0.73 0.50 0.37 0.29
1.so
System 2 (M,= 23 000) 0.959 2.117 3.1 IO 4.430 6.286 9.727 13.30 19.12 24.65 33.08 40.96
10.73 8.79 7.97 6.87 4.96 4.05 3.26 2.40 2.06 1.55
9.17 7.50 6.75 5.75 4.15 3.35 2.75 1.97 1.71 1.28
10.04 7.76 6.31 5.62 4.67 3.43 2.75 2.23 1.58 1.39 1.06
0.883 1.797 2.908 4.443 6.371 8.723 11.40 18.07 23.03
14.63 11.49 9.49 7.8 1 6.43 5.29 4.49 3.13 2.53
12.66 9.80 8.07 6.54 5.40 4.45 3.75 2.61 2.09
10.69 8.30 6.80 5.48 4.46 3.63 3.04 2.14 1.73
8.05 6.02 4.90 4.32 3.57 2.60 2.04 1.60 1.15 0.97 0.70
System 3 (M,= 29000) 8.39 6.41 5.19 4.18 3.36 2.72 2.21 1.51 1.17
TABLE III: Critical Parameters for Metbylcyclohexane + Polystyrene Mixtures
system
P/A
1
II f 2 3.7 f 0.8 2.7 f 0.5
2 3
Y
0.59 f 0.02. 0.65 f 0.02 0.67 f 0.02
xo/(
X2/Na
0.58 0.37 0.38
m3 J-I)
7.1 f 2.1 4.4 f 0.6 2.8 f 0.4
Y
X’/W
1.28 f 0.04 1.22 f 0.02 1.24 f 0.02
0.59 0.82 0.20
Reduced chi-squared values ( x 2 / N ) are defined in ref 16; N is the number of degrees of freedom.
oa
I
1
02
0.1
0.0
4
0
500
1000
1500
1
2000
5 /A Figure 3. log x as a function of log [(T- T c ) / T c ] .The symbols have the same meaning as those in Figure 2. The lines are calculated from eq 2 with the parameters given in Table 111.
specified is the value at the maximum in the transmission of each filter. The full width at half-maximum for the filters is no greater than 100 A, so there is no significant difference between (A“) and Amax+. Values of the correlation length and susceptibility at each temperature were obtained by fitting the turbidity-wavelength data to eq 3. The results are shown in Figures 2 and 3. If one assumes that [ and x are independent, then the uncertainties in F and x. when F is not too small, are about 2%. The susceptibility and correlation lengths determined from the fits are strongly correlated, however, and the real uncertainties are typically 5 times larger. We found, however, that the ratio x / € = ( X 0 / P ) [ ( T- Tc)/Tcl-(y-”) (6)
Figure 4. Relative errors as a function oft: 0,5; 0, x ; A, x / &
could be determined more precisely because the covariance between the parameters cancels much of the contribution to the error in the ratio arising from the individual uncertainties in F and x (see Figure 4). For small a , f ( a )approaches the value and eq 3 becomes T
= X(.3/A04)(an2/a~)2k,Tx
(7)
Thus, when a is small, large uncertainties in 5 and in the ratio €/x can be expected. The estimated errors in and x, including the effects of temperature fluctuations, are shown as error bars in Figures 2 and 3. log-log plots of F and x against ( T - T c ) / T care linear, and least-squares fits give the values of Y, y, p, and xo listed in Table 111. The values of the exponents agree reasonably well with the
3379
J . Phys. Chem. 1991, 95, 3379-3383
TABLE I V 9, xe, and x0#
for Methylcyclobexane + Polystyrene
Mixtures'
Fit I
* 0.13 * 0.09 0.09
I 2 3
5.41 f 0.13 5.30 0.13 4.93 0.09
5.85 4.23 3.73
I
7.9 f 0.9 4.5 0.7 3.7 0.4
Fit 2 9.3 f 1.1 3.6 0.5 2.7 0.4
2 3
* *
108 80 76
*4
3 2
0.59 0.28 0.29
119 f 6 79 f 4 73 f 4
0.67 0.29 0.98
2
116 f 4 78 f 2 74 2
2.58 0.88 0.98
3
= 0.63; Y = 1.241. Reduced chi-squared values ( x 2 / N ) are defined in ref 16; N is the number of degrees of freedom. ay
theoretical predictions," but the errors in the prefactors are greater than 20%. A more satisfactory procedure is to fix the values of y and u at their theoretical values, 1.241 and 0.630, respectively. When this was done, we extracted values of p and xo from the experimental data by three different methods: (1) r-A-T data were fitted to eqs 1 and 4 simultaneously to obtain the two prefactors. (2) F-x-T data were fitted to eqs 1 and 2 to obtain the two prefactors. (3) The ratio x/[ was fitted to eq 6 to obtain x0/p. The results of the three procedures are listed in Table IV. Differences between the values of the prefactors determined by procedures 1 and 2 are significantly larger than the estimated ~~~~
(14)
p Mf
(8)
0:
Fit 3 1
errors. This is not surprising because any errors excluded in our error analysis, such as those in the determinations of the refractive indices and the coupling constants and those introduced from the background corrections, would affect the values of p and xo determined by procedure 2 because of the strong correlation between the parameters. We therefore believe the prefactors obtained from procedure 1 are more reliable. The dependence of p on M, can be described by a power law
~
LeGuillou, J. C.; Zinn-Justin, J. J. Phys. Rev. B 1980, 21, 3976.
where scaling argumentsI5 give f = (1 - v)/2. It was reportedlo that the measured correlation lengths for polystyrene cyclohexane's2 can be represented by relation 8 with f = the mean-field value. Similarly, Shinozaki et al." found that f = 0.28 f 0.03 for polystyrene + methylcyclohexane for M , 1 50000. The range of molecular weights that we have studied is much smaller than that employed by Shinozaki et al., and we are therefore unable to evaluatef. Indeed, the trend in p with increasing M, for the fitting procedure that we believe most reliable appears to be toward lower values. The differences between the Q's are small and are at best barely significant. It should be noted, however, that for M, < 50000 Shinozaki et al. found that f 0.1, so the weak dependence that we observe may not be inconsistent with their results.
+
-
Acknowledgment. This work was supported by the National Science Foundation. We thank Dr. Didier Roux for his suggestions about the experimental method. Registry No. Polystyrene, 9003-53-6; methylcyclohexane, 108-87-2. (1 5 ) DeGennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (16) Bevington, P. R. Data Reduction and Error Analysis for Physical Science; McGraw-Hill: New York, 1969.
-
Temperature- Independent Electron Transfer in Rhodobacter capsu/atus Wild-Type and HisM2O0 Leu Photosynthetic Reaction Centers Lynda M. McDowell, Christine Kirmaier, and Dewey Holten* Department of Chemistry, Washington University, St. Louis, Missouri 631 30 (Received: September 17. 1990)
-
The kinetics and relative yields of the two decay pathways of the initially observed transient state ( D') in photosynthetic reaction centers from the HisMZm Leu mutant of Rhodobacter capsulatus have been studied at 285 and 77 K. At both temperatures, the lifetime of D*,which has mainly the character of the lowest intradimer charge-transfer state of the bacteriochlorophyll/bacteriopheophytinheterodimer, is about 17 ps; the yields of electron transfer from ' D to the normal bacteriopheophytin acceptor and of internal conversion (charge recombination) to the ground state are both about 50% at 285 and 77 K. The finding that the rates of these two energetically different decay pathways of ' D are both essentially independent of temperature is discussed in terms of molecular factors that may underlie activationless electron transfer in the reaction center and contribute to the high quantum yield of charge separation.
Introduction The availability of crystal structures for bacterial reaction centers ( R C ~ )from RhdopseudomoMs &idis and Rh&obacter and theoretical efforts sphaeroides~-3has invigorated (1) Deisenhofer. J.: EDD. .. 0.:Miki. K.:Huber. R.:Michel. H. J . Mol. Biol. 1w;180. 385. (2) Allen, J. p.; Feher, G.; YateS, T.0.; ReeS, D. c.; Deisenhofer. J.; Michel, H.; Huber, R. Proc. Natl. Acad. Sci. (I.S.A. 1986, 83, 8589. 13) Chann. C.-H.: Tide. D.: Tann. J.: Smith., U.:. Norris.. J.:. Schiffer. M.
FEBS Lett. ik, 205.82.
'
0022-3654/91/2095-3379%02.50/0
to elucidate the factors that underlie the near-unity quantum yield of charge separation. The primary photochemistry in the bacterial R C involves a series of electron-transfer reactions initiated by excitation of the dimer of bacteriochlorophyll (BChl) molecules called P. The excited primary donor (P*) transfers an electron to a bacteriopheophytin molecule associated with the L polypeptide 1 with a time constant of -3 DS at 295 K. followed bv (BPhl . movement of an electron from BPhL- to a quinone (QA) in aboit 200 ps. when the secondary quinone ( Q ~ is ) absent, charge recombination between p+ and QA- Occurs with a time constant of 100 ms at 295 K. Interestingly, the rates of these three processes 0 1991 American Chemical Society
