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The Journal of Physical Chemistry, Vol. 83, No. 22, 1979
U. P. Strauss, B. W. Barbieri, and G. Wong
-
Consequently, since y I1,eq 38 could overestimate singlet 0.7,24even if oxygen lifetimes. However, because y primary geminate reaction is symmetry forbidden, eq 38 should provide reasonably accurate singlet oxygen lifetimes.
where
References and Notes (1) J. Grlfflths and C. Hawkins, J. Chem. Soc., Chem. Commun.,463 (1972); J . Chem. SOC.,Perkin Trans. 2 , 747 (1977). (2) N. Kuramoto and T. Kitao, Nippon Kagaku Kaishi, 2, 258 (1977). (3) W. F. Smith, P. B. Merkel, and W. G. Herkstroeter, to be submitted. (4) T. Wilson, J. Am. Chem. SOC.,88, 2898 (1966). (5) J. Olmsted and T. Akashah, J . Am. Chem. Sac., 95, 6211 (1973). (8) B. Stevens, J. Photochem., 3, 393 (1974/75). (7) B. Stevens, J. A. Ors, and M. L. Pensky, Chem. Phys. Lett., 27, 157 (1974). (8) W. Drews, R. Schmidt, and H. D. Brauer, J. Photochem., 6, 391 (1976/77). (9) K. Kawaoka, A. U. Khan, and D. R. Kearns, J. Chem. Phys., 46, 1842 (1987). (10) B. E. Algar and B. Stevens, J. Phys. Chem., 74, 3029 (1970). (1 1) P. B. Merkel and D. R. Kearns, J. Am. Chem. Soc., 94, 7244 (1972). (12) 0.L. J. Gljzeman, F. Kaufman, and G. Porter, J. Chem. Soc., Faraday Trans. 2 , 69, 708 (1973). (13) The expression for aOx can be cast into two equivalentforms. In the form of eq 9 reverse energy transfer appears as a quenching reactlon of ’A. Alternatively, reverse energy transfer may be considered as an inefflciency in the formation of ‘A, in whlch case
(14) As noted in R. M. Noyes, J . Am. Chem. Soc., 77, 2042 (1955). (15) See, for example, W. R. Ware, J . Phys. Chem., 66, 455 (1962). (16) E. E. Wegner and A. W. Adamson, J. Am. Chem. Soc., 88, 394 (1966). 117) C. S.FooteandTaNenCheno. J. Am. Chem. Soc..97.820911975). (18) D. R. Adams and F. W. Wilkkon, J. Chem. Soc.; Firaday bans. 2, 68, 586 (1972). (19) R. H. Young, D. Brewer, and R. A. Keller, J . Am. Chem. Soc., 91, 375 (1973). (20) R. Higgens, C. S. Foote, and H. Cheng, Adv. Chem. Ser., No. 77, 102 (1968). (21) In the ground state at high pH dye 111 may also lose a proton from the pendant sulfamoyl group. However, this produces no spectral changes and is expected to have littie effect on the photochernlcal propertles of the dye. (22) A. A. Gorman and M. A. J. Rodgers, Chem. phys. Lett., 55, 52 (1978). (23) B. Stevens and S. R. Perez, Mol. Photochem., 6, 1 (1974). (24) B. Stevens, Chem. Phys. Lett., 3 , 233 (1969).
Analysis of Ionization Equilibria of Polyacids in Terms of Species Population Distributions. Examination of a “Two-State” Conformatlonal Transition U. P. Sfrauss,* B. W. Barblerl, and G. Wong Department of Chemistry, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903 (Recelved February 8, 1979) Publication costs assisted by the Natlonal Instltutes of Health
The potentiometric titration curves of two hydrolyzed 1-1 copolymers of maleic anhydride and alkyl vinyl ethers are described in terms of successive ionization constants of appropriately chosen oligomeric subunits in order to follow the population distribution among the various deprotonation states of the subunits with the progress of the titration. For the methyl copolymer the species distribution functions behaved normally, but for the butyl copolymer they showed two distinct peaks in the pH range in which a transition from compact to random coil conformation is known to occur. The results provide a quantitative characterization of the “two-state” nature of the conformational transition.
Introduction While many methods have been developed for treating the ionization equilibria of weak polyelectrolytes, the description in terms of successive ionization constants has been thought to provide insufficient benefits to warrant the inherent laborious calculation^.^-^ We want to show here that this description can, if applied to reasonably sized subunits of the polymer chain, extract valuable information from potentiometric titration data of polyacids. By allowing the resolution of the subunits into species according to their states of deprotonation the method turns out to be especially useful for deepening our insight into the nature of the conformational transitions which certain polyacids are known to undergo with changes in ionizationa4 Theory The theory has been given previ~usly,~ and only a brief summary will be presented here. Our treatment applies 0022-3654/79/2083-2840$0 1.0010
to an entity, AHN, which may be considered either a polyacid molecule or a polyacid subunit containing N acidic groups. The dissociation of this entity is described by the overall reactions AHN .-, AHN& + iH+ 1 Ii IN (1) If a constant excess concentration of simple electrolyte is maintained so that activity coefficients may be considered to be constant, overall dissociation constants may be conveniently defined by the relations
6; = UH+’[AHN_[~J/[AHN] 0 Ii IN
(2)
where brackets denote concentrations of the species. It should be noted that Po = 1. The mole fraction of the polyacid species with i dissociated protons, x i , is defined by the expression
0 1979
American Chemical Society
The Journal of Physical Chemishy, Vol. 83,No. 22, 1979 2841
Ionization Equilibria of Polyacids
TABLE I: Overall and Stepwise Ionization Constants for
The application of eq 2 converts eq 3 to (4)
Methyl and Butyl Copolymers at N = 8 butyl copolymer methyl copolymer
i
where h denotes uH+-l. The average number of dissociated protons per polyacid species is given by N
(i)
=
C jxj
j=O
which becomes, on using eq 4 N
N
j=O
j=O
( i ) = C jpjhj/CPjhJ Remembering that Po = 1, we may recast eq 6 into the form
c(j N
(i) =
-
(i))pjhj
j= 1
(7)
The quantities (i) aand h are simply related to the degree of deprotonation, a, and the pH, respectively. Therefore, from at least N experimental (a,pH) data pairs, we can obtain N pairs of ( ( i ) , h )values, which when substituted into eq 7 produce N linear equations from which the N parameters pl, P2, ..., Pi, ..., PN may be determined. Knowledge of the values of these overall ionization constants then allows the calculation of the species mole fractions, xi, by eq 4 at any desired stage of the titration, as well as the calculation of the stepwise ionization constants, Ki,defined by the relation
Kc = Pi/Pi-1
(8)
Applications We have applied this method to two polyacids which represent different types of behavior. One, an alternating copolymer of maleic anhydride and methyl vinyl ether, behaves as a normal polyacid having random coil conformations over the whole neutralization range. The other, an alternating copolymer of maleic anhydride and n-butyl vinyl ether, is known to undergo a conformational transition from compact to random coil structures with increasing degree of ne~tralization.~ The methyl copolymer was obtained from GAF Corp. (their sample Gantrez An 139) and purified by repeated precipitations from tetrahydrofuran into ethyl ether. The butyl copolymer was our laboratory sample B-11, the preparation and properties of which have been described previ~usly.~ The potentiometric titrations were performed at 30 "C under nitrogen by adding 0.2 M LiOH or 0.2 M HC1 from a 2.5-mL Gilmont ultraprecision microburet to 6 X monomolar solutions of the polyacids contained in 0.2 M LiC1. A Radiometer 26 pH meter equipped with an expanded scale and with Radiometer K401 calomel and G202-B glass electrodes was used. The degree of deprotonation, a, of the polyacids is defined by the equation a = ((LiOH)
+ [H+] - [OH-lJ/C,
(9)
where (LiOH) is the number of moles of LiOH added per liter of solution being titrated, [H'] and [OH-] are the molarities of free hydrogen m d hydroxyl ions, respectively, determined from the pH together with results from potentiometric titrations of appropriate blank solutions, and C is the copolymer concentration in monomoles per liter. (&e monomole contains one maleic acid and one alkyl vinyl ether residue, so that a = 2 at complete deproton-
PP i 2.82 6.37 10.18 14.56 20.68 27.48 34.71 42.72
PKi 2.82 3.55 3.81 4.38 6.12 6.80 7.23 8.01
PP i 3.00 7.87 11.34 16.01 22.39 29.79 37.62 46.22
PKi 3.00 4.87 3.47 4.67 6.38 7.40 7.83 8.60
ation.) Since the success of the method requires a very precise knowledge of the titration curve, extreme care was taken in all aspects of the experimental procedure. The calculations were performed on an IBM 370/158 computer with the use of APL/SV language. The N pairs of (( i),h) values needed for the solution of eq 7 were obtained from the much larger number of experimental data pairs as follows. First, all values of a were converted to ( i )by the relation (i) = N a / 2 (10) Next, interpolated values of the pH corresponding to all half-integral values of (i) ranging from (i) = 1/2 to ( i ) = N - '1 were obtained by piecewise-cubic Langrange interpolation6 and converted to h values by the relation pH = log h (11) Equations 7 were then solved for the N values of Pi by the Gauss-Jordan elimination method.' The fit of the Pi's with all the experimentaldata is tested by calculating, by means of eq 7 (together with eq 10 and ll),the value of a corresponding to each experimental pH value and comparing this calculated value of a with the experimental one. We consider the fit to be satisfactory if the differences between the calculated and experimental values lie within the precision limits of a,which we estimate to be k0.02 for the data reported here. Values of N used ranged from 4 to 13. The lower limit is the minimum number of parameters needed to describe the titration curve analytically according to eq 6. The upper end of the range is limited by the well-known practical difficulties involved in obtaining meaningful mathematical solutions when the number of parameters, Pi, becomes large. As has already been mentioned, the theoretical species containing N acidic groups are considered to be subunits of the actual polyacid molecules containing of the order of lo3 acid groups. Inherent in this treatment is the assumption that the contributions to the binding behavior of the polyacid arising from the interactions within subunits outweigh the contributions arising from the interactions among different subunits. At the high ionic strength used here this assumption does not appear to be unreasonable. The ionization constants obtained for the two polyacids with subunit size, N , taken equal to eight are shown in Table I The species mole fractions, xi, calculated by eq 4 from the values of poi (poi = -log pi) in Table I are given for selected interpolated values of (a,pH) pairs in Tables I1 and 111. The results in Table I1 for the methyl copolymer show a gradual progression of normal-appearing distributions towards higher ranges of i as the overall deprotonation increases. Each distribution function peaks close to its average value of i determined by eq 10. The pronounced sharpening around i = 4 of the distribution function
2842
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979
U. P. Strauss, B. W. Barbieri, and G. Wong
TABLE 11: Species Mole Fractions for Methyl Copolymer with N = 8
i o!
PH
0
1
2
3
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
2.95 3.47 3.86 4.31 5.27 6.27 6.79 7.26 7.83
0.37 0.09 0.02
0.49 0.40 0.16 0.02
0.12 0.34 0.34 0.14
0.02 0.15 0.37 0.44 0.10 0.01
4 0.02 0.11 0.39 0.79 0.35 0.09 0.01
5
6
7
8
0.01 0.11 0.48 0.39 0.13 0.01
0.14 0.38 0.38 0.13
0.02 0.14 0.41 0.52
0.07 0.34
5
6
7
8
0.01 0.11 0.58 0.44 0.14 0.01
0.11 0.38 0.38 0.13
0.01 0.12 0.40 0.51
0.01 0.07 0.35
TABLE 111: Species Mole Fractions for Butyl Copolymer with N = 8
i o!
PH
0
1
2
3
0.2 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8
3.36 3.98 4.13 4.25 4.35 4.54 5.51 6.66 7.34 7.85 8.43
0.29 0.06 0.03 0.02 0.01
0.67 0.58 0.43 0.31 0.21 0.09
0.02 0.07 0.08 0.07 0.06 0.04
0.02 0.24 0.35 0.44 0.48 0.49 0.11
0.6
I
;lp L a=oo.a
0.0 0
I
2
3 4 5
7
(I
8
910111213
L
Figure 1. Progress of population distribution of species with idissociated protons through conformational transition for N = 13. Species with
i < 4 are in compact conformation; species with i > 4 are in random coil conformation.
corresponding to a = 1 is a direct consequence of the large difference between the first and second intrinsic ionization constants of the dicarboxylate groups4which causes a large preponderance of these groups to be singly ionized at a = 1. The same narrowing of the distribution function corresponding to a = 1 is also observed for the butyl copolymer results in Table 111. However, with this copolymer there appears a new striking feature which characterizes the region 0.4 Ia I0.8 in which the conformational transition is known to O C C U ~ . ~In, ~this region the distribution functions of the species do not have a single maximum close to their average values of i, but are bimodal with prominent peaks at i = 1 and i = 3 separated by a minimum at i = 2. This effect arises from the dip in successive pKi values of the butyl copolymer seen in Table I and necessarily follows from the functional dependence of xion pi given by eq 4. It seems reasonable to assign the species with i < 2 to the compact conformation and those
4 0.05 0.10 0.16 0.23 0.37 0.78 0.30 0.05
with i > 2 to the random coil conformation. More precisely, each bimodal distribution function may be viewed as a superposition of two simple distribution functions with an overlap which, in view of the low population of the i = 2 state throughout the transition region, is slight. It should be noted that this value of i is the integer which, according to eq 10, corresponds most closely to a = 0.6, the known midpoint of the transition region. In order to show that these results are not an artifice of the particular value chosen for N , and also in order to illustrate the phenomenon graphically, we present the change in the population distribution with the progress of the conformational transition for N = 13 in Figure 1. The two population peaks, well separated by a deep minimum at i = 4, are clearly marked. As the transition progresses, the population of the random coil state is seen to increase at the expense of the population of the compact state. The preservation of the minimum throughout the transition demonstrates convincingly that the conformation does not change gradually, but jumps discontinuously and abruptly from one state to the other. Conclusion The findings reported here provide valuable new information concerning the nature of the conformational transition of the butyl copolymer and demonstrate conclusively its "two-state" character. It is noteworthy that no a priori theoretical molecular model is needed to describe the conformational states. The method sets out to resolve the species according to their degrees of deprotonation only. The resolution into states of different conformation follows spontaneously, because the two conformations are separated by a sufficiently large gap in their ionization states. Acknowledgment. The support of this research by a grant from the United States Public Health Service (Grant GM 12307) is gratefully acknowledged. References and Notes (1) C. Tanford, "Physical Chemistry of Macromolecules", Wiley, New York, N.Y., 1961, pp 526-586.
Anion Solvation Properties of Protic Solvents (2) E. J. King, “Acid-Base Equilibria”, Pergamon, Oxford, 1965, pp 218-247. (3) H. Morawetz, “Macromolecules in Solution”, 2nd ed,Wiley, New York, N.Y., 1975, DD 376-387. (4) P. L. Dubin and U. P. Strauss, J . Pbys. Chem., 74, 2842 (1970). (5) J. Wyman, Adv. Protein Chem., 4, 407 (1948).
The Journal of Physical chemistry, Vol. 83, No. 22, 1979 2843
(6) S. D. Conte and C. de Boor, “Elementary Numerical Analysis”, McGraw-Hill, New York, N.Y., 1972, p 233. (7) E. D. Nerzing, “Elementary Llnear Algebra”, W. B. Saunders Go., Philadebhia, 1974. DD 1-35. (8) U. P. Stiauss and M: Schiesinger, J . Pbys. Chem., 82, 571, 1627 (1978).
Anion Solvation Properties of Protic Solvents. 1. Spectroscopic Study J. Hormadaly and Y. Marcus* Department of Inorganic and Analytical Chemistry, The Hebrew University, Jerusalem, Israel (Received November 22, 1978; Revised Manuscrlpt Received April 3, 1979) Publication costs assisted by US-Israel Binational Science Foundation
A spectroscopic index for the polarity of solvents, such as Dimroth and Reichardt’s ET, is also a measure of the solvating ability of these solvents toward anions. Few data for protic solvents, in particular acidic ones, have been reported in the literature. Measurements of ET have been made with the betaine dye 2,6-diphenyl-4-(2r,4’,6r-triphenyl-l-pyridino)phenoxide for over 40 protic solvents, such as the alcohols from methanol for to dodecanol and various substituted phenols, and with the dye 4-(2’,4’,6’-triphenyl-l-pyridino)phenoxide some 20 of these solvents. For some more acidic solvents, such as carboxylic acids, Kosower’s 2 values have been determined with 4-cyano-l-ethylpyridiniumiodide, and Mayer, Gutmann, and Gerger’s AN values with tributylphosphineoxide. The values were intercompared, and the effects of the presence of base (triethylamine) and water on the ETvalues have been studied. These indexes have been correlated with structural factors for the alcohols and phenols, and with the acidity of the phenols. These correspondences permit the prediction of ET and the solvation properties of solvents which have not been studied yet.
Introduction Solvents for electrolytes are characterized not only by their bulk dielectric constants, but also by their donor and acceptor properties. The former determine their dissociating power for the electrolytes, the latter the solvation of the ion pairs or of the ions produced on dissociation. The cations are Lewis acids, so that their solvation is mainly determined by the donor properties of the solvents, which can be expressed, e.g., by Gutmann’s donor numbers’ DN. The anions, as Lewis bases, are not solvated much by aprotic solvents, even if dipolar. Protic solvents, however, solvate anions well, and their acceptor properties play the major role in this respect. The (electron pair) acceptor properties of protic solvents measure, inter alia, their ability to form hydrogen bonds. They can be expressed by indices such as Dimroth and Reichardt’s2E T , Kosower’s32, or Mayer, Gutmann, and Gerger’s4 AN. These indices are based on spectroscopic observations on indicator compounds dissolved in these solvents, the former two in the ultraviolet-visible range, and the latter of nuclear magnetic resonance chemical shifts. Each index has its advantages and drawbacks, but they are mutually well ~ o r r e l a t e d Solvents . ~ ~ ~ which are inaccessible by the one method can be studied by another, so that a unified solvent scale can be set up. A relation exists between the acceptor properties and the solvating power of the solvents toward anions, i.e., the Gibbs free energy of solvation of the anions, AGoWI,(X-,S), where X- is the generalized anion and S the solvent. The transfer Gibbs free energy of the anion X- from water to the solvent S is the accepted measure of the anion solvating power of the solvents S (relative to ~ a t e r ) . ~ - ~ AGotr(X-,H20+S) = AGo,,~,(X-,S) - AGohy,(X-) (1)
It is the purpose of this paper to present information on the solvent properties of a fairly large number of protic 0022-3654/79/2083-2843$0 1.OO/O
solvents, in particular alcohols and phenols, in terms of
ET,and to compare the data with information available from other properties. In a subsequent paper,8 the acceptor properties of the solvents will be compared with the anion-solvating properties, both in terms of AGOtr data from the literature, critically examined, and in terms of a novel extractive procedure to obtain approximate individual transfer Gibbs free e n e r g i e ~ . ~ The Dimroth and Reichardt3 index EThad been selected because the indicator compound (betaine no. 30, see Experimental Section) used for the construction of this scale has a large solvent sensitivity. The charge transfer band (first low-energy, long-wavelength ?r H* absorption band) ranges from -130 kJ mol-’ (925 nm) for hexane to -264 kJ mol-’ (453 nm) for water. Combined with the precision attainable, h0.5 kJ mol-’, this range yields a very fine resolution of the properties of similar solvents, comparable, e.g., with the 2 scale,3 and does not require a series of measurements with extrapolation to zero concentration of the indicator compound, as does the AN scale.4 A difficulty with the E T scale concerning slightly acidic solvents, of which the AN scale is free, has been overcomelofor the protic solvents of interest in the present connection. This, admittedly, is not the case for carboxylic acid solvents, for which the AN scale seems to be the more practical one available.
-
Experimental Section Materials. The solvents were generally of chemically pure grade, except where noted below. Only practical or technical grades of the following solvents were available: 2-chloroaniline, N-methylaniline, 2,4-dimethylphenol, 2-tert-butyl-5-methylpheno1, 2-sec-butylphenol, 4-secbutylphenol, 2-sec-propylphenol, 2-chlorophenol, nonylphenol, 2-hydroxyethyl salicylate, and trichloroethanol. A further sample of the latter and 4-methoxybenzyl alcohol 0 1979 American Chemical Society
