(17C) Harris, C. M.,Lockyer, T. X., Chem. Ind. (London) 1958, 1231. (18C) Jorgensen, K., “Inorganic Complexes,” Academic Press, New York, 1963. (19C) Knobler, C. >I., “Existence of a hlolecular Oxygen Dimer,” doctoral dissertation, Leiden University, 1961, Drukkeij Pasmans ’S-Gravenhage, 1961. (20C) Kobayashi, H., Haseda, T., blori, M.,Bull. Chem. SOC.Japan 38, 1455 (1965). (21C) Koski, G. B., Inorg. Chem. 4, 665 (1965). (22C) Lasheen, R. A., Acta Cryst. 17, 1588 (1964). (23C) Mathis, &I., Sweeny, M., Fox, &I.E., J . Chem. Phys. 41, 3652 (1964). (24C) Nichaelis, Id., Granick, S., J. A m . Chern. SOC.65, 481 (1943). ( 2 3 2 ) Mulay, L. N., Fisher, W., Bull.
Am. Ceram. SOC. 44(4), 343 (1965). (Further work is being continued by L. N. Mulay and D. Collins.) (26C) Mulay, L. N., Fox, M. E., J . Chem. Phys. 38, 760 (1963). (27C) hlulay, L. N., Hofmann, N. L., Abstracts (Division of Physical Chemistry), 36\’, 150st Meeting ACS, Atlantic City, N. J., September 1965. (28C) Mulay, L. N., Keys, L. K., J . A m . Chem. SOC.86, 4489 (1964). (29C) Ibid., 87, 1192 (1965). (30C) Mulay, I. L., Mulay, L. N., “Magnetic Susceptibility and Resonance Studies on Normal and Cancer Tissues, Instrumentation for Bulk Tissues and (Possibility of) Single Cell Measurements,” “Proceedings of 6th International Conference on Medical Electronics and Biological Engineering, Tokyo (1965), “Okumura Printing Co.,
Tokyo, 1965. (31C) Mulay, L. N., Naylor, hl. C., “Advances in the Chemistry of the Coordination ComDounds.” S. Kirschener. ed.. Macmillin. New York. ~1961. (32C) ‘Mufay, L. N., Withstandley, V., J . Chem. Phys. 43, 4522 (1965). (33C) blusher, J. I., Zbid., 43,4081 (1965). (34’2) Nakajima, T., Saijo, T., Yamaguchi, H., i”etrahedron 20(9), 2119( 1964). (35C) Nowakowski, J., Acta Phys. Polon. 2 5 , 841 (1964). (36C) Schneider, W., Anderegg, G., Gut, R., “Essays in Coordination Chemistry,” Birkhausen Verlag, Base1 and Stuttgart, 1964. (37C) Schoffa, G., 2. Naturforsch. 20b (2), 167 (1965). (3%) Selwood, P. W., “Adsorption and Collective Paramagnetism,” Academic Press, New York, 1962. I
Kinetic Aspects of Analytical Chemistry Garry A. Rechnitz, Department of Chemisfry, University o f Pennsylvania, Philadelphia, Pa.
S
previous review (65) on this subject, several significant advances in the area of reaction kinetics have been made from both the theoretical and experimental viewpoints. The growing impact of kinetic concepts and measurements on analytical chemistry was effectively underscored by a recent symposium ( 3 ) devoted entirely to the subject of the application of kinetics to analytical problems. The accompanying sharp increase in the volume of published work in this area, up to December 1966, prohibits a n exhaustive coverage of the literature and limits this review to a critical examination of the most important and useful developments in kinetic theory and practice as pertinent to analytical chemistry. The major theoretical advance, in the reviewer’s opinion, has been the formulation and exposition of the Marcus theory of electron-transfer reactions. The consequences of this theory are of direct relevance to our understanding of oxidation-reduction reactions in solution, on the one hand, and electrode processes, on the other hand, as well as t o the interrelation of these two reaction classes. Basically, the theory provides means for predicting the rate constants of outer-sphere redox reactions between aquated or weakly complexed metal ions on the basis of equilibrium and isotopic-exchange data and, second, for correlating the specific rates of homogeneous electron-exchange reactions and of the corresponding electrode reactions. The first of these operations is accomplished through the expression INCE THE
where
Klz and klz are the equilibrium- and rateconstants, respectively, for the cross reaction kii
0x1
+ Red2 + Redl + Ox2
(3)
while kll and Icn are the rate constants for the two electron (isotopic) exchange reactions and Z is the collision frequency (about 10”~%f-~sec.-l). The electrochemical rate constant, k,l, is related to the corresponding homogeneous electron-exchange rate constant, k,,, through
(4) where ZBolnand Z,I are again the appropriate collisional frequencies (Zel equals about lo4 cm. sec.-l). The reader is referred to the comprehensive review by Marcus (43) for details of the derivation and for other consequences of the theory. Through comparison with experimental data, the validity of the Marcus theory has been confirmed for many, but not all, reaction systems. Endicott and Taube (22) confirmed expression 1 for several reactions of ruthenium(I1) and (111) complexes, while Campion, Purdie, and Sutin (12) provide additional supporting evidence for about a dozen reactions involving cerium(1V) and iridium(1V) as oxidants. Correlations of homogeneous and electrode reaction rates have been obtained by Candlin, Halpern, and Trimm (IS) for the oxidation of europium(II), vanadium(II), and Cr(dipy),+z with cobalt(II1) complexes and a t the drop-
ping mercury electrode, respectively. On the whole, agreement between theory and experiment has been good enough to suggest that the application of the Marcus theory t o chemical and electrochemical reactions should provide useful guidelines for the selection of analytical reactions and for the exploitation of electroanalytical methods. On the experimental side, considerable strides have been made in the development of techniques for the direct study of rapid reactions, so that there are no longer any major classes of solution reactions too rapid t o be measured. The principles and practical aspects of these techniques, which include photochemical, relaxation, flow, and electrochemical methods, have been lucidly treated in the excellent new book by Caldin ( I I ) , which also summarizes many of the key experimental results obtained in recent years. The use of one of these techniques, pulse radiolysis, has resulted in the discovery and characterization (SI) of the aquated electron, e,,-, the most elementary and powerful of all reducing agents. The aquated electron has a distinctive absorption spectrum with maximum (63) at 578 and 720 mp (e‘s = 1.06 X lo4 and 1.5 X lo4, respectively), a standard potential of roughly -2.6 volts, and a diffusion coefficient of approximately 4.7 x 10-5 cm.2 set.-' Its lifetime in scavengerfree water is limited by the processes
--
+ eaq- HZ+ 2 0 H esq- + HaO+ H + HzO eaq- + H20 H + OH-
ea,-
with specific rate constants of 1 VOL 38, NO. 5 , APRIL 1966
(5)
(6)
(7)
x
10’0
513 R
-
~
Jf-1 sec.-l, 2.36 X 101oM-l set.-', and 5 4 . 4 X lo4sec.-l, respectively (62). The kinetics of reactions of the aquated electron with both organic (4, 5 , 55) and inorganic (6, 76) reagents have already been extensively investigated and have yielded some interesting correlations between specific rates of reaction and the reduction potentials or structural features of the oxidants. The aquated electron has also been proposed (66) as an intermediate in homogeneous reactions involving powerful chemical reducing agents. The first direct analytical use of the aquated electron has been demonstrated by Hart and Fielden (32), who used this reagent for the determination of nanomolar concentrations of oxygen, hydrogen peroxide, nitrous oxide, acetone, and thymine in water by comparing the half life of the aquated electron in pure water with that in the sample solution. The newer fast reaction techniques have also been profitably applied to the study of complex formation reactions (40). Three general kinds of meohanisms have been recognized for complex formation reactions of the type M"'(Hz0).
+L
+ yHzO
-d [Fe(11) ] = k'[Ce(IV)][Fe(II) 1 at
(8)
(9)
the specific rate increases with increasing hydrogen ion concentration and is accelerated by the presence of bisulfate or fluoride ions. The effect of bisulfate ions upon the reaction scheme is to favor the path
+ Ce(OH)z+2-. Fe(II1) + Ce(II1)
(13)
where k ~ ,kl, k ~ ,and k3 have been evaluated as 5865 + 1500M-l sec.-l, 1000 =t 200M-1 set.-', 4830 + 500M - l set.-' (all a t 0.3' C. and p = 2.OM) and about 5000 Jf-l sec.-l (at 0°C. and p = 0.23M), respectively. From the standpoint of rates there is, thus, little to be gained by abandoning the traditional sulfuric acid medium for this titration in favor of a noncomplexing medium. Some provocative experiments by Conocchioli, Hamilton, and Sutin (14) seem to indicate that iron(1V) can be formed as a transient intermediate when iron(I1) is oxidized by two-equivalent oxidants. The reaction squence Fe(I1)
+ oxidant
+ CeS04+z
4
Fe(II1)
2 equiv.
Fe(1V)
+ Fe(I1)
product
-
(14)
rapid
[Fe(III)12 (15) where HOC1 or 03 are the oxidants in perchlorate media, has been suggested to explain the formation of significant quantities of the dimer (FeOH)2+4as a product. Further evidence is necessary to confirm this mechanism. The whole question of the role of iron(I1) species in redox reactions of that reducing agent has recently been re-examined by Wells and Salam (80, 81), who were able to assess both the kinetic and equilibrium properties of various elementary iron(I1) complexes through their influence upon the reaction sequence
+ HzOz+ki Fe(II1) + OH. + OHFe(I1) + OH. Fe(II1) + OHFe(I1)
(16)
+
(17)
Since the rate of step 16 is dependent upon the effective charge of the iron(I1) reactant, any observed ionic strength effects with the addition of anions must be due to equilibria between various forms of iron(I1) present in solution. I n the presence of sulfate ions, for example, the rate of step 16 will be determined by the pre-equilibrium
+ Ce(II1)
Fez+ (10)
in addition to the normal mechanism
+ Ce+4-ko
+
Kc
ks
Fe(II1)
514 R
(12)
k2
Fe(I1)
Fe(1V)
involving, respectively, ligand attack, loss of coordinated water, or hydrolysis as rate determining steps. The formation of manganese(I1) sulfate complexes, for example, proceeds by the second (7) of these mechanisms, as does the formation of complexes between many divalent metal ions and 1,lOphenanthroline or 2,2'-bipyridine (86). A number of specific kinetic studies are of interest because the reactions involved are useful for analytical purposes. The important standardization reaction between cerium(1V) and iron (11), for example, has finally been examined (1) from the kinetic viewpoint in both perchloric acid and complexing media. I n 0.3M HClO4 and a t 0.3' C. the reaction proceeds with a specific rate of 840 f 40M-l sec.-1 according to the rate expression
Fe(I1)
+ Ce(II1)
Fe(II1)
-t
Mn+(HzO).-,L
Fe(I1)
+ Ce(OH)+3-.
ki
Fe(I1)
+ Ce(II1)
ANALYTICAL CHEMISTRY
(11)
+ SO4+ F? FeS04
(18)
thus, by measuring the rate of step 16 under noncomplexing conditions and in the presence of varying ligand concentrations the authors were able to arrive a t values for both K , and kl for a number of iron(I1) complexes having
one or more chloride, sulfate, or phosphate ligands. Once such fundamental data are available it is a relatively simple matter to resolve more complicated reaction systems-e.g., the aquo-cobalt (111)-iron(I1) reaction-and to explain the mechanism of anion catalysis. The chloride-catalyzed oxidation of iron(I1) by cobalt(III), for example, clearly proceeds (15) via an inner-sphere mechanism with a rate-determining step of the type CoC1+2
+ Fe+z k
+
-+
FeC1+2
(k
C O +X ~ 300M-1 sec.-l)
(19)
because the iron(II1) product contains chloride (Le., FeC1+2) even in 3M HClO4 solution. .An important analytical consequence of this finding is that undesirable side reactions, such as the possible reduction of cobalt(II1) by chloride or the oxidation of iron(I1) by chlorine, can be minimized through the proper choice of an electron mediator to maintain acceptable stoichiometry through acceleration of the primary reaction. Once again, the kinetics of cerium (IV) reactions received a good deal of attention. Detailed studies of the reduction of cerium(1V) by Fe(CN)6-4, W(CN)s-*, M o ( C N ) ~ - ~( I @ , iodine (57), oxalate (20),ethylene glycol (57), and by glass surfaces (27) have been described. The reactions of the three cyanide complexes presumably proceed via outer-sphere mechanisms because their experimentally determined specific rates agree particularly well with values calculated from the Marcus theory. Other strong oxidants whose reactions have been examined from the kinetic standpoint include silver(I1) (41,62, 68) manganese(II1) (17, 79), and cobalt (111) (58). The latter reaction, oxidation of chromium(II1) by cobalt(III), is unexpectedly slow in simple perchlorate media but is enormously accelerated by catalytic amounts of silver(1). I n the presence of the catalyst, the overall reaction probably takes place through the sequence Co(II1)
+ .4g(I) F?k2ki Co(I1)
Ag(I1)
+ Cr(II1)
+ Ag(I1)
(20)
ka +
+ Cr(W AgW) + Cr(IV) Ad11 + Cr(W A d W + Cr(V) AgU) + Cr(V1)
-
Ag(U
(21)
(22)
+
(23)
where k1, kz, and k3 have been evaluated as 110, 150, and 48M-1 set.-' in 3M
HC104 a t 25" C., respectively; the rate of the net reaction is thus brought nicely into the range required for normal titrations. Reactions of chromium in the +6 state, as an oxidant, and in the +2 state, ab a reductant, continue to be of interest to analytical chemists. Haight, Richardson, and Coburn (29) and, also, Tong (7'7) have provided valuable data on the distribution of possible reactive chromium(V1) species in solution, while the rates of formation of chromate from dichromate (and vice versa) were recently measured (74) using a relaxation technique. Using such data, Mason and Kowalak (51) were able to show that the reaction 3As(III)
+ 2Cr(VI) = 3As(V) + 2Cr(III)
(24)
actually proceeds in parallel reaction steps involving HCr04- and Cr207-2 a t low and high chromium concentrations, respectively, the C r ~ 0 7 - ~path being nearly 100 times faster than the HCr04path. Similar behavior has also been found for the reactions of chromium (VI) with vanadium(1V) (24) and neptunium(V) (7'2). Aikens and Carlita (2) have taken analytical advantage of the slow ligand exchange on chromium(II1) to devise an ingenious means of generating chromium(I1) in acid solution. Their method is based on the fact that compounds like C r B r ( H ~ 0 ) 5 + while ~, thermodynamically unstable, have a sufficient lifetime to be electrolytically reduced a t potentials more positive than that required for the reduction of aquochromium(II1); thus, chromium(I1) can be generated without simultaneous hydrogen evolution. Since chromium (TI) is labile, the final product is the same in either case. Among the redox reactions of chrcmium(I1) studied in recent years, the reduction of iron(II1) is important because of its use in volumetric analysis, Dulz and Sutin (19) have shown that this reaction is of the inner-sphere bridge type because, in the presence of chloride, the oxidation product is almost entirely Cr(H20)&1+2 in accord with the sequence
+
Fe(H20)5C1+2 Cr(Hz0)6+23 [ (H20) bFe-Cl-Cr (HzO)5 1+4
(25)
[(H~0)5Fe-Cl-Cr(H~0)~] +4 3 Fe(H20)6+z Cr(Hz0)&1+2 (26)
+
Analogous hydroxide-bridged intermediates of the type V(OH),CrS-n have also been proposed (23) for the reduction of vanadium(II1) by chromium(I1) in perchlorate media. Recent kinetic studies of other powerful reducing agents such as indium(1) (78), vanadium(I1) (18, 55-56, 7 3 ) , and ruthenium(I1) (66) may lead
to use of these novel reagents in analytical chemistry because of unexpected properties arising from rate and mechanistic considerations. Chromium(11), for example, reduces perchlorate ion a t tt rate too slow to be useful for analytical purposes, while certain ammine complexes of ruthenium(II), despite their relatively mild reducing power, react with perchlorate a t appreciable (k 0.03M-l sec.-l) rates. Endicott and Taube (21) have already proposed an analytical method for the determination of perchlorate involving the use of ruthenium as a catalyst. Perchlorate is reduced by the ruthenium(I1) which, in turn, is regenerated by reaction with chromium (11); the net reaction is thus the reduction of perchlorate by chromium(II), but the overall rate is considerably faster than that of the direct reaction. A number of reactions have been studied specifically with an analytical objective in mind. Florence and Shirvington (26), for example, examined the kinetics of the uranium(1V)-iron(I1) reaction in various media in order to test electrometric methods of end-point detection and concluded that the use of a n amperometric technique with the dropping mercury electrode yields best results. Similarly, Taylor, Smith, and Swift (75) established the rate law for the mercury(I1)-thioacetamide reaction so as to evaluate the reagent for the gravimetric determination of mercury(I1). The cystine catalysis of the iodine-azide reaction was extensively studied by Dah1 and Pardue (16) who present useful data for the selection of optimum reaction conditions in the analytical utilization of that reaction. ANALYSIS VIA KINETIC MEASUREMENTS
The growing body of fundamental mechanistic studies is accompanied by a similar volume of work dealing with the application of kinetic principles to practical problems of analysis. No spectacular advances in this area are discernible since the last review, but there has been a steady extension, through the improvement of instrumentation and data handling techniques, of the various rate methods into new areas of organic and inorganic analysis as well as a growing appreciation of both the strong and weak points of kinetic methods when applied to practical analyses. There has perhaps been a tendency to overstate the case for kinetic methods of analysis, in general; this is unfortunate because it may obscure the very real and, often, unique contributions which the kinetic approach can provide for the analysis of difficult, but selected, systems. Catalytic Reactions. The main advantages of analyses based on ion or enzyme catalysis are their great sen-
sitivity and potential selectivity. Such applications of catalysis in chemical analysis range all the way from the simple use of copper(I1) to accelerate the slow oxidation of thiosulfate by dichromate, so as to permit the direct use of this reaction in titrimetry (64,to the highly sophisticated coordination chain reactions of Margerum (45-47) for the selective determination of metals a t ultra-trace concentration levels. The latter method utilizes reaction systems involving ligand exchange between metal complexes, such as triethylenetetraminenickel(I1) and (ethylenedinitri1o)tetraacetatocuprate(II), by chain reaction mechanisms where the chain centers are the free ligands. The rate of exchange depends on the concentration of the free ligands which, in turn, depends upon the concentration of metal ions in the system. Thus, there is a relationship between the reaction rate and the metal ion concentration which can be used for the quantitative (f5%) determination of many metals a t the 10-*M concentration level. The remarkable sensitivity of catalytic methods is also illustrated by the work of Bognar (9), who detected as little as 0.5 fig. of iodide a t the 1: 107 dilution level by means of the catalytic effect of iodide upon the rate of the iodate-arsenite reaction and, also, copper(I1) in the microgram range through its effect on the iron(II1) thiosulfatesulfosalicilic acid reaction; the analytical methods based upon these catalytic systems show a relative error of about 10% a t the 1-10 fig. catalyst level. Using the same principle, Fishman and Skougstad (25) devised an excellent method for the determination of vanadium (in the 0.1 -8.0 pg. per liter range) in natural waters. Their method has its basis in the catalytic effect of vanadium on the rate of oxidation of gallic acid by persulfate. The promise of selectivity coupled with sensitivity is nowhere better realized than in analysis by enzymecatalyzed reactions. Enzymes often show the desirable property of catalyzing the reaction of a single, specific component while leaving other components of the system unaffected. Guilbault (28) recently offered a critical review of the use of enzymes in analytical chemistry and pointed out some of the potentialities of using enzymes to specifically determine various substrates inhibitors, and activators. Enzyme methods can be expected to be particularly powerful when used in conjunction with novel experimental techniques such as that described by Hicks and Updike (56) involving immobilized enzymes in acrylamide gels. Some of the promising results obtained with enzymatic methods are exemplified by the work of Blaedel and Olson ( 8 ) , V O L 38, NO. 5, APRIL 1966
515 R
who determined glucose by measuring (with a tubular, flow-through platinum electrode) the rate of appearance of products from the glucose oxidase catalyzed oxidation of glucose as well as the differential method of Mark (48) for the analysis of alcohol mixtures via their rates of reaction in the presence of dehydrogenase. Another example is furnished by Pardue and Frings (60) in the specific enzymetic determination of galactose; here galactose reacts in the presence of galactose oxidase, producing hydrogen peroxide, which in turn oxidizes iodide to iodine in the presence of a molybdenum(V) catalyst. The iodine so produced is detected amperometrically to provide a measure of the primary reaction; despite the complexity of the sequence, a relative standard deviation of about 2% is obtained for the determination of 50-500 p.p.m. galactose. That the general method can equally well be turned to the determination of the enzyme was recently shown by Hicks and Blaedel (34), who used a coupled reaction system for the determination of transaminase enzymes. Differential Rate Methods. The full exploitation of the potentialities of differential reaction rate methods of analysis still awaits the compilation of appropriate rate data, on the one hand, and a more critical examination of the various data handling techniques, on the other. A valuable step in this direction was recently taken by Mark, Greinke, and Papa (50), who evaluated the three major differential kinetic methods currently in use-e.g., proportional equations, graphical extrapolation, and single point-and performed an error analysis in terms of optimum concentrations, magnitude of rate constants, and rate ratios. Hopefully, this work will provide guidelines for the selection of the best method and optimum reaction conditions to be used in the solution of specific analytical problems. A modification of the differential kinetic method to complex reaction systems having mixed stoichiometries was described by Bond, Scullion, and Conduit (IO),who illustrated their method by resolving the hydrolysis reactions of a mixture containing cycle trimethylenenitramine and cyclotetramethylenetramine. Hanna and Siggia (30) extended the usefulness of differential kinetic measurements to rapid reactions having reaction times in the millisecond range through the use of the continuous flow technique, which provides rapid mixing of the reagents but leisurely observation of the extent of reaction. Siggia and coworkers (71) also demonstrated the application of dialysis methods to the kinetic analysis of mixtures; two and three component mixtures of sugars and amino acids could be resolved by 516 R
0
ANALYTICAL CHEMISTRY
dialysis through thin films on the basis of their differing diffusion rates. Amides and nitriles mere analyzed (70) with good accuracy by measuring the rate evolution of ammonia generated by the alkaline hydrolysis of their compounds. Spectrophotometric monitoring of reaction rates was used by Willeboordse and Critchfield (86) to analyze binary and ternary mixtures of alcohols undergoing reaction with phenylisocyanate and by Mark, Backes, and Pinkel (49) in the determination of sugar mixtures using 2,3,5-Triphenyl-2H-Tetrazolium chloride as a specific reagent. An interesting and, as yet, incompletely resolved question has been raised by the observation of so-called synergistic (69) effects. In some binary mixtures of ketones, alcohols, amines, and oleates the presence of the faster reacting component substantially decreases the specific reaction rate of the slower reacting component. While this effect is actually of analytical advantage, its origin is not yet fully understood. Siggia and Hanna suggest that the effect arises from changes in activity coefficients brought about by the presence of the faster reacting component or its reaction products, but the observed changes in specific rates seem aItogether too large to be entirely accounted for in this manner. Clearly, further investigation of the phenomenon is indicated. Instrumentation. With the growing popularity of rate and other kinetic measurements in analytical chemistry, it is not surprising t h a t considerable effort should be expended on the invention and perfection of new measuring techniques. Notable progress has been made toward the automation of rate measurements for analytical purposes, with the benefits of greater reliability and improved convenience. Pardue (68),for example, has described an automatic method for measuring the slopes of rate curves using an electronic slope-matching device and has employed this technique for the quantitative determination of cystine and of glucose (69), both with 1-2% relative accuracy in the parts-per-million concentration range. h later refinement of this measuring technique even provides digital read-out in concentration units (611.
Other new techniques have been oriented more toward the investigation of the kinetics of analytical reactions, particularly fast reactions. The electrochemical method of O'Dom and Fernando (56),for example, was effectively applied to the study of fast bromination reactions and is capable of measuring rate constants as large as 10~M-1set.-', as is the more limited steady-state controlled-potential coulometric technique (46). A modification of the constant current method, involving
current pulses, extends the measurement capabilities of such electrochemical methods into the 108M-1 sec.-1 range (39), at least, for certain bromination reactions. The use of cation-sensitive glass electrodes (67) and other specific ion electrodes may provide yet another means for following the rates of specific reactions in solution. The reviewer is confident that the field of analysis by reaction rates will attract the attention of commercial instrument makers and will eventually result in the manufacture of appropriate devices which could greatly facilitate the necessary measurements and lead to the introduction of such kinetic methods into the realm of conventional chemical analysis. LITERATURE CITED
( 1 ) Adamson, M. G., Dainton, F. S., Glentworth, P., Trans. Faraday SOC. 61, 689 (1965). (2) Aikens, D. A., Carlita, Sister M., ANAL.CHEM.37, 459 (1965). ( 3 ) American Chemical Society, Division of Analytical Chemistry, 150th National Meeting, Atlantic City, N. J., Sentember 1965. (4) Anbar, M., Hart, E. J., J . Am. Chem. SOC.86,5633 (1964). (5) Anbar, M., Hart, E. J., J . Phys. Chem. 69, 271 (1965). (6) Zbid., p. 973. (7) Atkinson, G., Kor, S. K., J. Phys. Chem. 69, 128 (1965). f8) Blaedel. U'. J.. Olson. C.. ANAL. CHEM.36, 343 (1964). (9) Bognar, J., Hungarian Academy of \
I
,
,
Science, Miskolc, private communication, 1964. (IO) Bond, B. D., Scullion, H. J., Conduit, c. P., ANAL.CHEM.37, 147 (1965). (11) Caldin. E. F.. "Fast Reactions in ' Solution." Wilev.'New York. 1964. (12) Campion, R: 'J., Purdie, 'NI, Sutin, N., Znorg. Chem. 3, 1091 (1964). (13) Candlin, J. P., Halpern, J., Trimm, D. L., J . Am. Chem, Soc. 86, 1019
(i964j. (14) Conocchioli, T. J., Hamilton, E. J., Sutin, N., J . Am. Chem. SOC.87, 926 (196.5). (15) Conocchioli, T. J., Nancollas, G. H., Sutin, N., Ibid., 86, 1453 (1964). (16) Dahl, W. E., Pardue, H. L., ANAL. CHEM.37, 1382 (1965). (17) Diebler, H., Sutin, N., J . Phys. Chem. 68, 174 (1964). (18) Dodell, P. H., Taube, H., 2.Physik. Chem. 44, 92 (1965). (19) Dulz, G., Sutin, N., J . Am. Chem. Soc. 86, 829 (1964). (20) El-Tantawy, Y. A,, Rechnitz, G. A., ANAL.CHEM.36, 1174, 2361 (1964). f21) Endicott. J. F.. Taube., H.., Znora. ' Chem. 4, 437 (1965). (22) Endicott, J. F., Taube, H., J . Am. Chem. SOC.86, 1686 (1964). (23) Espenson, J. H., Inorg. Chem., 4, 1025 (1965). (24) Espenson, J. H., J . Am. Chem. SOC. 86, 5101 (1964). (25) Fishman, M. S., Skoustad, M. W., ANAL.CHEM.36, 1643 (1964). (26) Florence, T. M., Shirvington, P. J., Ibid., 37, 950 (1965). (27) Grant, D., J . Inorg. Nucl. Chem. 26, 337 (1964). (28) Guilbault, G. G., Division of An\ - - - - I -
alytical Chem stry, 150th Meeting, ACS, Atlantic City, N. J., September 1965. (29) Haight, G. P., Richardson, D. C., Coburn, N. H., Inorg. Chem. 3, 1777 (1964).
(30) Hanna, J. G., Siggia, S., ANAL. CHEM.36,2022 (1964). (31) Hart, E. J., Science 146, 19 (1964). (32) Hart, E. J., Fielden, E. M. Division of Physical Chemistry, 150th Meeting,
ACS, Atlantic City, N. J., September
1965. (33) Hart, E. J., Gordon, S., Thomas, J. K., J . Phys. Chem. 68, 1271 (1964). (34) Hicks, G. P., Blaedel, W. J., ANAL. CHEM.37, 354 (1965). (35) Hicks, G. P., Updike, S.J., Division of Analytical Chemistry, 150th Meeting,
ACS, Atlantic City, N. J., September
1965. (36) Holyer, R. H., Hubbard, C. D., Kettle, S.F. A., Wilkins, R. G., Inorg. Chem. 4, 929 (1965). (37) Katai, A. A., Kulshrestha, V. K., Marchessault. R. H.. J . Phvs. Chem. 68, 522 (1964). (38) Kirwin, J. B., Proll, P. J., Sutcliffe, L. H., Trans. Faraday SOC.60, 119 (1964). (39) Kozak, G. S., Fernando, Q., Freiser, H., ANAL.CHEM.36, 296 (1964). (40) Kustin, K., Watkins, K. O., Inorg. Chem. 3, 1706 (1964). (41) Lloyd, C. P., Pickering, W. F., Talanta 11, 1409 (1964). (42) McClure, J. E., Rechnitz, G. A., ANAL.CHEM.36, 2265 (1964). (43) Marcus, R. A., Ann. Rev. Phys. Chem. 15, 155 (1964). (44) Ibid., J . Chem. Phys., 43, 679 (1965). (45) Margerum, D. W., Division of Analytical Chemistry, 150th Meeting,
ACS, Atlantic City, N. J., September 1965.
(46) Margerum, D. W., Carr, J. D., Division of Analytical Chemistry, 150th
Meeting, ACS, Atlantic City, N. J., September 1965. (47) Margerum, D. W., Steinhaus, R. K., ANAL.CHEM.37, 222 (1965). (48) Mark, H. B., Zbid., 36, 1668 (1964). (49) Mark, H. B., Backes, L. M., Pinkel, D., Talanta 12, 27 (1965). (50) Mark, H. B., Greinke, R. A., Papa, L. J., Division of Analytical Chemistry, 150th Meeting, ACS, Atlantic City, N. J., September 1965. (51) Mason, J. G., Kowalak, A. D., Znorg.
Chem. 3, 1248 (1964). (52) Matheson, M. S., Rabini, J., J . Phys. Chem. 69, 1324 (1965). (53) Newton, T. W., Baker, F. B., Inorg. Chem. 3, 569 (1964). (54) Newton, T. W., Baker, F. B., J . Phys. Chem. 68, 228 (1964). (55) Ibid., 69, 176 (1965). (56) O’Dom, G., Fernando, Q., ANAL. CHEM.37, 893 (1965). (57) Pan, K., Chen, S.,J . Chinese Chem. SOC.11, 71 (1964). (58) Pardue. H. L.. ANAL. CHEM. 36. 683 (1964). (59) Zbid., p. 1110. (60) Pardue, H. L., Frings, C. S.,J . Electroanal. Chem. 7, 398 (1964). (61) Pardue, H. L., Frings, C. S., Delaney, C. J., ANAL.CHEM.37, 1426 (1965). (62) Pickering, W. F., Australian J . Chem. 17, 731 (1964). (63) Rabini, J., hlulac, W. A., Matheson, M. S., J. Phys. Chem. 69, 53 (1965). (64) Rao, P. R., Sarma, B. S. V., ANAL. CHEM.37, 1373 (1965).
(65) Rechnitz, G. A., Ibid., 36, 453R (1964). (66) Rechnitz, G. A., Catherino, H. A., Inorg. Chem. 4, 112 (1965). (67) Rechnitz, G. A., McClure, J. E., Division of Analytical Chemistry, 150th
Meeting, ACS, Analytical City, N. J., SeDtember 1965. (68)-Rechnitz, G. A., Zamochnick, S.B., Talanta 11, 713, 1645 (1964); 12, 479 (1965). (69) Siggia, S., Hanna, J. G., ANAL. CHEM.36, 228 (1964). (70) Siggia, S., Hanna, J. G., Serencha, N. M.,Zbid., p. 227. (71) Zbid., p. 638. (72) Sullivan, J. C., J . Am. Chem. SOC. 87, 1495 (1965). (73) Swinehart, J. H., Znorg. Chem. 4, 1069 (1965). (74) Swinehart, J. H., Castellan, G. W., Inorg. Chem. 3, 278 (1964). (75) Taylor, D. C., Smith, D. M., Swift, E. T., ANAL.CHEM.36, 1924 (1964). (76) Thomas, J. K., Gordon, S.,Hart, E. J., J . Phys. Chem. 68, 1524 (1964) (77) Tone. J. Y.. Inora. Chem. 3, 1804 ‘ (1964).-’ (78) Visco. R. E.. J . Phus. Chem. 69, 202 (1965). (79) Wells, C. F., Davies, G., Nature 205, 692 (1965). (80) Wells, C. F., Salam, M. A., Nature 203, 751 (1964). (81) Ibid., 205, 690 (1965). (82) Willeboordse, F., Critchfield, F. E., ANAL,CHEY.36, 2270 (1964). %
Light Scattering losip P. Krafohvil, Department of Chemistry and Institute of Colloid and Surface Science, Clarkson College of Technology, Potsdam, N. Y .
T
HZ developments and advances made in the last two to three years in respect to the fundamental aspects of scattering of light are well characterized by the impression one carried from the Second Interdisciplinary Conference on Electromagnetic Scattering (ICES-11), held in June 1965 at the University of Massachusetts, Amherst, Mass. Coming three years after ICES-I (181), ICES-I1 brought very few new contributions, but a lot of improving, “tidying up and polishing in a well-worked field” (21). As for the applications, however, the pace is accelerating, the field is branching out into new areas, and the polishing and tidying up of the fundamental aspects have had a beneficial influence on the applications of light scattering. The author’s files contain about 700 references dealing with light scattering that appeared during 1964 and 1965, the period covered in this review. A few references from 1963, which were not included in the last review in this publication (191), are also discussed. The pattern of the previous review is followed, with emphasis on general aspects of the utilization of
light-scattering methods in chemistry. The Brillouin scattering, Doppler shifts, and similar nonlinear phenomena are not discussed. A critical data center for light scattering has been established a t Clarkson College of Technology as a component of the ’National Standard Reference Data System. The center, sponsored by the National Bureau of Standards and operated by Milton Kerker and the author, is concerned with the compilation and critical evaluation of the data in various areas of scattering of light. The proceedings of ICES-I1 will be published by Gordon &- Breach Publishers. For a short report of this conference see (21). Many contributions of John William Strutt (third Baron Rayleigh) to scattering theory are discussed by Twersky (308). Rayleigh’s “Scientific Papers” have been reissued by Dover Publications. The book by Shakhparonov (280) covers many theoretical and experimental contributions, particularly by Soviet workers, on scattering by liquids and liquid mixtures. Debye (74, 75, 76) reviewed some aspects of
electromagnetic scattering by polymer solutions. The application of light and small angle x-ray scattering to the investigation of biological macromolecules is the subject of a review by Timasheff (305). Light scattering in relation to other methods for the molecular weight characterization of polymers is discussed by Billmeyer (22) and Wijga (329). An excellent end extensive review was prepared by Eskin (95) with emphasis on the interpretation of light-scattering measurements in terms of molecular and thermodynamic properties of macromolecular solutions, A chapter in Morawetz’s book (230) is along similar lines. Kretschmar (197) wrote a concise summary of the theoretical basis and experimental techniques as applied to macromolecules, whereas Weber and Teale (328) limited their review to proteins. In a comprehensive treatment of the thermodynamics of multicomponent solutions, Casassa and Eisenberg (37) also discuss in detail light scattering as well as osmotic pressure, partial volumes, refractive increments, and sedimentation equilibrium. VOL. 38, NO. 5 , APRIL 1966
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