FAUSTO W. LIMA
1052
Vol. 56
ON THE VISCOSITY OF BINARY LIQUID MIXTURES BY FAUSTO W. LIMA Departnbent of Chemistry, Escoh Politemica, University of SBo Paulo, B r a d Received October IS,1861
A formula for the viscosity of binary liquid mixtures as a function of the viscosit and the density of the pure components and tho density of the mixtures is proposed. It is ap lied to binary mixtures of torueno, bromobenzenc and nitrobenzene a t different temperatures and to mixtures of primary arcohols and organic acids in benzene and carbon tetrltchloride a t 25'. The formula accounts for the presence of the minima found in the graph for viscosity versus concentration and it applies when there are large differences in the viscosities of the pure components.
Introduction By the application of the notions of parachor and molar refraction to mixtures of pure compounds much success has been achieved in the study of surface tension and refractive index of mixtures. The following reasoning will illustrate the above. Let F equal an additive-constitutive property such as parachor or molar refraction. F is always the product of a molar volume M / d ( M = molecular weight in grams and d = density in g./cc.) times a function of a physical property: 7'14 in the case of parachor and (n2- l)/(n2 2) in the case of molar refraction (y = surface tension and n = refractive index). By putting this function 2) of a physical property 7'14 or (n2 - l)/(n2 asf(p), then F = f(p) M / d for a pure compound. Now, if, for the ith component of a mixture of i components, the additive-constitutive property is designated by Fi, the molecular weight by M i , and the density of the mixture by d, the function of the physical property for the mixture by f(p), the value of F for this mixture as has been showii by Smyth2 and co-workers and others, is obtained by
+
+
F
e ZisiFi
rlF1
+
+ 23Fs + . . .
Z ~ ' Z
(1)
or by F
f(p)ZiziMi/d
f(p) X
+
(ZIMI
+
~2Mz
23M3
+.. . )/d
(2)
(xi is the mole fraction of the ith component of the mixture) By equating formulas (1) and (2) we get and thus the physical property p (surface tension or refractive index) is obtained i n terms of the properties of the components. The values of Fi can be calculated from the additivity of group or atomic values for the molecule. Katz and co-workers8 applied this type of reasoning t o the notion of parachor and were able to predict the value of surface tension for three binary mixtures at temperatures up to 90' and pressures up t o 100 atmospheres. The application of formula (3) to the case of molar refraction was made by Smyth, Engel and Wilson,2Koening-Gresmann" and W ~ e l h m . ~ ~ (1) Part of this material was submitted to the University of Wisconsin as Thesis in partial fulfillment of the requirements for the Master'a Degree in Chemistry, June, 1950. Presented a t the XIIth International Congress of Pure and Applied Chemistry, New York, September, 1951. (2) C. P. Smyth, E. W. Engel and E. B. Wilson, Jr., J . A m . Chem Soc., 81, 1736 (1928). (3) D. L. Kate and G. J. Reno, I n d . Eng. Chem.. Ind. Ed., 86, 1091 (1843); D. L. Kate and C. F. Weinang, ibid., 86, 239 (1943). (4) (a) M. L. Koening-Gressmann, Thesis, University of Munich, 1938; (b) J. Welhm, Thesis, Universit.y of Kfinigsberg. 1934.
The present work was undertaken to establish whether or not formula (3) could be applied to Souders' viscosity constant Is I
=
A4 (log log 7
+ k)/d
viscosity in millipoise; IC = constant = 2.9 in Souders' work; the logarithms are on decimal base). By using formula (3) the viscosity of a binary mixture can be calculated as log log = d(2lZl z J z ) / ( a M , 4- 2 2 4 4 2 ) - k (4) The values of 1, and I , can be calculated from Souders' work. To test formula (4) viscosity and density measurements were made on binary mixtures of toluene, bromobenzene and nitrobenzene using various concentrations a t temperatures from 25 to 35'. Experimental and Results (7 =
+
Viscosities were determined by an Ostwald type viscometer. Densities were measured in pycnometers provided with a thermometer and a glass cap to prevent evaporation. Tcmperatures were controlled within 10.03'. Viscometers, pycnometers and the flasks in which mixtures were stored were cleaned with dichromate-sulfuric acid solution, rinsed with dust-free distilled water and dried. That the viscometer constant remained uniform was verified at, intervals during the experiment. For every mixture the times of flow were recorded five times and the results averaged; the agreement among the flow times for every mixture was within less t,han 0.2%. The liquids used were purified by distillation and crystallization. After purification, the refractive index and density were determined and were found to be in very good agreement with values listed in the literature. Differential evaporation of the two componmts during an experiment cannot be completely eliminated. However the surface of the liquid which is in contact with air is small and t,he differential evaporation in most mixtures is not appreciable. Eight. mixtures were made for cvcry pair of compounds and results a t 25,.70and 35" arc presented in Tahlcs I, I1 and 111, t,ogcthcr with t,hc values calculated with formula (4). For t,ho t,oluenc-l,romobon7.cnc mixture measurement's wcrc iiiadc a t 25 and 30",only.
TABLB I OBSERVEDAND CALCULATED V~scosnwsI N TOLUENENITROBENZENE MIXTURES Mo!e fraction nitrobenzene
0.000 .115 .227 .344 .457 .577 .675 .787 .a70
1.o00 (5)
2.50
Obsd.
Calod.
5.52 6.22 7.02 8.03 8.94 10.30 11.69 13.74 15.42 18.20
5.52 6.20 6.95 7.96 9.09 10.55 11.83 13.80 15.68 18.20
30' Obsd. Calcd.
5.25 5.86 6.60 7.43 8.37 9.56 10.80 12.52 14.20 lG.82
5.25 5.80 6.58 7.42 8.48 9.79 10.97 12.71 14.13 16.82
350 Obsd. Calcd.
4.86 5.54 6.18 6.94 7.83 9.22 10.42 11.57 13.13 15.50
M. Souders, Jr., J . Am. Chem. Soc., 60, 154 (1938).
4.86 5.49 6.08 6.99 7.96 9.21 10.25 11.96 13.28 15.50
THEVISCWITYOF BINARYLIQUIDMIXTURES
Dec., 1952
1053
Discussion
TABLE I1 OBSERVED AND CALCULATED VlSCOSITIES I N BROMOBENZENE-NITROBENZENE MIXTURES
For the almost ideal solutions of bromobenzene, nitrobenzene and toluene, the constant k was taken Mole a,a 2.9000. The decimals were taken empirically up fraction 25' 30' 350 to the fourth place, although Souders reports the nitrobenzene Obsd. Calod. Obsd. Calcd. Obsd. Calcd. mean value as being 2.9. The average error be0.000 10.68 10.68 10.08 10.08 9.38 9.38 tween observed values and the values calculated .117 11.06 11.40 10.36 10.52 9.73 9.83 by formula (4) is &2.4% for all the concentration .225 11.64 12.00 10.75 11.21 10.15 10.45 ranges of these mixtures. .345 12.27 12.75 11.30 11.86 10.60 11.05 For the non-ideal solutions of primary alcohols .464 12.96 13.55 12.09 12.58 11.17 11.72 and organic acids in benzene and carbon tetra.554 13.52 14.17 12.46 13.17 11.73 12.28 chloride the same value for k (2.9000) was used, .676 14.65 15.15 13.55 14.20 12.51 13.05 except for the mixtures of butyl alcohol, hexyl al.790 15.56 16.20 14.59 15.17 13.45 13.99 cohol and amyl alcohol in benzene. For these the .887 16.73 17.20 15.51 15.96 14.23 14.60 value of k was calculated knowing the viscosity of 18.20 18.20 16.82 16.82 15.50 15.50 1.000 the mixtures at a known concentration when the TABLE I11 resultjng k was used. The maximum error was OBSERVEDAND CALCULATED VISCOSITIESOF TOLUENE- smaller than when the k of the universal value (2.9000) was used (Table V). Values for the acetic BROMOBENZENE MIXTURES Mole acid-carbon tetrachloride mixtures are also given fraction 25' 30 ' in Table V. bromobenzene Obsd. Calcd. Obsd. Calcd. 0.000 .129 .267 .379 .505 .629 .736 .853 .882 1 ,000
5.52 6.13 6.72 7.20 7.86 8.51 9.10 9.81 9.96 10.68
5.52 5.92 6.51 7.00 7.65 8.29 9.01 9.72 9.84 10.68
5.25 5.74 6.26 6.74 7.29 7.92 8.57 9.20 9.38 10.08
5.25 5.57 6.10 6.56 7.16 7.77 8.43 9.10 9.30 10.08
Since binary solutions of toluene, bromobenzene and nitrobenzene arc almost ideal it was decided that the applicability of formula (4) should also be tested for non-ideal solutions. Formula (4) was applied to mixtures of primary alcohols and organic acids in benzene and carbon tetrachloride, et 25', using the data of Jones and co-workers.6 Table IV gives the maximum error in calculated viscosities. Although the maximum error, in some cases, is large, the average error is only 2.9% (the value of Souders' constant used was k = 2.9000). MAXIMUMERROR
TABLE IV CALCULATEU VISCOSITIES FROM (4) EQUATION
IN
Coniponen t B
Component
A
Max. % error
Methyl alcohol Ethyl alcohol Propyl alcohol Butyl alcohol Hexyl alcohol Heptyl alcohol Octyl alcohol Decyl alcohol Acetic acid Butyric acid Caproic acid Heptylic acid Caprylic acid Butyric acid Valeric acid Caproic acid Heptylic acid Caprylic acid
Carbon tetrachloridc Carbon tetrachloride Carbon tetrachloridc Carbon tetrachloridc Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachbride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Benzene Benzene Benzene Benzene Benzene
6.4 5.3 7.8 10.8 11.4 7.3 3.7 5.4 4.8 5.0 9.0 15.0 3.6 5.5 4.8 3.4 4.2 3.3
% B at
max. error
50
70 20 20 20 80 20 20 15 15 80 80 15 50
50
40 40 60
(6) W. J. Jones. 8. T. Bowden, W. W. Yarnold and W. H. Jones, THIUJOURNAL, 62, 753 (1948).
TABLE V MAXIMUMERRORIN CALCULATEDVISCOSITIESFROM EQUATION (4) USING THE UNIVERSAL VALUEFOR k AND A VALUEPREVIOUSLY DETERMINED Com onent
%
Butyl alcohol Amyl alcohol Hexyl alcohol Acetic acid
Component
A
Benzene
.
Max. k
2.9000 2.9184 Benzene 2.9000 2.9119 Benzcne 2.9000 2.9195 Carbon tetra- 2.9000 chloride 2.9060
%
error
15.0 6.0 9.0 2.8 12.9 8.5 4.8 1.8
%B
at
m8X.
error
80 40 20 40 80 40 15 80
Jones and co-workersBexamined the many rela,tionships suggested for the variation of the viscosity of a mixture of liquids with composition and came to the conclusion that they do not afford proper representations when applied to the binary systems carbon tetrachloride-acids and alcohols, and benzene-acids and alcohols. The equation of Arrhenius,? Kendall,s Lees,s Bingham, lo Drucker and Kasse1,ll and Meyer and Mylius,12do not give curves with the minima in the graph for viscosity versus concentration in the mixtures containing the lower alcohols or the fatty acids. The formula of Kendall and Monroe,I3 Dolezalek and Schulze,14 Sachanov and Rjachowsky, l5 Van der Wyk, l6 Lederer, l7 Powell, Roseveare and Eyring, l8 Tuomikoski, (7) 9. Arrhenius, 2. physik. Chem.. 1, 289 (1887). (8) J. Kendall, Medd. Velenskapsadad. Nobdinsl., 2 , n. 25, 1 (1913). (9) C. H. Lees, PhiE. Mag., 1, 139 (1901). (10) E. C. Bingham, Am. Chsm. J., 86, 195 (1906). (11) K. Drucker and R. Kassel, Z . phyeik. Chem., 76, 376 (1911). (12) J. Meyer and B. Mylius, it~id.,96, 374 (1920). (la) J. Kendall and K. P. Monroe, J . Am. Chem. SOC.,89, 1788 1917). (14) F. Doleaalek and A. Schulze, Z. phyeik. Cham., 88, 74 (1913). (15) A. Sachanov and N. Rjachowsky, ibid., 86, 532 (1914). (16) A. J A. Van der Wyk, Nature, 188, 846 (1936). (17) E. L. Lederer, ibgd., 189, 27 (1937). (18) R. E. Powell, W. E. Roseveare and H. Eyring, Ind. Enu. Chem., 88, 432 (1941). (19) P. Tuomikoski. &"men. Kamialilehti, la,19 (1942).
1054
W. WEST,B. H. CARROLL AND D. H. WHITCOMB
LutschinskiZ0 and KottlerZ1 cannot be a.pplied when one of the components is partly associated. In order to compare the results with formula (4) with other expressions, formula (4)was applied t o n-octyl alcohol-carbon tetrachloride mixtures a t 2.5'. The resulting data (Table VI) together with the values given by the application of the formulas of Kendall and Monroe," Sachanov and Rjachowsky,ls Ishikawa,22 and Arrhenius,' indicates that only Sachanov-Rjachowsky formula gives better agreement than equation (4). However, as was observed by Jones and co-workers,B the SachanovRjachowsky formula cannot be applied in a general fashion, for instance in the case of acetic acidcarbon tetrachloride mixture where a minimum occurs, Spells2' and MacleodZ4 equations give better results for this same mixture, in one region of concentration, than formula (4). Both equations are inapplicable when there is great disparity between the viscosities of the pure components. The examination of all previous formulas shows a lack of generality; although for some types of mixtures they give good results, they are not applicable to all type of mixtures, for instance in the case where there is great disparity between the viscosities of the components, or when there is a (20) 0.P. Lutschinski. Symposium on Lha Viscosilu o/ Liquids and Colloid.. A c d . Sc. U.S.S.R., 1, 41 (1941). (21) F. Kottler. T H I.lOUBNAL. ~ 47, 280 (1943); 48, 76 (1944). (22) T. Iahikawa, BdE. Chem. Soe. Japan. 4, 7 (1929). (2.3) K. E. Spella. Trans. Faraday Soc.. a$, 537 (1936). (24) D. B. Macleod. ibid., 10, 20 (1923).
Vol. ,56
TABLE VI FORMULAS MIXTURES OF n-0cm-L ALCOHOL-CARBON TETRA-
COMPARISON OF ItESULTS OBTAINED BY VARIOUS
FOR THE
CHLORIDE, AT
W%ht alcohol 0 5 10 15 20 40 50
60 80 100
Sachanov
RiaKendall hlonroe chowsky 9.02" 9.02" 10.72 9.98 12.58 11.27 14.61 12.86 16.80 14.74 27.23 24.83' 33.41 31.23 40.23 38.41 55.7 54.8 73.3' 73.3"
25"
IshiAryhenius kawa 9.02" 9.02 10.63 10.94 12.33 13.05 14.13 15.33 18.03 17.83 29.28 24.83' 30.14 35.84 42.72 36.23 51.6 67.6 73.36 73.3
Present
work
9.02 10.33 11.61 13.23 15.07 24.49 30.48 35.31 51.05 73.3
Obsd. 9.02 10.00 11.39 12.97 14.70 24.83 3.124 38.47 65.8 73.3
a Values used by the respectivc authors to calculate constants of their equations.
minimum in the curve viscosity versus concentration. Although, in some cases, the application of formula (4) gives a large maximum error, formula (4) is quite general, and can be used for different types of mixtures and at different temperatures. The application of formula (4)to mixtures of normal paraffins, 2,+dimethylpentane and benzene has been presented by Lima26in another paper. Acknowledgments.-The author wishes to thank Professor Ethel L. French of the Chemistry Department, University of Rochester, for her kindness in improving the style in the manuscript. (25) F. W. Lima, J . Cham. Phys., 19, 137 (1981).
THE ADSORPTION OF SENSITIZIXG DYES IN PHOTOGRAPHIC EMULSIONS1 BY W. WEST, B. H. CARROLL AND D. H. WHITCOMB Coniniunicution No. 1468 from the Kodak Research Laboratories, Easlman Kodnk Company, Rochester, N . Y . Receivad December 16, 1061
Many cyanine dyes are adsorbed to the grains of photographic emulsions according to the lmigmuir equation, the molccules in the saturated monolayer being oriented with their planes parallel and projecting away from the surface at an average intermolecular distance of about 4.6 A. Les~well adsorbed dyes often exhibit a discoiitinuity between adsorption as isolated molecules and a c0-0 erative phase with different spectral characteristics. Polylayer adsorption also occurs, and merocyanines conform to fangmuir or approximate Freundlich curves according to the CIBSR. Non-planar dyes are feebly adsorbed compared with corresponding plenar dyes. Heats of adsorption, determined from the C l a p e - C l a u s i u s equation are about 10 to 12 kcal. per mole for the first additions of well-adsorbed cyanine dyes in silver ha i e gelatin emulsions, and decrease with increasing coverage. Both electrostatic and van der Waals forces contribute to the adsorption of cyanines, while some kind of linkage between Ag+ and doubly bonded S figurw for certain merocyrtnines. While correlations appear between the adsorption and optical sensitization of individual dyes relative adsorbability and relative efficiency of aensitizattbn of different dyes are not, in general, parallel quantities. The inefficient optical sensitization of non-planar dyes cannot be explained by their low adeorbability, nor is supersensitization caused by any material increasc of the strcngth of binding of the sensitizer f,o the silver halide in the presence of the supersensitizer.
Part I. Adsorption Isotherms and Heat of Adsorption
It has long been realized that a necessary condition for optical sensitization is the presence of the sensitizing dye in the adaorbed state a t the surface of the silver halide grains in the photographic emulsion. Stimulated by the realization that the nature of dye adsorption on silver halide grains is of inberest in the theory of optical sensitization ( 1 ) Read in part at the Symposium on the Colloid chemistry of the Photogrsphic Process. 119th National Meeting of the Amoricsn Cliomical Soeioty. Boston, Mass., April 1-5, 1951
Sheppard and Crouch2 initiated, in 1928, the determination of adsorption isotherms in silver halide suspensions. This and subsequent studies by Sheppard and his co-workers3-' established some of the fundamentals of dye adsorption on silver halide for cyanine sensitizers. They recognized thaC typical cyanine dyes ure flat molecules consisting of a coplanar arrangement of two heterocyclic nuclei linked by a methine or polymethine ( 2 ) R F: Slirpparcl and It. Crouch. J . Pligs. Chcm.. 89, 751 (1928). (3) S. E. Sheppard, R. H. Lambert and R. L. Keenan, ibid.. 86, 174
was.
(4) 8. E. Slicppard, Plryr., 7, 285 (1938).
R. TI. Lalnbcrt and R. D. Walkcr, J . Chem.
