AQUEOUS SOLUTIONS OF FLUORINATED SURFACTANTS
909
The Physicochemical Properties of Aqueous Solutions of Fluorinated Surfactants by K6zG Shinoda,* Masakatsu Hat& and Takao Hayashi Department of Chemistry, Faculty of Engineering, Yokohama National University, Oolca-8, Minami-ku, Yokohama, Japan (Received August 8 , 1971) Publication costs borne completely by The Journal of Physical Chemistry
The surface tension and the solubility of aqueous solutions of fluorinated surfactants (C,FZ,++~SO~M, C,F,,COOM, etc.) have been measured. The cmc's and the Krafft points of the fluorinated surfactants were determined from these data. The cmc of fluorinated surfactant is close to that of ordinary surfactant whose hydrocarbon chain length is about 1.5 times longer than a fluorocarbon chain. This relation is explained assuming the free energy change of transferring the -CFr group from the singly dispersed state (aqueousenvironment)to the micellar state is 1.6kT. The surface tension of several fluorinated surfactants whose chain length is longer than -8 or 9 was not depressed as low as expected. This is because the Krafft points of these surfactants are higher than the experimental temperature at which the hydrated solid form precipitates and the concentration of singly dispersed material does not increase. If the Krafft point were low, the surface tension would have attained as low as 20 dyn/cm above the cmc, as in the case of ethanolammonium perfluorooctanesulfonate. The correlation between the Krafft points and the structure of fluorinated surfactants is explained by the theory that a Krafft point is a melting point of hydrated solid agent.
Introduction Fluorinated surfactants are much more surface active than ordinary surfactants and stable against acidic, alkaline, oxidative, and reductive reagents as well as elevated temperature. Several dealing with the surface and colloidal properties of fluorinated surfactants in aqueous solution have been published, but they deal with only limited types of surfactants due to the difficulty of the synthesis of fluorinated compounds. In the present paper, (1) the effect of fluorocarbon chain length on the solubility and surface tension, (2) the effect of the kinds of gegenions on the Krafft point,9 and (3) the effect of the structure of fluorocarbon chain on the Krafft point have been studied in order to increase the solubility and to attain lower surface tension. If the Krafft point is depressed by use of the appropriate gegenion, the surface tension attains low values and the solubility increase enormously.
Experimental Section Materials. Metal salts of perfluorooctanoic acid, n-C7F&OOM, were the same materials described in earlier Potassium perfluorooctanesulfonate, C~FI~SO~ obtained K, from the Minnesota Mining and Manufacturing Co. was repeatedly washed by water to remove water soluble impurities after the recrystallization with absolute ethanol and dried at 110". Perfluorooctanesulfonic acid, CSFI~SO~H, was obtained by distillation of the potassium salt in the presence of 95% sulfuric acid (bp 150"; 14 mm).ll Metal salts were obtained neutralizing the acid by respective metal hydroxides. C71i'li30sISa, cgFlsSO~l/~Mg. 2H20, (211F z ~ S O ~ ~ / Z M ~ .(CF~)ZCF(CFZ)~COOH ~H~O, (mp = 13 14"), and (CFa)zCF(CFz)4CH=CHCH2COOH (mp = 63 68") were synthesized by T. H. The procedure of the synthe& will be published elsewhere.
- -
C7F16SOaNa and CeFlsSOs1/2Mg.2H20 were recrystallized from water and dried at 110". CsF19S03K was prepared by adding excess aqueous KC1 solution to an aqueous solution of C g F ~ s S O ~ 1 / ~ M g ~at 2 H80", z 0 well above the Krafft point of CgF~gSOa1/~Mg.2Hz0, then filtered and washed at 70 80". Potassium salt of (CFa)2CF(CF2)&H=CHCHzCOOHwas obtained neu80". tralizing by an aqueous KOH solution at 70 Excess amount of KOH (2%) was added in order to suppress hydrolysis. (CF3)2CF(CFz)4COOM were prepared by neutralizing an aqueous (CF&CF(CF2)4COOH solution with respective metal hydroxides. The electrical conductivity of water used was 1.2 1.4 pmholcm at 25". Procedures. Solubility Measurement. The solubility of surfactants was determined either by electrical conductivity (at low solubility) or by weighting the dried solution (at high solubility) after vigorous stirring of solutions over 1-2 hr which were kept in a
-
-
-
(1) J. H.Simons, Ed., "Fluorine Chemistry," Vol. 5,Academic Press, New York, N. Y.,1964,p 370. (2) N. 0.Brace, J . Org. Chem., 27,4491 (1962). (3) M. K. Bernett and W. A. Zisman, J . Phys. Chem., 63, 1911 (1959). (4) C. H.Arrington and G. D. Patterson, ibid., 57,247 (1953). (5) H.M. Scholberg, R. A. Guenthner, and R. I. Coon, ibid., 57, 923 (1963). (6) H.B. Klevens and M. Raison, J . C'him. Phys., 51, 1 (1954). (7) L. A. Schits, B/III, 143, 5th International Congress on Surface Active Substances, Barcelona, Spain, 1968. (8) K . Shinoda and H. Nakayama, J . Colloid Sci., 18,705 (1963). (9) The Krafft point is a temperature above which the hydrated solid surfactant melts and dissolves as micelles in water. So the solubility of surfactant increases enormously. Cf. K . Shinoda, et al., "Colloidal Surfactants," Academic Press, New York, N. Y., 1963, pp 7-9. (10) H.Nakayama and K . Shinoda, Bull. Chem. SOC. Jap., 40, 1797 (1967). (11) T.Gramstad and R. N. Haszeldine, J . Chem. SOC.,2640 (1957). The Journal of Physical Chemistry, Vol. 76, No. 6, 197.2
K. SHINODA, M. HATO,AND T. HAYASHI
9 10
thermostat controlled within f0.02". Further stirring caused no change in the solubiIity. Prior to the determination of the concentration the solution was allowed to stand about 30 min. The relations between the concentrations us. the conductivity at various temperature were determined using solutions of known concentration. These relations were used as calibration curves to determine the concentrations. It is confirmed that both measurements agree with each other. The solubility data are the means of more than two determinations. The respective values did not deviate more than 0.5% from the mean. Surface Tension Measurement. Surface tension was measured by a drop-weight method in an air thermostat controlled within 3t0.2". The correction by Harkins and Brown12 was applied. The time duration for 1 drop was 3-45 min depending on the time required to attain the equilibrium. The eurface tensions are average values of 2-4 measurements whose accuracy was =!=O,l dyn/cm around the cmc and zt0.3 dyn/cm at lower concentration.
I
IO1
I
0 000 I
0001 Concentration (mcle/l )
0 01
01
Figure 1. The surface tension of C,Fz,+lSOaM in water a t 25". Purity of C9FleSOaKis lower than the other surfactants (see text). .
.
,
,
.
,
50 D 5.
:[
Results and Discussion
c" 30
Surface Properties of Fluorinated Surfactants. The surface tension us. the concentration curves of metal salts of perfluoroalkanesulfonic acids are shown in Figure 1. Dotted lines illustrate the surface tension of solutions in which the hydrated solid agent precipitates. The surface tension of sodium dodecanesulfate is also shown for comparison. The surface tension us. the concentration curves of normal and branched perfluoroalkanecarboxylates are plotted in Figure 2. The minima of surface tension and the cross sectional areas per molecule at 25" are listed in Table I. The cross
Table I : The Surface Tension Minima and Cross Sectional Areas of Fluorinated Surfactants at 25'
Compound
n-C7F15S03Na n-CsF17S03Li n-CsF17S03Na n-CsFi7SOaK n-CsFi7S03NH4 n-CsF17S03NH3C~H40H n-CgFigS031/zMg.2Hz0 n-C7F&OONa (CFa)zCF(CFz)4COONa TL-C~F~SCOOK (CF~)SCF(CFZ)~COOK n-C7Fl&OOH (CFa)zCF(CF2)aCOOH (CF3)zCF (CFz)lCH=CHCHzCOOKa a
Minima of surface tension, dynes/cm
37.3 29.8 40.5 34.5 27.8 21.5 22.0 24.6 20.2 20.6 19.5 15.2 15. 36 ~ 1 5 . 5 19.4
In 0.02 N aqueous KOH solution.
The Journal of Physical Chemistry, Vol. 76, N o . 6, 1978
lot
I
I
b
I
0 0001
0001 Concentration
0 01 (mole/l
01
1
Figure 2. The surface tension of n-C7FleCOOMand (CF~)ZCF(CF$)~COOM in water a t 25'. The surface tension of (CF&CF(CFZ)~CH=CHCH~COOK was measured in 0.02 iV KOH aqueous solution in order to suppress hydrolysis.
sectional area of surface active ion, a2 = i/rzN, is calculated from the equation**13
Cross
sectional area, AI/ molecule
52.5 55.2 52.5 45.1 41.0 42.5 45.2 42.0 43.5 43.0 47.5 41.5
...
where CI is the concentration of surface active ion, rzis the surface excess of surface active ion, x is the number of charges of gegenion, and K , is 0.52 for n-CTF15COOK'3 and assumed 0.5 for the other surfactants. This equation takes into account the effect of gegenions on the surface tension us. the concentration curve.* The slope, (d-y/b In C,),, was determined by curve fitting a linear relationship in surface tension vs. the concentration just below the cmc. It is clear from Figures 1 and 2 that the surface activity of fluorinated surfactants is much larger than corresponding ordinary surfactsnts with the same chain length. The minima of the surface tension of fluorinated surfactants whose
48.0 (12) W. D. Harkins and F. E. Brown, J . Amer. Chem. Soc., 41, 519 (1919). (13) K. Shinoda and K. Katsura, J.Phys. Chem., 68, 1668 (1964).
AQUEOUS SOLUTIONS OF FLUORINATED SURFACTANTS
911
Table 11: The Effects of the Kinds of Gegenions and the Structure of Fluorocarbon on the Krafft Points Compound
Krsfft point, OC
Compound
Krrtfft point, "C
56.5 below 0 75 80
below 0 8.0 25.6 20.2 below 0 20 2.5 below 0 below 0 below 0 below 0
41 below 0 below 0
41 90 f 5
65
45
25' I
I
35 I
0 OC
IO
25 I
I
I
\
A\
\
A'
I
2.7
2.9
I
I/T
I
3.1
I
I
3.3
XI@
Figure 3. The solubility of CnFzn+lSOaMin water as a function of temperature. Purity of CoF1,SOsK is lower than the other surfactants (see text).
Krafft points are higher than 25' is generally high, whereas surfactants whose Krafft points are lower than 25" attain lower surface tension. The Krafft point of ethanolammonium salt is below 0" and the surface tension of aqueous solution is 21.5 dynes/cm. The Kraft Points and the Solubility of Fluorinated Xurfactants in Water. The solubility of fluorinated surfactants in water was determined as a function of temperature and shown in Figures 3 and 4. The dotted curves indicate that the data were less accurate than the other owing to the measurement at high or low temperature or to the small solubility. The temperature at which the solubility increases abruptly corresponds to the Krafft point, as summarized in Table 11. It is clear from Figures 3 and 4 that one should select surfactants whose Krafft points are lower than the experimental temperature in order to increase the solubility.
3.2
3.4 V T xi03
3.6
Figure 4. The solubility of n-C7F1&OOM in water as a function of temperature.
The saturation concentration of singly dispersed species, cmc, is not directly related to the solubility. It is evident from Table I1 that the Krafft points are raised with an increase of chain length as in the case of ordinary surfactants and the increment of the Krafft points with an increase of chain length of fluorinated surfactants is much larger14than that of corresponding ordinary sodium alkanesulfonate. Thus, the chain length of surfactants which form micelles around room temperature is restricted. It is also important to select a suitable gegenion of fluorinated surfactant whose (14) M. Hatti, and K. Shinoda, J . Chem. SOC.Jap., 91,27 (1970). (15) N. V. Tartar, and K. A . Wright, J . Amer. Chem. SOC., 61, 539 (1939).
The Journal of Physical Chemistry, Vol. 76, N o . 6, 107.@
912
K. SHINODA, M. HATO,AND T. HAYASHI
Krafft point is low in order to dissolve the surfactant at lower temperature. The Effect of the Kinds of Gegenions on the Krafft Point. It is evident from Table I1 that the Krafft points are markedly dependent on the kinds of gegenions. Krafft points may be affected by several factors such as bond nature between surface active ion and gegenion, structure of hydrated solid agents, or degree of hydration. Among these factors, the degree of hydration of solid agent seem8 most important. I n many cases, the more hydrated the gegenions, the lower the Krafft point. R b and Cs salts are exceptions. The low Krafft point of ethanolammonium salt can be explained in that the ethanolammonium is an organic group of low melting point and is likely to hydrate well. The Relation between Kraflt Point and the Structure of Fluorocarbon Chain. It is well known that melting points of organic compounds change drastically with the structure such as branching of and double bond in a hydrocarbon chain. This is also the case for Krafftpoint as can be seen in Table 11. A moderately branched compound shows a much lower Krafft point as well as melting point than a corresponding straight chain compound as shown in Table 111,but the melting point of
90
”
.2
0
.4
6
.8
1.0
mole fraction of CeFliSOnK Figure 5 . T h e Krafft point of binary surfactant mixtures. K e y : I, C8FI7SOsNH4 CsF17SOaK; 11, CsF17SOsH CsF17SOaK ; 111, CsFi7SOsNHaCzHaOH CsF17SOsK.
+
+
+
Table 111: T h e Melting Points and the Krafft Points of Straight and Branched Perfluorooctanoic Acids Compound
mp, ‘C
Krafft point, O C
n-C,F&OOH (CFs)&F(CFa)&OOH
56.4-57.9 13-14
20 below 0
symmetrically branched compounds such as (CF3)ZCFCF(CF3)Z (mp = -16.7016) is higher than n-C6Fl4 (mp = -87.1-86.05°17) just as in (CH3)3CC(CH& (mp = 100.63 100.69°1s)and n-CsH18(mp = -56.8 -56.918). The Kraft Point of Binary Surfactant Mixtures. It is expected that the Krafft point is depressed by mixing with another surfactant or by replacing with suitable interesting to examine whether g e g e n i o n ~ . ~ ~It * ~seems O the Krafft point of surfactant mixtures can be explained quantitatively by our m0del.l9*~~ The Krafft points of binary surfactant mixtures are estimated from the solubility of 5% solution of respective mixtures and shown in Figures 5 and 6 as a function of mole fraction. It is clear from Figures 5 and 6 that the Krafft points are depressed by adding another surfactant. The lower the Krafft point of surfactant added, the larger the depression of the Krafft point. The addition of a suitable salt into an aqueous solution of surfactant is also an efficient way to obtain the lower Krafft point, i.e., to increase the solubility. Actually the solubility of CsF17S03K in water increases by adding sulfuric acidz1 because the Krafft point of CBF17S03His below 0”.
-
N
The Journal of Physical Chemistry, Vol. 76, N o . 6,1978
0
I
I
I
I
,2
.4
6
8
I 1.0
mole fraction of ~ - C ~ F I S C O O K Figure 6. T h e Krafft point of binary surfactant mixture: n-C7FlbCOONa n-C7FlrCOOK.
+
By the analogy of a phase diagram of melting points of binary mixture, the curves in Figures 5 and 6 can be explained, since the curves illustrate a temperature at which a solid phase appears from the liquid mixture (mixed micelle). If the mole fraction of the second component in the micelle is small, the activity of the first component is estimated by the Raoult’s law. Then, the change in Krafft point of surfactant mixtures may be expressed just as the well-known equation on freezing point depressionz2 (16) G. A. Crowder, M.S. Thesis, University of Florida, (1961); p 177 in ref 3.
(17) V. E . Stiles and G. H. Cady, J . Amer. Chem. Soc., 74, 3771 (1952). (18) J. TimFermans, “Physico-Chemical Constants of Pure Organic Compounds, Elsevier, Amsterdam, 1950, pp 85, 96. (19) K. Shinoda, T. Nakagawa, B. Tamamushi, and T . Isemura, “Colloidal Surfactants,” Academic Press, New York, N. Y., 1963, P 7. (20) K. Shinoda and E . Hutchinson, J.Phys. Chem., 66,677 (1962). (21) Reference 1, pp 374-377. (22) W. J. Moore, “Physical Chemistry,” Prentice-Hall, Englewood Cliffs, N. J., 1962, p 134.
913
AQUEOUSSOLUTIONS OF FLUORINATED SURFACTANTS Table IV : Cmc of Fluorinated Surfactants Cmc mol/l.
Temp, W
0.0175 0.0063 0.0085 0.0080 0.0055 0,0046 0.00064 -0.00014 0.036 0.027 0.027 0.028 0.0090 0.0080, 0.0091 0.033 0.032 0.030 0.0085 ~0.0015~
56 25 75 80 41 25 41 90-100 8.0 25.6
Compound
n-Cbl&OaNa n-CeF1~SOaLi n-CsHI7SO3Na n-CsF17SOaK n-CSirSOaNHa n-CsFirSOaNHsCzHaOH n-CgFigSOal/zMg.2Hz0 n-CiiFpaSOa'/zMg 2Hz0 n-C7F16COONa n-C7FisCOOK
~-CTFISCOONH~ (CF&CF(CFz)&OONa (CFs)zCF(CFz)aCOOK (CFa)zCF(CFa)4COOH
(CFa)zCF(CFz)aCH=CHCHzCOOK 0
Method
Solubility Surface tension Solubility Solubility Solubility Surface tension Solubility Solubility Solubilitylo Solubility10 Dye method6 Solubilit y lo Solubility10 Surface tension'0~a Solubility lo Surface tension Surface tension Surface tension Surface tension
20.2 20 25 2.5 25 25 25 25
In 0.02 N KOH aqueous solution.
In XIm = -(AHlf/R)(l/T - l/Tto)
(2)
where Xlm is the mole fraction of first component in the micellar phase, AHlf is the heat of fusion of hydrated solid surfactant (component l), T is the absolute temperature and TfO is the Krafft point of surfactant (component 1). Introducing the heat of fusion, AHlf = 9.6 kcal/mol,2a and the Krafft point 25.6" of C7FIsCOOK into eq 2, we can evaluate the change of Krafft point of mixtures as a function of mole fraction of first component in the micelle. The calculated values are shown in Figure 6 by a dotted curve. The initial slope well agrees with the experimental curve. Change of the Krafft point over the mole fraction range will be discussed in the succeeding paper which deals with the Krafft point of mixtures of calcium salts. Cmc of Fluorinated Surfactants. Cmc's were determined either fram the solubility us. temperature curves or from surface tension us. concentration curves and are summarized in Table IV. It can be concluded from Table IV that the cmc values of fluorinated surfactants are mainly determined by the fluorocarbon chain length and the valency of gegenions. Difference in species of gegenion of the same valency has less effect on the cmc. The smaller cmc values of C,F&OOH than those of corresponding salts may be the result of the incomplete dissociation of the acid. Cmc values of univalent salts of perfluorononanesulfonic acid (CgFlgSO3M) are estimated to be 0.003-0.001 mol/l. from the change in cmc with chain length. This value is about 4-5 times larger than that of the bivalent salt C9FlsSO3'/zMg. 2H20 in Table IV, just as the relation of the cmc values of univalent and bivalent salts of ordinary alkane~ulfonate.~~ This dif-
ference is explained by the smaller electrical potentia of the micellar surface, h, of bivalent saltz4
where Zr is the number of charges of the gegenions, C , is the concentration of gegenions, and Q is the charge density of micellar surface. Thus, it is clear that the electrical contribution for the micelle formation of fluorinated surfactants is also explained as a function of the number of charges of the gegenions, the concentration of gegenions, and the charge density of the micelle surf ace. The cmc values of fluorinated surfactants and ordinary surfactants26p26are compared in Table V. The cmc is expressed as a function of chain length, in the case where no salt added.27s28 Table V: The Comparison between the cmcs of Fluorinated Surfactants and those of Ordinary Surfactants cmc, mol/l.
Compound
C8F17S03Na CaF1$30aK C7Fl6COONa C~FI~COOK
Temp, "C
0.0085 75 0.0080 80 0.036 8 0.027 25.6
Compound
cmc, mol/l.
ClzHz6SOaNa C12H26S04Na CllHe3COONa CllHp8COOK
0. 0O8lz4 0.0081 0. 02626 0.
Temp, 'C
25 25 25 25
(23) K. Shinoda, S. Hiruta, and K. Amaya, J. Colloid Interface Sci., 21, 102 (1966). (24) See p 50,eq 1.52 in ref 19. (25) R. J. Williams, J. N. Phillips, and K. J. Mysels, Trans. Faraday Soc., 51, 728 (1955). (26) H.B.Klevens, J . Amer. Oil Chem. Soc., 30,74 (1953).
The JOUTTUL~ o j Physical Chemistry, Vol. 76, No. 6,1978
914
F. R. MCFE~LY AND G. A. SOMORJAI In cmc =
-
___ ( " @ ) + K
(4) 1 + K , kT where m is the number of carbon atoms in the chain, w is the free energy difference per methylene group between micellar state and singly dispersed state, K and K , are the experimental constants, T is the absolute temperature, and k is the Boltzmann constant. K, and K are determined experimentally from the change of cmc with the concentration of the gegenions and the change of cmc with the number of carbon atoms in a paraffin chain. The free energy difference of transferring a -CH2- group from aqueous environment to micellar aggregate is estimated to be 1.08kT for ordinary surfact a n t ~ and ~ ' that for -CF2- is extimastedto be 1.6kT from __.
the change of the cmc values with the fluorocarbonchain length. As the K value in eq 4 does not change much with the kinds of surfactants, the cmc of a fluorinated surfactant is close to that of an ordinary surfactant whose hydrocarbon chain length is about 1.5 times longer than the fluorocarbon ~ h a i n . ~ 9 (27) P 37-42, eq (1.44)and (1.45)in ref 19. (28) K. Shinoda, Bull. Chem. SOC. Jap., 26, 101 (1953). (29) Tables of surface tension and solubility data will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth St., N.W., Washington, D. C. 20036,by referring to author, title of article, volume, and page number. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche.
Studies of the Vaporization Kinetics of Hydrogen-Bonded Liquids by F. R. McFeely and G. A. Somorjai* Inorganic Materials Research Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, California 947.80 (Received July $3,1971) Publication costs assisted by the U . S . Atomic Energu Commission
The vacuum evaporation rates of glycerol, ethylene glycol, and triethylene glycol have been measured in the temperature range 5-50' using a microbalance. The activation enthalpies of vaporization of the three liquids were found to be different from their enthalpies of vaporization. The vacuum evaporation rates for glycerol and triethylene glycol were about one-third of the maximum rate that can be calculated from the vapor pressures, and one-twentieth of the maximum rate for diethylene glycol. It appears that breaking one or more hydrogen bonds at the surface is the rate-limiting step in the mechanism of vaporization of these largely hydrogen-bonded liquids.
Introduction To date there have been many studies of the vaporization kinetics of single crystal surfaces. These investigations have revealed a variety of vaporization mechanisms.I For some of the solids the desorption of loosely bound surface species was rate limiting (most metals). For other compounds, bond-breaking at well-defined surface sites, surface chemical reactions, association or dissociation were rate limiting. I n cases where desorption of molecules at the vaporizing surface was not the rate limiting step, the observed vaporization rate was frequently found to be less than the maximum possible rate, J,,,c, that can be calculated from the kinetic theory of gases. The vaporization coefficient av = Jobsd/Jmaxhas been used to indicate the magnitude of the deviation of the observed rate, J 0 b s d , from the maximum rate. I n contrast, the vaporization kinetics of liquids have not been investigated. WyllieZhas measured the vacThe Journal of Physical Chemistry, Vol. 76, No. 6, 1078
uum vaporization rates of several liquids at one temperature and has thus obtained values for the vaporization coefficient cyv. However the lack of information about the activation enthalpy of vaporization, AH,*, which can only be obtained from studies of the vaporization rates as a function of temperature, precludes any deduction of the vaporization mechanism. We have studied the vacuum vaporization rates of glycerol (CH20HCHOHCH20H), diethylene glycol (CHZOHCH~OCH~CH~OH), and triethylene glycol (CHZOHCH~OCH~CH~OCH~CH~OH) in the temperature ranges 18-50', 5-30', and 10-40°, respectively. From the data the vaporization rates and AH,* for each' liquid were obtained. The experimental results indicate that the breaking of a specific number of hydrogen bonds may be the rate limiting step in each case. (1) G.A. Somorjai and J. E. Lester, Progr. Solid State Chem., 4, 1 (1967). (2) G.Wyllie, Proc. Roy. Sac., Ser. A , 197,383 (1949).
