MOLECULAR ASSOCIATION INDUCED BY FLOW IN SOLUTIONS OF SOME MACROMOLECULAR POLYELECTROLYTES BY M. JOLY Service de Biophysique, Institut Pasteur, Paris Received 23rd Janiiary, 1958 The molecular solutions of several types of macromolecular polyelectrolytes are stable only at rest. As soon as a laminar flow takes place in the solutions, aggregation of the macromolecules occurs giving rise to particles of colloidal dimensions. Such an aggregate formation is reversible or not as a function of the velocity gradient depending on the nature of the solutions studied, but even where reversible, the phenomenon shows hysteresis. These behaviours are investigated by streaming birefringence measurements, mainly with several kinds of protein systems. A tentative interpretation of the flow-induced associ- ation is given on the basis of the collision and orientation theory.The sizes, mean-lives and formation kinetics of the aggregates are derived in terms of intermolecular forces and velocity gradient. A few consequences of this aggregdtion, such as dynamic turbidity are briefly indicated. It has been well known for a long time that laminar flow increases the velocity of aggregation of colloidal particles in unstable sols. An explanation of this phenomenon was first proposed by Smoluckowski 1 on the basis of the collision theory. A survey of the behaviour of suspended particles under laminar shear has been recently given by Mason and Bartok.2 For macromolecular poly- electrolytes, it is sometimes observed with suspensions which are perfectly stable at rest that the aggregation occurs as soon as they are submitted to a laminar flow of sufficiently high velocity gradient.Consequently the size of the particles in these solutions increases with the rate of shear. On the other hand, the shearing forces, if large enough, can break the particles,3 and a decrease of the pzrticle size is observed at high velocity gradient. This disruption has been shown with tobacco mosaic virus particles.4 By superposition of these two processes the size of particles in the flowing solution can successively increase and decrease with increasing velocity gradient. Such a behaviour has been described in mixtures of tobacco mosaic virus and sodium dodecylsulphate.5 The purpose of the present paper is the experimental study of the variations of the particle size (as a function of the velocity gradient), due to the aggregation or disaggregation induced by flow in dilute solutions of various polyelectrolytes. The size of the particles is determined by streaming birefringence. EXPERIMENTAL MATERIALS The acrylic acid + acrylonitrile copolymers (Acan) have been prepared and analyzed by Clavier.6 Actomyosin and myosin, prepared by Schapira and Dreyfus,7 were re- spectively obtained by the methods of Greenstein and Edsall8 and of Mommaerts.9 Metam yosin, a new muscle protein, was isolated and purified by Marcaud-Roeber.10 L-meromyosin was prepared by Broun and Kruh11 by partial trypsin hydrolysis of a myosin extracted according to Szent-Gyorgyi 12 and purified according to Mommaerts.9 Horse serum proteins, obtained by salting-out with (NII4)2S04 were purified by Barbu.13 Salmine sulphate was a commercial Roussel product, and histone sulphate was prepared by Rybak 14 from calf thymus by HCl extraction, picric acid precipitation and ethanol purification. METHODS The solutions under investigation are forced to flow between two coaxial cylinders, the inner of which rotates at various but well-defined speeds.For each value of the 150M. JOLY 151 velocity gradient g , or as a function of the time t for a given value of g , the extinction angle x is determined with an accuracy of & 0.1" by the differential method of Frey- Wyssling and Weber.15 The design of the apparatus has been given elsewhere.16 All the systems investigated here are polydisperse.Therefore the streaming birefring- ence measurements allow us to determine only the order of magnitude of the particle size. Indeed, as we have shown 17.18,19 for very elongated or of quasi-globular particles rigid enough to be undeformed by the flow in the experimental conditions, the length or the diameter of the ellipsoids hydrodynamically equivalent to the most frequent particles in a given suspension and the corresponding polydispersity ratio can be derived from the values of the apparent particle length or diameter for two suitably chosen values of the velocity gradient. But this derivation is only valid with the assumption that the particle- size distribution does not depend on the rate of shear. Now this is not the case with the present systems since they are characterized by their ability to form aggregates by flow.Consequently we can only consider the values of the apparent length I, or diameter d, of the particles and their variations as a function of g, which gives only the order of mag- nitude of the true value of the particle size since we cannot determine the polydispersity ratio in the present case. Noting that the apparent length I,(g) of the particles of any system for a given velocity gradient is defined as the length of the particles in an infinitely dilute monodisperse system of rigid ellipsoids which for the same g would give the same value of x as obtained with the system studied. Such a definition does not imply that the true particle shape is an ellipsoid. The values of I, or d, are deduced from those of the rotational diffusion constant D by means of the Gans re1ation;zo the relationship between x, g and D has been determined with high accuracy.21 For monodisperse systems, I, evidently does not vary with g ; for polydisperse systems all particles of which consist of the same substance, I, or d, decreases with increasing g and this variation is reversible.Consequently, if the apparent size increases with g over a given range of rate of shear, it can be concluded that the true size of the particles increases with g. This could be due to the deformability of the particles, but in such a case the apparent size variation would be reversible with respect to g , except perhaps for a small hysteresis. But when such a variation is largely irreversible, one can affirm that there is aggregation induced by the flow.Likewise, when I, or d, irreversibly decreases with increasing g for sufficiently high values of it, this means that, even if this flowing system is a poly- disperse one, the particles are more or less broken by the shearing forces. RESULTS Already in 1912 it was shown 22,23 that the agitation of a Cu(OH)2 sol increases the size of the suspended particles, and much more recently very large fibres of the 1 : 1 copper + cystin complex were obtained 24 by stirring dilute solutions. Concerning the shear-breaking of particles in flowing solutions, we shall not consider the rupture of covalent linkage at very high rate of shear 25 but only that of low energy bonds like hydrogen bridges or van der Waals forces as observed with tobacco mosaic virus,4 denatured serum albumin 26.27 or deoxyribonucleic acid.28 An interesting case is when the shear-broken particles are small liquid droplets suspended in a liquid phase, as observed by Winsor 29 with mixtures of cyclohexane, sodium tetradecane-5 sulphonate, water and nonylamine or cyclohexanol, by Silberberg and Kuhn 30,31 with mixtures of 1.1 % polystyrene and 1.7 % ethylcellulose in benzene a few degrees above the critical temperature of dissolution, and by Barbu and Joly 13, 18 with compressed serum albumin solutions.Our purpose is to determine the quantitative correlation between the size variation, the flow characteristics and the other parameters of the solutions. ACRYLIC ACID + ACRYLONITRILE COPOLYMERS With a 0.1 % aqueous solution of a sample of Acan, the molecular weight of which is 11.5 x 104 and an acrylic acid content of 20 %, do of the aggregates grows from 375 8, to 405 8, when g increases from 104 to 2 x 104 sec-1.With higher concentrations, the aggregation occurs very rapidly at low value of g. For instance, with 1 % solution, d, = 3300 8, for g = 400 sec-1. At higher velocity gradients, the aggregates are disrupted by the shearing forces and the particle size decreases: g = 1200 sec-1, d, = 2300 A ; g = 5500 sec-1, d, = 1300 A. One obtains similar results with such copolymers of various compositions and lower molecular weights, but all these systems do not show a good reproducibility, even in presence of KC1 or dimethylformamide, and the results are not accurate enough to characterize the effects of the different parameters.152 FLOW ASSOCIATION OF MACROMOLECULES HORSE SERUM ALBUMIN IN PRESENCE OF TRIVALENT IONS Similar behaviour has been observed with horse serum albumin (SA) in presence of trivalent cations in the range of velocity gradient for which the flow remains laminar (fig.1, curves 7 and 8). As said before, the flow aggregation is demonstrated by the irre- versibility of the d,(g) variations. Thus for g increasing from 450 to 9900 and then de- creasing from 9900 to 450 sec-1, d, measured at g = 450 sec-1 before and after g variation increases from 3450 to 3800 A with 0.6 % SAY pH 5.6 in 0.0002 M A1C13 : from 2700 to 3500 8, with 2.4 % SA, pH 6.0 in 0.001 M AICl3 and from 2900 to 3200 A with 4 % SA, PH 3.8 in 0.002 M AlC13.i f 3000 d 0 2COG I000 0 FIG. 1 .-Particle-size variations induced by flow. 1. Compressed horse serum albumin. A, 1 h ; 8000 kg/cm2 ; 37°C. (1) 4 ”/, ; pH 6-9 ; c = 1 %. (2) id. pH 7-4 ; B, 16 h ; 10,OOO kg/cm2; 37°C. (3) 6.9 % ; pH 6.3 ; c = 1-2 %. (4) 8.3 % ; pH 4.35 ; c = 1-66 %. (5) id. pH 4.4. (6) id. pH 4.45. (c = con- centration of flowing solution.) 11. Horse serum albumin with trivalent cations: (7) 0.6 %; 0.0004 M AlCl3; pH 6.9. (8) 2.4 %; 0.0002 M FeC13; pH 6.2. COMPRESSED HORSE SERUM ALBUMIN A similar study has been done with SA solutions submitted to very high hydrostatic pressures. This treatment causes the separation in the solutions of submicroscopic droplets more concentrated in protein than the surrounding medium.13.18 As shown in fig. 1, the flow behaviour of these very viscous droplets is quite analogous to that of SA in presence of trivalent ions.The comparison of the curves 4, 5 and 6 shows the con- siderable effect of the pH value near the isoelectric point on the ability of the droplets to coalesce by flow collisions. Curves 1 and 2 indicate that the pH effect is still important quite far from the isoelectric point. MYOSIN AND RELATED MUSCLE PROTEINS The amplitude of the size variations with g is often larger with elongated particles than with globular particles, as seen, for instance, in fig. 2. Curves 1 and 2, for concentrated and highly aggregated rabbit myosin solutions, show the powerful effect of the pH on the resistance of the particles to flow break-up. Curve 3 shows the rapid aggregation of the sheep foetus metamyosin molecules, the apparent length of the aggregates being twice as large for a four-fold increase in velocity gradient.The high sensitivity to the flow of this muscle protein is clearly seen in the variation with flow duration of I, measured at constant g. For instance, with a 0.01 % solution of adult rabbit metamyosin, the values of la measured after 2, 4, 6 and 8 min of laminar flow at g = 5500 sec-1 are respectively 1050, 1950, 2950 and 4300 A ; afterwards the solution becomes turbid. Rabbit L-mero- myosin (curve 4) is much less dependent on the velocity gradient. PROTEIN COMPLEXES The competition between the building-up and the breaking-up of the aggregates is clearly evidenced by the shape of the Za(g) curves obtained with mixtures of acid and basicM.JOLY 153 proteins that give rise to complex f0rmation.32~33 These curves exhibit in the range of laminar flow a wide and almost symmetrical maximum (fig. 3). The comparison of the curves 3 and 4 shows the remarkable influence of salt on the aggregate stability of such protein complexes. On the other hand, it is to be noticed that by long stirring at low rate of shear these solutions can give rise to macroscopic fibres. l a 4000 2000 0 I 3 6000 8ooooo 1000 2000 - 3000 4000 5000 60 9 sec-' FIG. 2.-Particle-size variations in flowing solutions of muscle proteins. I. 0.11 % rabbit myosin, 1-0 M KCI. (1) pH 6.8. (2) pH 6-7. 11, 0.05 % sheep foetus metamyosin. (3) pH 6.8; 0.4M KC1 + 0.1 M phosphate buffer. 111, 0.01 % rabbit L-meromyosin.(4) pH 6.65 ; 0.6 M KCl + 0.1 M phosphate buffer. 5000 L- I 0 1000 2000 -3000 9 sec-' FIG. 3.-Particle-size variations due to flow. (1) 0.16 % SA + 0.04 % SH; (2) id. + 0.01 % colchicin; (3) 0.06 % SA + 0.09 % SS ; (4) id. + 0.04 M NaCl; (5) 0-18 % EG + 0.012 % SS; 0.25 M NaCI; (6) 0-25 % EG + 0.018 % SS; 0.18 M NaCl; 0.07 % ATP. (SA: horse serum albumin; SH: histone sulphate ; SS : salmine sulphate ; EG : horse serum euglobulin). RABBIT ACTOMYOSIN It is of interest to compare the flow aggregation of the preceding artificial complexes with the behaviour of a natural protein complex like actomyosin. In fig. 4 the curves have been roughly classified according to the existence of a flat or cf a maximum in the Z, variation at rather high velocity gradient, in relation to resistance of the aggregates to the shear1 54 FLOW ASSOCIATION OF MACROMOLECULES break-up. All these curves exhibit a flat part at low g and then an abrupt variation of slope in a narrow range of g, the sign of the curvature changing at a rate of shear of about 2OOOsec-1.This suggests the need of a critical extent of particle orientation to enable the collisions to be efficient for aggregation. As with myosin solutions there is an important effect of pH on aggregation and dissociation as shown in the curves 10-14. The effect of ionic strength on aggregate stability clearly appears in curves 6 and 13, 12 and 16, and 18 and 20 ; it depends on the protein concentration and pH. d l a 7000 9300 i; 8000 fa 6000 - - 4 003 I I 3000// 5 I8 10 0 FIG.4.-Particlesize variations in flowing solutions of rabbit actomyosin. I. 0.01 % ; 1.0 M KCI; (1) pH 8-65. 11. 0.025 % ; 1.0 M KCl ; (2) pH 8.3 ; (3) pH 8.4. 111.0.05 %. A, H20 ; (4) pH 3.65 ; (5) pH 4. By 0.25 M KCl ; (6) pH 8-4 ; (7) pH 8-5. C, 0.5 M KCI ; (8) pH 6.7 ; (9) pH 8-2. D, 1.0 M KC1 ; (10) pH 6.8; (11) pH 7-5; (12) pH 8.3 ; (13) pH 8.4; (14) pH 8-6. E, 1.5 M KCl; (15) pH 6-9; (16) pH 8.3. F, 2.0 M KCl; (17) pH 6.95. IV. 0.12 %. G, 0.25 M KC1; (18) pH 7.2. H, 0.5 M KCl ; (19) pH 6.5 ; (20) pH 7-2. 5000; ' - - I 1000 2000sec-,3000 4000 9 HEATED HORSE SERUM ALBUMIN Solutions of horse serum albumin denatured by moderate heating have been exten- sively studied from the view-point of flow aggregation. The main experimental results are summarized in fig.5, 6 and 7. The curves of the fig. 5 relate to particles the Iength of which never decreases with increasing g in the range of laminar flow ; the curves plotted in the upper part of the graph concern solutions heated in presence of salt. With all these solutions the apparent length of the aggregates fist increases more or less rapidly with g and then remains practically constant at a value of g that is smaller the higher the protein concentration, ionic strength and heating temperature, the nearer the pH is to the isoelectric point and the longer the duration of heating. The length of the flat part of the curves increases with increasing protein and salt concentration and with tem- perature; the corresponding aggregates are all larger as the pH value approaches the isoelectric point.Fig. 6 and 7 show the behaviour of SA aggregates the size of which more or less rapidly reaches a maximum before it decreases; fig. 6 refers to solutions heated without salt and fig. 7 in presence of salt. Generally the solutions for which the particles pass through a maximum size for a defined value of g are characterized by a higher ionic strength or a pH nearer the isoelectric point than those of the solutions the ldg) curve of which does not exhibit a maximum. For almost all these solutions &(g) very sharply increases with g at low rate of shear, denoting an easy flow aggregation, whereas after the maximum, la rather slowly decreasesM. JOLY 155 FIG. 5.-Particle-size variations in- 500 duced by flow in heated horse serum albumin solutions.I, 10 rnin at 80°C. A, 0.75 % ; (1) 0-002 M NaN03 ; pH 7. B, 2 % ; (2) pH 7.3. C, 2.4 %; (3) pH 7 ; (4) pH 5oo 7.4 ; (5) id., 0.0004 M NaC1; (6) pH 6-9; 0.0002 M BaC12; (7) pH 3.9; 2ooo 0.02 M acetate buffer. D, 2-9 % ; (1 1) pH 3.9; (13) pH 4. E, 3 %; (20) 0.01 M Na2S04; pH 8.6. F, I 500 3.9 % ; (21) pH 3.7 ; (22) pH 7.9. 11, 5 min at 100°C; 2.4 %; (8) 0.02 M acetate buffer ; pH 3-9. III,20 min I 090 at 55°C; 2.9 %; (14) pH 4.4. IV, 10 rnin at 60°C; 2.9 %; (15) pH 530 4.4. V, 10 rnin at 70°C; 2.9 %; I 5 0 0 rnin at 100°C. G, 2.5 ; (9) pH 4.4. l a I000 i f a (10) pH 3.9; (16) pH 4.4. VI, 10 H, 2.9 %; (12) pH 3.9; (17) pH 7.1 ; IOOC -Qa 500 (19) 7.5. 2 ooc i &I I50C I ooc 5 OC ii 2000 1, I500 1000 50C FIG. 6.-Particle-size variations induced by flow in heated horse serum albumin solutions.I, 10 min at 80°C. A, 1.6 %; (1) pH4.4. B, 2 % ; (2) pH 4-3 ; (3) pH 6.7. C, 2-4 %; (4) pH 4.3; (5) pH 4.4; (6) pH 6.6; D, 2.5 % ; (7) pH 7.8. E, 2.9 %. (8)pH4-1; (9)pH7-1. F,3*1 %; (10) pH4; (11) pH 7. 11, 8.1 % SA heated 10 rnin at 60°C and diluted to 3.3 % after storage G, pH 4-3 ; (12) 22 h ; (13) 28h ; (14) 19 days. H, pH 4.5; (15) 19 days. 111, 2.5 % SA heated 10 rnin at 80°C and pH 7.8; measured at (16) pH 7.8 ; (17) pH 7.2.156 FLOW ASSOCIATION OF MACROMOLECULES with increasing g as a consequence of a strong resistance of the aggregates to the flow break-up. As a first approximation the maximum is higher and reached at a lower value of g as the protein concentration and ionic strength are greater and the pH value is nearer the isoelectric point.The preceding examples indicate that flow association is a frequent phenomenon. Thus, it is often observed with liquids extracted from biological medium. For instance, the sap obtained by grinding of cooled tobacco leaves infected by mosaic virus contains particles which aggregate very easily by laminar flow of this sap. Therefore it might be asked if in some cases the structure of living matter is not due in part to its state of motion in the cells.34 it l a I500 2ooc I000 A l a 1500 2 000 1000 2 500 8 1, 2000 I 5 0 0 1000 I 5 I IL 2500 5000 ,7500 I00 9 sec- FIG. 7.-Particle-size variations induced by flow in heated horse serum albumin solutions. I, 2.4 %; 10 min at 80°C; (1) pH 4 ; O.OOO4 M KCN ; (2) pH 4.15 ; 0.02 M ace- tate buffer; (3) pH 6.6; 0.002 M NaCl; (4) pH 6.9 ; 0.0005 M BaC12.A, pH 7 ; ( 5 ) 0.01 M NaF; (6) 0.01 M NaCI. B, 7.4; (7) 0.001 M NaCl; (8) 0.002 M NaC1; (9) 0.004 M NaCl ; (10) 0.01 M NaCI. 11, Various concentrations ; 10 min at different temperatures. C, 0.19 % ; pH 7 ; 0-005 M Na~S04; (11) 80°C; (12) 100°C; (13) 0.38 %; pH 7 ; 0.005 M Na2S04; 80°C; (14) 0.6 % ; pH 4-15 <A0-02 M acetate buffer ; 100°C; (15) 1-5 %; pH 7 ; 0.002 M NaN03 ; 80°C; (16) 1.6 %; pH 4.4; 0-01 M CaC12; 60°C. 111, 3.1 %; 10 min at 80°C. D, pI-1 4 ; (17) 0-0017 M NaCl; (18) 0.002 M LiCI. E, pH 7 ; (19) 0.0008 M NaCl ; (20) 04017 M NaCl ; (21) 0.0033 M NaCl. DISCUSSION Besides the irreversibility of the l,(g) or d,(g) variations, a supplementary proof that the increase of particle size with g is due to aggregation and not only to particle deformation, even when the extent of this variation is small, is indicated by the following fact.The increase of 1, or d, is very often accompanied by an extremely sharp increase of the turbidity, and frequently, if the flow duration is long enough and the rate of shear sufficiently low not to break up the aggregates, precipitation occurs. For interacting globular particles a tentative interpretation has been recently given 35 for the flow aggregation, assuming that the rate of shear is low enough to avoid breaking up the particles. The calculations were based on an extension 13 of the treatment given by Tobolsky 36 in polymerization kinetics by introducing a flow collision term derived from the relationship given by Mason.37~ 38 As a first approximation the variation of the mean volume of a globular ag- gregate built up by the flow is given byM.JOLY 157 for low values of the rate of shear and concentration. 00 is the volume of each initial solute particle before solution flow and aggregation ; no is the total number of initial solute particles or molecules per ml; A = (2kT/3n~) F(U), 7 being the solvent viscosity and F(U) the probability of a particle surmounting the potential barrier of height U which separates two initial particles before collision; B~(kT/21n)*exp (- W/kT), where nz is the mass of each initial elementary particle or molecule and W the mean value of the interaction energy between each molecule and all its neighbours in an aggregate. A more elaborated treatment including the shear break-up of the particles is now in progress.The case of flow aggregation and disaggregation of elongated particles leads to a more difficult mathematical derivation, the principle of which has been given before.35.39 These calculations will be published in full in a forth- coming paper. They give a good approximation for the order of magnitude of the experimental results of streaming birefringence and dynamic turbidity, and enable one to determine the values of the potential barrier and interaction energy between the aggregating particles and to compare them with the theoretical values when available.40 1 Smoluchowski, Z. physik. Chem., 1918, 92, 129. 3 Mason and Bartok, Brit. SOC. Rheology Meeting (Swansea, 1957). 2 Kuhn, Z.physik. Chem. A , 1932, 161, 1 and 427 ; Kolloid Z., 1933, 62, 269. 4 Joly, Bull. soc. Chim. biol., 1948, 30,404 ; 1949, 31, 108. 5 Joly, Biochim. Biophys. Acta, 1952, 8, 134, 245. 6 Clavier, Thesis (Paris, 1956). 7 Joly, Schapira and Dreyfus, Arch. Biochem. Biophys., 1955, 59, 165. 8 Greenstein and Edsall, J. Biol. Chem., 1940, 133, 397. 9 Mommaerts and Parrish, J. Biol. Chem., 1951, 188, 545. 10 Raeber, Schapira and Dreyfus, Compt. rend., 1955, 241, 1000. 11 Schapira, Broun, Dreyfus and Kruh, Compt. rend. SOC. Biol., 1956, 150, 944. 12 Szent-Gyorgyi, Arch. Biochem. Biophys., 1953, 42, 305. 13 Barbu and Joly, Faraday SOC. Discussions, 1953, 13, 77. 14 Rybak, Bull. SOC. Chim. biol., 1950, 32, 703. 15 Frey-Wyssling and Weber, Helv. chim. Acta, 1941, 24, 278. 16 Joly, in Techniques de Laboratoire (Loiseleur) (Masson, Paris, 1954), 1, 538. 17 Joly, Trans. Faraday SOC., 1952, 48, 279. 18 Barbu, Basset and Joly, Bull. SOC. Chim. biol., 1954, 36, 323, 19 Barbu and Joly, J. Chim. Physique, 1956, 53, 95 1. 20 Gans, Ann. Physik, 1928, 86, 628. 21 Scheraga, Edsall and Gadd, J. Chem. Physics, 1951, 19, 1101. 22 Paine, Kolloidchem. Beih, 1912, 4, 24. 23 Paine, Kolloid-Z., 1912, 11, 115. 24 Kahler, Lloyd and Eden, J. Physic. Chem., 1952, 56, 768. 25 Frenkel, Acta physicochim., 1944, 19, 51. 26 Joly and Barbu, Bull. SOC. Chim. biol., 1949, 31, 1642. 27 Barbu and Joly, Bull. SOC. Chim. biol., 1950, 32, 116. 28 Barbu and Joly, Bull. Soc. Chim. Belg., 1956, 65, 17. 29 Winsor, Trans. Faraday Soc., 1948, 44, 376. 30 Silberberg and Kuhn, Nature, 1952, 170, 450. 31 Silberberg and Kuhn, J. Polymer Sci., 1954, 13, 21. 32 Joly and Rybak, Compt. rend., 1950, 230, 1214. 33 Joly and Rybak, Bull. SOC. Chim. biol., 1950, 32, 894. 34 Joly, in Deformation and flow in biological systems (Frey-Wyssling), (North Holland 35 Joly, Kolloid-Z., 1956, 145, 65. 36 Blatz and Tobolsky, J. Physic. Chem., 1945, 49, 77. 37 Trevelyan and Mason, J. Colloid Sci., 1951, 6, 354. 38 Manley and Mason, J . Colloid Sci., 1952, 7, 354. 39 Joly, Kolloid-Z., 1952, 126, 77. 40 Isihara and Koyama, J. Physic. SOC. Japan, 1957, 12, 32. Pub. Co., Amsterdam, 1952), p. 51 1.