The Study of Nitrocellulose Solutions by Light Scattering Measurements Citation Gilman, Theodore Silkman (1946) The Study of Nitrocellulose Solutions by Light Scattering Measurements. Master's thesis, California Institute of Technology. doi:10.7907/78w8-vm82. https://resolver.caltech.edu/CaltechTHESIS:07232025-180526666 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Badger, Richard McLean Thesis Committee: Unknown, Unknown Defense Date: 1 January 1946 Record Number: CaltechTHESIS:07232025-180526666 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:07232025-180526666 DOI: 10.7907/78w8-vm82 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17548 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 25 Jul 2025 18:23 Last Modified: 25 Jul 2025 18:51 Thesis Files PDF - Final Version See Usage Policy. 7MB Repository Staff Only: item control page

A port i on of this thesis (Parts IV, V, and VI) cont a ins cls.ssified information. He nce only P a rts I, II, and III have been submitted to the Che mistry Division. The classified material has been deposited in the files of OSRD Contract OEivisr-881 (Room 159, Crellin Laboratory). This is to certify that Mr. T. s. Gilman has completed the whole of his thesis and has turned over the classified portion of it to be deposited in the files of OSRD Contract OEMsr-881. THE STUDY OF NIT?. OCE:LLULOSI<~ SOLUTIONS BY LIGHT SCATTERING 1/JEASUREMENTS Thesis by Theodore Silkman Gilman In Partial fulfillment of the Requirements for the Degree of Master of Science California Institute of Technology Pasadena, California 1946 Acknowledgements The majority of the experiments described in this thesis h ave been c arried out e.s p art of a research project conducted at the Californie. Institute of Technology under contract with the Office of Scientific Research and Development ( Contr act OElvlsr-881), Dr. Linus Pauling, Official Investigator, and Dr. Robert B. Corey, Director of Research. I am indebted to Professor Pauling for permission to use the results of investigations carried out on this project as thesis material. Through the kindness of Dr. Corey permission was obt ained to use the extra. copies of the figures from the project investigation reports. The investigations on which the material presented in this thesis was based have been under the supervision of Professor Richard M. Badger. I grateful to him for his advice and direction. 9.'11 I also wish to the.Ilk Dr. Jurg Waser for many helpful suggestions and criticisms. All of the supporting osmotic pressure and viscosity data to be presented have been determined by Messrs. Robert M. Blaker and George J. Doyle under the direction of Dr. Richard IvI. Noyes. The use of a high speed centrifuge was made possible through the kindness of Dr. Dan H. Campbell. The design and construction of the optical and electrical parts of the apparatus used in the light scattering studies are to be credited to Professor Badger, Dr. Waser, and Dr. Austin L. Wahrhaftig. TABLE OF CON'£EI'JTS I. Introduction II. Theory 1. 2. 3. 4. 5. III. Description of Apparatus 1. 2. 3. IV. Refractive index measurements Light scattering measurements Discussion 1. 2. 3. VI. Optical system Electrical system Scattering standard Experiments and Results 1. 2. V. General development Application to the determination of molecular weights The effect of heterogeneity of the solute I!iolecular ·,veights from viscosity data Interpretation of the slopes of light scattering curves General remarks Discussion of errors Suggested improvements and experiments Summary A STUDY OF NITROCELLULOSE SOLUTIONS BY LIGHT SCATTERING MEASUREl'ilENTS I. Introduction In recent ye ars the me a surement of the light scattered by dilute solutions of high polymers has been em.ployed for the determination of the molecular weights of these polymers and for the estimation of their molecular weight distributions. It is the purpose of' this thesis to present a brief summary of the theory of light scattering, to give the results of' the application of this technique to solutions of nitrocellulose, and to compare these results with those obtained in osmometric and viscosimetric studies by other workers in this laboratory. II. Theory 1. General development The first theoretical tre atment of light scattering was carried out by Lord Rayleigh 1 who derived a formula for the turbidity of a. perfect gas using the optical properties of the individual n:olecules. This approach becomes quite complicated in the case of liquids and real gases because of the interactions which arise from the proximity of the mol e cules. A different theoret i cal approach to the problem by von Smoluchowski 2 at~ Einstein 3 led to a succe ssful treatment of the scattering phenomenon for liquids and solutions. They tre ated the scattering from a. statistical,. inste ad of a molecular point of view. Their derive,tions form the basis for the discussion in the succeeding paragraphs. The sc attering of light by a solution may be thought of as resulting fro m st atistic al fl u ctue.tions in the refractive index of the scattering medium. The fluctuations may arise from. two ef f ects, one caused by density 2 fluctuations and the other by concentration fluctu&tions throughout the liquid. If I cH1r J..V is defined as the amount 01' light scattered by a volume element cl.V of solution into a. solid angle d.fi a.t 90° to the incident beam., the quantity I c a.n be represented by the expression: I"'l, +I;!_ in which I, represents the scattering due to density fluctuations and I?-. that due to concentration fluctuations. A consideration of the work necessary to produce these fluctuations leads to the following equations: ( 1) and (2) in which 1, - the ratio of the intensity of the light scattered at 90° ,. I, , (as a result of density fluctuations) to the intensity of the unpolarized incident light, I 0 , the gas constant (in cm. 3 - atmospheres per moledegree) ,. T= the absolute temperature (298° in all experiments reported here), the isothermal compressibility ( in reciprocal atmospheres),. the wave length ( in vacuo) of the light used ( in cm.), Avogadro's nUJnber, p = the density of the seat tering medium ( in grams per cm.. 3) , the refractive index of the sce.ttering medium, 3 the ratio of the intensity of the light scattered at 90°, I2, , ( as a result of concentration fluctuations) to the intensity of the incident light, the molecular weight of the solvent, the weight fraction of the solute (in grams per gram of solution), the fugacity of the solvent,. the scattering volume (in cm. 3 ), Y and = the distance (in cm.) at which the scattering is observed. If' the plausible assumption is ma.de that ! 1 and 12. are essentially independent of each other in dilute solutions, I I may be replaced by I,., , where I+,. &_J), represents the light scattered per unit volume of the pure solvent. The quantity .12,. can thus be determined as the difference between the scattering from the solution and that from the solvent. It should be emphasized that Equation (2) was derived for the case of a solute which consists of only one molecular species, i.e. for the case in which the weight average and number average molecular weights of the sol~te a.re equal. In polymolecular systems the right hand member of the equ&tion is replaced by a. sum of terms referring to the respective solute components (see below). Furthermore Equation (2) was derived for solute particles which are small compared to the wave length of' the incident light. Under such con- ditions the fraction of the incident light, le , which is scattered at an angle 8 to the incident beam is given by Re.yleight.s law: 4 where 1. is the fraction of the unpolarized incident light which is scattered at 90° to the incident beam. When the size of the solute particles becomes of the same order of magnitude as the wave length, this angular dependence no longer holds, and the simple form of the scattering equation can no longer be applied. 4 The simplified assumptions on which the above discussion is based lead to the conclusion that with unpolarized incident light the sce,ttered light should be linearly polarized in a plane perpendicular to the plane formed by the incident beam and the direction of observation. amount of depolarization is always observed. Actually a certain i:: Cabannes 0 has shown that, in certain circumstances at least, the ex presEions derived above for the total theoretical intensity of light scattered at 90° (i.e. the sum of the intensities of the per pendicular and parallel components) must be multiplied by the factor (known as the Cabannes Factor),, in which the depolarizatio n ., 6., is the ratio of the intensities of the parallel and perpendicular components of the light scattered at 90°; the incident unpolarized beam and the direction of observation determine the plane of reference. For this reason the observed valu es of the t otal scattering intensity were divided by the proper v alue of the Cabannes factor in all the experiments described in this thesis in which the depolarization was measured. Aside from their use in determining the Cabannes factor, depolarization values may provide useful information as to the size and anisotropy of polymeric subst ances. For a c omplete classific ation as to size and anisotr o:py, hov,ever, a furt her depolarization measurement is necessary. 6 That is the 5 depolarization of the scattered light when the incident light is polarized in a plane perpendicular to the pla.ne formed by the incident be run and the direction of observation. Me a snrements of this latter quantity were not made, however. 2. Application to the determination of molecular weights It was Debye 7 who first demonstrated that the relation. between the osmotic pressure and the light scattered by solutions makes light scattering measurements a.n absolute method for molecular weight determination. The d ~ -£,) can be related to any colligative property of a d c:t. 'P,T quantity (- solution. The relationship to osmotic pressure has been selected as most. convenient for the study of high polymer solutions. It has been founds, that the osmotic pressures of dilute high polymer solutions can be expressed to a good approximation by the equation: (3) in which IT is the osmotic pressure in atmospheres, R and T are the srune as in Equation (1), M,_ is the molecular weight of the solute (the number average in the c a se of a polymolecul ar system), and K is a constant depending on the particular solvent-solute system in question,. but not on the solute molecular weight. I 'What evidence there is for the effect of the term containing ~ sug gests that I K is a consta-nt which may be assumed to be independent of the solute molecular weight for the systems of interest in this work. The relationship between the osmotic pressure,IT , and the fugacity, b D' , will now be derived. The fugacity, V' , of the solvent in a solution at constant temperature is defined by the equation: 6 where F. constant. is the r arti al molal free energy* of the sol vent and C is a Hence where -P is the pressure. But since and ( -dd"PF.) -V > llC.2, - I where V, is the partial molal volume of the solvent, it follows that (- d Jt.-. £ d c.a. I ) _ V, ( 0 p ) ,,~ T - 'RT a c:.a. ~ ..f,, • The osmotic pressure of a solution at equilibrium is defined, hovaver, as that pressure, -P , which must be exerted on the solution to make the fugacity of the solvent the same in the solution as in its pure state; hence Therefore (4) * G. N. Lewis' nome nclature 7 W'hen use is made of Equations ( 3) and ( 4), when the approximation is made that V1 = V1 ( -- M,~ ff , where VI is the total molal volume of t he solvent), and when small changes in f with the concentration are neglected, Equation (2) becones which on rearrangement yields , (5) Hence, if the scattering is measured at several different concentrations and is plotted against c~ , extrapolation of the best curve through the points shou ld yield an intercept which is a measure of the molecular weight M:l., and from which M2.. ch.,__ is known. may be calculated provided the value of the quantity ~ o c.._ As has been previously pointed out the above considerations are limited to monomolecular systems in which the number average and weight average molecular weights are equal. In such cases a simple relation exists between the measurements of osmotic pressure and light scattering. is plotted against C If Jr;C , the solute concentration in grams per cubic centi- meter (= f c2.), the value of the intercept obtained should yield the same molecular we :i.ght as was found from light scattering measurements on the same polymer. 3. The effect of heterogeneity of the solute When the solute contains a number of different molecular species, the osmotic pressure Equation (3) assumes a new forir?: 8 IT :: z_ ~~ I Ci -t- K( c~ + K/13 c; + • • ) (6) l where Ci is the concentr ation ( in gr ams per grem of solution) of the i tL. species of molecular weight Mi . ( ~ Ci = c~ - ) C (= f <:4 ) , Vfuen IT/( is plotted against the intercept is l but in which'(, is defined and "r\.i is the number of molecules or molecular weight Mi per gram of solution. Hence But the right hand term in the above equations is by definition the reciprocal of the number average molecular weight, M~• The intercept is therefore This shows that the number average molecular weight i.s obtained from osmotic pressure data. Likewise the light scattering Equation (2) must be modified for a polydisperse system9 : 9 Strictly speaking, the quantity d ~~ )2-. ( ;-contained in H should be included c, C2,, inside the summation as ('h'\2-)~ act • But since the theory is being applied here to a homologous system of molecular apecies, it is reasonable to a 1'\.:l assume that ~ is independent of the molecular weights of various CJ C;_ species, which would enable it to be factored out of the sum. The validity of this assumption is suggested by the results of some experiments which will be described in a later section. Since Equation (4) is true, and thus, with the aid of Equation (6),. which on rearrangement yields ( 7) This may be expanded in Macla.urin 1 s Series in c 2 to give c4/. - Fl i:t- /H """"M· 4- iyi ( I- "l and by further expansion (8) 10 where Mus is the weight average molecular weight. Hence, when c.A,./i'). is plotted against C2. , extrapolation of the curve should yield an intercept, H~w- from which the weight average molecular weight can be calculated. , It was shown above that, for a molecularly homogeneous solute, the molecular weight determined by light scattering measurements is the same as that determined by osmometry, that is M i..s-.::: Mn . Ordinarily,. however, high polymers contain many different molecular species, in which case Mw- > M'n 4. Moleculs.r weights from viscosity data (a) General theory Another property of high polymer solutions which yields information about molecular weights is the viscosity. Since viscosity data have been obtained in this laboratory for all the nitrocelluloses for which light scattering data will be reported in this thesis, a brief summary of the means whereby molecular weights were determined from these viscosities and of the significance of such molecular weights seems appropriate here. As a basis for the determination of the molecular weight a modification of Staudinger's empirical rule has been used: (9) where [~] is called the intrinsic viscosity (defined below), ~ is a constant depending on the temperature, the solute-sol vent system,. and the concentration uhits used, and M is an average molecular weight (hereafter called the 11 viscosity molecular weight"). Staudinger' s ru.le 10 was Originally the expression for 11 where ~si, is the specific viscosity and C various units. the concentration in any of The specific viscosity is defined by the following equation: ) where ~ is the me a.sured vise osity of the solution and Y(o the measured viscosity of the pure solvent. with C It was found, however, that l15 P/C varied and so, in order to make comparison of viscosity date. more con- venient, and to effect consistency with the simple theory of viscosity, the intrinsic viscosity, [~] , was brought into use and defined as follows: where C is now the concentration in grams per 100 ml. of solution. Some further remarks about Staudinger's rule should be made here. In the first place the rule assumes linearity between [ ~] and M. Actually the relationship is more complicated, and deviations from linearity are not only found experimentally for some systems but are expected on the basis of the more advanced theories about high polymer solutions 11 • The quantity Mis obviously a weighted average molecular weight, since the heavier solute molecules have a relatively greater effect on the viscosity than the lighter ones. For a randomly kinked molecule the theory predicts M MW--•u For other chain configurations, however, other averages have been derived. Despite these uncertainties, it has been found profitable in this laboratory to attempt the assignment of molecular weights to various nitrocelluloses on the basis of viscosity data. 12 (b) Application to nitrocellulose The calculation of the viscosity molecular weight of a nitrocellulose sample is complicated by the fact that the Staudinger constant~ in Equation (9) varies with the nitrogen content of the material 12 • Hence it has been necessary to determine the relationship between M_ and the nitrogen content. The establishment of this relationship enables the molecular weight to be calculated by merely dividing the intrinsic viscosity by the appropriate value of -({ • The molecular weight thus obtained is considered to be an approximation to the weight average. It should be pointed out that this calculation rests on the not too well verified assumption that the intrinsic viscosity is proportional to the molecular weight throughout the range of nitrogen contents (between 12 and 14 percent) of the nitrocelluloses which have been studied in connection with light scattering me a su r emeots. 5. Interpretation of the slopes of light scattering curves A consideration of Equation ( 3) leads to the conclusion that a plot of TI/c against C will be a straight line provided the concentration 3 range is low enough so that the higher order terms> K f c,_ + · • • , can be ' 3 neglected. In general, osmotic studies are made at concentrations at which a 11 this provision is true. The slope of this straight line will be~constant, K, for a given solute-sol vent system and ¥till be independent of the solute molecular weight. From Equation (5) it is concluded that, at low concentrations, a plot of c1/i.2.. against C2. will be a straight line with a slope equal to v'1-+ ( ~';t-) . Hence for monomolecular systems the slopes of the osmotic and light scattering curves at low concentrations should be in proportion by the factor f7'H( ~-f), provided the data are plotted as described above. 13 For polydisperse systems the osmotic curve will still be a straight line with slope K at low concentr ations (Equ ation (6)), but the light sc attering curve will exhibit negative (dov..'Uward) curvature in the same conce ntration range owing to the fact that the higher order terms can no longer be neglected (Equation (8)). 4 The extent of this curvature will depend on the degree of dispersion of the molecular weights of the species about the average value. The initial slope of the curve of Equation (8) is given by the following equation: Since K is the slope (at low concentrations) obtained when 1[/c is plotted a.ga.inst C (hereafter referred to as "' fl Kos ) ,. the value of the quantity ~ M~v, (~Mi yJ~ may be determined if the initial slope of the scattering curve is known. For this determination it is convenient to define a quantity KL as follows: (11) ca ➔ O Combining Equations (10) and (11), we have _ ~M:xi KL - Kos ( L. M· _)< i ) t '( l which on rearrangement becomes K. I (12) where, by definition Hence by calculating a value for KL from the initial slope of the light scattering curve and comparing it with the slope of the os:notic pressure curve, Kos ,. for a given sol'lrent-solute system, useful informa- tion on the molecular heterogeneity of the polymeric system being studied may be obtained; the quantity is the second moment of the molecular weight distribution curve and determines the degree of dispersion of molecular weights about the average value. In the case of a monodisperse system } ) as was sho1vn before. In practice the determination of ( II\L /K I~ Os) c., = o is difficult, if not impossible. This results from the uncertainty involved in extrapolating the light scattering data to zero concentration; not only are the data themselves increasingly inaccurate as the concentration decreases, but also there may be considerable curvature above and below the experimentally accessible concentration region. The extent of this curvature and the con- centration region over which it is exhibited are dependent on the degree of dispersion of moleclJ.lar weights. This in effect means that, s:iince there is a lower limit to the concentration at which light scatt ering data may be obtained with accuracy,. extrapolation to zero concentration cannot be satisfactorily performed without a knowledge of the molecular weight 15 distribution, which is what this treatment of the data was supposed to deterni.ine. A detailed treatment of the limitations to this approach to the determination of molecular weight distributions has recently been pub- . . d • 13 1 i.sne III. 1. Description of Apparatus Optical system A schematic diagra.'11 of the optical system of the apparatus used to study light scattering is presented in Figure 1. The light from a General Electric A-H4 100-watt mercury arc lamp, L, was passed through a didymium filter and a pale yellow filter, F, (Corning Nos. 5120 and 3486r respectively) in order to isolate the green line ( /\ = 5461 A0 ). A portion of the fil- tered light was reflected into a compensating phototube, C,. which served to eliminate the effect of fluctuations in the intensity of the initial light, and the remainder of the light was reflected upwards by a prism, R, into a bottle, S, containing the scattering medium. at 90° was measured with a second phototube, M. The light scattered A polaroid disc, P,. could be inserted between the bottle and the phototube and a.ould be rotated through goo· in order to measure the depolarization. It was found that the light which entered the scattering bottle vrns slightly polarized by the reflecting prism in a plane perpendicular to the plane formed by the incident and reflected bea.-n. The extent of this polarization was measured, and the observed depolarization of the light scattered by the various solutions studied was corrected using the following equation: Figures land 2 are in the classifie d portion. 16 where is the depolarization which would be observed with un- .LlCo-z..,7... polarized incident light, sc~ttered light, and S t:!' is the observed polarization of the incident light The value of S by the prism. is the observed depolarization of the was determined to be 1.25; hence the corrected depolarization values were about 90 percent of the observed values. Originally the scattering bottles, S, were oil sample bottles of 100 ml. capacity,. the bottoms of which were fl at and polished in order to minimize distortion of the incident light. The walls were coated with transparent red lacquer except in the region through which the scattered light was observed. Because of the serious effect of dust particles on the scattering power of the liquid in which they are suspended, all of the sarnples which were studied were forced into the scattering bottles through a Seitz asbestos filter disc and a piece of hardened filter paper. was effected with compressed air. 'rhe filtration The filter unit was tapered to fit the ground-glass necks of the bottles and was fitted with an outlet tube so that it was unnecessary to disconnect the filter and bottle at any time during a run. The bottle could be totally or partially emptied throu gh this outlet by inverting the system while pressure was applied to the f ilter. Because of the results of su11e of the earlier experiments, it was decided to obviate pouring off any of the solution during the course of an experiment. Larger scattering bottles (of 150 ml. capacity) were put into use for this purpose. These were made by sealing a 3 1/2 inch length of 35 mm.. soft glass tubing onto an oil sa.n1ple bottle the bottom of' which had been blown off. A polished glass disc had been previously fused onto the other end of the tubing with the aid of a low-melting glass cement. 14 17 2. Electrical system A diagram of the electrical circuit is presented in Figure 2. The phototubes were of the electron-multiplier type and were supplied with a constant D. C. potential,. 1000 volts, throu gh a vacuum tube voltage regulator. The spurious currents, called "dark currents;;, which flowed when the phototubes were not exposed to light from the arc could easily be balanced out with the two potentiometers in the lovrer right hand corner of the diagram. The currents produced when the tubes were illuminated set up potential differences across two potentiometers which were connected to ground. The slid i.>1.g contacts on the two potentiometers were connected to each other through a galvanometer, and readings were made by adjusting these contacts until a nul reading was obtained with the gal vanom.eter. The step contacts on the main potentiometer were arranged so that the scales of adjoining steps overlapped. This made it possible to avoid changing the step contact setting, when the sliding contact poteniometer was near one end of its scale, every time a small change in the balance of the circuit took place. 3. Scattering standard The absolute scattering of the solutions studied was not measured directly, but was determined by comparing the intensity of the light scattered from these solutions with that scattered from a standard liquid of known absolute scattering power. By means of this procedure it was possible to eliminate the necessity for the evaluation of the V/,,.. in Equations ( 1) and (2) and in all the subsequent equations in which is contained in the quantity H (Equations (5), (7), etc.). terms V/--r 2. 18 Carbon disulfide was chosen as a standard because its scattering power is of the same order of magnitude as that of the nitrocellulose solutions studied, and because the absolute value of 2. , the fractional intensity • ht seat+ • d experimen• t, a11 y 15 ; o f th ·, e 1 ig · ..,ere d at 90° , h as been d e t ermine ( 1 = 120 x 10-6 at 22° C. for l A :: 4358 Ao and Yri= 1). The value of at a different wave length may be calculated by the use of the equation for the scattering at 90° of a pure liquid (Equation (1)), and with the aid of the Lorenz-Lorentz formula: - constant. The result for = 5461 A0 is, for carbon disulfide, A i ( )\ = 5461 A0 ) • 0.329 x i ( A = 4358 A0 ). Thus the value of l is 39 .5 x 10- 6 for A = 5461 Ao and for V/-r:J.. = 1. The temperature at which the scattering studies were made was assumed to be 25° C., which is 3° C. higher than the temperature at which the value of l. was determined. However, the value of l. is only negligibly changed in going from 22° c. to 25° C. One scattering standard was pre p ared by filtering reagent grade carbon disulfide into a scattering bottle with the apparatus described in Section 1 above, and a similar sac71ple was prepared from some C.P. liquid obtained from another source. The precision of the measurements of scattering was about one percent, and the two samples did not differ significantly in scattering power. Filtration of the C.P. specimen several times did not affect its scattering. Therefore it was concluded that a scattering standard of dust- 19 free carbon d.isulfU. e coule.. be reprociuced at will, and the reagent grade material was adopted for comparison with the nitrocellulose solutions. After about ten months of use, this stanaart was compared with a sample of carbon disulfide which had been slowly iistillea several times in an all-glass system which had been sealelil off umler a vacuum. parison showed no significant tifference between the two liquiis. Parts IV, V, and VI of thie thesis contain classifiea information a.nt have been depositet in the files of OSRD Contract OEMsr-881 (Room 159, Crellin Laboratory). The com- References Citei 1 Lord Rayleigh, Scientific Papers IV, 397 2 M. von Smoluchowski, Ann. der Physik _gs_, 205 (1908) 3 A. Einstein, Ann. der Physik TI, 1275 (1910) 4 P. M. Doty, B. H. Zimm, and H. Mark, J. Chem. Phys. ll, 159 (1945) 5 J. Cabannes, Ann. de Physique 15., 29 (1921) 6 P. Doty and H. S. Kaufman·, J. Phys. Chem. !!:2., 583 (1945) 7 P. Debye, J. Appl. Phys. 15., 338' (1944) g M. L. Huggins, J. Am. Chem. Soc. 64, 1712 (1942) P. J. Flory, J. Chem. Phys. 10, 51(1942) 9 B. H. Zimm and P.H. Doty, J. Chem. P~..ys. 12, 203 (1944) 10 H. Staudinger, 11 Die hochmoleculs.ren organischen V'er'bindungen 11 , Berlin, J. Springer, 1932 11 M. L. Huggins, Ind. Eng. Chem. 15., 980 (1943) 12 H. A. Wa,nnow, Kolloid z. :J:Qg, 29 (1943) 13 J. Waser, R. M. Badger, and V. Schomaker, J. Chem. Phys. 14, 14 G. G. Wright ands. M. Swingle, Science 2]_, 564 (1943) 15 K. s. Bai, Proc. Ind. Acad. of Sci. 15., 347 (1942) 43 (1946)