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The scattering of light by small particles Johnson, Arthur C. 1946

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THE SCATTERING OF LIGHT BY SMALL PARTICLES by Arthur C. Johnson A Thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree MASTER OF ARTS i n the DEPARTMENT OF PHYSICS at the UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1946. ACKNOWLEDGEMENT It is a pleasure at this time to express my gratitude to Dr. Wm. Petrie , now at the University of Manitoba, and to Dr. A. M. Crooker, of the Department of Physics at the University of B r i t i s h Columbia, for their assistance in this work. A l -ways they gave freely of their time, and I am sure, that any training that I have acquired by this study has been due to their experience and guidance. To them both, I wish to extend my thanks. TABLE OF CONTENTS Introduction Theory Rayleigh»s Relation Mie Ts Theory Further Developments Experimental The Samples , The Spectra The Deduction of Results Results Typical Calculation Burnt Decalin Sample Sodium Electrode Sample Summary and Recommendations Bibliography THE SCATTERING OF LIGHT  BY SMALL PARTICLES INTRODUCTION The e f f e c t of the small p a r t i c l e s i n c o l l o i d s or suspensions upon the behaviour of an Incident l i g h t beam i s an extremely complex study. Usually the solu-t i o n gives the transmitted beam an o v e r a l l absorption and very often large absorptions of s p e c i f i c wave-lengths or regions. Further, and sometimes even more int e r e s t i n g , i s the f a c t that the p a r t i c l e s have a tendency to scatter the l i g h t i n a l l d i r e c t i o n s . The v a r i a t i o n of i n t e n s i t y with wavelength and the p o l a r i -zation of t h i s scattered l i g h t i s of great importance. This report gives f i r s t , a summary of the theory of l i g h t scattering from the l i t e r a t u r e on the subject, and seoond, experimental r e s u l t s obtained from a study of the absorption and sca t t e r i n g by small p a r t i c l e s suspended i n decalin. This study was i n i t i a l l y undertaken to solve an astrophysical problem suggested by Dr. B e a l s 1 of the •'•The Material of I n t e r s t e l l a r Space - C. S. Beals, Popular Astronomy Vol.LII No. 5, May 1944. 2. Dominion Astrophysical Observatory at Victoria. Apparently there are in the spectra of certain stars very pronounced absorption lines and regions, a mysterious one of which is at 4430A0. Observations indicate that these are not due to the stars themselves nor to any gases in their immediate vicinity. Further-more, calculations show that the density of gas in in-stellar space, which is known with fair accuracy, is not sufficient to account for such great absorptions as those observed. Thus it is felt that the material of instellar space causes these absorptions. In fact many of them are now definitely identified with certain elements. Although the chemical composition and dimensions of the solid particles in interstellar space st i l l con-stitutes a fascinating field for speculation and study there is a certain amount of quite reliable information pertinent to absorption. There is known to exist in space evidences of sodium, calcium, potassium, Iron and titanium. The dimensions of the particles, if they are to create sufficient absorption and agree with other phenomena connected with Interstellar material, must be between 10"*2 and 10"*^  centimeters. At the beginning, therefore, the problem was to attempt to make suspensions of any of the above sub-stances and observe their absorbing effect on a trans-mitted light beam. There was little chance perhaps of 3. finding an absorption region near 4430A0, but it was felt that any information regarding the optical effect of small particles would be of value. Small particles are known to be obtainable from the electrodes of an arc. This method was applied to several different substances and for the case of sodium electrodes in decalin there was obtained a product which no doubt contained sodium particles, but which proved also to contain other small particles. The latter were due to a decomposition of the decalin i caused by the high temperature created by the arc. This sample was checked for its absorbing properties and there were found several sharp absorption lines. The scattering was also checked and a rather unusual effect was found. Ordinarily scattering varies, ex-cept perhaps in regions very olose to absorption lines, in some manner with wavelength. However, for this case the scattered spectrum had discontinuities not only near absorption lines but also In other places. It was evident that this sample gave selective scat-tering. Another sample made by burning the decalin gave very similar results and consequently a more thorough examination of these samples was made. The observa-tions and results of this study are contained herein. The manner of presentation of this report is first to give an outline of the theory of light scattering with p a r t i c u l a r reference to Mie's work, and then to give the preparation of the samples and a compilation of data obtained from the transmitted and scattered spectra. F i n a l l y a few recommendations f o r the future study of t h i s problem are made. s. THEORY The most conspicuous and f a m i l i a r example of l i g h t scattering i s the blue of the sky. I t was when t h i s phenomenon arrested the attention of the early p h i l o -sophers that the study of l i g h t s c a t t e r i n g began. How-ever, i t was not u n t i l Leonardo da V i n c i suggested that the colouring was due to suspended p a r t i c l e s i n the atmosphere that the phenomenon was recognized as a l i g h t s c attering problem. I t was working on th i s problem i n 1869 that Tyndal 1 and Rayleigh 2 began both the experi-mental and th e o r e t i c a l study which f i n a l l y l e d up to our present day theory of l i g h t s cattering. Tyndal worked with a r t i f i c i a l clouds, smokes, c o l l o i d s , etc., f o r he f e l t that the blue of the sky was explanable on a suspended p a r t i c l e basis. Rayleigh? at f i r s t worked on a s i m i l a r hypothesis but l a t e r discarded i t and i n 1899 published a treatment on l i g h t s cattering which i s now known as the Rayleigh treatment. In p a r t i c u l a r , i t explained the sky's colour without'postulating sus-pended p a r t i c l e s , and i n general, provided the clue f o r the explanation of the three most outstanding features, colour, i n t e n s i t y , and po l a r i z a t i o n , of scattered l i g h t . • L P h l l . Mag. 37, 384 (1869) 2 p h i l . Mag. (4) 41, 107, 274, 447 (1871) ? P h i l . Mag. (47) 373, (1899) 6. Consider a spherical part ic le of volume/having die lectr ic constant € -+<d£ embedded in a medium 6" . If a beam of l ight of e lectr ic intensity E i s incident upon and goes past the part ic le we w i l l have equations (1) and (2) outside and inside the obstacle re -spectively. (1) Do = ea (2) 2>i ~ (e+A£)£ - '£(/+ Equation (2) gives the same as (1) i f we regard E as having been replaced Qy^+4£j £ . The presence of the obstacle has therefore the effect of creating a secondary electric intensity AJL^ per unit volume e at i t s center. Radiation w i l l be emitted in a l l directions with an intensity proportional to(=~) £ Y. It is this radiation that constitutes scattered l ight . There i s no need of l imit ing the theory to par-t ioles of co l lo ida l size, for in the work of Rayleigh and Mie the theory is equally val id i f the small par-t i c l e considered is a molecule and the medium i s space. RAYLEIGH'S RELATION If a part ic le small i n size compared to the wavelength of l ight i s at 0, and an unpolarized i n -cident beam travel l ing i n a negative sense para l l e l to the OZ axis s t r i k e s i t , then i t can be replaced by-secondary o s c i l l a t i n g e l e c t r i c i n t e n s i t i e s . Since X the incident beam i s unpolarized i t consists of two equal e l e c t r i c i n t e n s i t i e s tas27Tvt) i n the planes ZOX and ZOT, so that the secon-Fi g . 1 dary i n t e n s i t i e s os- 1 ' ' ' c i l l a t e p a r a l l e l to OX and OY. With t h i s ar-rangement Rayleigh ob-tained (3) J3rt ^  = fjLl • JL. S'» x0/7+ COS *#) where I 0 i s the i n t e n s i t y of the wavelength A i n the incident beam, •Zfrfs?) ±3 the i n t e n s i t y of the scattered l i g h t at a point i n the coordinate system, and c/ i s the p o l a r i z a b i l i t y of the p a r t i c l e given by^ L ^ ^ . And f o r the s p e c i a l case along the OY axis at Q, (3) becomes (4) - I^.^l There are three important features that can be seen from Rayleigh's theory (1) the scattered l i g h t ' s i n t e n s i t y varies as the second power of the p o l a r i z a b i l i t y (2) the scattered l i g h t ' s i n t e n s i t y varies as the minus fourth power of the wavelength (3) the scattered l i g h t along OX or OY w i l l be polarized since the secondary v i b r a t i o n set up p a r a l l e l to the OX axis can give a ra d i a t i o n out along OY axis but can give no in t e n s i t y out along OX, and vice versa f o r the OY vi b r a t i o n . "f• ifi in niilf! IT f S 1 1 1 s uur, iffliiiiiiffiimBiiiiiJfiii^iiffiiiiiiiiT r , V . , . i . . , „ T „ " T ' * * S * * S U U P , i , , fiiiiiitiiS in „x • j u u f j l F i g . 2 Scattered l i g h t (90°) from a solution of Naphthalene (Cio-Hs) i n decalin (C I Q H ^ ) showing depolarization. Experimentally i t was found i n the case where the p a r t i c l e was a molecule, that the l i g h t at &(r> Jfylf} was not completely polarized as i t should be by (3) above. Consequently the theory had to be adapted to take into consideration t h i s depolarization e f f e c t . The trouble lay i n assuming that the molecule o p t i c a l -l y had spherical symmetry. When the case of an anisotropic 1 molecule was considered, a f a c t o r 2 (^^.yja) A system where the properties vary depending on the axis considered. L. V. King, Nature 111, 667, 1923 P.R.S. Vol.l04A, 333, 1923.2 was inserted in ( 4 ) , where / ° i s a measure of the polarization determined with a Nico l . MIE'S THEORY1 Mie's contribution was the extension of the l ight scattering theory to include^complex index of refrac-t ion. Let the refractive index be m = v ( l - iw), where v is the real number that i s the usual index, and w i s the coefficient of absorption. In the case of a non-absorbing medium (e.g. water) m is equal to v with w = 0, but for metals the w / 0. A co l lo ida l metal solution often has different colours. Whether the colour variance i s due to d i f -ferent al lotropic modifications of the substance which do not occur i n the compact state, or whether i t i s due to varying size and shape of part ic les , i s a question s t i l l to be decided. More experimental data would be helpful . Metals generally crys ta l l i ze i n quite regular forms such as octohedrons, but perhaps due to unusual precipitat ion, etc. distorted crystals of rod or lamina shape might be formed. In Mie's discussion, for convenience only, the particles are assumed to be spherical; however, for a thorough study the mathematics for other shapes would have to be developed. Mie, Ann. der Physiko 25 , 1908 pp 377-445 Maxwell's Equations: The coordinate system used Is the polar (See F i g . 3). If ^, A are re-spectively the perme-a b i l i t y , d i e l ee tr i c i ty , and conductivity of the medium, Maxwell's wave equations in this system w i l l be given by F i g . 3 (5) 3t dr ( ' It Jr^ / j ^ The electric and magnetic components are (6) ^ - ^0 '<f To faci latate the work i t i s convenient to apply (7), (8), and (9) to have E and H introduced into the equations i n a similar manner. So that the very con-venient form of Maxwell's equations which i s to be used i n the theory i s given by (10) 7/ /rt (8) 2J?J»J~ = x A (where A i s the wavelength i n a vacuum, and m is the complex refractive index of the medium for the given A) (9) -j'^uA flr 9/fr. -//^ /fc. • i / 3x{ , r ' (10) * « ^ , = J_ / ff\ _ j _ „ • Ax b & Boundary Conditions: Consider a spherical p a r t i c l e of radius f the center of which coincides with the o r i g i n of our coordinate system. Let subscripts i n and p ref e r to properties of medium and p a r t i c l e r e -spectively. Assume permeability i s the same i n both the medium and p a r t i c l e so that^/^>« On the boundary the variable x i s seen to change, so that (11) Af =zirmf>r^ XM - zjfm* ir ^ zTfh where \ ^ i s the wavelength i n the solvent. Further-more, on the surface of the sphere the following l i m i t i n g conditions (12) have to be f u l f i l l e d . (12) D i f f e r e n t i a l Equation: With proper elimination from equations (6) the d i f f e r e n t i a l equations (13) of the problem are obtained (13) /3. Solutions of Maxwell»s Eguations: The solutions of the wave equations (10) can be grouped as those solu-tions (a) which are produced by the electrical vi-brations of the sphere characterized by E r / 0, Mr » 0; (b) which are produced by the magnetic vibra-tions of the sphere characterized by E r » 0, Mp ^ 6 ; (e) which are obtained by adding the integrals of (a) to those of (b). The technique of solving is to assume a solution E r of the differential equation from group (a), then determine in terms of E r the other components « ^ /f^ » /fr,0,/f*ttfp*& P e r equations (14) The assumed solution E r in general can be expressed as a sum of terms, each one of which satisfies the differential equation (13) and is a product of a function in x and a function in and . There-fore the v*11 term will be of the form: where Ky and P v must fulful the relations (13) It-. (15) 57>r 10 J exit*-I n (15) the va lue C v i s any r e a l o r complex number but on ly those P Y and Ky. f u n c t i o n s which have C v = v ( v + 1) are c o n s i d e r e d . P v i s a sphere func -t i o n o f both v a r i a b l e s O and ^ and o f order v (where v i s an i n t e g e r ) , w h i l e K v I 3 c l o s e l y r e l a t e d to the c y l i n d e r f u n c t i o n s . Group (b) i s handled i n an analogous manner. Thus (16) i s a set o f s o l u t i o n s to M a x w e l l ' s equa t ions . Group (a) Group (b) (16) Af}- o /f/"l-/fed . ^ *fr ^V*; The Function K v : Equation (15) has for the case v = o, particular integral solutions Ko (x ) = e l x and Ko ( - x ) « e" l x . It can be shown by substitution that i f Ky is a solution so also i s Ky + ^ thus a recursion formula is obtainable. Furthermore, cer-tain l inear combinations of these particular integral solutions are also solutions, such a combination i s (18) * ^ / * * & . ^ C-*>) which in turn has a recursion formula (19) (1?) (2* + l)li!L . ^ , + Expansion in series of K 0 (x) = e l x and K o ( - x ) = e l x and differentiation give (20) and (21) which can give numerical values in f u l l for I v (x) and Iy(x) to be used in (16) - — C O S JC -h ^/H >C X. - - s/st x. — 5 cos M 3 s//t *e (20) ^ >c^ Ilo. - .57/7 X -f COS x S//r The Functions P v and B v : The usual spherical func-tions which depend only on one variable are not satisfactory for determining P v and By. It is neces-sary to use functions of the following forms (22) to obtain a solution (22) fi^fa?)^ if Substituting into (15) shows 7Jy- must satisfy re-lation (23) 77. A solution for ease v = 1 i s 7fJ(l4r)- /, and as before recursion formulae can be"obtained to give a l l values of ^Iv- and 77 t^. . Such formulae are (24) ' fep--r/)w7fr - ^ ^ T y / 77>~, (2*+,) , T £ „ - ^ Final ly for use in (16) are the equations (25) and (26) b0 J0 COS 0 COS f (26) J / x r f co?20 cosp> y§2: - 3 sin 20 sin 0>cos be *° b9 % 0^ y -U—'A3t --d (7rJ^os0cosf sin is. The Integration of the Spherical Functions; To c a l -culate the t o t a l r a d i a t i o n that i s influenced by the sphere i s equivalent to f i n d i n g the following surfaces, integ r a l s (27) _ 9 7 F o o o o ( 2 7 z r zn TT^TT o o a o These r e s u l t s w i l l be used l a t e r i n the section en-t i t l e d "The Absorption". The Plane Incident Wave; To complete the derivation we need now only to express the plane incident wave i n terms of (16). Consider a straight polarized wave t r a v e l l i n g along OZ axis i n a negative sense, such that the e l e c t r i c o s c i l l a t i o n i s i n the ZOX plane and the magnetic i n the ZOY plane. Take A equal to zero, as would be the case f o r a medium l i k e water,^i.e. consider only a non conducting mediumj Such a wave would have i n r e c t i l i n e a r coordinates 27Tc n t i x uf £x =- e £y * ^£ = o (28) but i n the coordinates used i n t h i s derivation /<?. Then transforming . (2°) into the known terms I v , P^,, By and their derivatives the plane wave i s f i n a l l y expressed as (30) (30) rft*t) x*%3 *p £;up**) '^~'ds M0-*k S"-£s- . i ^ ' £ 4 The Refracted and Reflected Waves: The radiation at the interior of the partic le can be represented thus: (31) ^  • tft^L i ^ - l t • i iL 1fi ~'<h.iW**t i& <YWO * 1 /lip* - "kfzik - ^ iBt + l J L - . £zl . k±A where by and q v can be determined from the boundary conditions given in (12). Outside the particle space ref lect ion i s added to the plane wave so that the re-f lect ion i s given by (32) ^ = / ( ^ / j * S,H& ff- -it-^^o J /%> . J A £ ^ " . . / ^ A J . ere 7 where » value of Xp. when K = r / ° , i.e. <*: ^ Z7f/° A m1 » ratio of refractive indices, i.e. hi* - tl£ i v cJl^ , U-v- , 0 X 9 quantities which approach 1 for small values of . A study of the co-efficients a v shows that they rapidly decrease as v increases. In fact a^  decreases so rapidly that there is always some value of v after which the coefficients are so small that the terms can he ignored. In the case of small particles (2/?= 1800 A°) only the first few a v fs need be considered and for very small par-ticles only a^  need be. Therefore, it can be said that the reflected light from a small sphere is es-sentially composed of a finite number of partial waves, the number increasing as the sphere increases. Further-Zl. more i t can be shown that the same holds f o r the magnetic o s c i l l a t i o n s . The Diffuse Radiation Sideways; The i n t e n s i t y of the di f f u s e dispersed l i g h t i s given by where J6 vibrates p a r a l l e l to the meridian and J\> equator. p a r a l l e l to the oquation. I f observation i s along the OY axis, theory shows Jif should be zero. How-ever, experiment does not v e r i f y the l a s t statement e n t i r e l y , so Mie f e e l s that i t i s incorrect to as-sume pe r f e c t l y spherical p a r t i c l e s even though a l l other o p t i c a l q u a l i t i e s are i n agreement with such an assumption. Up to t h i s point only polarized i n -cident l i g h t has been discussed. I f however the incident beam i s unpolarized then the two e l e c t r i c a l vibrations can be considered as two independent polarized waves i n planes at 90° to each other. Each would be handled i n the same way as the case already discussed. Extension to Many P a r t i c l e s ; So f a r there has been considered the case of only one p a r t i c l e . The ex-tension to more than one would need to take into consideration the f a c t that the p a r t i c l e s not only receive the incident l i g h t but also the d i f f u s e l y dispersed l ight from the other part ic les . The work of L . Lorenz. and J . C. Maxwell-Gamett, however, indicates that the particles must be extremely close together before the dispersed l ight from other particles w i l l have any noticeable effect on the molecule considered. Therefore i t can be said that the tota l radiation i s proportional to the concentration in c .c . ' s of par-t i c les per c .c . of medium. I f N i s the number of particles per c .c . and^/? i s the part ic le diameter then (35) £-A/v- N±!¥[ \*tf<<* T ' err2-The total radiation w i l l be given by R - F-jC, where for small particles and for very small particles Here m 1 represents the ratio m p to u^. Both (55) and (36) express the radiation effect which i s dependent on the size of the part ic le and wavelength of the i n -cident l ight , but i s independent of the concentration. The concentration is taken care of by the function G. It should be noted from (37) that in scattered l ight a. 2-the shorter wavelengths prevai l providedj^*. ~ l \ does not tend to vary too much with wavelength. In tne case of metals this factor does vary considerably so that the last statement does not apply to metals. However, for any case where the factor is constant it can be stated that the intensity of the scattered light varies as A . The Polarization: Consideration of the intensities of the components of the scattered light shows the fol-lowing polarization. Fig. 4 Fig. 5 Infinitely small Imaginary perfectly gold sphere. conducting infinitely small sphere. Fig. 6 Fig. 7 Gold sphere of Gold sphere of diameter l600°A diameter 1800°A In figures 4, 5, 6, and 7 "the outer boundary represents the total radiation and the inner one the unpolarized l ight , so that the length of the radius between the boundaries represents the polarized radiation. The large shift of the maximum of polarization (Figs. 6 and 7) i s a special optical quality of gold, for other metals the shift i s smaller. The Absorption: The amount of absorption by a par-t i c l e can be obtained by examining the amount of energy which i s given off by the secondary radiation. Take a r spherical surface of radius^around the part ic le such that x » i s a large number. The density of energy flow from outside to inside can be chosen as unity* The energy flow outwards w i l l then be given by rr Z7r (38 Now I represents the energy flow of the passing l ight ray, as i t would be i f there were no partic le to i n -fluence i t , therefore 1=0 . Part III i s a positive quantity representing the tota l amount of sideway radiation. Part II is negative and represents the loss of energy of the passing ray. Now applying the. relations of (10), (12), and (27) and substituting in to (38) there i s obtained as r e s u l t s (39) ^ 2 7T Zt*uzf. faffj 2.rr 2?-+/ From (39 II) the c o e f f i c i e n t of absorption of the so lu t ion can be obtained. I f N i s the number of p a r t i c l e s per c . c . then the c o e f f i c i e n t of absorption per mi l l imeter of so lu t ion i s (40) / = N AM" X, X7T r S i m i l a r to the r a d i a t i o n i t i s only necessary to de-termine a^, p^, and &2 f or small p a r t i c l e s . Figure 8 shows a graph obtained from t h e o r e t i c a l c a l -cu lat ions for various s i zed gold p a r t i c l e s as i n d i c a t e d . From the graph i t can be seen how the v a r i a t i o n of colour from one c o l -l o i d a l gold so lu t ion to another can be ex-pla ined on a basis o f d i f f e r e n t p a r t i c l e s i z e . ) / \ \ / I \ a \ \ s V \ \ • ft m <- \ —\ \ \ 7 \ > \ go 0 1 a V to 'I X in A —*- F i g . 8 Absorption for c o l l o i d a l gold so lu t ions . Plott ing the radiations from (36) for the same sized particles give curves very similar to the absorption curves. Summary: The Mie theory has been based on two funda-mental assumptions: f i r s t , that the particles are spheres, second, that the cloudiness is in f in i t e ly thin . The important results are: (1) l ight which i s radiated by small particles can be calculated as two series of par t ia l waves, an e lectric series and a magnetic series. (2) these series for small particles need be calculated at the most for only the f i r s t and second terms (3) the maximum of polarization for particles up to about 1000 A° in diameter i s at 90° but above this the angle increases up to approximately 120° (4) for completeness this theory should be ex-tended to include partic les of other shapes. FURTHER DEVELOPMENTS In recent years there has been further study and experiment done on l ight scattering. Three of the more significant developments w i l l be brief ly men-tioned. Debye'3 Formula: In Mie's relations (35) and (36) the value m 1 » /> was used. Now the index nip i s quite d i f f i c u l t to measure and so Debye introduced a new value m^  which is the overall index for the solu-t ion, a measurement reasonably easy to make. Debye fs re lat ion for the turbidity i s -T2-where ^ i s the number of particles per unit volume. Extension to Larger Part ic les: Very recent experi-mental work with particles which have dimensions of the order of the wavelength of l ight show that scat-tered radiation does not always vary as A . Figure 9 gives an indication of these experimental re -sults for a case where m 1 = 1.25. Actually curves of this type are now being used to de-termine the size of part ic le that any par-t icu lar solution pos-sesses. 10 000 S i z e F i g . 9 Radiation for particles of size of wavelength of l i g h t . Raman Effect: Perhaps the most important outcome of t the study of l ight scattering i s the Raman effect. While doing extensive experimental work on scattering, Raman and workers in 1928 found in certain cases the scattered radiation contained wavelengths which were not present in the or ig inal source. Thus the solution under observation had the property of not only scat-tering the light but also shifting the energy distri-bution. This effect has now proved to be another aid to solving the atom. EXPERIMENTAL The experimental phase of t h i s study oan be des-cribed conveniently i n three parts. F i r s t , there i s the description of the samples including preparation, appearance, chemical composition, and p a r t i c l e s i z e . Second, there i s the apparatus which i s needed i n order to obtain the transmitted and scattered spectra. This includes l i g h t source, o p t i c a l system, spectrograph, and photometric d e t a i l s . Third, there i s the apparatus and technique necessary to determine the absorption and scattering from the spectra. THE SAMPLES Many samples were made using electrodes of d i f -ferent materials, using d i f f e r e n t arcing conditions, and using d i f f e r e n t organic l i q u i d s as a medium. There were two, however, which i n i t i a l l y gave the most i n t e r -esting r e s u l t s , and a more thorough study of these samples was made. Therefore t h i s report i s being l i m i t e d to these two, namely, the one of sodium elec-trodes i n deca l i n and the one of "burnt" decalin. Preparation; In order to prepare the f i r s t sample, sodium electrodes had to be made. A piece of pure sodium metal was softened by hand and then wrapped t i g h t l y around the end of a piece of copper wire. Thread was t i e d around the sodium i n order to press i t against the wire thus ensuring a good contact and no arcing between the sodium and the wire. Two of these were made and the sodium ends of the wire were Immersed completely i n d e c a l i n . The t i p s were then scraped clean. A d i r e c t current voltage of 110, connected i n series with an ammeter and about 15 ohms resistance was placed across the two unimmersed p l a i n ends of the electrodes. No continuous arc was obtained, but by continual tapping of one of the electrodes, i n such a way that i t brushed the other, there was obtained a f l a s h which drew about 6 amps, through the c i r c u i t . With each contact gas and black p a r t i c l e s flew o f f . Due to the arcing the temperature rose to about 60°C. Incidentally, any time the electrodes were not brushed against each other c o r r e c t l y , they would fuse together and would have to be pried apart. A f t e r arcing i n t h i s manner f o r two hours the decalin became a very dense black. The sample was then allowed to stand f o r a couple of days, by which time the black p a r t i c l e s s e t t l e d to the bottom leaving an apparently c l e a r solu-t i o n . The second sample was prepared by heating decalin slowly u n t i l i t burst into flame. A f t e r a few minutes the flames were suffocated and i n the s o l u t i o n was found a residue which s e t t l e d to the bottom over night. Appearance: A f t e r s e t t l i n g both samples were trans-parent but coloured. The.one made with sodium el e c -trodes gave a yellow transmitted l i g h t and sky blue r e -f l e e t e d l i g h t . Whereas the burnt decalin gave yellow transmitted l i g h t and yellow green r e f l e c t e d l i g h t . The property of giving one colour to transmitted l i g h t and another to r e f l e c t e d i s c h a r a c t e r i s t i c of a solu-t i o n which contains small p a r t i c l e s . Chemical Composition 1: In the preparation of both samples some of the decalin i s subjected to f a i r l y high temperatures. The preoise reactions which take place would be very d i f f i c u l t to determine but deca l i n i s known to behave i n the following way. At tempera-tures of 200°C and over, c i s decahydronaphthalene 2 be-gins to decompose. The decomposition i s accompanied by the loss of hydrogen and the production of t e t r a l i n . At s t i l l higher temperatures naphthalene i s formed. Above 350°C both the c i s and trans forms decompose y i e l d i n g highly unsaturated d i c y c l i c and monocyclic compounds as well as gaseous hydrocarbons. The highly unsaturated products recombine to form black ta r r y substances of such high molecular weight that c o l -l o i d a l solutions are formed giving dark green or blu i s h colour to the o r i g i n a l decalin. Because of the com-pl i c a t e d nature of the decomposition process usually iThe author i s indebted to Dr. W. F. Seyer of the Chemistry Department f o r the information on the chemi-stry of t h i s problem. Dr. Seyer has taken an i n t e r e s t i n t h i s work and his suggestions have been very greatly appreciated. ^Decalin, a c t u a l l y a commercial l a b e l , has the correct chemical name of decahydronaphthalene. I t consists of two isomers known as trans and ois-decahydronaphthalene. 3Z. no d e f i n i t e substance can be separated or even i d e n t i -f i e d by any simple a n a l y t i c a l method. Therefore i n the "burnt" decalin sample there might by any of the above mentioned compounds. In the sodium electrode sample the same compound might be produced along with small sodium p a r t i c l e s . These l a t t e r could cause the d i f -ference i n colour of the r e f l e c t e d l i g h t from the two samples. As the chemistry of analysis f o r pure sodium i s also very complicated, no analysis was c a r r i e d out. However, sodium at present i s thought to be very i n -active with decalin and so i t was f e l t because of the arc that there was c e r t a i n to be sodium p a r t i c l e s i n the f i r s t sample. P a r t i c l e Size; Microscopic examination of the f i r s t sample indicated p a r t i c l e s ranging i n size from 10"^ to 10"*4 centimeters, An attempt to observe i f there was Brownian movement present merely showed, fo r both samples, many flashes of l i g h t from the p a r t i c l e s but no movement. THE SPECTRA In establishing an o p t i c a l system f o r t h i s par-t i c u l a r problem there were several p r i n c i p l e s which had to be born i n mind. These were the p r i n c i p l e s of maximum i n t e n s i t y , to reduce exposure time; of proper density to obtain s a t i s f a c t o r y contrast between regions of non-absorption and absorption i n the spectra; of s a t i s f a c t o r y c a l i b r a t i o n to permit density readings to be taken from the spectra; and f i n a l l y , of s i m p l i c i t y to minimize the time required i n adjusting the system. A f t e r many o p t i c a l systems were t r i e d , the ones des-cribed here were found to be the more s a t i s f a c t o r y . Light Source: At f i r s t an ir o n emission l i n e source was used along with the Hilger Spekker. Later, how-ever, i t was f e l t that t h i s technique did not give f i n e enough scrutiny, to record the^ type of absorption wanted, and so a continuous source was employed. The one used was a 250 watt General E l e c t r i c GX lamp. At a l l times, i n order to reduce the energy i n the red, a Corning #5900 f i l t e r was inserted. Optical Systems: For the transmission case a p a r a l l e l beam of l i g h t from the above source was passed through the sample and then focused onto the s l i t of the spec-trograph. The sample had to be contained i n a c e l l with plane p a r a l l e l ends. The length of the o p t i c a l path In the sample was quite c r i t i c a l i n as much as i t was d i f f i c u l t to get s a t i s f a c t o r y contrast between non-absorption and absorption regions i f the path was either too short or too long. In order to obtain the scattered (90°) spectrum the l i g h t beam had to pass through the sample i n a v e r t i c a l d i r e c t i o n p a r a l l e l to the s l i t of the spectrograph. The s l i t was c a r e f u l l y shielded so that no l i g h t entered I t except that which l e f t the solutio n at 90° to the o r i g i n a l beam. To determine the po l a r i z a t i o n of the scattered beam a Wallastoh prism 3¥. was inserted inside the spectrograph a short distance behind the s l i t . Spectrograph: A l l work was done with a Hilger quartz spectrograph (medium). The various s l i t widths and ex-posures are given under r e s u l t s . In order to compen-sate f o r l o s s of o p t i c a l path i n the Wallaston when determining p o l a r i z a t i o n i t was necessary to move the collimator lens and camera lens towards the prism 0.25 and 0.28 centimeters respectively. Photometric D e t a i l s : I t was found that Eastman II-F spectroscopic plates met the requirements f o r t h i s work the most s a t i s f a c t o r i l y . The developer used was D-19 with developing time of four minutes; and the f i x e r was F-5 with f i x i n g time of f i f t e e n minutes. THE DEDUCTION OF RESULTS In general, when quantitative r e s u l t s are required, the photographic method of determining spectra presents many d i f f i c u l t i e s . The reaction of the spectroscopic emulsion depends on many factors, such as exposure time, colour of the l i g h t , and development conditions. I t i s th i s variance of reaction which causes the most trouble. Step Density Wedge: In t h i s work the c a l i b r a t i o n of the plates was done with a step density wedge. The wedge consisted of many steps each of which had a den-s i t y 0.15 greater than the one previous. I t was placed immediately i n front of the s l i t and using the same source as was used f o r the spectra an exposure of the 3S. order of seconds was made. Thus by t h i s separate opera-t i o n there was placed along with each spectrum a pattern from which the c a l i b r a t i o n of the plate could be made. Tracings: A Moll's recording microphotometer was used to make the tracings which appear under r e s u l t s . On each tracing there are the step density marks which are used f o r plate c a l i b r a t i o n , the traces showing the energy d i s t r i b u t i o n of the source and the p l a t e 1 , and markings showing the wavelength. The density marks were obtained by running the wedge pattern perpendicu-l a r l y through the microphotometer; the trace giving the energy of the source was obtained from one of the steps of the wedge pattern; and the wavelength markings were obtained by running the wavelength scale through the microphotometer. Because of the narrowness of the steps i n the wedge pattern i t was impossible to obtain a l l traces without readjusting the microphotometer. Therefore, i t was necessary to know accurately the positions of "clear" plate and "black" plate f o r each trace. This d i f f i c u l t y was s i m p l i f i e d by adjusting s l i t widths to give the same positions every time. C a l c u l a t i o n s 2 ; The f i n a l r e s u l t s are a c t u a l l y given iThe expression plate refers to either the transmitted or the scattered spectra. 2Throughout t h i s paragraph there are two densities and two transmissions to which reference i s made. The density and transmission of the absorbing medium are designated by the word medium (Dm and Tm), whereas those of the spectroscopic plate are designated by the word plate. In both cases the r e l a t i o n l o g 1 = D applies. ~f"~ i n the form of a graph showing the extincti o n versus wavelength. Now to obtain t h i s f i n a l graph i t i s neces-sary to plot two preliminary ones. The firs -}; i s a plate c h a r a c t e r i s t i c curve showing the log--- exposure f o r any p a r t i c u l a r plate density. Actually the log of ex-posure i s not used, instead the density of the ab-sorbing medium which i s proportional to the log of ex-posure i s used. The pro p o r t i o n a l i t y can be seen from the following r e l a t i o n s : * exposure i s proportional to transmission -l o g transmission equals density . . log E = l o g k + log T m = constant -D^ where E i s exposure, k i s a propo r t i o n a l i t y constant, T m and are respectively the transmission and density of the absorbing medium. Plate density i s given by the following r e l a t i o n l o g i - - D p = l o g i o where Tp i s plate transmission and D p i s plate density. To determine T p, the t o t a l distance (d Q) on the tracing from "clea r " plate to "black" plate i s measured and divided into d, the distance from black plate to any p a r t i c u l a r point on the trace. Now the density marks give t h i s f i r s t graph since they indicate the plate density f o r c e r t a i n known medium densi t i e s . The second graph required i s the medium density versus wavelength. 'All logs used are to the base ten. The points of t h i s graph are obtained by taking from an energy trace the values of plate density f o r various wavelengths, and then determining from the f i r s t graph the corresponding values of medium density. These l a t -t er can then be plotted against wavelength. This tech-nique i s applied to both the source and the plate energy d i s t r i b u t i o n s and both are plotted on t h i s second graph. From t h i s second graph the difference between the two curves i s measured f o r a l l wavelengths. These d i f -ferences are then plotted against wavelength to give the f i n a l graph of ext i n c t i o n versus wavelength. Interpretation: The amount of absorption i s indicated by the heighth of the curve. In the transmitted plates, therefore, the high points are i n t e r e s t i n g since they, indicate absorption l i n e s . However, i n the scattered plates the low points are i n t e r e s t i n g , since they i n -dicate l i n e s i n the scattered spectra. F i n a l l y , the f a c t that no account of the difference i n times of the plate and wedge exposures has been made, means that the t h i r d graph gives no i n d i c a t i o n of the absolute amount of absorption. RESULTS Typioal Calculation In determining the extinct i o n curve from a microphotometer t r a c i n g there i s a great deal of tabulating and c a l c u l a t i n g . In t h i s report only the graphs f o r Plates 2, 3, and 4 are given but f o r Plate 1 both the c a l c u l a t i n g tables and graphs are given i n order to demonstrate a t y p i c a l deter-mination. Sample: "Burnt Deoalin" Plate 1 i s the microphotometer tracing f o r the absorption spectrum of t h i s sample. Plate 2 i s the scattered spectrum. Graphs (1.1, 1.2, 2.1, and 2.2) are obtained from these Plates i n order to determine the ex-t i n c t i o n curves of graphs (1.3 and 2.3). Plate 3 gives the p o l a r i z a t i o n of the scattered spectrum. Sample: "Sodium Electrode" Plate 4 i s the microphotometer t r a c i n g f o r the absorption spectrum of t h i s sample. Plate 5 i s the scattered spectrum. Graphs (4.1, 4.2, 5.1» and 5.2) are obtained from these Plates i n order to determine the ex-t i n c t i o n curves of graphs (4.3 and 5.3). Plate 6 gives the p o l a r i z a t i o n of the scat-tered spectrum. Sample: "Sodium Electrode" Another set of r e s u l t s are given f o r the sodium sample. This set was obtained by v i s u a l readings d i r e c t l y from the spec-troscopic plates. Although t h i s technique i s not as accurate as the previous one, i t does give a very easy and rather nice com-parison of the absorption and scattered spectra. 3<*. SAMPLE CALCULATION The following demonstrates the technique used i n deducting the r e s u l t s from a microphotometer tr a c i n g . The example used i s Plate I. Tables I - IV give the information required before the f i n a l r e s u l t s (graph 1.-3) are obtained. Readings for graph 1.1 (plot l o g E vs Dp) TABLE I - WEDGE TRACE Step l o g E ^  -Dm d * 0 0 . 0 1 - .15 1.5 1.824 2 - .30 4 1.398 3 - .45 12 .921 4 - .60 28.5 .546 5 - .75 56 .252 6 - .90 78.5 .106 7 -1.05 92 .036 8 -1.20 99 .004 d D = 100 Readings f o r graph 1.2 (plot ?i TO % ) TABLE I I - SOURCE TRACE d * V Dm* d V Dm * 3950 51 .292 -.73 4150 15 .824 -.50 3975 43 .366 4175 14.5 -.49 4000 47 .432 -.66 4200 13.5 .886 -.47 4025 32 .494 -.62 4225 12.5 .915 -.45 4050 26 .582 -.58 4250 11 .958 -.44 4075 23 .638 -.56 4275 10 1.000 -.43 4100 20 .699 -.54 4300 9 1.042 -.41 4125 18 .745 -.52 4400 8 1.097 -.40 d Q = 100 4500 7 1.154 -.38 means read from Trace means calculated means read from another graph 40. TABLE I I I - PLATE TRACE d DP Dm d DP m 3960 99 .004 -1.5 4215 28.5 .542 -.60 3965 98 .008 -1.2 4225 26 .586 -.58 3980 97 .013 -1.14 4230 23 .638 -.56 3985 97 .013 -1.14 4240 19 .722 -.52 3990 96.5 .015 -1.12 4250 18 .745 -.51 3995 96.5 .015 -1.12 4270 15 .824 -.50 4000 95 .022 -1.08 4280 14 .854 -.47 4010 94 .027 -1.06 4285 14 .854 -.47 4015 93 .032 -1.05 4300 15 .824 -.49 4020 93.5 .038 -1.06 4310 17 ' .770 -.50 4025 2? .036 .064 -1.04 4315 17 .770 -.50 4050 86 - .99 4325 15 .824 .958 -.49 4075 79 .104 - .91 4335 11 -.44 4100 71 .150 - .85 4345 8 1.097 -.40 4125 .236 - .87 4350 8 1.097 -.40 4150 46 .347 - .70 4365 6 1.221 -.36 4160 43 .366 - .69 4385 5 1.303 -.33 4175 35 .456 - .64 4400 4 1.398 -.30 4190 31 .508 - .62 4425 2 1.699 -.20 4200 30 .523 - .61 4450 1.5 1.824 -.14 d 0 = 100 4475 1 2.000 -.09 Readings for graph 1.3 (plot ^ vs difference) TABLE IV - DIFFERENCE IN CURVES IN GRAPH 1.2 diff. > diff. diff. diff. 3985 76 4125 54.5 4270 37 4385 26 3990 75 4150 49.5 4280 34.5 4385 24 4000 72.5 4175 45 4290 35.5 4400 20 4015 71.5 4200 44 4300 37.5 4425 11 4020 74 4215 43.5 4315 39 4450 5 4025 72 4225 43 4325 .58.5 4475 1 4050 70 4230 41 4335 33.5 4075 65 4240 37.5 4345 30 4100 61 4250 37 4350 30 5* •1 BURNT DECALIN SAMPLE  Plate 1 Absorption Spectrum Length of c e l l • 20.05 mm. Width of s l i t - .0125 mm. Height of s l i t = 3.5 mm. Exposure time - 150 sec. Plate number = 83 Plate 2 Scattered Spectrum Width of s l i t - .5 mm. Height of s l i t = 5*5 mm. Exposure time = 7 hours Plate number «* 89 Plate 3 P o l a r i z a t i o n Wallaston prism Width of s l i t « .5 mm. Height of s l i t • 1 mm. Exposure time = 46 hours Plate number = 90 -t j -H | ^ f r f r 4 r i r ; p : "Burnt; ; HGVa:ph::2 T - f - f t 1-4 --t 4- !--,-* 4 + "4- 4-T i m i^ri : : r : r r n : ; ± t : 1 r l i ! , ,• -T T T -H-H 4+4-Charac t e r i s t i c f f f t 144 4-4 HT J T T -- —+-4i •j—i—j~1—i-2v0* i i ;• T + T Htrr: . - . 4 - t - v ••-•I T - + 4 - 4 - + — 4" -r-ti-t mm . i - * - . 4i —44 ::L1 t r . 1 : f 4 4 t TT+ ^ -n- 4 4 -| — 4 T - T r T—I- r - ! t -14 U 4 - U tt4i.44|Ui-TT • U 4 - 1 -f-44444 4 - 4 - r 1 P+ r "t - • i t 4- - i - ' - U 1 -144- r r t 4 -4 4 •4 < 4 4 . i 4 -V •:• 4 :- 4---1-4 • f t m n m r -,.4 4 - l - t 4-4-4 4 T .w 4 ! I i n 4 - L • til-44 4 4-4-4-4-4 -4-4-4—!-. 4- -t—(—1— -* • 4 - 4 - 4 i j t f f i i it 4-4--1- t — - j * -4 * - ; 4—4 ! • - • - + - - ; 4 - H-4 - T 1 l + l 4- I 1--: r : . i - n - t : t M- i . J - 1 : 4- j - t 4 - 4 - 4 ; + •+-(• 4-4 -4 -4 sii + n 4 4 4 !'44 4 1 -f !4'f4f!. •:• 4 - f t t '"t t 4 Medium Density ' K * ' f t 4 t f - , s a +.-; - j - j 4 j - - . ; 4-i -t : 1 1 1 ! I i 1 ! : 8 1 • 6 ^_ H a i * : l i t : u • : i ' f ; f - + -. 4 i i t j ! f - -f + -, + 1 f i i - i , i i t • t • 1 i . i 1 i a l i i a l j i a al l • i"i i i i a ] ; ; + i . : i i k i l l 1 : , 1 , 1 J t ' | ; Plat 1 s i Graj i 1 f' a_a e h il • : ; , . 4 | 1 .3 i |wBt TlJ8 rrit .Decall 4 t - . i i nsmittedi£ 4 i 4 4 4 i . , - 4--H * :-, -n» pectrim • 4 '- ' 4 j i 1 t • i i t i i . ! i t : ; 1 1 i " 1 l-1 • 1 II ! i f 1 ' t I i i 14 •{• l \ . 1 I' t T ililil I t * * : -i 1 I 1 1 • > ; i • M i l l , i ! 1 i i \ ' i ; t ! i> t- 1 • i | i . • ! ! i ! - * 1 t * - + 1 4 1 i ' : _a t a it a t i \ i i ! ! 4 1 a 1 1 a i . i i i | '; | - , 4 ; 4 ' !-" a f a t i ; , I • > i i * \ i t-t • i i , i i , i • t 4 ; . 4 4 . ; . . a , i 4 <_ i 1 , . . . 1 j i , a . 1 . 1 , 1 | a a t ; [ : , -1 -t t j 1 t 1 ! 1 s; •H, S i i 1 i j i i • n i l a t 1 H j . 1 i -H t 1 . 4 • 1 , 1 a i t 4 i " 1 i i-rja a 4 in: i a i a a a a i ' i 4 T V i ! 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T .. - 4 . , 4 , 00 : • - i -t + . 1 i . ' ; ..' i i ; - i i ' f t j ! I l l • 1 . j • i • > • , r ' r 1 i -• • . - H , ,-•* 1 i ; 1 f i t , . , ! - i I i l ! i m iiji ' ' ' I • a f i 1 ! . ! " \ \ ' [ \ \ J j . ! 4 ! i 1 1 ' i Plat ' 1 1 Glia'l ; i ,- ^ i- 4 ; a - • 4 - j -•!-'*%••>} • 4 • - I - | & 2 . 3 | " i ' i *Sc:a 4 i . + * ' • t rnt - - i tt1©;] 4 - t i 4 i 4 a - *" Cecal! cjed Spe i 4 r ; n" | 1 ' : ;' ctrum i i i ; ; i , • • t t i : 1 ; t 1 ' { i" h>| t : * • • fl[ t ' ' a Si a I - 1 l '4 j • i • t i-: * I , < • *• at ' ' i i i • i H l 1 r ~ j t t f • i i n 1 4 1 t > f f , i - i r • ' • t • * - t ' 4 • t l . -~ t , 4 • ' 1 1 , 1 4 4 1 4 I ' • I I , i 4 t- 4 -i ' t i -t : - r - l . • |. 4 1 t 1 i 1 j"l"t! n a a 4 i • 4 ;j-t i a a f • a -iliji. 'A V.\\\\ • •• \ Irt ! 4 3 a l l : t ( 4 1 i f j ; 1 1 t j i f :1 4.. . i I i 1 i I • 1 < t I | t T t 4 ; i . 4-1 \ j i J 1 1 • iiMiii iiiiii] I f ! ! ' t T i ; ' j t i l l | ! t i 1 ; . . . 4. ; > j -: - » | 4 4 -L ' i 1 1 ' 1 i l l -( i. y i • . • r 4 4 4 - i ^ i 1 -^ s f i a f ; : L \ - ' , - > . ' > \ 4 4 4 ! : ! ! H Hi iii a a : ; ; ; ! . }--4 -: * -|. 1 -f i t; 1 t i : | i -1 • ; i i d - r • - 1 • i I i-i f • J , ! -. •j i I f i -i ; 1 i ' \\\y\ • i i < • ii H I 4 -1 1 >; 4 4-t t 1 i t ' • * i < 4i ; H " ' J r r a t i . ; j 1 11 a ! • t : 1 f J > -i-I ' ! * t 4 , J . j ;f .. J | }. ! | ! . . i > 4 4 .. j ! | i 1 4 j | ! i a / i i i . . i f a f fi! 1 ! f i ; • : ii -i 4 11 • r 4-' ' t " 1 - ! ! r • ' t 1 H • • •a 1-14;! ' •! > ; t • • i : i ; i i , 1 40 4-00 y j . ^ l • 1 • I I - i - i p t i u * . l i t - * i 4 i !" OA • t ' ' } i i i i i Vavele I a a * ng it ! i 30; } ;4 1 i 43 th.pi. . | r... j , oo,: i . r j -~i---3 1 4 ' 1 ' i 44 i ' - 4 f : : i -t -: -t t-4 ' - -1 ' r 0 i i i : 4 .U ; : f ! 1 ! ' + i 00; i ; ' i : -4 1 i ; • ! j i : i ; ; i | ! • i M i i i i , i ! 1 : i ; 1 4 • i Mia i j I j ' ' ; i ; • ' ' ' ' 4 i i 4 • 1 4 1 SODIUM SAMPLE Plate 4 Absorption Spectrum Length of c e l l = 279 mm. Width of s l i t - .075 mm. Height of s l i t - 9 mm. Exposure time = 60 min. Plate number =87 *7. Plate 5 Scattered Spectrum Width of s l i t = .5 mm. Height of s l i t • 5 mm. Exposure time = 20 hours Plate number = 93 J Plate 6 P o l a r i z a t i o n Wallaston prism Width of s l i t - .5 mm. Height of s l i t » 1 mm. Exposure time = 46 hours Plate number = 92 s~o. 1 : 1 ' i ' i ! 1 i f , . | - ; . ' ! , ; ; ; ; j . . 1 •4 t 4 1 t i 4 1 6 4,.1 4 : ! i" — - f - r T * + i~~ - • ; i ! 4 4 4 14: i j l i l - j : ! ; : T"i 1 I"; 1 i * f 4 !:, . Pla • - ] ! '- 4. 4. : -; 4 t 4 ' 4 ' be: 4r - ; j "S ?h 4.3; Tr . [ ', : . ' 4 1 4-1 : . - .. . 4 ... )dium Samp insmitte;d 4 4 + 4 - ,.4- * -LeMt Spectrum 4 4 t ' : 41 4 ' ; . ' . , - - , .4 4 4 ; 1::. 4 4 4 4 4 44 ] ; ; 4 4 " ; 4 t ! • 1 ! 4 '4 44 ! ; i * I;' .1 J. 1 -yl i I ; 4 4 . ; . 4 1 ; 4 : + i i f- • 4- 4 4 i i 4 t 4 - -, 41"! 4 - i 4 T .. > J - .:. 4 t ; t ! - • • | ; i • • , , . ; j ; , rii iHili-\ 4 ' 4 ' r n - -4 • f f :f-"f 4 4 4 4 4 4 : . ,- |-4 4 4 , • • f * r • . 4 f 11:4;. i — •f * • ! '-• • * ( -r ( 4 • - • • i • I 4- 4 4 • 4 4 1 .-4 :;-:ln;:-. 4 s": 1 . , O 4 ; 4- 4 -t 4 t .H| -j ! i ' • - : £ : 1 2 + ' + ;-) -f -r 1 i 1 r 1 i 1 4 4 H:.' 4 1' i " -i. r . i 1 t4 -+-r J 4 .1 ; \ t , r } 4 r I 4 -• 4 . 1 ( 4 • ! 1- 1 j + 1 t 1 i 4 1 M -• j , I 1 . 1 . T V -4 1 i f I'M 14 • \ M r 4 -H- -. » 4 - 1 4 1 j- 4 . fV-i i i f . : t l 4 4 +-f ;-• 4 \ : ! 4 1 -4 4-4-4 -i-4-4--- [• 1 - 1 4 : 44444 4,4' 4-4 4-4-1 4 4 -.-4 -.44 i t i i - 4 --4 } 4 -4 1 1 4-J 4 • . 1 , - 4 - - , : • • - 4 4 4 4 , H < 4 r 4- • . - ; - r + . 4 . 4- 4- , _ , - - i - i - 4 - . - - 4 r - -. , f . 4 . 1 , F . . + ). F . | : 1. 4- : , -; 4 j : _ i 4 ; l 44 - !• H | ' -! 1 4 ••- i .;.;!5iri;l 4.-. p ; - t . . . 4 j-! ; 4 ; -I; J r \" i 0 4 4 i ; ; 1 i 4 ; i i U ! 4 j (.4 4 41-4 4 4 4 i | J 4 4 I i l f - i n i r 1 + : r-f r -, 1 . , , , 4 , -; 4• i 4 ' -I 1-4 i f 4 ' 4 "if t i l l 4 4 4 I i - . 4 . 4 : 1 41 ! ' 4 + l ;4t 14 1 4 t : 4 Vt;j!. 1 1 t 4 4 4 4 T1' ~ 1 ; 4 i ' . 4 . 1 , . r ji 4-.4 - f 4 * '• ""r 41 j 14...., 4 ' 4 4 144 :| 4 " ; ... 4 , . ; . . 4 ' 4 4 : 4 i •" 44 ; • 4 -4 i * -4 4 4 i f f f .... u , ; • ; ' f • i 4 • •' -+ t - r • r -: *-r i • f f f f i fl - . 1 ! 4- 4 4 4 i.; 4-41.141 - »• | • --+!-•• -:4-4 4 "41 ~ + • 4000 ; ; 41 -' i-1 i 4-4 , . . - • - . 4 4 4 - 4 4-4- 4 ,- 4- --- , 4 ; 4 - 4 -00 , •4 f . j ;Wav • 4- 4- i i 4 t ! +4 4 - t t + -j • t-t-fri ; .42 J.4.: - 4 . eierig - 4 4 : .. 14 4 - 1 +-4 o p r J 4 ; : 4 3 . th > — 144 4 i ] 4 i .44; ; 4 i - : ; . , 4 - : - 4 - 1 4 . J - .. .. ... 4 , . . t 4 - : -4 -r rvr'< t 4 T )p,.  : : : : : : M L -: ; J. 4 ;.;.;.: :. |: 444: - ) . -4 ..4-4 - .4 4 . f . • -' • , -:• --• 4 - 4-4 • •ri * 4 " i - u v 1 : r . i 4 4 1 • , 14 4 4 4 - - i | 4 4 4 -4 . ; , ( . , . 4 f 4—] t .; , j 4 J 4 - - i , , , . , f • 1 * - - 1 •'. - - -:44J!:.:-1. :.n 4.1! ;4 ; 44 : . 4 4 6 4 ' ' - ' : -+ -= + - • : ^ : J + r • t | , •! • | | t + i " I - " ' _ 1 ' ,• + -+> 1 . ,- -•: • • * t - ;• 1 - * 4 ! '• j-- 4 ' 1 l i t ! ' 1 *~ ' ; i i - \ ', * ' 1 i i : J i 4 n: j ' 1: 1 Pla "i: 4 / 4 j: l i f t ; G r a t i !!•; ;! be, 5; | j J "s 4 4 i - ; 4 4-i. 4 ph 5.3i 1 So ., . -4 1 { ! j. • . . ... 4 t i . 4 . - • 4 - ! - r ; , . 4 , . i . » . 4 - 4 ium' Samp bared 4 % 4 i 4 "* ; , t - ' • • * - t Le'» 4 4 4 • '- * - • . 9ctrum * I " : ; ; i . i - 1 + i r ' t -t j , } 4 ' i f i f f - S 4 •fl 4-4 t. ! j f 1 sLJji! : l 4 f l i ! -L ! 1 ' • i j : i + * 4 -j- 1 4- - - (-4 I..4 4 4 4 l' . T" ' " 5 1 -4 4 f 4 4 4 4 i i ! 4 4 4- • L> r 4 4 , 4 ; ' ;' ! . 1 1 11 ' :4 4 { f j i 4 , 4 - 4 4 r ' t ; " 1 ; i -i { f i . ; 4. J ' . 1 . 4- ' T4.if: 4 4 * - . t -j - . . 4 -4. . . 4 4 - - . • 4 4 ; 4 : ; 44 ri!:, " 4 4 4 4 4 t 4 4 - . - 1 4 < • . ! 4 i 4 .4 i -T , 4 , i 11: +.::: 4 4 • i -1 < • . , t . . . , r i 7,. ;i 4 , . ^ 4 • 4 . , • § : 2 : i • i 1. 1 4. 1 . 4 J • h 1 ' 4 t i , ... j 4 4 1 1 j ' ' • ' ' •1 : .4 A ,. 1 I , i i i ! \ 1 M 4 ' - 1- 4 , 4 i \ ; i 4 f 4 j } 4 -T < ( 4 . i -.- -4 ; . | • • . i : 4 I \ 1 i r 4 - M I 4 -• i t + -; |" 7 • 4 4 ^ 4 4 4 4 . . .4 .: | . - 4 1 ; ^ ! ' ; . 4 11 . 4 - 4 : - 44 4 4- 4-4.1 .1 • - : - - 4 1 1 1 , _ L . +_ . • 4 : !• - —4 :--4 ..4.-4.-4-• -S t - 4 4 4 : & : . •: 1 . 4 . 4. f 1 j ; ; , 4 . ••?! 1 n j ; :'o 4 , 'I ; • t ' > f * 4 j i t H-11 4 4 j 4 1 ! i ; i f T-44 4 14 1 i V iti-Hffl: 4 ] ' } j i-44 t.i ' 1 \ : f If i 4 V < ^ 4 * |H ,4 .. J ! 1 4 j . 1 •: - ! ' * 1 1 1 ^ 4 1 4 ; i f - i f - 4 4 * 1 ' ' 4 . 4 4 44 - 4 -f • , • ,~ 1- 1 . 4 1 ^ 1 .t* 4 ,' ' • . . , . 4 4 4 -T " " + • 1 i 4 4 4 : i r f i ;4 4 - 4 r i | 4 t 4 4 4000 ; 41 . ; t : ,.. 4 ] . | . 3.C } n ]4 Jm Waveleng .,- !--• 4- i 4-4 Ii 1 t f r ).o::;. :43' 11 w <- 4 t : • bh' A 1 4 .• . 4 :- 4 -.;_ 4 4 - 1 T . . 1 4 : i !*"[ ' )0 4i.i4..i.44( • • r J- -1- 1 1 ! • • " - ^ i 1 i • )0 -4-4 t 1 4 4 3 1 4 r -4-i -i * - ! - ' + ., + . ; + )0.; . 460C . 4 - -. j 4 - 4- 1 1 .4 ', , ... 4- f 4 -! , • - . 4 4 4 4 i 1 i \ 1 I i i . 1 1 1 1 ' ' : , 4 1 1 ' 1 ! ' ' ! 1 1 ! 1 1 ; : 1 ; • i 1 ' 1 ' : ; : 1 ' • . 1 • 1 1 1 ' : 4 ! 4 ' 4 4 1 ! 4 ' : 4 4 4 4 . I ABSORPTION Length of c e l l Width of s l i t Height of s l i t Exposure time Plate number £3. 279 mm. .0125 mm. 2.5 mm. 55 min. 57 ABSORPTION SPECTR mi 1 4000 4100 4200 4300 4400 SCATTERED SPECTRUM 4;500 4600 Each of these s t r i p s has a d i f f e r e n t p r i n t i n g exposure time. In t h i s way the absorption and scattering l i n e s are emphasized. SCATTERING Width of s l i t Height of s l i t Exposure time Plate number .375 mm. 5 mm. 12 hours 49 SUMMARY AND RECOMMENDATIONS In summary it can be said that there are two phases of this report. First, the theoretical aspects of the scattering of light by small particles are considered with special emphasis given to Mie's theory. Second, the results of certain experimental work regarding the light scattering properties of two colloidal solutions are presented. From the theory the following can be concluded: (1) Rayleigh's relation shows that light scattering should vary in a continuous manner, inversely proportional to the fourth power of the wave-length. (2) Mie's theory shows that the scattered light can be calculated as two series of partial waves, an electric series and a magnetic series; for both cases if the particles are small with re-spect, to the wavelength of light, only the first and second terms of the series need be considered. From the experimental the following can be concluded: (1) decalin when subjected to heat either from straight heating or from an arcing process tends to produce tarry substances of rather high mole-cular weights. (2) the tarry substances in the decalin tend to give in the transmitted spectrum certain absorption bands. (3) the tarry substances in the decalin tend to give in the scattered spectrum definite lines not only corresponding to the absorption bands of the transmitted spectrum, as might be expected, but also in other places; this latter effect is contrary to the usual scattering where the scat-tering varies continuously with the wavelength. (4) the sample made using sodium electrodes gives a slightly different and more pronounced effect than the burnt decalin sample. Burnt Deoalin Sodium Sample Absorption Scattered Absorption Scattered Lines Lines Lines Lines 4315A0 4320A0 4305A° 456OA0 4220 42?0 4205 4460 4270 4140 4140 4400 4040 4095 4065 4310 4060 4210 4150 4040 There are several suggestions for the extension of the experimental part of this work which are worth-while mentioning. (1) Rather than using photographic methods for determining the energy distributions i t might be much easier and more accurate to use a photocell technique. (2) The precise nature of the substance causing the unusual scattering effect i s not known. Further experimental work using s l ight ly d i f -ferent methods of preparation, such as d i f -ferent currents in the arcing process, might give more definite information on the physical and chemical nature of the solutions. 5^. BI BLI0 G-RAPHT Tyndal Strutt Rayleigh Lorentz Mie E i n s t e i n Cabannes Cabannes Raman King Ramanathan Bhagavahtam P h i l . Mag. 37, 384 (1869) P h i l . Mag. (4) 41, 107, 274, 447 (1871) P h i l . Mag. (47) 375 (1899) Collected Papers 3, 329 (1910) Ann. der Physik 33, 377-445 (1908) Ann. der Physik 33, 1275-98 (1910) J. Comptes Rendues 160, 62-63 (1915) Ann. der Physique 15 (1921) "Molecular D i f f r a c t i o n of Lig h t " (1922) Nature 111, 667 (1923) P. R. S. A.102, 151 (1922-3) "Scattering of Light and Raman E f f e c t " (1940) 

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