Optical properties of wax surfaces

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Optical properties of wax surfaces

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Manuscript Theses Unpublished, theses submitted for the Master's and Doctor's degrees and deposited in the Northwestern University Library are open for inspection, but are to be used only with due regard to the rights of the authors. Biblio­ graphical references may be noted, but passages may be copied only with the permission of the authors, and proper credit must be given in subsequent written or published work. Extensive copying or publication of the thesis in whole or in part requires also the consent of the Dean of the Graduate School of Northwestern University. Theses may be reproduced on microfilm for use in place of the manuscript itself pr «rided the '’ules listed above are strictly adhered to and the rights of the author arv in no way Jeopardized. ........... This thesis by .ffUngA' has been used by the following persons, whose^signatures attest their accept­ ance of the above restrictions. A Library which borrows this thesis for use by its patrons is expected to secure the signature of each user.



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uest ProQ uest 10061008 Published b y ProQ uest LLC (2016). C o p y rig h t o f th e Dissertation is held by th e A uthor. All rights reserved. This w ork is p ro te c te d a g a in st una u th o rize d c o p y in g u nd e r Title 17, U nited States C o d e M icroform Edition © ProQuest LLC. ProQ uest LLC. 789 East Eisenhower Parkway P.O. Box 1346 A nn Arbor, Ml 48106 - 1346







To Joan





/— v

O^CJ. Diogenes,

C\J» W : - o . ' I .

oc 'ijl

ACKNOWLEDGMENTS To Dr. Arthur A. Frost for his careful guidance, his generous consideration, his endless patience, and his benevolent understanding, the author is deeply indebted. To the S. C. Johnson and Sons Company, the author* s most grateful appreciation is ex­ pressed for the financial assistance which made this investigation possible.

TABLE OF CONTENTS Page I N T R O D U C T I O N .........................................


THEORETICAL C O N S IDERATIO N S ..........................


EXPERIMENTAL M E T H O D S .................................. Instrumental T e c h n i q u e s ............. . ..........

17 17

Refractomet r y ..................................


Extinction Turbi dime t r y .......................


Optical Microscopy . .


Electron Microscopy


. . . . . .




Experimental R e s u l t s .............................. Indices of Refraction

19 20 29





Optical and Electron Micrographs ...............


G o n i o p h o t o m e t r y ................................


D I S C U S S I O N .............................................


S U M M A R Y ...............................................


Optical Densities





Barkas A n a l y s i s .......................



Diagram of G o n i o p h o t o m e t e r ..........



Phototube Characteristics ..................



Optical Densities ..........................



Polar Curves for Magnesium Carbonate



Polar Curve for a M i r r o r .............


Barkas Analysis of Rough Black Glass




Polar Curves for Two Different Backgrounds.



Polar Curve for Black Background


... 46



Polar Curves for C a m a u b a Wax Emulsions . .




Scattering Plot for Mixed Waxes





Scattering Plot for Carnauba Waxes




Intensities for Mixed Waxes




Intensities for Carnauba Waxes . .





It was desired to make a study of some aspects of the physical chemistry of waxes.

An examination of the

literature on waxes revealed that there exists a summary1 of the properties of a self-polishing wax both in the bulk and as a film.

From this exhaustive list it seemed well to

select for detailed study the luster of the wax because of its intimate relationship with other optical properties, such as surface structure, particle size, index of refrac­ tion, and internal structure.

Since all such optical prop­

erties are concerned with the wax as it exists in a film applied to a surface, the work was confined to measurements on waxes in films rather than in bulk. Two important considerations were seen immediately: first, to what type of surface should the wax be applied in order to form the film; and second, what method of applica­ tion should be employed.

The lack of standardization in

these two respects has been cited in many papers12 as the main problem in making measurements of reliable quality.

1M. Fuld, Soap (Sanitary Products Sect.), 15, No. 8, 99 (1939). zHarrison, "Definition and Measurement of Gloss," PATRA, W. Heffer and Sons, Ltd., Cambridge, 1945*

It is to be noted at the outset that the films under investigation are quite thick compared to the wave­ length of visible light, but they are of the same order in thickness as one would find in ordinary application of a floor polish.

In order to circumvent the difficulty of

deciding how to buff the film mechanically after it has dried, the work was confined to wax emulsions of the socalled "self-polishing" type.

This facilitated the solution

of the application problem in that once the emulsion was applied, no further work had to be done on it.


techniques were developed whereby a film could be laid down in a satisfactory way. The question of a surface to support the film was answered by selection of two from a large number which were tried.

They consist in general of a black non-refleeting

but somewhat porous background which can be set conveniently into the measuring apparatus. The objective of the research was to make measure­ ments of various optical properties and then to interpret these data so as to give an insight into the structure of the wax film.


The law of reflection in geometrical optics states that when a ray of light strikes the boundary of a medium and is reflected, the reflected ray is in the plane of incidence and the angle of reflection is equal to the angle of incidence. When a beam of light is incident on a matte surface, the light is scattered in all directions. L aw3


relates the intensity of the incident beam with that

of the scattered light through the angle of viewing, R, defined as the

direction of the scattered ray measured from

the normal; it

is stated as follows:

X =

c d

cos i cos R

where I is the intensity of the reflected beam, I Q the incident intensity, d the distance between surface and viewer; i is the angle of incidence, R the angle of viewing, and c is a constant defining the brightness of the surface. There is no known surface for which this law holds exactly, though some surfaces approach it very closely.

3Lambert, Photometria (Augsburg) Part I, Chap. 2 (1760) as quoted by Harrison.

Between these two extremes of reflectivity lie most of the surfaces with which we are familiar, and it has been the subject of considerable investigation to attempt to explain deviations from these laws.


Hypothesis* considers a surface to consist of countless small regularly reflecting facets which may be set at all angles of inclination with respect to the plane of the surface.

Berry^ tried to explain diffuse reflection by

constructing a surface made up of a large number of bubbles of the same size all in the same plane each in contact with six others so as to give approximately a hexagonal close-packing of spheres.

This surface resembles an ideal

matte surface at angles of incidence less than sixty degrees. By considering an equivalent surface made up of both regularly reflecting and diffusely reflecting facets, which may be set at any inclination with respect to the plane of the surface, Barkas6

attempted to explain surfaces

which show small deviations from Lambert's law.


diffusely reflecting facets obey Lambert's law, and the regularly reflecting facets obey Fresnel's equations7

^Berry, J. Ont. Hoc. Am e r ., 7, 627 (1923). 5Ibid. 6Barkas, Broc. Phys. H o c ., 51 (2), 274 (1939). 7Jenkins and vvhite, "Fundamentals of Physical Optics," McGraw-Hill Book Company, New York, 1937, p. 389.

for dielectric reflectivity.

These equations are the


2 -sm sin

where i is the angle of incidence, j is the angle of refrac­ tion, and r is the intensity of the reflected beam, s referring to the incident light vibrating perpendicular to the plane of incidence and p to the light vibrating parallel to the plane of incidence.

In the unique case of normal

incidence, these equations reduce to a simple one:

where n is the index of refraction. Barhas®

shows polar curves for a substance called

Bristol Board, which has a very small specular reflectivity, and resolves them into specular and diffuse components.


plotting a polar reflectivity curve, the origin of coordi­ nates is considered to be at the center of the surface,

8Barkas, op. cit., p. 285

and the reflected intensity is plotted as a radius vector3. Barkas*

curves are presented in Figure 1.

The full curves

show the total flux as measured experimentally; the dotted curves give the calculated diffuse flux, and the dashed curves give the calculated specular flux.

He presents the

same type of analysis for a surface of magnesium oxide, which is very nearly an ideal matte surface.

Barkas states

that his analysis is successful for surfaces which give symmetrical scattering curves for normal illumination, and whose specular reflectivity is very low. Harrison?

however, has made measurements on

magnesium oxide and attempted the Barkas-type analysis. He concludes that this analysis is not successful for sur­ faces as matte as magnesium oxide.

He concludes further

that LambertTs law does not hold for a surface of magnesium oxide except for the special case of forty-five degree

9There is a distinction between brightness and intensity which appears on the polar plot. If the illuminated area viewed increases with increasing angle of viewing, then the polar curve for an ideal matte surface will be a semi-circle with center at the origin, and will be a measure of brightness. If the illuminated area is small, however, so that the illuminated area viewed does not increase with angle of viewing, the polar curve will be a circle tangent to the horizontal axis at the origin of coordinates, and will be a measure of intensity. /0Harrison, Broc. Bhys. s o e ., 58, 408 (1946).




incidence, for which the polar curve is a circle.


smaller angles of incidence, the curves are sections of prolate spheroids; for larger angles of incidence up to sixty degrees, the curves are sections of oblate spheroids. For any angle of incidence less than sixty degrees, the polar equation of an ellipse with the origin of polar coordinates at one end of the major axis is followed within experimental error.

j _

This equation is as follows:

2ab2 cosR______ a2 sin2 R + b2cos2R

where a and b are the semi-major and semi-minor axes. Harrison presents experimental curves for magnesium oxide which are slightly more symmetrical than are those of Barkas.

It is considered that the Barkas type of analysis

is the best quantitative approach to the problem of the description of surfaces having good light-scattering characteristics. Since a wax emulsion is a colloidal system, it may be of significance to consider the scattering of light from colloidal particles within the film.

The equation for

the scattering of light from small isotropic particles has been derived on the basis of the electromagnetic theory3 .1


"Optik," lulius Springer, Berlin, 1933, P* 371.

The equation is as follows:

I - I.

(1 + cos2 6)

where n is the number of particles per unit volume, a is the polarizability of the particles, 0 is the angle between the direction of the original beam and the direction of the scattered beam, and A is the wave length of the light incident on the particles.

This equation holds for particles

smaller than 0.05 microns in diameter.

For spherical

particles, M ie12 has obtained an expression for scattered intensity for arbitrary sizes and indices of refraction. Curves are given by Born23 for the intensity distribution of light scattered from particles of increasing size. When the difference in refractive index between that of solvent and solute is quite small, the simpler intensity distributions are found to apply.

For particles

with dimensions equal to the wave length of light, which have an index of refraction only slightly different from that of the medium, the equation for light scattered from small isotropic particles will apply.14

The wavelets will

i2Mie, Ann. Physik, 25, 377 (1908). 23Born, op. oit., p. 291. 140ster, Chem. R e v ., 43., 2, 319 (1948).

interfere, however, and more light will be scattered in the forward direction than in the backward direction.


radiation envelope is smooth, and the forward scattering will increase with increase in particle size.

Debye/r has

shown the relationship between this angular dissymmetry and the size of the particle.

This treatment has been

derived for the case of a solution, however, rather than for the ease of solute particles embedded in a solvent which has solidified.

Any scattering from individual

particles is considered in this case to be negligible in comparison with the scattering from the surface.

/sDebye, J. Phys. Colloid Chem., 51, 18 (1947)


Instrumental Techniques Refractometry. A Bausch and Lomb Abbe Refractometer was employed for the measurement of the refractive indices of the dried wax films.

The normal procedure could not be used because

of the following difficulties encountered in the two general methods.

When the water emulsion of the wax was introduced

between the two prisms and allowed to dry slowly, a con­ traction of the film destroyed the contact necessary for a reading.

On the other hand, closure of the lower prism

upon a dried film of wax applied directly to the measuring prism would not establish the necessary contact, and it was found impossible to effect this contact using a liquid of higher refractive index because of the solubility of the wax components in both water and organic solvents.


fore, the method of total internal reflection was employed. In this method, light is incident on the front face of the measuring prism and encounters the glass-wax interface where it is either refracted or reflected, depending upon the angle of incidence and the index of refraction of the wax.

The critical angle for total inter­

nal reflection gives rise to the boundary between the two halves of the field, as in normal operation it is given by

the critical angle of refraction; the dark half of the field, however, will now be on the opposite side of the boundary, and the contrast will not be nearly as great, since light can reach the "dark” side of the field by partial reflection of rays which are generally transmitted at the glass-wax interface.

This method of measurement

of the refractive index of a wax film is subject to the criticism that the wax may be in a slightly different arrangement at the glass surface than will be the case at the air interface due to evaporation of water into the air, creating a somewhat more porous structure.

It is assumed,

however, that if there is a real difference, it is a very small one, and one would predict that the measured refrac­ tive index would be the upper limit. Extinction Turbidimetry. The Beckmann Ultraviolet Spectrophotometer was used to determine the optical densities of 50 to 1 dilu­ tions of the wax emulsions at a wave-length of 500 milli­ microns in order to get an idea of the relative particle sizes in the emulsions.

The optical density of a given

solution will be roughly proportional to the particle size. Optical Microscopy. A Bausch and Lomb Chemical Microscope was used to study the surface of the wax films.

An attempt was made

to discover crystallinity in the film using crossed hicol prisms with negative result.

It was seen, however, that

the highly reflecting waxes, which appear smooth to the eye, have definite surface structures when one can bring out the contrast necessary to see them.

In this case, the

contrast was brought out by evaporation of a metal onto the wax surface at very low pressures.

The photomicrography

was performed with Eastman Kodak Plus-x 35 millimeter film in an attachment for the optical microscope called the Visicam.

This attachment enables one to focus the image

on a ground glass screen; and then by rotating a small mirror through ninety degrees, one throws the image in the direction of the photographic film.

The camera has a

variable speed shutter. A series of exposures was made on a given sample in order to determine the proper focus and the exposure time.

The final exposures were made at ten seconds.


opment was in Eastman Microdol (fine grain) developer for sixteen minutes at twenty degrees Centigrade.

The projec­

tion prints were made at an enlargement of 5 to 1, giving a total magnification of 1050 diameters. Electron Microscopy. The RCA Electron Microscope was employed in order to determine the particle size of the waxes in various emulsions.

Preparation of the wax specimen was done in

the following way.

The emulsions were diluted with water

in two series, one having a 50 to 1 ratio, the other a 250 to 1 ratio by volume, rendering emulsions having solids

contents of about 0.23 and 0.06 per cent respectively.


drop of each of these solutions was allowed to evaporate on a thin film of Formvar '6 which had previously been mounted on an electron microscope mesh.

In order to in­

crease the contrast, each film was shadowed by evaporation of a film of chromium metal or of wolfram oxide7


samples so prepared were photographed in the electron microscope at magnifications of 8280 and 15350 diameters. Projection printing of these negatives at an enlargement of 4 to 1 gave pictures of the wax particles at 33120X and 61400X .'8 Goni o ph ot ome t r y . A goniophotometer was constructed for the purpose of measuring the reflectivity of samples as a function of the angle of viewing.

The instrument is a modified spectro­

meter in which the slit is replaced by the filament of a tungsten lamp and the crosshair by a very small circular aperture; the eyepiece is replaced by a phototube and the prism by the material whose reflectivity is to be measured. A schematic diagram of the instrument is shown in Figure 2.

16Formvar is the trade name for an organic resin, polyvinyl formal. /7Formerly named tungsten oxide. ,8The author wishes to acknowledge the assistance of Mr. A. L. Ellis of the International Harvester Company of Chicago and of Mr. Harold A. May of Northwestern University in production of these optical and electron micrographs.




2oo A



AA/V 500



The illuminating lamp is a 6 -8 volt twenty-one candlepower automobile taillight having a very concentrated filament.

The lamp is placed with the filament at the focal

point of lens (1), so as to give a collimated beam.


sample is placed on the table so that the plane of the surface exposed to the beam contains the vertical axis of rotation of the table.

The table has been equipped with a

graduated semicircle for measuring roughly the angle of incidence.

A small circular aperture (2 mm. in diameter)

is placed at the focal point of lens (2 ) so that the photo­ tube receives only those rays leaving the reflecting sur­ face parallel to the optic axis of the viewing arm.


RCA 929 vacuum type phototube is situated such that the base of the cone of light emerging from the aperture fills the width of the cathode. The electrical circuit, also shown in Figure 2, consists of the phototube, a ninety volt D. C. supply, and a high resistance, all in series, and an electrometer which measures the voltage drop across the resistor.

The char­

acteristics of the phototube are given in Figure 3 .


can be seen that the anode current will be a linear function of the incident light intensity, since the smallest re­ sistance used is ten megohms for a maximum potential drop of 1 .3 volts. In order to accommodate a broad range of light intensity, a bank of resistors is incorporated in the


Taowra phototube for light isaaauramante haring a eeeiua-antimony alloy cathode with exceptionally high roopoiito to hiti* and groon radiation and a negligible response to rod radiation* The aurfaoo has a low dark current*

I .«IT

F lV *

- l - O M I H i *.< ? .l

Anode Micro­ amperes








Anode Volts Table lb Spectral Response

laagfeh fMicronsj OM 0.37$ 0*40 0*45 0*50 o*|5 OtOO

^ ■ am



ti e s r ,a,vd

Distribution froa a .Tungsten S o w M ... 0.02 0*035 0*06 0.13 0*24 0.37 0.50

iatom" BOA 929 Msponse 0.40 1.00 0*93 0.70 0.46 0.25 0.05

Orerail Response

0.008 0.035 0.056 0.091 0.110 0.093 0.025

Figure 3 *RCA Phototube Manual, Form PT-2GR1, April 1941. 6O'Konaki, Thesis, Northwestern, June 1946*

circuit so as to be able to switch to any desired value of resistance present and thus to vary the sensitivity of the circuit.

The electrometer is a Laboratory Model G Beckmann

pH Meter operated on the millivolt scale; the measured voltages are proportional to the photocurrent. In operation, the azimuth scale is set by allow­ ing the light from the fixed arm of the spectrometer to travel directly into the viewing (moveable) arm and finding the maximum response.

This will be the zero setting.


one selects the angle of incidence to be used and sets the viewing arm at twice this angle from the fixed arm.


then places the sample on the spectrometer table and rocks the table back and forth about its vertical axis to get the maximum response.

The table is then rocked about a

horizontal axis in the plane of the surface to be measured in a similar search for the maximum.

Then it is certain

that the angle of incidence is as desired and that the surface is perpendicular to the plane of incidence.


taining this angle of incidence, the viewing arm is then moved to various selected angles and the goniophotometric curve is recorded.

The exclusion of all extraneous light

is accomplished by working in a dark room. For any readings taken with the instrument, a correction must be applied to eliminate the effect of dark current.

These dark currents are measured each time the

instrument is used, and they are found to be quite low and


In summer when the humidity is high, the values

rise considerably.

In Table % are given the nominal value

of each resistor in the circuit, a normal value for the potential drop across each due to dark current as measured experimentally, and the corresponding calculated dark currents.

It can be seen that the nominal values of

resistance are not correct.

By measuring the potential

drop across each resistor for a given light intensity, it is possible (after subtraction of the dark current) to calculate relative values of resistance;

choosing the

Table &






Potential Drop (Millivolts)






Dark Current (Microamperes x 10'*')





















Nominal Resistance (Megohms)

Calibrated Resistance (Megohms) Potential Drop (Millivolts) Dark Current (Microamperes x 10'5')

100 megohm resistor as a standard, it is possible to calibrate the others with a fair degree of accuracy. calibrated resistances are given in the table.


Using the

data obtained on August fifth of this year, for example, for potential drop, and the calibrated resistances, the calculated dark current is found to be constant. data are included also in the table.


It is to be pointed

out that the potential drop in millivolts due to the dark current is the quantity actually measured and applied as the correction to the goniophotometric curves. The illuminating lamp is operated between six and eight volts in normal operation from a Powerstat connected to the A.

C. line.

at ten volts

The lamp can be operated for some time

if a higher intensity is needed, as for

example, with good light-scatterers such as MgCO^. It is desirable that the illuminated area on the surface of the sample be kept circular.

If this is the

case, then one can move the viewing arm in either direction from the angle of specular reflection by the same amount and the same illuminated area will be viewed at both posi­ tions.

If, on the other hand, the illuminated area should

be elliptical, then a smaller illuminated area will be viewed at

an angle between the normal to the surface and

the angle

of specular reflection than will be viewed at

the same distance from the angle of specular reflection in the direction of the plane of the surface.

To eliminate

this difficulty, a series of elliptical apertures was cut to fit between the sample and the lens on the illuminating arm so that for any given angle of incidence, the area on

the sample which is illuminated is a circle. The surface upon which the wax films were cast consists of a polished brass square two inches on an edge and a quarter of an inch thick to which has been applied a thin film of a wax emulsion containing colloidal carbon black !9

The purpose of the black film was to eliminate

the effect of reflection of light from the back face of the wax film by absorption of the light in the carbon black. Incorporation of the carbon black in a wax emulsion elimi­ nates the possibility of a large change in refractive index at the interface between the wax film and the black back­ ground.

The surface produced by application with a small

camel*stair brush of a thin film of this black wax emulsion is very smooth and at the same time quite matte.


alternative is the production of a surface in a similar manner using Dag Dispersion Number 6 0 .20 Application of the wax emulsion to be investigated is done in one of two general ways, depending upon the film thickness desired.

For thick films, a brass ring 21

13An industrial wax emulsion, product of the S. C. Johnson and sons Company. 20A dispersion of colloidal carbon in a wax emulsion,^ commercial product of the Acheson Colloids Corporation, Port Huron, Michigan. 2JCovered with paraffin to eliminate the effect of surface tension.

one-quarter inch in thickness cut from brass tubing of inside diameter one and one-half inches is set on the square prepared as above, and a volume of wax emulsion is pipetted into the cell thus produced.

The proper volume

is calculated on the assumption that the emulsions contain approximately twelve per cent of solids. can know roughly the film thickness.

In this way, one

For thin films, on

the other hand, the ring is not used and the amount of wax applied must, be governed by spreading a certain small volume over a measurable area, assuming about twelve per cent solids.

The lower limit in thickness is achieved by

upending the brass square and draining off excess wax, but this gives a film thinner than is useful in producing good reflectivity and is subject to the criticism that there is produced a thickness gradient. Various methods of drying the wax films were investigated.

These include passing a slow stream of

clean, dry air over the films, drying over a desiccant, drying over a solution giving constant humidity, drying in a closed desiccator, and drying out in the open.

An approach

to optical flatness is highly desirable for this work, and the closest approach to this condition was produced by drying the films in the open.

Experimental Results Indices of Refraction. The indices of refraction of various wax emulsions 22 are given in Table 3 .

Emulsion numbers one and two are

the same formulation with the exception that one constituent present in the amount of five per cent was replaced by a cheap substitute.

Numbers three to six are emulsions con­

taining Carnauba as the only wax wherein the differences arise from a change in the amount of emulsifying agent. This change is indicated by the decimal in parenthesis,

0 .5 indicating the use of half of the amount of emulsifier chosen as a reference standard.

Numbers seven to twelve

are formulations containing two-fifths Carnauba and the rest other waxes which give the emulsion desirable properties, wherein again the only difference is in the amount of emulsifying agent as indicated. Optical Densities. The optical densities of the wax emulsions are given in Table 3. In .Figure

Per cent transmission is included. 4

are plotted the optical densities

as a function of the amount of emulsifier for the two

zzThese emulsions were prepared at the research laboratory of the S. C. Johnson and Sons Company. The author^ wishes to acknowledge the cooperation of Dr. L. Keith Coad in supplying them. See Appendix.

Table 3



Refractive Index


Optical Density


ErL 0 0 3 5 (L)



0 .308




4 2 .0






1 .162


Carnauba(0.75 )

















1 3 .0




























o - C a r n a u b a Wax A ' Mixture

Optical Density


0 .4




Amount of

Emul si fi er



series, Carnauba wax, and Mixed Wax. Optica}, and Electron Micrographs. On the following pages are printed the pictures of the emulsions taken with the light and electron micro­ scope.

Each page has five pictures, and each page contains

only one wax formulation.

The top picture is the optical

micrograph of the surface structure at a magnification of

1050 diameters,

in the center are two pictures of the

emulsion at the dilution of 50 to 1 , the print on the left being at 33120S and that on the right at 61400X.

At the

bottom are similar magnifications of the 250 to 1 dilution ratio.

The emulsions are numbered as they are in Table 3.

Goniophotometry. There are two general methods of graphical presentation of the goniophotometric curves, depending on the reflectivity of the surface.

For good light scatterers,

the polar plot is used, where the surface is considered to be situated at the origin and the light intensities are plotted as radius vectors.

For a surface following

Lambert’s Cosine Law, the curve so generated should be a circle whose center is on the normal to the surface and whose diameter is equal to the length of the vector in the direction normal to the surface.

In Figure

5 are


> ii





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