THE SYNTHESIS, CHARACTERIZATION, AND SIZINGOF

MONODISPERSE SILICA DISPERSIONS

BY

HARK A. TRACY

THESIS

for theDEGREE OF BACHELOR OF SCIENCE

INCHEMICAL ENGINEERING

College of Liberal Arts and Sciences University of Illinois

Urbana, Illinois1986

UNIVERSITY OF ILLINOIS

19.;..'..

THIS IS TO CERTIFY THAT THE THESIS PREPARED UNDER MY SUPERVISION BY

MARK A. THACY

N T IT L K I ) . . Tills 1 ’YM'i'HisA I » CilAMA(: ITlhl MATI ■ T , AMY YIYIMM Y Ml M) I uM

IS APPROVED RY ME AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE

DEGREE OF..JlNICLEMKKHJ.U':';.

iiiK z ia iiz i']Instructor in Charge

A pproved: ....(kdkyi! /

HEAD OF DEPARTMENT OF..CJUmiCAL.MUiWmUI.a

O 1364

TABLE OF CONTENTS

TOEIS BASE iIntroduction ISurvey of Literature ^Experimental Procedure ^Results ii

Size Variation With Reagent Concentration nParticle MorphologyMass Fractions 19Temperature Effects l0Diameter Correlation Function

Conclusions 91Recommendations 93Acknowledgements ^References q*Appendix A: Sample Calculations ^Appendix B: Solution Concentration and Size Data mAppendix C; Size Versus Ammonia Plots 5^Appendix D: Size Verus TEOS Plots coAppendix E: Mass Fractions mAppendix F: Correlation Constant Curves

#12345678

910

1112

1314151617181920

21

22

FlflUfiE TABLE

TITLEParticles Formed With Insufficient Water Particles Formed Near 4:1 Water:TEOS Threshold % Standard Deviation vs. Particle Diameter Size vs. Water Concentration (.17 M TEOS)Size vs. Water Concentration (.3 M TEOS)Size vs. Water Concentration (.5 M TEOS)Particles at 50 nmParticles at 170 nmParticles at 275 nmParticles at 450 nmHonodisperse ParticlesTypes of Dispersed Systems ObservedPolydisperse ParticlesBimodal ParticlesFlocculated ParticlesParticle Size Variations With Temperature Size Variations With [TEOS] and Temperature Particle Flocculation at 0°C Monodisperse Particles at 45#C Percent Deviation of Correlation at .17 M TEOS Percent Deviation of Correlation at .3 M TEOS Percent Deviation of Correlation at .5 M TEOS

EASSL*ail

icniintotiit111814

nif1112 n

ii

1110

SUMMARY

This thesis investigates the synthesis of colloidal silica dispersions in order to verify existing results, to expand them to new regions of phase space, to investigate temperature effects, and to use the data to develop a correlation relating the average particle diameter to the initial reactant concentrations.

The system studied involves three reagents, tetraethyl- orthosilicate (TEOS), ammonia, and water in an ethanol solvent medium. Three TEOS concentrations were studied .17, .3, and .5 M. At each TEOS concentration, runs were made from 1 to 14 M H2O at four ammonia concentrations .5, 1, 2, and 3 M.

The sizes of the particles reached a maximum within both the water and the ammonia ranges investigated. The behavior of TEOS was more specific to the concentration region and showed no universal size trends. Temperature studies indicated a decrease in particle size with increasing temperature. Finally, a cor­relation was derived which predicted the data to within 20% of the experimental value.

UilRQDUCTIQM

Developing a reliable, reproducible method of creating monodisperse colloidal dispersions is important in both the scientific study and commercial processing of ceramic powders. These dispersions are important scientifically because they are uniform and thus can be used to test theoretical models of colloid behavior. Monodisperae particles also make good standards for use in calibrating analytical instruments. Monodisperse colloidal suspensions have great promise commercially for several reasons.1 First, because they can be well characterized, processes used to produce these particles can be more easily scaled up. Also, the narrow size distribution facilitates characterization and study of the dispersions making the design of process control devices possible. Finally, since the stability of dispersions against flocculation is quite sensitive to the colloid size distribution , monodisperse colloids are the most easily handled.1

Because of the many advantages of a monodisperse system, it is scientifically and economically imperative that such systems be investigated so that monodisperse particles of a predictable size can be synthesized reproducibly. In the study described here, monodisperse silica particles were synthesized using the method developed by Stober, Fink, and Bohn 2 and confirmed by Van Helden, Jansen, and Vrij.* The goal of this project is to verify the results obtained in these two studies, to expand them to new regions of phase space, to investigate temperature effects, and to use the data to produce a correlation relating the expected

I .

average particle diameter to the initial reactant concentrations.

\\ i

X

SURVEY OF LITERATURE

Some previous work has been done to learn about both the chemical reaction involved in producing the silica dispersion and the nature of this colloidal system. The silica dispersion was produced by reacting ammonia and water with tetraethylortho- silicate (TE0S).2 Two specific reactions occur to produce the opalescent, milky product.* During the first reaction, the TEOS is hydrolyzed to silicic acid. This species undergoes a condensation polymerization reaction in which silicic acid molecules at supersaturated levels combine and eliminate water to produce the colloid. Ammonia acts as a morphological catalyst by reacting with the silicic acid to produce its conjugate base. The resulting negative charge on the silica species creates a stable colloid due to electrostatic repulsion between the particles. The condensation of silica from supersaturated silicic acid solutions has been found to be very dependent on pH and the initial silicic acid concentration. In fact, Makrides, Turner, and Slaughter showed that an increase of one pH unit results in a ten-fold increase in the rate of the condensation reaction.5 Though the temperature effects are less firmly established, Makrides showed that the condensation was independent of temperature since the increasing rate with temperature was counteracted by decreased supersaturation.5 A lower degree of supersaturation caused a decrease in the particle nucleation rate so fewer particles were formed.

Several important trends have been observed from experiments by Stober, Fink, and Bohn and Van Helden, Jansen and Vrij on the

TEOS system discussed in this report.3 Tests have shown that the average particle size depends on the concentrations of water and ammonia in the reaction mixture . At a TE08 concentration of .28

M, the size range obtained was between 50-900 nm for ammonia concentrations up to 8 M and water concentrations up to 15 H. Van Helden reported that, for a TEOS concentration of .17 M, ammonia

concentrations of up to 4 M, and water concentrations up to 3 M, the size range was between 20 and 300 nm. He also stated that the particle composition was 91.5% silicon, 5.25% water, and .97% carbon. Stober proposed that the monodispersity of this system was due to the presence of ammonia because, in the absense of ammonia, the silica flocculated in irregularly shaped particles rather than in the usual spherical particles. With ammonia present, however, the spherical particles were so uniform that only 5% of them differed from the median size by more than 8%.3

To explain these results two models of particle growth have been proposed. The classical model is that of deposition growth. In this model, silica is postulated to deposit on the surface of nuclei that form. Monodispersity is achieved because all particles nucleate in a small period of time and afterwards grow at the same rate. According to the coagulative growth model however, nuclei are colloidally unstable so they tend to coagulate until they reach a stable size. Monodispersity stems from the surface chemiscry of the particle which establishes the smallest stable colloid. The particles grow quickly until they reach this stable size after which the growth rate decreases dramatically. Currently, there is little experimental evidence to support either model. The present study was undertaken to

explore the effects of initial reagent concentrations on particle size and monodispersity, and thus provide a data set with which growth models can be tested.

To produce these silica particles, Stober, Fink and Bohn used the following recipe. Technical grade TEOS was distilled before use. Anhydrous ammonia from a tank was passed through a

drying column filled with sodium hydroxide pellets and then bubbled through ethanol at 0*C until a concentration of 5 M NH3 was reached. Ammonium hydroxide was used as supplied at a concentration of 14.2 M. Before each run, absolute ethanol, ammonia, and water were mixed in Erlenmeyer flasks with stoppers or in rubber sealed injection bottles in the desired concentrations of ammonia and water. Actual ammonia concentrations were measured by withdrawing small samples and titrating with 1 M hydrochloric acid. The total water concentration was calculated by adding fractional amounts of water introduced by the components. Finally, the TEOS was added and the flasks were mounted either on a shaker or in a water bath under ultrasonic vibration. Some tests were made using a magnetic stirrer as the agitator. All methods of agitation were effective. The total amount of solution added differed from 50 to 110 ml. Condensation was observed to start in 10 minutes, but the reaction was allowed to proceed another 110 minutes before the electron microscope grids were taken. These Formvar coated grids were dipped in the solutions and put on filter paper to remove excess solution. Sisea of random particle samples of 100 to 1000 in number on each micrograph, taken with a Zeiss EM9 or Phillips IM10QB electron microscope, were counted with a Zeiss

TGZ3 particle analyzer.Van Helden, Jansen, and Vrij followed this same recipe with

only a few differences. First-, they distilled both TEOS and

absolute ethanol. The grids used were covered with carbon coated Parlodion films. Also, the glassware was cleaned with 2% hydrogen fluoride followed by distilled water and absoluted ethanol. The reaction was stirred for 18 hours at ambient temperature. At this lower TEOS concentration, the opalescence of each solution became noticeable starting at . 5~2 hours afteradding the TEOS. No change in opalescence was noticed after 10hours. Finally the total volume of solution prepared variedbetween .2 and 3 1.

T

E m ^ m n A L - E R Q Q K D m E

In this study, the methods of Stober and Van Helden were closely followed. Before each run, the reagents were properly prepared for use. Reagent grade TEOS (Fisher Co.) was distilled 170 ml at a time under a vacuum of 28 inches of mercury at a temperature of 98°C. This required approximately 1.5 hours. The first and last 10 ml of distillate were discarded leaving 150 ml of pure TEOS after the simple distillation was complete. Two types of ammonia solutions were used. An ammonia in ethanol solution was prepared for low water concentration systems and ammonium hydroxide was used at high ammonia and water con­centrations. The ammonia in ethanol solution was prepared by bubbling anhydrous ammonia gas from a tank through a phosphorous pentoxide drying column into the absolute ethanol (U.S. Indus­trial Chemicals Co.) for about 15 minutes at 25#C to insure saturation. Concentrations of 2.9-3.1 M were obtained using a special titration procedure in which 5 ml of the ammonia solution was dissolved in 100 ml of deionized water to reduce the rate at which ammonia would escape from the solution during the titration. Methyl red was used as the indicator and 1 M HC1 was the titrant. Ammonium hydroxide (Baker Co.) was used as supplied at a concentration of about 14.0 M. Deionized water was also used.

Before each run, the glass and plastic ware was cleaned as Van Helden suggested. First, the dirty items were rinsed with a 2% hydrofluoric acid solution to etch away silica residues. Then the items were rinsed with soapy water followed by distilled

water. A final rinse with ethanol was done to insure no residualwater remained in the clean item and to allow for more rapid drying.

After the glassware was cleaned and dried, the solutions were prepared. First, the appropriate amount of each reagent was calculated according to the method outlined in Appendix A. The calculated amount of the solvent ethanol was first pipetted into each reaction flask. This was followed by adding the water and then the ammonia after which the flask was quickly sealed to minimized the escape of ammonia. The initial ammonia concentration was determined by titration with 1 M HC1. Slow stirring of the solutions was begun to mix the reagents. Finally, the TEOS was added. The total volume of the solutions ranged between 69-105 ml. All reactions were run in a water bath at constant temperature. For runs not at room temperature (25# C), all reagents were cooled or heated to the desired temperature before mixing.

Two types of flasks and stirrers were used during the course of the experiments. For the .17 M TEOS run, 250 ml three-neck glass round bottom flasks were used and stirring was done using an electrically driven half-moon propeller .25 in. from the bottom of the flask. For the rest of the experiments, Nalgene polyethylene bottles were used. Magnetic stirrers were placed in each bottle and each bottle was placed in a water bath constructed on a six head magnetic stirring apparatus. There were no differences in the particles synthesised in the different bottles. Stirring was performed at a slow speed (100-150 rpm) large enough to insure mixing but not too large to cause

1.

shear-induced flocculation. Solutions were stirred for 20 hours to insure the reaction was complete but the first opalescence appeared in the solutions between 30 sec. and 30 min.

After ceasing the stirring, a copper grid was dipped into each solution to obtain a sample. Excess solution was removed by placing the grid on filter paper. These grids were coated with both Formvar and carbon before being used to take samples. Electron micrographs of each sample were then made. The magnification of each electron micrograph was determined by using a calibration grid with 2160 lines/mm. Most of the negatives were photographed at 17,000 and 60,000 times creating a magnification of between 45,000 and 150,000 times after the negatives were printed.

The particle average diameters were obtained directly from the calibrated photographs. The diameters of thirty particles, or as many as possible if there were not thirty in a photo, were measured for each sample using a vernier caliper. The sises were then averaged to obtain a mean particle diameter and the standard deviation was oalculated. For particles that were not spherical, a major and a minor axis was measured and the two were averaged to obtain a particle diameter. For bimodal samples, the two sises were measured and averaged separately. Only the most numerous sise was used in the the graphs, though.

Finally, silica mass fractions were taken for many of the samples. This was done simply by weighing an empty glass weighing bottle before and after adding the solution. After leaving the sample dry in an oven at 75*C for twenty four hours, the bottle was again weighed. The bottles were handled with

lo.

gloves. The mass of silica in the sample was obtained by difference.

n.

RESULTS

Size Variation with Reagent Concentration

Silica particles were synthesized and their average dia­meters calculated over a wide range of phase space at 25 • C Three TEOS concentrations were investigated .17, .3, and .5 M. (Appendix B) At each TEOS concentration, ammonia concentrations of .5, 1, 2, and 3 M were examined. Finally, at each ammoniaconcentration, the water concentration was varied. The range of water concentrations that could be tes ed depended heavily on the TEOS and ammonia concentrations used. Since the stoichiometry of the hydrolysis reaction of TEOS requires four moles of water for each mole of TEOS, the smallest possible water concentration must be four times the TEOS concentration to obtain distinct particles (Figures 1,2). Also, low concentrations of water were impossible to obtain at the high ammonia concentrations because the watercontent of the required amount of ammonium hydroxide was already

/

higher than the desired water concentration of the test solution. As a result, at .17 M TEOS, the water concentration varied from 1-14 M at .5 M NHt to 5-14 M at 3 M NH». At .3 M and .5 M TEOS, 2 M HaO was the lowest water concentration used.

The diameters of the particles synthesized over this region of phase space varied significantly. The smallest particle had a diameter of 13.6 nm while the largest had a diameter of 777nm. Standard deviations in the sizes measured were small overall and decreased with increasing size. These standard deviations were smaller than those Van Helden reported (Figure 3).

f i S 3 T T 3 » A lf* J

F«toft€ 2 *Pa*t»cuts Mm * /

WurcA-TeoS Tn^eswocO ne,ootx{.nm T\Eo5> .5»i N#j /* «iO 4i8**0

□avi

atio

n (X)

IS.

Fig. 3i X Standard Davlatlon va. Parfclela Olaaatar

Several important size trends were observed. First, as the water concentration increased to 14 M, the size went through a maximum (Figures 4-10). This same trend was observed by Stober, Fink, and Bohn at .28 M TEOS. At .17 M the maximum occurred at about 7 M H2O but it grew to 10 and 11 M H2O for .3 and .b M TEOS. At the maximum, the particle diameter increased from 705 to 777 nm as the TEOS concentration increased from .17 M to .5 M.

The size dependence on the ammonia concentration is shown in Appendix C. For ammonia concentrations under 2 M, the particle diameter increased with increasing ammonia concentration. This was precisely what both Stober and Van Helden observed. Beyond 2 M NHs though, Stober observed that the diameter increased slowly as the NHs concentration grew at .28 M TEOS. This study indicates that the size did grow at .3 M TEOS but decreased with ammonia at the other TEOS concentrations. More tests must however be done to verify these trends.

The size trends with increasing TEOS concentration were found to depend heavily on water and ammonia concentrations (Appendix D). Thus, there was no overall maximum or minimum. At low water (2-3 M) and ammonia (.5-1 M) there was a small peak in size at about .17 M TEOS. As the water concentration increased though, this peak grew until (at 10-14 M H2O) the size increased over the entire TEOS concentration range. The size of the small peak increased from about 150 nm at .5 H NHs to 600 nm at 3 M NHs. This data supports the conclusions of both Stober and Van Helden. Stober stated that he observed no significant change in particle sise by increasing TEOS. This conclusion is verified by tne data presented here at low water and ammonia concentrations.

Part

icle

Diameter

(nm>

ic .

<

Fig. 4. Size vs. Water Concentration (. 17 M TEOS)800

700

600

590

400

300

200

100

0

Water Concentration (eolee/liter)

Average Pa

rtic

le D

iaeeter

<ne)

<7.

Fig. 5s Size ve. Water Concentration (. 3 M TEOS)

Water Concentrati on (eo1mm/1i ter)

II.

Fig. 61 Slzo v«. Motor Concentration C. 5 H TEOS)

Puiprici-e* AT $0 *#*t,n « Ttos, 1*1 )

0,00 o x

Mute? rPrtrt-r»Ct£S At no >*m

(.urn TtoiS , 2m MjO, »*w*3)n ta o O A

(.nm TCxtS t17,000 a

mrpoo'u

S t l i l u l n'«*q$h ** sn^*±**d

• <» ju*9M

23.

Van Helden, however, reported that at .82 M NHa and 2.5 M H2O as the TEOS concentration increased, the particle size decreased. This is also observed in Figure 2 of Appendix D at TEOS concentrations above .17 M. The size dependence trends then were found to depend on the region of phase space that was investigated

Particle Morphology

Four types of disperse systems were observed from the photographs taken of the samples. The most common were the monodisperse systems. These systems are characterized by smooth, spherical particles with a small size standard deviation (Figure 11). Other kinds of systems seen were polydisperse, bimodal, and flocculated dispersions (Figure 12). Polydisperse systems were seen exclusively in samples taken from solutions with low water concentrations (2-3 M) (Figure 13). These particles are uneven in shape and less uniform in size than the monodisperse particles. Bimodal dispersions were observed at .17 M and .5 M TEOS (Figure 14). No such dispersions were seen at .3 M TEOS which supports Stober’s failure to observe this at .28 M TEOS. These dis­persions of two clearly different size spherical particles were observed primarily at high ammonia concentrations (2-3 M) near the water concentration that gave the maximum average particle diameter. Finally, flocculated dispersions were seen at .5 M TEOS, 2-3 M NHs and 10-12 M H2O (Figure 15). Thus, monodisperse particles w^re most common at .3 M TOS. At .17 M

Ftdme M :fflo«jo o>5 Ptn.se faii r*ct-£ 5

l5«TCoS, .SPIN!*,, ,SV)w^)n, eoox

7*.

F i c u g g U : I y p s 5 of DisPcnseo Sy s t e m s O a s g u v e r p

.171*1 TEOS" \ C n«,7

.5M 1.0 2.0 1.0

.S in PO - — —

1.0 PD PD — —

l.o PD PI —

3.0 PO PI pi

5,0 PI m 6 e

1.0 m n m 0

10.0 m m m 6

u .o pi n p i pi

li.Q — in pi m

.SM t e o S-■” -— .. .. T_r-i rw-.5*1 1.0 2.0 3.0

.5 — ~ — —1.0 PC - — -2.0 - PD PO —3.0 — PO PO —5.0 - — —BT O 6 6 — SF10,0 W - — Fu.o P) Pi m FW.o in m SF P

.30 M T E 05

.5 /. 0- ■ -.

2.0 ; y

i f o i__

_

■ S — - —

i o — — — -

2.0 PO PD Pb —

3.0 PD PO PO —

So PI — —

1.0 m -

10.0 m - —

u.o M m M

u .o pi m m M

J j u .

Po r P o t r oispp«iero

M - M ON 0 0I5PF^ JEQ

6 r BftfooauSF * SLIGHTLY FlOC~

OJLAtFDF r Floccvcateo

im «ttw«}0 ,00® X

KJIWriocS

(.n rn TIPDtS> *** **? mm)n tOn T> x

C-SunTtfOS,*7,oooi

TEOS, monodisperse particles were observed at medium to high water concentrations away from the diameter maximum. At .5 M TEOS though, the monodisperse particles were restricted to medium to high water and low ammonia concentration systems.

These observations led to two conclusions. First, there is a threshold water concentration that depends on the TOES concentration above which monodisperse particles form. Second, high ammonia concentrations affect the stability of the system at .17 M and .5 M TEOS. At .17 M TEOS, bimodality resulted, but at .5 M TEOS both flocculation and bimodality occurred.

Mass Fractions

Mass fractions of samples at .17 M and .3 M TEOS were taken to determine the percent of silica in each sample (Appendix E). The data varied only with the TEOS concentration. The data indicated an average mass fraction of 1.331.06% at .17 M TEOS and 2.301.12% at .3 M TEOs. The ratio of these percents is 1.73 which compares well to 1.76, the ratio of the TEOS concentrations (.3:.17 M). The variations in the readings differed from the average by a maximum of 11% which was within the experimental error due to weighing and drying.

Upon heating, the silica dried into several different forms depending apparently on the size of the particles. The smallest particles (0-50 nm) termed a clear silica film at the bottom of the flask. Particles in the range 50-500 nm formed a thin layer of irridescent silica "paint” on the side of the flask.

Occasionally, at the lower end of this size range the silica dried and formed thin clear fibers reaching away from the glass towards the center of the flask. At the largest sizes (500-800 nm), a fine white, dusty powder was formed upon drying.

Temperature Effects

In addition to the tests at 25*C, the TEOS concentration wasvaried between .1 and .35 M at 0 , 9 , 25 , 35 , 45 , and 55*C.These tests were performed at 1 M NHa and 7 M H2O. Figure 16 shows that the particle size decreased as the temperature increased. According to Figure 17, the particle sizes generally increased with increasing TEOS concentration with the largest increases occurring at low temperatures. It must be notedthough, that this applies only at 1 M NHa and 7 M H2O so thiscannot be generalized to other concentration regions. Also, at the highest four TEOS concentrations at 0 C and the highest two at 9#C, the particles were partially or totally flocculated (Figure 18). At all other temperatures the particles were monodisperse throughout the entire range of TEOS concentrations (Figure 19). This implies that temperature is an important factor in monodispersity.

Part

icle

Dl

1

Fig* 109 Particle Size Variation* With Tamparatura

Port

icli

Siz

e

a.

Fig. 17* Slza Variation* With CTE0S1 and Tawparotur*

( is** ms, >«**%

*

*9 *Phat»clcJ Hr

i7®*o X

D i a m e t e r C o r r e l a t i o n F u n c t i o n

As a final goal in characterizing and describing thissystem, a mathematical correlation was derived that predicts the data obtained at the three TEOS concentrations to within 20% ofthe experimental values. This equation was derived in a trialand error fashion. First, the mathematical form of the diameter versus water concent> ion plot was determined to be :

u w r , NT)

This form involves three constants whose dependence on the TEOS had to be determined. A value for N was guessed, twoexperimental data points were selected far from each other and the constant B was evaluated. The value for A was thencalculated by choosing the water concentration at the maximum experimental diameter. This equation was then compared to the experimental data. Twelve such equations were derived; one at each of four ammonia concentrations at each TEOS concentration. These were compared. Since TEOS had a much greater effect on N and B than ammonia, these constants were assumed to be functions of TEOS alone in order to simplify the problem. The values obtained for the three TEOS concentrations were plotted versus TEOS concentration and a curve was fit to the points (Appendix F):

N s -3.5i ♦ Ni.ia [>»•*! -8 * -»n.

The constant A depends on both TEOS and ammonia con* centrations. Each A value was plotted versus TEOS at constant

a m m o n i a c o n c e n t r a t i o n a n d e a c h o f t h e s e c u r v e s w a s f i t t e d t o a

quadratic requiring three additional constants that were functions ammonia alone.

A - « (D*«C + b)2 C ( *, b, c owwo •« »w«»0Each a, b, and c was plotted versus ammonia concentration

and a curve was found for each plot.

-b * - . 1 * CmmjH + . on j £>#sll*

C* 1J.01 SS.03 C»«jll - >1.48 CNMj3 1

Finally, a special factor was added in the denominator to lower the values at low water concentrations to make a more precise fit.

F a £ (i*C reoa)/

Thus, the final equation has the following form:

C i t o w a + o ^ O [ X <0» ♦ F * 5 Ch,oD m

Its predicted results are plotted in figures 4-6.Figures 20, 21, and 22 show that the equation satisfactorily

predicts the data at .17, 3, and .5 M TEOS to within 20% of theexperimental value. The largest deviations occurred at thesharpest peaks. This means the 2 M NHs curves have the deviations closest to 20%. Since the coefficients of B and Nchange significantly over a short TEOS concentration range, predicting values for TEOS concentrations far from the three

T7.

examined may result in significant error, Thus, the behavior of the system at intermediate conc< rations must be determinedbefore the correlation can be universally applied.

Ex

pe

rim

en

tal

Dia

me

ter

(rt«

)

n.

Fig. 20» Porcont Deviation of Correlation at .17 M TEOS

Ex

pc

ria

an

tal

Dia

me

tor

Cnm

)

11.

Fig* 21: PttrcQnt Dovlotion of Corr®lotion ot *3 M TEOS

4o.

Fig. 22s Porcont Doviotion of Correlation at . 5 M TEDS

Si.

CflHCLUfilQMS

This study of the monodisperse silica particle system has led to the following conclusions.

1. A sharp maximum was observed as the water concentration was increased with the TEOS and ammonia concentrations held constant. This was observed by Stober.

2. As ammonia concentration was increased, it came to a smooth peak except at .3 M TEOS where it gradually increased. This supports Stober’s prediction of a slow rise in diameter with increasing ammonia at .28 H TEOS.

3. Both the predictions of Stober and Van Helden regarding changes in size with the TEOS concentration are suppported in specific regions of phase space. The conclusions of these two studies are shown here not to be universally true though.

4. In addition to monodisperse particles, polydisperse,bimodal, and flocculated particles were observed. Polydisperseparticles were seen at low water concentrations. Bimodalityoccurred around the maximum size point at high ammonia con** centrations. Flocculation occurred at high ammonia, TEOS, and water concentrations.

5. Mass fraction data showed that the fractions varied only with the TEOS concentration.

6. Drying of the silica resulted in several morphologies including clear glasses, "paint", fibers, and powders. Particle size determined the morphology.

7. Temperature studies showed that an increase in

t e m p e r a t u r e r e s u l t e d i n a d e c r e a s e d p a r t i c l e d i a m e t e r .

8. A correlation was derived that predicts the experimental results to within 20%. More tests must be done to insure that it is accurate at intermediate TEOS values.

RECQMMENBAT tQMS

in order to answer questions arising from this study and to

further probe the silica system, much future work can be done.

1. Particles should be synthesized at higher ammonia con­centrations in order to determine the effects on size in this concentration region.

2. Intermediate concentrations of TEOS should be used in

future tests so the derived equation can be fully tested and adjusted as necessary.

3. Temperature effects should be reexamined at a variety of concentrations to see where the temperature dependence is strongest and if it affects flocculation and monodispersity.

4. The areas where bimodality occurred should be inves­tigated to identify its cause.

6. The properties of the dried silica powders should be studied for possible commerical applications.

I would like to express thanks and appreciation to Dr. Charles Zukoski and Greg Bogush for their guidance throughout the project. I also wish to thank Jeanne Chang for helping in preparing this manuscript.

REFERENCES

* Barringer, E., et al., "Processing Monosized Powders," in Ultrastructure Processing of Ceramics, Gl&ases, and Compositea, John Wiley and Sons, New York, 1984.

2Stober, Werner, Finis, Arthur, and Bohn, Ernst, "Controlled Growth of Monodisperse Silica Spheres in the Micron Size Range," Journal ofColloid and Iniarlacs.Science, 26, 62-69 (1968).

$Van Helden, A.K., Jansen, J.W., and Vrij, A., "Preparation and Characterization of Spherical Monodisperse Silica Dispersionsin Nonaqueous Solvents," Jo urnal ,q!__C.QlIsld__and . InterfaceScience. 81, 354-68 (198G).

^Greenberg, Sidney A., and Sinclair, David, "The Polymer­ization of Silicic Acid," Journal of Physical__Chemistry, 59,(1955).

SMakrides, Alkis C., Turner, Maryjane, and Slaughter, John, "Condensation of Silica from Supersaturated Silicic Acid Solutions," Journal of Colloid and Interface Science, 73, (1980).

u.

ApMtMom A:

■Sa m P L E - G a l CHI ^ T l Q M S .

X .T P O S CoNCci^m^TiON U « « * * ‘n M (Va* #«•»«* nee*))*=.1320 M * I W e

... . W I O V W =CNO«E Hm. Tt»S ^Tx OOMMT ""iW x -j-

I . U < |« « * * » >» E t 0 H * 0» « r i » i l ( E * . ! « « , , » ¥ )

A. A , « n - C.«w«.n.N » ff « ~ *■""*>PINAL lUMrr AlAAIME ? W.20 ml|r„Tull *“ «»“* ; S-Ht ^ 1|(,gr|-- -------- - WiM ML "‘'"Cl

. * w * * - x = i-IH w nh3Vi22 ml x *•••* x Tilt ikl * S-"**

B. W * ” E” “ "m m•m v n u N .SW^Hi $*«m**«

o »m m x - ^ ^ s L * .St\ 3.JH "l x iqS m l w h l

^ V o w * NHj in EiOH = It 5i*». . aA mm

muIt0w> X 8 Mfc *

.. ivml a l — i j ios*l

C. L w * « « « ~ “ """ A C“* ° *' S *1%y yjfittu x —L— x imiessh 5(1): X ml x I%*l * it.M% town* **«l

■afr X * .S«L H^O

C a l c a j l a t i o n S ( c o n t>b. )

tit Usin« NM*|0H joivt/on (f. $. NHj} 5M fljO)

n, ComccniktrntN Of NH, im NHOW (fvTrnumw) ; Cn«iD

8. Voiuntf *f NHs0« AOOVO To QfT CnMj^ s 2A|

W.H n WMH x - fe'V - 2.0 i*\IOSi TAL

^ x = m.t

C. M*t« »r Ha0 in WHhOH

IH.H fn NMi|0H • 3*03 %w. = Sol.H Y * ■ %

^ s ^ * ,0oy>-

(JOO V, ' Ses.*H ) * 7 ^ s Z,,S ^ H»° ,N ^

• 2 /.15 ^ M * .0 N € ! MHxOH r 3 Z O ^jp

^ t o t a l moi.«J °P in 5*1 H^O

5-/»| x ./OS $ Tcrrot Voiomf * .S25 im. M*0 r*mL

E. Aouwnr of W«rw to tr aooco

, ff25 «hl H*0 Tor/w. - .320*«t H»0 w NlUfOM s .70Sm. #00*0

.205 mot X ^'ttZVu. * ■^*1, s 3,7 ml HiCfeAOb

A p a e .v o i x 8 : S o l u t i o n C oncentration and SilET D a t a

D a t pS ^ P t e

N u m a e n

' • W k i T

T E O S< " • 0

t « w c .

T ^ O S0 1 )

V f ti .u a * £

N h 3

t « i . )

^ o n c .

n h 3

C M )

Vou#«%C

W a t e r

C « c )

C g n C .

W i^ -re nW )

v 5 u i * » e

S t f c H0 * * 0

C o N C ,

f r O H

C « )

T e m p .

C ° c }

A v e f u t c

D iA m C T E R

• U s | « f e i H . n 1 1 . ‘/ 9 ‘y . 9 5 1 , S o 21!

* 3 ’ 5 S 2 51

i

> 3 t t 2 j

2 / S 2 H . n• ' I

! W ? 1/ < 7 j t OVj ? 2 . / / 3 91

»

2 S 2 5 -i H J 1

V S H . ' 7 n . “9 9 V 3 ? 2 . C C S o 2 ! ; ? . /i

2 S ? 3 . 9 t 7 o 1

V S H ■H : o 1 71 .• /9 V ! r * 7 ! ? • 75 . ? i 2 .S ' j 2 . S ' 5 c t ( o i

2 / 6♦

l H ; . O , 9 ? 4 i 9 S 5 0 2 7 3 S < 2 . 0 I S 2 W i / 6

7 l < * 2 H . f 1 1 f ? : M K i 3 . 2 U * ; t 9 ? ' / 4 2 S ^ 2 5 V > 2 o

l i t , j 3 ! w n : 1 ? . H t t < 9 0 ; j o . c : W . o > 0 . H * 5 2 7 y r i ?

V H 1 . n ! . ? | 7 2 . 1 1 2 . 0 I U . 5 j 9 S 2 5 2 f V 2 ) 2

2 / 7 i H I. / i H I 1 . 0 0 » 9 / O o 5 ? . / i 9 5 i 2 S S o ? * H ■

V l 2 h ! , / 7 | H Ii

1 0 0 3 5 2 . 0 0

.......................

5 C 2 ! 9 2 ! I S ■ < ? t / /

2 / 7 3 H . ! 7* ' 0 0 w * Of 3 5 . ? l S 2 7 9 2 1 5 j

2 / 7 H *-/ . / 7 H i J . O o I S S \ G 2 S o . S ? . . 2 I S 9 V . f r i 7

2 / i / 1 4--<

< 1k _ _ —

H Z < 0 0l l Z -

> 0 0L -

3 ? 5 C 5 i s V j f r < 2

A p p e n o ix 6 : S o l u t i o n C oncentration and S i lE D a t a

D A T eSa ih p c C

N u« 8£*

V lC M f f

T £ 0 5(« *•]

t«W C.

T E O St « )

VfcLWilfn h 3 |

^OIMC.n h 3c n ) I

V o ui«m£

W a rs** j C?*o

Cd«c.

W atcAw ?

SfGH j Cmc) !

C o m c .!

l " ) 1

lE **p .

C °c )

1----------------------

■ AveRAfe€

OiApACTEAC*|«)

Z l u 2 H . n i . o c j O . o !1l b / j 5 9 2 5 H S £ i z v !

i i u1

* ; 4 l l 1 i Do 22 .7 : •2. 0 ?o 3 ! J C ;7 Y I / b .

I h li

H

..... t

h ! n 4 ? 1 Ov 2C 1 ’ T 0 2 C .S ^ 9 37 ✓ 3 7 2 r 2 0 ;

1 2 h s

— ■ . • *

■ i H : n <v t 2 . o o 0 * l o K 9 / 7 / 2 S 7 jV I 2 o j -------------------------*

H ' S z H , n /V t 2 DO 1 1 ‘ s . o $ 2 .7 / ? : 2S i h t i c

1 I t ' S 0D H f 1 IV fc 2 . 0 0 1 s * 7.0 ")9 9* I E.J> 2S l O i l i l

1 l l ' i.J M . ' 7 **y 3 2 . 0 o ll 9 * iO.O H.Z 2S iC‘92 l?.7;

U > i l [ i • ' 7 iV 3 2 . o o . c V U O 7 t . o n .G 2S' V ? Y 2 ' 2

l h l 3 Ll • ' 7 <v. 3

r2 . 0 & ! / 3 '7 1 JY y - 1 3 f >. t 2S i

Zh$ 1 M / 7 22 .5 ? 00 • ?S * C n«*■ V*' 7 * 1—

■2.1 2S 5 7 / r l v :

2 /,$ 1Sm M .(7 2Z.S i ? o o ! 4.o *j; 7 . 0 3-.S » z . i 2 * SSffr/ftj

2//.C 3 l i J l 72 S ? 0 0 97 ' / 0 , C c?.? n z 2 S f V / r / /

v » s H . n 12 5 3 o c '? 5 ’ >2-0 cs 10.* Z S | *fy/t 9_j______________

A p p e n d i x 8 : S o l u t io m C omcentxatiom and S ize D ata

D a t c *V ltO A lff

T £ 0 S<««o

C.T e o S

cm)n h 2("*-)

Ca n c

n h 3( t t )

Voui«lCWater

Cr»c)

ComC.

W *r«nW )

StG H 1 (.m l ) 1

Co*#c.

EYOHcm )

T d h p .

C °c )

A v e R **€

D ia « cteh(•#«) j

I l l S H 4 n 2 /. 9 ? . o o O S * i 14 0 j t i . 3 1 0 .D ■ 2 .S ' 4 0 ^ t7 .2 1

H h J | 1 30 2 o.O ! .*194 ? 7 S I 2 .0 j 7 3 2 S ] I / . 9 ' ? 5 :

---------------!------------------------------ 1---------------H h \ 1 T | 3 0 2 0 . 0 1 7 9 4 ‘ 5 . « 1 3 0 i ?/ ?* | II Q 2 S' ' ^ 2 7 5 j

H i t ! 3 1 . 3 o 2 o .o i . 4 9 4 ■ 9 ?7 • S O j t ? ' , 3 ; 1 ( 0 ! 2 5 2 ^ S 2 '7 ? '

i s / / , 4 T , 3 o ! 2 o o .*#9^ ; ->o i ‘ 1 0 . 4 • 25- 4 7 0 *2 7 $

I. — ----------------;--------------- :

4 / , ; $ ! 1 \ . 3 0 I 2 0 . 0i £ _ 7 >0 . 0 5 S 2 G ^ 2 )

.4 9 4 f c .S L’ .o S 4 . S 2 5 3 ^ 2 . 7 9W/< ! 1 , -3o i 2 0 . 0

4 / 3 1 j 1 j J o I *9 .0 i .V 9 7 j Z t . 2 : 14 0 ! S i S O , S . 4 2 S' • ^ r 0 . 7 .

H f i 1 7 J o j 3 S . o j .9 9 4 | ? 7 5 i 2 .0 i ^ $ .7 S I 9 .0 |

HI 3 3 1 J O 3 S . 0 . 9 9 4 ! S t 2 i 3-0» :

S U S j ? ."? I 2 5 •• ?o £»?. i

H l 3 4 7 3o

i--------------

3S\o 99*f l ,< j 1 7 0 j 4$ 90 9 . S 2 5 V 9 £ i ' 7 . 7 j

4 /3 s 7 3 o 3S .0 .994 22 J 1? .0 7 (.So £ .9 4 2 ^ (52

HI 3, . ,,

c, 1 3c 3 ? . o .9 9 4 i t 2 . >4 .0 | 3 ? ? o s s Z S 4< jSt if 3

h p p E N o ix 8 1 S o l u t io n C oncentratio n and S i 2.ET D a t a

D a t e - $ AfnpLe

T £ O S(" •0

U n c .

T E oSWO

n h 3l*c )

Cowc.n h 3( * )

Vou/«*£ j

Wate* ! C V>

Com :.

1*1)

Vou#%*£"SfGHCMC)

Co*»C.£rO HCM)

T e m p .

C°c)11 Ave<U<r€ ! OmmcTEn

(Aim)

H H I *7 ?0 * 3 2 .0 0 3 9 5 2 .1 lo . z s 7.t>0 2 5 ;VS222.V

H l i 2•

1 3 o n 2.0o 5 6 3 .0 r n / . € 2 5 32%i ?o ,

H H ■j 1 ?o jc i 9 9 ?.'C * 7 0 7S.I IH H 2 5 ? O t ' C |

4 / v H 1 ?0 »s / 9 9 K , i * '2 .0 r r o X7SV i a . 6 IS

H H c ' .3 o / £ /.<?? 2 0.i9* '5 .0 62.0 ) | 3 I S 6 2 1 1 f i 3

1 . ?0 2 3 3 oK 0 ' 5 // i y , o i H . l 2S8«o

H iS 1 1 .3 0 1 3 3 o 6 2 5 ? ' 7 . 0 l o M 2 !3 G* ft4©

C* f o

H IS 2 , 3 o ' l l 3 o C......

I l l * fo .o f=v-?9 I2 .S 2 6 . 6 ? o : i C 5 ;

H IS 3 7 3o 2 1 . 3 OC a . i t * i p . c r . i o 9 M .T 25* 5 ? 2 r i 7 2 i

H IS H 1 l o 2 1 * 0 6 ’ C ? 0 * / v o 1 1.0 2 5 ; s s / 1 ? c ;

212% 1 IQ .S o M S o .S o .199 C l 2 J2 .3 26NO 1«C»C7/0*vi I

2 l W 1 Jo . s o N .5o 1 Co ».o Ci V U . 2 2 5

------------------- j

H2. o*-C

1 I2S 3 ' 0 • S O >1 5 o 3 - 2 / ? .o U .S i t . 6 Z 5Van

| .-<'0

ht>PEMoiX 8 : S o l u t i o n C owcentaation and S i" - D ata

D * T eSii^PLe

No«ae*

V l t g u f fT £ 0 S

<«•-]

t*w c ,

T t o sU1)

n h 2t"V>

^Ofi c.n h 3CN)

Vou/«%€Water )

Come.Wr-ts*

W

VftU»««£’E fttHCm.)

Co*#c.TrOHl " )

T e> ,p.

C°c)

A v e ^ ^ cD«A«€TCT

( « * )

3 / 7 / JO .S o i? .S .So j V S / j ? . o COT n j 2 S'Oao£«'£>

317 7 ! /oi .So •J.S ■Si/ </ 0 c rv«1O j1 ' Alta !

S ? s t l . l . I S | c-To-----------------1—— ■ t" *

5/7-----------------i----------------- ; : 1 -

3 10 j S o I J 5 - i -So n . 2 : 7 o 1 S</3* ! ______________________ ;----------------- ;-----------------

/O.1/ ' 2 5 ! v 5 V K 3 (i----------------- ------------------ - *

?|7 H { l o i .So j > 3 S .S o ICC i o o j V ? S I S |

M l j 5 / o ; ,5b j i? .s So ' ° i 7 ! i2 .o vc 3 ; ? . * 25 . '

?/T Q : l o .So ' ? S ! -So ?Z.W ' V O ! V $ G ? • * iS ; S S o l'Z !"

V S , 1 ' 0 : .S o 3 o .o .M9M 3.2/ 2.0 VS .S- J . l 2 S ( 0 3 - 9 S

v % 2 JO 5 o | 3o .o .991/ i *-/£/ j 3.o | ^ ¥» 9 j ! '2^ : ' ;

M i x 7 io - H .5 o ! 3 o.O ; 1 00 j i2 ! 1 0 ! V l2 ( , j $.7. | 2 5- V V 5 £ '1 7 |

v s i iO1

So i 300 ! .W V i i9?S 1 /2 .J! ■ . . . ______ i___________ i______

29.75 S i 1 5 ; 12?* 5 .2 '

V S H IO •S o 3o .o .V7v ! 22 MS >H o l i .S S s . i I S ! V0521 1 3 1

V S s f o • S o 6 o .o /.<79 3 . 2 1 2 . 0 tS So 2.1 2 *> f s f i :? .v...— "•'

V S Q> *0 .So 6c. 0 /. 99 H U 3 . o IV ( f 2.-7 2 5 3 2 ? * io

IKp p e h o ix B : S o l u t i o n C o hcentaation and S i lE D a t a

«n

AppenoiX 8 : S o l u t i o n C oncentration and S»ZE D ata

D at e SampleH u m e *

V k o w S-T£OS("*•]

C«wc,T E oSon)

nh 3t«c)

CdN C.NH3

Voui*€WArEAC c)

U nC.WarrenW )

ou»«iCSfftH | lp* 0 1

Cone.

l")

Tkmp.C°c)

AvEfUfeED iAiETEA(*-*)

H h S 2 3-5o .n Vo, o I. 0 0 j 11 ?s ; t 0 3S 2 3 S.l 1 9 1 5V22 6? 1

Hhi 3 V.o3 ,2 o Vo.o f. 0 0 ! it is 1 7 0 19 62 C-( 1 I 5'2£? 7 ,

HliS 4 S.o3 2Si . j

VOO I *-oo 1/ ?S ! 7.o 1 1? CZ1C.W ? i ltS±HS\

Hlft S CoH i , ? 0 j Vo.O ! 1 . 0 0 •» J5 7 0 i 32.0 Q ~l y S/O^T^j

*f/«‘ | C l.oS j ,?s ! ° ! Cq 0 J/.?5 7 o i ^ Cj i C c 9... - i » -. • ■■ -----------" —Kjlzz j 1 I 2.o | j o | 3o.o : i.o h i s T o ' 96 65 S 9 I S . ^S|r?2 ;

V/a j 2 ?.S , > 7 ?o.O : >0 II.?5 7.0 i 95’5 ?•* 25 VC/n6

Vlll 3 4 0 .20 i 3o.o i.o | 1/ ?s ! ■» 0 W.65 ! ?.c ; 2 5 ! SSVJ/I ;

4/ri 4 S.ot

.25 ; 3o.o 1.0 j M.?S 1 7 0 «/?.g5 j * 3 j 25 ' C5/2V9 !

4/22 S 6,o • ?0 j Jo.o I.O 1 M 35 1 7 a V2C5 i j 25 | C-92/1_______ _ . i .— . * . —'ll 22 C T O • ?S | 3 o.o t.o ; 1 1.?s | 7 0 Vf.cS 1 ? 2 5 ! C7S-2-H.Sj

4/23 J 2.0 J O 79 J I.O n is 1 0 V? cc 9.0 35 J'lOilS.S

4/23 , ■■■.Z 3.S .11 290 i.o n 35 7.0 46 if ?.$ 3 b 37^120

A p p e n d i x 8 : S o l u t i o n C oncentration and S h e D ata

D ATeSa*)0l6 VclumC

T £ O S(«<0

t«NC»TEOS

cm)n h *l«4.)

Conc.NH3 ! C*l)

Voum£Ware* I

(/■*«-) !

C«mC.W^nren

(*t)SfOH0*M.)

Came.£rOHCM)

T b k p .

C*c>

A v tfu teD iApi TEH

C*ip%)

V/23 3 H o .20 29 .0 / .o 1 h i s ; 7-o 95 -(£ ^ 70 • 1 35 903 r i 7 |

9 /i3 H s . o .Z? 29.0 * 0 !t

» ?s • 7 O 99 C 5 c * ?S 3 ? / i / 3 i

V/23'

S SO .?o 0 ' 0 1/ ss ! 7 0 V? 45 * 3 • 3 5 V j j r / a j

9 /l3 € 7 0 29 0 i . Q Ii ?5 7 J 92. GS * 1 35 W t / o—'— 1 1 "1

9f2-/ f l o i o 3 io 1 . 0 1/ ?5 i 7 0 95 55 1 . 1 95 ?2 o ii7 5 ■

----------------i2 — •'? }f.O t . o 1/35 7 0 UY r$ I ' i Ms Z?<fTm£ :

h u h 7 V 0 Zo 3<-0 ) 0 i> <s 7 0 97.cs ? 3 9 5 z iS * a 5.

i h t H S o .25 3/.o i i o H i s 7.0.......

92. (,5 ? . l 95 Z7Y*

H t V i 5 Co 3 o1

3 ( 0 i 2.0 1)35 7 0 9/C5 7 7 i ‘'5 1*°Zi2 i

' I f t H C 7.o 3 5 3f .o L o 1/-?? 7 0 9o.',S 1 7 1 Ul1 *7 __________3S<?i 9 '

H U S / 2 .0 .10 ?S.oi

J.Q u i s 7 0 9/ CS * *t

I fel2/ 'S i ______ 1

H ( i S 2 ?.S . ' 7 1 S . o 1 . 0 It ?s 7.0 7 c 55 I ' s l t l ?

U I t s 3 H o .20 B5.o * .0 t> ? s 7 0 3?. c<$ 7.C 55 i 9?i S a

A p p e n d i x 8 1 S o l u t i o n C oncentration and Sh e D a t a

D*Te Sa^ aleNumSOI

Vm.umS'T£OS

(«*0

C«NC.TEOSc*>

VjLVuCNH3

owc.nh3cn) 1

Voui«%£Water("O

ComC.WRren

W)GtGHCpac)

Cowc,EtQHC")

Te*hp.C°c>

AvenueDiameter

(*•*)

W/2? H S.o .15 K .o l.o j /M5 | 7.0 i j 95- ! l a m

HUs $■ ! c.q 3 o vu C O -J 0 ^7yS 7.2. . i SS ' z t i i ;o '

HU s■c ”Ko .^S | 35 o j u ?S i “7.o ! K C,S ! 7.0! • : * i SS r>u>a j

■ i ! ! ■ i i ; : ii! 1 ! ! - !j | : I ! i

| i | ;I i : 1 !

1 i ! 1 1 i______________i________!_______ !_______ ________:________:_______ ;________

j i i ! I. _ _ ... L -______ i

i 1! ;\ 1

i i !

*

t

<000

9oo

A»»«*oix C i FitwftgiLP««ntL« Si« Vf. Ow w«hi» CoHaivrmTittj.

(.17 «Teos)

1

1*0

tooAvotftfcSDiA*erE4(Mm) 5to

1*

l#o

Sf** i

i

;> s<ju»»r*‘« In lht> ( .m ii im t t 'r

5 S q m i't * to tin ' < i ni In n 1*i’«

>*|i <>> « u « n h s

\I

o

••f

• • l

<*0l

008

ooS.t**>j9»*iAy00$

tot

( CMN W S ' )

Noumi«a3M«3 S 0 3 X H M l 'S J ISIIWgI H W T j— (J *> Q f&73Y

oo|

008

ttoo*

•wo

V0«

A Mgfrom ft Flfttt.at.2..Pail' <jji Siztr. Yu I £ Q i _C«Nggr<rUTiaoi

( IM NHj)

"too

5«*AviimiCts%MCrn<«*) <roo

Hot

lot

loo

too

0

1

SqiiMii , lo lh<- < ii iitinu'tft

AS q u a m the C rn lim H rr

1 2 3 4 5 6

Square* hi the Centimeter

A p p e n d i x : E

M *ss Fr a c t i o n s

. n n t e o s

H,0COMC.

——. is nNH>

1.0*1 2,on

w 3

.SM .0/1? - -

1.0 ,o m .0I4W - —

2.6 ,0IHL|

— -

,0140

Vo .0141 .out .0131 —

S.O .013C .0132 ,<nj< -

7.0 .OUS .0133 ,0114 -

>0.0 .Odo .OUH .Ol]o, , , —

*2,0 .0131 .0121 .0177

IH.O - .QUO .0/22 .0 U1

* * i.nt .o« v.

.j o m TEO S

«40 ,SM /.o n i.o n V o nC O N t, tiHj NH J N M j

. $ *— - - —

1.0 - - - —

2.0 .01*1 .01HC .02$ 2 -\A

> o ,oi4! .0111 .013? —

■" "

5 .0 .«HH - - .Oiog

1 .0

------

---1

% w &o\__

J .o u t .0 1 1 1 .Oi/S

lo.o .oLp. - — .0222

12.0 ,«1 i t , o ia .0 U S .0X20

ty.o .C tlX ,OUO ,0221 .021 7

t e i . j o t .11 %

JtM’fSiW'r ... OUO'OLIO'tUQ'Svto-wo**sro'Sf

im'tout'tl*0‘Uto‘Lfto1Uto'— . ..otto’orlot '*bWL bio1b'O'Lb> o’Ulo*fLIO-Si<0’Sfint'% W9Sio'9S«o*L5t0‘>»Sio‘ghio-orjM-ueio'Lfio-Llio'Ul9‘fiflO'hn#'

..- -froio*Lr

h*«' + ISL to'TV.oo‘l Sloo-Sbtoo’LUOO-moo"uor•J Atf.s s.Sh.Si.Sr.6%o'<\vCi*aO dW3lv\

(o*HUil 'fHN Wl)S-Noix^vaj fSV^|

3 : xi(3N3ddy

Si

f t » f S MMX F Pj Ql f tg 1 : N C o m iT t -T i t t * .

T ••

*»'

N

CaMt>.*n.»LN * *isa* *.12 0*3 - « . « M l

& Mquaru* lo thr (k n tin u ter

«7.V

F Flame 1 ; 8 C ^ t ^ nat

Squunn to t hr Centimeter

1C«.

U Square* to the Centimeter

f,

* >*)WWvh !-■ tu H tM ftf f A

5 Nquttrin to the O n tlim -lir

3

*1

Ofc

I

rL