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This is to certify that the

thesis entitled
Prediction of Colloidal Suspension Stability
for SiC/Si3N4 and FeAl/A1203
Using Material and System Parameters

Fiber Systems

presented by

Brett Allen Wilson

has been accepted towards fulfillment
of the requirements for

”’5’ degree in Wd/(JWCL

 

Date W 2/9622.

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Michigan State
University

 

 

 

PLACE IN RETURN BOX to remove thie checkout from your record.
TO AVOID FINES remrn on or before one due.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l {Far 1 a 1998

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MSU le An Affirmetlve ActioNEquel Opportunity Institution
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Prediction of Colloidal Suspension Stability
for SiC/Sifih and FeAl/Algh Fiber Systems
Using Material and System Parameters.

BY

Brett Allen Wilson

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Materials Science and Mechanics

1992

' V-

/ (J A‘ --

ABSTRACT

Prediction of Colloidal Suspension Stability
for SiC/Sifih and FeAl/Algh Fiber Systems
Using Material and System Parameters.

BY

Brett Allen Wilson

In this investigation a method to predict the stability
of multicomponent colloidal suspensions at different pH
values from system and material data such as particle size,
volume fraction, electrolyte concentration, zeta potential
verses pH, and Hamaker constant data was developed from an
existing method. A computer program was written and used
for a SiC/Sifih powder system. The predictions of stability
ranges were found to be within a half a pH unit of actual
stability ranges as found from sedimentation results, but
was dependent upon accurate zeta potential data. The
dependency of the program on temperature variations,
relative component volume fraction variations, and the
accuracy of the input Hamaker constants was examined. For a
FeAl/Algh fiber composite, the method the predicted ideal
processing conditions when the components were mixed at pH 5
followed by an increase to pH 8, which would prevent

differential separation of the compbnents.

DEDICATION

To my Mom and Dad
without whom, for me, none of this would have been possible.

ACKNOWLEDGEMENT S

First of all I would like to acknowledge my entire
family for their encouragement, love, and support. I would
also like to acknowledge Mr. J.W. Ertle for challenging me
to think in high school chemistry, for as a result of this I
realized that learning could be so much more than simple
regurgitation and that I could actually enjoy learning. I
would also like to acknowledge Dr. F. Edward Wall for
bringing out the scholar in me, if you can call it that. I
would like to thank Kelly Ann Therrien for reminding me why
I came to graduate school at a time when I needed to hear it
most. I would also like to thank Jim Stout and Sharon Thoma
for helping me keep my perspective, and my sanity. I would
like to acknowledge and thank Lonza Inc. for samples of
their SiC powder. I must also acknowledge and thank Dr.
M.J. Crimp, my advisor, for finding funding for my project
and especially for her help and increased availability as my
thesis work wound down. I also must thank Dr. M.A. Crimp
for his intercession and help, despite his tried patience
with me, along with thanks for use of his office, computer

and printer for the completion of this manuscript.

ii

TABLE OF CONTENTS

LIST OF FIGURES....... .................................. iv
INTRODUCTION............................................ 1
LITERATURE REVIEW.... ................................... 5
EXPERIMENTAL PROCEDURE .................................. 39
RESULTS.... ................. . ........................... 63
DISCUSSION.......... .......................... .......... 124
CONCLUSIONS................. ................. . ..... ..... 142
APPENDIX A..................... ..... ... ................. 145
APPENDIX B............ .................................. 147
APPENDIX C........... ................................... 214

BIBLIOGRAPHYOOOOOOOO0...... ..... O ..... I ....... 00.0.00... 239

iii

Figure

Figure

Figure.

Figure

Figure

Figure

Figure
Figure
Figure

Figure

Figure

Figure

Figure

10

11

12

13

Lgsr or FIGURES

Illustration of a) the attraction of
counter-ions to the surface of particles
and the effects of distance from the
surface on b) ion concentration and c)
potential (taken from(15)).

Illustration of a) the double layer
surrounding a colloidal particle and b)
the change of potential with distance from
the particle surface (taken from (15)).

Computer flow diagram
STABILITY PREDICTION.

for the main program

Computer flow diagram for subroutine FDATA

INPUT.

Computer flow diagram for subroutine

CALCPZC.

Computer flow diagram for subroutine

CALCZP.

Computer flow diagram for subroutine

Computer flow diagram for subroutine WC.

Computer flow diagram for subroutine SI.

Computer flow diagram for subroutine

WVFCN.
flow for subroutine DATA

Computer diagram

STORAGE.

Electrophoretic zeta potential measurents
for SN-Elo Sign at varing electrolyte
concentrations (M) (from (76)).

Electrophoretic zeta potential measurents
for UF-IO Sic at varing electrolyte
concentrations (M) (from (76).

iv

 

20

44

45

46

47

48
49
50
51

52

55

56

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

14

15
16
17
18
19

20

21

22

Electrophoretic zeta potential measurents
for UF-lO SiC at varing electrolyte
concentrations (M) with regression
analysis.

SEM micrograph of sedimented FeAl powder.
SEM micrograph of chopped alumina fiber.

ESA zeta potential measurements for LS-5
SiC at an electrolyte concentration of
10'3 M KNO3.

ESA zeta potential measurements for UF-lO
SiC at an electrolyte concentration of
10'3 M KNo3 .

ESA zeta potential measurements for UF-15
SiC at an electrolyte concentration of
10‘3 M I<No3 .

ESA zeta potential measurements for SN-ElO
Sign at an electrolyte concentration of
10'3 M mo3 .

Stability ratio data from the predictive
program using the constant potential
repulsive equation and electrOphoretic
zeta potential for a) LS-S SiC/SN-Elo
Sign, b)UF-1O SiC/SN-EIO Sign, and c)
UF-15 SiC/SN-EIO Sign where: temperature
is 25 °C, volume fraction of components
is 0.5 and electrolyte concentration of
10-3 M KNO3.

Stability ratio data from the predictive
program using the constant potential
repulsive equation and ESA zeta potential
for a) LS-S SiC/SN-Elo Sign, b)UF-10 SiC/
SN-ElO Sign, and c)UF-IS SiC/SN-Elo Sign
where: temperature is 25 °C, volume
fraction of components is 0.5 and
electrolyte concentration of

10-3 M KNO3.

58

61

62

64

65

66

67

69

72

Figxire 23 Stability ratio data from the predictive
program using the constant charge
repulsive equation and ESA zeta
potential for a) LS-S SiC/SN-EIO Sign, b)
UF-10 SiC/SN-Elo Sign, and c) UF-IS SiC/
SN-E10 Si3N, where: temperature is 25 °C,
ovolume fraction of components is 0.5
and electrolyte concentration is 10"3 M.

Figure 24 Interaction potential data from the
predictive program using the constant
potential repulsive equation and electro-
phoretic zeta potential for LS-S SiC/
SN-ElO Si3N, where: temperature is 25°C,
volume fraction of components is 0.5 and
electrolyte concentration is 10'3 M and

a) pH = 4.0, b) pH = 4.5, c) pH = 5.0,
d) pH = 5.5, e) pH = 6.0, f) pH = 6.5,
9) pH = 7.0, h) pH = 7.5, i) pH = 8.0,
j) pH = 8.5, k) pH = 9.5, l) ph = 9.5,
m) pH = 10.0, n) pH = 10.5, 0) pH = 11.0

Figure 25 Stability ratio data from the predictive
program using the constant potential
repulsive equation and electrophoretic
zeta potential for a) LS-5 SiC/SN-EIO
UF-15 SiC/SN-Elo Sign where: temperature
is 25 °C, volume fraction of components
i320.5 and electrolyte concentration is
10’ M.

Figure 26 Stability ratio data from the predictive
program using the constant potential
repulsive equation and electrophoretic
zeta potential for a) LS-S SiC/SN-Elo
Sign, b)UF-10 SiC/SN-Elo Sign, and c)
UF-lS SiC/SN-EIO Sign where: temperature
is 25 °C, volume fraction of components
i550.5 and electrolyte concentration is
10’ M.

Figure 27 Total stability ratio data from the
program VARYN using data from the
predictive program which used the constant
potential repulsive equation and electro-
phoretic zeta potential for a) LS-S SiC/
c)UF-lS SiC/SN-EIO Sign where: temperature
is 25»°C, volume fraction of components is
vafiied and electrolyte concentration is
10' M.

vi

Figure 28 Stability ratio data from the predictive 103

Figure 29

Figure

Figure

Figure

Figure

Figure

30

31

32

33

34

program using the constant potential
repulsive equation and electrophoretic
zeta potential for UF-15 SiC/SN-ElO Sign
where: temperature is a) 20, 25, and 30 W:
and b) 0, 25, 50, 75 °C volume fraction of
components is 0.5 and electrolyte
concentration is 10"3 M.

Stability ratio data from the predictive 105
program using the constant potential

repulsive equation and electrophoretic

zeta potential for UF-15 SiC/SN-Elo Sign

where: temperature is 25 °C volume

fraction of components is 0.5, the

electrolyte concentration is 10'3 M, and

the Hamaker constants in units of 1049.]

are varied by +/- 10% to the values noted

in a) and b).

Sedimentation samples for a single 108
component suspension of LS-S SiC with an
electrolyte concentration of 10'3 M KNO3

after sedimentation for a) 21 hours, b) 21

hours, 0) 21 hours, d) 73 hours, and e) 73

hours.

Sedimentation samples for a single 111
component suspension of UF-10 SiC with an
electrolyte concentration of 10'3 M KNO3

after sedimentation for a) 21 hours, and

b) 119 hours.

Sedimentation samples for a single 112
component suspension of UF-15 Sic with an
electrolyte concentration of 10"3 M KNO3

after sedimentation for a) 20 hours, and b)

118 hours.

Sedimentation samples for a single 113
component suspension of SN-Elo Sififi with

an electrolyte concentration of 10‘ M

KNO3 after sedimentation for a) 1.5 hours,

b) 24 hours, and c) 146 hours.

Sedimentation samples for a two component 115
suspension of 0.5 relative volume fraction

of LS-S SiC and SN-E10 Sign with an

electrolyte concentration of 10"3 M KNO3

after sedimentation for a) 0 hours, and b)

72 hours. ' .

vii

Figure

Figure

Figure

Figure

Figure

Figure

35

36

37

38

39

4O

Sedimentation samples for a two component
suspension of 0.5 relative volume fraction
of UF-10 SiC and SN-E10 Sign with an
electrolyte concentration of 10"3 M KNO3
after sedimentation for a) 29 hours, and b)
70 hours.

Sedimentation samples for a two component
suspension of 0.5 relative volume fraction
of UF-15 SiC and SN-ElO Sign with an
electrolyte concentration of 10'3 M KNO3
after sedimentation for a) 23 hours, and b)
64 hours.

Sedimentation samples for a two component
suspension of 0.75 relative volume fraction
of UF—10 SiC and SN-EIO Sign with an
electrolyte concentration of 10"3 M KNO;
after sedimentation for a) 22 hours, and b)
63 hours.

ESA zeta potential measurements for FeAl
powder at an electrolyte concentration of
10'3 M KNO; .

ESA zeta potential measurements for Alfib
fiber at an electrolyte concentration of
10'3 M KNO3.

Stability ratio data from the predictive
program using the constant potential
repulsive equation and ESA zeta potential
for FeAl and A155 radii of a) 3.5 and 15.0
microns, b)7.5 and 15.0 microns, and c)
12.5 and 15.0 microns respectively, where:
temperature is 25 °C, volume fraction of
components is 0.5 and electrolyte
concentration is 10"3 M KNO3.

viii

116

117

118

119

120

121

TABLE 1

LIST OF TABLES

Zeta potential values at several pHs from
acoustophoretic BSA and electrophoresis
measurements.

ix

INTRODUCT ION

Advanced ceramic materials are currently being used in
an increasing number of different fields. Areas in which
ceramics are presently found include electronics, dentistry,
automotive engines, industrial tooling, and biological
prostheses. Within these different fields ceramics are being
used in a wider variety of applications. In electronics,
for example, ceramic uses vary from electrical insulation to
chip carriers and substrates to piezoelectrics to
superconductors.

The vast majority of ceramic materials are made by the
processing of raw material powders into a green body and
subsequent heat treatment of the green body, which causes
the elimination of pores, densification, and microstructural
development. Uniformity in the green compact is very
important since it governs the microstructures of the final
sintered body, and the microstructure of the final body
determine the resulting properties of the body, such as
mechanical strength and various electrical and magnetic
properties. Problems with advanced ceramics arise from
difficulties in the ability to repeatedly process ceramics

with identical microstructures and properties. The

2
formation of non-uniform ceramics is caused by
inhomogeneities which are the result of unsuccessfully
making a uniform green body. Agglomerates are one of the
main causes of inhomogeneities since they tend to cause the
formation of a non-uniform green body containing an uneven
distribution of pores and a change in the pore size
distribution due to resulting larger pores. The preparation
of well dispersed, stable suspensions help alleviate the
problems caused by agglomeration and lead to the formation
of a uniform green body and consequently result in better
sintered bodies. It therefore becomes important to increase
control of the processing in order to reduce microstructural
defects and to maximize reliability. .

Processing of ceramics can be divided into three areas.
First is powder formation, then dispersion of the powder,
and finally powder packing during drying and compaction.

The dispersion of the powder consists of two elements:
dispersion of the powder into a suspension and the stability
of the suspension. While ideally it is desirable to have a
disperse, stable suspension in order to improve the final
microstructure by removing agglomerates, new processing
methods contain steps which call for switching from Stable
suSpensions to unstable coagulated suspensions containing
large loosely bound agglomerates and switching back to a
stable suspension. Coagulated suspensions with loosely

bound agglomerates prevent segregation of the different

3

system components and make it possible to remove excess
salts and surfactants by washing. Due to the marked
importance of preparing stable suspensions and the combined
use of stable and unstable suspensions, the prediction of
the stability of ceramic suspensions would be an important
tool to aid in the control of processing advanced ceramics.

Pioneering work in this area was done in the 1940’s and
is known as DLVO theory. This theory describes the total
interaction energy between particles in a single component
suspension. From this information some insight into the
stability behavior of the suspension can be inferred.
However, with the increasing use of multi-component systems
due to the addition of reinforcements and of processing
additives (e.g. sintering aids, stabilizers, composites,
etc.), it is necessary to develop a theory for the
prediction of the stability of multi-component systems.
While work has been done to develop theories to predict the
stability behavior of two-component systems, the majority of
the application and experimental verification of these
theories has been done by colloid chemists with little work
done with advanced ceramic systems. This demonstrates the
need for further research in this area of ceramics.

The following work will investigate the stability
behavior of multi-component ceramic systems. The prediction
of their stability will be examined by inputing system and

material data (such as pH, electrolyte concentration,

4
particle size, Hamaker constant, and zeta potential) into a
computer program which uses a method that is an adaptation
of a method originally developed by Healy, Hogg, and
Fuerstenau from the pioneering DLVO theory, while
experimental investigations will examine their actual

stability states.

LITERATURE REVIEW

The vast majority of ceramic materials are made by the
processing of raw material powders into a green body,
followed by subsequent heat treatment of the green body
which causes the elimination of pores, densification, and
microstructural developments (1). Uniformity in the green
body is very important since it governs the microstructures
of the final sintered body (2, 3), which in turn determines
the resulting properties of the body, such as mechanical
strength, and various electrical and magnetic properties (4-
6). The formation of non-uniform ceramics is caused by
inhomogeneities which are mainly the result of the formation
of agglomerates of particles in the ceramic suspension(8,
9). New processing methods use temporary aggregation of the
suspension in order to prevent segregation of the system
components between processing steps(9-11). The prediction
of the state of aggregation would therefore be an important
tool in the control of processing advanced ceramics.

The knowledge gained in predicting the stability of
ceramic suspensions may be readily applied to a wide variety

of other applications where similar colloid theory is being

6
applied. Such applications include selective flocculation
in waste treatment (12-15), biological/medical studies of
blood coagulation (16) and cholesterol stability (17), paint
stability (18) and retention (19), and deposition and
adhesion of material coatings (20-22).

To understand colloidal suspension stability, it is
first important to elaborate on what is a colloidal
suspension. The first important characteristic of a
colloidal suspension is the size of the particles. For the
case of a ceramic colloidal suspension, which is a lyophobic
solid in a liquid, the size of the solid particles should be
large enough so that they are not considered to be in
solution with the liquid and small enough so that they are
affected by collisions with the liquid (23). There is no
absolute size range for colloidal particles (23, 24);
however, a range of 1 nm to 1 um is often regarded as the
typical range for a colloidal suspension (15, 23, 24).
Because of the small size of particles in a colloidal
suspension another important characteristic of these
suspensions is that the particles, because of their small
size, have a large surface area when compared to their
volume (23, 25).

Another important characteristic of colloidal particles
is that when the particles are put in the suspending liquid
they develop a surface charge. There are several different

ways in which this charge is developed which all depend on

7
the specific chemistry and thermodynamics of the system (the
system includes the particle surface, the liquid, and any
electrolytes that may be present in the liquid). One
mechanism for surface charge generation is the creation of
crystal lattice defects through the replacement of ions in
the crystal lattice structure of the particle by ions of
lower charge (25). This type of charge generation mechanism
is seen most often in clay minerals where ions in the
crystal lattice structure with a valence of three are
substituted for by ions from the liquid with a valence of
two causing a net charge on the surface (25).

If the colloidal particles have an ionic crystal
structure then one mechanism for surface charge generation
is the unequal dissociation and adsorption of oppositely
charged ions from the particle surface (25, 26). This
unequal dissociation and adsorption of surface ions results
in a slight imbalance in the number of crystal cations
(positively charged ions) and anions (negatively charged
ions) which causes the development of a net positive or
negative charge on the surface (25). The classic example of
this is given in most colloid texts (15, 18, 25, 27, 28).
This example is AgI which has Ag* and I‘ ions which
dissociate from the surface in equal numbers according to
equilibrium conditions determined by the solubility product

(25). However, the iodine ions are preferentially adsorbed

8
back onto the surface (compared to the silver ions) which
results in the net surface charge.

Another mechanism for surface charge generation is the
dissociation of ionic surface groups or the interaction of
ionic surface groups with H+ and OH“ ions in water (25, 26) .
Hunter (25) notes that it is sometimes quite difficult to
discern between the two because their net results are the
same. For oxide particles in water the surfaces are
hydroxylated and these hydroxyl groups can then undergo
further ionization (29). An example of this is given by
James and Parks for alumina (29):

A1 +A10+H20 '- 21110}!

A101! -- AlO' +H‘
H’ +A10H .. AIOH,+

where: A1 = aluminum (III) ion on the surface
A10 = oxide ion bound to surface Al ion
AlOH = hydroxylated group
AlO‘== ionized hydroxyl group
AlOHf = ionized hydroxyl group.
In a general form after hydroxylation this can be written as

(25):

M01! - MO'+H*
M0H+0H' a MO'+H,0.

Extensive investigations and modeling have been done to
describe this type of surface charge generation and charge

generation from the dissociation of ionic surface groups

(29-32).

9

It is important to point out what a potential
determining ion is. A potential determining ion is an ion
which helps determine the potential of a particle surface or
as in the previous discussion helps generate charge on the
particle surface. For the example mentioned earlier of AgI
particles, Ag+ is a potential determining ion (28). For.
particles with surface charge generation resulting from the
interaction of ionic surface groups with H+ and OH‘ ions as
was the case for alumina, the potential determining ions are
H+ and OH’. In this case adding more H+ and OH‘ through the
addition of an acid or base will change the concentration of
potential determining ions which will change the degree of
interaction of the potential determining ions with the ionic
surface groups and consequently will change the charge on
the particle surface. Similarly, changing the concentration
of any potential determining ion will result in a net change
of surface charge.

As a consequence of the characteristics described
previously the interface between the solid particles and the
liquid medium becomes tremendously important in the behavior
of colloidal suspensions. This is why physical chemistry of
surfaces and interfaces has become such an integral part of
colloid chemistry.

From a physical standpoint, particles in a colloidal
suspension are in continual motion due to a variety of

different types of motion. Particle movement in the medium

10
is caused by collisions of the particles with the molecules
of the medium, gravitational forces, and convection forces
(23, 33). Movement caused by particle collisions with the
suspending medium is termed Brownian motion (23). This
motion is completely random with millions of changes in
direction per second (34). As the particle size increases,
compared to the size of the molecules of the liquid, the
effects of Brownian motion are reduced (15). Gravitation
movement is seen as sedimentation as the particles are
slowly forced by gravity to ’fall' through the liquid
medium. This gravitational movement is increased as the
particle size is increased. Thermal movement is caused by
convective forces resulting from thermal gradients through
the liquid medium and rapidly decreases as particle size is
increased. The net result of these different types of
motion is that the particles in the suspension are in
continual motion and will approach one another for
collision. Collision, however, depends upon the forces
interacting between colloidal particles.

Forces which are acting on approaching colloid
particles are van der Waals forces, steric forces and
repulsion forces which are the result of the electrical
charges on particle surfaces. Steric forces are forces
caused by co-polymers which are added to a colloidal
suspension and which are adsorbed on the surfaces of

particles (15). The work of this thesis will be for

11
suspensions which do not contain co-polymers so that steric
repulsion forces will not be considered hereafter. Van
der Waals forces are caused by three different types of
attraction. The first type is called a Keesom interaction
and is where a dipole molecule orients and attracts another
dipole molecule. Another type is called a Debye interaction
and is where a dipole molecule induces a dipole in a
polarizable molecule and attracts it. The third type is
called a London force and is where a fluctuation in a
molecules' electron distribution results in an instantaneous
dipole which causes a dipole in another molecule and so
attracts this other molecule (35).

London forces are dominant in suspensions unless the
materials are highly polar(15). Hamaker (36-38) calculated
the force due to van der Waals attraction which results from
London forces by using a simple pair-wise addition of atomic
forces with the potential decreasing as the inverse of the
sixth power of separation distance (39). Casimer and Polder
(40-42) showed that for larger separations there was a
retarding effect which made the potential decrease as the
inverse of the seventh power of separation distance (33).
This retarding effect results because, at larger
separations, by the time the electric field from one dipole
reaches and causes a dipole in another molecule; the
electron distribution of the first molecule will have

already changed (39). J. T. G. Overbeek notes, however,

\

12
that for most colloidal suspensions retardation effects are
not important (33). Van der Waals attraction without
retardation for two different interacting particles of
radius, aland.a,, separated by a distance, H, can be

represented by an expression derived by Hamaker (38):

 

 

 

V‘ = -.i[ Y + Y +2109 xz‘UQ’Ix ] [1]
12 x3 +xy+x x3 +xy+x+y x2 +xy+x+y
where: A Hamaker constant

X=H/(a1+a2)
=allaz

The Hamaker constant, A, must be calculated in order to
evaluate the force of attraction due to van der Waals
forces. There are two methods for calculating the Hamaker
constant. The first is a microScopic method which was
developed by Hamaker. This method integrates over all pairs
of atoms in order to get a total energy for the macroscopic
body (43), but uses molecular constants for evaluation which
are difficult to ascertain. The second method is a
macroscopic method and was developed by Lifshitz (44, 45).
This method uses macroscopic properties such as refractive
index and dielectric constants in calculating the Hamaker
constant. J. Gregory shows the following expression derived

using the Lifshitz method (46):

 

(e -1)2
.A=0.230hv ° [2]
V (e°+1)3/2 (e°+2)1/2
where: coi= limiting dielectric constant
2,, = n

O
limiting refractive index in visible region

13

h = Plank's constant
vv== characteristic dispersion frequency.

Bleier simplifies this expression to (47):

(61-1) 2
(61mm (61+2l1” '

 

mum -113.7 [31

The previous calculation determines the Hamaker
constant for particles in a vacuum. Particle interactions
in a medium are less than in vacuum due to the molecules of
the medium being between the two interacting particles. To
account for this an effective Hamaker constant is used. For

two identical particles in a medium (15):

A...= w“ 41.1") 2 [41
where: Aeff = the effective Hamaker constant

1n = Hamaker constant of particle i in vacuum
A, = Hamaker Constant of medium in vacuum.

For two different particles in a medium (15):

A.::=(A11/2‘A.1/2) (AJ1/z_A-1/2) . [5]

As stated previously, the repulsive forces in a
colloidal suspension are due to electrical charge on the
particle surfaces which is generated by the various methods
described earlier. What transpires is that the charged
particle surfaces attracts ions in the liquid to the

particle surface. These attracted ions can be from the

14
liquid medium itself or from electrolytes in the medium.
For a water medium, ions from the medium itself would be
hydrogen and hydroxide ions since water dissociates into
these two ions. The concentration of each of these ions is
determined by the pH which is defined as the negative of the
log of the hydrogen ion concentration. For example, at a pH
of 7 the concentration of [HS] and [GET] is 10"7 M and for a
pH of 4 the concentration of [H7] and [CHI] is 10"4 M and
107” M, respectively.

Electrolytes are materials which when added to the
suspension which will go into solution with the liquid and
are generally added in concentrations ranging from 10'2 M to
10"5 M. Common examples of electrolytes are potassium
hydroxide (KOH), sodium chloride (NaCl), calcium carbonate
(CaCOg), and magnesium chloride (MgClz). KOH, NaCl and CaCO3
are called mono-valent electrolytes because when they go
into solution each molecule forms the same number of cations
as anions, while MgCl2 is called a di—valent electrolyte
since one molecule will form an unequal number of cations
compared to anions upon going into solution. KOH and NaCl
are called monatomic electrolytes since both of the ions
formed in solution ions have a valency of one, while CaCO3
is not a monatomic electrolyte since the ions formed upon
solution have valencies of two.

As shown previously, the concentration of H“ and OH‘

ions changes fairly dramatically with pH. Electrolytes are

15
added in order to overwhelm this effect and to keep a
constant concentration of ions. An illustration of the
reason for this can be found in the following example, for
water at a pH of 7 with an electrolyte concentration of 10’3
M the electrolyte ions are more dominant than the water
since the concentration of ions in the water is 10'7 M which
means that the electrolyte ion concentration is 4 orders of
magnitude greater. Now if the pH in this example is changed
to 4 then the H” ion concentration will change to 10" M
which is still an order of magnitude less than the
electrolyte concentration.

Another important point about electrolytes is the
concept of indifferent electrolytes as opposed to potential
determining ions. As mentioned earlier, potential
determining ions are specifically adsorbed (chemisorption)
by the surface and result in surface charge generation.
Indifferent ions, on the other hand, are not specifically
adsorbed on the particle and result in no net surface charge
generation. The adsorption of indifferent ions is merely
attraction due to the charge of the ions and the charge of
the particle surfaces (physisorption).

The particle surface attracts ions of opposite charge
which are initially physically adsorbed to the surface.
These ions are termed counter-ions since they are of
opposite charge to the surface and counter the charge of the

surface. The concentration of counter-ions is very high

16
close to the surface, but their concentration decreases as
the distance from the surface is increased until the
concentration is eventually the same as the concentration of
the ions in the bulk liquid (15). The opposite is true for
ions with the same charge as the surface. These ions are
called co-ions and their concentration is very high at the
surface, but increases as the distance from the surface is
increased until the concentration eventually becomes the
same as that in the bulk liquid (15). The distance where
co-ions and counter-ions reach their bulk concentration is
of the order of tens of nanometers (25).

Figure 1 illustrates this phenomenon. Figure 1a shows
the particle surface as the vertical line with a positive
surface charge shown to the left. To the right of the
surface are the ions which have been attracted to the
surface. The reason that the particle surface is shown is
shown as having no curvature is due to the extremely small
size of the ions (on the order of a few tenths of a
nanometer or less) compared to the amount of particle
surface area (on the order of 105 square nanometers for a
0.1 micron particle (28)) which makes it such that as far as
the ions are concerned, the particle surface is a big flat
plate.

Figure 1b shows how the concentration of ions changes
with distance away from the particle surface as previously

explained. The distance l/K shown in the figure is known as

17

 

 

1?

~— . wo

g Counter-Ions

‘2- A.

7.5, ~3—

g é’

° .52
U "o ------- 8

l Co—ions l

 

 

 

O
\
K

O

l/K

Distance (x) Distance (x)

Figure 1 Illustration of a) the attraction of counter-ions

to the surface of particles and the effects of distance from

the surface on b) ion concentration and c) potential (taken
from (15)).

18
the Debye length. The Debye length is used to characterize
the size of the layer of adsorbed ions. The quantity K is
known as the Debye-Hfickel parameter and is a function of
concentration of ions in the bulk, the valency of those
ions, and the temperature. An exact function for the Debye-
Hfickel parameter will be derived in more detail later.
Figure 1c shows how the potential changes with distance away
from the particle surface. The figure shows how the
potential begins at “g due to the charge on the surface and
decreases in magnitude as distance is increased due to the
countering of the surface charge by the adsorbed counter-
ions.

If an electrolyte is added to the medium of a colloidal
suspension the concentration of the electrolyte in the
medium is usually in the range of 10'5 to 10'2 M. As the
concentration of ions in the liquid is increased through
electrolyte addition, the distance from the particle surface
to where the ion concentration reach its bulk value is
decreased (23, 25), which as will seen later reduces the
amount of interparticle repulsion. Adding an electrolyte
which has ions with a valency of more than one (e.g. di-
valent and tri-valent ions) will also cause a decrease in
the distance from the particle surface where ion
concentrations reach bulk values (23), which is why

monatomic electrolytes are most often used.

19

Gouy and Chapman (48, 49) described this phenomenon of
ion adsorption to charged particle surfaces by saying that
particles in a medium have a double layer of charge which
consists of two distinct layers of ions around the particle.
The first layer is the compact inner layer of adsorbed
counter-ions, which is often termed the Stern layer after 0.
Stern who later developed a model describing this layer in
more detail (50). The second layer is a diffuse layer of
both counter-ions and co—ions with a distribution which
depends on electrical considerations and random thermal
motion (15). Gouy and Chapman modeled this layer (48, 49).
Their model assumes that the particle surfaces are flat
(with respect to the ions) and uniformly charged, that the
ions can be considered to be point charges from a symmetric
electrolyte of charge 2, that the distribution of the point
charges is a Boltzmann distribution, and that the only
influence of the medium is through the dielectric constant
which does not vary in the liquid (15).

Figure 2 shows this phenomenon. Figure 2a shows the
particle surface as the vertical line with positive surface
charge to the left. The dotted vertical line closest to the
surface is the Stern plane which is the outer boundary of
the compact inner layer of adsorbed counter-ions (the Stern
layer). The bumpy curved line which is the next furthest
out from the particle surface is known as the surface of

shear. This is the surface where if the particle itself

20

Particle surface

Stern plane

Surface of shear
l

 

CDC-96368636368

 

6963

 

 

 

Stern layer

\ ‘ Diffuse layer
I
I
I
l
l
I

Potential

 

 

 

6 l /K Distance

Figure 2 Illustration of a) the double layer surrounding a
colloidal particle and b) the change of potential with

distance from the particle surface (taken from (15)).

21
nnoves the ions inside this surface of shear move with the
particle as if they were a part of the surface and those
outside the surface of shear do not.

Figure 2b shows the potential as a function of distance
from the surface. The potential begins with a value of W8
at the surface. The potential then decreases quickly to the
valueeug at a distance of 8 which corresponds to the edge of
the Stern layer. The potential decreases as a result of the
specifically adsorbed counter—ions which counter the charge
at the surface. The potential then decreases gradually in
the second, diffuse layer also due to the counter-ions in
this layer. The potential at the surface of shear is shown
in Figure 2b to be equal to a value C and is commonly
referred to as the zeta potential. The zeta potential will
be discussed in more detail later, especially with respect
to ways of measuring the zeta potential and the difference
(if any) between C and Va. The Debye length, l/K, shown in
Figure 2b is often called the double layer thickness, even
though it is actually only an indication of the actual size
of the double layer and not an absolute thickness (28).

The repulsive force upon particle interaction results
from the energy of interaction of each particles' double
layer as they begin to overlap. Consequently, the repulsive
force is a function of the magnitude of the charge generated
on the particle surface and the size of the double layer

around the particle (25). An expression of this interaction

22

energy is extremely difficult to obtain. Derivations for an
texpression usually use the Poisson equation to describe the
flow of the electric field in a dielectric medium and the
Boltzmann equation to describe the charge distribution in
the diffuse layer (51-63). Specific derivations of
repulsive double layer interactions will be discussed
extensively later.

Several interesting characteristics of colloidal
particles with an electrical double layer are grouped
together as electrokinetic phenomena. Generally,
electrokinetics is the combination of particle electrical
effects and particle motion (28). An important classical
example of electrokinetics is electrophoresis in which
motion of the particle in suspension is caused by the
application of an external electric field (25). Actually in
electrophoresis when the charged particle moves it takes
with it some adsorbed ions(namely those inside the plane of
shear) and this movement is relative to the medium which
does not move (15). The velocity at which the particle
moves is directly proportional to the magnitude of the
applied electric field (25) and the constant of
proportionality is called the electrophoretic mobility, u,
(25). Microelectrophoresis is the experimental technique of
using optical microscopy to visibly see the particle motion
and measure its net velocity for a given electric field (15)

in order to find the mobility, u,.

23

As referred to earlier, the plane of shear separates
t:he layer of ions which moves with the particle and the
layer of ions which remains stationary with the liquid. The
potential at this plane of shear is called the zeta
potential, C, and is determined by using the electrophoretic
mobility. For particle suspensions where the particle
radius is much larger than the size of its double layer
(i.e. such that r/tc'1 >> 1), the equation to calculate the
zeta potential is known as the Helmholtz-Smoluchowski

equation (25):

 

c: ”on

[6]
Gael

where: 8.0 = permitivity in a vacuum

a, = relative permitivity

n = viscosity of liquid medium.
The Helmholtz-Smoluchowski equation is generally valid for
aqueous suspensions. For particle suspensions where the
particle radius is much less than the double layer thickness
(i.e. such that r/trt'1 << 1), the equation to calculate the
zeta potential is known as the Hfickel equation (15):

c.1531“.

[7]
£06!

The Hfickel equation is generally valid for non-aqueous

suspensions with low conductivity (15).

24

The potential at the plane of shear is often assumed to
toe equal to the potential at the outer edge of the stern
layer (15, 64). Lyklema (64) reports in his investigations
that within experimental error the zeta potential equals the
potential at the Stern layer.

Other examples of electrokinetic phenomena are
electroacoustic phenomena and are described in detail by O’
Brien and Oja (65-67). The first of the two electrokinetic
phenomena results from the application of an alternating
pressure field in a colloidal suspension in the form of an
acoustic wave. As a result of the density difference
between the particles and the liquid there is a relative
motion between the particles and the liquid. An alternating
dipole is formed at the frequency of the acoustic wave as a
result of the relative displacement of the particles and the
oppositely charged particles in the double layer caused by
the relative motion. The formation of this alternating
dipole is termed the Ultrasonic Vibration Potential (UVP),
and is measured as voltage per amplitude velocity of the
acoustic wave applied.

The other electroacoustic phenomena results from the
application of an alternating electric field to a colloidal
suspension. An acoustic wave is generated by the particles
as they move back and forth in the electric field due to
their charge and a density difference between the particles

and the liquid. The formation of this acoustic wave is

25
termed the Electrokinetic Sonic Amplitude (BSA) and is
Ineasured as pressure amplitude per unit electric field
applied.
The dynamic mobility can be found for both these
electroacoustic phenomena by using equations derived by O’

Brien (65, 66):

"4“" 'W

and

M(U) Xe

“4(0) ‘ W [9]

where: pd = dynamic mobility
to = angular frequency
(b = volume fracture of particles

Ap = density difference of particles and liquid

c = velocity of sound in suspension

ESA = pressure amplitude per unit electric field

UVP = voltage per amplitude velocity of wave

IC = high frequency conductivity correction.
The zeta potential can be calculated using the mobility as
in electrophoresis with the addition of a correction for the
inertia of the particle in an alternating field since this
reduces the velocity amplitude of particle motion. The
equation to calculate the zeta potential was derived by O’
Brien using the Helmholtz-Smoluchowski equation (65, 66):

C = L‘“ |G(a)’1| [10]
£6:

at

|G(a)'1|-Jx’+Y’ [111

———.—.

the.
RI.“

26

3
9(2A3+2a+1)

 

2A23<1+A) [13]
9 (2A3+2A+1)

 

= 2 [141

A z
B=(3+2Ap2) [15]
”Gt—:22, [16]

where: a = particle radius.

The stability of a colloidal suspension refers to
whether or not particles come together in clusters called
agglomerates or whether particles stay as individual
particles (25). Suspensions which are from agglomerates are
said to have coagulated and are unstable. Suspensions which
do not form agglomerates are said to be stable. It should
be noted that contrary to popular usage in the literature
the term flocculation refers to the formation of loose
agglomerates formed as the result of polymers adsorbed onto
particle surfaces and not just from normal coagulation (25).
Therefore, in this thesis the term coagulation will be used
to describe agglomeration and not flocculation since as
mentioned before all suspension considered for this thesis

will not contain polymers.

27

Colloidal suspensions, as Hunter points out (25), are
t:hermodynamically metastable. This means that a stable
suspension is only stable in a kinetic sense and that
coagulation is a rate process. The study of colloidal
stability predictions should therefore be more a study of
the rate of these processes than the thermodynamics of them
(33).

Pioneering work in describing particle interactions of
single component colloid systems was done by Derjaguin,
Landau, Verwey, Overbeek (51, 52). The compilation of their
.work is known as DLVO theory. DLVO theory describes the
energy of interaction for identical particles in an
electrolyte solution. In DLVO theory, the particles are
treated as having a double layer of ions which surround them
as described previously by Gouy and Chapman (48, 49). This
double layer, as described earlier, consists of a diffuse
layer in which ions are treated as paint charges which can
be described by a Boltzmann distribution, and a rigidly held
inner layer of essentially adsorbed ions.

The interaction energy between two particles is
described as a sum of the potential energy of attraction and

repulsion energies:

v, -- VnV. [171
where:VT = total energy ,
V, = attractive energy

repulsive energy.

28
I The attraction energy is due to van' der Waals attraction and
:is described by equations derived for two equal spheres by

Hamaker (38):

Aa
Vz— — 18
. (123’ [ 1
where:H = interparticle separation distance
a = particle radius
A = Hamaker constant (from Equation [4]).

The repulsive energy during particle interaction is caused
by the overlapping of particles' double layers. This
repulsive interaction is described by the Poisson-Boltzmann

equation:

 

 

= _ 1 O _ 216* 1
V? 50‘: $111216 exp( kT ) I 9]

wherezv2 is the Laplacian operator

w'= particle surface potential
e°== permitivity in a vacuum
8., = 8.854E-12 (Cz/J m)

s,== relative permitivity

In = number of ions of type i
21 = valence of ion i

e = electron charge

e = 1.6023-19 (C)

k = Boltzmann's constant

k = 1.381E-23 (J/K)

T = temperature (K).

This equation is the combination of the Poisson
equation which describes the flow of the electric field in a

dielectric medium as detailed by Hunter (25):

We = -—L - [20]

‘9‘!
where:p = density of charges

and the Boltzmann equation which described the distribution

of charges in the diffuse double layer:

111 = nfexp(-—:-%) [21]

wherem1 = number of ions of type i at the distance
from the surface where the potential is‘v
n1° = number of ions type i in the bulk
or = work to bring ions from the bulk medium
to this distance.

.As an approximation an is assumed to be:
01 = 219* [22]

so that the density of charges becomes

P = 21710219 = gnfaxph-fg!) ' [23]
which in combination with the Poisson equation results in
the Poisson-Boltzmann equation [19] shown previously.

In DLVO to get an expression for the energy of
repulsion the Poisson-Boltzmann equation was solved using
the Debye-Hfickel approximation. The Debye-Hfickel

approximation assumes that (28):

|ze¢l<kT
or:

solving this for V at [24]

room temperature (zs'c)
e<25 .7mV.

30
This allows for the following simplification if only the

first term of the series expansion is taken (15):
a .zfl +£fl_ 25
xp( kT)-1 k1, [ 1

So that the Poisson-Boltzmann equation becomes:

 

2 z o
v2 =- 1 ° - 31335
I [213212; I let 1'

at

[26]

Due to the need for electroneutrality in the bulk medium the

sum of the charges must equal zero, so (25):
2:216:11 = 0. [27]

The Poisson-Boltzmann equation then simplifies to:

2 3 o
.__1_ 323.51
W" e095: kT 1' [281
or:
Vzt‘ltz' [29]

where:K=Debye-Hfickel parameter

 

x=\J 92:: ”1°21: [3°]
kT '
The linear form of this equation becomes (28):

Jigsaw. [311

The linear form of this equation is then solved in DLVO

with the boundary conditions that (28):

(1

(‘D

31

rota as x~0
and [32]
e~o as x-m

where: x = distance from the surface.

The solution of which is (28):

v = toexm-xx). [33]

The repulsion for identical spheres was then found by

Derjaguin (68, 69) to be:

V, = Zeoextzlnu + 6xp(-KH°)] [34]

where: H°== shortest distance between particle
surfaces.

Now the total potential energy interaction as a function of
interparticle distance can be calculated (and subsequently
graphed) in the DLVO method by using Equation [34] and [18]
to solve Equation [17] as a function of varying distance of
particle separation, H. The graph of total potential energy
versus particle separation is used to indicate the stability
of a single component system and a maximum potential energy
of 20 kT is often noted to indicate that a suspension will
be stable (25). However, this does not indicate the
stability for multicomponent systems and does not address
the kinetic aspect of stability at all.

Empirically, colloid experimentalists have noted that
colloid suspensions which have room temperature zeta
potential values above 25.7 mV generally will be stable

(70). One way in which this empirical relationship would be

»32
used would be for a system where H+ and OH‘ ions are
potential determining ions and the zeta potential would be
measured over a range of pHs. Since changes in pH will
change the concentration of potential determining ions, the
magnitude of the surface charge generated will change and so
the magnitude of the zeta potential will change.
Measurements of these changes in the potential will indicate
the change in the repulsive force of particle interaction.
The empirical theory then implies that if for any pH the
zeta potential is greater than 25.7 mV then the suspension
will be stable at that point. Again, however, this does not
indicate stability for multicomponent systems and does not
address the kinetic aspect of stability. A solution of the
interparticle potentials for multicomponent systems is
therefore needed together with a means of incorporating the
kinetic aspect of stability.

For the case of nonidentical particles with varied
potential, an exact solution of the Poisson—Boltzmann
equation is extremely difficult or impossible (71).
Consequently, approximate solutions of the Poisson-Boltzmann
equation must be made for nonidentical particles. One of
the first solutions for nonidentical particles was in the
mid 1950’s by Derjaguin (54) who extended DLVO theory to
systems with nonidentical particles. Other extensions of
the DLVO theory to systems with nonidentical particles were

made by Bierman (61) and by Devereux and de Bruyn (55).

33
These solutions, however required extensive numerical or
graphical iterations making them extremely difficult to
apply to actual systems (53).

In the mid 1960's, Hogg, Healy, and Fuerstenau built
upon DLVO theory to develop a quantitative kinetic stability
theory for nonidentical particles which was more easily
applied to actual systems (53). Their solution was for
systems in which the particle potentials remain constant.
Their theory has come to be known as HHF theory. HHF theory
uses the same approach to describe the total potential
energy of interaction as DLVO theory, but uses an expanded
attraction and repulsion force equations in order to take
into account the differences between the two different
particle types. The attraction force equation then becomes:

A‘31": [35]

V“ 3 - 6 (a1+a,)H

where: H = interparticle distance

A = Hamaker constant (from Equation [5])

a1 = radius of particle of type i.
In developing an equation to describe the repulsive energy
of interaction, the linear form of the Debye-Hfickel form of
the Poisson-Boltzmann equation (Equation [31]) is used just
as in DLVO. In the development of the HHF theory, though,
Hogg, et al. show that the approximation is good for “a and
v5 values of less than 50 to 60 mV as opposed to the less

than 25 mV that is assumed in DLVO.

34
To solve Equation [31] in HHF the two different types
of particles are treated as two plates separated by a

distance, 2d, with the boundary conditions:

t=¢°1 as x-oO
and
ewe, as x-02d.

The solution then becomes:

to. - tacosh (2rd)

 

a [36]
V 'ecwm‘x) H sinh(2xd)
The energy of repulsion for HHF was then found using
Derjaguin's method (68, 69), as in DLVO:
_ a132 2 z '
[37]

2‘53“. 1+exp(-nH) _ _
[mln(1_9xb(_m )+ln(1 exp( ZKHH] .

 

The total potential energy as a function of interparticle
distance for two nonidentical spherical particles is
calculated by using Equation [35] and [37] to solve Equation
[16] as a function of varying separation distance, H.

In order to better describe the effects of mutual
agglomeration and to develop a quantitative theory for the
overall kinetic stability of the system of nonidentical
particles, Hogg et al. (53) develop a variable, Wt, which is

similar to an equation by Fuchs (72):

35

We” [_n_+ (1-n)3+2n(1-n)]-1 [33]
"11 "22 ”12
where: n = overall proportion of particle type 1
If = probability type 1 particles will
encounter each other
(l-n) = overall proportion of particle type

2 in the system.

The factor, W., is a factor by which rapid coagulation,
as described by von Smoluchowski (73, 74), is slowed due to
a potential barrier to coagulation caused by the repulsive
potential energy of particle interactions (33, 34). This
factor is called the stability ratio and is essentially the
ratio of particle collisions to collisions resulting in
coagulation (25). For identical particles with radius, a,
and a distance of separation, r, (measured from particle
center to particle center) Fuchs showed the stability ratio
to be (34):

_V)__ Cir. [39]

w-2a2fexp(k—t T"

For two nonidentical particles of radius, a1 and a,, the

stability ratio becomes:

8 (apaj) [exp(-k—t) d:. [40]
ope, I

As previously stated the HHF solution of repulsive

interparticle potential was for systems in which particle

36
potentials remain constant, Wiese and Healy later derived a
similar solution with the same form as the constant
potential form for systems with particle charges which

remain constant (56):

 

a a,
.11.; www *

2'01'0. 1+exg(-I:H) _
[mln(1_6xp(_‘m ) lfl‘l

‘§=§f5*(
[41]
-exp(-2x))].

Kar, Chander and Mika used an approach similar to the one
used by Hogg, et al. and developed a solution for systems in
which one of the components has constant charge and the
other one has constant potential (75). Barouch and
Matijevic have done work with various others (57-60) to
develop an extremely complex quantitative theory to describe
the interaction potential for nonidentical particles that
uses an approximate solution of the Poisson-Boltzmann
equation in its two dimensional form by assuming constant
potential.

In their work Barouch and Matijevic (59) compare the
results of their solution for the interaction potential with
that of Hogg, Healy and Fuerstenau (53). The authors say
that the two models agree fairly well for unlike particles
with potentials of opposite sign and similar magnitudes, but
claim that for particles with the same sign and different
magnitudes the HHF equation overestimates the interparticle

repulsion. However, the model developed by Barouch,

37
Matijevic et al. is extremely complex mathematically and its
solution is quite complicated involving intricate use of
various algorithms as the authors acknowledge (60).

With all of these different models of the repulsive
interaction for unlike particles the HHF method, though,
still remains as the only quantitative theory for the
overall stability of a system of nonidentical particles.
This overall method is therefore best suited for use in
prediction of suspension stability. Another advantage of
this method is that various different adjustments can be
made within the model to help improve the fit of the
method’s stability prediction. One of the first adjustments
which could be made would be to use zeta potential data for
the particle potential, w; instead of using point of zero
charge data to calculate a surface potential, as was done
originally by Hogg, et al (53). This would be an
improvement since calculation of the surface charge from
point of zero charge data requires use of a model for
surface charge generation which requires considerable
knowledge of ion groups present on the particle surface and
how these groups react with the medium to generate charge
Zeta potential, on the other hand, is simply an experimental
measurement which requires little knowledge about the
particle, other than particle size and density (67), has
recently become a more common measurement technique and has

recently become a much easier measurement than in the past

38
(67, 70). Other adjustments which could be made would be
alternate expressions for attraction and repulsion potential
as well as alternate methods for calculating the Hamaker

constant.

EXPERIMENTAL PROCEDURE

A model was used to predict the stability of
suspensions over a given pH range which was an adaptation of
a method originally developed by Hogg, Healy and Fuerstenau
(53). The adaptation included several changes or
adjustments to the original method. The first of these was
the use of zeta potential vs. pH data for the potential,‘v,
instead of using a surface potential calculated at the given
pH, a calculation which relies on models for surface charge
generation and point of zero charge data. Another change or
adjustment was the use of an effective Hamaker constant
(Equation [5]) instead of just using an in vacuo Hamaker
constant. This allows the effect of the medium to be taken
into account in reducing interparticle attraction. Along
with this is the addition of the Lifshitz method for
calculating Hamaker constants (Equation [3]) since a method
for their calculation was not addressed by the original
theory.

Another change was the use of an expanded expression
for the potential of interparticle attraction (Equation [1])
instead of the equation used in the original method

(Equation [35]) which is a simplification of Equation [1]

39

40
which assumes small particle separation. For the potential
of interparticle repulsion the original HHF equation
(Equation [37]) was used although, the constant charge
solution of Wiese and Healy (Equation [41]) (56) was used in
some cases.

The repulsion equation was not changed for several
reasons. The first reason was that the equation was
reported to be accurate in many cases (59). The second was
that use of this constant potential equation made
substitution of a constant charge solution (namely that of
Wiese and Healy) quite simple due to the almost identical
nature of the two equations. Another reason was that other
solutions for interparticle repulsion which are reported to
be more accurate (59), require very elaborate calculation
schemes which would have required much more calculation time
than needed with the HHF equation. The final reason was
that even if the equation proved unsatisfactory it could
easily be substituted for in later versions of this adapted
method.

The equation for total overall kinetic stability
(Equation [38]) and the equation for the stability factor
(Equation [40]) were used as in the original method.
However, instead of using the overall relative proportion of
particles of type 1 in the system, n, as a system input as
in the original method, a relationship was derived which

related the relative volume fraction of particle of type 1

41
to type 2 and the particle radii to the overall number
proportion, n. This derivation which can be found in
appendix A allowed use of the relative volume fraction of
components as an input. This was an improvement since, from
an experimental viewpoint, volume fraction is a much more
realistic and useful quantity than number fraction.

With the adapted method described, the total overall
kinetic stability at a certain pH was calculated by solving
Equation [38]. For the equation n was found by using input
values for particle radii and relative component volume
fraction to solve Equation [All] and was W11 found by
solving Equation [40]. The solution of Equation [40] was
found by using particle radii, the input temperature and
total interparticle potential vs. separation distance to
integrate from a minimum separation distance (a1+a,) to an
infinite separation distance. The interparticle potential
was found using the solutions for the attractive potential
described by Equation [1] and the repulsive interaction
potential described by Equation [37] (or Equation [41]) to
solve Equation [16] for different separation distances.
Solving Equation [1] required particle radii input data and
effective Hamaker constants which were found by solving
Equation [5] using input Hamaker constants. The input
Hamaker constants were either calculated values found by
using dielectric constant data to solve Equation [3] or were

values found in the literature. Solving Equation [37] (or

42
Equation [41]) required use of input particle radii and zeta
potential versus pH data along with the Debye-Hfickel
parameter. The value for this parameter is calculated by
using the input bulk monatomic ion concentration and
temperature data to solve Equation [30] All electrolytes,
acids and bases are assumed to be monatomic with this
method, but this assumption could be eliminated in future
versions.

The input data necessary for using this method were in
vacuo Hamaker constants, particle radii, relative component
volume fraction, concentration of monatomic electrolyte,
temperature, zeta potential data as a function of pH, and
finally the pH range where stability calculations were
performed. A computer program was necessary to perform these
calculations since, to calculate the total overall stability
ratio at just one pH, it would be necessary to calculate the
stability ratio, W”, for each of the three different types
of particle interactions (i.e. Wu, W”, W”). Theoretically,
this would require integration to infinity and evaluation of
the attractive and repulsive interactions to infinity. This
would have to be repeated for each pH.

The computer program was written in Fortran code for
use on a PC. The program code was edited using Personal
Editor (version 4.21) and was compiled using Microsoft
Fortran Compiler (version 5.00.03). The program consisted

of a main program and ten separate subroutines. Computer

43
flow diagrams can be found in Figures 3 though 11 and list
files of the code can be found in appendix B. The program
was run from a DOS operating system batch file which allowed
the program to run many times successively with different
input data without requiring the operator to wait for one
program run to end in order to input new data as normal
program lasted anywhere from 30 minutes to 2 hours.

The program starts with the main program, STABILITY
PREDICTION. The input data is read into the program from a
file by the subroutine FDATA INPUT. The subroutine CALCZP
calculates the total overall stability ratio at each pH
using zeta potential data. Subroutine WKO finds the
stability ratio for each of the possible interaction types
and at each pH writes the interparticle potential vs.
separation distance data for each of the different
interactions to an ASCII data file. The subroutine WC
actually calculates the stability ratio for a given
interaction and returns the value to subroutine WKO.
Integrating to infinity was accomplished by integrating in
interval steps to avoid integrating infinity. When
integration passed a minimum limit of integration,it was
allowed to stop before infinity if the area added by a
certain interval steps of integration was smaller than a
specified tolerance. This decreased program time with the
introduction of minimal error. The actual integration was

done using Simpson's rule in subroutine SI. The values for

44

 

OPEN DATA INPUT FILE
GET CURRENT DATE
GET STARTING TIME

CALL FDATA INPUT

CALCULATE HAMAKER
CONSTANTS

IF ZPQ='P’
THEN ELSE

CALL CALL
CALCPZC CALCZP

GET FINISHING TIME
CALL DATA STORAGE
CLOSE FILE
END

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3 Computer flow diagram for main program STABILITY
PREDICTION. .

45

 

READ TEMPERATURE
READ VOL. FRACTION PARTICLE #1

READ CONC. OF ELECTROLYTE
READ PARTICLE #l RADIUS
READ PARTICLE #2 RADIUS
READ Z. P. QUESTION

IF ZP?='PZC'
THEN ELSE
READ PZC #I DO L=l TO 2

READ PK: #2 READ #21:.
READ SPH DO |=i .#ZP
READ FPH REAP PH

READ ZP
READ PHSS CONTINUE

CONTINUE
READ SPH

READ FPH
READ PHSS

READ MEDIUM HAMAKER CONST
READ PARTICLE #1 HAMAKER
READ PARTICLE #2 HAMAKER

RETURN TO MAIN PROGRAM
END

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4 Computer flow diagram for subroutine FDATA INPUT.

46

 

INITIALIZE, AZ,(ALMOST ZERO)
SO WT WON'T GO TO INFINITY

 

INITIALIZE MINIMUM
PARTICLE SEPARATION

 

INITIALIZE pH COUNTER

 

 

DO K=l TO pH COUNT

 

DO I=I TO 2

 

CALCULATE SURFACE
POTENTIAL

 

 

CONTINUE

 

CALL WKO, WKI'W, OR WKTH

 

CALCULATE WTCK)

 

CHANGE CURRENT pH

 

 

CONTINUE

 

RETURN TO MAIN PROGRAM

 

END

 

 

 

Figure 5 Computer flow diagram for subroutine CALCPZC.

47

 

INITIALIZE, AZ.(ALMOST ZERO)
SO WT WON'T GO TO INFINITY

INITIALIZE MINIMUM
PARTICLE SEPARATION

 

 

INITIALIZE pH COUNTER

 

DO K=I TO pH COUNT
DO |=l TO 2

IF CPH=O Z.P. DATA PT.
THEN ELSE

POTENTIAL FIND NEAREST

EQUALS THAT 2 DATA PT.S
DATA PT. & INTERPOLATE

CONTINUE
CALL WKO, WKTW, OR WKT H

CALCULATE WT(K)
CHANGE CURRENT pH

CONTINUE

RETURN TO MAIN PROGRAM
END

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6 Computer flow diagram for subroutine CALCZP.

48

 

INTERACTION TYPE l:l

 

CALL WC

 

WOO(K)=WCALC

 

INTERACTION TYPE 1:2

 

CALL WC

 

WOT(K)=WCALC

 

INTERACTION TYPE 2:2

 

CALL WC

 

WTT(K)=WCALC

 

STORE V DATA TO FILE

 

RETURN TO CALCPZC OR ZP

 

 

END

 

 

Figure 7 Computer flow diagram for subroutine WKO.

49

 

INTSIZE=T nm

 

WHILE INTERVAL<MAX

 

LOW INITIAUZED AS MIN. SEP.

 

HIGH=LOW+INTSIZE

 

CALL SKSIM P)

 

CO NTRIB=SIMP

 

AREAN=AREATL+CONTR|B

 

DIFFN=CONTRIBIAREATL

 

 

IF DIFFN<TOL 8c HIGH>M|

 
 

 

 

 

TH EN E LS E
WCALC= AR EAT L=
AREAN“ R0 AREAN
RETU RN TO LOW=HIGH
WKO. ETC.

 

 

IF(5<HIGH<T Onm) INSIZE=2.5nm

IF(T 0<HIGH<25nm) INTSIZE=5.0nm
lF(25nm<HlGH<85nm) INTSIZE=T Onm
IF(85<HIGH<990) INTSIZE=T OOnm

 

 

CONTINUE

 

WCALC=AREAN'RO

 

RETURN TO WKO. WKTW. OR WKT H

 

END

 

 

 

Figure 8 Computer flow diagram for subroutine WC.

50

 

A=LOW & B=HIGH

 

CALL WVFCN

 

FA=WFC N

 

CALL WVFCN

 

FB=WFCN

 

WHILE NSECTS<NMAX

 

DX=(B-A)/ NSECTS

 

DO L=T TO NSECTS-T BY 2's

 

SEP=A+L'DX

 

CALL WVFCN

 

 

ODDS =ODDS+WFCN

 

CONTINUE

 

DO L=2 TO NSECTS-2 BY 2's

 

SE P=A+L"DX

 

CALL WVFCN

 

 

EVENS = EVENS+WFCN

 

CONTINUE

 

AREAN=DX/3'(FA+FB+4’ODDS+2’EVENS)

 

DIFFN=(AREAN-AREAO)/AREAN

 

 

  
  

IF DIFFN < TOL

  

 

 

 

 

 

 

 

 

 

THEN ELSE
SIM P=AREAN AREA0=AREAN
RETURN To wc [ NSECTS=2'NSECTS
CONTINUE
SIMP=AREAN
RETURN TO wc
END

 

 

 

Figure 9 Computer flow diagram for subroutine SI.

51

 

CALCULATE V(011Tacfion)

 

CALCULATE V(repulsion)

 

CALCULATE V(IOI0|)

 

EXW=VI/kT

 

WFCN=EXP(EXW)/(R0*Ro)

 

RETURN TO SI

 

 

END

 

 

' ure 10 Computer flow diagram for subroutine WVFCN.

52

TFLNME :12 'PDF'

CURRENT DATE

N
CL

TFLNME :1 '.DAT'

W I

WOO WOT WTT WT H

 

Figure 11 Computer flow diagram for subroutine DATA STORAGE.

53
the evaluation of the integral were calculated by the
subroutine WVFCN.

Much care in writing the program was taken since values
for the variables used in the program often approached zero
or infinity leading to fatal math overflow errors and
premature termination of the program. Checks and
corrections for values which were becoming too large or
small in magnitude were written into most of the
subroutines.Once all the calculations were made the data was
then stored in ASCII data files by subroutine DATA STORAGE.
This ASCII data was later imported into a plotting program,
Harvard Graphics (version 3.0), in order to plot the data.
This allowed for more flexibility for the final graphical
form of the data than if the data were plotted directly in
the Fortran program itself.

Systems for which the program was applied were the SiC
powder/Sigh powder system and the FeAl powder/Algh fiber
system. Extensive work was done with the SiC/Sifih system
since much was known about the colloidal and surface
characteristics of the system due extensive investigations
of this system by Crimp (76, 77). For this system there
were three different SiC powders used, all of which were a-
SiC and manufactured by Lonza Inc. The three types used
were LS-5, UF-lO and UF-15 for which the manufacturer
reported 50% cumulative mass percent of particles with

diameters finer than 5.5, 1.8, and 0.8 microns,

54
respectively. The Sign used was an a—Sifih manufactured by
UBE. The type used was SN-E10 which the manufacture reports
has an average particle diameter of 0.5 microns.

This system was suspended in deionized water which had
a variable indifferent electrolyte concentration of 10"2 M,
10"3 M and 10"5 M. The indifferent electrolyte used was KNO3
and the bulk of the work was carried out with an electrolyte
concentration of 10"3 M. The pH was varied for this system
by the addition of HNO3 and KOH. The systems were dispersed
using an ultrasonic probe which would eliminate previous
particle agglomeration.

The zeta potential data used in this investigation was
of two different types. The first was microelectrophoresis
zeta potential data previously collected by Crimp (70) using
a PEN-KEM SYSTEM 3000 automated electrokinetics analyzer.
These data were collected for the SN-ElO Sign and the UF-lO
SiC at all three different electrolyte concentrations
mentioned above. These data is shown in Figures 12 and 13.
The data shown in Figure 13 stop at pH 5 since the zeta
potential values level off (70) at this point. A
logarithmic regression was done in order to extend this data
to higher pHs using the standard logarithmic regression
program of a HP-llC calculator and is shown in Figure 14.
The other type of data used was Electrokinetic Sonic
Amplitude (ESA) zeta potential data collected in this

investigation using a Matec ESA-8000 system.ESA zeta

55

20

O

Zeta Potential (mV)
lb
0

 

Figure 12 Electrophoretic zeta potential measurents for
SN-Elo SiaN, at varing electrolyte concentrations
(M) .

56

x

I " 43$
' :- >.:-~..
2C1 e ‘EW*
. _ _ \-
5.

C3

$33..
. %

Zeta Potential (mV)
A Tb
CD CD

 

Figure 13 Electrophoretic zeta potential measurents for
UF-lo Sic at varing electrolyte concentrations
(M).

57
potential measurements were performed on all of the
different types of SiC powders and on the Sign powder. The
suspensions were all prepared in an electrolyte solution of
concentration 0.001 M. The pH of the suspensions was
initially decreased by addition of I-INO3 to pH 4.0 and the
suspensions were dispersed by an ultrasonic probe before
loading into the ESA testing equipment. Once testing began,
the system automatically changed the pH up to pH 11 or back
down to pH 4 with the titration of acid and base and also
automatically measured the mobility and calculated the zeta
potential. The Hamaker constants used for this system were
found by Bleier (47) using the Lifshitz method. The values
reported and used were 3.0E'19 J and 1.6E43 J for SiC and
Sign, respectively.

Extensive stability prediction program runs were
performed for this system. Predictive program runs were
performed for the three main two component systems of LS-S
SiC/Sifih, UF-10 SiC/Sifih and UF-lS SiC/Sifih. Experimental
verification of the predictive model was performed for these
systems, but only at an electrolyte concentration of 10'3 M.
verification consisted of sets of sedimentation experiments.
Sedimentation experiments were performed for single
component suspensions of each of the four powder types as
well as for suspension of each of the three main two
component systems listed above which were done with equal

relative volume for each of the components. One more two

58

40

20

CD

Zeta Potential (mV)
4; r'o
o o

 

H

Figure 14 Electrophoretic zeta potential measurents for
UF-lo SiC at varing electrolyte concentrations (M)
with regression analysis.

59
component sedimentation experiment was performed for the UF-
10 SiC/Sifih system in which the relative volume fraction of
SiC to Sign was 0.75 instead of 0.5.

The sedimentation experiments were carried out by
making a 500ml suspension in a 10'3 M electrolyte solution
with a solid content of 0.5 volume percent. The suspensions
were initially dispersed with an ultrasonic probe to break
up agglomerates which were already formed, and then the pH
was measured while the sample was stirred by a magnetic stir
bar. The pH was then lowered to 4.0 by the addition of
HNO3. The suspension was again dispersed with the
ultrasonic probe and approximately 40 ml of the suspension
being poured into a test tube labeled with the appropriate
pH. The pH was then increased in increments of half of a pH
unit with the suspension being sonicated and about 40 ml
being poured into an appropriately labeled test tube. This
procedure was performed until pH 11.0 was reached for a
total of 15 specimens for each sedimentation experiment set.
These samples were then set where they would not be
disturbed and photographs were taken at varying time
intervals in order to record the sedimentation.

The other system of FeAl/Algh fiber was investigated
in only a preliminary manner in order to predict the ideal
pH for processing at which the individual components would
be stable, but at which heterocoagulation occurs (i.e. where

the powder and fiber are attracted to each other, but not to

. 60
themselves). The FeAl powder used was AMDRY FeAl and was
manufactured by Alloy Metals, Inc. The as received powder
had a particle size range of 177 microns down to tenths of
microns. The powder was sedimented down to a size range of
10 microns to tenths of microns through the efforts of Jeff
Bajt and Chris Suydam. The average particle diameter was
determined to be 7 microns, and a SEM micrograph of this
sedimented powder can be seen in Figure 15. The Alfih fiber
was manufactured by DuPont and is a continuous, pure alumina
fiber of type Fiber PP. The average fiber diameter was
reported by the manufacturer to be 25 to 30 microns which
was confirmed by SEM observations. The fibers were chopped
up and ground to smaller lengths with mortar and pestle. A
SEM micrograph of the chopped fiber can be seen in Figure
16.

This system was also suspended using a KNO, electrolyte
solution in deionized water and pH changes were made with
rank and KOH as with the previous system, but only a KN03
concentration of 10'3 M was used. The zeta potential data
used for this system was collected in this investigation
using the Matec ESA-8000 system. The Hamaker constant for
the alumina fiber was calculated from refractive index data
(78) using the Lifshitz method (Equation [3]) and found to
be 1.1E"19 J. Since no refractive index or dielectric
constant data could be found for the FeAl, the Hamaker

constant used was a value for metals given by Shaw (15) to

61

__————-—_,—‘——I
11:”: .;.IIM ‘

 

Figure 15 SEM micrograph of sedimented FeAl powder.

62

I

A

" T. .,
L/ " w.

[77 ,-

EH31? 25K 12*4NN-

Figure 16 SEM micrograph of chopped A1203 fiber.

 

63
be 2.2E"19 J.

Three different predictive program runs were performed
for the FeAl/Algb fiber system. The first was performed
using the particle size data mentioned earlier (i.e.
particle diameters of 7 microns and 30 microns for the FeAl
and alumina fiber, respectively). The other two predictive
runs used increasing FeAl particle size to see if larger
FeAL particle sizes would also be possible to get the ideal
processing conditions of individual component stability

coupled with heterocoagulation.

RESULTS

The results for the acouStophoresis (ESA) measurement
data for LS-5 SiC, UF-lO SiC, UF-15 SiC and the SN-ElO Sign
can be seen in Figures 17, 18 19, and 20, respectively.
Predictive program runs were performed for the three main
two component systems of LS-S SiC/Sifih, UF-10 SiC/Sifin, and
UF-15 SiC/Sifih. The first of these experimental runs was
performed using the constant potential repulsive equation
and electrophoretic zeta potential data at a concentration
of 10'3 M. The results of this data run are shown in Figure
21. Another of these experimental runs was performed using
the constant potential repulsive equation along with ESA
zeta potential data at a concentration of 10"3 M. The
results of these data run are shown in Figure 22. The
constant charge form of the repulsive potential equation was
used along with electrophoretic data for an electrolyte
concentration 10"3 M for the third run for these systems.
These results are shown in Figure 23. The interparticle
potential vs. interparticle separation distance for each pH
of the first data run(i.e. Figure 21) is plotted in Figure
24. A fourth program run was performed which used the

constant potential form for the repulsive potential equation

63b

Zeta Potential (mV)

64

CD

lb
0

  

4';
c

Figure 17 ESA zeta potential measurements for LS-5

Sic at an electrolyte concentration of 10’3 M
3.

65

pH range tested
‘°' 4 To 11
+ 11 To 4

   
  

Zeta Potential (mV)
lb
(3

4';
0

Figure 18 ESA zeta potential measurements for UF-10
Sic at an electrolyte concentration of 10‘3 M
KN03.

66

O

   
  

Zeta Potential (mV)
r'o
O

is.
o

. . . _ pH range tested
-60 " j "'4To11

+11To4
+4T011

Figure 19 ESA zeta potential measurements for UF-15
SiC at an electrolyte concentration of 10" M
KNOJe

67

. . -:~
... VX‘F‘
‘\ fig“.

Zeta Potential (mV)

pH range tested
"'4To 11
+11 T04
*4To 11

 

Figure 20 ESA zeta potential measurements for SN-ElO
Si3N, at an electrolyte concentration of 10‘3 M
3'

68
and used electrophoresis zeta potential data for an
electrolyte concentration of 104 M. This data is plotted
in Figure 25, while Figure 26 is plotted data for a similar
program run which uses an electrolyte concentration of 10'5
M instead of 10"2 M.

All of the previous mentioned program runs were done
for relative volume fractions of 0.5. The effect of
different relative volume fraction of components on the.
total overall stability ratio is shown in Figure 27 for
electrophoresis zeta potential data at concentration of
0.001 M. Since relative volume fraction only changes the
total overall stability ratio and not the three different
interaction stability ratios (i.e. Wu, Wu, and Wu) and
since it is the calculation of these stability ratios which
takes the vast majority of the program execution time
another program called VARYN was written. This program
simply uses the stability ratios calculated in the Stability
Prediction program runs to calculate the total overall
stability ratio for a number of different relative volume
fractions. This program takes 2 to 3 seconds to execute
five different relative volume fractions as opposed to the
Stability Prediction program which takes from 30 minutes to
2 hours per different volume fraction.

Predictive program runs were also performed to see the
sensitivity of the programs to variations of the input data.

The first of these program runs varied the temperature for

1 E30

Figure 21

 

Interactions
"'SiC/SiC
+SiC/Si3N‘

*5i,N,/ST,N.

 

(a)

Stability ratio data from the predictive program
using the constant potential repulsive equation
and electrophoretic zeta potential for a) LS-S
SiC/SN-Elo SigN4, b)UF-lo SiC/SN-Elo SigN,, and c)
UF—15 SiC/SN-Elo SigN, where: temperature is 25 °C,
volume fraction of components is 0.5 and
electrolyte concentration is 10'3 M KNOr

70

    
 
  
  
     

1E30
1E20 _
Interactions
.. SIC/Sic
W + SIC/SEN]
are si,N,/ST,N.
'5 Total
1E10

 

(b)

Figure 21 cont.

71

 

IOI'IS
iC/ SIC

to.
a
r
ms
Mr

4

N

3

iC/S

+S

 

pH

(c)

Figure 21 Cont.

1 E20

 

Interactions
.r SiC/SiC

+ SIC/SiaN,

are sum/5w]

* Total

 

(a)

Figure 22 Stability ratio data from the predictive program

using the constant potential repulsive equation
and ESA zeta potential for a) LS-S SiC/SN-ElO
SiC/SN-Elo Sin, where: temperature is 25 °C,
volume fraction of components is 0.5 and
electrolyte concentration is 10'3 M KNOP

73

 

1E30
1E20
Interactions
. . . . . -p-SiC/SiC
W f I I - - .; +SiC/Si,N,
it Si,N./SI,N,
lElO
1

 

(b)

Figure 22 Cont.

74

     
  
 
 
     

Interactions
-r SiC/SiC
W + SIC/Sim.
at- Si,N./Si,N,
" Total
1E10

 

(C)

Figure 22 cont.

1E30
1E20
Interactions
. . -r SiC/SiC '
w '-‘ ... _ + SIC/SEN]
* Si,N./Si,N,
1E10

 

 

(a)

Figure 23 Stability ratio data from the predictive program
using the constant charge repulsive equation and
ESA zeta potential for a) LS-S SiC/SN-Elo Sign,
b) UF-lO SiC/SN-EIO Sign" and c) UF-15 SiC/SN-ElO
Sign where: temperature is 25 °C, volume fraction
of components is 0.5 and electrolyte concentration
is 10'3 M KN03.

76

      
  
   

1E30
1E20
Interactions
-r SiC/SiC
W + SiC/Si,N,
* Si,N./Si,N,
1E10

 

(b)

Figure 23 Cont.

77

 

1E30
1E20

Interactions

A _, -- srcxsrc
vv .eh%&_ . I 3: _i: l '1 z '. ." T'SKHSEN4
it- Si3N4/Si, N,

1E10
1

 

(C)

Figure 23 Cont.

78

Interactions
.. SiC/SIC

+ SiC/SisN,
* SIN/Sim,

Potential Energy (kT) (Thousands)

 

0 10 20 30 40 50 60 70 80 90100
Separation Distance (nm)

(a) pH=4.0

Figure 24 Interaction potential data from the predictive
program using the constant potential repulsive
equation and electrophoretic zeta potential for
LS-S SiC/SN—Elo Sign where: temperature is 25%;
volume fraction of components is 0.5 and
electrolyte concentration is 10'3 M.

79

Interactions
... SiC/SiC

+ SIC/Sim.
* Si,N,/Si,N.

Potential Energy (kT) (Thousands)

 

0 1o 20 30 4o 50 60 7o 80 90100
Separation Distance (nm)

(b) pH= 4.5

Figure 24 Cont.

80

(X was
\‘WKNV‘N- z:
33> '1‘) ‘Q‘;

Interactions
.. SIC/SIC

+ SIC/Sim,
* Si,N./ST,N.

 

Potential Energy (kT) (Thousands)

 

o 10 20 30 4o 50 60 7o 80 90100
Separation Distance (nm)

(C) H= 5.0
Figure 24 Cont . p

81

Interactions
... SIC/SIC

Potential Energy (kT) (Thousands)

 

0 10 20 30 40 50 60 70 80 90100)
Separation Distance (nm)

(d) pH= 5.5

Figure 24 Cont.

82

Interactions
-- SiC/SiC

+ SIC/SiaN,
* Si,N,/Si,N,

 

Potential Energy (kT) (Thousands)

 

0 10 20 30 40 50 60 70 80 90 100
Separation Distance (nm)

(e) pH= 6.0
Figure 24 Cont.

83

)

Interactions
.. SiC/SiC

+ SiC/Si,N.
* Si,N,/SI,N,

  

I
“J

1 Energy (kT) (Thousands

Potentia
A

0 10 20 30 40 50 60 70 80 90100
Separation Distance (nm)

(f) pH= 6.5

Figure 24 Cont.

84

Interactions
.. SiC/SiC

+ SIC/SEN,
.- Si, N,/Si,N,

0

 

I
i

I
“3

Potential Energy (kT) (Thousands)

 

0 10 20 30 40 50 60 70 80 90100
Separation Distance (nm)

(9) pH= 7.0

Figure 24 Cont.

 

A

m

‘o

C:

(U

U}

a

o

I:

t:

1’: Interactions
x .4 SIC/SIC
v

g + SIC/SEN,
a) * Si,N,/Si,N,
F -1

LU

Potentia
ii:

0 10 20 30 40 50 60 70 80 90100
Separation Distance (nm)

(h) pH= 7.5

Figure 24 Cont.

86

 
 
 
 
 
 
  

_L

Interactions
.. SIC/SIC

+ SIC/Sim,

CD

I
A

l
“D

"5
' «>519: .- .59;} \
tf‘x
x.

is

 

,
ta

. _ '13»-

 

Potential Energy (kT) (Thousands)

4% t.
’1‘. Iii-fl»
\

x

0 10 20 30 40 50 60.70 80 90100
Separation Distance (nm)

(i) pH= 8.0

Figure 24 Cont.

87

Interactions
.. SIC/SIC

+ SIC/Sim,
* Si,N./Si,N4

1

Potential Energy (kT) (Thousands)

 

0 1o 20 30 40 5o 60 7o 80 90100
Separation Distance (nm)

(:1) pH= 8.5
Figure 24 Cont.

88

.h

00

DD

Interactions
.. SIC/SIC

d

A. .e tat?
ERI‘YKR

§=g>xs

w.

. “kg
‘:-.

a:-

"'4‘

(ESE ‘

Potential Energy (kT) (Thousands)

 

o 10 20 30 4o 50 60 7o 80 90100
Separation Distance (nm)

(k) pH= 9.5
Figure 24 Cont.

89

h)

Interactions
-- SiC/SiC

+ SIC/SIGN,
* Si,N./SI,N,

CD

Potential Energy (kT) (Thousands)

I
h)

 

0 10 20 30 40 50 60 70 80 90100
Separation Distance (nm)

(1) pH= 9.5
Figure 24 Cont.

90

5
4
7:?
E
to
m 3
:1
o
.r:
I; 2
I: Interactions
5 1 .. SiC/SiC
g + SiC/Si,N.
o * ST,N./ST.N.
r:
UJ
E
...o
C:.
a 1
4—0
a
D.
-2

s

'S

O 10 20 30 40 50 60 70 80 90100

Separation Distance (nm

 

(m) pH= 10.0

Figure 24 Cont.

91

00

RD

.E: . V [s . .
R I AW . ‘ I _ I
1...th s .‘ Interactions
. .
.2. . ' '
.ggw n-EhC/SKD
+ SIC/SEN]

“Nils
.- - a
Sr, N./Sr3 N,

 

A

 

 

. . xix.
......e
\k' .

.~

'x
xx
x -. §$\

r

Potential Energy (kT) (Thousands)

 

o 10 20 30 4o 50 60 7o 80 90 100
Separation Distance (nm)

(n) pH= 10.5

Figure 24 Cont.

92

5
4
’6?
E
to
w 3
a
2
l- 2
I: Interactions
x -.-SiC/SiC
V 1
> +SiC/SiaN‘
E’
o "SiaNJSiaN.
c 0
DJ
.71?
H
CI-
o 1
4—0
0
LL
-2

 

0 1o 20 30 4o 50 60 7o 80 90100
Separation Distance (nm)

(0) pH = 11.0

Figure 24 cont.

93

Interactions
-- SiC/SiC
+ Ste/Sim.
at SiaNJSiaN.

* Total

 

 

(a)

Figure 25 Stability ratio data from the predictive program
using the constant potential repulsive equation
and electrophoretic zeta potential for a) LS-S
SiC/SN—Elo Sign, b)UF-lO SiC/SN-Elo Sign, and C)
UF-IS SiC/SN-Elo Sign where: temperature is 25 °C,
volume fraction of components is 0.5 and
electrolyte concentration is 10'2 M.

94

1 E30

1E20
Interactions

-— SIC/SIC
I " Es 3;.<*. -f ‘ _ '
W - --':g_ ..zgjw'f _ _. -' +SiC/Si,N,
s * Si,N,/Si,N,

cfig
{is s . . ~- ~ . .
Fess ..U ‘. . a
' g. \:'\x . .. _ :..-. -. I. . ‘ 5 Total
I x

 

1E10

 

(b)

Figure 25 Cont.

95

      
  
 
    
 

 

  
   

1an
1E20 '
Interactions
.. SiC/SiC
W + SiC/Si3N4
* Si,N4/Si,N.
* Total
1E10 R
1

(C)

Figure 25 Cont .

1 E30

1E20

1E10

 

96

Interactions
.. SiC/SiC

+ Ste/Siam
x- Si,N./Si,N.

 

(a)

Figure 26 Stability ratio data from the predictive program

using the constant potential repulsive equation
and electrophoretic zeta potential for a) LS-S
UF-15 SiC/SN-Elo 819% where: temperature is 25 °C,
volume fraction of components is 0.5 and
electrolyte concentration is 10'5 M.

97

1 E20
Interactions
.. SiC/SiC
W
1 E10

 

 

4 5 6 7 8 9 10 11

(b)
Figure 26 Cont.

98

 

1E30

1E20
Interactions
--SiC/SiC

W ' gig-x - at: . -; -. +SiC/Si,N.
*sLNanN.

1510

1

 

(C)
Figure 26 Cont.

1 E30

1E20

 

+ 0.25
*050 -

 

(a)

Figure 27 Total stability ratio data from the program VARYN

using data from the predictive program which used
the constant potential repulsive equation and
electrophoretic zeta potential for a) LS-5 SiC/
SN-Elo Sin4, b)UF-lo SiC/SN-Elo Sin4, and c)
03-15 SiC/SN-Elo Sin‘ where: temperature is 25 °C,
volume fraction of components is varied and
electrolyte concentration is 10'3 M.

100

{a}.

sass

mm w

 

 

H

(b)
Figure 27 Cont.

101

1‘ .-.~§§\ ., a “.1:-

‘\ - . \

~saafififias

stsa-'~ s-
‘sa.a{%

1a saw X‘s

. .%.Kx
§sfl

w- "3.

. a"
. ’ “A":
Wat:

 

 

(C)
Figure 27 Cont.

102
the system with variations from room temperature of plus or
minus 5 °C being shown in Figure 28a) and larger temperature
changes being shown in Figure 28b). The Hamaker constant
was another input of the system which was varied with the
results shown in Figure 29. There were six different
variations in the values where one or both of the input
Hamaker constants was increased or decreased by 10% from
their original input values of 3.0x10"19 and 1.6x10'19 J for
Sic and Sign, respectively.

The photographs showing the changes in sedimentation as
a function of time for the four single component systems can
be found in Figures 30 through 33 for LS-S SiC, UF-lO SiC,
UF-15 SiC, and SN—ElO 519%, respectively. The
sedimentation photographs for the three two component
systems of LS-5 SiC/Sifih, UF-lO SiC/Sifih , and UF-lS
SiC/Sifih with equal relative volume fractions can be found
in Figures 34 through 36 and photographs for the
sedimentation behavior of the one two component system with
unequal relative component volume fraction can be found in
Figure 37.

The ESA zeta potential measurements for the FeAl/Alfih
fiber system in an electrolyte solution of concentration
equal to 10"3 M are shown in Figures 38 and 39. These data
was used along with the constant potential solution for the
repulsive interaction potential in stability prediction runs

for the system. This data generated in these prediction

1 E30

 

 

(a)

Figure 28 Stability ratio data from the predictive program
using the constant potential repulsive equation
and electrophoretic zeta potential for UF-15
SiC/SN-Elo Sign where: temperature is a) 20, 25,
and 30 °C and b) 0, 25, 50, 75 °C volume fraction
of components is 0.5 and electrolyte
concentration is 104 M.

104

 

 

pH

(b)

Figure 28 Cont.

1 E20

   

     
 

     
  

 

, 3"

M‘. f“-
w .s -.
§§v\“{i‘$§\“

 

 

(a)

Figure 29 Stability ratio data from the predictive program
using the constant potential repulsive equation
and electrophoretic zeta potential for UF-15
SiC/SN—Elo SifiN. where: temperature is 25 °C volume
fraction of components is 0.5, the electrolyte
concentration is 10'3 M, and the Hamaker
constants in units of 10'19 J are varied by +/- 10%
to the values noted in a) and b).

106

1E20

(b)
Figure 29 Cont.

A(SiC).A(SLN.)
+ 3.0, 1.6
+ 3.0, 1.4

* 3.3. 1.4

 

 

 

107

runs are plotted in Figure 40.

 

(b)

Figure 30 Sedimentation samples for a single component
suspension of LS-S SiC with an electrolyte
concentration of 10'3 M KNO3 after sedimentation
for a) 21 hours, b) 21 hours, c) 21 hours, d) 73
hours, and e) 73 hours.

109

 

(d)

Figure 30 Cont.

110

 

(e)

Figure 30 Cont.

111

 

(a)

(b)

Figure 31 Sedimentation samples for a single component
suspension of UF-lo SiC with an electrolyte
concentration of 10'3 M KNO3 after sedimentation
for a) 21 hours, and b) 119 hours. .

112

V
l'|".;tv:'1(‘

{ r
‘Imhw
. o

1","! “(Nit t 'r

”jirvp

 

(b)

Figure 32 Sedimentation samples for a single component
suspension of UF—15 Sic with an electrolyte
concentration of 10"3 M after sedimentation
for a) 20 hours, and b) 118 hours.

113

mm] . .

"I“ i‘ O" I. H l . I “I, ['01. Man“ :r'l‘ " . ..'"“.'.'1."
r 11%? r :

lllt
' tuftl I

' ,‘

 

(a)

~. I'll-'1 . __
:IQKhfiEEéWw; .:

‘ 1
M):

In)“: ‘.
- .m' Mn '0.) .n m; :1", ~ .- 1.,
t "7' {t WIN?919114;!113111‘311111

11111
'1’111

 

(b)

Figure 33 Sedimentation samples for a single component
suspension of SN-Elo Sign with an electrolyte
concentration of 10'3 M KNO3 after sedimentation
for a)1.5 hours, b)24 hours, c)48 hours and d)l46 hours.

114

31'.
‘ .... v‘ y I Huh” 1.
1‘": J ‘

. .
‘1 13 um rrnmmlr

1:111

11.1l'iitl"

Mn 1'” "’5‘“ “O h". ("'0 "”1"”! I”! (1 .fl). ‘0'I'J .1"
. t O ' ‘

‘1‘ ’ f! [1511? :7 cup 1:

 

d)
Figure 33 Cont.

115

to! ‘ - o. ‘ (n ' ’
(1.11 '1.."..I"“‘.m .‘1’u“.{.‘.;"y'll§“!0mm“) l ‘ It
I "1" I t I ‘ I '

1 .

at”?

. | ljyt.‘|‘,
xl“§-!_I’on

 

(b)

Figure 34 Sedimentation samples for a two component
suspension of 0.5 relative volume fraction of LS-S
SiC and SN-ElO Sign with an electrolyte
concentration of 10’3 M KNO3 after sedimentation
for a) 0 hours, and b) 72 hours.

116

9‘23, )Htt

 

(b)

Figure 35 Sedimentation samples for a two component
suspension of 0.5 relative volume fraction of
UF-lO SiC and SN-Elo Sign with an electrolyte
concentration of 10'3 M KNO3 after sedimentation
for a) 29 hours, and b) 70 hours.

117

1 1

mt: . . 1"
I . ‘1 ‘ 1 r ‘ ' 1‘ l 1 ‘0!
"4h ‘1' .- 1‘14”"‘11‘f¥,0"1'09+.‘”\Jf8‘¢’L‘W/’u
_ V . . 1 - ._

 

(a)

 

(b)

Figure 36 Sedimentation samples for a two component
suspension of 0.5 relative volume fraction
of UF-lS SiC and SN-Elo Sign with an electrolyte
concentration of 10'3 M KNO3 after sedimentation
for a) 23 hours, and b) 64 hours.

118

uneasy; gamma!
1, 1.111.111'11'"'111.~‘.o.u9m. 1‘11'
‘.|1'.uln't|n..

. 1

1:1. 'I‘.|1
1 1 . 111111113111 mm 1111*,
.I’It“;..*1;l HI)!

 

(b)

Figure 37 Sedimentation samples for a two component
suspension of 0.75 relative volume fraction of
UF-lO SiC and SN—ElO Sifin with an electrolyte
concentration of 10'3 M KNO3 after sedimentation
for a) 22 hours, and b) 63 hours.

119

Zeta Potential (mV)

    
  
 
   
   

rangetested
"'4To 11
‘1' 11 To 4
*4To 11
* 11 To 4

 

Figure 38 ESA zeta potential measurements for FeAl powder at
an electrolyte concentration of 10"3 M 1010,.

 

120

100

:2.
}

"Ds
. IC<
s

Zeta Potential (mV)
N
0

pH range tested
"‘ 4 To 11
+ 11 To 4

 

Figure 39 ESA zeta potential measurements for A1203 fiber at
an electrolyte concentration of 10'3 M 1010,.

 

 

1E20 .
Interactions
-.- FeAI/FeAI
+ FeAI/A1203
s * A1203/A1208
gags? * TOTAL

 

(a)

Figure 40 Stability ratio data from the predictive program
using the constant potential repulsive equation
and BSA zeta potential for FeAl and Algh radii of
a) 3.5 and 15.0 microns, b)7.5 and 15.0 microns,
and c) 12.5 and 15.0 microns respectively, where:
temperature is 25 °C, volume fraction of
components is 0.5 and electrolyte concentration is
10‘3 M KNOa.

122

1E10

(b)

Figure 40 Cont.

Interactions
°'- FeAI/FeAI
+ FeAI/A1203
* A1203/A1208

"' TOTAL

 

 

123

   
 
  
   
   

1E20
Interactions
"' FeAI/FeAl
W + FeAl/A1203
* A1203/A1203
"' TOTAL
1 E10

 

(C)

Figure 40 Cont.

DISCUSSION

The zeta potential data measured in the experimental
portion of this investigation were acoustophoretic (ESA)
measurements. The values for these measurements on the
SiC/Sifih system are found in Figures 17 through 20. For
some of the types of powder, the acoustophoretic ESA
measurements compare well with the electrophoretic values
shown in Figures 12 through 14 and for others there are
major differences in the magnitudes of the values. A
summary of values for each of the different powders at
several pHs for the two different measurement techniques can
be found in Table l. The acoustophoretic ESA data for the
LS-S and UF-lO Sic are similar in magnitude to the
electrophoresis data for pH values greater than 5, while the
magnitude of the acoustophoretic ESA data at lower pHs are
less. The magnitude of the acoustophoretic ESA data for UF—
15 SiC is much lower than the electrophoretic data for the
UF-lO SiC.

This discrepancy could be due to the powders not being
of the same type, but the chemistry of the two different
types of SiC powder is very similar according to the
manufacturer and so surface charge generation and zeta
potential values would be expected to be similar.
Examination of the Sign acoustophoretic ESA data shows a

similar behavior, with the magnitude of the acoustophoretic

124

125

Table 1 Zeta potential values at several pHs from

acoustophoresis (BSA) and electrophoresis

 

 

 

 

 

 

 

measurements..
pH ESA ESA ESA ESA Electro- Electro-
Values LS—S UF-lO UF—lo SN-Elo phoresis. jphoresis
UF-lO SN-ElO
4 -10 -14 -2.2 8.0 -34 44
5 -20 -26 -5.5 5.7 -44 29.4
7 -39 —38 -11 -3.5 -54 -24
8.5 -52 -47 —16 -5.8 -58 -38
10 -61 —52 -19 -7.8 -60 ~43

 

 

 

 

 

 

 

 

 

ESA zeta potential data being much lower in magnitude than
the values of the electrophoresis data for the same type of
Sign powder. Both the UF-15 81C and Sign powder are of a
similar small size range. A similar discrepancy between
measured acoustophoretic ESA data and electrophoresis data
was discussed by James, Hunter, and 0' Brien (79) in testing
several different types of alumina powders and UBE SN-ElO
Sign. For Sign, these authors showed that if an effective
radius was used for the average particle size to calculate
the zeta potential with the acoustophoretic ESA technique,
the results were found to approximately match the
electrophoresis data. The reason was found in Equations
[10] through [16]. Equation [10] calculated the zeta
potential once the dynamic mobility was found using the
measured ESA amplitude to solve Equation [8]. The term 6(a)
was the inertial contribution to the dynamic mobility which
was dependent upon both the frequency of the acoustic wave
and the particle size and was found by solving Equations
[11] through [16]. Generally, G(a) was an inverse function
of the particle radius. If the radius was underestimated,
the inertial contribution Gta) was overestimated, resulting
in an underestimation of the zeta potential. James et al.
showed calculations where the reported particle size was
half of the true particle size, resulting in a 6(a) 1.75
times higher. This indicates that the zeta potential will

be reported as 1.75 times smaller in magnitude than it

126

127
should be.

Part of the problem in finding the correct particle
size to calculate the acoustophoretic ESA zeta potential was
that each method used will give different average particle
sizes. For example for Sign, the manufacturer reports an
average particle radius of 0.25 pm, Crimp reports a BET
equivalent spherical radius of 0.06 um (76), James et al.
(79) report a particle analyzer mass average radius of 0.275
um and a light scattering radius of 0.55 um. James et al.
found the best results using photon correlation spectroscopy
(PCS). A major factor responsible for the difference in
the particle radius and need for use of an effective radius,
was agglomeration of particles into larger sized particles
during ESA testing (71). As will be discussed later and can
be seen in Figures 30 through 32, SiC agglomerates at low pH
values. These were the pH values where the acoustophoretic
ESA measurements were slightly lower than the
electrophoresis values for LS-S and UF-lO SiC. This
agglomeration and the need for an effective particle radius
would explain this behavior. Electrophoresis does not "see"
the need for an effective particle radius for two reasons.
The electrophoresis measurements are carried out at much
lower particle volume percents of solids to liquids in the
suspension and the electrophoresis values do not require
particle size in the calculation of the zeta potential.

Figure 21 is the first of the graphs of stability vs.

128
pH from data produced by the predictive program for the
SiC/Sifih system. Figure 21(a) is the predictive data found
using the constant potential repulsion equation along with
electrophoresis data for the LS-S SiC/Sifih system with
equal relative component volume fraction in an electrdlyte
concentration of 10"3 M at room temperature (ZSWS). Figure
21(b) and (c) are for the same system conditions, but are
for UF-lO SiC/Sifih and UF-15 SiC/Sifih, respectively. For
all of the stability vs. pH plots, the maximum value plotted
for the stability ratio is 1031 due to limitations of the
available graphics software. Four different curves were
plotted on each graph. The curves represent the different
types of interactions which are possiblefor the system.
SiC/SiC, SiC/Sifih, and Sigh/Sigh represent the interactions
of Sic particles with themselves (Wu), SiC particles with
Sign particles(W 12), and Sign particles with themselves
(Wu), respectively. The curve for the total interaction
represents the total overall particle interaction (WJ.

The SiC/SiC curves in Figures 21(a), (b), and (c) are
horizontal lines at a value of W equal to 10”. This means
that the SiC particles are predicted to be stable with
respect to themselves at all pH values from a pH of 4 to 11.
the Sigh/Sigh curves for these plots begins at stability
values of 1031 at pH 4 to 5, decreasing to lower values for
pH 5.5 to 7, and increases to the maximum for pH 7.5 and

above. The prediction is then that Sign is stable at low

129
pH values and high pH values, but is unstable for
intermediate pH values with respect to itself.

The SiC/Sifih curves differ in the three plots of
Figure 21. In Figure 21(a) the curve is constant at
stability values of about 103 from pH 4 to 8, decreases to a
value of less than 1 at pH 8.5, and then increases to values
above 10”. This means that the method predicts SiC and
Sign particles will be attracted to one another to form
agglomerates for pH less than 9 and so instability is
predicted in this range. For pH 9 to 10 it is unclear if
the stability ratio is large enough to predict stability or
partial stability (i.e. where the particles will be stable
but only for smaller time periods). The actual stability
ratio values which delineate stability from instability or
partial stability will have to be determined by application
to a real system. For Figures 21(b) and (c), the SiC/Sifin
curves are very similar with instability predicted for pH
less than 7, partial stability for pH 7, and stability for
pH values greater than pH 7. For the three curves plotted
in Figure 21 the total stability is predicted to follow
closely each of the SiC/Sifin interaction curves with only
small shifts in stability values. This would indicate total
system instability below pH 9, partial stability from 9 to
10 and stability above pH 10 for the 18-5 SiC/Sifin system
and instability below pH 7 with stability above pH 7 for

both the UF-lO and UF-lS/Sifih systems. Figure 22 contains

130
plots of computer predicted stability for the same three
systems except that the ESA zeta potential data was used
instead of the electrophoretic data. All three of the plots
predict complete instability of the SiC/Sifih, Sigh/Sigh,
and total interactions at all pH values. This is due to the
smaller magnitudes reported for the Sign ESA zeta potential
data compared to the electrophoresis. Figures 22 (a) and
(b) predict instability for the SiC/SiC interactions at low
pH values and stability at higher pH values, while Figure 22
(c) predicts instability at all pH values (again this is due
to the lower ESA zeta potential values).

Figure 23 contains plots of computer predicted
stability for the same systems as Figure 21, but uses the
constant charge repulsion equation instead of the constant
potential equation. Figure 23 (a) predicts SiC/SiC
interaction stability for all pH values and Sigh/Sigh
stability for pH below 6 and above 6.5. The SiC/Sifih and
total interactions are predicted to be unstable below pH 7.
Figures 23 (b) and (c) are almost identical predicting
SiC/SiC interaction stability for all pH values and
Sigh/Sigh stability for pH below 6 and above 6.5. The
SiC/Sifih and total interactions are predicted to be stable
below pH 6.5.

Figure 24 (a) through (0) are plots of the potential
energy of interaction versus particle separation distance

for each of the 15 pH values for which data was calculated

131
for the LS-5 SiC/Sifih system with equal relative component
volume fraction in an electrolyte of concentration 10‘”3 at
room temperature (corresponds to stability data in Figure 21
(a)). In the figures the higher the maximum repulsive peak,
the larger the barrier to agglomeration, the higher the
corresponding stability ratio will be in Figure 21 (a). An
example of this can be seen for the Sigh/Sigh interaction.
Figure 24 (f) shows the potential energy at pH 6.5 for this
interaction. This curve is the middle curve of the three and
is shown as barely reaching a positive potential value and
corresponds to a low stability value in Figure 21 (a).
Figure 24 (j) shows the potential energy at pH 8.5 for this
interaction. This curve is the middle curve of the three and
is shown as reaching a positive potential peak of
approximately 100 kT or so and corresponds to a stability
value in Figure 21 (a) which indicates stability.

These figures illustrate an advantage of the stability
prediction theory used in this investigation over methods
which simply look at the interparticle potential curves.
Instead of using one figure (e.g. Figure 21 (a)) to predict
the system stability over a pH range, as in this theory, it
would be necessary to look at a plot of potential verses
separation for each pH in the pH range (e.g. the 15 plots in
Figure 24) in order to use the interaction energy versus
separation to predict stability.

The plots in Figure 25 are for data from the predictive

132
program using the constant potential repulsion equation and
electrophoresis data for the three main two-component
systems with equal relative volume fraction as in Figure 21,
but with an electrolyte concentration of 104 M. The curves
predict instability for SiC/SiC interactions at pH below 7.5
and below 8.5 or 9 for Sigh/Sigh interactions. For the
SiC/Sifin and total interactions instability is predicted
for all pH values for the LS-S SiC/Sifih system and for pH
below 10 and 9 for the UF-lo and UF-lS SiC/Sifih systems,
respectively.

The plots in Figure 26 are the same as in Figure 25,
but with an electrolyte concentration of 10"5 M. For each
of the three systems shown, stability is predicted for the
SiC/SiC interaction for pH above 5 and for the Sign
interaction stability is predicted for pH below 5.5 or above
7.5. The SiC/Sifih and total interactions are different for
each of the three systems. For the LS-S SiC/Sifih system,
the method predicts instability at all pHs. For the UF-lo
SiC/Sifih system, instability is predicted for all pHs below
10.5, while for the UF-lS SiC/Sifih system, instability is
predicted for all pHs below 8. The method predicts changes
in stability behavior with changes in the electrolyte
concentration. This is expected since variations in
electrolyte concentration will change the size of the
repulsive double layer as was discussed earlier. An

increase in electrolyte concentration reduces the double

133
layer size since the ion concentration reaches the bulk
value in a shorter distance from the particle surface.
Increasing the electrolyte concentration fromlO"3 M to 10'2
M reduced the predicted stability behavior which is seen by
comparing the plots of Figure 21 and Figure 25.

The effect of variations in the relative volume
fraction of components on the total overall stability is
shown in Figure 27. The conditions chosen to show the
variation were for systems in which there was the largest
difference between the stability behavior for Sic and Sign.
Therefore, the largest changes in the total stability should
be seen for these systems. All three systems show that for
these conditions the method does not predict much change in
the total overall stability of each system for different
relative volume fractions.

The effect of temperature on the total overall
stability is shown in Figure 28. Figure 28 (a) shows the
total overall stability for room temperature and room
temperature +/- 5W3. This figure shows that stability is
predicted to barely change for the temperature range of
normal laboratory temperature fluctuations. Figure 28 (b)
shows the total overall stability for much larger
temperature changes. Even the large variations in
temperature show little change in predicted stability except
at pH 7 where the stability might change from complete

stability to partial stability for a temperature increase of

134
50°C. A plot of the log of the stability ratio versus pH
shows all curves as being almost identical except for the
(PC curve which is shifted to the left of the other curves
by about a half a pH unit. This indicates that processing
in an ice bath or similar low temperature environment, would
allow for stability at a half a pH lower than if the
processing was done at room temperature. This could be an
important processing aid for systems in which components are
soluble at high pH or have surface groups which are unstable
at high pH as is the case for Sign (70).

Figure 29 shows the effect on the predicted stability
from variations in the input Hamaker constants of plus or
minus 10% for SiC and/or 519%. This was done because the
values for the Hamaker constants vary depending on the
:method (i.e. microscopic method Equation [2] or macrosc0pic
method of Equation [3]) used to calculate them. Figure 29

Jnittle change in the overall stability predicted even for
‘raariations as large as a 10% increase in one and a 10%
ciaacrease in the other input Hamaker constant. This means
that the predictions are not strongly sensitive to the

a<'=curacy of the Hamaker constants input.

To verify the stability predictions, sedimentation
experiments were performed. With the small size and similar
a'3'F>']g.'>earance of all the powders upon dispersion, it was not
DQassible to identify any heterocoagulation between SiC and

Esii~3N,. For future investigations the heterocoagulation

I
Ira“
Uni.
.

:':e

u
._....
out

 

a
I‘~'
bod

e'u

D‘l'

:hn

r,
(f)

b

5“
EV‘

In
I’ I)
s

Q‘-

ll
t,
A n

1

h 1

5".

135
predictions could be examined using SEM or TEM studies. In
the current investigation, single component sedimentation
experiments were performed along with the two component

systems tested so that the each of the SiC/SiC and

Sigh/Sigh interactions could be known experimentally along

with the total overall stability for the two component

systems. The sedimentation of each of these single and two
component systems at varying time intervals can be seen in

Figures 30 through 37.
The reason sedimentation experiments indicate the

agglomeration state and stability for a system results from

the fact that as agglomerates form, the sizes of these

agglomerates are larger than the single particle. The more

agglomeration that takes place larger the agglomerates

(The larger a particle or agglomerate becomes the

become.
’ Factors

Inore gravity affects it and the quicker it falls.'
uthich indicate the degree of agglomeration are sedimentation

sedimentation height and whether the liquid above the

rate,
If the

sedimentation level is clear or cloudy (80).
£3edimentation height is small, the system is strongly

cOagulated. Larger sedimentation heights with clear liquid

ak><3ve the sedimentation show a partially stable suspension
and suspensions which remain cloudy above any sedimentation
11Qight show stable suspensions (70).

Figure 30 shows the sedimentation behavior for LS-S SiC

At a time of 21 hours, the suspension is

by itself.

136
unstable below pH 5.5, partially stable at pH 6.0, and
stable for all higher pH values. At 73 hours, the same
stability is shown. Figure 31 shows the stability of UF-lO
SiC. At 21 hours the UF—lO is unstable for pH values less
than 6 and stable for values of 6 or greater. After 119
hours, the UFélo is unstable for pH less than 6, is
partially stable for pH 6 and 6.5, and stable for higher
pHs. Figure 32 shows the stability for UF-15 SiC. At 20
hours, the UF-lS is unstable for pHs less than 6, partially
stable for pH 6, and stable for values of greater than 6.
After 118 hours, the UF-lS is unstable for pH 6 or less, is
partially stable for pH 6.5, and stable for higher pH
values. Figure 33 shows the stability for SN-Elo Sign. At
24 hours, the SN-ElO is stable for pH less than 5, unstable
for pH 5 to 8, partially stable for pH 8.5, and stable for
thalues greater than 8.5. At 48 hours, the SN-Elo is stable
for pH less than 5, unstable for a pH 5 to 8.5, partially
stable for pH 9 and 9.5, and stable for values greater than
£3 -5. At 146 hours, the SN-ElO is stable for pH less than 5,
‘tllfistable for a pH 5 to 9, partially stable for pH 9.5 and
:1-C). and stable for values greater than 10.0.

For the two component systems of LS-S SiC/Sigh in
{63‘3Dual volume fractions Figure 34 shows the total stability.
.ZK1:. 72 hours, the system is unstable for pH less than 7.5,
I>a-zc'tially stable for pH 7.5 and 8, and stable for pH greater

t:]blan 8. For the UF-10 SiC/Sifih in equal volume fractions,

137

Figure 35 shows the total stability. At 29 hours, the
system is unstable for pH less than 7, partially stable for
pH 7, and stable for pH greater than 7. At 70 hours, the
system is unstable for pH less than 7, partially stable for
pH 7 to 8.5, and stable for pH greater than 8.5. For the
UF-lS SiC/Sifih in equal volume fractions, Figure 36 shows
the total stability. At 23 hours, the system is unstable
for pH less than 7, partially stable for pH 7 to 8, and
stable for pH greater than 8. At 64 hours, the system is
unstable for pH less than 7, partially stable for pH 7 to
8.5, and stable for pH greater than 8.5. For the 0.75 v%
UF-lO SiC/0.25 v% Sign Figure 37 shows the total stability.
At 22 hours, the system is unstable for pH less than 6,
partially stable for pH 6 and 6.5, and stable for pH greater
than 7. At 63 hours, the system is unstable for pH less
than 6.5, partially stable for pH 6.5 to 7.5, and stable for
F”! greater than 7.5.

The prediction for LS-5 and UF-lO SiC using the
a<=c>ustophoretic ESA data and the constant potential
reF>ulsion equation predicts the change from partial
stability to stability to occur for pH 5 to 5.5 and 5.5 to
6' respectively. The single component sedimentation
e’"E>eriments for these powders at 21 hours show this
transition to be at 5.5 to 6 for both of the powder types.
The prediction for the SiaN, using the acoustophoretic ESA

data and the constant potential equation predicts stability

g 138

for pH less than 5.5 and greater than 7. The single
component sedimentation experiment for Sign shows stability
of less than 5 and greater than 8.5. This prediction is
close for the lower pH range, but while the program did
predict the second stability range, it was not very close as
to where this range began.

For the total overall stability of the LS-5 SiC/Sifih

system with the constant potential repulsion equation and
zeta potential data used for prediction, a stability
prediction determines the suspension to be unstable below pH
9 and partially stable at 9 to 10 and stable for pH above
10. The sedimentation results after 72 hours for this
system indicate a stable suspension below 8.5 and stable at
8.5 and above. For the total overall stability of the UF-lO
SiC/Sifin system with the constant potential repulsion
equation and zeta potential data used for prediction, a
Stamfility prediction determines the suspension to be
unstable below pH 7 and partially stable at 7 and stable
for pH above 7. The sedimentation results after 29 hours
for this system indicate a stable suspension below 7 and
stlable at 7.5 and above.

Some of the results can be seen as quite encouraging,
butwith the acoustophoretic ESA data not being correct for
SisN‘I or UF-15 SiC, much of the accuracy of the predictions
is decreased. This points out how necessary accurate zeta

potential measurements are. For future work with the

139
program, acoustophoretic ESA zeta potential data need to be
taken using an effective particle radius.

The FeAl zeta potential curves are shown in Figure 38.

The zeta potential data curves are relatively flat over the
pH range. Shaw (15) shows a zeta potential curve for latex
particles-which is also fairly flat over the pH range. The
flatness of the curve indicates one of two things. Either
hydrogen and hydroxyl ions are not the potential determining
ions for FeAl or there are competing charge generation
mechanisms. The charge generation mechanism is unknown, but
could be a variety of different mechanisms such as various
corrosion reactions or hydroxylation reactions. This points
to another advantage of this prediction method. From a
purely processing standpoint, a prediction of the stability
for this system can be made with accurate zeta potential
data without knowing the charge mechanisms, although from a
«scientific standpoint the it would be desirable to know the
Charge mechanisms.

The ESA zeta potential data for the alumina fibers are
53110wn in Figure 39. The magnitude of the values are similar
t3<> values reported by James et al. (79) for alumina powder
aind an i.e.p. that is similar to that shown by James et al.
(779). However, the shapes of the curves differ. -This is
probably due to the authors taking approximately ten data
I>Chints and then drawing a best fit curve through them. The

data scatter of the ESA zeta potential data is probably due

140
to the large distribution of fiber lengths as can be seen in
the SEM photograph in Figure 61. To improve the
acoustophoretic ESA data, a better method for shortening the
fibers is needed.

The stability prediction curves in Figure 40 show
complete instability of FeAl. Observation of the FeAl
suspensions made in this investigation show this not to be
true. This poor prediction is due to the use of an
inaccurate average particle radius in calculating the ESA
zeta potential. An improved method for finding an effective
particle radius is needed. If it is assumed that correct
particle size would shift the stability up, it would follow
that the FeAl would be stable for all pH values, although
there might be instability above a pH of 9 where the
acoustophoretic ESA curve dips slightly.

The stability for alumina is predicted to be stable for
PH under 6.5 to 7 or above 10.5 or 11. The FeAl/alumina

irrteraction is shown to be stable for the whole pH range,
1311t if the FeAl stability curve were shifted up, the
IEsau/alumina curve would be also. The curve is at a maximum
Eit: pH 7 and drops off for higher and lower values of pH.
”Erie ideal pH for processing this composite system would be
‘Vllere the FeAl/FeAl and alumina/alumina interactions would
IDG! stable, but the FeAl/alumina interaction would be
unStable so that the matrix and fiber are attracted to each

other. This would occur at pH 5 or 6. If after initial

141
mixing of the composite at pH 5 to allow for a uniform
distribution of FeAl and alumina fibers the pH was increased
to 8, in order to induce total coagulation of the system, so
differential settling of the composite components could be

reduced or eliminated.

CONCLUSIONS

Due to the importance of using both stable and
agglomerated suspensions in ceramic processing along with
the increasing use of ceramic processing for multicomponent
and composite systems, a method for predicting the stability
of multicomponent colloidal suspensions at different pH
values was developed from a method originated by Hogg,
Healy, and Fuerstenau (53). A computer program was written
to perform the calculations required in using this method.
Material and system data such as particle radii, relative
volume fraction of components, monatomic electrolyte
concentration, Hamaker constants, and zeta potential versus
pH measurements were input into the computer program. The
stability ratio versus pH data was output by the program
into ASCII files for plotting using graphics software.

The SiC/Sifih system was investigated in detail using
tMJth electrophoresis and electroacoustic zeta potential

data. The method was used to make general predictions to be
<3C>rnpared with actual stability experiments, and to show the
efzfect of relative volume fraction of components,
tamperature and the accuracy of the Hamaker values on the
IDImedicted stability. The regions of stability predicted by
the method were found to be within a half a pH in some
in3tances. However, the predictions were found to be
strongly dependent‘upon the accuracy of the electroacoustic

142

143
zeta potential measurement data. Problems with these data
were discovered and found to be the result of the particle
sizetdarta which were used to calculate the electroacoustic
zeta potential from the measured dynamic mobilities.
Contrary to what was intuitively expected, the predicted
total (sverall stability was found to be only slightly
changeg<3 for different relative volume fractions of
Components. This was also shown for actual stability in the
sedimentation results for a SiC/Si3N, system with.0.75
relatlisve volume fraction of Sic. The prediction method was
ShowTi .not to be dependent on the precision of the Hamaker
constant values‘used for stability calculations nor upon the
System temperature.
The stability prediction method was also applied to a

FeAl /A1203 fiber composite system. The method was used to
determine the pH where the processing conditions would be
idteal. The ideal composite processing would have the fiber
COated by the matrix while having the fiber and the matrix
‘stable enough to form a uniform distribution of fiber within
the matrix. This would occur at the pH where the fiber and
Inatrix were attracted to each other and agglomerated
tlogether while the fiber and the matrix were individually
stable with respect to themselves. The method predicted
t:llat the ideal pH where this would occur would be 5 and that
ii subsequent increase to pH 8 would then prevent

qifferential settling of the fiber and powder.

144

In general, future investigations should include: 1)
electroacoustic ESA data collected using effective particle
radius versus pH data, 2) should use the log of the
Stability ratio to better indicate stability, 3) should have
the heterocoagulation predictions investigated through SEM
or TEM studies, and 4) should try to better determine at
which values of the stability ratio suspensions become
stable - For the FeAl/A1203 fiber system, future
investigations should include 1) the general recommendations
listed above, 2) a better method for shortening the fibers
f°r the electroacoustic ESA measurements, and 3)

determination of the surface chemistry of FeAl.

APPEDIX A

Derivatidn relating n.to particle radii and
relative component volume fraction.

145
In the HHF method n is the overall number of particles
of component 1 in the system. In other words n is the ratio
of the total number of type 1 particles to the.total number
of all particles in the system:

11g

-——————w [A1]
amn+1mg

n:
This was deemed as quite impracticle from an experimental
viewpoint. In real experimental systems variables which are
known include the particle radii (r3 and rs) and the

relative volume fraction of component 1 (RVFCfi:

IWQ

______.. [A2]
QWQ+IW§

RVFC1=

Since the method beibg used assumes spherically shaped
particles and the particle radii are known, the volume of an

individual particle i is:
V1=-§1tr13. [A31
The total volume of all particles of type i is then:
TV1=1N1V1=-§xm1r13. [A41
JEquation [A2] for component 1 then becomes:

4
ml '5- “El,

ml-gnrlhma-‘ler,’

 

RVFC1= [A51

Trhis simplifies to:

 

146

133

RVFC =TN .
1 1 m1r13+m2r23

 

Now if Equation [A1] is solved for TN}, the result is:

TN
nth—1 —m1=m1(l -1) .
n n
Substituting Equation [A7] into [A6] results in:

TTQLf
m1r13+ [1156-1) ] :23

 

RVFq:

which can be simplified to:

flagrf .
7N1[r13+(%-1)r33]

 

raw-'01:

The equation then becomes:

I 3
RVFC1= 1

 

113+(%-1)r,3

Solving this equation for n through simple algebra:

1
r13(1-RVFC1) +1
rzz‘RVFC1

 

 

[A6]

[A7]

[A8]

[A9]

[A10]

[A11]

APPENDIX B

List files of the computer program

STABILITY PREDICTION and its subroutines.

147

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Line#

OQQOSU'IOMNH

Source Line

CCCCC

ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
cccCc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc

PROGRAM STABILITY PREDICTION
REV. 06-22-92

IMPLICIT NONE

CHARACTER CODE*6

CHARACTER ZPQ*1,FLDIR*7

INTEGER L,NZP1,NZP2

INTEGER*2 CDATE,STIME,FTIME

DIMENSION CDATE (3) , STIME (4) , FTIME (4)

REAL APR,PHCZI,N,AHP,PHSS,SPH,FPH,PH,AHM,TAH
REAL ZPPHl,ZPDP1,ZPPH2,ZPDP2,CONCL,TEMP,V
REAL*8 WOO,WOT,WTT,WT
DIMENSION PHCZI(2), AHP(2),
DIMENSION APR(2)

DIMENSION ZPPH1(200), ZPDP1(200),

DIMENSION ZPPH2(200), ZPDP2(200)

DIMENSION WOO(200),WOT(200),WTT(200),TAH(2:4)

WT(200), PH(200),

N= OVERALL PROPORTION OF PARTICLES OF COMPONENT

ONE IN SYSTEM
V= VOLUME PERCENT OF COMPONENT ONE IN SYSTEM
APR= ATOMIC PARTICLE RADIUS (ARRAY VARIABLE)
PHCZI= PH OF ZERO-POINT-OF-CHARGE (ARRAY

VARIABLE)
HAMAKER CONSTANT OF PARTICLE
‘VARIABLE)(J)
AHM= HAMAKER CONSTANT OF MEDIUM(J)
TAH= TOTAL HAMAKER CONSTANT(J)
TAH(2)=A131
TAH(3)=A132
TAH (4) =A232
TEMP=TEMPERATURE OF SYSTEM (deg. C)
SPH= STARTING PH
FPH FINISHING PH
PHSS= PH STEP SIZE
MSS= MINIMUM STEP SIZE
FLNAME= NAME OF FILE DATA WILL BE STORED IN
FLDIR=NAME OF DIRECTORY DATA FILE IS STORED IN
CICS= CORRECT INPUT CHARACTER STRING
CI= CORRECT INPUT ANSWER VARIABLE
RICS= READ INPUT CHARACTER STRING
WOO,WOT,WTT=INVERSE OF THE PROBABILITY THAT A
GIVEN PARTICLE
COLLISION LEADS TO ADHESION

WT=OVERALL STABILITY RATIO
PH=PH COORESPONDING TO AN OVERALL STABILITY

RATIO VALUE

AHP= (ARRAY

148
Source Line

CCCCC ZPQ=ZETA POTENTIAL QUESTION VARIABLE

CCCCC (’Z’=ZETA POTENTIAL DATA USED FOR

CCCCC CALCULATIONS)

CCCCC ('P’=POINT-OF-ZERO-CHARGE DATA USED FOR
CCCCC CALCULATIONS)

CCCCC NZP=NUMBER OF ZETA POTENTIAL DATA POINTS
CCCCC ZPDP=ZETA.POTENTIAL DATA.POINT (ARRAY VARIABLE)

 

 

 

 

 

 

 

 

 

 

 

CCCCC ZPPH=COORESPONDING ZETA POTENTIAL PH (ARRAY
CCCCC VARIABLE)
CCCCC CONCL=CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM
CCCCC (MOLE/L)
CCCCC L=INTERGER USED AS A COUNTER FOR DO LOOPS
CCCCC CDATE=CURRENT DATE
CCCCC STIME=STARTIMG TIME OF RUN
CCCCC FTIME=FINISHING TIME OF RUN
10 OPEN(14,FILE='FLEINPUT.DAT’,STATUS=’OLD’)
CCC GETTING SYSTEM DATA PROM
c FILE
20 CALL FDATA INPUT (v, APR, PHCZI, AHP, AHM, SPH,
& FPH, PHSS, ZPQ, NZPl, NZP2,ZPPH1, ZPDPl, ZPPHZ,
ZPDPZ, CONCL, FLDIR, TEMP)
CC GETTING CURRENT DATE AND
C PROGRAM RUN STARTING TIME---
30 CALL GETDAT (CDATE(1),CDATE(2),CDATE(3))
40 CALL GETTIM (STIME(l), STIME(Z), STIME(3),
& STIME(4))
CCC CALCULATING TOTAL HAMAKER
C CONSTANT
50 TAH(2)=(SQRT(AHP(1)) - SQRT(AHM)) *
(SQRT(AHP(1)) — SQRT(AHM))
60 TAH(3)=(SQRT(AHP(1)) - SQRT(AHM)) *
(SQRT(AHP(2)) - SQRT(AHM))
7o TAH(4)=(SQRT(AHP(2)) - SQRT(AHM)) *
(SQRT(AHP(2)) - SQRT(AHM))
CCC INITIALIZING WT & PH VALUES TO
C ZERO
80 DO 140 L=1,200,1
90 WT(L) = 0.0
100 PH(L) = 0.0
110 WOO(L)=0.0
120 WOT(L)=0.0
130 WTT(L)=0.0
140 CONTINUE

149

Source Line

 

CALCULATING WT & PH VALUES FOR

 

 

SPECIFIED
PH RANGE & STEP SIZE -----

 

IF (ZPQ.EQ.’P’) THEN

CALL CALCPZC(V, APR, PHCZI, TAH, SPH, FPH,
& PHSS, WT, PH, CONCL, WOO, WOT, WTT, FLDIR,
& TEMP)
ELSE
CALL CALCZP(V, APR, TAH, ZPDPl, ZPPHl, ZPPHZ,
& ZPDPZ, SPH, FPH, PHSS, WT, PH, CONCL, NZPl,
& NZPZ, WOO, WOT, WTT, FLDIR, TEMP)

A END IF

GETTING PROGRAM RUN FINISHING

 

 

 

TIME
CALL GETTIM (FTIME(1), FTIME(Z), FTIME(3),
& FTIME(4))

 

STORING INPUT & CALCULATED

 

 

DATA
CALL DATA STORAGE (N, APR, ZPQ, AHM, AHP, PHCZI,

& NZPl, NZPZ, ZPPHl, ZPDPl, ZPPHZ, ZPDPZ, WT, PH,

& CONCL, WOO, WOT, WTT, CDATE, STIME, FTIME,TEMP)
CLOSE(14)

FORMATTING READ STATEMENTS----

 

Line#
83 CCC
C
84 C
85 150
86 160
87
88 170
89 180
90
91 190
92
93 (x:
C
94 200
95
96 CCC
C
97 210
98
99
100 220
101
102 CCC
103 800
104
105 998
106 999
main Local
Name
PH. . . . .
STIME . . .
L . . . . .
N . . . . .
V . . . . .
.AHM . . . .
.AHP . . . .
CODE. . . .
'TAH . . . .
FPH . . . .
CDATE .
JAPR .

FORMAT (A1)

STOP
END
Symbols
Class Type Size Offset
. . . . local REAL*4 800 0000
. . . . . local INTEGER*2 8 0002
. . . . local INTEGER*4 4 000a
. . . . . local REAL*4 4 000e
. . . . . local REAL*4 4 0012
. . . . . . local REAL*4 4 0016
. . . . . local REAL*4 8 001a
. . . . . . local CHAR*6 6 0022
. . . . . . local REAL*4 12 0028
. . . . . . . local REAL*4 4 0034
. . . local INTEGER*2 6 0038
. . . local REAL*4 8 003a
. . . . local INTEGER*4 4 0046

150

main Local Symbols

Name Class Type Size
NZPZ. . . . . local INTEGER*4 4
SPH . . . . . local REAL*4 4
CONCL . . . . . local REAL*4 4
FLDIR . . . . local CHAR*7 7
FTIME . . . . local INTEGER*Z 8
TEMP. . . . . local REAL*4 4
ZPQ . . . . local CHAR*1 1
PHSS. . . . local REAL*4 4
PHCZI . . local REAL*4 8
WT. . . . local REAL*8 1600
ZPDPl . local REAL*4 800
ZPDPZ . local REAL*4 800
ZPPHI . local REAL*4 800
ZPPHZ . local REAL*4 800
WOO . local REAL*8 1600
WOT . local REAL*8 1600
WTT . local REAL*8 1600
Global Symbols

Name Class Type Size
CALCPZC . . . . extern *** ***
CALCZP. . . . . . . . . . extern *** ***
DATASTORAGE . . . . . . . extern *** ***
FDATAINPUT. . . . . extern *** ***
GETDAT. . . . . . . . . . extern *** ***
GETTIM. . . . . . . . . . extern *** ***
main. . . . . . . . . . . FSUBRT *** ***
Code size = 044b (1099)

Data size = 002b (43)

Bss size = 0078 (120)

No errors detected

Offset

004a
004e
0052
0056
005e
0066
006a
006C
0070
0320
0960
0c80
0fa0
12c0
15e0
1c20
2260

Offset

***
***
***
***
***
***

0000

Line#

\OGQQUMbw NH

151

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line

SUBROUTINE FDATA INPUT (N, APR, PHCZI, AHP, AHM,

& SPH, FPH, PHSS, ZPQ, NZPl, NZPZ, ZPPHl, ZPDPl, ZPPHZ,
& ZPDP2, CONCL, FLDIR, TEMP)

 

SUBROUTINE TO READ IN SYSTEM

 

DATA FROM A DATA FILE -----

REAL N,APR, PHCZI,AHP,AHM, SPH, FPH, PHSS,TEMP
REAL ZPDPl , ZPPHl , ZPDP2, ZPPHZ, CONCL, SPHL, FPHL
DIMENSION PHCZI (2) ,AHP (2) ,APR(2) , ZPDPl (200)
DIMENSION , ZPPHl (200) , ZPPHZ (200) , ZPDPZ (200)

DETERMINING PH RANGE FOR

 

 

 

Z.P. DATA

CCCCC REV. 05-03-92
CCC
CC
IMPLICIT NONE
CHARACTER ZPQ*1,FLDIR*7
INTEGER I,NZP1,NZP2
CCCCC MSS=MINIMUM STEP SIZE
10 READ (14,800)TEMP
20 READ (14,805)N
30 READ(14,810)CONCL
40 READ(14,815)APR(1)
50 READ(14,815)APR(2)
60 READ(14,820)ZPQ
70 IF (ZPQ.EQ.’P’)THEN
80 READ(14,825)PHCZI(1)
90 READ(14,825)PHCZI(2)
100 READ(14,830)SPH
110 READ(14,830)FPH
120 READ(14,835)PHSS
13o ELSE IF (ZPQ.EQ.’Z') THEN
14o READ(14,840)NZP1
150 D0 180 I=1,NZP1,1
160 READ(14,830)ZPPH1(I)
17o READ(14,845)ZPDP1(I)
180 CONTINUE
19o READ(14,840)NZP2
200 DO 230 I=1,NZP2,1
210 READ(14,830)ZPPH2(I)
22o READ(14,845)ZPDP2(I)
230 CONTINUE
c
C
240 IF (ZPPH1(1).LE.ZPPH2(1))THEN
250 SPHL=ZPPH2(1)
260 ELSE
27o SPHL=ZPPH1(1)

FDATAINPUT Local Symbols

Name

TEMP.

FLDIR .
CONCL .

ZPDPZ

ZPPHZ .

ZPDPl
ZPPHl

Source Line

280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460

CCC

END IF
IF (ZPPH1(NZP1).GE.ZPPH2(NZP2))THEN
FPHL=ZPPH2(NZP2)

ELSE

152

FPHL=ZPPH1(NZP1)
END IF
READ(14,830)SPH
READ(14,830)FPH
READ(14,835)PHSS

END IF

READ(14, 850)AHM

READ(14, 850)AHP (1)

READ(14, 850)AHP (2)

IF (ZPQ.NE.’P'.AND.SPH.LT.SPHL)THEN
SPH=SPHL

ELSE IF (ZPQ.NE.’P’.AND.FPH.GT.FPHL)THEN
FPH=FPHL

END IF

READ(14,855)FLDIR

 

800
805
810
815
820
825
830
835
840
845
850
855

998
999

FORMAT
FORMAT
FORMAT
FORMAT

(F4.

(F4
(F7

(F7.

FORMAT (Al)

FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT

RETURN
END

(F5.
(F5.
(F5.

(12)

1)
.3)
.5)
1)

(F4.1)
(E10.2)

(A7)

Class

. param
. param

param
param

. param
. param
. param

FORMAT ING READ STATEMENTS----

Type Size Offset
0006
000a
000e
0012
0016
001a

001e

153

FDATAINPUT Local Symbols

Name Class Type Size Offset
NZP2. . param 0022
NZPl. . param 0026
ZPQ . . . param 002a
PHSS. . param 002e
FPH . . . param 0032
SPH . . param 0036
AHM . . . param 003a
AHP . . param 003e
PHCZI param 0042
APR . param 0046
N . . . param 004a
I . . local INTEGER*4 4 0002
FPHL. local REAL*4 4 0006
SPHL. local REAL*4 4 000a
Global Symbols

Name Class Type Size Offset
FDATAINPUT . . FSUBRT *** *** 0000

Code size = 04a1 (1185)
Data size = 00f7 (247)
Bss size = 000e (14)

No errors detected

Linef

HrAPJH
Lunawwauaa) ~Joun¢>u> eova

H
b

15

154

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line
SUBROUTINE CALCPZC (V, APR, PHCZI, TAH, SPH,
& FPH, PHSS, WT, PH, CONCL, WOO, WOT, WTT, FLDIR,
& TEMP)

CCCCC REV. 06-22-92

 

 

 

 

CCC SUBPROGRAM TO CALCULATE
C OVERALL STABILITY RATIO USING
C POINT-OF-ZERO-CHARGE DATA

IMPLICIT NONE
CHARACTER FLDIR*7
INTEGER L, K, ONE, TWO, IPHC, IWIDTH

MAL*8 WT, WOO, WOT, WTT, OOWL Az ,AZN,AZP
REAL N, APR, PHCZI, SPH, FPH, PHSS, PH, CONCL,
REAL HOA, HOR, APRC, TEMPK, v, OON
REAL CPH, PSI, RPHC, DELTPH, TAH, KRL, TEMP,
DIMENSION PH(200), WT(200), APR(2), PHCZI(2),
DIMENSION PSI(2), APRC(2)
DIMENSION WOO(200),WOT(200),WTT(200),TAH(2:4)

CCCCC OOWT=ONE OVER WT

CCCCC CPH=CURRENT PH

CCCCC RPHC=REAL VARIABLE PH COUNTER(FOR DO LOOP)
CCCCC IPHC=INTEGER VARIABLE PH COUNTER(FOR DO LOOP)
CCCCC PSI=SURFACE POTENTIAL CALCULATED FROM

CCCCC POINT-OF-ZERO-CHARGE (V)
CCCCC HOA=MINIMUM PARTICLE SEPERATION FOR ATTRACTIVE
CCCCC TERMS(M)

CCCCC HOR=MINIMUM SEPERATION FOR REPULSIVE TERMS(M)
CCCCC TEMPK=TEMPERATURE OF SYSTEM IN DEGREES KELVIN
CCCCC IWIDTH=WIDTH OF INTERAGER K (1 DIGIT,2 DIGITS,

CCCCC ETC.)
CCCCC DELTPH=CHANGE IN PH FROM FINISHING PH AND
CCCCC STARTING PH

CCCCC KRL=REAL VARIABLE REPULSION OF VARIABLE K
CCCCC K=INTEGER VARIABLE USED AS A COUNTER FOR DO LOOP
CCCCC WHICH CALCULATES OVERALL STABILITY AT EACH
CCCCC SPECIFIED PH

CCCCC L=INTEGER USED AS COUNTER.FOR VARIOUS DO LOOPS
CCCCC ONE=INTEGER VARIABLE EQUAL TO ONE

CCCCC TWO=INTEGER VARIABLE EQUAL TO TWO

CCCCC AZ=VARIABLE REPRESENTING ALMOST ZERO (1 . 0E-309)
CCCCC AZP=POSITIVE VALUE OF AZ USED TO PREVENT AN
CCCCC INVERSE FROM GOING TO INFINITY WHICH CAUSES
CCCCC A MATH OVERFLOW ERROR RESULTING IN PROGRAM
CCCCC TERMINATION

CCCCC AZN=NEGATIVE VALUE OF AZ USED AS AZP IS

155

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(PHCZI (L) 'CPH)

CCCCC APRC=ATOMIC PARTICLE RADIUS CUBED

CCCCC OON=ONE OVER N

CCCCC WKO=SUBROUTINE TO CALCULATE W VALUES IF K IS 1
CCCCC DIGIT IN LENGTH

CCCCC WKTW=SUBROUTINE CALCULATING W VALUES IF K IS 2
CCCCC DIGITS LONG

CCCCC WKTH=SUBROUTINE CALCULATING W VALUES IF K IS 3
CCCCC DIGITS IN LENGTH

1 0 TEMPK=TEMP+273 . 2

20 ONE=1

30 TWO=2

CCC CALCULATING VALUES FOR

C AZP,AZN

40 AZ=1 . 0E-25

50 DO 70 K=l,11,l

60 AZ=AZ/1 . 0E25

70 CONTINUE

80 AZP=AZ/l.0E9

90 AZN=-1 . 0 *AZP

CC CONVERTING PH COUNTER TO

C INTEGER VARIABLE

100 DELTPH = FPH-SPH

110 IF (PHSS.EQ.0.0 .OR. DELTPH.EQ.0.0)THEN

120 IPHC=1

130 ELSE

140 RPHC = (FPH-SPH) /PHSS

150 IPHC = NINT(RPHC)

160 IPHC = IPHC + 1

170 END IF

CC CALCULATING N FROM V
180 APRC(1) = APR(1)**3
190 APRC(Z) = APR(2)**3
200 OON = ((APRC(1))-(V*APRC(1)))/(V*APRC(2))

210 OON = OON + 1.00
220 N = 1.00/OON

CC INITIALIZING CURRENT PH -------
230 CPH = SPH
CC CALCULATING OVERALL STABILITY
C RATIO FOR SPECIFIED PH RANGE

C & STEP SIZE
240 D0 530 K=1, IPHC,1
250 KRL=REAL(K)

260 IWIDTH=INT (LOG10 (KRL) +1)

C CALCULATING POTENTIAL,PSI,FOR
C THE TWO DIFFERENT PARTICES
C FOR CURRENT PH
270 DO 290 L=1,2,1
280 PSI(L)=(8.6205E-5)*(TEMPK)*(2.3026)*

110
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Source Line

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

29o CONTINUE

C SETTING MINIMUM PARTICLE

C SURFACE

C SEPERATION FOR VA & VR

C CALCULATIONS

300 HOR = 1.08-10

310 HOA = 0.0

CC FINDING VARIOUS (INVERSE)

C PROBABILITIES OF PARTICLE

C COLLISION & ADHESION FOR

C COLLISION OF TWO PARTICLES

C OF TYPE #1

320 IF(IWIDTH.EQ.1)THEN

330 CALL WKO(K, WOO, WOT, WTT, APR, TAH, PSI,
& CONCL, HOA, HOR, CPH, FLDIR, TEMPK)

34o ELSE IF(IWIDTH.EQ.2)THEN

350 CALL WKTW(K, woo, WOT, WTT, APR, TAH, PSI,
& CONCL, HOA, HOR, CPH, FLDIR, TEMPK)

360 ELSE IF(IWIDTH.EQ.3)THEN

37o CALL WKTH(K, WOO, WOT, WTT, APR, TAH, PSI,
& CONCL, HOA, HOR, CPH, FLDIR, TEMPK)

380 END IF

CC FINDING THE OVERALL STABILITY

C RATIO AT CURRENT PH

C MAKING SURE INVERSES WILL NOT

C GO TO INFINITY so A.MATH

C OVERFLOW ERROR DOES NOT

c RESULT IN PROGRAM

C TERMINATION

39o IF(WOO(K).LE.A2P .AND. WOO(K).GE.AZN)THEN

400 WT(K)=WOO(K)

410 ELSE IF(WOT(K).LE.AZP .AND. WOT(K).GE.AZN)

THEN
420 WT(K)=WOT(K)
430 ELSE IF(WTT(K).LE.A2P .AND. WTT(K).GE.AZN)

THEN

 

ACTUALLY CALCULATING OVERALL

 

 

STABILITY

OOWT=OOWT+((1.0-N)*(1.0-N)/WTT(K))
OOWT=OOWT+(2.0*N*(1.0-N)/WOT(K))

440 WT(K)=WTT(K)

C

C

450 ELSE

460 OOWT = (N*N/WOO(K))
470

480

490 WT(K)=1.0/OOWT

500 END IF

Line#
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132

133
134

CALCPZC
Name

TEMP.
FLDIR .
WTT .
WOT .
WOO . .
CONCL .
PH. .
WT. .
PHSS.
FPH .
SPH .
TAH .
PHCZI
APR . .
V . . .
TEMPK .
DELTPH.
OOWT. .
IWIDTH.
K . .
L .
N .
HOA
CPH
AZ.
ONE .
IPHC.
.APRC. .
KRL . .
HOR,,

157

 

 

 

 

 

 

 

 

Source Line
CC SETTING COORESPONDING PH VALUE
C FOR WT (K)
510 PH(K)=CPH
CC SETTING NEW CURRENT PH
C VALUE
520 CPH = CPH + PHSS
530 CONTINUE
CC RETURNING WT & PH VALUES TO
C MAIN PROGRAM ----- CCCCCCCC
998 RETURN
999 END
Local Symbols
Class Type Size Offset
. . param 0006
. . param 000a
. . param 000e
. . . param 0012
. . . param 0016
. . param 001a
. . param 001e
. . param 0022
. . . . param 0026
. . . . param 002a
. . . . param 002e
. . . . param 0032
. . . . param 0036
. . . . param 003a
. . . . param 003e
. . . local REAL*4 4 0000
. . . local REAL*4 4 0004
. . . local REAL*8 8 0008
. . local INTEGER*4 4 0010
. . local INTEGER*4 4 0014
. . local INTEGER*4 4 0018
. . local REAL*4 4 001C
. . local REAL*4 4 0020
. . local REAL*4 4 0024
. local REAL*8 8 0028
. local INTEGER*4 4 0030
. local INTEGER*4 4 0034
. local REAL*4 8 0038
. local REAL*4 4 0040
local REAL*4 4 0044

158
CALCPZC Local Symbols

Name Class Type Size Offset
AZN . . . . . . local REAL*8 8 0048
AZP . . . . . . local REAL*8 8 0050
OON . . . . . . . . . . . local REAL*4 4 0058
PSI . . . . . . . . . . . local REAL*4 8 005C
RPHC. . . . . . local REAL*4 4 0064
TWO . . . . . . local INTEGER*4 4 0068

Global Symbols

Name Class Type Size Offset
CALCPZC. . . . . . . . . . FSUBRT *** *** 0000
WKO . . . . . . . . . . . extern *** *** ***
WKTH. . . . . . . . . . . extern *** *** ***
WKTW. . . . . . . . . . . extern *** *** ***
Code size = 082d (2093)

Data size = 003C (60)

853 size = 006C (108)

No errors detected

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Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line

& ZPPHZ,
& NZPl, N2P2, woo, WOT, WTT, FLDIR, TEMP)

SUBROUTINE CALCZP (V, APR, TAH, ZPDPl,
ZPDP2,

ZPPHl,
SPH, FPH, PHSS, WT, PH, CONCL,

ccccc REV. 06-22-92

CCC --------------------- SUBPROGRAM To CALCULATE

c ------------------------- OVERALL STABILITY RATIO
C---------------- --------- USING ZETA POTENTIAL DATA--

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

IMPLICIT NONE

CHARACTER FLDIR*7

INTEGER ONE,TWO,IPHC,IWIDTH

REAL N, APR, ZPDPl, ZPPHl, ZPDP2,
REAL FPH, PHSS, PH, TEMP, TEMPK
REAL CPH, RPHC, DELTPH, TAH, KRL, POT, CONCL,
REAL*8 WOO,WOT,WTT,OOWT,WT,AZ,AZP,AZN
DIMENSION PH(200),APR(2),POT(2),TAH(2:4)
DIMENSION WT(200),WOO(200),WOT(2oo),WTT(2oo)
DIMENSION ZPDP1(200), ZPPH1(200), ZPDP2(200),
DIMENSION ZPPH2(200)

INTEGER K,NZP1,NZP2

REAL ZPD,APRC,V,OON

REAL DELTA,HOA,HOR

DIMENSION ZPD(2),APRC(2)

DIMENSION DELTA(2)

ZPPH2, SPH,

OOWT=ONE OVER WT
=REAL FCN. USED IN FCN.
WOO,WOT,WTT
CPH=CURRENT PH

TEMPK=SYSTEM TEMPREATURE IN DEGREES KELVIN
DELTA=DISTANCE FROM PARTICLE SURFACE To STERN

LAYER(M)

RPHC=REAL VARIABLE PH COUNTER(FOR Do LOOP)
IPHC=INTEGER VARIABLE PH COUNTER(FOR Do LOOP)

POT=ZETA POTENTIAL FOR PARTICLES AT CURRENT PH
ZPD=ZETA POTENTIAL DATA AT CPH FOR

PARTICLE(ARRAY VARIABLE)
DELTPH=CHANGE IN PH FROM FINISHING PH To
STARTING PH
K=INTEGER VARIABLE USED AS COUNTER FOR LOOP To
CALCULATE STABILITY RATIO FOR EACH SPECIFIED

PH

KRL=REAL REPRESENTATION OF VARIABLE K
IWIDTH=WIDTH OF INTEGER K (EX: 1 DIGIT, 2

DIGITS,ETC.)

SUBPROGRAM TO FIND

Line#

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160

 

 

 

Source Line

CCCCC ONE=INTEGER VARIABLE EQUAL TO ONE

CCCCC TWO=INTEGER VARIABLE EQUAL TO TWO

CCCCC HOA=MINIMUM PARTICLE SEPERATION FOR ATTRACTIVE
CCCCC TERM (M)

CCCCC HOR=MINIMUM SEPARATION FOR REPULSIVE TERMS (M)
CCCCC.AZ=VARIABLEIREPRESENTINGuALMOST ZERO (1.0E-309)
CCCCC AZP=POSITIVE VALUE OF AZ USED TO PREVENT AN
CCCCC INVERSE FROM GOING TO INFINITY WHICH WILL
CCCCC CAUSE A MATH OVERFLOW ERROR RESULTING IN
CCCCC PROGRAM TERMINATION

CCCCC AZN=NEGATIVE VALUE OF AZ USED AS AZP IS USED
CCCCC WKO=SUBROUTINE TO CALCULATE STABILITY IF K IS
CCCCC ONE DIGIT WIDE

CCCCC WKTW=SUBROUTINE TO CALCULATE STABILITY IF K IS
CCCCC TWO DIGITS WIDE

CCCCC WKTH=SUBROUTINE TO CALCULATE STABILITY IF K IS
CCCCC THREE DIGITS

10 TEMPK=TEMP+273.2

20 DELTA(1)=0.50E-9

30 DELTA(2)=0.50E-9

40 ONE=1

50 TWO=2

CC — CALCULATING VALUES FOR AZP AND
C ----- — -- ----- AZN — —

60 AZ=1.0E-25

70 Do 90 K=1,11,1

80 AZ=AZ/1.0E25

9O CONTINUE

100 AZP=AZ/1.0E9

110 AZN=-1.0*AZP

CC ---------------------- CONVERTING PH COUNTER T0

C --------------------------- INTEGERVARIABLE ---------
120 DELTPH = FPH-SPH

130 IF (PHSS.EQ.0.0 .OR. DELTPH.EQ.0.0) THEN

140 IPHC=1

150 ELSE

160 RPHC = (FPH-SPH)/PHSS

170 IPHC = NINT(RPHC)

180 IPHC = IPHC+1

190 END IF

CC --------------------- CALCULATING N FROM V ----------
200 APRC(1) = APR(1)**3

210 APRC(Z) = APR(2)**3

220 OON = ((APRC(1))-(V*APRC(1)))/(V*APRC(2))

230 OON - OON + 1.00

Line#

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161

 

 

 

 

Source Line
240 N = 1.00/OON
CC ---------------------- INITIALIZING CURRENT PH -------
250 CPH = SPH
CC ---------------------- CALCULATING OVERALL STABILITY
C ------------------------- RATIO FOR SPECIFIED PH RANGE
C & STEP SIZE
260 D0 550 K=1,IPHC,1
27o KRL=REAL(K)
280 IWIDTH=INT(LOG10(KRL)+1)
C ----------------------- GETTING ZETA POTENTIAL VALUES
C ---------------------------- FOR SPECIFIED PH VALUES--
290 CALL INTERP(ZPDP1, ZPPHl, ZPPH2, ZPDP2, CPH,
& NZPl, NZP2, ZPD)
C ----------------------- CHANGING UNITS OF V FROM mV---
300 POT(1)=ZPD(1)*1. 0E-3
310 POT(2)= ZPD(2)*1. OE- 3
320 HOA = DELTA(1)+DELTA(2)
330 HOR = 1.0E-10
CC ---------------------- FINDING VARIOUS (INVERSE)
C ------------------------- PROBABILITIES OF PARTICLE
C COLLISION & ADHESION --------
34o IF(IWIDTH.EQ.1)THEN
350 CALL WKO(K, WOO, WOT, WTT, APR, TAH, POT,
S: CONCL, HOA, HOR, CPH, FLDIR, TEMPK)
360 ELSE IF(IWIDTH.EQ.2)THEN
37o CALL WKTW(K, WOO, WOT, WTT, APR, TAH, POT,
& CONCL, HOA, HOR, CPH, FLDIR, TEMPK)
380 ELSE IF(IWIDTH.EQ.3)THEN
390 CALL WKTH(K, WOO, WOT, WTT, APR, TAH, POT,
& CONCL, HOA, HOR, CPH, FLDIR, TEMPK)
400 END IF
CC ---------------------- FINDING THE INVERSE OF THE
C ------------------------- OVERALL STABILITY RATIO AT
C ------------------------- CURRENTPH -----------------
C ----------------------- ENSURING INVERSES WILL NOT GO
C ------------------------- TO INFINITY, CAUSE A MATH
C—- ------------ OVERFLOW ERROR, AND RESULT
C ------------------------- IN IN PROGRAM TERMINATION--
410 IF(WOO(K) .LE.AZP .AND. WOO(K) .GE.AZN)THEN
420 WT(K)=AZP
430 ELSE IF(WOT(K).LE.AZP .AND. WOT(K).GE.AZN)THEN

162

Line# Source Line

127 440 WT(K)=AZP

128 450 ELSE IF(WTT(K).LE.AZP .AND. WTT(K).GE.AZN)THEN

129 460 WT(K)=AZP

130 470 ELSE

131 480 OOWT = (N*N/WOO(K))

132 490 OOWT = OOWT+((1.0-N)*(1.0-N)/WTT(K))

133 500 OOWT = OOWT+(2.0*N*(1.0-N)/WOT(K))

134 510 WT(K)=1.0/OOWT

135 520 END IF

136

137 CC ---------------------- SETTING COORESPONDING PH VALUE

C -------------------------- FOR WT(I) -----

138 530 PH(K)=CPH

139

140 CC ---------------------- SETTING NEW CURRENT PH VALUE--

141 540 CPH = CPH + PHSS

142 550 CONTINUE

143

144

145 CC ---------------------- RETURNING WT & PH VALUES TO

C -------------------------- MAINPROGRAM --------------

146 998 RETURN

147 999 END
CALCZP Local Symbols
Name Class Type Offset
TEMP. . . . . . . . . . . param 0006
FLDIR . . . . . . . . . . param 000a
WTT . . . . . . . . . . . param OOOe
WOT . . . . . . . . . . param 0012
WOO . . . . . . . . . . param 0016
NZPZ. . . . . . . . . . . param 001a
NZP1. . . . . . . . . . . param 001e
CONCL . . . . . . . . . . param 0022
PH. . . . . . . . . . . . param 0026
WT. . . . . . . . . . . . param 002a
PHSS. . . . . . . . . . . param 002e
FPH . . . . . . . . . . . param 0032
SPH . . . . . . . . . . . param 0036
ZPDPZ . . . . . . . . . . param 003a
ZPPHZ . . . . . . . . . . param 003e
ZPPHI . . . . . . . . . . param 0042
ZPDPl . . . . . . . . . . param 0046
TAH . . . . . . . . . . . param 004a
APR . . . . . . . . . . . param 004e
V’. . . . . . . . . . . . param 0052
TEMPK . . . . . . . . . . local REAL*4 0000

CALCZP
Name

DELTPH.
OOWT. .
IWIDTH.
K . . .
N . . .
HOA . .
AZ. . .
CPH . .
ONE . .
IPHC. .
APRC. .
HOR . .
AZN . .
KRL . .
DELTA .
AZP . .
OON . .
RPHC. .
ZPD . .
POT . .
TWO . .

Local

Symbols

163

Class

local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Type

REAL*4
REAL*8
INTEGER*4
INTEGER*4
REAL*4
REAL*4
REAL*8
REAL*4
INTEGER*4
INTEGER*4
REAL*4
REAL*4
REAL*8
REAL*4
REAL*4
REAL*8
REAL*4
REAL*4
REAL*4
REAL*4
INTEGER*4

Size

boomSP-oooobooc-oopbnoobpc-hmn

Offset

0004
0008
0010
0014
0018
001C
0020
0028
002C
0030
0034
003C
0040
0048
004C
0054
005C
0060
0064
006C
0074

Line}

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164

Source Line

CCCCC

& CPH, NZPl,

SUBROUTINE INTERP(ZPDP1,
NZP2, ZPD)

ZPPHl, ZPPH2, ZPDP2,

REV. 03-05-92

CCC --------------------- SUBPROGRAM TO CALCULATE
C ------------------------- OVERALL STABILITY RATIO
C ------------------------- USING ZETA POTENTIAL DATA---

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

CCCCC
CCCCC
CCCCC

IMPLICIT NONE

REAL ZPDP1,ZPPH1,ZPPH2,ZPDP2
REAL CPH

DIMENSION ZPDP1(200),
DIMENSION ZPPH2(200)
INTEGER M,NZPI,NZP2
REAL ZPD, ZPDN, ZPDD, ZPGT, ZPLT, PHGT, PHLT

REAL PZPGT, PZPLT, PGTDIF, PLTDIF, CGTDIF, CLTDIF
REAL PPHGT, PPHLT

DIMENSION ZPD(2)

ZPPH1(200), ZPDP2(200),

ZPDN=NUMERATOR TERM USED TO CALCULATE ZPD

ZPDD=DENOMENATOR TERM USED TO CALCULATE ZPD

PPHGT=PRESENT/PERMANENT PH VALUE GREATER THAN
CPH (i.e.PH PRESENTLY NEAREST TO CPH, BUT
STILL GREATER THAN CPH)

PPHGT=PRESENTIPERMANENT PH VALUE LESS THAN CPH
(i.e.PH PRESENTLY NEAREST TO CPH, BUT
STILL LESS THAN CPH)

PZPGT=PRESENTIPERMANENT ZETA POTENTIAL VALUE
COORESPONDING TO PPHGT

PZPLT=PRESENT/PERMANENT ZETA POTENTIAL VALUE
COORESPONDING TO PPHLT

CCCCC PGTDIF=PRESENT/ PERMANENT GREATER THAN DIFFERENCE

BETWEEN PGTPH AND CPH
PLTDIF=PRESENTIPERMANENT LESS THAN DIFFERENCE
BETWEEN PLTPH AND CPH

CCCCC CGTDIF=CURRENT ( i . e . THIS ITERATION) GREATER THAN

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

DIFFERENCE BETWEEN CPH AND THE CURRENT
ZPPH VALUE IF IT Is GREATER THAN CPH(THIS

ITERATION)

CLTDIF=CURRENT(i.e.THIS ITERATION) LESS THAN
DIFFERENCE BETWEEN CPH AND THE CURRENT
ZPPH VALUE IF IT IS LESS THAN CPH(THIS
ITERATION)

PHGT=PH GREATER THAN (CPH AND NEAREST To IT)

PHLT=PH LESS THAN (CPH AND NEAREST To IT)

CCCCC ZPGT=ZETA.POTENTIAL‘VALUE COORESPONDING TO PHGT

Line#

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Source Line
CCCCC ZPLT=ZETA.POTENTIAL‘VALUE COORESPONDING'TO ZPLT

CCCCC M=INTEGER VARIABLE USED AS COUNTER FOR VARIOUS
CCCCC DO LOOPS

 

 

 

 

 

CC ---------------------- INTERPOLATING Z.P. DATA To GET
c -------------------------- VALUESFOR ----------------
C ------------------------ CURRENT PH (IF NEED BE) -----
10 PLTDIF=2o.o

20 PGTDIF=2o.o

30 Do 220 M=1,NZP1,1

CC ---------------------- IF CPH= a ZPPH VALUE:

CC ------------------------ RETURNING THAT ZPAS THE

C DESIRED ZP VALUE

40 IF (ZPPH1(M) .EQ. CPH) THEN

so ZPD(1) = ZPDP1(M)

60 GOTo 300

CC ---------------------- IF CPH.NE. a ZPPH VALUE:THEN
cc ------------------------ MUST INTERPOLATE To GET A

c ------------------------- ZPD FOR THIS CPH -----------
c ----------------------- TRYING To FIND THE NEAREST PH
C ------------------------ To CPH THAT Is LESS THAN CPH-
70 ELSE IF (ZPPH1(M) .LT. CPH) THEN

30 CLTDIF = CPH-ZPPH1(M)

90 IF (CLTDIF .LT. PLTDIF) THEN

100 PPHLT = ZPPH1(M)

110 PLTDIF = CLTDIF

120 PZPLT = ZPDP1(M)

13o END IF

C ----------------------- TRYING To FIND THE NEAREST PH
c ------------------------- To CPH THAT IS GREATER THAN
C —"PH

140 ELSE IF (ZPPH1(M) .GT. CPH) THEN

150 CGTDIF = ZPPH1(M) - CPH

160 IF (CGTDIF .LT. PGTDIF) THEN

17o PPHGT = ZPPH1(M)

180 PGTDIF = CGTDIF

190 PZPGT = ZPDP1(M)

200 END IF

210 END IF

220 CONTINUE

c ----------------------- INTERPOLATING WITH NEAREST

c ----------------------- VALUES

230 PHLT = PPHLT

24o ZPLT = PZPLT

250 PHGT PPHGT

Line}

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166

 

 

 

 

Source Line

260 ZPGT = PZPGT

27o ZPDN = ZPLT*(CPH-PHGT) + ZPGT*(PHLT-CPH)
280 ZPDD = PHLT - PHGT

290 ZPD(1) = ZPDN/ZPDD

CC— -- ---------- INTERPOLATING Z.P. DATA TO GET
C -------------------------- VALUESFOR ----------------
c ------------------------ CURRENT PH (IF NEED BE) ------
300 PLTDIF=20 . 0

310 PGTDIF=20 . 0

320 Do 510 M=1,NZP2,1

CC ---------------------- IF CPH= a ZPPH VALUE:

CC ------------------------ RETURNING THAT ZP AS THE
C ------------------------- DESIRED ZP VALUE -----------
330 IF (ZPPH2(M) .EQ. CPH) THEN

34o ZPD(2) = ZPDP2(M)

350 GOTO 998

CC ---------------------- IF CPH.NE. a ZPPH VALUE: THEN
CC ------------------------ MUST INTERPOLATE TO GET A
C ------------------------- ZPD FOR THIS CPH ------------
C ----------------------- TRYING TO FIND THE NEAREST PH
C ------------------------ TO CPH THAT IS LESS THAN CPH-
360 ELSE IF (ZPPH2(M) .LT. CPH) THEN

37o CLTDIF = CPH-ZPPH2(M)

380 IF (CLTDIF .LT. PLTDIF) THEN

390 PPHLT = ZPPH2 (M)

400 PLTDIF = CLTDIF

410 PZPLT = ZPDP2(M)

420 END IF

C ----------------------- TRYING TO FIND THE NEAREST PH
C -------------------------- TO CPH THAT IS GREATER THAN
C —CPH

430 ELSE IF (ZPPH2 (M) .GT. CPH) THEN

440 CGTDIF = ZPPH2 (M) - CPH

450 IF (CGTDIF .LT. PGTDIF) THEN

460 PPHGT = ZPPH2(M)

470 PGTDIF = CGTDIF

480 PZPGT = ZPDP2(M)

490 END IF

500 END IF

510 CONTINUE

C ----------------------- INTERPOLATING WITH NEAREST
C -------------------------- VALUES

520 PHLT = PPHLT

530 ZPLT = PZPLT

540 PHGT = PPHGT

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Line}

280
281
282
283
284
285

286
287

INTERP
Name

ZPD .
NZP2.
NZP1.
CPH .
ZPDP2
ZPPH2
ZPPHl
ZPDP1
PPHGT
PLTDIF
ZPGT.
PPHLT
ZPLT.
M . .
PZPGT
PZPLT
CGTDIF
ZPDD.
PHGT.
CLTDIF
PHLT.
ZPDN.
PGTDIF

Global Symbols

Name

CALCZP

INTERP.

WKO .
WKTH.
WKTW.

Source Line

550 ZPGT = PZPGT
560 ZPDN = ZPLT*(CPH-PHGT) + ZPGT*(PHLT-CPH)
570 ZPDD = PHLT - PHGT
580 ZPD(2) = ZPDN/ZPDD
CC ---------------------- RETURNING WT & PH VALUES TO
C -------------------------- MAIN PROGRAM -----
998 RETURN
999 END
Local Symbols

Class Type Size Offset
. . . . . . . . . param 0006
. . . . . . . . . param 000a
. . . . . . . . . param 000e
. . . . . . . . . param 0012
. . . . . . . . . param 0016
. . . . . . . . . param 001a
. . . . . . . . param 001e
. . . . . . . . . param 0022
. . . . . . . . . local REAL*4 4 0078
. . . . . . . . . local REAL*4 4 007c
. . . . . . . . . local REAL*4 4 0080
. . . . . . . . . local REAL*4 4 0084
. . . . . . . . . local REAL*4 4 0088
. . . . . . . . . local INTEGER 4 008c
. . . . . . . . . local REAL*4 4 0090
. . . . . . . . . local REAL*4 4 0094
. . . . . . . . . local REAL*4 4 0098
. . . . . . . . . local REAL*4 4 009C
. . . . . . . . . local REAL*4 4 00a0
. . . . . . . . . local REAL*4 4 00a4
. . . . . . . . . local REAL*4 4 00a8
. . . . . . . . . local REAL*4 4 00ac
. . . . . . . . . local REAL*4 4 00b0

Class Type Size Offset
. . . . . . . . . FSUBRT *** *** 0000
. . . . . . . . . FSUBRT *** *** 079e
. . . . . . . . . extern *** *** ***
. . . . . . . . . extern *** *** ***
. . . . . . . . . extern *** *** ***

167

168

Code size
Data size
Bss size

0ec7 (3783)
0044 (68)
00b4 (180)

No errors detected

Line#

HOKDGQQU‘IAUNH

H)-

169

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line

CCCC

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

10
20
30

CC----
C .....
C .....

C .....
C .....

40
50
60
70
80
90
100

110

SUBROUTINE WKO(K, WOO, WOT, WTT, APR, TAH,

& PSI, CONCL, HOA, HOR, CPH, FLDIR, TEMPK)

REV. 05-04-92

IMPLICIT NONE

CHARACTER FLNME*28,FLDIR*7

INTEGER ONE,TWO,K,POS,KI,L

REAL APR,TAH,PSI,CONCL,HOA,HOR,CPH,x,TEMPK
REAL*8 WOO,WOT,WTT,WCALC,VOO,VOT,VTT
DIMENSION X(250), VOO(250), VOT(250),
DIMENSION VTT(250), TAH(2:4), APR(2), PSI(2)
DIMENSION WOO(200), WOT(200), WTT(200)

ONE=INTEGER VARIABLE EQUAL To 1
TWO=INTEGER VARIABLE EQUAL To 2
WCALC=CALCULATED W VALUE FROM SUBROUTINE WC
KI=INTEGER VARIABLE REPRESENTATION OF K USED
To MAKE A CHARACTER VARIABLE REPRESENTATION
OF K FOR FILENAME
=SEPARATION DISTANCE (ARRAY) (M)
VOO,VOT,VTT=POTENTIAL FOR A GIVEN PARTICLE
INTERACTION AT COORESPONDING
SEPERATION DISTANCE x (ARRAY)

ONE=1
TWO=2
KI=K

.................. FINDING VARIOUS (INVERSE)
-------------------- PROBABILITIES OF PARTICLE
-------------------- COLLISION & ADHESION------

------------------ FOR COLLISION OF TWO
--------------------- PARTICLES OF TYPE #1-----
FLNME(1:14)='C:\JK\LL\DATA\’
FLNME(15:21)=FLDIR

FLNME(22:22)=’\’

FLNME(23:23)=’V'
FLNME(24:24)=CHAR(MOD(KI,10)+ICHAR(’0’))

FLNME(25:28)=’.DAT’

CALL WC(WCALC, APR, TAH, PSI, ONE, ONE, CONCL,

& HOA, HOR, CPH, voo,VOT,VTT, x, FLDIR, TEMPK)

WOO(K)=WCALC

170

Line} Source Line

42 C ----------------------- FOR COLLISION OF PARTICLES 1
43 C ------------------------ a 2 ------------------------

44 120 CALL WC(WCALC, APR, TAH, PSI, ONE, TWO, CONCL,
45 & HOA, HOR, CPH, voo,VOT,VTT, x, FLDIR, TEMPK)

46 130 WOT(K)=WCALC

47

80 c ----------------------- FOR COLLISION OF TWO

49 C ------------------------- PARTICLES OF TYPE #2 -----

50 140 CALL WC(WCALC, APR, TAH, PSI, TWO, TWO, CONCL,
51 & HOA, HOR, CPH, voo,VOT,VTT, x, FLDIR, TEMPK)

52 150 WTT(K)=WCALC

53

54 CC ---------------------- WRITING V DATA To FILE -----

55 160 OPEN(15,FILE=FLNME,STATUS='NEW’)

56 170 WRITE(15,*)'CPH,APR(1),APR(2)’

57 180 WRITE(15,*)CPH,APR(1),APR(2)

58 190 WRITE(15,*)’PSI(1),PSI(2),CONCL,TAH’
59 200 WRITE(15,*)PSI(1),PSI(2),CONCL,TAH
60 210 WRITE(15,900)

61 220 WRITE(15,910)

62 230 Do 300 L=1,240,1

63 240 IF(X(L).NE.0.0)THEN
64 250 WRITE(15,920)X(L),VOO(L),VOT(L),VTT(L)
65 260 END IF

66 270 CONTINUE
69 280 CLOSE(IS)

7o

71 CCC --------------------- FORMAT STATEMENTS -----------
72 900 FORMAT (5X,’SEP’,12X,’V11',12X,

73 & 1X,’V12’,12X,

74 & 1X,’V22’)

75 910 FORMAT (5x,'---',12x,'---',12x,

76 & 1x,'---',12x,

77 & 1x,'---')

78 920 FORMAT (1X,E12.4,1X,’,’,1X,E12.4,1X,',',
79 & 1X,E12.4,1X,’,',

so & 1X,E12.4,1X)

81

82 998 RETURN
83 999 END
84

Name

TEMPK
FLDIR
CPH .
HOR .
HOA .
CONCL
PSI .
TAH
APR
WTT
WOT
WOO
K .
X .
L .
KI. .
ONE .
WCALC
POS .
FLNME
TWO .
VOO .
VOT .
VTT .

Local

Symbols

Global Symbols

Name

WC. .
WKTW.

Code size =
Data size =
Bss size =

NO errors

0456 (1118)
0089 (137)
003e (60)

detected

171

Class

param
param
param
param
param
param
param
param
param
param
param
param
param
local
local
local
local
local
local
local
local
local
local
local

Class

extern
FSUBRT

Type

REAL*4
INTEGER*4
INTEGER*4
INTEGER*4
REAL*8
INTEGER*4
CHAR*29
INTEGER*4
REAL*8
REAL*8
REAL*8

Type

***
***

Size

Size

***
***

Offset

0006
000a
000a
0012
0016
001a
001e
0022
0026
002a
002e
0032
0036
0000
0002
0006
000a
000e
0016
001a
0038
03e8
0bb8
1388

Offset

***
0000

Linef

HOKOQQO‘UIhUNH

H)-

172

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line

CCCC

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

10
20
30

CC----
C .....
C -----

C .....
C .....

40
50
60
70
80
90
100
110
120
130

140

SUBROUTINE WKTW(K, WOO, WOT, WTT, APR, TAH,

& PSI, CONCL, HOA, HOR, CPH, FLDIR, TEMPK)

REV. 05-04-92

IMPLICIT NONE

CHARACTER FLNME*29,FLDIR*7

INTEGER ONE,TWO,K,POS,KI,L

REAL APR,TAH,PSI,CONCL,HOA,HOR,CPH,X,TEMPK
REAL*8 WOO,WOT,WTT,WCALC,V00,VOT,VTT
DIMENSION X(250), VOO(250), VOT(250),
DIMENSION VTT(250), TAH(2:4), APR(2), PSI(2)
DIMENSION W00(200), WOT(200), WTT(200)

ONE=INTEGER VARIABLE EQUAL TO 1
TWO=INTEGER VARIABLE EQUAL TO 2
WCALC=CALCULATED W VALUE FROM SUBROUTINE WC
KI=INTEGER VARIABLE REPRESENTATION OF K USED
TO MAKE A CHARACTER VARIABLE REPRESENTATION
OF K FOR FILENAME
X=SEPARATION DISTANCE (ARRAY) (M)
VOO,VOT,VTT=POTENTIAL FOR A GIVEN PARTICLE
INTERACTION AT COORESPONDING
SEPERATION DISTANCE X (ARRAY)

ONE=1
TWO=2
KI=K

------------------ FINDING VARIOUS (INVERSE)
.................... PROBABILITIES OF PARTICLE
-------------------- COLLISION & ADHESION------

------------------ FOR COLLISION OF TWO
--------------------- PARTICLES OF TYPE #1-----
FLNME(1:14)=’C:\JK\LL\DATA\’
FLNME(15:21)=FLDIR

FLNME(22:22)=’\'

FLNME(23:23)=’V'

Do 110 POS=25,24,-1
FLNME(POS:POS)=CHAR(MOD(KI,10)+ICHAR(’0'))
KI=KI/10

CONTINUE

FLNME(26:29)=’.DAT’

CALL WC(WCALC, APR, TAH, PSI, ONE, ONE, CONCL,

& HOA, HOR, CPH, VOO,VOT,VTT, X, FLDIR, TEMPK)

W00(K)=WCALC

173

Line! Source Line

45 C ----------------------- FOR COLLISION 0F PARTICLES 1
C ------------------------ & 2 ------------------------
46 150 CALL WC(WCALC, APR, TAH, PSI, ONE, TWO, CONCL,
47 & HOA, HOR, CPH, VOO,VOT,VTT, x, FLDIR, TEMPK)
48 160 W0T(K)=WCALC
49
50 C ----------------------- FOR COLLISION OF TWO
C ------------------------- PARTICLES OF TYPE #2 -----
51 170 CALL WC(WCALC, APR, TAH, PSI, TWO, TWO, CONCL,
52 & HOA, HOR, CPH, VOO,VOT,VTT, x, FLDIR, TEMPK)
53 180 WTT(K)=WCALC
54
55 CC ---------------------- WRITING V DATA To FILE -----

56 190 OPEN(15,FILE=FLNME,STATUS=’NEW')

57 200 WRITE(15,*)’CPH,APR(1),APR(2)’

58 210 WRITE(15,*)CPH,APR(I),APR(2)

59 220 WRITE(15,*)'PSI(1),PSI(2),CONCL,TAH'
60 230 WRITE(15,*)PSI(1),PSI(2),CONCL,TAH
61 240 WRITE(15,900)

62 250 WRITE(15,910)

63 260 Do 300 L=1,240,1

64 270 IF(X(L).NE.0.0)THEN
65 280 WRITE(15,920)X(L),VOO(L),VOT(L),VTT(L)
66 290 END IF

67 300 CONTINUE
68 310 CLOSE(IS)

69

70 CCC --------------------- FORMAT STATEMENTS -----------
71 900 FORMAT (SX,’SEP’,12X,’V11',12X,

72 & 1x,'v12',12x,

73 & 1X,'V22’)

74 910 FORMAT (5x,'---',12x,'---',12x,

75 & 1x,'---',12x,

76 a 1x,'---')

77 920 FORMAT (1X,E12.4,1X,’,',1X,E12.4,1X,',',
78 & 1X,E12.4,1X,’,',

79 & 1x,E12.4,IX)

80

81 998 RETURN
82 999 END

174

WKTW Local Symbols

Name Class Type Size Offset
TEMPK . . . . . . . . . param 0006
FLDIR . . . . . . . . . param 000a
CPH . . . . . . . . . . param 000e
HOR . . . . . . . . . . param 0012
HOA . . . . . . . . . . param 0016
CONCL . . . . . . . . . param 001a
PSI . . . . . . . . . . param 001e
TAH . . . . . . . . . . param 0022
APR . . . . . . . . . . param 0026
WTT . . . . . . . . . . param 002a
WOT . . . . . . . . . . param 002e
WOO . . . . . . . . . . param 0032
K . . . . . . . . . . . param 0036
X . . . . . . . . . . . local REAL*4 1000 0000
L . . . . . . . . . . . local INTEGER*4 4 0002
XI. . . . . . . . . . . local INTEGER*4 4 0006
ONE . . . . . . . . . . local INTEGER*4 4 000a
WCALC . . . . . . . . . local REAL*8 8 000e
POS . . . . . . . . . . local INTEGER*4 4 0016
FLNME . . . . . . . . . local CHAR*29 29 001a
TWO . . . . . . . . . . local INTEGER*4 4 0038
V00 . . . . . . . . . . local REAL*8 2000 03e8
VOT . . . . . . . . . . local REAL*8 2000 0bb8
VTT . . . . . . . . . . local REAL*8 2000 1388
Global Symbols

Name Class Type Size Offset
WC. . . . . . . . . . . . extern *** *** ***
WKTW. . . . . . . . . . . FSUBRT *** *** 0000

Code size 045a (1118)

Data size = 0089 (137)
855 size = 003C (60)
No errors detected

Line!

HODmQGMhUNl-I'

Hra

12

14
15
16
17
18

19
20
21

22
23
24
25
26
27
28
29
30
31
32

33
34
35
36
37
38
39
40
41
42
43
44

175

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line

CCCC

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

10
20
30

CC----
C .....
C .....

C .....
C .....

40
50
60
70
80
90
100
110
120
130

140

SUBROUTINE WKTH(K, woo, WOT, WTT, APR, TAH,

6 PSI, CONCL, HOA, HOR, CPH, FLDIR, TEMPK)

REV. 05-04-92

IMPLICIT NONE

CHARACTER FLNME*30,FLDIR*7

INTEGER ONE,TWO,K,POS,KI,L

REAL APR,TAH,PSI,CONCL,HOA,HOR,CPH,x,TEMPK
REAL*8 W00,W0T,WTT,WCALC,V00,VOT,VTT
DIMENSION VOO(250), VOT(250), VTT(250), X(250)
DIMENSION TAH(2:4), APR(2), PSI(2)

DIMENSION W00(200), WOT(200), WTT(200)

ONE=INTEGER VARIABLE EQUAL TO 1

TWO=INTEGER VARIABLE EQUAL TO 2

WCALC=CALCULATED W VALUE FROM SUBROUTINE WC

KI=INTEGER VARIABLE REPRESENTATION OF K USED

TO MAKE A CHARACTER VARIABLE REPRESENTATION
OF K FOR FILENAME

X=SEPARATION DISTANCE (ARRAY) (M)

VOO,VOT,VTT=POTENTIAL FOR A GIVEN PARTICLE
INTERACTION AT COORESPONDING
SEPERATION DISTANCE X (ARRAY)

ONE=1
TWO=2
KI=K

------------------ FINDING VARIOUS (INVERSE)
-------------------- pROBABILITIES OF PARTICLE
-------------------- COLLISION 6 ADHESION------

------------------ FOR COLLISION OF TWO
-------------------- PARTICLES OF TYPE #1------
FLNME(1:14)=’C:\JK\LL\DATA\’
FLNME(15:21)=FLDIR

FLNME(22:22)=’V’

FLNME(23:23)=’\’

D0 110 POS=26,24,-1
FLNME(POS:POS)=CHAR(MOD(KI,10)+ICHAR('O’))
KI=KI/10

CONTINUE

FLNME(27:30)='.DAT’

CALL WC(WCALC, APR, TAH, PSI, ONE, ONE, CONCL,

6 HOA, HOR, CPH, VOO,VOT,VTT, x, FLDIR, TEMPK)

W00(K)=WCALC

176

Line# Source Line

45
46 C ----------------------- FOR COLLISION OF PARTICLES 1
C ------------------------ 6 2 ------------------------
47 150 CALL WC(WCALC, APR, TAH, PSI, ONE, TWO, CONCL,
48 6 HOA, HOR, CPH, VOO,VOT,VTT, x, FLDIR,TEMPK)
49 160 W0T(K)=WCALC
50
51 C ----------------------- FOR COLLISION OF TWO
0 ------------------------ PARTICLES OF TYPE #2 -------
52 170 CALL WC(WCALC, APR, TAH, PSI, TWO, TWO, CONCL,
53 6 HOA, HOR, CPH, VOO,VOT,VTT, x, FLDIR, TEMPK)
54 180 WTT(K)=WCALC
55
56 CC ---------------------- WRITING v DATA TO FILE ------

57 190 OPEN(15,FILE=FLNME,STATUS=’NEW’)

58 200 WRITE(15,*)’CPH,APR(1),APR(2)’

59 210 WRITE(15,*)CPH,APR(1),APR(2)

60 220 WRITE(15,*)’PSI(1),PSI(2),CONCL,TAH’
61 230 WRITE(15,*)PSI(1),PSI(2),CONCL,TAH
62 240 WRITE(15,900)

63 250 WRITE(15,910)

64 260 DO 300 L=1,240,1

65 270 IF(X(L).NE.0.0)THEN
66 280 WRITE(15,920)X(L),VOO(L),VOT(L),VTT(L)
67 290 END IF

68 300 CONTINUE
69 310 CLOSE(15)

70

71 CCC --------------------- FORMAT STATEMENTS ----------
72 900 FORMAT (5X,'SEP’,12X,’V11’,12X,

73 6 1X,’V12’,12X,

74 6 1X,'V22’)

75 910 FORMAT (5x,'---',12x,'---',12x,

76 6 1x,'---',12x,

77 6 1x,'---')

78 920 FORMAT (1X,E12.4,1X,’,’,lX,E12.4,1X,’,’,
79 6 1X,E12.4,1X,',’,

80 6 1X,E12.4,1X)

81

82 998 RETURN
83 999 END

WKTH

Name

TEMPK
FLDIR
CPH .
HOR .
HOA .
CONCL
PSI .
TAH .
APR
WTT
WOT
WOO

X .
L .
KI. .
ONE .

WCALC

POS .
FLNME
TWO .
VOO
VOT
VTT

Local

Symbols

Global Symbols

Name

WC. 0
WKTH.

Code size =
Data size =
Bss size =

NO errors

045e (1118)
0089 (137)
0036 (60)

detected

177

Class

param
param
param
param
param
param
param
param
param
param
param
param
param
local
local
local
local
local
local
local
local
local
local
local

Class

extern
FSUBRT

Type

REAL*4
INTEGER*4
INTEGER*4
INTEGER*4
REAL*8
INTEGER*4
CHAR*30
INTEGER*4
REAL*8
REAL*8
REAL*8

Type

***
***

Size

1000

bObmh-bh

2000
2000
2000

Size

***
***

Offset

0006
000a
000e
0012
0016
001a
001e
0022
0026
002a
002e
0032
0036
0000
0002
0006
000a
000e
0016
001a
0038
03e8
0bb8
1388

Offset

***
0000

178

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Line#

31

32
33

34
35
36
37

38
39

40

Source Line
SUBROUTINE WC(WCALC, APR, TAH, PSI, I, J,
& CONCL, HOA, HOR, CPH, VOO, VOT, VTT, X,
6 FLDIR, TEMPK)

CCCCC REV. 05-04-92

CCC ----------- SUBPROGRAM TO INTEGRATE FROM

CCC ------------- MINIMUM PARTICLE SEPARATION TO AN
CCC ------------- INFINITE SEPARATION IN SEGMENTS SO
CCC ------------- THAT WHEN AN AREA OF A SEGMENT ADDS
CCC ------------- A SMALL ENOUGH AMOUNT TO THE TOTAL
CCC ------------- AREA OF ALL THE SEGMENTS SO FAR THEN
CCC ------------- CAN STOP INTEGRATING BEFORE GET TO
CCC ------------- INFINITY ----------------------------

IMPLICIT NONE

CHARACTER FLDIR*7

INTEGER I,J,XN

REAL*8 AREAN,CONTRIB,DIFFN,SIMP,AREATL,TOL
REAL*8 CONTMX,SUMARG,SUMMAX,SUMMIN,OOAT,SOC
REAL HIGH,LOW,HIMAX,HIMIN,APR,TAH,PSI,CONCL
REAL HOA,HOR,ROR,CPH,INTSIZE,LOWEST,X,TEMPK
REAL*8 WCALC,VOO,VOT,VTT

DIMENSION APR(2),PSI(2),TAH(2:4)

DIMENSION X(250),VOO(250),VOT(250),VTT(250)

CCCCC XN=COUNTER FOR TRACKING POSITION IN ARRAYS IN
CCCCC SUBROUTINE SI FOR ENTIRE INTERVAL OF
CCCCC INTEGRAL

CCCCC I=FIRST PARTICLE TYPE OF INTERACTION

CCCCC J=OTHER PARTICLE TYPE OF INTERACTION

CCCCC HIGH=HIGH VALUE OF LIMITS OF INTEGRATION OF

CCCCC CURRENT SEGMENT
CCCCC LOW=LOW VALUE OF LIMITS OF INTEGRATION OF
CCCCC CURRENT SEGMENT

CCCCC INTSIZE=INTERVAL SIZE FOR EACH SEGMENT
CCCCC LOWEST=LOWEST VALUE OF LOW VALUE OF LIMITS OF

CCCCC INTEGRATION
CCCCC =MINIMUM SEPARATION DISTANCE
CCCCC TOL=TOLERANCE FOR A DIFFERENCE IN TOTAL AREA
CCCCC UPON ADDITION OF AREA OF CURRENT SEGMENT
CCCCC AT WHICH MAY RETURN A VALUE FOR COMPLETE
CCCCC INTERVAL IF PASSED MIMIN
CCCCC HIMIN=MINIMUM VALUE OF INTEGRATION LIMITS
CCCCC BEFORE A VALUE FOR COMPLETE INTEGRAL MAY
CCCCC BE RETURNED IF TOLERENCE IS MET

CCCCC HIMAX=MAXIMUM VALUE OF INTEGRATION LIMITS AT

Line!

41
42

44

45
46

47
48
49

50
51

52
53

54
55

56
57
58
59
60
61
62

63
64
65
66
67
68
69
70
71
72
73
74
75

76
77
78
79

179

Source Line

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

CCCCC

CCCCC
CCCCC
CCCCC
CCCCC

CCCCC

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

CC----
C .....

05
10
15
20
25
30
35
40
45
50
55

C .....
C .....

60

cc----

65'

WHICH TIME THE PRESENT VALUE FOR THE
COMPLETE INTEGRAL WILL BE RETURNED EVEN
IF TOLERENCE HAS NOT BEEN MET SO THAT
THE PROGRAM DOES NOT RUN FOREVER OR
CAUSE A MATH OVERFLOW ERROR AND PROGRAM
TERMINATION
SUMMAX=MAXIMUM POSITVE VALUE FOR A REAL
VARIABLE BEFORE A MATH OVERFLOW ERROR
OCCURS AND CAUSES PROGRAM TERMINATION
SUMMARG=ARGUMENT USED TO CALCULATE SUMMAX
SUMMIN=MINIMUM POSITVE VALUE FOR A REAL
VARIABLE BEFORE A MATHOVERFLOW ERROR
OCCURS AND CAUSES PROGRAM TERMINATION
SIMP=VALUE OF SEGMENT INTEGRAL CALCULATED BY
SUBROUTINE SI
CONTRIB=CONTRIBUTION BY AREA OF CURRENT SGMENT
TO TOTAL AREA
CONTMX=MAXIMUM CONTRIBUTION TO TOTAL AREA
BEFORE A MATH OVERFLOW ERROR CAUSES
PROGRAM TERMINATION
AREATL=TOTAL AREA OF ALL PREVIOUS SEGMENTS OF
INTEGRAL
AREAN=NEW AREA WITH ADDITION OF CURRENT
SEGMENT AREA TO AREATL
DIFFN=DIFFERENCE IN AREA CONTRIBUTED TO TOTAL
AREA WITH TOTAL AREA
OOAT=ONE OVER AREA TOTAL
SOC=SUMMAX OVER CONTRIB

------------------ SETTING VARIOUS INITIAL
---------------------- VALUES------------------
XN=1

SUMARG=663.0

SUMMAX=EXP(SUMARG)

SUMMAX=SUMMAX*1.0E+20

SUMMIN=1.0/SUMMAX

HIMIN=100.0E-9

TOL=1.0E-5

HIMAX=APR(I)+APR(J)+HOA

HIGH=HOR

LOWEST=HOR

INTSIZE=1.0E-9

------------------ SENDING PROGRAM PROGRESS
-------------------- MESSAGE TO SCREEN---------
WRITE(*,900)FLDIR,CPH,I,J

------------------ BEGIN ITERATION LOOP--------
IF (HIGH.LT.HIMAX) THEN

180

Line# Source Line

80 70 LOW=HIGH
81 75 HIGH=LOW+INTSIZE
82
83 CC ---------------------- CALCULATING AREA OF CURRENT
c ------------------------- SEGMENT -------------------
84' 80 CALL SI(SIMP, LOW, HIGH, APR, TAH, PSI, I,
85 6 J, CONCL, HOA, CPH, VOO,VOT,VTT, x,
6 XN, TEMPK)
86 85 CONTRIB=SIMP
87
88 CC ---------------------- CALCULATING VARIABLES To
89 c ------------------------- PREVENT MATH OVERFLOW
c ------------------------- ERRORS AND PROGRAM
C ------------------------- TERMINATION ---------------
90 90 CONTMX=SUMMAX-AREATL
91 95 IF (CONTRIB.GE.1.0)THEN
92 100 SOC=SUMMAX/CONTRIB
93 105 IF (AREATL.LT.SUMMIN)THEN
94 110 OOAT=SUMMAX
95 115 ELSE
96 120 OOAT=1.0/AREATL
97 125 END IF
98 130 ELSE
99 135 SOC=1.0
100 140 OOAT=0.0
101 145 END IF
102
103 CC ---------------------- CALCULATING AREAN AND
104 C -------------------------- PREVENTING MATH OVERFLOW
c -------------------------- ERRORS AND PROGRAM
C -------------------------- TERMINATION --------------
105 150 IF (LOW.EQ.LOWEST)THEN
106 155 AREAN=CONTRIB
107 160 AREATL=AREAN*2
108 165 ELSE IF (CONTRIB.GE.CONTMX)THEN
109 170 AREAN=SUMMAX
110 175 ELSE
111 180 AREAN=AREATL+CONTRIB
112 185 END IF
113
114 CC ---------------------- CALCULATING DIFFN AND
115 C -------------------------- PREVENTING MATH OVERFLOW
C -------------------------- ERRORS AND PROGRAM
c -------------------------- TERMINATION --------------
116 190 IF (AREATL.EQ.0.0)THEN
117 195 DIFFN=0.0
118 200 ELSE IF (AREAN.EQ.SUMMAX) THEN
119 205 DIFFN=0.0
120 210 ELSE IF (OOAT .GE. SOC)THEN

121 215 DIFFN=0.0

Line#

122
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181

Source Line

220 ELSE
225 DIFFN=(ABS((AREATL-AREAN)/AREATL))
230 END IF
cc ---------------------- RETURNING AREA VALUE IF
C ------------------------- DIFFERANCE BETWEEN
c ------------------------- SUCCESSIVE ITERATIONS IS
c ------------------------- WITHIN TOLERENCE AND
c ------------------------- SEPERATION IS MORE THAN
C ------------------------- MINIMUM -------------------
235 IF (DIFFN.LT.TOL .AND. HIGH.GE.HIMIN) THEN
240 ROR=HOA+((APR(I)+APR(J))/l.0E+9)
245 WCALC=ROR*AREAN
250 RETURN
c ---------------------- RESETTING AREATL IF NOT ------
255 ELSE
260 AREATL=AREAN
265 IF (AREATL.LT.SUMMIN)AREATL=SUMMIN
270 END IF
CC ---------------------- RETURNING AREA VALUE SINCE
C ------------------------- UPPER INTEGRATION LIMIT IS
C ------------------------- TOO LARGE -----------------
275 ELSE IF(HIGH.GE.HIMAX)THEN
280 WRITE(*,*)’ I
285 WRITE(*,*)’WHILE INTEGRATING INTERACTION'
290 WRITE(*,*)’BETWEEN PARTICLES’,I,J
295 WRITE(*,*)'UPPER INTEGRATION LIMIT’,
6 'EXCEEDED’, HIMAX,’nm’
300 ROR=HOA+((APR(I)+APR(J))/1.0E+9)
305 WCALC=AREAN*ROR
310 RETURN
315 END IF
CC ---------------------- SINCE DIFFERENCE IS NOT
C ------------------------- WITHIN TOLERANCE THEN
c ------------------------- PREPARE FOR ANOTHER
C ------------------------- ITERATION -----------------
c ----------------------- INCREASING INTSIZE AS
0 ------------------------- SEPARATION INCREASES ------

320 IF(HIGH.GT.5.0E-9 .AND. HIGH.LE.25.0E-9) THEN
325 INTSIZE=2.5E-9
330 ELSE IF(HIGH.GT.25.0E-9 .AND.

& HIGH.LE.85.0E-9) THEN
335 INTSIZE=5.0E-9
340 ELSE IF(HIGH.GT.85.0E-9 .AND.

& HIGH.LE.170.0E-9) THEN
345 INTSIZE=10.0E-9

350 ELSE IF(HIGH.GT.170.0E-9 .AND.

182

Line# Source Line

& HIGH.LE.500.0E-9) THEN
161 355 INTSIZE=100.0E-9
162 360 ELSE IF(HIGH.GT.500.0E-9) THEN
163 365 INTSIZE=1000.0E-9

164 370 END IF
165 375 GOTO 65

166

167 CCC --------------------- MESSAGE REPORTING CURRENT

168 CC ------------------------ FILE, CURRENT INTERACTIONS

169 CC ------------------------ BEING CALCULATED AND THAT
cc ------------------------ THE COMPUTER Is RUNNING A
cc ------------------------ LONG PROGRAM -------------

170 900 F0RMAT(/:/:/:/./7/,/711X: 58(’C’)/,

171 & 11X,’C’,4X,’This computer is currently’,
6 26X,’C’/,
172 & 11X,’C’,4X,’running a program’,35X,’C’/,
173 & 11X,’C’,4X,’which has many lengthy’,30X,’C’/,
174 & 11X,’C’,4X,’calculations.’,39x,’C’/,
175 6 11X,’C’,56X,’C’/,
176 & 11X,’C’,4X,’PLEASE DO NOT INTERUPT THE’,
6 ’PROGRAM!!’,16X,’C’/, -
177 & 11X,’C’,56X,’C’/,
178 & 11X,’C’,4X,’If there is a problem’,
& ’contact’,23X,’C’/,
179 & 11X,’C’,4X,5X,’Brett Wilson: Office’,
6 ’A234’,22X,’C’/,
180 & 11X,’C’,56X,'C’/,
181 6 11X,58(’C’)/,
182 6 11X,’C',28X,A7,21X,'C’/,
183 & 11X,’C’,28X,’CURRENT PH: ’,F5.2,11X,'C'/,
184 & 11X,’C',28X,’INTERACTIONS BETWEEN: ',
6 Il,’,’,Il,3X,’C’/,
185 & 11X758(’C')7/././,/,/./)
186
187
188
189
190 CCC --------------------- RETURNING TO CACLUL

cc ------------------------ SUBPROGRAM ----------------
191 999 END -

WC Local Symbols

Name Class Type Size Offset
TEMPK . . . . . . . . . . param 0006
FLDIR . . . . . . . . . . param 000a
X . . . . . . . . . . . . param 000e

VTT . . . . . . . . . . . param 0012

WC Local
Name

VOT .
VOO .
CPH .
HOR .
HOA .
CONCL . .

J .
I .
PSI . . .
TAH . . .
APR . . .
WCALC . .
SUMARG. .
CONTRIB .
SUMMIN. .
CONTMX. .
SUMMAX. .
LOWEST. .
HIGH. . .
SOC . . .
INTSIZE .
XN. . . .
DIFFN . .
AREAN . .
TOL . .
LOW . . .
ROR .
OOAT.
HIMIN .
HIMAX .
AREATL. .
SIMP. . .

Symbols

Global Symbols

Name

SI. 0 O 0
WC. . . .

Code size
Data size
Bss size

No errors

0643 (1603)

= 00dd (221)
= 0082 (130)
detected

183

Class

param
param
param
param
param
param
param
param
param
param
param
param
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Class

extern
FSUBRT

Type

REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*4
REAL*8
REAL*4

INTEGER*4

REAL*8
REAL*8
REAL*8
REAL*4
REAL*4
REAL*8
REAL*4
REAL*4
REAL*8
REAL*8

Type

***
***

Size

mmhhoobhmooooohmbboooooooooo

Size

***
***

Offset

0016
001a
001e
0022
0026
002a
002e
0032
0036
003a
003e
0042
0002
000a
0012
001a
0022
002a
002e
0032
003a
003e
0042
004a
0052
005a
005e
0062
006a
006e
0072
007a

Offset

***
0000

Linef

HomooqmmAuNI-a

H)-

19

20
21
22
23
24
25
26
27
28
29
30
31
32

33
34

35
36

37
38
39

40

184

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Source Line

CCCCC

CCC---
C .....

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC

SUBROUTINE SI(SIMP, A, B, APR, TAH, PSI, I, J,

6 CONCL, HOA, CPH, VOO,VOT,VTT, x, XN, TEMPK)

REV. 05-04-92

------- SUBPROGRAM TO INTEGRATE A GIVEN SEGMENT
---------- OF AN INTEGRAL USING SIMPSON’S RULE-

IMPLICIT NONE

INTEGER I,J,L,NSECTS,NMAX,XN,VN

REAL A, B, Dx, APR, TAH, PSI, HOA, SEP, CPH,
REAL CONCL, x, xv, TEMPK

REAL*8 ODDS,EVENS,DIFFT,FA,FB,AREAO,CONTMX
REAL*8 AREAN,DIFFN,VFCN,WFCN,SUMARG,SUMMAX
REAL*8 SIMP,V,VOO,VOT,VTT

DIMENSION APR(2),PSI(2),X(250)

DIMENSION VOO(250),VOT(250),VTT(250)
DIMENSION V(140),XV(140),TAH(2:4)

NSECTS=NUMBER OF SECTIONS INTERVALL TO BE
DIVIDED INTO

DIFFT=TOLERABLE DIFFERANCE BETWEEN SUCCESSIVE
ITERATIONS

=MAXIMUM NUMBER OF SECTIONS TO BE TAKEN

A=LOWER LIMIT OF INTEGRATION

=UPPER LIMIT OF INTEGRATION

WFCN=STABILITY CALCULATED BY SUBROUTINE WVFCN

VFCN=POTENTIAL CALCULATED BY SUBROUTINE WVFCN

FA=FUNCTION VALUE AT A

FB=FUNCTION VALUE AT B

DX=WIDTH OF SECTIONS

ODDS=SUM OF FUCTION VALUES AT ODD SECTIONS

EVENS=SUM OF FUCTION VALUES AT EVEN SECTIONS

AREAO=AREA CALCULATED IN PREVIOUS ITERATION

AREAN=AREA CALCULATED IN PRESENT ITERATION

DIFFN=DIFFERENCE BETWEEN PRESENT AND PREVIOUS
ITERATION

CONTMX=MAXIMUM CONTRIBUTION TO TOTAL AREA
BEFORE A MATH OVERFLOW ERROR CAUSES
PROGRAM TERMINATION

SUMMAX=MAXIMUM POSITVE VALUE FOR A REAL
VARIABLE BEFORE A MATH OVERFLOW ERROR
OCCURS AND CAUSES PROGRAM TERMINATION

SUMMARG=ARGUMENT USED TO CALCULATE SUMMAX

SUMMIN=MINIMUM POSITVE VALUE FOR A REAL
VARIABLE BEFORE A MATH OVERFLOW ERROR
OCCURS AND CAUSES PROGRAM TERMINATION

V=INTERPARTICLE POTENTIAL AT A COORESPONDING

Line#

41
42

43

44
45
46
47
48
49

50
51
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58

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79
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185
Source Line

ccccc DISTANCE XV(ARRAY)

CCCCC XV=INTERPARTICLE SEPARATION DISTANCE (ARRAY)

CCCCC VN=COUNTER FOR TRACKING POSITION IN V AND xv

CCCCC ARRAYS

CCCCC XN=COUNTER FOR SAVING v AND xv IN VOO,VOT,VTT
ccccc AND K ARRAYS

CC ---------------------- INTIALIZE AREAO TO ZERO--—-
05 AREAO=0.0

CC ---------------------- SET DIFF,NSECTS,6 NMAX

c ------------------------- VALUES --------------------
10 DIFFT = 0.0001

15 NSECTS=64
20 NMAX=2.0E+6
25 SUMARG=663.0
30 SUMMAX=EXP(SUMARG)

35 SUMMAX=SUMMAX*1.0E+20

CC ---------------------- EVALUATE FUNCTION AT UPPER &

C ------------------------- LOWER BOUND ---------------

40 CALL WVFCN(WFCN, VFCN, A, APR, TAH, PSI, I, J,
& CONCL, HOA, TEMPK)

45 FA=WFCN

50 XV(1)=A

55 V(1)=VFCN

60 CALL WVFCN(WFCN, VFCN, B, APR, TAH, PSI, I, J,
6 CONCL, HOA, TEMPK)

65 FB=WFCN

70 XV(130)=B

75 V(130)=VFCN

CC ---------------------- BEGIN ITERATION LOOP --------
80 IF (NSECTS .LE. NMAX) THEN

CC ---------------------- CALCULATE WIDTH 0F SECTIONS-
85 Dx = (B-A)/REAL(NSECTS)

cc ---------------------- RE-INITIALIZE ODDS 6 EVENS

c ------------------------- TO ZERO -------------------
90 ODDS = 0.0

95 EVENS = 0.0

100 VN=1

CC ---------------------- CALCULATING SUM OF ALL ODD

C ------------------------- FUNCTION VALUES -----------
105 D0 170 L=1,NSECTS-1,2

110 SEP = A+(L*DX)

115 CALL WVFCN(WFCN, VFCN, SEP, APR, TAH, PSI,

Linef

82
83
84
85
86
87
88
89
90
91
92
93
94

95
96
97

98

99
100
101
102
103
104
105
106
107
108
109
110

111
112

113
114
115
116
117
118
119
120
121
122
123
124
125

186

Source Line

6 I, J, CONCL, HOA, TEMPK)
120 CONTMX=SUMMAX-ODDS
125 IF (WFCN.GE.CONTMX)THEN
130 ODDS=SUMMAx
135 ELSE
140 ODDS=ODDS + WFCN
145 END IF
150 IF(NSECTS.EQ.128)THEN
155 XV(VN+L)=SEP
160 V(VN+L)=VFCN
165 END IF
170 CONTINUE
cc ---------------------- CALCULATING SUM OF ALL EVEN
c ------------------------- FUNCTION VALUES -----------
175 D0 240 L=2,NSECTS-2,2
180 SEP = A+(L*DX)
185 CALL WVFCN(WFCN, VFCN, SEP, APR, TAH, PSI,
6 I, J, CONCL, HOA, TEMPK)
190 CONTMX=SUMMAX-EVENS
195 IF(WFCN.GE.CONTMX)THEN
200 EVENS=SUMMAx
205 ELSE
210 EVENS=EVENS + WFCN
215 END IF
220 IF(NSECTS.EQ.128)THEN
225 XV(VN+L)=SEP
230 V(VN+L)=VFCN
235 END IF
240 CONTINUE
cc ---------------------- SAVING V DATA FOR WRITING TO
0 ------------------------- FILE ----------------------
245 IF (NSECTS.EQ.128 .AND. B.LT.300.0E-9)THEN
C ----------------------- FOR INTERACTION OF PARTICLE
c ------------------------- ONE WITH ONE --------------
250 IF (I+J.EQ.2)THEN
255 VOO(XN)=V(1)
260 X(XN)=XV(1)
265 XN=XN+1
270 D0 290 L=20,100,20
275 VOO(XN)=V(L)
280 X(XN)=XV(L)
285 =XN+1
290 CONTINUE
295 VOO(XN)=V(130)
300 X(XN)=XV(130)
305 XN=XN+1
c ----------------------- FOR INTERACTION OF PARTICLE

c ------------------------- ONE WITH TWO --------------

187

Line} Source Line

126 310 ELSE IF (I+J.EQ.3)THEN
127 315 VOT(XN)=V(1)
128 320 XN=XN+1
129 325 D0 340 L=20,100,20
130 330 VOT(XN)=V(L)
131 335 XN=XN+1
132 340 CONTINUE
133 345 VOT(XN)=V(130)
134 350 XN=XN+1
135 c ----------------------- FOR INTERACTION OF PARTICLE
c ------------------------- TWO WITH TWO-- ------------
136 355 ELSE IF (I+J.EQ.4)THEN
137 360 VTT(XN)=V(1)
138 365 XN=XN+1
139 370 D0 385 L=20,100,20
140 375 VTT(XN)=V(L)
141 380 XN=XN+1
142 385 CONTINUE
143 390 VTT(XN)=V(130)
144 395 XN=XN+1
145 400 END IF
146 405 END IF
147
148 cc ---------------------- ADDING ALL FUNCTION VALUES
149 C ------------------------- THIS TO FIND AREA OF
C ------------------------- ITERATION -----------------
150 410 IF (ODDS.GE.SUMMAx .OR.
6 EVENS.GE.SUMMAX)THEN
151 415 AREAN=SUMMAX
152 420 ELSE
153 425 AREAN = (DX/3.0)*
6 (FA+FB+4.0*ODDS+2.0*EVENS)
154 430 END IF
155
156 cc ---------------------- RETURNING AREA VALUE IF
157 c ------------------------- DIFFERANCE BETWEEN
c ------------------------- SUCCESSIVE ITERATIONS IS
c ------------------------- TOLERABLE -----------------
158 435 IF (AREAN.EQ.0.0)THEN
159 440 DIFFN=0.0
160 445 ELSE
161 450 DIFFN = ABS( (AREAN-AREAO) / AREAN)
162 455 END IF
163 460 IF (DIFFN.LT.DIFFT)THEN
164 465 SIMP = AREAN
165 470 RETURN
166
167 CC ---------------------- SINCE DIFFERENCE IS NOT
168 C ------------------------- WITHIN TOLERANCE THEN

c ------------------------- PREPARE FOR ANOTHER

188

Line# Source Line

C ------------------------- ITERATION -----------------
169 475 ELSE
170 480 AREAO = AREAN
171 485 NSECTS = NSECTS*2
172 490 ENDIF
173 495 GOTO 80
174
175 CC ---------------------- RETURNING AREA VALUE SINCE

C ------------------------- NSECTS Too LARGE ----------
176 500 ELSE
177 505 SIMP=AREAN
178 510 WRITE(*,*)’NSECTS TOO LARGE IN SIMPSONS’,

& 'INTEGRATION,’
179 515 WRITE(*,*)’RETURNING AREA(LOW,HIGH) FOR’,
& ’PH:’

180 520 WRITE(*,*)’(’,A,’,’,B,’)’,’FOR:’,CPH
181 525 PAUSE
182 530 ENDIF
183
184 CCC --------------------- RETURNING TO WCALC

C ------------------------- SUBPROGRAM ----------------
185 998 RETURN

186 999 END

SI Local Symbols

Name Class Type Size Offset
TEMPK . . . . param 0006
XN. . . . . . param 000a
X . . . . . . param 000e
VTT . . . . . param 0012
VOT . . . . . param 0016
V00 . . . . . param 001a
CPH . . . . . param 001e
HOA . . . . . param 0022
CONCL . . . . param 0026
J . . . . . . param 002a
I . . . . . . param 002e
PSI . . . . . param 0032
TAH . . . . . param 0036
APR . . . . . param 003a
B . . . . . . param 003e
A . . . . . . param 0042
SIMP. . . . . param 0046
V . . . . . . local REAL*8 1120 0000
EVENS . . . . local REAL*8 8 0002
FA. . . . . . local REAL*8 8 000a
FB. . . . . . local REAL*8 8 0012

SI Local
Name

L . . .
SUMARG.
NSECTS.
CONTMX.
SUMMAX.
DX. . . .
VN. . . .
DIFFN . .
AREAN . .
AREAO . .
SEP . .
ODDS. .

VFCN. . .

DIFFT
WFCN.
NMAX. . .
XV. . . .

Symbols

Global Symbols

Name

SI. . . .
WVFCN . .
Code size
Data size

Bss size

No errors

0a5e (2654)
00a7 (167)
0082 (130)

detected

189

Class

local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Class

FSUBRT
extern

Type

INTEGER*4
REAL*8
INTEGER*4
REAL*8
REAL*8
REAL*4
INTEGER*4
REAL*8
REAL*8
REAL*8
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
INTEGER*4
REAL*4

Type

***
***

Size

oncommoohooooooc-Sooovooh

U1
0‘

Size

***
***

Offset

001a
001e
0026
002a
0032
003a
003e
0042
004a
0052
005a
005e
0066
006e
0076
007e
0460

Offset

0000
***

190

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Line# Source Line

GUIPUNH

Dad

10
11
12

13
14

15
16
17
18
19
20
21
22
23
24
25
26
27
28
29

30
31
32
33
34
35
36
37
38

39

CCCCC

CCC---
CC---

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCC

CCCCC
CCCCC
CCCCC

CCCCC

CCCCC

SUBROUTINE WVFCN(WFCN, VFCN, SSEP, APR, TAH,

& PSI, I, J, CONCL, HOA, TEMPK)

REV. 05-04-92

------------------ EVALUATING THE FCN.S W AND V
-------------------- AT GIVEN SEPERATIONs------
IMPLICIT NONE

INTEGER I,J

REAL EC, BOC, SSEP, PIE, CONCL, CONCM, NA
REAL APRM, DIEL, PSEP

REAL APR,TAH,PSI,HOA,RSEP,RSEPSD,TEMPK

REAL*8 EARGMX,EARGMN,EXARG,EXAMAX,X,Y

REAL*8 TTWKT,TTH,FR,FV,KAP

REAL*8 DIELM,DIELV,EXW,WFCN,VFCN

REAL*8 TTWN,TTWNKT,TTWD,SI,SE,VRKT,FRE,FVNE
REAL*8 TTHN,TTHD,FRN,FRD,FVN,VTKT

REAL*8 VAKT,VANKT,VAD,KAPN,KAPD,KAPS

DIMENSION APR(2),PSI(2),APRM(2),TAH(2:4).

EC=ELECTRON CHARGE (COUL)

PIE=NUMERIC VALUE OF PIE (UNITLESS)

DIELM=RELATIVE DIELECTRIC CONSTANT OF MEDIUM

(@25 C)(DIMENSIONLESS)

DIELV=DIELECTRIC CONSTANT OF VACUUM (C‘2/JM)

DIEL=DIELECTRIC CONSTANT OF MEDIUM (C‘2/JM)

BOC=BOLTZMAN CONSTANT (J/ATOM K)

NA=AVAGADRO’S CONSTANT (ATOMS/MOLE)

CONCL=CONCENTRATION OF ELECTROLYTE (MOLE/L)

CONCM=CONCENTRATION OF ELECTROLYTE (MOLE/M‘3)

APR=ATOMIC PARTICLE RADIUS (NM)

APRM=ATOMIC PARTICLE RADIUS (M)

SSEP=SEPERATION DISTANCE [BETWEEN STERN
SURFACES] (M)

PSEP=SEPERATION DISTANCE [BETWEEN PARTICLE
SURFACES] (M)

RSEP=SEPERATION DISTANCE [BETWEEN CENTERS] (M)

RSEPSD=RSEP SQUARED (M‘2)

TAH=TOTAL HAMAKER CONSTANT (J)

HOA=MINIMUM SURFACE SEPERATION FOR VAN DER

WAALS ATTRACTION (M)
HOR=MINIMUM SURFACE SEPERATION FOR REPULSION
(M)
VTKT=T0TAL INTERACTION POTENTIAL IN UNITS
OF KT
VAKT=ATTRACTION INTERACTION POTENTIAL IN UNITS
OF KT
VRKT=REPULSION INTERACTION POTENTIAL IN UNITS

Line#

40
41
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43

44
45

46
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191
Source Line
OF KT

CCCCC KAP=KAPPA THE DEBYE-HUCKEL PARAMETER (1/M)
CCCCC X,Y,VAN,VAD=VARIABLES USED TO BREAK DOWN

CCCC EQUATION FOR THE ATTRACTION

CCCC INTERACTION POTENTIAL SO IT MAY BE
CCCC SOLVED IN FORTRAN CODE WITH

CCCC LIMITED LINE LENGTH

CCCCC TTWKT,TTWNKT,TTWN,TTWD,TTH,TTHN,TTHD,FR,FRN
CCCC 6 FRD,FRE,FV,FVN, SI,SE,KAP,KAPN,KAPD,KAPS

CCC = VARIABLES USED TO BREAK DOWN

CCC LARGE EQUATION FOR THE REPULSION
CCC INTERACTION POTENTIAL 80 IT MAY
CCC BE SOLVED IN FORTRAN CODE WITH
CCC LIMITED LINE LENGTH

CC ---------------------- INITIALIZING THE CONSTANTS-
10 CONCM = CONCL*1.0E+3

20 EC = 1.602E-19

30 NA = 6.02E+23

40 PIE = 3.1416

50 DIELM = 78.54

60 DIELV = 8.8542E-12

70 DIEL = DIELM*DIELV

80 BOC = 1.381E-23

90 APRM(I) = APR(I)/1.0E+9
100 APRM(J) = APR(J)/1.0E+9
110 PSEP=SSEP+HOA

120 EARGMx=709.0

130 EARGMN=-745.0

CC ---------------------- EVALUATING FCN. BY BREAKING
c ------------------------- INTO SMALLER TERMS 6

c ------------------------- RECOMBING THEM ------------
cc ---------------------- CALCULATING VA --------------

140 x=PSEP/(APRM(I)+APRM(J))
150 Y=APRM(I)/APRM(J)
160 VANKT=0.0-(TAH(I+J)/(12.0*BOC*TEMPK))
170 VAD=(Y/(X**2+(X*Y)+X))+(Y/(X**2+(X*Y)+X+Y))
180 VAD=VAD+(2.0*LOG(X**2+(X*Y)+X) /

6 (X**2+(X*Y)+X+Y))
190 VAKT=VANKT*VAD

CC ---------------------- CALCULATING VR TERMS --------
200 TTWN=PIE*DIEL*APRM(I)*APRM(J) *
6 (PSI(I)**2+PSI(J)**2)

210 TTWNKT=TTWN/(BOC*TEMPK)
220 TTWD=(APRM(I)+APRM(J))
230 TTWKT=TTWNKT/TTWD

83
85
86
S7
88
'89
90
91

93
94
95
96
97
98
99
100

101

102
103
194
105
106
107
108
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110
111
112
113
114
115

116
117
118
119
120
121
122
123
124
125
126

127
123

192
Line} Source Line

83

84 240 IF (PSI(l).EQ.0.0 .OR. PSI(2).EQ.0.0)THEN
85 250 TTH = 0.0

86 260 ELSE

87 270 TTHN = 2*PSI(I)*PSI(J)

88 280 TTHD = PSI(I)**2+PSI(J)**2
89 290 TTH = TTHN/TTHD

90 300 END IF

91

92 310 KAPN = 2.0*CONCM*EC**2*NA

93 320 KAPD = DIEL*BOC*TEMPK

94 330 KAPS = KAPN/KAPD

95 340 KAP = SQRT(KAPS)

96

97 350 FRE = 0.0 -(KAP*SSEP)
98 360 IF (FRE.LT.EARGMN) THEN

99 370 FRE=EARGMN
100 C ----------------------- PREVENTING MATH OVERFLOW

c ------------------------- ERROR ---------------------
101 380 ELSE IF (FRE.LT.1.0E-4 .AND.

6 FRE.GT.-1.0E-4)THEN

102 390 IF (FRE.GE.0.0)THEN
103 400 FRE=1.0E-4
104 410 ELSE
105 420 FRE=-1.0E-4
106 430 END IF

107 440 END IF

108 450 FRN = 1.0 + EXP(FRE)

109 460 FRD = 1.0 - EXP(FRE)

110 470 FR = LOG(FRN/FRD)

111

112 480 FVNE =(0.0-(2.0*KAP*SSEP))
113 490 IF (FVNE.LT.EARGMN)THEN

114 500 FVNE=EARGMN
115 C ----------------------- PREVENTING MATH OVERFLOW
C ------------------------- ERROR ---------------------
116 510 ELSE IF (FVNE.GT.-1.0E-16)THEN
117 520 FVNE=-1.0E-16

118 530 END IF
119 540 FVN = 1.0 - EXP(FVNE)
120 550 FV = LOG(FVN)

121

122 560 SI=TTH*FR

123

124 570 SE=SI+FV

125

126 CC ---------------------- RECOMBINING TERMS TO

c ------------------------------ CALCULATE VR --------
127 580 VRKT=TTWKT*SE
128

Line#

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153
154
155

156
157

193
Source Line
CC ---------------------- CALCULATING VT FROM VA 6 VR-

590 VTKT = VAKT+VRKT
600 VFCN=VTKT

cc ---------------------- CALCULATING VT OVER KT AND
C -------------------------- PREVENTING MATH OVERFLOW
C -------------------------- ERRORS -------------------
610 IF (VTKT.GT.EARGMX)THEN

620 EXW=EARGMX

630 ELSE IF (VTKT.LT.EARGMN)THEN

640 EXW=EARGMN

650 ELSE

660 EXW=VTKT

670 END IF
680 EXARG=EXP(EXW)

cc ---------------------- CALCULATING WFCN ------------
690 RSEP = PSEP+APRM(I)+APRM(J)

700 RSEPSD=RSEP**2

710 EXAMAX=EXP(EARGMX)*RSEPSD

720 IF (EXARG.GT.EXAMAX)THEN

730 WFCN=EXP(EARGMX)

740 ELSE

750 WFCN=EXP(EXW)/RSEPSD

760 END IF

cc ---------------------- RETURNING FUNCTION To

c ------------------------- SUBPROGRAM ----------------
998 RETURN

999 END

WVFCN Local Symbols

Name

TEMPK

HOA .
CONCL
J . .
I . .
PSI .
TAH .
APR .
SSEP.
VFCN.
WFCN.

Class Type Size Offset
. . . . . . . . . param 0006
. . . . . param 000a
. . . . . param 000e
. . . . . param 0012
. . . . . param 0016
. . . . . param 001a
. . . . . param 001e
. . . . . param 0022
. . . . . param 0026
. . . . . param 002a
. . . . . param '002e

O
I)...

1‘}.

.h-

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mp

WVFCN Local Symbols

Name

TTWD.
VANKT

EXAMAX.
EARGMX.

VRKT.
EC. .
VTKT.
TTWN.
NA. .
RSEPS
BOC .
SE. .
FR. .
X . .
Y . .
VAD .
FRD .
SI. .
KAP .
FV. .
FRE .
TTWKT
DIEL.
PIE .
KAPD.
FRN .

O O I O O O O

194

Class

local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Type

REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*8
REAL*8
REAL*4
REAL*4
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*8
REAL*4
REAL*8

(D
(...).
N
(D

00.6-00500000000006-000000000000000000006-a0000000000000000000000bphoneme-0000000000

Offset

0000
0008
0010
0018
0020
0028
002C
0034
003e
0040
0044
0048
0050
0058
0060
0068
0070
0078
0080
0088
0090
0098
00a0
00a4
00a8
00b0
00b8
00c0
00c8
00d0
00d8
00e0
00e8
00f0
00f8
00fc
0104
010C
0114
011C
0124
0128
0130
0134

195

Global Symbols

Name
WVFCN . .
Code size
Data size
Bss size

No errors

Class Type

. . . . . . . . FSUBRT .***

086a (2158)
0074 (116)
0130 (316)

detected

Size

***

Offset

0000

196

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Linef Source Line

1

ounc- OON

OMQ

10
11
12

13
14

15
16
17
18
19
20
21
22
23
24
25
26
27
28
29

30

31
32
33
34
35
36

37

38

CCCCC-

CCCCC

CCC---
CC---

CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCCC
CCCC

CCCCC
CCCCC
CCCCC

CCCCC

SUBROUTINE WVFCN(WFCN, VFCN, SSEP, APR, TAH,

6 PSI, I, J, CONCL, HOA, TEMPK)
-------- CONSTANT CHARGE CALCULATIONS----------
REV. 05-04-92

------------------ EVALUATING THE FCN.S W AND V
-------------------- AT GIVEN SEPERATIONS------
IMPLICIT NONE

INTEGER I,J

REAL EC, BOC, SSEP, PIE, CONCL, CONCM, NA
REAL APRM, DIEL, PSEP

REAL APR,TAH,PSI,HOA,RSEP,RSEPSD,TEMPK

REAL*8 EARGMX,EARGMN,EXARG,EXAMAX,X,Y

REAL*8 TTWKT,TTH,FR,FV,KAP

REAL*8 DIELM, DIELV, Exw, WFCN, VFCN

REAL*8 TTWN, TTWNKT, TTWD, SI, SE, VRKT, FRE, FVNE
REAL*8 TTHN, TTHD, FRN, FRD, FVN, VTKT

REAL*8 VAKT, VANKT, VAD, KAPN, KAPL KAPS

DIMENSION APR(2),PSI(2),APRM(2),TAH(2:4)

EC=ELECTRON CHARGE (COUL)

PIE=NUMERIC VALUE OF PIE (UNITLESS)

DIELM=RELATIVE DIELECTRIC CONSTANT OF MEDIUM

(@25 C)(DIMENSIONLESS)

DIELV=DIELECTRIC CONSTANT OF VACUUM (C‘Z/JM)

DIEL=DIELECTRIC CONSTANT OF MEDIUM (C‘Z/JM)

BOC=BOLTZMAN CONSTANT (J/ATOM K)

NA=AVAGADRO’S CONSTANT (ATOMS/MOLE)

CONCL=CONCENTRATION OF ELECTROLYTE (MOLE/L)

CONCM=CONCENTRATION OF ELECTROLYTE (MOLE/M‘B)

APR=ATOMIC PARTICLE RADIUS (NM)

APRM=ATOMIC PARTICLE RADIUS (M)

SSEP=SEPERATION DISTANCE [BETWEEN STERN
SURFACES] (M)

PSEP=SEPERATION DISTANCE [BETWEEN PARTICLE
SURFACES] (M)

RSEP=SEPERATION DISTANCE [BETWEEN CENTERS] (M)

RSEPSD=RSEP SQUARED (M‘Z)

TAH=TOTAL HAMAKER CONSTANT (J)

HOA=MINIMUM SURFACE SEPERATION FOR VAN DER

WAALS ATTRACTION (M)
HOR=MINIMUM SURFACE SEPERATION FOR REPULSION
(M)
VTKT=TOTAL INTERACTION POTENTIAL IN UNITS
OF KT
VAKT= ATTRACTION INTERACTION POTENTIAL IN UNITS

Line#

39

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43

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80

197
Source Line

OF KT
CCCCC VRKT=REPULSION INTERACTION POTENTIAL IN UNITS
OF KT
CCCCC KAP=KAPPA THE DEBYE-HUCKEL PARAMETER (1/M)
ccccc x,Y,VAN,VAD=VARIABLES USED To BREAK DOWN

CCCC EQUATION FOR THE ATTRACTION

CCCC INTERACTION POTENTIAL SO IT MAY BE
CCCC SOLVED IN FORTRAN CODE WITH

CCCC LIMITED LINE LENGTH

CCCCC TTWKT,TTWNKT,TTWN,TTWD,TTH,TTHN,TTHD,FR,FRN
CCCC & FRD,FRE,FV,FVN, SI,SE,KAP,KAPN,KAPD,KAPS

CCC = VARIABLES USED TO BREAK DOWN

CCC LARGE EQUATION FOR THE REPULSION

CCC INTERACTION POTENTIAL SO IT MAY

CCC BE SOLVED IN FORTRAN CODE WITH

CCC LIMITED LINE LENGTH

CC ---------------------- INITIALIZING THE CONSTANTS-
10 CONCM = CONCL*1.0E+3

20 EC = 1.602E-19

30 NA = 6.02E+23

40 PIE = 3.1416

50 DIELM = 78.54

60 DIELV = 8.8542E-12

70 DIEL = DIELM*DIELV

80 BOC = 1.381E-23

90 APRM(I) = APR(I)/l.0E+9‘
100 APRM(J) = APR(J)/l.0E+9
110 PSEP=SSEP+HOA

120 EARGMX=709.0

130 EARGMN=-745.0

 

cc ---------------------- EVALUATING FCN. BY BREAKING
C ------------------------- INTO SMALLER TERMS 6

c ------------------------- RECOMBING THEM ------------
CC ———— ---------- CALCULATING VA --------------

140 x=PSEP/(APRM(I)+APRM(J))
150 Y=APRM(I)/APRM(J)
160 VANKT=0.0-(TAH(I+J)/(12.0*BOC*TEMPK))
170 VAD=(Y/(X**2+(X*Y)+X))+(Y/(X**2+(X*Y)+X+Y))
180 VAD=VAD+(2.0*LOG(X**2+(X*Y)+X) /

6 (X**2+(X*Y)+X+Y))
190 VAKT=VANKT*VAD

CC ---------------------- CALCULATING VR TERMS --------
200 =PIE*DIEL*APRM(I)*APRM(J) *
6 (PSI(I)**2+PSI(J)**2)

210 TTWNKT=TTWN/(BOC*TEMPK)

198
Line! Source Line

81 220 TTWD=(APRM(I)+APRM(J))

82 230 TTWKT=TTWNKT/TTWD

83

84 240 IF (PSI(l).EQ.0.0 .OR. PSI(2).EQ.0.0)THEN
85 250 TTH = 0.0

86 260 ELSE

87 270 TTHN = 2*PSI(I)*PSI(J)

88 280 TTHD = PSI(I)**2+PSI(J)**2
89 290 TTH = TTHN/TTHD

90 300 END IF

91

92 310 KAPN = 2.0*CONCM*EC**2*NA

93 320 KAPD = DIEL*BOC*TEMPK

94 330 KAPS = KAPN/KAPD

95 340 KAP = SQRT(KAPS)
96

97 350 FRE = 0.0 -(KAP*SSEP)
98 360 IF (FRE.LT.EARGMN) THEN

99 370 FRE=EARGMN
100 c ----------------------- PREVENTING MATH OVERFLOW

C ------------------------- ERROR ---------------------
101 380 ELSE IF (FRE. LT. 1. 0E-4 .AND.

6 FRE.GT.-1.0E-4)THEN

102 390 IF (FRE.GE.0.0)THEN
103 400 FRE=1.0E-4
104 410 ELSE
105 420 FRE=-1.0E-4
106 430 END IF

107 440 END IF

108 450 FRN = 1.0 + EXP(FRE)

109 460 FRD = 1.0 - EXP(FRE)

110 470 FR = LOG(FRN/FRD)

111

112 480 FVNE =(0.0-(2.0*KAP*SSEP))
113 490 IF (FVNE.LT.EARGMN)THEN

114 500 FVNE=EARGMN
115 C ----------------------- PREVENTING MATH OVERFLOW
C ------------------------- ERROR ---------------------
116 510 ELSE IF (FVNE.GT.-1.0E-16)THEN
117 520 FVNE=-1.0E-16

118 530 END IF
119 540 FVN = 1.0 - EXP(FVNE)
120 550 FV = LOG(FVN)

121

122 560 SI=TTH*FR

123

124 570 SE=SI-FV

125

126 CC ---------------------- RECOMBINING TERMS TO

c ------------------------------ CALCULATE VR --------

Line#

127
128
129
130
131
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136
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155

156
157

199
Source Line
580 VRKT=TTWKT*SE
cc ---------------------- CALCULATING VT FROM VA 6 VR-

590 VTKT = VAKT+VRKT
600 VFCN=VTKT

cc ---------------------- CALCULATING VT OVER KT AND
C -------------------------- PREVENTING MATH OVERFLOW
C -------------------------- ERRORS -------------------
610 IF (VTKT.GT.EARGMX)THEN

620 EXW=EARGMX

630 ELSE IF (VTKT.LT.EARGMN)THEN

640 EXW=EARGMN

650 ELSE

660 EXW=VTKT

670 END IF
680 EXARG=EXP(EXW)

cc ---------------------- CALCULATING WFCN ------------
690 RSEP = PSEP+APRM(I)+APRM(J) ,

700 RSEPSD=RSEP**2

710 EXAMAX=EXP(EARGMX)*RSEPSD

720 IF (EXARG.GT.EXAMAX)THEN

730 WFCN=EXP(EARGMX)

740 ELSE

750 WFCN=EXP(EXW)/RSEPSD

760 END IF

CC ---------------------- RETURNING FUNCTION TO -

C ------------------------- SUBPROGRAM ----------------
998 RETURN

999 END

WVFCN Local Symbols

Name

TEMPK
HOA .
CONCL
J . .
I . .
PSI .
TAH .
APR .
SSEP.
VFCN.
WFCN.

Class Type Size Offset

. . . . . . . . . param 0006
. . . . . . . . . param 000a
. . . . . . . . . param 000e
. . . . . . . . . param 0012
. . . . . . . . . param 0016
. . . . . . . . . param 001a
. . . . . . . . param 001e

. . . . . . . . . param 0022
. . . . . . . . . param 0026
. . . . . . . . . param 002a

. O O C O O O O O param 002e

WVFCN Local Symbols

Name

NA. .

RSEPSD
BOC .

SE.
FR.
X .
Y .
VAD
FRD
SI.
KAP
FV.
FRE

5

DIEL.
PIE .
KAPD.

KAPN.
FVN .
DIELM
TTWNKT
KAPS.
FVNE.
TTH .
APRM.
CONCM
TTHD.
EXW .
DIELV
VAKT.
EXARG
PSEP.

EARGMN.

RSEP.
TTHN.

200

Class

local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Type

REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*8
REAL*8
REAL*4
REAL*4
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*4
REAL*8
REAL*4
REAL*8

U)
..a.
N
(D

00h004>00000000004>000000000000000000me00000000000000000000004>AJ>0000440000000000

Offset

0000
0008
0010
0018
0020
0028
002c
0034
003c
0040
0044
0048
0050
0058
0060
0068
0070
0078
0080
0088
0090
0098
00a0
00a4
00a8
00b0
00b8
00c0
00c8
00d0
00d8
00e0
00e8
00f0
00f8
00fc
0104
010c
0114
011c
0124
0128
0130
0134

201

Global Symbols

Name
WVFCN . .
Code size
Data size
Bss size

NO errors

Class Type

. . . . . . . . FSUBRT ***

086e (2158)
0074 (116)
013c (316)

detected

Size

***

Offset

0000

202
Microsoft FORTRAN Optimizing Compiler Version 5.00.03

Linef Source Line

1 SUBROUTINE DATA STORAGE(V, APR, ZPQ, AHM, AHP,

2 6 PHCZI, NZPl, NZP2, ZPPHl, ZPDP1, ZPPH2,

3 6 ZPDP2, WT, PH, CONCL, WOO, WOT, WTT,CDATE,
6 STIME, FTIME, TEMP)

4

5 CCCCC REV. 06-22-92

6

7 ccc --------------------- SUBPROGRAM TO STORE INPUT 6

cc ----------------------- CALCULATED DATA ------------

8

9 IMPLICIT NONE

10 CHARACTER IFLNM*17,FLDSC*100,ZPQ*1,FLNME*20
CHARACTER FLXT*4,TEMPC*34,AHMC*33,CONCC*42

11 CHARACTER APRC*35,PHCZIC*28,RICS*16,AHPC*33

12 CHARACTER TFLNME*34

13 INTEGER K,L,NZP1,NZP2

14 INTEGER*Z CDATE,STIME,FTIME

15 DIMENSION CDATE(3),STIME(4),FTIME(4)

16 REAL PH,APR,PHCZI,AHP,AHM,ZPPH1,ZPDP1,CONCL

17 REAL ZPPH2,ZPDP2,TEMP,V

18 REAL*8 WT,WOO,WOT,WTT,WMAx

19 DIMENSION WT(200),PH(200),APR(2),AHP(2),
DIMENSION PHCZI(2), ZPPH1(200),ZPDP1(200)

20 DIMENSION ZPPH2(200), ZPDP2(200)

21 DIMENSION WOO(200),WOT(200),WTT(200)

22

23 CCCCC IFLNM=INPUT FILE NAME FOR DATA STORAGE
24 CCCCC FLXT=FILE EXTENSION FOR DATA STORAGE FILE
25 CCCCC FLNME=COMPLETE FILE NAME (I.E. FILE NAME &

CCCCC EXTENSION)
26 CCCCC TFLNME=TOTAL FILE NAME FOR DATA STORAGE
CCCCC (INCLUDES DIRECTORY)

27 CCCCC FLDSC=DESCRIPTION OF FILE
28 CCCCC WMAX=MAXIMUM W VALUE ALLOWABLE FOR PLOTTING

ccccc PROGRAMS
29
30 CCC --------------------- ASSIGNING CHARACTER

cc ------------------------ VARIABLES -----------------

31 05 APRC = ’ATOMIC PARTICLE RADIUS OF COMPONENT’

32 10 PHCZIC ’POINT-OF-ZERO-CHARGE OF COMPONENT’

33 15 RICS = ’VALUE(S) INPUT :'

34 20 AHPC ’HAMAKER CONSTANT OF COMPONENT’

35 25 AHMC ’HAMAKER CONSTANT OF MEDIUM ='

36 30 CONCC = ’CONCENTRATION OF 1-1 ELECTROLYTE IN'
6 ’SYSTEM’

37 35 TEMPC = ’TEMPERATURE OF SYSTEM (IN DEG. C.)’

38

39 ccc --------------------- COLLECTING A FILE NAME AND

203

Source Line
C ------------------------- SYSTEM DESCRIPTION FOR THE
C ------------------------- DATA FILE TO STORE
c ------------------------- INFORMATION IN ------------
40 READ(14,800)FLDSC
45 READ(14,810)IFLNM
50 TFLNME(1:14)=’C:\JK\LL\DATA\’
CCC --------------------- WRITING DATA To A PRINTABLE
CC ------------------------ DATA FILE -----------------
55 FLXT = ’.PDF’
60 FLNME(1:16)=IFLNM(2:17)
65 FLNME(17:20)=FLXT(1:4)
70 TFLNME(15:34)=FLNME(1:20)
75 OPEN(4,FILE=TFLNME,STATUS=’UNKNOWN’)
80 WRITE(4,875)
85 WRITE(4,880)
90 WRITE(4,885)
95 WRITE(4,890)FLNME,FLDSC
100 WRITE(4,895)CDATE(2),CDATE(3),CDATE(1)
105 WRITE(4,900)STIME(1),STIME(2),STIME(3),
6 STIME(4) -
110 WRITE(4,905)FTIME(1),FTIME(2),FTIME(3),
6 FTIME(4)
115 WRITE(4,910)V,CONCC,CONCL,APRC,APR(1),
6 APRC,APR(2)
120 WRITE(4,915)TEMPC,TEMP
125 WRITE(4,930)AHMC,AHM,AHPC,AHP(1),AHPC,AHP(2)
130 IF (ZPQ.EQ.’P’)THEN
135 WRITE(4,920)
140 WRITE(4,925)PHCZIC,PHCZI(1),PHCZIC,
6 PHCZI(2)
145 ELSE
150' WRITE(4,935)
155 WRITE(4,940)1
160 D0 170 K=1,NZP1,1
165 WRITE(4,945)ZPDP1(K),ZPPH1(K)
170 CONTINUE
175 WRITE(4,940)2
180 D0 190 K=1,NZP2,1
185 WRITE(4,945)ZPDP2(K),ZPPH2(K)
190 CONTINUE
195 END IF
200 WRITE(4,955)
205 D0 225 K=1,200,1
210 IF (PH(K).NE.0.0) THEN
215 WRITE(4,960)WOO(K),WOT(K),
6 WTT(K) ,WT(K) ,PH(K)
220 END IF
225 CONTINUE
230 CLOSE(4)

204

Source Line

CCC --------------------- WRITING DATA TO DATA FILE

CC ------------------------ FOR PLOTTING --------------

cc ---------------------- WRITING DATA FILE WITH ALL W

C ------------------------- VALUES --------------------

235 FLXT = ’.DAT'

240 TFLNME(31:34)=FLXT

245 OPEN(3,FILE=TFLNME,STATUS=’UNKNOWN’)

250 WRITE(3,850)FLNME,FLDSC

255 D0 275 L=1,200,1

260 IF (PH(L).NE.0.0)THEN

265 WRITE(3,860)PH(L),WOO(L),WOT(L),WTT(L),
6 WT(L)

270 END IF

275 CONTINUE

280 CLOSE(3)

cc ---------------------- WRITING DATA To FILE WITH

c ---------------------------- ALL W VALUES WITH A

C ---------------------------- MAXIMUM OF WMAx--- -----

285 FLXT=’.DAM’

290 TFLNME(31:34)=FLXT

295 OPEN(3,FILE=TFLNME,STATUS=’UNKNOWN’)

300 WRITE(3,850)FLNME,FLDSC

305 WMAX=9.9999E+30

310 D0 350 L=1,200,1

315 IF (PH(L).NE.0.0)THEN

320 IF(WOO(L).GT.WMAX)WOO(L)=WMAX

325 IF(WOT(L).GT.WMAX)WOT(L)=WMAX

330 IF(WTT(L).GT.WMAX)WTT(L)=WMAX

335 IF(WT(L).GT.WMAX)WT(L)=WMAX

340 WRITE(3,860)PH(L),WOO(L),WOT(L),WTT(L),

WT(L)

345 END IF

350 CONTINUE

355 CLOSE(3)

CC ---------------------- WRITING DATA FILE WITH ONLY

c ------------------------- WT VALUES -----------------

360 FLXT=’.DWT’

365 TFLNME(31:34)=FLXT

37o OPEN(3,FILE=TFLNME,STATUS=’UNKNOWN’)

375 WRITE(3,850)FLNME,FLDSC

380 D0 400 L=1,200,1

385 IF (PH(L).NE.0.0)THEN

390 WRITE(3,860)PH(L),WT(L)

395 END IF

400 CONTINUE

Lixaeai

126
127
128
129

:1:3<>
:12311
:1332
:1233
1:344
1:325
1:345
1:3‘7
1:363
:LEIS
1A4.0
141:1
111,2
zi<1r3
111.4
141:5
114166
141/7
14113
JquQ

150
151

152
153
154

155
15565
157

155a;

1555;
160
161
162

163
164

165
166

205

Source Line

405 CLOSE(3)
cc ---------------------- WRITING DATA FILE WITH ONLY
c ---------------------------- WT VALUESWITH A MAXIMUM
c ---------------------------- OF WMAX ----------------
410 FLXT = ’.DWM’
415 TFLNME(31:34)=FLXT
420 OPEN(3,FILE=TFLNME,STATUS=’UNKNOWN’)
425 WRITE(3,850)FLNME,FLDSC
430 D0 455 L=1,200,1
435 IF (PH(L).NE.0.0)THEN
440 IF(WT(L).GT.WMAX)WT(L)=WMAX
445 WRITE(3,860)PH(L),WT(L)
450 END IF
455 CONTINUE
460 CLOSE(3)
CCC --------------------- FORMATTING READ STATEMENTS--
800 FORMAT(A70)
810 FORMAT(A17)
CCC --------------------- FORMATTING WRITE STATEMENTS-
850 FORMAT(IX,A70)
855 FORMAT(lX,24(/),
6 1X,’TYPE IN A NAME FOR A FILE To STORE DATA’,
6 ’IN.’/,
6 1X,’(MUST BE 8 CHARACTERS IN LENGTH WITH NO’,
6 ’SPACES.)’,15(/))
860 FORMAT(IX,F5.2,1X,’,’,1X,E12.4,1X,’,',1X,
6 E12.4,1X,’,’,1X,
6 E12.4, 1X,’,’,1X,E12.4)
865 FORMAT(lX,24(/),
6 lX,’DO YOU WANT A PRINTED COPY OF DATA?(Y’,
& ’Or N)’,15(/))
870 FORMAT(IX,24(/),
6 1X,’READY PRINTER FOR PRINTING.’/,
6 1X,’WHEN PRINTER IS READY FOR PRINTING’,
6 ’TYPE: "Y"’/,
6 1X,’IF PRINTER IS IN-OPERABLE TYPE:’,
& IflNfll’13(/))
C ----------------------- FORMATTING TITLE BLOCK ------
875 F0RMAT(/7/././:/:/,/.11X. 58(’C’)/.

mmmmmmmm

11X,’C’,40X,’Rev. 06-22-92’,3X,’C’/,
11X,’C',4X,’MASTERS THESIS RESEARCH’,
29x,'c'/,

11X,'C’,4X,’BRETT A. WILSON’,37X,’C’/,
11X,’C',4X,’MICHIGAN STATE UNIVERSITY’,
27x,'c'/,

11X,’C’,4X,’COLLEGE OF ENGINEERING',30X,’C’/,
11X,’C’,4X,’DEPARTMENT OF METALLURGY,’,

6 (MECHANICS, (,16x,(C(/,
167 6 11x,(C(,4x,5x,(AND MATERIAL SCIENCE',
6 27x,(C(/,
168 6 11X,’C’,56X,’C’/,
169 8‘ 11x158(’c’)I/I/I/I/I/I/)
1'7 0 C ----------------------- FORMATTING PROGRAM
C ------------------------ DESCRIPTION ----------------
1'71 880 FORMAT(/,/,llX,58(’C’)/,
1'72 6 11x,(C(,56x,(C(/,
1.73 6 11x,(C(,4x,(THIS PROGRAM USES MEASURABLE’,
6 (MATERIAL DATA TO( ,
1‘74 6 7x,(C(/,
1'75 6 11x,(C(,4x,(CREATE INFORMATION WHICH SHOULD(,
(PREDICT THE(,9x,(C(/
1'76 6 11X,’C’,4X,'FLOCCULATION STATE OF TWO’,
6 (COMPONENT COLLOIDAL(,
1'77 6 7x,(C(/,
178 6 11X,’C’,4X,’SUSPENSIONS.’,40X,’C'/,
1‘7 9 6 11x,(C(,56x,(C(/,
18 o 6 11x,(C(,4x,(THE PROGRAM RELIES ON A METHOD(,
6 ’WHICH IS A MOD-(, .
13 l 6 6x,(C(/,
182 6 11x,(C(,4x,(IFICATION OF THE H.H.F. METHOD,(,
(WHICH IS BASED ON(,
13 3 6 3x,(C(/,
18 4 6 11x,(C(,4x, ’THE DEBYE-HUCKEL APPROXIMATION’,
(FOR THE REPULSION(,
185 6 4x,(C(/,
18 6 6 11X,’C’,4X,’BETWEEN TWO PLATES OF CONSTANT(,
’POTENTIAL.’,11X,’C’/,
187 6 11x,(C(,56x,(C()
188 885 FORMAT(llX,’C’,4X,’MODIFICATIONS INCLUDE:(,
6 30x,(C(/,
189 6 11x,(C(,5x,(-USING AN EFFECTIVE HAMAKER(,
6 (CONSTANT FOR TWO(,7x,(C(
190 6 11x,(C(,6x,(PARTICLES IN A DISPERSING(,
6 ’MEDIUM.’,18X,’C’/,
191 6 11X,’C’,5X,’-USING ZETA POTENTIAL DATA(,
6 (INSTEAD OF CALCULAT-’,
192 & 4X’ICII’
193 6 11x,(C(,6x,(ING THE SURFACE POTNTIAL FROM(,
6 (POINT-OF-ZERO-(,6x,(C(
194 6 11x,(C(,6x,(CHARGE DATA.’,38X,’C’/,
195 6 11x,(C(,56x,(C(/,
196 6 11x,58((C(),/)
197 890 FORMAT(1X,(FILE NAME:(,A12/,
198 6 1x,(FILE DESCRIPTION:(/,
199 6 1x,A70)
200 895 FORMAT(lX, (THIS DATA WAS AQUIRED ON:(,
201 6 1x,12.2,(/(,Iz.2,(/(,I4.4)

Line} Source

206

Line

207
Line! Source Line

202 900 FORMAT(lx, ’AQUISITION BY THE PROGRAM STARTED’,

6 (AT...(,
203 6 1X,IZ.2,’:’,I2.2,’:’,IZ.2,’:’,12.2)
204 905 FORMAT(lX,21X,’AND FINISHED AT...(,
205 6 1X,IZ.2,’:’,IZ.2,’:’,IZ.2,’:’,IZ.2)

2 O 6 910 FORMAT(lX, ’OVERALL PROPORTION OF COMPONENT 1’ ,

6 (IN SYSTEM =(,
207 6 F4.3/,
208 6 1x,A42,1x,(=(,1x,F7.5/,
209 6 1x,A35,1x,(1(,1x,(=(,1x,F7.1/,
21.0 6 1X,A35,1X,'2’,1X,’=’,1X,F7.l)

211 915 FORMAT(IX,A34,1X,’=’,1X,F4.1)
212 920 FORMAT(IX,(ZERO-POINT-OF-CHARGE DATA WAS(,

6 (USED(,
213 6 ( FOR CALCULATIONS.()
21.4 925 FORMAT(lX,A33,lX,’l’,1X,’=’,1X,F5.2/,
215 6 1X,A33,1X,’2’,1X,’=’,1X,F5.2)
216 930 FORMAT(lX,A28,1X,E10.2/,
217 6 lX,A29,1X,’l =’,1X,E10.2/,
218 6 1X,A29,1X,’2 =’,1X,E10.2)
219 935 FORMAT(lX, (ZETA POTENTIAL DATA WAS USED FOR(,
22 0 6 ( CALCULATIONS.()

22 1 940 FORMAT(Ix, (ZETA POTENTIAL DATA FOR PARTICLE(,
6 lX,Il,’:’/,

22 2 6 1x, (ZETA POTENTIAL VALUES: ( ,10x,
6 (CORESPONDING PH VALUES:’)

223 945 FORMAT(23X,F5.1,29X,F5.1)

22 4 950 FORMAT(IX, (CALCULATED OVERALL STABILITY( ,
6 (RATIO DATA:(/,

22 5 & 1X, ’OVERALL STABILITY RATIO: ’ , 28X,
8 ’ CORESPONDING PH’ , / ,
22 6 & 1X’ (W11,W12,W22,WT)’,44X,’VALUES:’)

227 955 FORMAT(Ix,/,/,/,/,/,/,(CALCULATED OVERALL(,
6 (STABILITY RATIO(,

228 6 1x,(DATA:(/,

229 6 1x,(0VERALL STABILITY RATIO:(,28x,
6 (CORESPONDING PH(,/,

230 6 1X’(W11,W12,W22,WT)’,44X,’VALUES:’)

231 960 FORMAT(lX,E12.4,’, (,E12.4,(, (,E12.4,(, (,
6 E12.4,8x,F5.2)
232
233 CCC --------------------- RETURNING TO MAIN PROGRAM---
234 998 RETURN
235 999 END

DATASTORAGE
Name

TEMP.
FTIME
STIME
CDATE
WTT . .
WOT . . .
woo . . .
CONCL . .
PH. . . .
WT. .
ZPDP2
ZPPH2
ZPDP1
ZPPHI
NZP2.
NZPL
PHCZI
AHP .
Arm .
ZPQ . .
APR . .
V . . .
PHCZIC.
TFLNME.
K . . .
L . . .
AIiDMC. .
AHPC. .
CONCC .
APRC. .
FLDSC .
RICS. .
FLNME . . .
IFINM . . .
TJEEMPC . . .
FLXT. . . .

Local Symbols

Gl obal Symbols

Nfiinua
DA'I'ASTORAGE

C°de size

0C65 (3173)

gate, size = 0311 (785)
8 size = 01a2 (418)
errors detected

208

Class

param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
param
local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Class

FSUBRT

Type

CHAR*28
CHAR*34
INTEGER*4
INTEGER*4
CHAR*33
CHAR*33
CHAR*42
CHAR*35
CHAR*100
CHAR*16
CHAR*20
CHAR*17
CHAR*34
REAL*8
CHAR*4

Type

***

Size

28
34
4
4
33
33
42
35
100
16
20
17
34
8
4

Size

***

Offset

0006
000a
000e
0012
0016
001a
001e
0022
0026
002a
002e
0032
0036
003a
003e
0042
0046
004a
004e
0052
0056
005a
0002
001e
0040
0044
0048
006a
008c
00b6
00da
013e
014e
0162
0174
0196
019e

Offset

0000

Line}

209

Microsoft FORTRAN Optimizing Compiler Version 5.00.03

CCCCC

C .....
C .....

10
11
12
13
14
15
16
17
18 CCCCC
CCCCC
19 CCCCC
20 CCCCC
21 CCCCC
22 CCCCC
CCCCC
CCCCC
24 CCCCC
25 CCCCC
CCCCC
26 CCCCC
27 CCCCC
CCCCC
28 CCCCC
29 CCCCC
CCCCC
30 CCCCC
CCCCC
31 CCCCC
CCCCC
32 CCCCC
33 CCCCC
34 CCCCC
CCCCC
35 CCCCC
36 CCCCC
37 CCCCC

38 CCCCC

1
2
3
4
5 CCC---
6
7
8
9

Source Line

PROGRAM VARYN
REV. 07-07-92

------- PROGRAM TO CALCULATE OVERALL STABILITY
--------- RATIO FOR VARYING VALUES OF V USING
--------- DATA FROM PROGRAM RUNS WITH V=0.5----

IMPLICIT NONE

CHARACTER NDIRNAME*7,NWFLNAME*34,TNFLNAME*34
CHARACTER A*70,B*70,PSC*1

INTEGER L,K,NFLS,I,J

REAL*8 WT,WOO,WOT,WTT,OOWT,WTN,AZP,AZN,AZ,WMAX

REAL N,PH,V,PR,OON,PRC

DIMENSION PH(200),WT(200),WTN(5),V(5)
DIMENSION N(5),PR(2),PRC(2)

DIMENSION W00(200),WOT(200),WTT(200)

N=OVERALL PROPORTION OF PARTICLES OF COMPONENT
ONE IN SYSTEM
V=VOLUME PERCENT OF COMPONENT ONE IN SYSTEM
WT=OVERALL STABILTY RATIO
OOWT=ONE OVER WT
WOO,WOT,WTT=INVERSE OF THE PROBABILITY THAT A
GIVEN PARTICLE COLLISION LEADS TO
ADHESION
NFLS=NUMBER OF FILES TO RUN PROGRAM ON
NDIRNAME=NEW DIRECTORY NAME WHERE WILL FIND
DATA FILE
NWFLNAME=NEW FILE NAME
TNFLNAME=TOTAL NEW FILE NAME INCLUDING DRIVE
AND PATH
K=INTEGER VARIABLE USED AS A COUNTER FOR DO
LOOP WHICH CALCULATES OVERALL STABILITY AT
EACH SPECIFIED PH

L,I,J=INTEGERS USED AS COUNTER FOR VARIOUS DO
LOOPS
AZ=VARIABLE REPRESENTING ALMOST ZERO
=(1.0E-309)

AZP=POSITIVE VALUE OF AZ USED TO PREVENT AN
INVERSE FROM GOING TO INFINITY WHICH
CAUSES A MATH OVERFLOW ERROR RESULTING IN

PROGRAM TERMINATION

AZN=NEGATIVE VALUE OF AZ USED AS AZP IS

PR=PARTICLE RADIUS

PRC=PARTICLE RADIUS CUBED

OON=ONE OVER N

Line#
39
40
41

42
43
44

45
46
47
48
49
50
51
52
53

54
55
56
57
58

59
60
61
62
63
64
65

66

67
68
69
70

71
72
73
74
75
76
77
78
79

210

Source Line

CCCCC PSC=PARTICLE SIZE CHARACTER WHICH INDICATES

CCCCC PARTICLE SIZE

CCCCC WTN=NEW WT VALUES CALCULATED FOR DIFFERENT

CCCCC VALUES OF N (OR V) ‘

CCCCC WMAX=MAXIMUM W VALUE ALLOWED BY PLOTTING

CCCCC PROGRAM

CC ---------------------- CALCULATING VALUES FOR

C ------------------------- AZP,AZN -------------------

10 A2 = 1.0E-25

20 DO 40 K=1,1l,l

30 AZ = AZ/l.0E+25

40 CONTINUE

50 AZP = AZ/1.E9

60 AZN = -1.0*AZP

70 WMAX=9.9999E+30

CC ---------------------- INITIALIZING DRIVE AND PATH

C ------------------------- FOR TNFLNAME --------------

80 TNFLNAME(1:14) = (C:\JK\LL\DATA\(

90 TNFLNAME(22:23) = ’\B’

100 TNFLNAME(31:34) = ’.DAT’

CC ---------------------- INITIALIZING VALUES OF V FOR

C ------------------------- CALCULATIONS --------------

110 V(l) = 0.001

120 V(2) = 0.25

130 V(3) = 0.5

140 V(4) = 0.75

150 V(5) = 0.999

CC ---------------------- READING DATA FILE WITH LIST

C ------------------------- OF FILES ------------------

160 OPEN(14,FILE=’C:\JK\LL\DATA\FILELST’,
STATUS=(OLD()

170 READ(14,800)NFLS

CC ---------------------- RUNNING CALCULATIONS FOR

C ------------------------- EACH FILE -----------------

180 D0 670 I=1,NFLS,1

C ----------------------- READING NEW DIRECTORY NAME--

190 READ(14,810)NDIRNAME

200 TNFLNAME(15:21) = NDIRNAME

210 TNFLNAME(24:30) = NDIRNAME

220 NWFLNAME = TNFLNAME

230 NWFLNAME(20:21)=’VN’

235 NWFLNAME(29:30)=’VN’

Line#

80
81

82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101

102
103

104
105
106
107
108

109
110

111

112
113

114
115

116
117
118
119

120

211

Source Line

c ----------------------- DETERMINING PARTICLE SIZE
c ------------------------ FROM DIRECTORY NAME --------
240 PSC = NDIRNAME(4:4)
250 PR(2) = 250
260 IF(PSC.EQ.(1()PR(1)=2750
270 IF(PSC.EQ.’2’)PR(1)=900
280 IF(PSC.EQ.(3()PR(1)=400
290 PRC(1) = PR(1)**3
300 PRC(2) = PR(2)**3
C ----------------------- READING DATA FROM N=0.5 DATA
310 OPEN(15,FILE=TNFLNAME,STATUS=(OLD()
320 READ(15,820)A
330 READ(15,820)B
340 OPEN(16,FILE=NWFLNAME,STATUS=(NEW()
350 NWFLNAME(31:34)=(.DAM(
360 OPEN(17,FILE=NWFLNAME,STATUS=(NEW()
370 WRITE(16,900)A,B
380 D0 630 K=1,15,1
390 READ(15,830)PH(K),WOO(K),WOT(K),WTT(K)
C ----------------------- CALCULATING N VALUES FROM V
c ------------------------- VALUES --------------------
400 D0 570 L=1,5,1
410 OON = ((PRC(1))-(V(L)*PRC(1))) /
6 (V(L)*PRC(2))
420 OON = OON + 1.00
430 N(L) = 1.00/(OON)
cc ---------------------- FINDING THE OVERALL
c ------------------------- STABILITY RATIO AT CURRENT
c ------------------------- PH ------------------------
c ------------------------ PREVENTING MATH OVERFLOW
c --------------------------- ERRORS AND PROGRAM
0 --------------------------- TERMINATION -------------
440 IF(WOO(K).LE.AZP .AND.
6 WOO(K).GE.AZN)THEN
450 WT(K)=WOO(K)
460 ELSE IF(WOT(K).LE.AZP .AND.
6 WOT(K).GE.AZN)THEN
470 WT(K)=WOT(K)
480 ELSE IF(WTT(K).LE.AZP .AND.
6 WTT(K).GE.AZN)THEN
490 WT(K)=WTT(K)
500 ELSE
510 OOWT = (N(L)*N(L)/WOO(K))
520 OOWT=OOWT+
6 ((1.0-N(L))*(1.0-N(L))/WTT(K))

530 OOWT=OOWT+

212

Line! Source Line
6 (2.0*N(L)*(l.0-N(L))/WOT(K))
121 540 WT(K)=1.0/OOWT
122 550 END IF
123 560 WTN(L) = WT(K)
124 570 CONTINUE
125
126 CCC --------------------- WRITING NEW DATA TO A
CC ------------------------ STORAGE FILE --------------
127 580 WRITE(16,910)PH(K),WTN(1),WTN(2),WTN(3),
& WTN(4),WTN(5)
128 590 DO 610 J= 1, 5, 1
129 600 IF(WTN(J). GT. WMAX)WTN(J)=WMAX
130 610 CONTINUE
131 620 WRITE(17,910)PH(K),WTN(1),WTN(2),WTN(3),
6 WTN(4),WTN(5)
132 630 CONTINUE
133 640 CLOSE(17)
134 650 CLOSE(16)
135 660 CLOSE(IS)
136 670 CONTINUE
137 680 CLOSE(14)
138
139 800 FORMAT(IZ)
140 810 FORMAT(A7)
141 820 FORMAT(A70)
142 830 FORMAT(lX,F5.2,3X,E12.4,3X,E12.4,3X,E12.4)
143
144 900 FORMAT(IX,A70,/,1X,A70)
145 910 FORMAT(IX,F5.2, (,E12.4, ’,E12.4,’
146 & E12.4,’ ’,E12.4, ’,E12.4)
147
148 999 END
main Local Symbols
Name Class Type Size Offset
PH. . . . . . . . . . . . local REAL*4 800 0000
A . . . . . . . . . . . . local CHAR*70 70 0002
B . . . . . . . . . . . . local CHAR*70 70 0048
OOWT. . . . . . . . . . . local REAL*8 8 008e
I . . . . . . . . . . . . local INTEGER*4 4 0096
J . . . . . . . . . . . . local INTEGER*4 4 009a
K . . . . . . . . . . . . local INTEGER*4 4 009e
L . . . . . . . . . . . . local INTEGER*4 4 00a2
N . . . . . . . . . . local REAL*4 20 00a6
NDIRNAME. . . . . . . . . local CHAR*7 7 00ba
TNFLNAME. . . . . . . . . local CHAR*34 34 00c2
V . . . . . . . . . . . . local REAL*4 20 00e4

main Local Symbols

Name

NWFLNAME.

AZ. .
PR. .
PRC .
PSC .
AZN .
AZP .
OON .
NFLS.
WTN .
WMAX.
WT. .
WOO .
WOT .
WTT .

Global Symbols

Name

main.

Code size
Data size
Bss size

No errors

06ef (1775)
016d (365)
017a (380)

detected

213

Class

local
local
local
local
local
local
local
local
local
local
local
local
local
local
local

Class

FSUBRT

Type

CHAR*34

REAL*8
REAL*4
REAL*4
CHAR*1
REAL*8
REAL*8
REAL*4

INTEGER*4

REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8

Type

***

Size

to)

b
wowspoooopoooomb

1600
1600
1600
1600

Size

***

Offset

00f8
011a
0122
012a
0132
0134
0130
0144
0148
014c
0174
0320
0960
0fa0
15e0

Offset

0000

FILE NAME:SSZl3SD\BSSZl3SD
FILE DESCRIPTION: RUN USING BMTHFWVB.EXE.
THIS DATA WAS AQUIRED ON:

AQUISITION BY THE PROGRAM STARTED AT...
AND FINISHED AT...

214

07

/08/1992

00:21:33:16
01:17:26:97

VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM =

ATOMIC PARTICLE RADIUS OF COMPONENT l =
ATOMIC PARTICLE RADIUS OF COMPONENT 2 =

TEMPERATURE OF SYSTEM (IN DEG. C.) =

HAMAKER CONSTANT OF MEDIUM =

HAMAKER CONSTANT OF COMPONENT 1
HAMAKER CONSTANT OF COMPONENT 2

ZETA POTENTIAL VALUES:

5.8
-2.2
-15.0
-26.0
-34.0
-40.0
-44.0
-48.0
-51.0
-53.0
-54.0
-56.0
-57.0
-58.0
-59.0
-60.0
-60.0
-61.0
-61.0

25.0
45E-19

250.0

.30E-18
.16E-18
ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:

ZETA POTENTIAL DATA FOR PARTICLE 2:

ZETA POTENTIAL VALUES:

44.0
38.9
29.4
9.1
-24.0
-33.0
-43.0
-43.0
-45.0

CORESPONDING PH VALUES:

CORESPONDING PH VALUES:

.00100
2750.0

HHHDOmeQO‘mUIUIabhwb-iww

r-c>o-
O
ocnc>

' WOUIOUIOWOU'IOWOUIOWO

HmeQmmbN
000000
OOHHOOW

Pao-
c>o

215

CALCULATED OVERALL STABILITY RATIO DATA:
OVERALL STABILITY RATIO:
CORESPONDING PH (W11,W12,W22,WT)

VALUES:
.1819+248, .2738E+00, .1105E+77, .1825E+03 4.00
.4761+303, .2738E+00, .1257E+55, .1825E+03 4.50
.4761+303, .2738E+00, .4842E+36, .1825E+03 5.00
.4761+303, .2738E+00, .9557E+09, .1825E+03 5.50
.4761+303, .2738E+00, .5053E+00, .5047E+00 6.00
.4761+303, .2738E+00, .4998E+00, .4992E+00 6.50
.4761+303, .2738E+00, .4468E+13, .1825E+03 7.00
.4761+303, .2738E+00, .4563E+31, .1825E+03 7.50
.4761+303, .2738E+00, .7460E+49, .1825E+03 8.00
.4761+303, .3677E-04, .6029E+72, .2451E-01 8.50
.4761+303, .8836E+18, .6955E+99, .5889E+21 9.00
.4761+303, .8792E+22, .3959+101, .5860E+25 9.50
.4761+303, .8792E+22, .3959+101, .5860E+25 10.00
.4761+303, .2195E+30, .4755+107, .1463E+33 10.50
.4761+303, .1257E+35, .8488+113, .8378E+37 11.00

216

FILE NAME:SSZl3ES\BSSZl3ES

FILE DESCRIPTION: RUN USING BMTHFWVB.EXE.

THIS DATA WAS AQUIRED ON: 07/08/1992

AQUISITION BY THE PROGRAM STARTED AT... 14:43:32:87
AND FINISHED AT... 16:38:15:92

VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT l = 2750.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-19

HAMAKER CONSTANT OF COMPONENT 1 = .30E-18

HAMAKER CONSTANT OF COMPONENT 2 = .16E-18

ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.

ZETA POTENTIAL DATA FOR PARTICLE 1:

ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
-13.0
-14.0
-15.0
-16.0
-18.0
-19.0
-20.0
-21.0
-23.0
-23.0
-23.0
-25.0
-26.0
-27.0
-28.0
-28.0
-30.0
-31.0
-32.0
-33.0
-34.0
-35.0
-35.0
-36.0
-37.0
-38.0
-38.0
-39.0
-40.0
-40.0
-41.0
-41.0
-42.0
-42.0
-44.0
-45.0

0000x)qqqqqqqmmmmmmmmmmmmmmbbhbbbbbpppu

00......CO.........OCOOCOICOOOOOOO
UFO@QO‘bUNOWQm-bNI-‘m\IGDUNHO‘meflGmbUNHOW

-47.0
-48.0
-48.0
-48.0
-49.0
-49.0
-49.0
-50.0
-50.0
-50.0
-50.0
-51.0
-51.0
-51.0
-52.0
-52.0
-52.0
-53.0
-53.0
-54.0
-55.0
-56.0
-57.0
-59.0
-61.0

217

ZETA POTENTIAL DATA FOR PARTICLE 2:

ZETA POTENTIAL VALUES:

quorum-IqumppmupmqpbmmOAmoooo

Hmwwupbbmmmmmmmmqqqqmm
00000

CORESPONDING PH VALUES:

HH

ooommommmmmmmmmmm
0

Nomooqmmhuur-(oxooommk

10.3
10.4
10.5
10.7
10.8
10.9
11.1
11.2

0.000 0000 00.00.00.000...
O‘bUNHDQQMhUNHO-‘O‘qumhUNI-‘06

mmmmmmmmmmmmmmm-uhbnhbhbpu

218

J8902358nw24678990123456789912345678901
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0
Aw66777778888888899999999999000600000011
11111111111
539504.82357902255790113557700156994670
1.2234445555566666667777777788888889990
......................................fi.

219

CALCULATED OVERALL STABILITY RATIO DATA:

OVERALL STABILITY RATIO: CORESPONDING PH
(W11,W12,W22,WT) VALUES:
.2269E+00, .2738E+00, .5009E+00, .5003E+00 4.00
.2269E+00, .2738E+00, .5004E+00, .4998E+00 4.50
.5914E+21, .2738E+00, .5000E+00, .4994E+00 5.00
.7792+134, .2738E+00, .4997E+00, .4991E+00 5.50
.1725+236, .2738E+00, .4994E+00, .4988E+00 6.00
.4761+303, .2738E+00, .4993E+00, .4987E+00 6.50
.4761+303, .2738E+00, .4996E+00, .4989E+00 7.00
.4761+303, .2738E+00, .4998E+00, .4992E+00 7.50
.4761+303, .2738E+00, .4999E+00, .4993E+00 8.00
.4761+303, .2738E+00, .5000E+00, .4994E+00 8.50
.4761+303, .2738E+00, .5003E+00, .4996E+00 9.00
.4761+303, .2738E+00, .5005E+00, .4999E+00 9.50
.4761+303, .2738E+00, .5009E+00, .5002E+00 10.00
.4761+303, .2738E+00, .5014E+00, .5008E+00 10.50

.4761+303, .2738E+00, .5027E+00, .5020E+00 11.00

220

FILE NAME:88213CC\BSS213CC
FILE DESCRIPTION: RUN USING BMTHFWVB.EXE.
THIS DATA WAS AQUIRED ON: 07/08/1992
AQUISITION BY THE PROGRAM STARTED AT... 11:04:37:77
AND FINISHED AT... 11:51:44:57
VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500
CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 2750.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0
HAMAKER CONSTANT OF MEDIUM = .45E-19
HAMAKER CONSTANT OF COMPONENT 1 ’ .30E-18
HAMAKER CONSTANT OF COMPONENT 2 .16E-18
ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
5.8
-2.2
-15.0
-26.0
-34.0
-40.0
-44.0
-48.0
-51.0
-53.0
-54.0
-56.0
-57.0
-58.0
-59.0
-60.0
-60.0
-61.0
-61.0
ZETA POTENTIAL DATA FOR PARTICLE 2:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
' 44.0
38.9
29.4
9.1
-24.0
-33.0
-43.0
-43.0
-45.0

OU‘OU’IOWOUIOUIOUIOUIOUIOUIO

Hoommmmqqmmmmbhuumw

HHH

OOOOHHOOD

HOOQQQU’IhN

HH

221

CALCULATED OVERALL STABILITY RATIO DATA:

OVERALL STABILITY RATIO: CORESPONDING PH
(W11,W12,W22,WT) VALUES:
.4761+303, .2738E+00, .4336+302, .1825E+03 4.00
.4761+303, .2738E+00, .4336+302, .1825E+03 4.50
.4761+303, .2738E+00, .4336+302, .1825E+03 5.00
.4761+303, .2738E+00, .7502+l44, .1825E+03 5.50
.4761+303, .2738E+00, .6674E+00, .6660E+00 6.00
.4761+303, .2738E+00, .4998E+00, .4992E+00 6.50
.4761+303, .9751E-07, .5189+181, .6499E-04 7.00
.4761+303, .2597+303, .4336+302, .4341+302 7.50
.4761+303, .2597+303, .4336+302, .4341+302 8.00
.4761+303, .2597+303, .4336+302, .4341+302 8.50
.4761+303, .2597+303, .4336+302, .4341+302 9.00
.4761+303, .2597+303, .4336+302, .4341+302 9.50
.4761+303, .2597+303, .4336+302, .4341+302 10.00
.4761+303, .2597+303, .4336+302, .4341+302 10.50

.4761+303, .2597+303, .4336+302, .4341+302 11.00

222

FILE NAME:SS223SD\Bsszz3SD

FILE DESCRIPTION: RUN USING BNHTFWVB.EXE.

THIS DATA WAS AQUIRED ON: 07/08/1992

AQUISITION BY THE PROGRAM STARTED AT... 01:17:28:56
AND FINISHED AT... 01:48:04:33

VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 900.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-19

HAMAKER CONSTANT OF COMPONENT 1 - .30E-18

HAMAKER CONSTANT OF COMPONENT 2 .16E-18
ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
5.8
-2.2
-15.0
-26.0
-34.0
-40.0
-44.0
-48.0
-51.0
-53.0
-54.0
-56.0
-57.0
-58.0
-59.0
-60.0
-60.0
-61.0
-61.0
ZETA POTENTIAL DATA FOR PARTICLE 2:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
44.0
38.9
29.4
9.1
-24.0
-33.0
-43.0
-43.0
-45.0

HOO‘ODWQQQO‘O‘U‘U‘b-fiUUNN
000000000

OUIOUIOU'IOUIOU'IOUIOUIOUIOUIO

HHH

HODNQO‘UPN
OOOOHHOOD

HP

223

CALCULATED OVERALL STABILITY RATIO DATA:

OVERALL STABILITY RATIO: CORESPONDING PH
(W11,W12,W22,WT) VALUES:
.1185E+85, .2926E+00, .1105E+77, .7121E+01 4.00
.1126+168, .2926E+00, .1257E+55, .7121E+01 4.50
.7627+235, .2926E+00, .4842E+36, .7121E+01 5.00
.1559+303, .2926E+00, .9557E+09, .7121E+01 5.50
.1559+303, .2926E+00, .5053E+00, .4909E+00 6.00
.1559+303, .2926E+00, .4998E+00, .4859E+00 6.50
.1559+303, .1057E+12, .4468E+13, .1658E+13 7.00
.1559+303, .1524E+39, .4563E+31, .4760E+31 7.50
.1559+303, .4540E+63, .7460E+49, .7783E+49 8.00
.1559+303, .9818E+91, .6029E+72, .6290E+72 8.50
.1559+303, .7745+122, .6955E+99, .7257E+99 9.00
.1559+303, .4593+127, .3959+101, .4131+101 9.50
.1559+303, .4593+127, .3959+101, .4131+101 10.00
.1559+303, .7530+136, .4755+107, .4961+107 10.50

.1559+303, .1342+143, .8488+113, .8855+113 11.00

224

FILE NAME:SSZ23ES\B88223eS

FILE DESCRIPTION: RUN USING BNHTFWVB.EXE.

THIS DATA WAS AQUIRED ON: 07/08/1992

AQUISITION BY THE PROGRAM STARTED AT... 16:38:17:89
AND FINISHED AT... 18:02:57:18

OVERALL PROPORTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 900.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-19

HAMAKER CONSTANT OF COMPONENT 1 ’ .30E-18

HAMAKER CONSTANT OF COMPONENT 2 .16E-18
ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:

-10.0

-11.0

-12.0

-13.0

-l4.0

-15.0

-16.0

-17.0

-18.0

-19.0

-20.0

-21.0

-22.0

-22.0

-23.0

-24.0

-25.0

-25.0

-27.0

-29.0

-30.0

-31.0

-32.0

-33.0

-35.0

-36.0

-36.0

-37.0

-38.0

-39.0

-39.0

-40.0

-41.0

-42.0

-43.0

-43.0

qqqdustummmmmmammmmmmmmwmmm-AbéAha-44:44.6.4:

00000000.0000000000000000...

-44.0
-45.0
-47.0
-48.0
-49.0
-49.0
-51.0
-50.0
-51.0
-52.0
-53.0
-53.0
-55.0
-54.0
-55.0
-55.0
-55.0
-56.0
-57.0
-57.0
-57.0
-59.0
-59.0
-59.0
-61.0
-61.0
-62.0
-63.0
-63.0
-64.0
-65.0
-68.0
-70.0
-70.0

225

ZETA POTENTIAL DATA FOR PARTICLE 2:

ZETA POTENTIAL VALUES:

Amwpmxn-(hmooOAmoooo

Sammuunmmmmmxquqoooo
0

CORESPONDING PH VALUES:

ommwommmmmmmmmmmmmmmooooxxqu

(.3
O
HommmmuuHHommmqmmhbuwr-Ioxaooq

00.00.00.000.
uhUNHHO‘OQQO‘hUNi-‘C‘D

mmmmmmhoSobc-nhhu

226

5789123467890.2358nw24678990.12345‘w7.80~917u34..5678901
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
555566666666—h—h—M—h—h88 888889999999ngangommmooooo11
11111111111
1....8371582753950482357902255790113557700156994670
L33221 .12234445555566666667777777788888889990
.......-................_............d.

CALCULATED OVERALL STABILITY RATIO DATA:
OVERALL STABILITY RATIO:

(W11,W12,W22,WT)
.2285E+00, .2926E+00,
.2285E+00, .2926E+00,
.2285E+00, .2926E+00,
.1357E+02, .2926E+00,
.1510E+46, .2926E+00,
.8030+108, .2926E+00,
.4518+152, .2926E+00,
.3056+214, .2926E+00,
.1559+303, .2926E+00,
.1559+303, .2926E+00,
.1559+303, .2926E+00,
.1559+303, .2926E+00,
.1559+303, .2926E+00,
.1559+303, .2926E+00,

.1559+303,

.2926E+00,

227

.5009E+00,
.5004E+00,
.5000E+00,
.4997E+00,
.4994E+00,
.4993E+00,
.4996E+00,
.4998E+00,
.4999E+00,
.5000E+00,
.5003E+00,
.5005E+00,
.5009E+00,
.5014E+00,
.5027E+00,

CORESPONDING PH

.4865E+00
.4860E+00
.4856E+00
.4858E+00
.4856E+00
.4855E+00
.4857E+00
.4859E+00
.4860E+00
.4861E+00
.4863E+00
.4865E+00
.4868E+00
.4873E+00
.4885E+00

VALUES:

4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50

10.00
10.50
11.00

228

FILE NAME:88223CC\BSSZZZ3CC

FILE DESCRIPTION: RUN USING BNHTFWVB.EXE.

THIS DATA WAS AQUIRED ON: 07/08/1992

AQUISITION BY THE PROGRAM STARTED AT... 11:51:46:16
AND FINISHED AT... 12:22:28:47

VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 900.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-l9

HAMAKER CONSTANT OF COMPONENT 1 * .30E-18

HAMAKER CONSTANT OF COMPONENT 2 .16E-18
ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
5.8
-2.2
-15.0
-26.0
-34.0
-40.0
-44.0
-48.0
-51.0
-53.0
-54.0
-56.0
-57.0
-58.0
-59.0
-60.0
-60.0
-61.0
-61.0
ZETA POTENTIAL DATA FOR PARTICLE 2:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
44.0
38.9
29.4
9.1
-24.0
-33.0
-43.0
-43.0
-45.0

“cowomeQmmmmfihwUNN
o 0 o 0 o o

PHI-4
omomomomomomomomomo

HOUmQO‘UIaP-N
000000.00
OOOOHHOOO

HP

229

CALCULATED OVERALL STABILITY RATIO DATA:

OVERALL STABILITY RATIO: CORESPONDING PH

(W11,W12,W22,WT) VALUES:
.1559+303, .2926E+00, .4336+302, .7121E+01 4.00
.1559+303, .2926E+00, .4336+302, .7121E+01 4.50
.1559+303, .2926E+00, .4336+302, .7121E+01 5.00
.1559+303, .2926E+00, .7502+144, .7121E+01 5.50
.1559+303, .2926E+00, .6674E+00, .6343E+00 6.00
.1559+303, .2450+16l, .4998E+00, .5215E+00 6.50
.1559+303, .9961+302, .5189+181, .5414+181 7.00
.1559+303, .9961+302, .4336+302, .4440+302 7.50
.1559+303, .9961+302, .4336+302, .4440+302 8.00
.1559+303, .9961+302, .4336+302, .4440+302 8.50
.1559+303, .9961+302, .4336+302, .4440+302 9.00
.1559+303, .9961+302, .4336+302, .4440+302 9.50
.1559+303, .9961+302, .4336+302, .4440+302 10.00
.1559+303, .9961+302, .4336+302, .4440+302 10.50
.1559+303, .9961+302, .4336+302, .4440+302 11.00

230

FILE NAME:SSZ33SD\BSSZB3SD
FILE DESCRIPTION: RUN USING BMTHFWVB.EXE.
THIS DATA WAS AQUIRED ON: 07/08/1992
AQUISITION BY THE PROGRAM STARTED AT... 01:48:06:04
AND FINISHED AT... 02:12:19:64
VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 400.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-19

HAMAKER CONSTANT OF COMPONENT 1 = .30E-18

HAMAKER CONSTANT OF COMPONENT 2 = .16E-18

ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
5.8
-2.2
-15.0
-26.0
-34.0
-40.0
-44.0
-48.0
-51.0
-53.0
-54.0
-56.0
-57.0
-58.0
"-59.0
-60.0
-60.0
-61.0
-61.0
ZETA POTENTIAL DATA FOR PARTICLE 2:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
44.0
38.9
29.4
9.1
-24.0
-33.0
-43.0
-43.0
-45.0

OUIOUIOUIOUIOUIOUIOUIOUIOUIO

HOODWQNQQGGU‘IUIthUNN

HHH

Howmqmmpw
000000000 000
OOOOHHOO‘D

Hr-

231

CALCULATED OVERALL STABILITY RATIO DATA:

OVERALL STABILITY RATIO: CORESPONDING PH

(W11,W12,W22,WT) VALUES:
.1765E+40, .3193E+00, .1105E+77, .1012E+01 4.00
.1920E+77, .3193E+00, .1257E+55, .1012E+01 4.50
.3301+107, .3193E+00, .4842E+36, .1012E+01 5.00
.1497+142, .3193E+00, .9557E+09, .1012E+Ol 5.50
.1161+17l, .3193E+00, .5053E+00, .4412E+00 6.00
.5052+191, .3194E+00, .4998E+00, .4385E+00 6.50
.2729+202, .1514E+29, .4468E+13, .6917E+13 7.00
.5347+224, .7590E+55, .4563E+31, .7062E+31 7.50
.1938+236, .1654E+79, .7460E+49, .1155E+50 8.00
.1324+248, .4834+105, .6029E+72, .9332E+72 8.50
.1707+260, .1116+134, .6955E+99, .1077+100 9.00
.4147+272, .1254+138, .3959+101, .6128+101 9.50
.4147+272, .1254+138, .3959+101, .6128+101 10.00
.1900+285, .1611+l46, .4755+107, .7360+107 10.50
.1900+285, .8486+151, .8488+113, .1314+114 11.00

232

FILE NAME:SSZB3ES\BSSZ33ES

FILE DESCRIPTION: RUN USING BMTHFWVB.EXE.

THIS DATA WAS AQUIRED ON: 07/08/1992

AQUISITION BY THE PROGRAM STARTED AT... 09:27:50:39
AND FINISHED AT... 11:04:35:90

VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 400.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-19

HAMAKER CONSTANT OF COMPONENT 1 = .30E-18

HAMAKER CONSTANT OF COMPONENT 2 = .16E-18

ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
-2.2
-2.6
-2.9
-3.2
-3.6
-3.9
-4.5
-4.7
-5.0
-5.3
-5.5
-6.0
-6.3
-6.4
-6.6
-6.9
-7.2
-7.3
-7.4
-7.7
-8.0
-8.1
-8.2
-8.6
-8.8
-8.9
-9.1
-9.3
-9.5
-9.8
-10.0
-10.0
-10.0
-11.0
-11.0
-11.0

0‘mmmmO‘OiO‘O‘GGQO‘UIMUIUIUIUIUIUIUIUIU)UlUIuhcfiuhuhub-hhfink-b

(00000qmmbuuNHHowmmqmmmhuuwpoomqmmhumpo

-11.0
-12.0
-12.0
-12.0
-12.0
-13.0
-13.0
-13.0
-13.0
-14.0
-14.0
-14.0
-14.0
-15.0
-15.0
-15.0
-15.0
-15.0
-15.0
-15.0
-16.0
-l6.0
-16.0
-16.0
-16.0
-17.0
-17.0
-17.0
-17.0
-17.0
-17.0
-17.0
-18.0
-18.0
-18.0
-18.0
-18.0
-19.0
-19.0
-19.0
-19.0
-20.0
-20.0
-21.0
-21.0
-21.0
-21.0

233

HHH -
ooow\onsoxoxooosotomooooooooooooooooooooooooooqqqqqqqqqqqqqq

[.3
O

motor-(ommummbuwt-(ommqmmpuuwpwoommm\lmmmbbuwwpo

H
O

10.6
10.7
10.9
11.0
11.1

234

CORESPONDING PH VALUES

ZETA POTENTIAL DATA FOR PARTICLE 2

ZETA POTENTIAL VALUES

90123467890112345789123467890235809.467899012345678

34444444445555555555666666667777788888888999999999

0.nw854..nu.8641754“284..183715827

5395
88~I.~I.nI.—I.666655554..4..4..33221 ..flanafl...”

-4.0
-4.4
-4.8
-5.2
-5.3
-5.5
-5.7
-5.9
-6.0
-6.2
-6.2
-6.5
-6.5
-6.7
-6.9
-7.0
-7.1
-7.1
-7.3
-7.5
-7.5

235

9912345678901
9900000000011
11111111111
7700156994670
7788888889990
..............m..

CALCULATED OVERALL STABILITY RATIO DATA:
OVERALL STABILITY RATIO:

(W11,W12,W22,WT)
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,
.2293E+00, .3193E+00,

236

.5009E+00,
.5004E+00,
.5000E+00,
.4997E+00,
.4994E+00,
.4993E+00,
.4996E+00,
.4998E+00,
.4999E+00,
.5000E+00,
.5003E+00,
.5005E+00,
.5009E+00,
.5014E+00,
.5027E+00,

CORESPONDING PH

VALUES:
.4089E+00 4.00
.4087E+00 4.50
.4085E+00 5.00
.4084E+00 5.50
.4083E+00 6.00
.4082E+00 6.50
.4083E+00 ' 7.00
.4084E+00 7.50
.4085E+00 8.00
.4085E+00 8.50
.4086E+00 9.00
.4088E+00 9.50
.4089E+00 10.00
.4091E+00 10.50
.4097E+00 11.00

237

FILE NAME:SS233CC\BSSZ33CC

FILE DESCRIPTION: RUN USING BMTHFWVB.EXE.

THIS DATA WAS AQUIRED ON: 07/08/1992

AQUISITION BY THE PROGRAM STARTED AT... 12:22:30:01
AND FINISHED AT... 12:49:50:91

VOLUME FRACTION OF COMPONENT 1 IN SYSTEM =.500

CONCENTRATION OF 1-1 ELECTROLYTE IN SYSTEM = .00100
ATOMIC PARTICLE RADIUS OF COMPONENT 1 = 400.0
ATOMIC PARTICLE RADIUS OF COMPONENT 2 = 250.0
TEMPERATURE OF SYSTEM (IN DEG. C.) = 25.0

HAMAKER CONSTANT OF MEDIUM = .45E-19

HAMAKER CONSTANT OF COMPONENT 1 = .30E-18

HAMAKER CONSTANT OF COMPONENT 2 = .16E-18

ZETA POTENTIAL DATA WAS USED FOR CALCULATIONS.
ZETA POTENTIAL DATA FOR PARTICLE 1:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
5.8
-2.2
-15.0
-26.0
-34.0
-40.0
-44.0
-48.0
-51.0
-53.0
-54.0
-56.0
-57.0
-58.0
-59.0
-60.0
-60.0
-61.0
-61.0
ZETA POTENTIAL DATA FOR PARTICLE 2:
ZETA POTENTIAL VALUES: CORESPONDING PH VALUES:
44.0
38.9
29.4
9.1
-24.0
-33.0
-43.0
-43.0
-45.0

Hoommmmqummmmnpuuuu
OUOU‘OWOUIOUIOWOUIOUIOUIO

PHI-
0

HO‘OQOm-bw
OOOOHHOOU’

HP

238

CALCULATED OVERALL STABILITY RATIO DATA:

OVERALL STABILITY RATIO: CORESPONDING PH
(W11,W12,W22,WT) VALUES:
.6932+302, .3193E+00, .4336+302, .1012E+01 4.00
.6932+302, .3193E+00, .4336+302, .1012E+01 4.50
.6932+302, .3193E+00, .4336+302, .1012E+01 5.00
.6932+302, .3193E+00, .7502+144, .1012E+01 5.50
.6932+302, .3193E+00, .6674E+00, .5113E+00 6.00
.6932+302, .2417+283, .4998E+00, .7737E+00 6.50
.6932+302, .5634+302, .5189+181, .8032+181 7.00
.6932+302, .5634+302, .4336+302, .4750+302 7.50
.6932+302, .5634+302, .4336+302, .4750+302 8.00
.6932+302, .5634+302, .4336+302, .4750+302 8.50
.6932+302, .5634+302, .4336+302, .4750+302 9.00
.6932+302, .5634+302, .4336+302, .4750+302 9.50
.6932+302, .5634+302, .4336+302, .4750+302 10.00
.6932+302, .5634+302, .4336+302, .4750+302 10.50

.6932+302, .5634+302, .4336+302, .4750+302 11.00

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IE5

mlwfiflfllculfi)[117111719