the sorption of cationic dyes by polyester fibers a …€¦ · dyeing polyester fibers mechanism...
TRANSCRIPT
THE SORPTION OF CATIONIC DYES
BY POLYESTER FIBERS
A THESIS
Presented to
The Faculty of the Division of Graduate
Studies and Research
by
Larry Clifford Kelley
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
in the A. French Textile School
Georgia Institute of Technology
March, 1972
GEORGIA INSTITUTE OF TECHNOLOGY LIBRARY
Regulations for the Use of Theses
Unpublished theses submitted for the Master's and Doctor's degrees and deposited in the Georgia Institute of Technology Library are open for inspection and consultation, but must be used with due regard for the rights of the authors. Passages may be copied only with permission of the authors, and proper credit must be given in subsequent written or published work. Extensive copying or publication of the thesis in whole or in part requires the consent of the Dean of the Graduate Division of the Georgia Institute of Technology.
This thesis by Larry Clifford Kelley
has been used by the following persons, whose signatures attest their acceptance of the above restrictions.
A library which borrows this thesis for use by its patrons is expected to secure the signature of each user.
NAME^D ADDRESS OF USER BORROW ING^^IBRARY DATE
^ ~ ~ slifjlS \
In presenting the dissertation as a partial fulfillment of the requirements for an advanced degree from the Georgia Institute of Technology, I agree that the Library of the Institute shall make it available for inspection and circulation in accordance with its regulations governing materials of this type. I agree that permission to copy from, or to publish from, this dissertation may be granted by the professor under whose direction it was written, or, in his absence, by the Dean of the Graduate Division when such copying or publication is solely for scholarly purposes and does not involve potential financial gain. It is understood that any copying from, or publication of, this dissertation which involves potential financial gain will not be allowed without written permission.
=^V5_
JI ~^r "
7/25/68
SORPTION OF CATIONIC DYES
BY POLYESTER FIBERS
Approved:
Chairrnan-
Date approved by Chairman:_
ii
ACKNOWLEDGMENTS
I would like to express my appreciation to my thesis advisor,
Dr. Walter C. Carter, whose guidance and counsel has made this thesis
possible.
I wish to thank Dr. James L. Taylor for the financial assistance
provided through the School of Textiles.
Dr. Charles L. Liotta and Mr. R. K. Flege served on the reading
committee and I am grateful to them.
I am grateful to Dr. L. Howard Olson for his generous assistance
in formulating the calculator program.
TABLE OF CONTENTS
ACKNOWLEDGMENTS
LIST OF TABLES
LIST OF ILLUSTRATIONS
SUMMARY
CHAPTER
I. INTRODUCTION
Statement of the Problem Review of the Literature
II. INSTRUMENTATION, EQUIPMENT, AND CHEMICALS
III. EXPERIMENTAL PROCEDURE
Analysis of Dye and Carrier Solutions Equilibrium Studies Rate Studies Determination of Fiber Radius
IV. DISCUSSION OF THE RESULTS
Calibration Curves Isotherms Rate Studies Apparent Diffusion Coefficients
V. CONCLUSIONS
VI. RECOMMENDATIONS
APPENDIX
BIBLIOGRAPHY
iii
Page
iv
1
10
12
19
41
43
44
54
•
LIST OF TABLES
IV
Table Page
1. Average Diffusion Coefficients Versus Carrier Concentration 38
2. Calculations . 45
3. Results of Rate of Dyeing Experiments 46
4. Program for the Hewlett-Packard Calculator 48
5. Calculator Output, Dt/r Versus Ct/Co) 51
6. Apparent Diffusion Coefficients for All Points in the Rate of Dyeing Experiments 52
LIST OF ILLUSTRATIONS
Figure Page
1. Spectrum of Basic Blue 22 in 50/50 Methanol/Water 20
2. Absorbance-Concentration Relation for Basic Blue 22 in 50/50 Methanol/Water (1.00 cm Cell at 635 nm) 21
3. Spectrum of Biphenyl in 50/50 Methanol/Water 22
4. Absorbance-Concentration Relation for Biphenyl in 50/50 Methanol/Water (1.00 cm Cell at 248 nm) 23
5. Sorption Isotherm for Dye in Polymer 25
6. Langmuir Plot of Sorption Isotherm for Dye in Polymer 26
7. Cross Section of Fiber After Sorption of 10 Percent Dye Based on the Weight of the Fiber 27
8. Sorption of Biphenyl by Teflon Liner (95°C) 29
9. Sorption of Biphenyl by Teflon Liner and Fibers (95°C) . . . 30
10. Sorption Isotherm for Biphenyl in Fiber (95 C) 31
11. Percent Dye Decomposition Versus Time (95 C) 33
12. Dye Sorption-Square Root of Time Curves With and Without Carrier (95°C) 34
13. Dye Sorption-Time Curves With and Without Carrier (95°C) 35
14. Log of Diffusion Coefficient Versus Amount of Carrier in Bath 39
vi
SUMMARY
This work involves a study of the dyeing behavior of polyester
fibers which have been modified so that they will sorb cationic dyes.
The equilibrium state and the kinetics of the dyeing process have been
determined as well as the effect of chemical dyeing accelerants called
dye "carriers" on the dye diffusion process.
It is concluded that this dyeing system obeys a Langmuir type
sorption process where the dye uptake is dependent upon the number of
sorption sites in the fiber. The rate of dyeing is low but can be
greatly increased when a dyeing carrier such as biphenyl is added to the
dyebath. The apparent diffusion coefficient is shown to increase with
increasing amounts of carrier in the dyebath, the log of the diffusion
coefficient being linearly related to the amount of carrier sorbed by
the fiber.
CHAPTER I
INTRODUCTION
Statement of the Problem
When polyester fibers were introduced in the late 1940's, their
density and impermeability presented special dyeing difficulties. It
was found that only nonionic disperse dyes could be used on the highly
hydrophobic fibers; however, under the usual dyeing conditions the rate
was extremely slow and higher dyeing temperatures were required to in
crease the rate of diffusion of the dye into the fiber. It was then
found that certain organic compounds, commonly referred to as "carriers",
when added to the dyebath, caused an acceleration in the diffusion of
the dye (1). Today, polyester fibers are normally dyed either at tem-
o o peratures. in excess of 100 C or at approximately 100 C in the presence
of carriers.
Even with the satisfactory dyeing rate by these methods the lati
tude of polyester fibers in the apparel industry was somewhat hampered
because of the restricted selection of available colors using disperse
dyes. In the mid 1950*s the E. I. duPont de Nemours Company (2,3)
introduced a modified polyester fiber capable of accepting cationic
dyes, thus presenting a new selection of brilliant and varied colors.
Since only general information of a practical nature is available
concerning the dyeing of cationic dyeable polyester fibers, it is the
purpose of this study to determine experimentally the characteristics
of the dyeing process, namely, the equilibrium state and the effect of
carriers on the kinetics of the dyeing process.
Review of the Literature
With respect to dyeing behavior, polyester fibers are of two
types: one that can be dyed only with disperse dyes, and one that can
be dyed with cationic as well as disperse dyes. There is an abundance
of information on the disperse dye-polyester fiber system, but very
little on the cationic dye-polyester fiber system which presumably re
sembles the cationic dye-acrylic fiber system. Therefore, this review
of the literature will include information on the dyeing of polyester
fibers with disperse dyes, the effect of carriers in accelerating the
dyeing process, and information on the dyeing of acrylic fibers with
cationic dyes.
Modifications of Polyester Fibers
Almost all of the polyester fibers on the market today are made
from a condensation polymer of terephthalic acid and ethylene glycol.
Polyester fibers chemically modified so that they can be dyed with cat
ionic dyes are now available (2,3). Sodium 3,5-di(carbomethoxy)ben-
zenesulfonate as a modifier is added to the polymerization process
providing acid groups as dye sites. Concentrations of 1 to 5 mol per
cent of the modifier are regarded as optimum and preferred. The re
sulting structure is as follows:
£ CH2-CH2-O-C-^ -1
-C-0 + J n
SO3 Na
Dyeing Polyester Fibers
Mechanism of Dyeing. Waters (4) has determined the saturation
values and the relative diffusion coefficients of disperse dyes in
polyester, nylon, and cellulose acetate fibers. At 85 C, the polyester
fiber was found to sorb a little less dye than the cellulose acetate but
twice as much as nylon. The relative diffusion of C. I. Disperse Orange
3 at 85 C was 680 times faster in nylon than in polyester, and at 100 C
this dye diffused into the polyester 48 times faster. Waters concluded
that the behavior of disperse dyes in polyester resembled their behavior
in nylon and cellulose acetate, and that the polyester fibers opened up
at higher temperatures allowing the dye to penetrate the fiber.
Remington and Schroeder (5) studied the equilibrium distribution
of disperse dyes between polyester fibers and water. Using three dif
ferent disperse dyes, they found in each case a direct proportionality
between the concentration of dye in the water phase and the concentra
tion of dye in the fiber which held until saturation occurred in both
phases. When two dyes were equilibrated simultaneously, each acted
independently of the other. The heat of dyeing for the polyester fiber-
disperse dye system was calculated to be only 4 kcal/mol. These results
indicated that the dyeing mechanism involved simple solution of the dye
in the fiber.
Patterson and Sheldon (6) have described work in which the dif
fusion coefficients were derived from the rates of dyeing. At 95 C, the
diffusion coefficients of C. I. Disperse Red 1 and C. I. Disperse Red 15
I A 9 —1 — 1 2 ? into polyester staple were 8.5 X 10 cm sec and 1.32 X 10 cm
sec , respectively. From other experiments the diffusion coefficients
were shown to be independent of concentration. They also found that
when additional dye particles were added to a saturated dye solution,
the rate of dyeing remained constant. It was their conclusion that only
single disperse dye molecules could diffuse within the fiber.
Vickerstaff (1) and Salvin (7) have conjectured that the dye mole
cules can diffuse only in the amorphous regions of a fiber. In the case
of disperse dyes, Glenz et al. (8) and Salvin (7) concluded that the
forces of attraction linking the dye to the fiber are short range forces
such as hydrogen bonding, dipole interaction and Van der Waals forces.
In a study using seventeen disperse dyes, Glenz et al. (8) found that an
increase in the number of groups available for hydrogen bonding on the
dye molecule decreased the diffusion rate.
Effect of Carriers. Schuler (9) investigated the role of carriers
in dyeing polyester fibers by using an isooctane system which was an ex
cellent solvent for disperse dyes and carriers. Surprisingly, the addi
tion of water to an isooctane dye bath increased the rate of dyeing six
fold indicating that water itself was a powerful carrier. When equimolar
concentrations of widely differing carriers were sorbed by the fiber, the
rate of dyeing was relatively independent of the structure of the carrier,
and increasing the concentration of the carrier in the fiber increased
the rate of dyeing. Schuler concluded that the mechanism of carrier
activity varied little and that the carriers entered the amorphous re-
tions of a fiber and loosened the polymer interchain forces.
Glenz et al. (8) tested Schuler's hypothesis in an aqueous medium
by determining the diffusion coefficient of disperse dyes when equimolar
concentrations of benzoic acid and trichlorobenzene were actually inside
the fiber. They found an increase of the diffusion coefficient by a
factor of 10-100, and concluded that the effect of a carrier depended on
the number of molecules present in the interior of the fiber.
Vickerstaff (10) observed that water insoluble carriers such as
biphenyl were 50 times more effective on a weight basis than soluble
carriers in increasing the dyeing rate of disperse dyes in polyester
fibers. Also, a fiber which had been pretreated with biphenyl exhibited
a much higher initial rate of dyeing than a fiber where biphenyl was
merely added to the dyebath. An explanation of this was that the bi
phenyl in the pretreated fiber modifies the fiber structure thus giving
a higher initial rate, but when the biphenyl is in the dyebath, the rate
can be accelerated only after the biphenyl has penetrated the fiber.
When a carrier modifies a fiber by loosening interchain forces,
the fiber will swell as the carrier molecules penetrate between polymer
chains. Rawicz et al. (11) studied the contraction of fibers, which is
a measure of its swelling, as a factor in carrier dyeing. Contraction
was shown to be dependent upon the concentration of carrier added to the
bath, and water-insoluble carriers tend to shrink polyester fibers more
than water-soluble carriers. A study of X-ray diffraction patterns dis
closed significant deorientation after a fiber had been treated with one
percent o-phenylphenol based on the weight of the fiber.
Balmforth et al. (12) examined the effect of carriers oil the
equilibrium uptake of disperse dyes in polyester fibers. They discov
ered that increasing the biphenyl concentration increased the equilib
rium uptake, but only up to a biphenyl concentration of 7 percent based
on the weight of the fiber. Higher concentrations of the carrier re-
duced the amount of dye sorbed by the fiber. They theorized that 7
percent biphenyl was the amount necessary to saturate both the fiber and
the dyebath, and any further additions led to a third phase consisting
of biphenyl containing the dissolved dye.
Dyeing Acrylic Fibers
Vogel et al. (13) investigated the equilibrium state of Orion 42
acrylic fiber obtained by dyeing fibers at 100 C with three cationic
dyes. When the reciprocal of the concentration of each dye in the fiber
i^/{p]f) was plotted against the reciprocal of the concentration of dye
in the bath (l/[D]g) straight lines were obtained which extrapolated to
approximately the same point on the 1/jjDJf axis. They concluded that
this system exhibited a Langmuir type isotherm and the maximum amount
of dye sorbed corresponded to the number of sulfate or sulfonate end
groups in the polymer.
Balmforth et al. (14) confirmed the findings of Vogel et al. and
stated that cationic dyes were sorbed by an ion exchange mechanism where
dye cations replaced the hydrogen or metallic cations present in the
fiber. Their results showed that the amount of dye sorbed decreased
with increasing concentration of electrolytes since the cations of the
electrolyte compete for the sites with the dye cations.
Beckmann (15) has stated that adsorption of the cationic dye on
the surface of the acrylic fiber is due to the negative electrical
potential at the fiber surface. He quotes a value of -44 mV for this
potential. This negative charge attracts the positively charged dye
to the surface of the fibers where sorption occurs.
Once the dye molecule is in the fiber the dye is transferred
from site to site progressively into the fiber. Feichtmayr and Wurz (16)
point out that energy must be applied to the dye molecules to lift them
out of the energy wells corresponding to anionic sites and push them
into adjacent sites. Cegarra (17) has measured this energy and found it
to be between 60 and 80 kcal. per mol which is the highest activation
energy encountered in any dyeing process.
Measurement of the diffusion coefficient of cationic dyes into
the acrylic fibers has been impeded by the difficulty of the mathematical
treatment and the irregular cross section of commercial acrylic fibers
(15). However, Peters et al. (18) in work with nylon and acid dyes have
shown by microdensitometric studies that the diffusion coefficient is
not constant, but increases as the concentration of dye in the fiber in
creases. As the ratio of the filled sites to the number of sites in the
fiber approaches unity, the diffusion profile will tend to form a sharp,
slowly advancing line. Using photomicrographs Goodwin and Rosenbaum
(19) confirmed this observation for cationic dyes in acrylic fibers and
concluded that difficulties in the experimental procedure and interpre
tation limited the scope of microdensitometric determination of the dif
fusion coefficient.
In an earlier study, Rosenbaum (20) found apparent diffusion
coefficients for cationic dyes in acrylic fibers using an equation which
included the number of sites available in the fiber and the external
surface area of the fiber. The apparent diffusion coefficients he
found were of the order of 10"" cm sec" at 97* C.
Summary
From a survey of the.literature, it can be stated that disperse
dyes enter polyester fibers by a simple solution mechanism which con
tinues until the system is saturated with dye. The diffusion of single
dye molecules takes place in the amorphous regions of the fiber, and
the diffusion coefficient is independent of dye concentration. Because
of the compact nature of polyester fibers, the diffusion of dye is
extremely slow, and once in the fiber the dye is held by short range
electrical forces.
Carriers enter the amorphous regions of fibers by the solution
mechanism where they loosen interchain forces and swell the fiber al
lowing dye molecules freer movement into the fiber. The efficiency of
a carrier depends on the number of molecules inside the fiber; however,
after the system is saturated the dye uptake is reduced.
The sorption of cationic dyes by acrylic fibers obeys the
Langmuir isotherm where the number of anionic sites control the amount
of dye in the fiber. Dyeing can be explained as an ion exchange between
dye cations and metallic or hydrogen ions on the sulfate or sulfonate
groups in the fiber. The dye diffuses by traveling from site to site
progressively into the fiber. The speed of diffusion is dependent upon
the concentration of dye molecules in the fiber; the higher the concen
tration, the faster the diffusion.
The purpose of this study is to determine the sorption mechanism
and measure the apparent diffusion coefficients of a cationic dye, with
and without carrier, into modified polyester fibers. From this survey
of the literature, it is believed that this system will closely resemble
the cationic dye-acrylic fiber system. As pointed out in the literature,
diffusion of disperse dyes is extremely slow in polyester fibers.
Therefore, it is to be expected that cationic dyes will also diffuse very
slowly. The effect of carriers in increasing the diffusion of dyes is
known, but the magnitude in the system under investigation is not reveal
ed in the literature.
10
CHAPTER II
INSTRUMENTATION, EQUIPMENT, AND CHEMICALS
Dacron type 161 "12 denier" staple was used in this work. This
fiber is manufactured by the E. I. duPont de Nemours Company. The dye
used throughout this study was C. I. Basic Blue 22 also obtained from
the E. I. duPont de Nemours Company. The commercial name of the dye is
"Sevron" Blue 2G. The biphenyl carrier, 99 percent purity, was obtained
from the Monsanto Company.
The constant temperature bath used in this work consisted of an
insulated metal tank filled with polyethylene glycol, A Fisher Propor
tional Temperature Control which included a heater and a thermistor
probe achieved temperature control to +.01°C. A constant source of heat
was provided by a 750-watt flexible immersion heater regulated with a
120-volt Staco Variable Autotransformer (type 2PF1010). A Gerald K.
Heller Company GT21 laboratory stirrer and accompanying motor controller
was used to insure a uniform temperature in the bath.
Agitation of flasks was provided by a Burrell Wrist Action Shaker.
When complete immersion of the dyebath was required, a tumbler device
provided constant rotation of 8-inch pressure tubes obtained from Ace
Glass Incorporated. The pressure tubes were sealed using standard
bottle caps with 5 mil Teflon film as a seal.
Absorbance measurements of dye and carrier solutions were made
using a Beckman DB-G grating spectrophotometer equipped with a Beckman
11
10-inch recorder.
Weighings were made with a Mettler H6T balance. Water purifi
cation was accomplished by passing tap water through a Corning LD-2a
demineralizer.
For determining the diameter of the polyester fibers, a Carl
Zeiss Microscope with an American Optical Filar Micrometer Eyepiece was
used. Calibration of the eyepiece was made with an American Optical
Company 2 mm micrometer slide.
Reagent grade methanol, acetone, glacial acetic acid, and N,
N-dimethylformamide were obtained from the Fisher Scientific Company.
Triton X-100 was obtained from the Rohm and Haas Company.
12
CHAPTER III
EXPERIMENTAL PROCEDURES '
In order to determine the dyeing behavior of cationic dyeable
polyester fibers and the effect of carriers on the dyeing behavior, it
was necessary to develop analytical methods for estimating the amounts
of dye and carrier sorbed by the fiber. In the determination of the
sorption isotherms for the dye, this is usually accomplished by either
a sorption or a desorption technique. In this work, the sorption tech
nique was used and the amounts of dye in the two phases were determined
by measuring spectrophotometrically the amounts of dye initially present
and the amount present at equilibrium. Thus, the amount of dye sorbed ;
could be calculated from the change in dye concentration, i.e., by
difference. This procedure was used since more direct methods for
measuring the concentration of dye in the fiber were unsuccessful. The
dye could not be easily "stripped" from the fiber, and no good solvent
for the dyed fiber was available.
An identical procedure was used for determining the amounts of
the carrier, biphenyl, sorbed by the fiber.
In studying the rates of dyeing, both in the absence and presence
of carrier, the amounts of dye sorbed were determined in a similar
manner, i.e., by measuring spectrophotometrically the dye concentration
initially and after specified times of dyeing.
In order to use the analytical method described, spectrophotom-
13
etric calibration data for both the dye and carrier were required. This
is described below.
Analysis of Dye and Carrier Solutions
A stock solution of the dye was prepared having a concentration of
.5 g/1 and a pH of 4.5 (2.5 g/1 glacial acetic acid). This stock, solu
tion was diluted with water and methanol such that the solution was 50/50
methanol/water. It was then examined spectrophotometrically, the ab-
sorbance values being recorded between 400 and 700 nanometers. The
maximum absorption peak was selected, and the absorbance values at the
absorption peak were plotted against the concentration of dye adjusted
so that the absorbance values would be between zero and one (1.0) when
using a one centimeter cell. In all cases the reference cell of the
spectrophotometer contained a solution identical to that in which the
dye was dissolved.
A stock solution of .2 g/1 biphenyl was made by dissolving the
carrier in 500 milliliters of methanol, then adding water until the
liter mark was reached in a volumetric flask. The procedure for
determining the wavelength for maximum absorbance and the calibration
curve was the same as for the dye except that the region between 200
and 300 nanometers was examined spectrophotometrically.
Equilibrium Studies
Dye in the Polymer
Preliminary experiments revealed that the sorption of the cationic
dye by the fiber was so slow that several hundred hours at the boil
would be required to reach equilibrium. One means of circumventing this
14
long contact time was to increase the surface area by dissolving the
fibers and then precipitating the polymer in a finely divided form.
First, to remove impurities from the polyester fibers, 20 grams
of the fiber were scoured with 4 percent Triton X-100 based on the
weight of the fiber for 15 minutes at the boil (liquor ratio of 40:1).
The fibers were washed thoroughly with water, air dried and conditioned
at room temperature. The fibers prepared in this way were used through
out the study.
Two grams of the fiber were dissolved in 125 milliliters of
boiling N,N-dimethylformamide and diluted to a liter with water contain
ing acetic acid. Twenty-five milliliter portions of this solution con
taining .05 grams of the polymer were pipetted into six 100 milliliter
volumetric flasks. Differing amounts of the dye stock solution were
then pipetted into the flasks so that they contained 20, 30, 40, 50, 60,
and 70 percent dye based on the weight of the polymer. When the dye
solutions contacted the solution of the dissolved polymer, precipitation
. of the polymer occurred in the form of a fluffy mass. All of the flasks
were filled to 100 milliliters with water, stoppered, and allowed to
equilibrate at room temperature for two days. Then the contents of each
flask were filtered through glass filters to remove the dyed polymer.
The filtrates were diluted with methanol and water to achieve a 50/50
methanol/water solution. These solutions were analyzed spectrophotom-
etrically.
Biphenyl in the Fiber
To relate the effect of the biphenyl on the diffusion of the dye
into the polymer, it was necessary to ascertain the amount of biphenyl
15
in the fiber. In the course of this study biphenyl was found to steam
distill making complete immersion of the dyebath mandatory; however,
the Teflon liner required when using pressure tubes was found to sorb
biphenyl. It was therefore necessary to determine the amount sorbed by
the Teflon liner.
Stock solutions of biphenyl dissolved in acetone were prepared
in concentrations of .1, .2, .3, and .4 g/1 so that when five milliliters
of these solutions were pipetted into a pressure tube, they would yield
2, 4, 6, and 8 percent biphenyl based on a weight of .125 grams of fiber.
Eight pressure tubes were used, two for each concentration, and the
acetone was evaporated by means of a water aspirator leaving a residue
of carrier in the bottom of the tubes. Twenty-five milliliters of water
were added to each tube, and .125 grams of fiber were placed in four of
the tubes resulting in one blank where only the Teflon liner would be
in contact with the biphenyl, and in one containing fiber (liquor ratio
of 200:1) for each carrier concentration. A two-inch square Teflon
liner was placed over the mouth of each tube which was capped and fas
tened onto the tumbler device. The tubes were immersed in the 95 C oil
bath and rotated at 48 r.p.m. for 22 hours.
When the tubes were uncapped, the Teflon liners and the fibers,
where applicable, were removed and rinsed in a beaker containing methanol
to dissolve any biphenyl on the fiber surface. The carrier solutions
in the tubes were poured into 100 milliliter volumetric flasks, and the
tubes were rinsed with methanol to dissolve any remaining biphenyl. The
biphenyl solutions were diluted with water and methanol such that the
final solutions were 75/75 methanol/water. These solutions were
16
analyzed spectrophotometrically.
Rate Studies
Dyeing Without Carrier
Cationic dyes have been found to be unstable at normal dyeing
temperatures, and decompose after prolonged dyeing times even in an
acidic dyebath. The dye used in this study, C. I. Basic Blue 22, has
been reported to be one of the most stable cationic dyes; nevertheless,
preliminary work, indicated that decomposition was occurring when dyeings
were conducted at times up to 25 hours.
To determine the percent dye decomposition, 50 milliliters of the
.5 g/1 dye stock solution (pH 4.5) were pipetted into each of the 100
milliliter volumetric flasks. The flasks were stoppered, attached to
o the shaker, and placed in the 95 C oil bath. The action of the shaker
was carefully controlled to insure the same amount of agitation through
out the experiment.
After contact times ranging from one to 25 hours the flasks were
removed, and diluted with methanol and water giving a 50/50 methanol/
water solution. These solutions were examined spectrophotometrically.
Once the amount of dye decomposition was known, the rate studies
were performed with the procedure being the same. Again, 50 milliliters
of the dye stock solution (10 percent dye based on the weight of the
fiber) were pipetted into each flask. To give a standard liquor ratio
of 200:1, .25 grams of the fiber were placed in each flask. They were
then attached to the shaker and placed in the oil bath. Several trials
were performed at each time interval to insure reliability of the re-
17
suits. When the flasks were removed, the fibers were withdrawn and placed
in a beaker where they were rinsed with methanol. The dye solutions were
diluted with methanol and water to give a 50/50 methanol/water solution.
These solutions were analyzed spectrophotometrically.
Dyeing with Carrier
As mentioned above, steam distillation of the biphenyl at 95 C
necessitated the complete immersion of the dyebath; therefore, the rate
experiments utilizing carrier required the use of the tumbler device
and pressure tubes. The effect of the biphenyl on the amount of dye
uptake was investigated using concentrations of 2, 4, 6, and 8 percent
biphenyl based on the weight of the fiber.
Five milliliters of the appropriate biphenyl stock solution were
evaporated in each pressure tube as described previously. Twenty-five
milliliters of the dye stock solution and .125 grams of the fiber were
added to the tubes giving a 200:1 liquor ratio and 10 percent dye based
on the weight of the fiber. As in the biphenyl sorption experiment,
the tubes were tumbled in the oil bath at 48 r.p.m.
After varying dyeing times the tubes were removed and the dye-
baths were poured into flasks. The Teflon liners and the fibers were
removed and rinsed with methanol. The dye solutions were diluted to
obtain 50/50 methanol/water solutions which were analyzed spectrophotom
etrically.
Determination of Fiber Radius
The average radius of the polyester fibers was determined so that
the apparent diffusion coefficient could be derived. About 30 fibers
18
were placed on a slide with a drop of mineral oil as the immersion
medium. Twenty diameter measurements were made microscopically using
a calibrated micrometer eyepiece.
*S
19
CHAPTER IV
DISCUSSION OF THE RESULTS
Calibration Curves
The peak, absorbance of Basic Blue 22 was discovered to occur at
635 nanometers as shown in Figure 1. When experiments on the absorbance-
concentration relationship were performed, a linear dependence of absorb
ance on concentration was found only if the dye solutions contained 50
percent methanol. At the higher concentrations the dye molecules
probably aggregated causing lower absorbance readings and thus a non
linear relationship. However, when methanol was used a linear relation
ship was obtained as is shown in Figure 2. The specific absorbance for
the dye (impure, commercial) was found to be 8.04 (1.00 g/1, 1 cm cell
thickness).
The spectrum of biphenyl revealed that the peak absorbance was at
248 nanometers as shown in Figure 3. The calibration curve when the
solvent was 50/50 methanol/water is shown in Figure 4, An excellent
linear relationship between absorbance and concentration was observed.
Isotherms
Dye in the Polymer
Figure 5 shows the sorption isotherm for the dye in the precip
itated polymer at room temperature. The equations for conversion of
the dyebath absorbance values to grams of dye per kilogram of fiber and
grams per liter left in the dyebath are given in Table 2 in the Appendix.
20
o o r
o m
O O vO
X! u 00 ti (U
r-4
<u > :3
o m m
>-i 0) u «
IS
H O
cd
o m o m
CM CM
(1)
FH
pq
o • H CO Cd
pq M-4
o
4J
o (U ex.
en
(U M
a 00
•H p>
o o o 00 o
xO o sr
o CM
m CM
m
aoupqjosqv
21
m CS CN f t CM
<U .-\
•H a pq m O ro
•H vO CO cd -u « CO
o ^1 TH
o O r-i 1-4 M^ 0)
• O
•H O .^"s i J H cd o
rH O 00 0) •
— • fi - ^
a c o O U
lO -ri •H 0) r- u 4J -U O cd Cd Cd
• M u rs •u 4-» ^ ^ d C rM a> (I) O o o fl a d cd o O rC
o O 4J
' ii (U S o c o o fd »n
m j a ' ^
o M O
• O lO CO
-9 ^ < -H
u 3
m 60 CM •H
o PM
o CM
O o
o CO
o o o CM
sDUBqjosqv
22
o o m
44
in r iH CM
X-N
i 43 4J
o m
e d c •H
rH rC >» •u d 00 0) d ,d
o 0) ex. m rH •H cs (U
> pq
ca -1
:s O
to CM CM
u « CO
en 0) M
3>
o o
o o o 00
o NO
o •>*
o CM
aoupqjosqv
23
00 d o •H o • r-4
>> fl (U
43 / - s (^ S •H S
00
O «N U-(
4J d CO o
vO •H i H O •U T H
o cd 0) • /~\ rH U
rH <>i p<i e
to o N - X c
O '-* c •H ^ - o •u
•H td u 4J U (U q} •U -U M d cd •P <u :3 C3 o — (U C r-t
- * o o o o Ci cj d o o 1 ta
o <U Xi o u
(d S 1 O
o m OT " ^ ^ o <; in
• -
cs (U o u o 3
• GO
Pt4
O
o o 00
o o o CM
aDu^qjosqv
24
The curve obtained is characteristic of a Langmuir type isotherm
where dye sorption is a function of the sites available, in this case,
the sulfonate groups. The equation for a Langmuir isotherm is:
1 1 1 [D]^ = k[S]^ [D]g + [S]^
where [D] is the concentration of dye in the fiber at equilibrium, k is
a constant, [S],. is the number of sites in the polymer available for
sorption of dye, and [D] is the concentration of dye in the bath at
equilibrium. In Figure 6, l/[D]f is plotted against l/[D]g giving a
straight line which extrapolates to .0027 on the 1/[D]£ axis. The above
equation reveals that this point corresponds to the reciprocal of the
number of sites; thus, the polymer has enough sites to sorb 370 grams of
impure dye per kilogram of polymer.
To determine the moles of pure dye sorbed, it was necessary to
derive the purity of the commercial dye. Using the absorbance relation
ship between known concentrations of pure and impure dye, the purity was
calculated to be 20 percent. Balmforth et al. (14) have found the
molecular weight to be 455. After appropriate calculations, the poly
ester fibers were found to sorb 0.16 moles of pure dye per kilogram of
fiber. Thus, the modified polyester fibers have extremely high site
content when one considers that nylon and acrylic fibers sorb approxi
mately .04 eq/kg and .05 eq/kg of dye, respectively.
Figure 7 gives an indication of the high affinity of Basic Blue
22 for modified polyester fibers. The photomicrograph shows the pene
tration of dye into the fiber after a 10 percent dyebath had been
25
00
>> •<t rH t—1 o
a •H (U
CN ^ T-* / - N
• r-^ M O
00 U^
c e o <u O •H ^ 1—1 4-1 • M
• « O U CO • u
c M
<u ti o o d •H
00 o 4J o u a M
O cn
• lO
v O O <u
• M
60 •H Pui
o
CM
o
o o
o o en
o o CM
o o
(3:51/3) paqaog :iunoniv
26
*!(
ba
u
I r-i
o d •H
0)
Q V4 O
4-<
(U JS • M O CO
fi O
•H 4-> CX M O
C/3
U-l O
u o
i H
U •H 3
fl H J
vO
(U
3 00
•H
(3/3^) ^[aj
27
Figure 7. Cross Section of Fiber After Sorption of 10 Percent Dye Based on the Weight of the Fiber
28
exhausted. A contact time of 81 hours at 100°C was required. The
fibers are narrowly ring dyed because most of the dye molecules are
captured by the sulfonic acid groups on and near the surface of the
fiber.
Biphenyl in the Fiber
Since the Teflon liner used to seal the dyeing tubes was found
to sorb the biphenyl, it was necessary to measure the amount sorbed.
The sorption by the Teflon is shown in Figure 8, and the sorption by the
Teflon liner plus the fibers is shown in Figure 9. By subtracting the
effect of Teflon, the isotherm for the sorption of biphenyl by the fiber
was determined as shown in Figure 10. The points on the curve represent
initial carrier concentrations of 2, 4, 6, and 8 percent based on the
weight of the fiber, and it can seen that at 8 percent carrier the fiber
appears to be approaching saturation.
When establishing the isotherms the fibers were left in contact
with the biphenyl for 22 hours at 95°C. At the end of this time it was
noted that fiber segments one-eighth of an inch long remained in the
bath after the main fiber mass had been removed. The number of fiber
segments ranged from a few for the 2 percent carrier concentration to
10 or 15 for the 8 percent concentration. It appears that the plasti-
cizing action of biphenyl coupled with hydrolysis of the polymer leads
to severe fiber damage. During the study, an attempt was made to
establish an isotherm for the biphenyl under the same conditions of pH
which existed in dyeing, namely 4.5. After 22 hours in this acidic bath
the fibers were completely broken down into minute segments. It was
concluded that under this acidic condition, hydrolysis is more severe.
29
o •
"?n ON •Sm^
u 0) d •H •-a 0 o
rH H-4
o (U CO - \ H
• T-i
•"^ >» 00 V - '
rH fl >> o C •H (U ^ ^ cd cu u •H 4->
d pq
0) >4-l
o G
o o O C cs a o • •H
4J a u o
CO
0) M S 00
•H
(S) peqjos ^unomv^
30
m o o m o\
OB VI 0)
1 <U
^ - N •H i H .-3
o 60 d 1—1 s - ^ o
• r-l c »4-(
o (U •H 4J
H
nj >» M • u
Xi
fl i H 0) >> u C c (U o x: o Cu
•H pq
«M O
d o m •H o •M
• O. M O
U3
OS
<0 U
60
v£> O O
m o o
o o en o o
CM O
o o o
(8) paqjog :iunomv
31
m o m o\
u Q)
JQ • r l Pt4
& (U
/-^ ^ rH ex
• • ^ . . ^ 1-C
00 » o ^ w '
•—1 u • C3 o
O •r( 4J (d
•4-1
M (U • U x: C u (U o o CO d o
M
o C3 O
•p( 4J
o. M O
CO
m • o o
T-*
0)
u
oo T * PM
o m o o 00
o CN
(3-JI/3) paqjog ^unorav
32
and biphenyl, because of its plasticizing action enhances the degrad
ation of the fiber.
Rate Studies
o The percent decomposition of the dye for various times at 95 C is
plotted in Figure 11. The amount of decomposition was subtracted from
all the points in the rate of dyeing experiments without carrier because
of the long dyeing times. The decomposition was ignored in the experi
ments with carrier since the longest dyeing time was eight hours where
only 3.2 percent of the dye decomposed.
Figure 12 and 13 show the rate of dyeing curves without carrier
and with carrier in concentrations ranging from 2 to 8 percent based on
the weight of the fiber. The points in both figures are an average of
the points at each dyeing time. Table 3 in the Appendix lists all the
values for various times and carrier concentrations. Figure 12 reveals
a linear relation between the amount of dye in the fiber and the square
root of dyeing time. The slopes of these curves are proportional to the
square root of the diffusion coefficient. Figure 13 gives a better
picture of the rate process. It appears that if no carrier is present
the surface sites are filled within two hours, and then the rate of
dyeing becomes much slower as the dye molecules move into the fiber.
When the biphenyl is added to the dyebath, the effects are very apparent
because the biphenyl immediately begins to penetrate the fiber loosening
the interchain forces and swelling the fiber. The dye molecules travel
to the sites in the interior of the fiber at a rate which increases with
carrier concentration. The increase in the rate of dyeing between 4 and
33
CO
u o
33
0) S
•H H
O O m a
09
09 M
C o
•H • P • H CO O a, B o o 0) Q
S a M (U
(l4
0) M
T-f Fc4
(:ju3Djad[) uox^Tsodmooaa
34
Q
\ \
1 *•
M M V4 » (U (U <U 1)
•H -H -H n-l M M V M M M M V (d cQ (Q cd u c_) o a
u u u u u 0) cJ d c d -H (U (U <U 0) M U O (J O U M M M M n) 0) 0) (U 0) O ^ PL« Pn p PM
O 00 vO -3- <N Z
• 1
<](p<]0 Q
1 1
\
< \
\ N
1*1 "^
Q.
^
\ \ \
\ \ \
\
, 1 1 1 1 1 1 ^
^ m
. . « *
en
CO M
o
o
0) M e« d cr
c l
u
M 01
•H M M «
O
4J
5
•xj
g •H IS CO (U
> u
CJ
cu s
M-l
o •p o
0> M efl
cr en
I 0 O
CU u o
CO
CM
00 •H Fl4
O vO
O
m o •4-
o CO
o CM
(3:^1/3) p a q j o s ^unonrv
35
M )-i M M 0) <U 0) 0)
•H -H -H - H M M M )M M M M M td (d cd (d o o o o
u u u u u <u cJ c ei c -H 0) 0) <U <U M
o o o o u M M M M (d <U <U (U (U CJ (l4 PH 0^ OLI —
o 00 vO < f CN4 2 1 1
<l([>^OQ 1 1
\ \FI
\ v \ \ " \
\ \ \
X^X H X ^ v i "^
^ ^ ^
TC^J I V I •••
\ \ \
1 1 t 1 1 r ^ =
o CV4
vO
CS
CO
u o
CO
— ^
o o m <7>
u <u
•rJ M M cd o
o ,CS
u •H IS X) fl Cd
x : •M
CO (U > M
a> 6 •H H I O •H • P O *
O C O
ro
a» M 9 60 •H V*4
O vO
o m o o ro
O
(3-^^/3) psqjog :jnnomv
36
6 percent carrier may be because the 6 percent concentration yields
enough biphenyl molecules to completely penetrate the fiber, or because
of experimental variability.
Apparent Diffusion Coefficients
The diffusion of dye in the fiber is the process which governs
the dyeing rate and may be regarded as a characteristic measure of the
dyeing rate. In this study the apparent diffusion coefficients were
determined by using Hill's (21) equation:
C^/CcD« 1 - .692 exp (-5.785 Dt/r^) + .190 exp (-30.5 Dt/r^)
+ .0775 exp (-74.5 Dt/r^) . . . J
In this equation C^ is the grams of dye per kilogram of fiber sorbed
after time t, COD is the grams of dye per kilogram of fiber sorbed at
2 -1 saturation or equilibrium, D is the diffusion coefficient in cm sec ,
t is given in seconds, and r is the radius of the fiber in centimeters.
Hill's equation allows the diffusion coefficient to be calculated using
the rate of dyeing curves if the fiber cross sections are circular, and
the concentration of dye at the surface is constant. As seen in Figure
7 the polyester fibers used in this study were circular, and the con
centration was kept nearly constant by utilizing a long liquor ratio
(200:1) and short dyeing times in the rate studies to maintain a small
dyebath exhaustion.
In his work Hill presented a table which expressed C^/Cco as a
? 2
function of Dt/r . The relationship between C^/Cco and Dt/r was also
presented graphically. Since the times of dyeing and the radius of the
37
fibers are known, the diffusion coefficient can be calculated quite
simply. However, in this study C values for dyeing without carrier were
so low that the C^/CCD ratio fell below the points in Hill's table. This
problem was solved by using a computer to calculate small values of C^/CcD
2 and the corresponding Dt/r values. The program and the output are given
in the Appendix in Tables 4 and 5, respectively.
Since the average radius of the polyester fibers was calculated
to be 1.73 X 10 centimeters, the apparent diffusion coefficients for
all the data points in Table 3 were easily determined and are presented
in Table 6 in the Appendix. Because of the variability of the points,
it was believed that choosing several points from the rate curves in
Figure 12 would yield more valid diffusion coefficients. The averages
of these points are shown in Table 1 revealing that the diffusion of
dye into the fiber is 17.6 times faster when 8 percent biphenyl based on
the weight of the fiber is in the dyebath as against no carrier. When
the log of the diffusion coefficient was plotted against the percent
carrier based on the weight of the fiber in the dyebath, a straight
line resulted as shown in Figure 14. Since the amount of biphenyl in
the fiber is proportional to the amount in the dyebath, it is concluded
that the log of the diffusion coefficient is proportional to the amount
of biphenyl in the fiber, a relationship similar to that exhibited by
nylon dyed with disperse dyes in the presence of phenol (22) .
The diffusion coefficient obtained for dyeing with no carrier,
4.4 X 10~ cm sec~ , compares favorably with results obtained by
Patterson and Sheldon (6) who found diffusion coefficients for disperse
dyes in polyester fibers at 95°C to be from 6.02 X 10 ^ to 8.5 X 10 -14
38
Table 1. Average Diffusion Coefficients Versus Carrier Concentration
Percent Carrier Based on the Weight of the Carrier
Average Diffusion Coefficients (cm sec" )
4.40 X 10 -14
1.04 X 10 -13
1.66 X 10 -13
5.50 X 10
7.76 X 10
-13
-13
39
« pq
(3 n4
M 0)
T »
M M 4 U M-l o 4J
c p /—\ Q u fl 1 (U o 0) M :3 0) CO
PL4 M V - - ' di
> M <U 4-1
•rC PI M 0) Kl •H c0 O
O •H m
<+-( m O 0)
o •M o a o fl g o 4 • H
CO
3 IH
»H O
00
o 1-3
0) M
3> •H
vO o •<t 0 0 CM vO o • • • • • • CM CN es CO cn < •
1-4
1 1 f*
I r-t 1
i-H 1
r-A I
( __oas mo) 5U3Totjj3oo uOTsnjjTQ JO 3oT
40
? -1 cm^sec . Glenz et al. (8) found diffusion coefficients ranging from
-13 -12 2 -1 3.3 X 10 to 6.2 X 10 cm sec when dyeing polyester fibers at
100 C with disperse dyes. They also discovered that the diffusion
coefficients were 10 to 100 times higher when carriers were used.
41
CHAPTER V
CONCLUSIONS
The sorption isotherm for a cationic dye by a precipitated
polyester polymer revels that a saturation value is reached. When
the reciprocal of the amount of dye in the polymer is plotted against
the reciprocal of the amount of dye in the bath, a linear relationship
results which is characteristic of a Langrauir type isotherm. The
amount of dye sorbed is dependent upon the number of sulfonic acid
groups in the modified polyester. The precipitated polymer sorbed .16
eq/kg of Basic Blue 22 which is a high value compared to nylon and
acrylic fibers where the maximum sorption is .04 eq/kg and .05 eq/kg
of dye, respectively.
The amount of biphenyl sorbed by the fiber is proportional to
the amount initially in the dyebath until a concentration of 8 percent
carrier based on the weight of the fiber (.4 g/1) where the fiber
approaches saturation. After a contact time of 22 hours at 95°C, the
biphenyl causes slight degradation of the fibers, and the degradation
is more pronounced with increasing concentrations of biphenyl. Under
the same conditions except at a lower pH of 4.5, the fibers are com
pletely degraded. It is concluded that the plasticizing action of the
biphenyl causes an enhancement in the hydrolysis of the ester linkages
in the polymer chain.
The rate of dyeing at 95 C is slow without the aid of a carrier.
42
The rate is accelerated by the addition of biphenyl, and it increases
as higher concentrations of biphenyl are employed in the dyebath.
o The apparent diffusion of the dye in the fiber at 95 C is con-
-14 2 -1 stant and very low (4.4 X 10 cm sec ). The addition of biphenyl
to the dyebath increases the speed of diffusion, and the diffusion
coefficient is 17.6 higher with 8 percent biphenyl based on the weight
of the fiber than with no carrier. The increase in the diffusion coeff
icient is proportional to the amount of biphenyl in the dyebath. Because
disperse dyes have similar diffusion coefficients, it is concluded that
the diffusion of dye in a polyester fiber is controlled by the fiber
structure and the changes in structure which occur when a carrier such
as biphenyl is sorbed by the fiber.
•T$
43
CHAPTER VI
RECOMMENDATIONS
?S
In this work the biphenyl and the dye were simultaneously added
to the dyebath. The effect of pretreating the fibers with biphenyl
would be an interesting and necessary study.
The determinination of the activation energy for the cationic
dye-polyester fiber system would be a valuable investigation.
It was found that biphenyl causes slight degradation of the
polyester fibers after long contact times at an elevated temperature,
and severe degradation in an acidic medium. An interesting study would
be to determine the effect of various dyeing accelerants on textile
fibers as a function of pH, time, and temperature. The literature
fails to mention this deleterious effect of carriers, presumably because
practical dyeing times have durations of only several hours.
4A
APPENDIX
-v1
45
Table 2. Calculations
Determination of Amount of Dye in Fiber and in Bath
B = Dye in bath (g/1)
C = Dye in fiber (g/kg)
Cj = Initial concentration of dye (g/1)
A = Absorbance at 635 nm
f = Dilution factor
a = Specific absorbance for the dye (8.04 for 1.00 g/1, 1 cm cell)
V = Volume of dyebath (ml.)
w = Weight of fibers (g)
B = A-
C = V (c - A_Ll) w ^ a
46
Table 3. Results of Rate of Dyeing Experiments
Amount of Carrier In Dyebath (percent o.w.f.)
Time of Contact Amount of Dye in (hours) the Fiber (g/kg)
4 12.2 4 10.4 4 14.8 4 13.4 9 16.0 9 14.8 9 17.2 9 18.6 16 28.0 16 24.2 16 22.4 16 21.8 25 34.4 25 34.4 25 35.2 25 31.4 1 8.0 2 13.4 2 15.4 4 18.4 4 19.4 6 25.4 6 24.4 1 9.4 1 10.0 2 15.4 2 15.4 4 22.8 4 23,8 8 40.4 8 37.8 0.75 16.4 0.75 16.4 2 28.4 2 30.4 4 44,2 4 43.2 6 52.2 6 52.2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6
47
Table 3. Results of Rate of Dyeing Experiments (Continued)
Amount of Carrier in Dyebath (percent o.w.f.)
Time of Contact (hours)
Amount of Dye in the Fiber (g/kg)
0.5 0.5 1 1 2.75 2.75 4 4
16.4 15.4 24.8 25.4 39.4 41.4 49.2 50.2
48
Table 4. Program for the Hewlett-Packard Calculator
PROGRAM 0
00 ENT EXT 5 CHG SON 1 0
20 FMT YTO 3 UP UP
40 7 FMT PI UP 1
60 FMT GTO X DN DN
80 IF X<Y 5 d 1 1
05 7 FMT YTO STOP UP
25 1 0 9 FMT PI
45 0 8 FMT PI X
65 UP UP 1 1 0
85 1 FMT PI UP 4
Oa 1 0 7 FMT
2a STOP UP 1 0
4a 1 0 9 FMT
6a FMT PI X DN
8a CHG SGN X 1 +
10 YTO 2 UP UP 1
30 9 FMT YTO CLR 1
50 PI UP X DN +
70 eX XEY DIV UP DN
90 UP DN DN END
15 0 8 FMT PI STOP
35 1 1 FMT YTO 2
55 1 CHG X 1 1
SGN 75 1
1 1 FMT +
la UP 1 0 8
3a FMT GTO 1 0
5a 0 FMT YTO 1
7a RDN ENT 6 CHG
EXP
SGN
49
Table 4. Program for the Hewlett-Packard Calculator (Continued)
PROGRAM 1
00 1 0 1 FMT PI
05 UP 1 0 6 FMT
Oa YTO 1 0 0
10 FMT + FMT PI UP
15 CLX XEY UP 3 FMT
la GTO RDN 1 0
20 3 40 YTO 60 UP 80 FMT FMT 1 1 YTO YTO 0 0 GTO 1 3 CHG SGN 2 0 FMT DIV 3
25 6 45 PI 65 1 85 1 FMT UP 0 0 PI lYl 6 0 UP DIV FMT FMT 1 1 YTO PI
2a 0 4a 0 6a (Yl 8a UP 0 4 1 UP FMT FMT 0 FMT + PI 5 STOP
30 FMT PI UP CLX XEY
50 UP lYl DIV DN X
70 FMT PI IF X>Y 8 5
35 UP 3 FMT GTO RDN
55 CLX IF X<Y 7 5 1
75 1 0 4 FMT PI
3a 1 0 4 FMT
5a 0 6 FMT PI
7a UP 1 0 3
/
50
Table 4. Program for the Hewlett-Packard Calculator (Continued)
PROGRAM 2
00 CLR 20 YTO 1 , FMT 0 0 FMT
* END
05
•
YTO
1 UP
'v-
Oa
1 0 1 FMT YTO
10 ENT EXP 5 CHG SGN UP 1
15 0 5 FMT
•5 •
YTO CLR
la 1 0 2 FMT
PROGRAM 3
Hewlett-Packard library routine for the 9100A calculator
computing the Bessel function of the first kind of order
n. This is Part # 09100 - 70025
51
Table 5. Calculator Output, Dt/r Versus C^/CcD
-•J
.00001
.00002
.00004
.00007
.00010
.00020
.00040
.00070
.00100
.00200
.00400
.00700
.01000
.02000
.04000
.07000
.10000
.20000
.40000
.70000 1.00000
0141881 0157251 0186014 0221853 0251091 0333939 0459591 0596739 0709559 0992999 1388350 1818374 2154950 2985829 4095999 5227611 6058242 7821475 9315687 9879283 9978705
52
Table 6. Apparent Diffusion Coefficients For All Points in the Rate of Dyeing Experiments
Amount Time of (sec X 10~ )
Carrier in Bath (percent o.w.f.)
0 1.44 0 1.44 0 1.44 0 1.44 0 3.24 0 3.24 0 3.24 0 3.24 0 5.76 0 5.76 0 5.76 0 5.76 0 9.00 0 9.00 0 9.00 0 9.00 2 0.36 2 0.72 2 0.72 2 1.44 2 1.44 2 2.16 2 2.16 4 .36 4 .36 4 .72 4 .72 4 1.44 4 1.44 4 2.88 4 2.88 6 .27 6 .27 6 .72 ,
CjCm D t / r 2 ( x 10^) Diffusion Coef f ic ien t 9 1 14
(cm'' sec"-*- X 10 )
.0329
.0281
.0400
.0362
.0432
.0400
.0464
.0502
.0756
.0654
.0605
.0589
.0929
.0951
.0848
.0929
.0216
.0362
.0416
.0497
.0524
.0686
.0659
.0254
.0270
.0416
.0416
.0616
.0643
.1091
.1021
.0443
.0443
.0767
93 30 97 37 50 97 10 20
15.50 85.00 7.40 7.00
17.50 18.00 14.70 17.50 0.65
37 25 75 35 35
8.65 03 20 25 25 50
8.20 20.50 21.00 4.00 4.00 11.70
01 ,70 ,17 ,92 24 ,75 ,80 ,82
8.03 40 83 63 81 81 98 81 40 84
13.50 9.86
11.10 12.90 12.00
8.55 9.97
13.50 13.50 15.60 17.00 21.30 21.80 44.30 44.30 48.60
53
Table 6. Apparent Diffusion Coefficients For All Points in the Rate of Dyeing Experiments (Continued)
Amount Time (sec X 10"^)
CjCCD of
Time (sec X 10"^)
Carrier in Bath (percent o.w.f.)
6 .72 .0821 6 1.44 .1194 6 1.44 .1167 6 2.10 .1410 6 2.10 .1410 8 .18 .0443 8 .18 .0416 8 .36 .0670 8 .36 .0686 8 .99 .1064 8 .99 .1118 8 1.44 .1329 8 1.44 .1356
Dt/r^(x 10^) Diffusion Coefficient
(cra sec"^ x lO-'-')
35.00 46.00 29.30 60.80 27.80 57.70 41.50 59.10 41.50 59.10 4.20 69.80 3.60 59.80 9.00 74.80 9.50 78.90 20.30 61.30 22.00 66.40 36.50 75.80 38.00 78.90
54
BIBLIOGRAPHY
1. Vickerstaff, T., The Physical Chemistry of Dyeing, 2nd ed., Oliver and Boyd, London (1954), pp. 484-493.
2. Griffin, J. M., and Remington, W. R., U. S. Patent No. 3,018,272 (1962).
3. Griffin, J. M., U. S. Patent No. 3,057,827 (1962).
4. Waters, E., Journal of the Society of Dyers and Colourlsts, 66, 609 (1950).
5. Remington, W. R., and Schroeder, H. E., Textile Research Journal, 21, 177 (1957).
6. Patterson, D., and Sheldon, R. P., Transactions of the Faraday Society, 55, 1254 (1959).
7. Salvln, V. S., American Dyestuff Reporter, 49, 600 (1960). ) 8. Glenz, 0., Beckmann, W., and Wunder, W., Journal of the Society of
Dyers and Colourlsts, 75, 141 (1959).
9. Schuler, M. J., Textile Research Journal, 27, 352 (1957).
10. Vickerstaff, T., Hexagon Digest, 20, 7 (1954).
11. Rawlcz, F. M., Gates, D. M., and Rutherford, H. A., American Dyestuff Reporter, 50, 320 (1961).
12. Balmforth, D., Bowers, C. A., Bulllngton, J. W., Gulon, T. H., and Roberts, T. S., Journal of the Society of Dyers and Colourlsts, 82, 405 (1966).
13. Vogel, T., De Bruyne, J. M. A., and Zimmerman, C. L., American Dye-stuff Reporter, 47, 581 (1958).
14. Balmforth, D., Bowers, C. A., and Gulon, T. H., Journal of the Society of Dyers and Colourlsts, 80, 577 (1964).
15. Beckmann, W., Journal of the Society of Dyers and Colourlsts, 77, 616 (1961).
16. Felchtmayr, F., and Wurzi A., Journal of the Society of Dyers and Colourlsts, 77, 626 (196^).
55
17. Cegarra, J., Journal of the Society of Dyers and Colourists. 87 149 (1971). "~
18. Peters, R. H., Petropoulos, J. H., and McGregor, R. , Journal of the Society of Dyers and Colourists, 77, 704 (1961).
19. Goodwin, F. L., and Rosenbaum, S., Textile Research Journal, 35, 439 (1965).
20. Rosenbaum, S., Textile Research Journal, 33, 159,291 (1964).
21. Hill, A. v., Proceedings of the Royal Society, B104, 39 (1928).
22. Jeschke, W. D., and Carter, W. C , "Diffusion Characteristics of Disperse Dyes in Nylon-66 and Their Relationship to Poljmier Structure," Paper, Fiber Society Meeting, Charlotte, North Carolina, April 16-17, 1964.