the sorption of cationic dyes by polyester fibers a …€¦ · dyeing polyester fibers mechanism...

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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

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Page 1: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

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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Unpublished theses submitted for the Master's and Doctor's degrees and deposited in the Georgia Institute of Technology Library are open for inspection and consultation,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

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Page 3: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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.

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7/25/68

Page 4: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

SORPTION OF CATIONIC DYES

BY POLYESTER FIBERS

Approved:

Chairrnan-

Date approved by Chairman:_

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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.

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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

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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

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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

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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.

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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

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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

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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

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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

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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-

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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

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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

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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.

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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.

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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

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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.

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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-

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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

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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

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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

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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-

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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

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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

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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.

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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

Page 30: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

Page 31: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

Page 32: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

Page 33: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

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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

Page 35: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

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27

Figure 7. Cross Section of Fiber After Sorption of 10 Percent Dye Based on the Weight of the Fiber

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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.

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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^

Page 39: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

Page 40: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

Page 41: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

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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

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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

Page 44: THE SORPTION OF CATIONIC DYES BY POLYESTER FIBERS A …€¦ · Dyeing Polyester Fibers Mechanism of Dyeing. Waters (4) has determined the saturation values and the relative diffusion

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

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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

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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

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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

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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

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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.

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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.

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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$

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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.

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4A

APPENDIX

-v1

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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

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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

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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

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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

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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

/

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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

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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

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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

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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

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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^).

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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.