Full text of DOI:10.1177/004051750007000308

223
3.
4.
5.
6.
7.
R.
M.,
Shed
Weft
1-10
on
and
76,
Insertion
(1985).
the
8.
9.
in ch.
7
of
Dawson,
H.
Machines."
Heinze,
VEB
K.,
Hahn, Ed.,
1966.
Geometry
"Weaving
Water-Jet
J.
Inst.
Textile
Loom,
The
Fachbuchverlag, Leipzig,
Germany,
Weaving
Applications,
R.
of
Orientation and Motion
the Weav-
Dawson,
M.,
K.
Our
H.,
Kessels,
Projectile
Range
pp.
P-105 Pneumatic Jet
Machine—High
J.
Textile Inst.
236-243
Reed,
ing
76,
(1985).
with
and
Wide
of
Sulzer
1988.
Ruti
Output
Weaving
R.
Geometric
a
Constraints
Raceboard:
Dawson,
M.,
Machine Bulletin no.
11,
3-13,
The Shuttle
Textile Res. J. 64640-4,74(1990).
Loom,
10.
Elitex
V.,
Machine,
Svaty,
Weaving
R.
The
M.,
Textile
Dawson,
Res. J.
Characteristic,
Shed-Shape
8
2-7
(1962).
(1),
Kovoexport
328-334(1991).
with the
Textile Inst.
R.,
Foster,
Ind.
1352-3,7(1974).
Loom,
Rapier
Weaving
received October
March
1999.
19, /998;
8,
Manuscript
accepted
New
Mathematical Model for
Determining
into
Fibers
Time-Dependent Adsorption
Curves
and
Diffusion of
Dyes
Through Dye Sorption
in
Combination Shades
Part II:
Kinetic Data from
Cotton with
a
Trichrome Direct
Dyeing
Dye System
H.
E.
E.
BACH,
CLEVE AND E. SCHOLLMEYER
DUFFNER
Deutsches
Nord- West e.
47798
V.,
Textilforschungszentrum
Krefeld, Germany
ABSTRACT
oftextile substrates
can be described
a
new mathemat-
and
Time-dependent dye uptake
by
ical model that
divides the
into two
dyeing process
parts, dye adsorption
dye
diffusion.
this
the
influence of
and NaCl concen-
model,
on the
(20-80°C)
Using
temperature
trichrome
tration
of a
of C.I.
combination
Direct
determined from
demonstrate differences
and outer surfaces of
(2.5-10.0
g/L)
dye uptake
and
dye
on
is
cotton
C.I.
Blue
Direct
Violet
C.I. Direct Yellow
27
225,
47,
uv-vis
curves obtained
This model can
sorption
in
by
spectroscopy.
of the
inner
disordered
the
temperature dependent dye
uptake
substrate and
also
reactions
that occur
displacement
during dyeing.
cellulosic materials with direct
is
models
All
are
on
of these
matrix
based
not
the
11,
a
9,
of
[8,
17].
Dyeing
dyes
mainly
influenced
and
and salt concentra-
and do
distin-
by temperature
dye
assumption
homogeneous
tions. Predictions of the
color shades of
between different accessible
of the sub-
oligochrome
guish
regions
are
based on monochrome
strate.
data,
dyeings
often
mainly
dyeing
deviations fromthe desired hue. This is
interactions of the in
in
selective
with re-
[ 10]
resulting
Rys
investigated
dye uptake
caused
he
not account for
to
but
did
different
partly
by
spect
competitive
sorption,
dyes
concentrated
and
structural differences offibers. The
in monoand
behavior of
is often
highly
dye liquors
by
sorption
displacement
on or
reactions
in the fibers
Different
[6].
dyes
oligochrome dyeing processes
Gouy-Chapman
during
dyeing
the
or the Donnan model
models have been
for
described
mathematical
by
suggested
descrip-
tions ofthe
The Donnan modelconsiders the standard
and diffusion of
substances into
the
[6, 7].
the
affinity,
charge
sorption
of
internal volume of the
and the fixed
matrix
fiber,
such as the
polymer
duringdyeing processes,
pore
that ofthe adsorbed
the substrate before
free
volume
and
diffusion/immobilization
[16],
[
18]
dyeing, plus
Gouy-Chapman
dye
the
affin-
the
standard
anions. In
model,
the accessible fiber surface for the
and the
dye,
ity,
1
the dissertation of Horst
from
Duffner.
of the substrate have to be deter-
surface
Excerpts
density
charge
Downloaded from trj.sagepub.com at UNIV OF CONNECTICUT on April 11, 2015

224
mined. Both
models are
used to
describe
of 0.5
a
hue on
cotton.
in
The
l.
dyeing
only
(co)
g/L,
achieving
grey
are
[6, 7]..
series,
chemical
structures
dyeing equilibria
ofthe
dyes
presented
Figure
In
Part
I
ofthis
we
a
new
mathemat-
The
dye
presented
solutions contained
0.23
C.I.
Direct
590
of
Blue
g/L
ical model
talline
that
describes
in
the
[2]
parts
dye
uptake
225
noncrys-
of 1056
(molecular
weight
nm),
1082
g/mol,
(molecular
Am.
of the
cellulose matrix as
time
dependent,
0.18
C.I.
Direct Violet 47
g/L
weight
divided into fast and slow
The
fast sub-
subprocesses.
of onto
520
and 0.09
C.I.
Direct
Yellow
nm),
of
g/mol,
27
Am.
g/L
the
describes
process
accessible outer
the
adsorption
and
dye
slow
easily
630
396
(molecular
weight
nm),
dyes
by
g/mol,
Åmax
fiber
the
surface,
subprocess
to
a
mixture ratio of 2.5:2:1.
All
three
relating
belong
describes diffusion of the
into
the
inner disordered
dye
The
to
the
SDC-class
and
which is
characterized
A,
of
the fiber
innerandouter
fiber
surfaces
[2].
regions
these
good
migration
(i.e.,
self-levelling
properties
in
of
cotton have been
size exclusion
investigated
using
[ 1 ],
are insensitive to
small
salt
concentra-
dyes
changes
Bredereck et al.
of
who
found that
chromatography
by
tiofi
and
temperature).
in the
generally
beginning
finishing
processes, uptake
oftextile
auxiliaries
takes
in
the macro-
diameter
and
mainly
place
with an effective
200 To for water
mean
of DP
mesopores
pore
~
swollen
cotton fiber. This
is
process
chemicals into
fast in
to the
diffusion of
very
comparison
located
the
between the
fibrils
micropores
elementary
with
an
effective
mean
of
diameter
30 A.
D~ --=
pore
mathematical
To
our new
we will
con-
model,
to
verify
duct
more
correlate the
far-reaching experiments
structural features
of
cotton
with the inner
and
outer
surfaces
and to
find the best fit
for fast
and
slow
subpro-
cesses to
and
diffusion
models. In
existing
adsorption
we
consider
of
addition,
the
simulta-
desorption
dye
with
at both
surfaces.
this
that
neously
concept
adsorption
dyeing process,
Relating
to the
it is
to
divide
possible
and
into
two
diffusion
process
with
parts,
dye
adsorption
dye
This
model
has been
direct
verified
subsequent
adsorption.
dyeing
for
monochrome
of
cotton with
[2],
combi-
dyes
but it
nation
of
is
also
transferable to
in
dyeing processes
shades. In
this
we
the
influence
and
paper,
investigate
such as
processing
parameters
dyeing
temperature
salt
concentration on
the
kinetics
and hue of
a
dyeing
FIGURE 1.
Molecular
structures of
the direct
dyes
trichrome
direct
at the
inner
and
outer sur-
of the
dye
system
trichrome
system.
faces of
cotton. These
are based on
et
investigations
dyeing
[4]).
data
in
work
al.
(Denter
previously published
DYEING
The
AND
CONDITIONS
EQUIPMENT
solution
Experimental
DYES
with
a
constant
concentration
dye
(co)
was
with
a
medium
pumped
pressure
chromatographic
SUBSTRATE
AND
model
Bfchi
from
a
reservoir
681,
a
pump,
column
through
with
yarns
filled
with
sited cotton
a
to
the
parallel
The
described in Part
cotton
I
of
Analogous
experiments
used raw
of 35%.
time
was 60
this series
we
minutes.
filling grade
from
[2],
the
was
dyeing
yarn
The
The
of
the
Grevener
the
column with
a
delivery
pump through
Baumwollspinnerei,
Germany.
yarn
for 45
of 150
mm
a
and
a
diameter
the
of 4.9
at 95°C
mm was
5
min-
length
pretreated
by
5
boiling-off
process
utes
with
mlJmin. At
the endof
the
3
Lufibrol KB
0.75
NaOH,
Germany),
absorbance
of
column,
detected
g/L
(BASF,
(E)
diode
g/L
and
the
solution was
a
uv-/vis
U
Ludwigshafen,
dye
g/L
by
Packard
Leophen
array
396, 520,
(BASF,
at
a
Hewlett
ratio
of
at
Ludwigshafen,
Germany)
spectrophotometer,
8452,
liquor
30:1.
Then
the
material was
and
washed
590
nm.
several
times with
A
schematic
of
the
drawing
experimental
occurred
hot
and
cold
demineralized
water.
the three
is
shown in
Part
I
All
equipment
[2].
dyeings
In all
direct
were
dyes
within
a
dyeing experiments,
without
of
20-80°Cunder
isothermal
temperature
range
used
further
in
a
total
concentration
purification
conditions.
Downloaded from trj.sagepub.com at UNIV OF CONNECTICUT on April 11, 2015

225
In
to
the
constant,
order
the
of 9.2
dye
keep
pH
solution was buffered with 1.7
The
g/L
dyeing
Na2B407.
involved the
condi-
boiled-off cotton
experiments
tioned at 20°C and 65%
yam
relative
humidity.
DETERMINING TIME-DEPENDENT DYE SORPTION
of the
data of the
Interpretations
eluate after
spectrophotometric
the column are based on the calibra-
passing
tion
ofthe trichrome
to
This is
dyeing.
dyes
dye system prior
done
total
the concentrations of the
within
a
by varying
concentration
the
of 0.5
by
liquor
g/L
applying
’
inverse Lambert-Beer law in the form
where
c
the concentration
E is the extinction
is
matrix,
is the coefficient matrix.
and
P
P
can be calcu-
after the P-
matrix,
lated
linear
(MLR)
by multiple
regression
matrix method
[
12J:
ET
where
The
is the
matrix of E.
uptake
transposed
of the cotton
dye
yarn
time-dependent
to the
of the concentration/time
corresponds
integral
in
the
max-
curve obtained
the absorbance
by
dye
absorption
imum of each
[ 12]:
FIGURE 2.
cotton
curves of the trichrome direct
system
of
Dye-uptake
cakulateddata:
dyeing
m,(t) dye
on
total
m(t)
dye uptake.
ofthe inner
uptake
the outer
surface,
surface,
dye
O experimental
ma(t)
uptake
is
where
the standardized total
m(t)
to
dye uptake (mg/g)
the concentra-
total
data,
dye uptake.
1
of
cotton,
dye
referring
g
represents
co
tion
time
correlated with the concen-
after 60
at
(t
0)
(mg/mL)
dyeing equilibrium
normal
a
white standard
a
10°
reference
observer,
ofthe eluate in
tration
minutes,
D
65. The color differences were
and
daylight
(BaS04),
>
is the
concentration at time
is
c(t)
(t
0)
(mg/mL), v
dye
to DIN 6174
determined
[5].
according
of the
solution
is the
the How rate
(mUmin),
and g
dyeing experiment.
in Part
dye
yam (g)
in
amount ofcotton
the
Results and Discussion
I
to the mathematical modeldescribed
According
the
ofthe
ON BOTH
ofthis series
total
DETERMINING TIME DEPENDENT DYE UPTAKE
COTTON SURFACES
cotton,
[2],
and
m(t)
dye
dye uptake
at the outer and inner surfaces ofthe
uptakesmit)
met)
2),
can be
and the
fibers
(see
velocity
Figure
constants k,
k~ds
ofcot-
2 with
Wedetermined the
time-dependent dye uptake
this
is the
and
by
ki
kjdd
computed
model; ke
in
as shown
ton for the trichrome
system
60°C and 2.5
Figure
the
constants of
and
of the
velocity
sorption (~)
quotient
NaCl-concentra-
curves simulated
at
measurements
g/L
at the
and
is the
outer
surface,
desorption (ds) processes
ki
shows
tion.The
figure
also
dye uptake
of the
constants of the
and
velocity
quotient
sorption (kd)
model with
to the
of
the mathematical
regard
of
sorption
on
by
at the inner
surface
[2].
desorption (dd) processes
based
cotton
the
inner surfaces
the outer and
of the three
ofthe three
constants
and
dyes.
velocity
ks, kd, ds
dd
COLORIMETRIC MEASUREMENTS
Wedetermined differences in the
at
As
dyes
few
inner surface takes much
at the
sorption equilibrium
expected,
within
a
cotton is achieved
surface of
hueofthe
the outer
dyed
grey
while
cotton
colorimetric measurements
(Ahiba/Datacolor,
3880. The
param-
minutes,
sorption
by
differences in
are
There
with
a
Switzerland)
eters included
quantitative dye
ofcotton. to
great
ofthe different accessible
spectrophotometer
longer.
uptake
mm
~/0°
a
12
regions
Up
aperture, special
geometry,
Downloaded from trj.sagepub.com at UNIV OF CONNECTICUT on April 11, 2015

226
is
225
Blue
C.I. Direct
20
time of
minutes,
surface
a
dyeing
the fiber.
of
the outer
adsorbed
Beyond
by
mainly
values
the ms
while
blue
still increases
curve
After
inner
the md
constant.
that
time,
is further
the
hour,
1
remain
dye
that
which
the
means,
surface,
achieved
adsorbed
dyeing
This
by
also
not
is
4).
(see
Figure
yet
C.I.
equilibrium
35
After about
Violet 47.
Direct
for
true
the
is also
but still increase
to
similar
values are
minutes
m.~
md
for
ma.
The
inner
27 at the
Yellow
lower
Direct
C.I.
values
md
of
those
than
are
cotton
ofthe
surface
This
m_s.
always
is the
it
because
has
a
molecule
mobility
possibly
higher
dye
so
and
of the
smallest
three,
pro-
used.
desorption
conditions
the
under
favored
are
cesses
dyeing
27
Yellow
Direct
to
ofC.I.
reactions
the
Also
displacement
with
such as
cotton,
a
molecules
affinity
higher
dye
by
take
could
225,
Direct Blue
47 and
Violet
Direct
place.
experi-
monochrome
has to be checked
This
dyeing
by
’
ments.
DYES
DIRECT
TRICHROME
KINETICS OF
SORPfION
DYE
SURFACES
,
ON BOTH COTTON
character-
are
of
The
kinetics
dye sorption processes
the acceleration
which describe
and
ized
by
vx(t)
of these
v,,(t),
processes
accessible
derivatives
obtained
different
at the
or
delay
are the first
and
ofcotton.
vx(t)
regions
vZ(t)
and
curves
curves
and
ofthe
m(t),
md(t)
ms(t),
dye uptake
Figure
The values of
3.
in
are
2. These
from
Figure
total
presented
of cotton:
direct
of trichrome
3.
FIGURE
v&dquo;,(t)
dyeing
diffusion
Velocity
attributed to
are
process.
adsorption process, v_(t)
v~(t)
sorption,
super-
based
vx(t)
vZ(t)
surfaces
inner
at the outer and
processes
imposed
on the
the
model.
of the
Therefore,
sorption
hypotheses
ex-
be
can
This
values.
with the
small
vx(t)
compared
of simultaneous
in the different
the
describes
model
dye uptake
desorption
only
diffusion-controlled
much slower
and
the
pro-
ofthe
by
plained
and
of
sorption
processes
areas
in the inner
of
cesses
desorption
sorption
dis-
but cannot
of the
accessible areas.
substrate,
exactly
the solutions
because
at the
of
velocities
The
substrate.
dyeing
time-dependent
of
is
them. This
between
tinguish
Direct
C.I.
Blue
Direct
with C.I.
inner surface
and C.I.
225,
from
and
of
and
are the
respec-
ksld.~
kdldd,
quotients
k~
ki
[2].
are
3
27
Direct Yellow
Violet
47,
Figure
tively
in
4.
in an
Figure
scope
presented
After
expanded
of
and
velocities
the
v,,(t)
vz(t)
dyeing
Considering
maximum
the
2.5
minutes,
substrate
dye-
approximately
in the inner
and
at the outer
and
the
processes
desorption
adsorption
is
value
gained
regions
velocity
ing
for
is
it
obvious
substrate in
of the
inner surfaces
3,
Figure
Direct
Violet 47. C.I.
Direct
225 and
C.I. Direct Blue
decreases
times
short
that after
fast,
very
The
velocity vx(t)
dyeing
outer surface.
ofthe
a
covering
rapid
indicating
of
the sub-
of
in the inner
region
dyeing
velocity
strate
vz(t)
of the
for
of the
I.
TABLE
optimum affinity
temperature
Comparison
then
value and
a
to maximum
increases
.
the
and
manufacturer
monochrome
trichrome
information)
up
slowly
systems (dye
values
from
calculated
system
the values
experimental
dyeing
to zero.
decreases
of
Therefore,
trichrome
asymptotically
rate.
as well as initial
for the
the initial
rates
pro-
dyeing
dyeing
shown in Table
cess of cotton at
60°C,
I,
exclusively
fiber.
ofthe
surface
at the outer
represent dye adsorption
if
and
0,
equilibrium
dyeing
Generally,
vx(t)
v,(t)
that
ad-
which means
is
at both surfaces
and
reached,
dye
of
order
rates are the same
mag-
very
desorption
sorption
~
are
values
t
minutes
the
nitude. At time
5
vz(t)
Downloaded from trj.sagepub.com at UNIV OF CONNECTICUT on April 11, 2015

227
4.
of trichrome
in the inner
3).
FIGURE
direct
Velocity
dyeing
vz(t)
of
curves of
cotton
Figure
region
(segmental
Yellow
the smallest
molecule ofthe
needs
27,
three,
be related
dye
twice that time. As mentioned
this
may
before,
reactions
to
or
desorption
displacement
during dyeing,
in
but also to the low concentration of
the
information about
more
the
yellow dye
To
trichrome
this
dye system.
get
of the
should be used. Wewill discuss this in Part III
similar molar concentrations
phenomenon,
three
dyes
of this series.
TEMPERATURE DEPENDENT DYE UPTAKE
DETERMINING
FIGURE 5.
and inner
trichronre direct
at the outer
OF BOTH SURFACES
dye
(ms)
Equilibrium
uptake
surfaces of cotton at different
(rria)
dyeing temperatures
5
a-c show the
for
Figures
each
equilibrium dye uptake
the
and
The
of cotton be-
at
outer
inner surfaces
are
dye
in
tween 20 and 80°C.
same data
presented
Yellow 27 seems to be
nearly completely displaced by
’
d-f for different
of the
in
the
5
amounts
dyes
surfaces of
Figures
47
70
Direct Violet
at
and 80°C.
to the
at the
trichrome
different
system adsorbing
optimum affinity
with the
Dyeing temperatures relating
of the trichrome
No
the substrate.
atures above
of cotton was done at
dyeing
80°C
temper-
system
dyeing
dye
correspond
of
in
because
the
decrease
dye
high
of
manufacturer for monochrome
the
specifications
of the blue and
and
NaCl concentration
hour.
yellow dye.
uptake
in
of cotton. The data are
Table
I.
dyeing
presented
1
was 2.5
time was
g/L
dyeing
the
ofthe trichrome
which also shows the initial
rate
dyeing
of all three
uptake
As
equilibrium dye
temperature.
expected,
depends
on cotton at
60°C.
dye system
the
on
This is valid for both
dyes
the inner and outer surfaces. For C.I. Direct Blue
225,
is maximumat 60°C at both
Atlow
surfaces.
CHARACTERIZATION OF DYEING RESULTS
. COLORIMETRIC
dye uptake
the outer
the
is
adsorbed
by
temperatures,
dye
mainly
inner
in
at
hue obtained
while above
of the
The differences
surface,
40°C,
dye uptake
dyeing tempera-
surface in relation to the outer surface is
ForC.I.
tures between 20 and 80°C can be demonstrated
by
higher.
outer
of
of the
is
measurementsofthe colordifferences
colorimetric
the
Direct Violet
at
surface
47,
dye uptake
while at
as shown in
Wechose
6. cotton
the inner surface the values are
ofthe outer surface
cotton,
at 50°C as the
70°C,
Figure
frame of
yarn dyed
ofthe smallest
highest
Forboth
reference because
or
of all
still
dyes,
of
increasing.
uptake
is
but it differs
deviations to blue/red
demonstrates that at low
yellow/green
samples.
nearly independent
temperature,
sig-
inner surface.
in
6
at the
nificantly
Figure
between 20
dyeing temperatures
and 40°C the color looks
behavior for C.I.
There are differences
dye
yellow-greenish,
sorption
color is
27.
the outer
at
while
above 50°C the red/blue
Direct Yellow
At
maximum
surface,
is obtained at 70°C and at the inner surface at
dye
temperatures
This
with
the
pro-
as
corresponds
dye uptake
predominant.
uptake
50°C.
in the
trichrome
system,
at both
is
of all three
surfaces
on
dyes
Dyeuptake
temperature.
highly dependent
portions
Atthe inner surface ofthe
C.I. Direct
shown in
5f.
fibers,
Figure
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228
of cotton
relation to the
at
different
FIGURE 6. Color differences
dyed
dyeing
yarn
sample
at
in
50°C.
dyed
temperatures
DETERMINING SALT DEPENDENT DYE UPTAKE OF BOTH
SURFACES
7
a-c show the
ofthe
Figures
equilibrium dye
uptake
on salt
inner
of
cotton
and outer surfaces
depending
for each
ofthe
trichrome
concentration
on
dye
experiments.
7
d-f
Based
the same
the dif-
data,
Figures
present
ferent
of
each
amounts
at the innerandouter surfaces
dye
at 60°C for
of cotton for
1
hour and NaCI
based on the
dyeings
concentrations between 2.5 and 10.0
g/L,
information of
The
the
manufacturer for
colors.
light
dye
of the outer surface for all
dye
improved
uptake
FIGURE 7.
inner
trichrome direct
at
outer
the
Equilibrium
dye
uptake
(ms),
is
to their
due
with
salt
and total surfaces of cotton at different salt concentrations.
dyes
concentration.
aggregation
increasing
(md),
at the fiber
a
multi-
Therefore,
surface,
adsorbed
molecules can
from which
a
of
form,
molecules can
layer
constant rate of
dye
be
and
Furthermore,
that occur
and
investigated.
tion
dissolve
displacement
during dyeing
desorp-
single dye
have to be ex-
reactions,
diffuse into
the inner surface ofthe
is
fibers.
this
Perhaps
amined for
and trichrome
monochrome, bichrome,
the reason that
at
the inner surface for C.I.
dye
dye
uptake
combinations at
tions. Our
and
similar
different molar
concentra-
Direct Yellow 47 is
ofNaCI
concentration.
Blue 225 and Direct Violet
concentrations ~5.0
independent
with
salt
This is also valid for Direct
experiments
and
concentration,
dyeing temperature,
are still in
These
are
47
at salt
dye
affinity
progress.
(see
7e).
g/L
Figure
on
based
the workofSumner
[13-15],
to fibers are
investigations,
because affinities of
very important,
highly dependent
dyes
Conclusions
model
on
and
in
a
temperature
change
sys-
con-
The mathematical
in Part
time
I
of this
presented
tematic
with
and/or
way
increasing dye
electrolyte
series seems
be valid
for
to
describing
dependent
centration
[
13].
and diffusion
that take
adsorption
processes
place during
in combination shades. We
have
this
for
verified
dyeing
ACKNOWLEDGMENT
a
trichrome
direct
to cotton. Thefirst
dye system
applied
can
We would like to thank the
of
Science and
Minister
results
in this
be described
only
presented
paper
of
Northrhine
for the institu-
Technology
Westphalia
under
there are still
that confirm
Thus,
phenomenological aspects.
tional
of
work.
our
support
about
many questions
dyeing experiments
the
differentiation between
and diffusion
of
of
adsorption
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and
onto fiber surfaces and
into the
inner
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the
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