Visible Light Shielding Performance of Fabrics with
Non-Circular Cross Section Fiber
Xiaosong Liu, Fumei Wang
College of Textiles, Donghua University, Shanghai CHINA
Correspondence to:
Fumei Wang email: jl_textile@mail.dhu.edu.cn
ABSTRACT
The models of polyethylene terephthalate (PET)
non-circular cross-section (NCCS) fibers were
established, and the characteristic parameters of
non-circular cross-section fiber used in this
numerical simulation were extracted. Furthermore,
the differences of refracted light intensity ratio Irz
and the direction of refracted light βt among
circular, trilobal and quadri-lobal cross-section
fibers were analyzed theoretically. The results show
that the refracted light intensity ratios Irz of these
fibers were in the range of 0.94~0.95. Both the
trilobal and quadri-lobal cross-section fibers' βt,
which was the angle of refracted light to Y-axis,
changed non-monotonically and much more
intricately than that of circular cross-section ones.
Moreover, according to the theory of geometrical
optics, the effects of trilobal and quadri-lobal
cross-section shapes on the changes of internal
refracted light and transmitted light in fibers were
also conducted. The results suggested that the
refracted and transmitted light were changed more
effectively in the quadri-lobal cross-section fiber.
The results of the experiment show that the
shielding properties of quadri-lobal cross-section
filament fabrics were better than that of the
counterparts with circular fibers, but the difference
was limited or insignificant.
Consequently, people began to study the effects that
the special technologies [2, 3] made on the NCCS
fibers with respect to the yarn’s and fabric’s
aesthetics, appearance and ‘feel’ in the early 1970s.
NCCS fibers usually have excellent capillary and
wicking properties for removing moisture,
therefore, it was suggested for use in many
applications, such as nappies, sanitary towels, filter
media, shoe liners and wound coverings [4, 5, 6, 7].
There is much research on the cross section of the
NCCS fiber, and the drafting behavior of the NCCS
polyester fiber was investigated to determine the
optimal conditions for spinning the P/C blend yarns
[8]. A new method was developed to calculate the
refractive index [9]. The Japanese [10-15] have
carried out studies on the properties of NCCS fibers,
to some extent, concentrating on performances of
the fiber assemblies, for instance the handle,
moisture permeability, or imitating the style of the
natural silk fiber fabric. Recently, various types of
NCCS fibers were used to produce fiber reinforced
composites (FRCs) [16-19]. Due to its high surface
adhesion on their larger specific areas, not only the
characteristics of the structure and surface were
improved, but also the properties of mechanical and
thermal conductivity.
Thorough studies on the optical performance of
single fibers with conventional circular cross
sections or cylindrical cross sections were
conducted [20-26]. The geometric and photometry
theory were used to analyse the optical property of
the light reflection and transmission [20-23],
dispersion [24, 25], the Descartes-ray and Rainbow
phenomenon [25, 26] of circular fibers. The
shielding fabrics were developed by [27-31]
adjusting the weaving process, developing
multi-layer or double-layer fabrics, coating the
surface of fabrics, or improving pigment printing
technology. Several studies were focused on the
reflection goniophotometric curves of woven
INTRODUCTION
The synthetic fibers, polyethylene terephthalate
(PET) and polyamide (nylon in market), were
normally round in their cross-sections, and natural
fibers don’t have a perfect circular cross-section.
Cotton has a ‘kidney-type’ or ‘dog-bone’ shape, and
silk has a roughly triangular shape. DuPont
developed the first non-circular cross-section
(NCCS) fiber made by the expanded adhesion spun
technology [1].
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fabrics [32-35]. Tsuneyo, et al [32], studied the
goniophotometric curves of the monochromatic
specular and diffuse light to evaluate the optical
properties and color change of fabrics, which was
suitable for fabrics made of conventional circular
fibers. Nobuo, et al [33,34], developed two models
on entire cross section of a yarn and simulated the
goniophotometric curves in a refractive index range
[35] from 1.3 to 1.8. The effects on the cross
sectional shape of the NCCS fiber on the radiative
properties, such as extinction and scattering
efficiencies [36], was carried out numerically to
predict the intensity distribution of the scattered
radiation using the finite element method (FEM).
Although the effects of light on the NCCS fiber
materials in nature was similar to sound [37] and
acoustics [38], there was little reported in the
literature on the effects on the light shielding
performance of fiber itself and its assembly.
Theoretical Calculation
The Cartesian coordinates were set as shown in
Figure 1, and it was clear that r1<r<R. The
refractive index of the outside medium and the fiber
were n0 and n1 (n0<n1), respectively. According to
the Fresnel formula [39], the reflection coefficient
R(θR) was obtained from Eq. (1).
(1)
And the refraction angle was derived from the
refractive formula as expressed in Eq. (2)
(2)
When the light on the surface of the fiber was a
vertical incidence, the reflection coefficient was
fixed value as shown in Eq. (3)
In this paper, a theoretical model was developed
based on the principles of geometrical optics; the
optical properties on the surface of a single trilobal
and quadrilobe cross-section fiber were conducted.
Then experimental studies were carried out on the
effect of a cross-section shape on the visible light
shielding properties of the fabrics with NCCS
fibers, and light shielding performance between the
fabrics with NCCS fiber were tested.
(3)
Now, the trilobal cross section of the fiber was set
to calculate the distribution, and the results of the
theoretical formula of each component are shown as
follows. On the surface of the protruded arc CA,
supposing θtCA was the angle of normal on one point
of arc CA in top ground circle O1 to Y axis forward,
the range was 0 to θtA, therefore
THEORETICAL CALCULATION OF NCCS
FIBERS
Model of Fiber Cross-Section Characteristics
The transverse cross-section of a trilobal and a
quadri-lobal fiber were painted using Pro/Engineer
Wildfire 4.0 under conditions where the surface was
smooth, and then the fibers’ cross-section shape
outlines were divided into several independent
parts, including circular arcs and linear portions
linked in sequences. Their design sketches are
shown as insets in the upper-right hand corner of
Figure 1, in which different colors stand for
different modalities of the NCCS fiber, and the
same colors represent the same properties of light
reflectivity on each segment surface.
Journal of Engineered Fibers and Fabrics
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(4)
And θRCA the incident angle on the surface of the arc
CA was calculated from Eq. (5).
(5)
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FIGURE 1. Sketches of a single trilobal (a) and a quadrilobe (b) fiber cross-section and the incident light coordinate of the trilobal and the
quadrilobe cross-section, respectively.
With θ0 and θt changed, the distribution of reflective
light intensity Ir(θRCA) on the surface of the arc CA
was derived. Taking no consideration of light
absorption in the fiber, the total incident light
intensity I0 was equal to the reflected light intensity
Ir (described as Eq. (6) plus the refraction light
intensity I0-Ir) so the relative intensity ratio Irz could
be
expressed
as
Eq.
(7).
TABLE I. Values of angles
Journal of Engineered Fibers and Fabrics
Volume 7, Issue 3 – 2012
t ~
(6)
(7)
and
 't ~
52
of single trilobal and quadrilobe.
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light intensity declined and formed a trough as
shown in Figure 2(c); or, under particular
conditions of θ0, the incident light would not fall on
the boundary point αt=2π/3rad. But, the simulation
was still working for these condition values at
tangent points, so there would be a sharp rise and a
peak was formed in βt shown in Figure 3(c), and
could not be calculated correctly due to the very
complex process at boundary point αt=2π/3rad.
TABLE II. Computation parameters.
In Figure 3, the platform regions represented the
angle value of βt, so that the refracted light to the
forward Y-axis, on the surface of AB and B1A1
linear segments of trilobal and quadri-lobal cross
section fibers, and βt at different locations on the
surface of the circular cross section, increased
gradually with αt.
* Refractive index is 1.65, a selected value of polyester
fiber (PET) [20].
Numerical Simulation
To investigate the reflective ability and the
distribution morphology of the reflected light
intensity on each segment’s surface, and predict the
effects of the optical properties on the assemblies of
the NCCS fibers, especially that of trilobal and
quadri-lobal fibers, the numerical simulation results
were obtained by writing MATLAB programs. The
values of the parameters, marked in Figure 1, used
in the programs were listed in Table I and Table II,
and θt of different circular arcs were divided into m
segments.
Simulation Results
(1) The relative intensity ratio Irz and the direction
of refracted βt:
The simulation results of the relative intensity ratio
Irz and the direction of refracted βt are shown in
Figure 2 and Figure 3, respectively. And αt in each
figure was the angle of any point on the surface of
the fiber with respect to the forward Y-axis, the
range of which was 0-π/2 both in circular and
quadri-lobal, but 0-2π/3 in trilobal.
From Figure 2, we can see that the overall light
intensity refractive ratio of the fiber-translucent
material was roughly in the range of 0.94-0.95. The
overall differences among the light intensity
refractive rations in different parts of the circular,
trilobal and quadri-lobal cross sections in different
conditions were not remarkable, so the differences
in cross-section morphology had little effect on the
light intensity.
As the fiber morphology itself could make the
incident light tangented at the border point
αt=2π/3rad on the surface of the trilobal
cross-section and, thus, the relative refraction of
Journal of Engineered Fibers and Fabrics
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FIGURE 2. Irz vs. αt of three cross section fibers
(a: θ0=π/3, b: θ0=π/4, c: θ0=π/6).
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(2) Geometrical Optics Analysis:
The bump point in the βt-αt line was for the value of
βt when the incident angle was 0 clearly in the
curves of the circular cross section, which was
exactly equal to the value of θ0. Under the three
light incident angles θ0, the values of βt for the
circular, trilobal and quadri-lobal cross sections
were 0.7, 0.7, 1.0rad, respectively. However,
compared with that of the circular cross section, the
number of changed frequencies on the optical path
of trilobal and quadri-lobal cross section were
increased significantly.
The light paths transmitted through the trilobal and
quadri-lobal cross section fibers could be drawn as
shown in Figure 4(a) and Figure 4(b) according to
the boundary conditions of the numerical simulation
results shown in Figure 2 and Figure 3. When
θ0=π/3, the emitted light in AB and B1A1 of trilobal
produced a total reflection phenomenon (Figure
4(a-1)). The total reflection phenomenon happened
partly due to the transmitted light in AB of the
quadri-lobal and less in B1A1 (Figure 4(a-2)), which
led to more luster in the trilobal than that of the
circular and quadri-lobal cross section.
When θ0=π/6rad partly transmitted light in AB, of
the trilobal and the quadri-lobal cross sections, it
generated a total reflection. θ0=π/6rad generated
transmitted light in B1A1, of the trilobal cross section
(Figure 4(b)). The recurrence of the reflection
phenomenon and refraction of partially transmissive
light falling on the bottom surface of the
quadri-lobal cross section was clearly shown, but
the intensity was reduced and messy in that
direction. Figure 4 suggested that the role of the
circular cross section was the focused light, and the
same thing also occurred on the arc AC and the arc
A1C1 in the trilobal and quadri-lobal cross sections.
The changes on these cross sections varied more
dramatically than that on the circular cross section.
However, the refracted light angle βt of the arc BB1,
expressed as a scattering of light, was gradually
decreased with the change of αt.
FIGURE 3. βt vs. αt of three cross section fibers
(a: θ0=π/3, b: θ0=π/4, c: θ0=π/6)
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MATERIALS AND EXPERIMENT
Fiber Materials
Two comparable chemical circular and quadrilobe
cross-section fibers made of the semi-dull
polyethylene terephthalate (PET) slices interwoven
with cotton plied yarns and knitted ones were used
to compare the light shielding properties. The
specifications of the different PET drawings of
textured yarns (DTY) are shown in Table III. In the
theoretical simulation, the most significant
difference in the light reflective properties between
the trilobal and quadri-lobal cross sections were
realized by the light reflection effects of the
concave arc. But a better dispersion of light
appeared in the non-circular cross-section fiber
compared to the surface light reflection of the
circular fiber.
Cross section morphological examinations of the
circular and quadri-lobal cross section fibers were
performed by using scanning electron microscope
(SEM) images as shown in Figure 5. As can be seen
from Figure 5(a) and Figure 5(c), the samples Y1#
and Y3# named the same as the quadri-lobal cross
section, but differed in their actual cross-section
because the Y1# cross-section was very close to the
theoretical mode described above as in Figure 1.
Under the same magnification, the lobes of sample
Y3# were significantly thicker and shorter, and the
degree of the uneven surface was lower than that of
Y1#, and this may have a pronounced effect on its
optical performance results.
TABLE III. Specifications of different cross-section polyester
filament yarns.
FIGURE 4. Geometrical optics analysis of transmitted light
(a: θ0=60°and b: θ0=30°).
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used as the warp. The fabric parameters were
calculated based on the covering factor [40] ET with
the value of 37.61% and the specific weaving
parameters are shown as follows in Table IV. The
knitted weft plain stitch samples and their
specification parameters of F6#, F7# in Figure 6(f)
and Figure 6(g) are shown in Table V. The alkali
boil-off and soaping processing on these fabrics
were carried out to remove the natural impurities of
the cotton fiber and the spinning oil on the polyester
filaments, thereby reducing the impact on the
fabrics’ shielding performance. All the samples
were placed for 24 hours at 20±2Ԩ and 65±5%
relative humidity before being tested.
Morphologies of Fabrics
Figure 6 shows the surface morphologies of the
treated fabrics viewed using a Koshida-1000 3D
microscope (United States) under 200 times
magnification.
The Shielding Properties Testing
A Hitachi U-4100 UV-Vis spectrophotometer tested
the light shielding properties of the non-circular
cross-section polyester/cotton union and the knitted
fabrics in the visible range. The average
transmission coefficient Tj was chosen as an
objective indicator for evaluating the shielding
performance of the fabrics by analyzing the
transmission coefficient spectrogram.
FIGURE 5. SEM images of different cross-sectional polyester
fibers.
RESULTS AND DISCUSSION
Figure 6 shows the surface images of the designed
fabric specimens described above. The number of
holes and its size distribution in the unit length of
0.5 mm indicates that the structure of the fabrics
impacted the light shielding properties as they were
different, but the light shielding performance was
influenced
by
the
cross
section
of
fiber/monofilament under the same fabrics’
structure.
Fabric Samples
Since there are many grooves on the surface, the
non-circular cross-section filament yarns cannot be
used as the yarns warp through sizing. Meanwhile,
the sizing agents have unpredictable effects on the
optical performance. To avoid this impact, the
non-circular cross section polyester filament yarns
were used as weft yarns to produce a suitable fabric
structure that could maximize the non-circular
cross-section polyester filament yarns appearing on
the surface of the fabric. Cotton plied yarns were
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TABLE IV. Structure parameters of woven fabric samples.
TABLE V.
Structural parameters of knitted fabric samples.
*measured date
FIGURE 6.
Surface images of the treated NCCS polyester fabrics (200×).
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The average transmission coefficient Tj using the
UV-Vis spectrophotometer analysis and the typical
measured curves of the transmission coefficient
spectrogram, for evaluating the shielding
performance of the fabrics, are shown in Table VI
and Figure 7, respectively.
This is because the refraction light intensity ratio Irz
on the surface of both the circular and quadrilobe
cross section PET fiber was roughly in the range of
0.94-0.95, according to the theoretical calculations of
optical properties on the surface of the single
non-circular cross section fibers. There was not as
much visible light absorption of the non-circular
cross section fibers. The quadrilobe cross section
fibers increased the number of surface reflection and
refraction and the frequencies of the light intensity
and the direction changed in the refraction lowered
the transmission coefficient of light intensity in the
range of 0°-90°(0-π/2), compared to that of circular
ones. This would reduce the amount of light
transmission, but the multiple reflection and
refraction have limited impacts on the attenuation of
light.
CONCLUSIONS
The differences of the refracted light intensity ratio
Irz and the refracted light direction among the single
circular, trilobal and quadri-lobal cross-section
fiber, and the effect of the different fiber cross
sections on the changes of refraction and the
transmission of light from the view of geometrical
optics in fiber were analyzed theoretically.
Experiments of different cross-section fibers and
their fabrics were carried out on the light shielding
performance and the following conclusions were
reached:
FIGURE 7. UV-Vis spectrophotometer transmissions coefficient
spectrums of fabrics.
The transmission coefficients of monochromatic
light and the average transmission coefficient of
fabrics (in Figures 6(a)F1#, (c)F3#, (f)F6#) with the
quadri-lobal cross section fibers were lower than
those of the circular cross-section ones (in Figures
6(b)F2#, (d)F4#, (g)F7#) looking at both Table VI
and Figure 7. This data suggested that the
transmission coefficient of fabrics would be
lowered by fibers’ cross-section shapes, which
meant higher light shielding performance, But, the
overall differences between them were small, which
indicated that the improvement in the fabrics’
shielding performance due to the fibers’
cross-section was limited.
(1) Under the same characteristic parameters, the
difference of the theoretical simulation on the
refracted light intensity ratio Irz of the circular,
trilobal and quadri-lobal cross section fiber did not
differ much in general. Irz was within the range of
0.94-0.95. Considering the different positions on the
surface of the trilobal and quadri-lobal cross section
fiber, the changes of the light refraction angle βt
were more complex than that in the circular one,
showing non-monotonic changes and reflected the
differences in the optical properties between the
fibers.
TABLE VI. Objective testing results of light shielding of
fabrics with non-circular cross section fiber.
Type
Weaved
Knitted
No.
Rj
Tj
F1#
60.11
29.78
F2#
59.59
30.11
F3#
71.85
19.90
F4#
69.10
21.48
F5#
71.86
20.64
F6#
67.25
26.56
F7#
65.78
27.49
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(2) As can be seen from the geometrical analysis on
the changes in the path of the refraction light in the
fiber before ejecting, the effects of the quadri-lobal
cross section in the refraction light path was more
obvious compared to that of the round and trilobal
cross-sections.
(3) Under the same parameters of the yarn count,
density and other structural conditions in the
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fabrics, the light shielding properties of the fabrics
with the quadri-lobal cross-section fibers were
superior to that of the ordinary circular ones. The
effect of fibers’ cross-section morphology on
differences in light shielding of the fabrics were not
very large.
[2]
[3]
[4]
ACKNOWLEDGMENT
This research was funded in partly by the National
Science Foundation of China (NSFC5097315). The
authors wish to thank Dr. Jin Luo in College of
Textiles and Materials Testing Center of Donghua
University for their help and efforts completing this
study.
[5]
[6]
[7]
Nomenclature
r1 =radius of top ground circular O1 [mm]
r = radius of center ground circular O [mm]
R = radius of circumscribed circular [mm]
I0 = incident light intensity [lx]
Ir = reflected light intensity [lx]
Irz = relative light intensity ratio [-]
θ0 = angle of incident light to forward of Y-axis
[rad]
θt = angle of the normal of the incident light to
forward of Y-axis [rad]
θR = incident angle of light on the surface of fiber
[rad]
=
refraction
angle on the surface of medium [rad]
φ
αt= angle of any point on the surface of fiber to
forward of Y-axis [rad]
βt= angle of refracted light on the surface of fiber to
forward of Y-axis [rad]
θt~ , θ’t~-the angles of incident light normal to Y axis
forward of each segments on surface of trilobal
and quadri-lobal fibers
θR , θ’R-the incident angle of each segment on the
surface of trilobal and quadri-lobal fibers
R(θR~),R(θ’R~)-the reflection coefficient of each
segments on surface of trilobal and
quadri-lobal fibers
Ir(θR~), I’r(θ’R~)-the distribution of reflected light
intensity of each segment on the surface of
trilobal and quadri-lobal fibers
Where, ~ could be arc CA, AB, arc BB1 ,B1A1, arc
A1C1 which were listed in Table I.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
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AUTHORS’ ADDRESSES
Xiaosong Liu
Fumei Wang
College of Textiles, Donghua University
2999 North Renmin Road, Songjiang District
Shanghai 201620
CHINA
Journal of Engineered Fibers and Fabrics
Volume 7, Issue 3 – 2012
61
http://www.jeffjournal.org