Optical properties of nanocomposites areimportant and useful in their consumer satisfaction capacities. In thisresearch, coloration properties of dyed PA6/nano TiO2 nanocompositeis studied using a combined Mie and Kubelka-Munk light scattering theory. Mietheory uses the relative refractive index of a small particle to calculate thelight scattering efficiency of a material while Kubelka-Munk theory inputsthese efficiencies in order to evaluate the optical properties of a multiplescattering opaque object. Optical properties of a Polyamide 6/Nano TitaniumDioxide films containing 0.01% and 0.03% nano TiO2 particles with40nm and 50nm radius respectively, was investigated after dyeing with twodifferent acid dyes and then compared to experimental measurements. Then thespectral reflectance and color values of nanocomposites with different particlesizes were predicted using the same method. Results show that by taking the refractiveindex as an intrinsic property of a particle, it is possible to estimate andmodel the coloration properties with a defined size while in addition; it canhelp to predict these properties for different particle sizes

Hoseinpour, A.

Rastar, A.

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 3 No 2, 02MAN02(4pp) (2014)   2304-1862/2014/3(2)02MAN02(4) 02MAN02-1  2014 Sumy State University Estimation of Coloration Properties of PA6/TiO2 Nanocomposites Based on  Combined Light Scattering Theories  Amir Rastar*, Alireza Hoseinpour  Department of Textile Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran  (Received 13 December 2013; published online 29 August 2014)  Optical properties of nanocomposites are important and useful in their consumer satisfaction capaci-ties. In this research, coloration properties of dyed PA6/nano TiO2 nanocomposite is studied using a com-bined Mie and Kubelka-Munk light scattering theory. Mie theory uses the relative refractive index of a small particle to calculate the light scattering efficiency of a material while Kubelka-Munk theory inputs these efficiencies in order to evaluate the optical properties of a multiple scattering opaque object. Optical properties of a Polyamide 6/Nano Titanium Dioxide films containing 0.01% and 0.03% nano TiO2 particles with 40nm and 50nm radius respectively, was investigated after dyeing with two different acid dyes and then compared to experimental measurements. Then the spectral reflectance and color values of nanocom-posites with different particle sizes were predicted using the same method.  Results show that by taking the refractive index as an intrinsic property of a particle, it is possible to estimate and model the coloration properties with a defined size while in addition; it can help to predict these properties for different particle sizes.   Keywords: Mie theory, Kubelka-Munk theory, TiO2, nanoparticle, Color value.   PACS numbers: 42.25.Fx, 42.68.Mj                                                             * amir.rastar@gmail.com  1. INTRODUCTION  Optical properties of particles are studied from very old time until recent years as one of their main charac-teristics. There are several theories and models along-side experimental tries in order to measure or calculate these characteristics. Many general definitions are made for various conditions in which the particle and its medi-um take part in the light scattering phenomena. [1-8].  Mie theory is widely used among all that mentioned in order to obtain scattering properties of a single spherical metal particle. Therefore it can be used for single scattering of light where the scattering happens only from a single particle with no relation to neighbor ones. [9]. On the other hand in a material, there are many scattering particles interacting and assisting each other in light scattering so it is the multiple scat-tering which really happens in the object. Researches usually combine a simple form of Mie theory for a sin-gle particle with a multiple scattering theory like Ku-belka-Munk in order to calculate the scattering effi-ciency of the whole collection [10].  In this study Mie theory’s results are used as an in-put to the Kubelka-Munk’s theory in order to calculate the reflectance factor of the nanocomposite. These theo-ries are briefly described in the next sections.  1.1 Mie theory  Mie theory is one of the most basic theories among the light scattering models presented from about a hundred years ago. It returns to 1908 when Lorentz Mie published an article about optical properties of spherical metal particles based on their complex refrac-tive index. In this theory from the relative refractive index and the size of particle, two main coefficients are derived and used to calculate the optical parameters of the material, such as optical efficiencies, cross sections and patterns [3].           ∑                   (1.1)          ∑        |  |     |  |  (1.2)                 (1.3)         (1.4)  in above formulas, Qext is the extinction efficiency, Qsca is the scattering efficiency, Qabs is the absorption efficiency, r is replaced by the particle radius and x represents the size parameter which is a factor of parti-cle size and the incident light’s wavelength.  an and bn are Mie coefficients and n is the number of it-erations in these functions which its maximum number is calculated according Bohren and Huffman as below [11]:              ⁄     (1.5)  Mie coefficients can be estimated as the Bessel func-tions of the particle’s relative complex refractive index.              [      ]       [        ]         [         ]          [        ]  (1.6)           [      ]       [        ]       [         ]          [        ]  (1.7)  From efficiencies, cross sections which are the area in which the light has its effects efficiently are calcu-lated.                                                  (1.8)  and G is the particle’s across sectional area.  AMIR RASTAR, ALIREZA HOSEINPOUR PROC. NAP 3, 02MAN02 (2014)   02MAN02-2 Finally the scattering patterns which demonstrate the amount of light scattering in different angles around the particles in the scattering plane are calcu-lated from the results of above formulas [11].  1.2 Kubelka-Munk theory  When multiple scattering occurs, a single particle takes part in its own scattering behavior while in the light scattering of many neighbor particles. Kubelka-Munkk theory is a multiple scattering theory which calculates the reflectance factor of a matte or semi-transparent material using its scattering (S) and ab-sorption (K) coefficients.               (1.9)  R is the reflectance factor in Eq. 1.9. These coefficients can be calculated by the efficien-cies of other single scattering theories like Mie theory as an input.                        (1.10)                   (1.11)  Where    is the particle volume and   is the asym-metry parameter or weighted cosine of the scattering angle of the scattered light [10].  2. MATERIALS AND METHOD  Virgin Polyamide 6 chips were provided from RTP Company with code number RTP200A and then mixed with P25 nano Titanium Dioxide particles from Degussa with the average radius of 21nm after proper drying. Virgin polyamide chips were separately mixed with the ratios of 0.01% and 0.03% per weight of the chips. Then the mixed material was fed to the Coperion Wener and Pfleiderer twin screw extruder in the average 235oC in order to create the blended PA6/TiO2 chips. These chips were converted to thin films using a Toyoseiki hotplate by pressing 7g of mixed material under 25mpa pressure and 235oC temperature for each film forming an approx-imate 30×30cm film. Philips EM208 transmission elec-tron microscope was used to capture images from the samples in order to evaluate the particle cluster sizes in the films. Five individual films were produced for each percent of nanoparticles. Each film was cropped to two 10×10cm film for the dyeing process.  Then, the produced films were dyed with two different Acid dyes, Telon Blue RR 01(C.I. Acid Blue 62) and Telon Red BN 03(C.I. Acid Red 42) manufactured by Dystar company. In this case, films were introduced to warm dye bathes with 40oC temperature and then the temperature was raised to boiling point in 20 minutes and dyeing was continued for 45 minutes after that.  Finally, spectral reflectance of the dyed films was measured by an Xrite ColorEye 7000a spectrophotometers. These measurements were per-formed for five positions for each film, four in the corners and one in the center. The mean value of all five meas-urements was reported as the experimental data. All computational evaluations were performed with MATLAB software from MathWorks.  3. RESULTS AND DISCUSSION  After mixing and extruding the films, aggregation of particles may take place in them therefore the particles form clusters in their media. The cluster size is used in the calculation as it is assumed that all clustered parti-cles are a single unit which led to single scattering of the light by them in their field. In order to access the size of particle clusters in the samples, TEM pictures were taken from the produced films. In Fig. 1 it is observed that the radius of particle cluster sizes for two different amounts of used nano TiO2 particles are approximately 40 and 50 nanometers approximately. Then the 40nm particle size is used for the 0.01% nano TiO2 and the 50nm is used as the radius for 0.03% nanoparticles.   Fig. 1 –  TEM picture of nanocomposite films: (a) 0.01% nano TiO2 (b) 0.03% nano TiO2  Single scattering is based on this fact that the dis-tance among particles are large enough so the light scattered from one particle does not interfere with the scattered light from another one. So, it can be assumed that by increasing the amount on particles the accuracy of the result would be decreased due to the lower dis-tances among the nanoparticles. Spectral reflectance of two different dyed nanocom-posite films are measured and observed in Fig. 2. As shown in this Fig. two different dyes were used with different spectral data in order to evaluate the method for different color values. The dyes were selected for their contrast so they would cover the whole steps of the visible light’s wavelength range.  With respect to the complex relative refractive index of the nanoparticles which changes against the light wavelength and according to equation 6 and 7 the Mie coefficients were calculated using MATLAB software’s Bessel functions. Then using these coefficients, the opti-cal efficiencies of nanoparticles were calculated based on equation 1 and 2. The scattering efficiency and the ab-sorption efficiency are used in acquiring the Keubelka-Munk’s absorption and scattering coefficients. In addition the scattering patterns are calculated in each wavelength step which demonstrates the amount of light scattering around the particle in each wavelength.  The Kubelka-Munk’s coefficients are computed ac-cording to formula 10 and 11. These coefficients (K/S) are in a direct relation with the material’s spectral reflec-tance based on formula 9. (b) (a)  ESTIMATION OF COLORATION PROPERTIES OF PA6/TIO2 … PROC. NAP 3, 02MAN02 (2014)   02MAN02-3    Fig. 2 – Spectral reflectance of two different dyed films    Fig. 3 – The measured spectral reflectance in comparison with the estimated one for the blue dyestuff    Fig. 4 – The measured spectral reflectance in comparison with the estimated one for the red dyestuff  Finally the spectral reflectance for the dyestuffs is cal-culated. Then these results are compared with the actual results measured by the experimental instruments. The results for each dye are shown in Fig. 3 and Fig. 4. It can be observed that the combined Mie and Ku-belka-Munk method is able to estimate the optical properties of colored materials as nanocomposite films  with an acceptable precision. The color values and color differences for these two dyes which are shown in Table 1 also proves the above conclusion. It is observed in Table 1 that the lower amounts of nanoparticles leads to more accurate results. By con-sidering the color differences it is shown that the samples with 0.01% nano TiO2 have less color differ-ence compared to the other sample. The color differ-ence for the low amount of nanoparticles are good but for the sample with higher amounts of nanoparticles, this difference is not very acceptable however, the correlation coefficient between the measured and the estimated data shows good correspondence between them. The correlation coefficient for the blue sample with 0.01% nanoparticle was 0.9631 while this num-ber was 0.9048 for the sample with 0.03% TiO2. Again, the coefficient for the red sample containing   AMIR RASTAR, ALIREZA HOSEINPOUR PROC. NAP 3, 02MAN02 (2014)   02MAN02-4  Table 1 – The color values and color differences for two dyestuffs  0.01% nano TiO2 Estimated blue Measured blue Estimated red Measured red 72.4123 71.2824 69.4894 68.5608 L* -10.7595 -10.5597 30.1926 28.0317 a* -30.4258 -32.5463 -17.9983 -19.2000 b* 2.4110 2.6412 Color difference 0.03% nano TiO2 Estimated blue Measured blue Estimated red Measured red 81.2981 79.6224 80.1922 76.5010 L* -12.0783 -10.0136 20.5237 16.4229 a* -21.3408 -26.8290 -14.2280 -17.3786 b* 6.0984 6.3536 Color difference  0.01% nanoparticles was 0.9904 versus 0.8978 for the red sample with 0.03% TiO2. This result is based on the distance among the particles in their medium which is lower in the sample containing higher amounts of na-noparticles. Therefore, it can be mentioned overally that the combined method of Mie and Kubelka-Munk theory is a good technique for estimating the coloration properties of nanocomposite films using the relative refractive index and the radius of particles as their intrinsic characteristics.    4. CONCLUSION  Optical properties of particles are one of their main characteristics. There are many ways to measure these properties using various devices; however with careful considerations it is possible to use different theoretical methods. Results showed that Mie approximations combined with Kubelka-Munk theory is a good way to predict and estimate the optical properties of dyed Polyamide nanocomposites containing nano TiO2 parti-cles however, the lower the amount of used nanoparticle is, the better the accuracy of the method would be. It is possible to estimate the reflectance factor of a polymer film using the particle’s relative refractive index to its medium. It is also possible to predict these properties for various particle sizes which could help to predesign the favorite product.  There could be also better selections in order to at-tain better results. In this research the particle cluster was accepted to be one particle unit. It is possible to calculate and aggregate the properties of each individ-ual particle in order to get better correspondence to the experimental data. However this method will signifi-cantly increase the complexity of the calculations which may not be actually very practical. Particle shape was assumed to be spherical while in fact, it is produced in an irregular shape. Other methods like T-matrix or EMT are able to estimate the properties of an irregular shaped particle. Other dyestuffs could also be used in order to investigate the results of this method. This study investigated the optical prediction of dyed polyamide 6 nanocomposites containing nano TiO2 particles which shows adequate and acceptable results.     REFERENCES  1. C. Ulrich, Hum. Ecol. 34, 1 (2006).  2. K. Nelson, Y. Deng, J. Colloid. Interf. Sci. 319, 130 (2007). 3. C.F. Bohren, and D.R. Huffman, Absorption and Scattering of Light by Small Particles, (USA:Wiley-Interscience:1983). 4. H.V. van de Hulst, Light Scattering by Small Particles, (New York: Dover Publications: 1957). 5. M.I. Mishchenko, L.D. Travis and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, (New York: NASA Goddard Institute for Space Studies: 2004). 6. G. Mie, Ann. Phys. 25, 377 (1908). 7. Light Scattering Reviews 5: Single Light Scattering and Radiative Transfer, Ed. A A Kokhanovsky, (New York: Springer Berlin Heidelberg: 2010). 8. A. Şahin and E.L. Miller, Recursive T-Matrix Algorithm for Multiple Metallic Cylinders, (Northeastern University, Center for Electromagnetics Research, Boston: 1997). 9. G. Mie, Contribution to The Optics of turbid Media, Particularly of Colloidal Solutions, Trans. P Newman, (Chicago: National translations center: 1978). 10. M. Quinten, App. Phys. B-Lasers O. 73, 317 (2001).  11. C. Matzler, Matlab Functions for Mie Scattering and Ab-sorption, (Institute of Applied Physics, University of Bern, Bern: 2002).  

Estimation of Coloration Properties of PA6/TiO2 Nanocomposites Based on  Combined Light Scattering Theories

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  
NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 3 No 2, 02MAN02(4pp) (2014) 
 
 
2304-1862/2014/3(2)02MAN02(4) 02MAN02-1  2014 Sumy State University 
Estimation of Coloration Properties of PA6/TiO2 Nanocomposites Based on  
Combined Light Scattering Theories 
 
Amir Rastar*, Alireza Hoseinpour 
 
Department of Textile Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran 
 
(Received 13 December 2013; published online 29 August 2014) 
 
Optical properties of nanocomposites are important and useful in their consumer satisfaction capaci-
ties. In this research, coloration properties of dyed PA6/nano TiO2 nanocomposite is studied using a com-
bined Mie and Kubelka-Munk light scattering theory. Mie theory uses the relative refractive index of a 
small particle to calculate the light scattering efficiency of a material while Kubelka-Munk theory inputs 
these efficiencies in order to evaluate the optical properties of a multiple scattering opaque object. Optical 
properties of a Polyamide 6/Nano Titanium Dioxide films containing 0.01% and 0.03% nano TiO2 particles 
with 40nm and 50nm radius respectively, was investigated after dyeing with two different acid dyes and 
then compared to experimental measurements. Then the spectral reflectance and color values of nanocom-
posites with different particle sizes were predicted using the same method.  
Results show that by taking the refractive index as an intrinsic property of a particle, it is possible to 
estimate and model the coloration properties with a defined size while in addition; it can help to predict 
these properties for different particle sizes.  
 
Keywords: Mie theory, Kubelka-Munk theory, TiO2, nanoparticle, Color value. 
 
 PACS numbers: 42.25.Fx, 42.68.Mj 
 
 
                                                          
* amir.rastar@gmail.com  
1. INTRODUCTION 
 
Optical properties of particles are studied from very 
old time until recent years as one of their main charac-
teristics. There are several theories and models along-
side experimental tries in order to measure or calculate 
these characteristics. Many general definitions are made 
for various conditions in which the particle and its medi-
um take part in the light scattering phenomena. [1-8].  
Mie theory is widely used among all that mentioned 
in order to obtain scattering properties of a single 
spherical metal particle. Therefore it can be used for 
single scattering of light where the scattering happens 
only from a single particle with no relation to neighbor 
ones. [9]. On the other hand in a material, there are 
many scattering particles interacting and assisting 
each other in light scattering so it is the multiple scat-
tering which really happens in the object. Researches 
usually combine a simple form of Mie theory for a sin-
gle particle with a multiple scattering theory like Ku-
belka-Munk in order to calculate the scattering effi-
ciency of the whole collection [10].  
In this study Mie theory’s results are used as an in-
put to the Kubelka-Munk’s theory in order to calculate 
the reflectance factor of the nanocomposite. These theo-
ries are briefly described in the next sections. 
 
1.1 Mie theory 
 
Mie theory is one of the most basic theories among 
the light scattering models presented from about a 
hundred years ago. It returns to 1908 when Lorentz 
Mie published an article about optical properties of 
spherical metal particles based on their complex refrac-
tive index. In this theory from the relative refractive 
index and the size of particle, two main coefficients are 
derived and used to calculate the optical parameters of 
the material, such as optical efficiencies, cross sections 
and patterns [3]. 
 
      
 
  
∑           
 
       (1.1) 
      
 
  
∑        |  |
 
    |  |  (1.2) 
                (1.3) 
   
   
 
 (1.4) 
 
in above formulas, Qext is the extinction efficiency, 
Qsca is the scattering efficiency, Qabs is the absorption 
efficiency, r is replaced by the particle radius and x 
represents the size parameter which is a factor of parti-
cle size and the incident light’s wavelength.  
an and bn are Mie coefficients and n is the number of it-
erations in these functions which its maximum number is 
calculated according Bohren and Huffman as below [11]: 
 
          
 
 ⁄    
 (1.5) 
 
Mie coefficients can be estimated as the Bessel func-
tions of the particle’s relative complex refractive index. 
 
    
        [      ]
       [        ]
 
        [   
      ]
 
   
   
   [        ]
 
 (1.6) 
    
      [      ]
       [        ]
 
      [   
      ]
 
   
   
   [        ]
 
 (1.7) 
 
From efficiencies, cross sections which are the area 
in which the light has its effects efficiently are calcu-
lated. 
 
     
    
 
      
    
 
      
    
 
                (1.8) 
 
and G is the particle’s across sectional area. 
 AMIR RASTAR, ALIREZA HOSEINPOUR PROC. NAP 3, 02MAN02 (2014) 
 
 
02MAN02-2 
Finally the scattering patterns which demonstrate 
the amount of light scattering in different angles 
around the particles in the scattering plane are calcu-
lated from the results of above formulas [11]. 
 
1.2 Kubelka-Munk theory 
 
When multiple scattering occurs, a single particle 
takes part in its own scattering behavior while in the 
light scattering of many neighbor particles. Kubelka-
Munkk theory is a multiple scattering theory which 
calculates the reflectance factor of a matte or semi-
transparent material using its scattering (S) and ab-
sorption (K) coefficients. 
 
 
 
 
 
      
  
 (1.9) 
 
R is the reflectance factor in Eq. 1.9. 
These coefficients can be calculated by the efficien-
cies of other single scattering theories like Mie theory 
as an input. 
 
   
         
  
 
    
  
 (1.10) 
 
   
 
 
         
  
 (1.11) 
 
Where    is the particle volume and   is the asym-
metry parameter or weighted cosine of the scattering 
angle of the scattered light [10]. 
 
2. MATERIALS AND METHOD 
 
Virgin Polyamide 6 chips were provided from RTP 
Company with code number RTP200A and then mixed 
with P25 nano Titanium Dioxide particles from Degussa 
with the average radius of 21nm after proper drying. 
Virgin polyamide chips were separately mixed with the 
ratios of 0.01% and 0.03% per weight of the chips. Then 
the mixed material was fed to the Coperion Wener and 
Pfleiderer twin screw extruder in the average 235oC in 
order to create the blended PA6/TiO2 chips. These chips 
were converted to thin films using a Toyoseiki hotplate 
by pressing 7g of mixed material under 25mpa pressure 
and 235oC temperature for each film forming an approx-
imate 30×30cm film. Philips EM208 transmission elec-
tron microscope was used to capture images from the 
samples in order to evaluate the particle cluster sizes in 
the films. Five individual films were produced for each 
percent of nanoparticles. Each film was cropped to two 
10×10cm film for the dyeing process.  Then, the produced 
films were dyed with two different Acid dyes, Telon Blue 
RR 01(C.I. Acid Blue 62) and Telon Red BN 03(C.I. Acid 
Red 42) manufactured by Dystar company. In this case, 
films were introduced to warm dye bathes with 40oC 
temperature and then the temperature was raised to 
boiling point in 20 minutes and dyeing was continued for 
45 minutes after that.  Finally, spectral reflectance of the 
dyed films was measured by an Xrite ColorEye 7000a 
spectrophotometers. These measurements were per-
formed for five positions for each film, four in the corners 
and one in the center. The mean value of all five meas-
urements was reported as the experimental data. All 
computational evaluations were performed with 
MATLAB software from MathWorks.  
3. RESULTS AND DISCUSSION 
 
After mixing and extruding the films, aggregation of 
particles may take place in them therefore the particles 
form clusters in their media. The cluster size is used in 
the calculation as it is assumed that all clustered parti-
cles are a single unit which led to single scattering of the 
light by them in their field. In order to access the size of 
particle clusters in the samples, TEM pictures were 
taken from the produced films. In Fig. 1 it is observed 
that the radius of particle cluster sizes for two different 
amounts of used nano TiO2 particles are approximately 
40 and 50 nanometers approximately. Then the 40nm 
particle size is used for the 0.01% nano TiO2 and the 
50nm is used as the radius for 0.03% nanoparticles. 
 
 
Fig. 1 –  TEM picture of nanocomposite films: (a) 0.01% nano 
TiO2 (b) 0.03% nano TiO2 
 
Single scattering is based on this fact that the dis-
tance among particles are large enough so the light 
scattered from one particle does not interfere with the 
scattered light from another one. So, it can be assumed 
that by increasing the amount on particles the accuracy 
of the result would be decreased due to the lower dis-
tances among the nanoparticles. 
Spectral reflectance of two different dyed nanocom-
posite films are measured and observed in Fig. 2. As 
shown in this Fig. two different dyes were used with 
different spectral data in order to evaluate the method 
for different color values. The dyes were selected for 
their contrast so they would cover the whole steps of 
the visible light’s wavelength range.  
With respect to the complex relative refractive index 
of the nanoparticles which changes against the light 
wavelength and according to equation 6 and 7 the Mie 
coefficients were calculated using MATLAB software’s 
Bessel functions. Then using these coefficients, the opti-
cal efficiencies of nanoparticles were calculated based on 
equation 1 and 2. The scattering efficiency and the ab-
sorption efficiency are used in acquiring the Keubelka-
Munk’s absorption and scattering coefficients. 
In addition the scattering patterns are calculated in 
each wavelength step which demonstrates the amount of 
light scattering around the particle in each wavelength.  
The Kubelka-Munk’s coefficients are computed ac-
cording to formula 10 and 11. These coefficients (K/S) are 
in a direct relation with the material’s spectral reflec-
tance based on formula 9. 
(b) (a) 
 ESTIMATION OF COLORATION PROPERTIES OF PA6/TIO2 … PROC. NAP 3, 02MAN02 (2014) 
 
 
02MAN02-3 
 
 
 
Fig. 2 – Spectral reflectance of two different dyed films 
 
 
 
Fig. 3 – The measured spectral reflectance in comparison with the estimated one for the blue dyestuff 
 
 
 
Fig. 4 – The measured spectral reflectance in comparison with the estimated one for the red dyestuff 
 
Finally the spectral reflectance for the dyestuffs is cal-
culated. Then these results are compared with the actual 
results measured by the experimental instruments. The 
results for each dye are shown in Fig. 3 and Fig. 4. 
It can be observed that the combined Mie and Ku-
belka-Munk method is able to estimate the optical 
properties of colored materials as nanocomposite 
films  with an acceptable precision. The color values 
and color differences for these two dyes which are 
shown in Table 1 also proves the above conclusion. 
It is observed in Table 1 that the lower amounts of 
nanoparticles leads to more accurate results. By con-
sidering the color differences it is shown that the 
samples with 0.01% nano TiO2 have less color differ-
ence compared to the other sample. The color differ-
ence for the low amount of nanoparticles are good but 
for the sample with higher amounts of nanoparticles, 
this difference is not very acceptable however, the 
correlation coefficient between the measured and the 
estimated data shows good correspondence between 
them. The correlation coefficient for the blue sample 
with 0.01% nanoparticle was 0.9631 while this num-
ber was 0.9048 for the sample with 0.03% TiO2. 
Again, the coefficient for the red sample containing  
 AMIR RASTAR, ALIREZA HOSEINPOUR PROC. NAP 3, 02MAN02 (2014) 
 
 
02MAN02-4 
 
Table 1 – The color values and color differences for two dyestuffs 
 
0.01% nano TiO2 
Estimated blue Measured blue 
Estimated 
red 
Measured 
red 
72.4123 71.2824 69.4894 68.5608 L* 
-10.7595 -10.5597 30.1926 28.0317 a* 
-30.4258 -32.5463 -17.9983 -19.2000 b* 
2.4110 2.6412 Color difference 
0.03% nano TiO2 
Estimated blue Measured blue 
Estimated 
red 
Measured 
red 
81.2981 79.6224 80.1922 76.5010 L* 
-12.0783 -10.0136 20.5237 16.4229 a* 
-21.3408 -26.8290 -14.2280 -17.3786 b* 
6.0984 6.3536 Color difference 
 
0.01% nanoparticles was 0.9904 versus 0.8978 for the 
red sample with 0.03% TiO2. This result is based on the 
distance among the particles in their medium which is 
lower in the sample containing higher amounts of na-
noparticles. Therefore, it can be mentioned overally 
that the combined method of Mie and Kubelka-Munk 
theory is a good technique for estimating the coloration 
properties of nanocomposite films using the relative 
refractive index and the radius of particles as their 
intrinsic characteristics.   
 
4. CONCLUSION 
 
Optical properties of particles are one of their main 
characteristics. There are many ways to measure these 
properties using various devices; however with careful 
considerations it is possible to use different theoretical 
methods. Results showed that Mie approximations 
combined with Kubelka-Munk theory is a good way to 
predict and estimate the optical properties of dyed 
Polyamide nanocomposites containing nano TiO2 parti-
cles however, the lower the amount of used nanoparticle 
is, the better the accuracy of the method would be. It is 
possible to estimate the reflectance factor of a polymer 
film using the particle’s relative refractive index to its 
medium. It is also possible to predict these properties 
for various particle sizes which could help to predesign 
the favorite product.  
There could be also better selections in order to at-
tain better results. In this research the particle cluster 
was accepted to be one particle unit. It is possible to 
calculate and aggregate the properties of each individ-
ual particle in order to get better correspondence to the 
experimental data. However this method will signifi-
cantly increase the complexity of the calculations which 
may not be actually very practical. Particle shape was 
assumed to be spherical while in fact, it is produced in 
an irregular shape. Other methods like T-matrix or 
EMT are able to estimate the properties of an irregular 
shaped particle. Other dyestuffs could also be used in 
order to investigate the results of this method. 
This study investigated the optical prediction of 
dyed polyamide 6 nanocomposites containing nano TiO2 
particles which shows adequate and acceptable results.   
 
 
REFERENCES 
 
1. C. Ulrich, Hum. Ecol. 34, 1 (2006).  
2. K. Nelson, Y. Deng, J. Colloid. Interf. Sci. 319, 130 (2007). 
3. C.F. Bohren, and D.R. Huffman, Absorption and Scattering 
of Light by Small Particles, (USA:Wiley-Interscience:1983). 
4. H.V. van de Hulst, Light Scattering by Small Particles, 
(New York: Dover Publications: 1957). 
5. M.I. Mishchenko, L.D. Travis and A. A. Lacis, Scattering, 
Absorption, and Emission of Light by Small Particles, (New 
York: NASA Goddard Institute for Space Studies: 2004). 
6. G. Mie, Ann. Phys. 25, 377 (1908). 
7. Light Scattering Reviews 5: Single Light Scattering and 
Radiative Transfer, Ed. A A Kokhanovsky, (New York: 
Springer Berlin Heidelberg: 2010). 
8. A. Şahin and E.L. Miller, Recursive T-Matrix Algorithm 
for Multiple Metallic Cylinders, (Northeastern University, 
Center for Electromagnetics Research, Boston: 1997). 
9. G. Mie, Contribution to The Optics of turbid Media, 
Particularly of Colloidal Solutions, Trans. P Newman, 
(Chicago: National translations center: 1978). 
10. M. Quinten, App. Phys. B-Lasers O. 73, 317 (2001).  
11. C. Matzler, Matlab Functions for Mie Scattering and Ab-
sorption, (Institute of Applied Physics, University of Bern, 
Bern: 2002). 
 


English

https://essuir.sumdu.edu.ua/bitstream/123456789/37230/1/rastar_nanoparticle.pdf

Estimation of Coloration Properties of PA6/TiO2 Nanocomposites Based on Combined Light Scattering Theories

Abstract

Similar works

Full text

Available Versions

Electronic Sumy State University Institutional Repository

SocioEconomic Challenges Journal (Sumy State University)