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Poly(methyl methacrylate)(PMMA)/poly(ethylene terephthalate) (PET) light scattering materials are fabricated by a simple, low-cost approach of melt blending and compression molding. We find that the competing effects of particle diameter versus number concentration of the scattering particles is the controlling factor to tailoring the optical properties of the materials, which is analyzed according to Mie scattering theory. The results show that the transmittance kept decreasing in the PET concentration range 0-10 wt% followed by a constant level in the range 10-20 wt%; however, the transmittance experienced a significant increase in the range 20-35 wt% and plateaued again after PET content exceeded 35 wt%. Therefore, the application of ordinary polymer dopant makes preparing light scattering sheets with high haze but not decreasing transmittance possible.
© 2015 Optical Society of America
1. Introduction
Solid state light sources are gradually replacing conventional incandescent light and other light sources due to their high efficiency in transforming electricity to light, and their environmental friendliness. The main element of solid-state light sources is the light emitting diode, LED. “Such ‘smart’ light sources can adjust to specific environment and requirements, a property that could result in tremendous benefits in lighting, automobiles, agriculture and medicine [1].” However, several considerations have to be kept in mind. The high brightness and strong intensity of LED light will do harm to our eyes. It is necessary to protect against the glare and achieve uniform illumination. Therefore, with the rapid development and wide application of LED technology, light scattering materials with both excellent transmittance and high haze become the research focus. Optically transparent polymer materials commonly used include polycarbonate(PC) [2], poly-dimethylsiloxane(PDMS) [3,4], polystyrene(PS), PMMA [5–11] and so on. Light scattering materials fabricated from the above-mentioned materials have all been reported. PMMA is not sensitive to ultraviolet light and can keep chemically stable even exposed outdoor [12]. Since PMMA is of exceptional clarity in the visible range, it can be used in a variety of optical devices such as polymer optical films for liquid-crystal displays, optical disks, etc [13]. Therefore, taking PMMA as the matrix of light scattering materials is more of research and practical value.
Inorganic additives and organic particles, such as silica (SiO2) [14], titanium dioxide (TiO2) [15] and polysiloxane [16],and so on, are commonly incorporated into PMMA in order to introduce scattering of light. “The underlying weakness of these traditional additives is that concentrations high enough to achieve a reasonable spread of transmitted light intrinsically, resulting in a significant degree of backscattering with consequent reduction of hemispherical transmittance [8].” Guo et. al, prepared PMMA/SiO2 nanocomposites by in situ polymerization [17]. Although the haze of PMMA doped with 8 wt% treated SiO2 increases from 6% to 82%, the transmittance experiences a significant decrease. The unchangeable morphology and size of these inorganic additives or organic particles when processed in polymer is responsible for this weakness. Because the number concentration, the number of particles per unit volume of the scattering particles, will increase with the increase of these particles mass fraction, resulting in more scattering centers and higher intensity of backscattered light, thus the transmittance will decrease significantly.
It is generally known that the size, morphology and orientation of the dispersed phase can all be tailored through tuning the composition and processing methods for immiscible and partially miscible polymer blends [18]. Namely, the number concentration and size of the dispersed particles will change simultaneously with increasing the mass fraction of the dopant polymer, indicating that there exists a competitive relationship between number concentration and particle diameter. Therefore, application of polymer dopant as light scatterers may avoids the paradox of traditional additives, which makes preparing light scattering sheets with high haze but not decreasing transmittance possible [19].
Therefore, we prepare PMMA/PET light scattering materials taking PMMA as the matrix and PET as the light scattering substance. We choose PET as scatterer for its refractive index difference from PMMA, which obviously improve the light scattering properties of the PMMA sheets. The composite can be used to create a thin and effective light scattering film coated on a bare glass substrate, which can be adapted to various applications for large-sized, flexible LED lighting, LCD backlights and others.
2. Experimental
2.1 Materials
The characteristics of the polymers used in this work are demonstrated in Table 1.
Table 1. Polymers used in this study
2.2 Sample preparation
The raw materials were dried under vacuum for 24 hours at 80 °C before using. Compound of polymer tablets with specific weight ratio was melt mixed at 265 °C for 8 minutes using a HAPROTM Rheometer (Harbin Hapro Electric Technology Co., Ltd), and the rotor speed was fixed at 30 rpm. The specimens with a thickness of 0.6 mm were prepared by compression molding at a temperature of 265 °C using the blends obtained above. The different specimen compositions are shown in Table 2.
Table 2. Constituents of the PMMA/PET blends
2.3 Transmittance and haze
Transmittance (T) and haze (H) are defined according to ASTM D1003-61 with a Transmittance-Haze testing instrument (WGT-S, Shanghai Precision and Scientific Instrument Corporation, China). According to this standard test method, haze is the percent of transmitted light that is scattered so that its direction deviates more than 2.5°. As shown in Fig. 1, all transmitted light within the hemisphere scope can be trapped using the integrating sphere. Haze and transmittance data are especially useful for quality control and specification purposes. They can be written as
Where It is the intensity of the transmitted light, I0 the intensity of the incident light and the intensity of a part of transmitted light with scattering angle more than 2.5° during passing through the sample.
Fig. 1 Optical system of the Transmittance-Haze testing instrument: (1) Source (2) Condenser (3) Aperture (4) Modulator (5) Lens (6) Sample (7) Integrating sphere (8) Photocell (9) Reflectance Standard (10) Emergent Window (11) Entrance Window.
2.4 Relative optical intensity
The instrument measuring the light scattering properties is shown in Fig. 2(a), including Helium-neon laser light source, attenuation sheet, sample cell, receiving screen and CCD camera. The attenuated laser impinges on the surface of the sample and a scattering spot was projected on the receiving screen made of translucent glass. The pattern on the receiving screen was recorded by a CCD camera manually focused on the receiving screen first and the origin 8.6 data processing software was used to analyze the recorded photograph.
Fig. 2 (a) Schematic of optical scattering test instrument (b) Schematic diagram of analysis for scattering light pattern.
By analyzing the pixels on the recorded photograph as shown in Fig. 2(b), we could get the average relative optical intensity of a group of cell in the X axis curve as a function of the scattering angle which was calculated from the following equation:
Where L is the distance between the sample and receiving screen, x the distance between certain point at the scattering spot and the middle of the spot.2.5 Scanning electron microscope (SEM) and statistical dispersed particle size
The specimens were immersed in liquid nitrogen for 4 hours and brittle fractures were performed. The fracture surfaces were coated with a layer of gold in a vacuum chamber for conductivity, and then examined with an SEM (FEI, INSPECT F, Netherlands). To determine the average particle size, 6 micrographs at the same magnification were obtained randomly from the liquid nitrogen fracture surface of each sample. The magnification was 10000Χ for all samples. For the micrographs, the particles were traced by hand. The manual trace was instantaneously scanned into the particle size analysis software named Nano-measurer and the edge of the particle was detected automatically by the software .Thus the diameter of the particle was calculated by the computer itself. We traced every particle we could see in the 10000Χ micrographs. The software could further magnify the micrograph to make sure every particle was traced. Average particle diameter of S10, S20, S30, S35 or S40 was the average of 550-800 particles, and that of S1, S2 and S6 was the average of 100-250 particles. Since enough number of particles was analyzed, the experimental result was reliable.
The particle diameter seen on a fracture surface could not all be the diameter of the spherical particle which has been sectioned away from its center. “To find the diameters of the original spheres, a set of simultaneous equations relating the measured drop size distribution to the original sphere size distribution must be solved [20].” The difference in the average particle size between the corrected values on the fractured samples and the uncorrected values for the same samples was less than 10%, and the trends were the same; thus, these corrections are neglected in the data presented.
3. Results and discussion
3.1 Optical properties
Figure 3 and Fig. 4 are photographs of scattering spots and relative optical intensity curves as a function of the scattering angle of PMMA light scattering sheets with different concentration of PET. As is shown in Fig. 2, pure PMMA sheet has nearly no ability to diffuse light, whereas the addition of PET spreads the point source into a circular light source, thus providing protection against glare and achieving uniform illumination. The scattering pattern is of a circular spot. With the increase of the PET content from 2 wt% to 10 wt%, the central brightness of the scattering spot becomes dimmer and the scattering area larger, revealing the better scattering ability of the sheet with larger concentration. Light is distributed almost uniformly when it passes through the sheets S6. A further increase of the PET content makes no difference to the scattering effect. However, relative optical intensity curves as a function of the scattering angle in Fig. 4(a) indicate that the central light intensity become lower gradually and scattering angles broader with the increase of the PET content. S10 has the lowest central light intensity, however, it should be noted that in Fig. 4(b) the light intensity value in center point increases and the angular spread is almost invariable with a further increase of the PET content.
Figure 5 shows the transmittance and haze as a function of PET mass fraction, indicating that PET content has a great influence on the transmittance and haze of the PMMA/PET light scattering sheets. (1) When the PET mass fraction is lower than 10 wt%, the transmittance of the PMMA/PET light scattering sheets keeps decreasing significantly from 93% of S0 to 59% of S10. In contrast to this, haze achieves a sharp increase from 3% of S0 to 95% of S10. In addition, haze increases rapidly at low concentrations but more slowly when PET content exceeds 6wt%. (2) In the range from 10 wt% to 20 wt%, transmittance almost remains constant and haze also levels off at a high value. (3) When the PET mass fraction increases from 20 wt% to 35 wt%, transmittance sees pronounced increase. Moreover, haze still remains a high value about 95%. (4) After PET content exceeds 35 wt%, transmittance plateaus again. The significant increase of the transmittance while maintaining a high haze value with the dispersed phase content has never been reported in polymer-inorganic or organic systems in which the preparation of light scattering materials with high haze are always achieved at the expense of the transmittance.
3.2 SEM analysis
The microstructures of the fracture surfaces of the PMMA/PET light scattering sheets were shown in Fig. 6. When PMMA and PET are melt blended, PET is mechanically dispersed inside the PMMA. The “ocean-island” structure reveals that phase separation takes place. This evidence clearly suggests that PET is immiscible with PMMA. It can be seen in Fig. 6 that, there are more and more large spherical particles appearing with the increase of the dispersed phase. A similar study was done by using a lower viscosity polypropylene matrix with a polystyrene minor phase, showing that coalescence increases the average dispersed phase domain size from 1.7μm to 5μm as the concentration of the dispersed phase increases from 0.1 wt% to 10 wt% [21]. Several processing parameters including rheology and the composition of the blend influence the size and shape of the dispersed phase. For uncompatibilized blends, the number of particles with larger diameter increases with the dispersed phase concentration, due to increased coalescence which will more easily occur at higher concentrations [21–23]. Flow-induced coalescence of two Newtonian liquid drops can be modeled as a three-step mechanism [24]. “First, two drops come close to each other and the pair rotates in the shear field. The film of the matrix phase between the two drops drains, the film thickness decreases to a critical value, and rupture of the interface occurs, resulting in coalescence.” Elmendorp and van der Vegt [25] found experimentally that polymers had a high coalescence probability during mixing and concluded that polymers had fully mobile interfaces. Therefore, polymer drops are easier to contact at higher concentrations, resulting in a significant increase of the amount of coalescence in blends.
Fig. 6 SEM micrographs of liquid nitrogen fracture surfaces of the PMMA/PET light scattering sheets.
The particle sizes were characterized utilizing the image analysis software introduced in section 2.5. The average particle diameter () can be calculated by the following equation:
where, ni represents the number of the particles with the diameter of di.The number concentration of the scattering particles, C, were calculated by the following equation:
Where Φ is the volume fraction of the dispersed phase, and the average particle diameter.The calculated result is shown in Table 3 and Fig. 7, indicating that the average particle diameter and number concentration of the dispersed phase increase slowly with the PET content when the mass fraction is lower than 10 wt%, whereas the average particle size increases more rapidly and the number concentration decreases about 5 times in the range from 10 wt% to 20 wt%. In the range of 20-35 wt%, the average particle diameter of the dispersed phase increases about 7 times, however, the number concentration decreases by 3 orders of magnitude. When the content of PET is beyond 35 wt%, there is only a slow increase in the average particle diameter and a slight decrease in the number concentration.
Table 3. Number concentration and average particle diameter as a function of PET mass fraction
Fig. 7 Average particle diameter and number concentration of the dispersed phase in PMMA/PET light scattering sheets as a function of PET mass fraction.
Another feature in Fig. 6 is that the particle size distribution broadens at higher concentrations. This was true for all the uncompatibilized blends studied. “Breakup and coalescence are occurring concurrently during the blending at the higher concentrations, resulting in a much broader distribution of drop sizes [21].” Breakup in the high shear regions may result in very small drops, while increased coalescence will result in very large drops. Figure 8 gives the minimum particle diameter, the average particle diameter and the maximum particle diameter of the dispersed phase corresponding to each sample. The distance between the maximum particle diameter and minimum particle diameter becomes broader as the mass fraction of PET increases. Such bars are used to characterize the particle size distribution.
Fig. 8 Maximum particle diameter, average particle diameter and minimum particle diameter of the dispersed phase in PMMA/PET blends as a function of PET mass raction.
3.3 Mie scattering theory
In these blending systems, the size of the dispersed particles is different and has a diameter distribution. For the sake of simplicity, we assume in this study that the diameters of the dispersed particles are the same, assuming the average diameter. The scattering characteristics of the spherical particles can be calculated using Mie scattering theory [26,27]. According to Mie scattering theory, the scattering light intensity profile of a particle can be calculated as follows:
Here, λ is the incident wavelength, r is the distance from the center of the sphere, d is the diameter of the sphere, θ is the scattering angle, I0 is the intensity of the incident light (watt/m2), m is the relative refractive index between particle and matrix and α is the size parameter. and are the Ricatti-Bessel functions, and Pn(cosθ), Pn(1)(cosθ) are Legendre and associated Legendre functions of cosθ, respectively. Figure 9 shows the single scattering profiles of particles with different size based on Eq. (6), which indicates that the bigger particles have less lightscattering effect at their surface and particles with a lager diameter transmit the light rather than scatter them. An increasing forward scattering and a decreasing backscattering is seen with a further increasing particle diameter, which will result in the increase of the transmittance. Besides, with the increase of particle diameter, the scattering angle of the forward scattered light decreases and approaches to 0°.Fig. 9 Calculated single scattering profiles of particles with different size based on Mie scattering theory. Dash lines are magnified diagrams beside which magnification are marked.The wavelength λ = 550nm. The refractive indices of the matrix and the scattering particles are n1(1.485) and n2 (1.578) respectively.
It should be noted that in the PET concentration range 1-10 wt%, the number concentration of the dispersed phase increases resulting in more scattering centers and increased intensity of the backscattered light [28]. Although the increasing particle diameter is favours scattering to the forward direction, the transmittance keeps decreasing in this range, indicating that the influence of the number concentration on the transmittance prevails at low concentrations. In the range from 10 wt% to 20 wt%, the increase of both the particle diameter and the number concentration have comparable effects on the transmittance, so the transmittance almost remains constant. However, in the range about 20-35 wt%, the significant increase of the particle diameter contributes to more obvious forward scattering effect according to Mie scattering theory. In addition, there is a huge drop in the number concentration resulting in less scattering centers and lower intensity of the backscattered light. Therefore, transmittance in this concentration range increases significantly which is totally different from that in polymer-inorganic/organic systems. When the mass fraction of PET approaches 40 wt%, the increase of the particle diameter and decrease of the number concentration become slower, so the transmittance levels off.
4. Conclusions
This work presents a simple, low-cost approach for fabricating PMMA/PET light scattering materials taking PET as dispersed particles by melt blending and compression molding. It is interesting that the transmittance of the light scattering sheets experiences a significant increase in the PET concentration range from 20 wt% to 35 wt%. Similar trend has never been seen in polymer-inorganic or organic systems. The anomaly is ascribed to a competition between the influences of the number concentration and the particle diameter on the optical properties of the materials, which is analyzed numerically according to Mie scattering theory. Although the increasing particle diameter favours the increase of forward scattering, the transmittance keeps decreasing in concentration range 0-10 wt%, indicating that the influence of the number concentration on the optical properties is the controlling factor at low concentrations. However, increasing particle diameter and decreasing number concentration combine to provide a substantial increase of the transmittance in concentration range about 20-35 wt%. As for haze, it increases significantly at low concentrations and keeps a high value at high concentrations. Therefore, the application of ordinary polymer dopant makes preparing light scattering sheets with high haze but not decreasing transmittance possible. The composite can be used to create a thin and effective light scattering film coated on a bare glass substrate, which can be adapted to various applications for the large-sized, flexible LED lighting, LCD backlights and others.
Acknowledgments
The research is financed by the Doctoral Scientific Fund Project of the Ministry of Education of China under grant no. 20120181110088, the Key Scientific and Technical Support Program of Sichuan Province under grant no. 2014GZ0031 and the National Natural Science Foundation of China under grant no. 51227802.
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