ABSTRACT Although many studies on graded index (GRIN) lenses have been reported over the past several years, it is extremely difficult to find reports that have used polymer GRIN lenses in

an atmosphere involving a large temperature change, which is mainly because of their lack of thermal stability. In this study, we propose a new method of fabricating organic–inorganic

microcomposite cylindrical GRIN lenses with high thermal stability. This method is based on the spontaneous frontal polymerization (SFP) technique and diffusion of two organic materials with

different refractive indices into an inorganic wet-gel. The refractive index profile of the GRIN lens is made by this diffusive process. We are able to determine the relationship between

technique also enabled high reproducibility of microcomposite cylindrical GRIN lenses with smooth periphery in this study, indicating the high potential of this process for practical

application. SIMILAR CONTENT BEING VIEWED BY OTHERS IR GRIN LENSES PREPARED BY IONIC EXCHANGE IN CHALCOHALIDE GLASSES Article Open access 26 May 2021 LUBRICANT-INFUSED DIRECTLY ENGRAVED

NANO-MICROSTRUCTURES FOR MECHANICALLY DURABLE ENDOSCOPE LENS WITH ANTI-BIOFOULING AND ANTI-FOGGING PROPERTIES Article Open access 15 October 2020 IN-VITRO DEHYDRATION KINETICS COEFFICIENT OF

KALIFILCON A AND OTHER CONTACT LENS MATERIALS Article Open access 03 April 2024 INTRODUCTION Lenses with a refractive index gradient are called graded index (GRIN) lenses. GRIN lenses have

excellent optical characteristics compared with spherical/aspherical lenses that consist of a material with a uniform refractive index. Hence, many researchers are motivated to expand the

understanding of this particular type of lens.1, 2, 3 Generally, the refractive index profile of the cylindrical GRIN lens is expressed by where _r_ is the distance from the cylindrical

axis, _A_ is the positive constant, and _n(r)_ and _n__0_ are the indices at the radius _r_ and on the axis, respectively. Variable _g_ is a refractive index profile coefficient (index

exponent), which characterizes the refractive index profile. The optimum value of _g_ for a GRIN lens is about 2.4, 5 The easy handling of organic material has also helped broaden this field

of study. However, the low thermal stability of organic cylindrical GRIN lenses has always been a major issue for practical application. Cylindrical GRIN lenses made of inorganic materials

with high thermal stability could be made only with a diameter of several millimeters at most, which is also undesirable for practical application factor.6 In this study, we present a new

method, the spontaneous frontal polymerization (SFP) technique, for the fabrication of organic–inorganic microcomposite cylindrical GRIN lenses with high thermal stability and a large

diameter (35 mm). In this SFP technique, the degree of polymerization advances after a certain period of time from the initiation of polymerization, which is accompanied by an increase in

viscosity of the polymerization solution. The heat of polymerization, therefore, cannot be easily discharged. As a result, the autoacceleration polymerization reaction occurs near the

central region of the container.7 This phenomenon is called the thermal storage effect, and the difference in refractive index of the high conversion area and low conversion area appears as

a border plane. This plane is observed as a front that progresses from the center of the container toward the peripheral region as polymerization proceeds. (This type of polymerization is

referred to as ‘frontal polymerization.’) We also present a refractive index distribution control method using diffusion. In addition, we clarify the optical characteristics of the

microcomposite cylindrical GRIN lens obtained by the SFP technique. EXPERIMENTAL PROCEDURE MATERIALS Tetramethyl orthosilicate (Tokyo Chemical Industry, Tokyo, Japan) was used as an

inorganic wet-gel without further purification. Anhydrous ethanol (EtOH; Wako Pure Chemical Industries, Ltd., Osaka, Japan) was used as the solvent, and a small amount of ammonia solution

(aqueous NH4OH; Wako Pure Chemical Industries, Ltd.) was used as a catalyst without further purification. Size 4A molecular sieves (Junsei Chemical Co., Ltd., Tokyo, Japan) were used for the

absorption of EtOH. Methyl methacrylate (MMA; Mitsubishi Rayon Co., Ltd., Tokyo, Japan), styrene (St; Junsei Chemical Co., Ltd., Tokyo, Japan) and 2,2,3,3-tetrafluoropropyl methacrylate

(4FMA; Mitsubishi Rayon Co., Ltd.) were used as monomers. Ethylene glycol dimethacrylate (Wako Pure Chemical Industries, Ltd.) was used as a crosslinking agent. Monomers and the crosslinking

agent were both purified by distillation at reduced pressure. Benzoyl peroxide (Nacalai Tesque, Inc., Kyoto, Japan) was used as an initiator without further purification. The function and

properties of each material are summarized in Table 1. FABRICATION OF ORGANIC–INORGANIC MICROCOMPOSITE CYLINDRICAL GRIN LENSES First, a wet-gel was prepared by dissolving tetramethyl

orthosilicate and H2O in EtOH, with a small amount of aqueous NH4OH as catalyst, in a glass tube with a 15-mm diameter. The molar ratio composition of this solution was tetramethyl

orthosilicate/EtOH/H2O=1:5:4. The reactive solution was agitated for 48 h at room temperature, gradually forming a gel. The obtained silica wet-gel was then washed by EtOH to remove residual

tetramethyl orthosilicate and catalyst, and soaked in M1 monomer twice (each for 48 h at room temperature) to replace EtOH with M1 monomer. Here, MMA was used as the M1 monomer, which is

composed of 10 wt% crosslinking agent and 1.0 wt% initiator. The silica wet-gel was completely saturated during this soaking process. Molecular sieves were also used as an absorption agent

for EtOH. The gas chromatography method confirmed that the amount of ethanol dissolved in the surrounding material was 0.8 wt% or less by the second soaking. After the wet-gel was thoroughly

soaked in M1 monomer, it was polymerized in air or in water to fabricate a microcomposite sample for the evaluation of its transparency. Unfortunately, the obtained silica wet-gel often

cracked when polymerized in air or in water, making the sample polymers inadequate for experimental use. Therefore, it was necessary to polymerize the gel in M1 monomer to avoid fabrication

of such defective samples. However, it is extremely difficult to detach the polymerized gel from the polymerizing M1 monomer surrounding it. To overcome this difficulty, the SFP technique

was used to polymerize only the gel contained within the M1 monomer.7 During the SFP technique, the surrounding monomer cannot polymerize, therefore, the polymerized gel was easily

extracted. In this study, the wet-gel was polymerized by the SFP technique in a constant-temperature bath at 60 °C, and the percentage of the monomer that diffused into an inorganic wet-gel

was about 85% of the obtained sample. The obtained sample was then heat treated for 24 h at 70 °C and for another 24 h at 90 °C. The sample was of a cylindrical form with a 14-mm diameter

and a 10-mm thickness. Its transmittance was measured using a spectrophotometer (Hitachi U-1000, Hitachi, Ltd., Tokyo, Japan), and the temperature dependence of its refractive index

(thermo-optical coefficient (TOC)) was measured by an Abbe refractometer (NAR-1T, ATAGO Co., Ltd., Tokyo, Japan). Another microcomposite GRIN lens sample was fabricated from the wet-gel

thoroughly soaked in M1 monomer. This sample was fabricated by diffusing a different monomer (M2) from the peripheral region of the gel. Here, 4FMA was used as the M2 monomer. Two diffusion

times were set for this experiment (0 and 60 min). During this process, a mutual diffusion occurred between the two monomers, thus forming a refractive index gradient within the gel. This

sample was also heat treated for 24 h at 70 °C and another 24 h at 90 °C after polymerization and then cut into a disk shape of about 1 mm in thickness. The refractive index profile of the

microcomposite sample made by M1 and M2 monomers was measured by an interference microscope (Carl Zeiss Jena Interphako, Carl Zeiss AG, Oberkochen, Germany). The value of the _g_ was

determined by fitting the obtained profile data using the Gnuplot program. RESULTS AND DISCUSSION SFP To observe the formation of the front in the center region, a wet-gel consisting only of

MMA was polymerized at 60 °C. Figure 1 shows a photograph taken from the side of the glass vessel placed in a constant-temperature bath. The elapsed time from the initiation of the

polymerization is indicated at the lower right of each figure. At 20 min after the initiation of polymerization, the wet-gel became translucent (refer to Figure 1, at 1354 s). After another

4 min, the front clearly forms at the center of the wet-gel (refer to Figure 1, at 1440 s). From these results, it could be assumed that polymerization begins 20 min after initiation. As

mentioned before, the SFP technique allows the polymerization reaction to begin from the center of the vessel, without complex procedures. Hence, it is possible to polymerize only the

microcomposite material and not the surrounding monomer. TRANSPARENCY OF MICROCOMPOSITE MATERIALS As shown in Figure 2, the obtained microcomposite GRIN lens has no haze, which indicates its

capability for optical applications. Figure 3 shows the spectral transmittance of the microcomposite material and poly(methyl methacrylate) (PMMA). The microcomposite material is visibly

transparent as is PMMA. The transparency does not exceed 90% because of the reflection effect. Surface reflectance is ∼4% on one surface and 10% or less on both surfaces when the refractive

index of the sample is 1.5. Therefore, it is assumed that there was hardly any absorption or light scattering. High transmittance also shows that the difference in microheterogeneous

structure between the organic phase and inorganic phase is small. Furthermore, the value of the refractive index of PMMA (_n_=1.49) and SiO2 (_n_=1.46) is close, which limits the influence

on light scattering. Notably, microcomposite materials have a lower transparency than PMMA in the short wavelength region (300–500 nm), which is most likely the effect of Rayleigh

scattering. In this case, Rayleigh scattering is inversely proportional to wavelength by the fourth power, caused by the generation of an inhomogeneous region smaller than the wavelength

order and in the matrix of the inorganic material. THE THERMAL STABILITY OF THE MICROCOMPOSITE LENS The TOC was derived from measurements by a temperature-controlled Abbe refractometer. The

plot in Figure 4 shows the relationship between the refractive index and temperature of PMMA. The slope of this plot is the TOC. The obtained TOC of PMMA was 1.1 × 10−4 K−1, which is similar

to previously reported data (1.1–1.2 × 10−4 K−1).8 Figure 5 shows the dependency of refractive index variation on the temperature for the microcomposite material (SiO2+PMMA+poly(ethylene

glycol dimethacrylate) (PEGDMA)) and a typical organic material (PMMA+PEGDMA). These materials were fabricated under similar conditions to those of the lens. The TOC of the microcomposite

material was 6.9 × 10−5 K−1 and that of organic material was 8.0 × 10−5 K−1. Here, it can be clearly seen that the organic material has a TOC that is about 14% smaller than the

microcomposite material. For organic polymers, the TOC exclusively depends on its volume expansion coefficient.8 From these results, it was assumed that the SiO2 network inhibited the

thermal expansion of organic polymers. The composition ratio of SiO2 in the microcomposite material was 15% (w/w), which almost corresponds to the decrease in TOC. These results also

indicate that almost all of the monomer components polymerized. Furthermore, the weight change of the obtained sample was <1 wt% and deformation was not observed after 48 h of heat

treatment at 120 °C. In other words, the increase in the ratio of SiO2 will further decrease the TOC and improve thermal stability. CONTROL OF REFRACTIVE INDEX PROFILES In order to use the

GRIN lens as an optical component, the refractive index profile of the GRIN optical element needs to be controllable. Contrary to the conventional method, our proposed method allows easy

control of formation of the refractive index profile. In this study, the refractive index profile was easily manipulated by controlling the monomer diffusion because the refractive index

profile was achieved by changing the composition distribution of monomers. Thus, simulations based on the diffusion equation were first executed to provide further insight into the

possibility to control the refractive index distribution. DIFFUSION EQUATION Generally, assuming that the length of the cylinder is infinite, the diffusion phenomenon in the cylinder shape

was given by the diffusion equation (Equation 2), using cylindrical coordinates. In Equation 2, _C_ is the concentration of the diffusion material at position _r_, _D_ is the diffusion

constant, _t_ is the diffusion time and _r_ is the distance from the center axis of the cylinder. The simulation was set so that diffusion started at _t_=0, and M2 monomer concentration on

the outside of the gel matrix was always set to 100% when _t_ >0. M2 monomer was also set to diffuse at rate _P_, which is defined as the ratio between the concentration of M2 monomer in

the outermost layer of the gel matrix and its surrounding region. First, the composition distribution was obtained from the simulation program that determined _D_ and _P._ Second, the

obtained composition distribution was converted into the refractive index profile by using the Lorentz–Lorenz equation, and _D_ and _P_ were decided by matching them to the refractive index

profile actually measured. The acceleration of polymerization was confirmed about 20 min after the initiation of polymerization; these 20 min were added to the diffusion time in the

simulation. RESULTS OF THE SIMULATION The _D_ and _P_ were determined by simulating the refractive index profiles of the microcomposite cylindrical GRIN lenses with diffusion times of both

20 and 60 min. _D_ was found to be 2.6 × 10−5 cm2 s−1 and _P_ was found to be 4.1 × 10−4 s−1, and both values were within the vicinity of those previously reported.9 Figure 6 shows the

refractive index profile of a sample with a diffusion time of 160 min, simulated by using these values for _D_ and _P_. Here, the vertical axis indicates the refractive index, the right

horizontal axis indicates the position, and the left horizontal axis indicates the diffusion time. From the perspective of the position and the refractive index distribution, the _g_ value

is large because of M2 monomer not being able to reach the central region of the cylinder during the first stage of diffusion. However, taking into consideration that the minimum diffusion

time is 20 min, the maximum value of _g_ was calculated to be 3.7. Simulations were further progressed to a diffusion time of 360 min to show that _g_ decreases up to 1.6 with an increase in

diffusion time. This result indicates the possibility that, with a certain diffusion time, the most optimized _g_ value can be achieved, or a _g_=2 profile. From these results, we predicted

that it was necessary to set the diffusion time to 40 min to obtain the best profile (substantial diffusion time=60 min). OBTAINED SAMPLES In total, three samples were fabricated, each with

a different diffusion time (20, 40 and 60 min). The dependence of the _g_ and the refractive index difference _dn_ on diffusion time are shown in Table 2. Both _g_ and _dn_ were calculated

from the obtained samples and by simulation. Figure 7 shows the refractive index profiles of the obtained GRIN rod lens. The sample with a 40-min diffusion time had a GRIN profile, and its

calculated _g_ value is in good agreement with simulation results. Figure 8 shows the images transmitted through the three samples (diffused for 20, 40 and 60 min). As shown in Figure 8,

sample B has a clear image with hardly any distortion, whereas sample A shows a pincushion distortion and sample C shows a barrel distortion. Hence, the refractive index profile of

microcomposite cylindrical GRIN lenses fabricated by this method can be controlled by diffusion time. Moreover, these obtained samples indicate that a wide variety of refractive index

profiles could be formed by combining two monomers with different characteristics. The refractive index profile is controlled by controlling the refractive index difference between the

central and peripheral region of the sample. This phenomenon can be realized by balancing the refractive index of M1 and M2 monomer. Two examples of controlling the refractive index profile

by monomer combination are given below. Figure 9 shows the refractive index profile of a polymer formed using MMA as M1 and St as M2. A GRIN lens with concave lens-like features could be

fabricated by this combination because St has a high refractive index, which increases the refractive index of the peripheral region of the sample. Figure 10 shows the refractive index

profile of a polymer with St as M1 and 4FMA as M2. A GRIN lens with convex lens-like features could be fabricated by this combination because the refractive index of St is extremely high.

The numerical aperture of the obtained GRIN lens was about 0.4. CONCLUSIONS In this study, we proposed a new fabrication method for organic–inorganic microcomposite GRIN lenses. There is no

specific limitation on the organic monomers that can be used by this method to obtain a refractive index profile. Hence, most organic monomers are applicable for this method. We have shown

that this method can be used to successfully fabricate GRIN lenses with high transparency and high thermal stability—two essential optical characteristics—due to the formation of an

organic–inorganic microcomposite structure. In addition, it is possible to control the refractive index profile coefficient, which was shown using simulations based on the diffusion

equation. With this method, we have successfully fabricated an MMA/4FMA-based microcomposite GRIN lens with the controlled refractive index profile coefficient of 2, with a refractive index

difference of 0.03. Another microcomposite GRIN lens, based on St-4FMA, was also fabricated with a refractive index difference of 0.057. Moreover, we have shown that an MMA-St-based

microcomposite GRIN lens with concave lens characteristics could be fabricated using this method. As shown clearly from these results, the GRIN lenses proposed in this paper highlight the

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25, 3062–3067 (2007). Article  Google Scholar  Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Center for Science and Technology for Designing Functions, School of

Integrated Design Engineering, Graduate School of Science and Technology, Keio University, Yokohama, Japan Eisuke Nihei, Junichi Oomoto, Soichiro Kimura & Koichi Asakura Authors * Eisuke

Nihei View author publications You can also search for this author inPubMed Google Scholar * Junichi Oomoto View author publications You can also search for this author inPubMed Google

Scholar * Soichiro Kimura View author publications You can also search for this author inPubMed Google Scholar * Koichi Asakura View author publications You can also search for this author

inPubMed Google Scholar CORRESPONDING AUTHOR Correspondence to Eisuke Nihei. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Nihei, E., Oomoto, J.,

Kimura, S. _et al._ Preparation and characterization of organic–inorganic microcomposite cylindrical GRIN lens. _Polym J_ 42, 941–946 (2010). https://doi.org/10.1038/pj.2010.105 Download

citation * Received: 07 July 2010 * Revised: 18 September 2010 * Accepted: 20 September 2010 * Published: 27 October 2010 * Issue Date: December 2010 * DOI:

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available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative KEYWORDS * diffusion equation * organic–inorganic microcomposite *

refractive index profile * spontaneous frontal polymerization