Ind. Eng. Chem. Res. 2000, 39, 79-83
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A New Processing Method for the Fabrication of Cylindrical Objects with Radially Varying Properties C.-W. Park* Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611
B. S. Lee, J. K. Walker, and W. Y. Choi Nanoptics, Inc., Gainesville, Florida 32609
Objects with spatially varying properties are often desirable for some applications such as the functionally gradient materials (FGMs) in the field of powder metallurgy and ceramics or the graded-index plastic optical fibers (GI-POFs) for communications. In the case of FGMs, the material composition of the composite materials may vary spatially, whereas the refractive index varies continuously in the radial direction in the case of GI-POFs. Because of the peculiar property of such objects, they can have very specialized functions. When an optical fiber has a specific refractive index profile, it is capable of transmitting more optical signals per unit time, corresponding to higher bandwidth communications. While the concept of the objects with spatially varying properties has a great potential for various applications, the major obstacle has been limited availability of fabrication techniques. Although there are some methods available, such as the “centrifugal casting” for FGMs and the “interfacial-gel polymerization technique” for GI-POFs, their capabilities are still limited, requiring further development. In this paper, a new fabrication method for cylindrical objects with radially varying properties is introduced with an experimental confirmation. While this method is shown to be capable of producing GI-POFs, its applicability may not be limited to GI-POFs. 1. Introduction It is often desirable to produce objects with spatially varying properties. These objects can be, for example, cylindrical forms made from polymeric or ceramic materials. The properties which may vary spatially can be any physical or chemical properties including optical properties (e.g., refractive index or light absorption coefficient), tensile strength, color, thermal expansion coefficient, porosity, chemical functionality, and so forth. In the field of powder metallurgy and ceramics, socalled functionally gradient materials (FGMs) have long been recognized as a new generation of composite materials. They represent an innovative concept, in that the microstructural distributions (concentrations, morphologies, textures, etc.) are designed to vary spatially so that certain specific technical requirements, which cannot be met otherwise, can be satisfied. For example, metal matrixes with continuously varying concentrations of ceramic particles can minimize thermal degradation and deformations in certain applications with severe thermal conditions such as surface materials for a supersonic aircraft, turbine blades, and vanes. One technique to make such composite materials is the centrifugal casting. In this method, a mixture of two different ceramic suspensions (or ceramic particles dispersed in molten metal) is subjected to rapid rotation and the centrifugal force makes denser ceramic particles to segregate in the radial direction, resulting in a continuous variation of the particle concentration. While the concept of FGMs is innovative, the major difficulty has been in the development of fabrication techniques. * To whom all correspondence should be addressed. Tel.: (352)392-6205. Fax: (352)392-9513. E-mail:
[email protected].
The utility of an object with radially varying properties was also recognized in polymer engineering for an application in the area of fiber optic communications. Fast advancement of microelectronics technology demands new media for high-speed data transmission in local area networks (LANs). While the standard data transmission rate for LANs is currently 100∼155 Mbs, this standard is expected to change to a much higher rate of about 1 Gbs in a few years. Although such a high transmission rate cannot be met by the metal cables currently in use for LANs, it can be achieved by singlemode optical fibers made of high-quality silica glass. However, the single-mode glass optical fibers are as thin as 5-10 µm in diameter. Consequently, they are extremely fragile and making the connection between them is difficult and very costly. Thus, their use in LANs, in which cables should be installed along very curved paths and frequent connections should be made, is not practical. As a viable substitute to meet such demand, gradedindex polymeric optical fibers (GI-POFs) have been recognized. Flexibility and durability of polymeric materials allow POFs to be large in diameter (in the order of 1 mm), although the special property of a graded index is required to meet the high data transmission rate. A graded index means that the refractive index of the optical fiber varies continuously in the radial direction, as described in Figure 1. To date, only a few methods have been suggested for the fabrication of GI-POFs, most of which are based on the preform manufacturing and subsequent fiber-drawing technique pioneered by Koike.1-3 Koike’s method is known as the interfacial-gel polymerization technique which utilizes mixtures of two monomers with different reactivities or diffusivities. While this technique has
10.1021/ie9902582 CCC: $19.00 © 2000 American Chemical Society Published on Web 11/24/1999
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Figure 1. Schematic of a cylindrical object with a radially varying property (A graded-index optical fiber is described as an example.)
Figure 3. Schematic three-dimensional view of the GI die block.
Figure 2. Schematic of the GI die block (GDB).
been successfully implemented to fabricate GI-POFs with several Gbs transmission rate over 100 m, this method is a batch process in which the optical fiber is made by preform manufacturing followed by thermal drawing.4-7 Recently, extrusion methods utilizing diffusional characteristics of low-molecular-weight materials have been suggested to produce GI-POFs.8,9 Because the refractive index profile of GI-POFs is solely determined by the properties of the materials in these processes, all of these methods are not capable of controlling the refractive index profile, which is one of the most important properties of GI-POFs, to achieve a high data transmission rate. In this paper, we introduce a new method for the fabrication of GI-POFs, which is a continuous process and is capable of controlling the refractive index profile by mechanical means. Although this new method has been developed mainly for the fabrication of GI-POFs, it can be applied to the general areas of producing cylindrical objects with radially varying properties including the functionally gradient materials (FGMs) in powder metallurgy and ceramics area. 2. New Fabrication Method The new method is a coextrusion process in which two polymers (materials “a” and “b”) with different properties (e.g., refractive index in the case of GI-POF fabrication) are fed separately to a novel die (which will be called a GI die block (GDB)) where they are mixed in a desired proportion and a continuous variation of a property (e.g., refractive index profile) is created. Figure 2 describes the GDB schematically, which consists of three major sections: manifolds (A and B), mixing chamber (D), and conical feed section (F). A threedimensional view of a GDB showing these three sections in the absence of the front/back plates and the two rotating elements (D1 and F1) is given in Figure 3. The slit channel C1 connecting the manifold A to the mixing chamber has a decreasing gap along the z direction whereas the slit channel C2 has an increasing gap (Figure 4). Thus, the flow rate of material “a” is higher at a smaller value of z whereas the converse situation holds for material “b”. Consequently, the right-hand side of the mixing chamber D (i.e., at a smaller value of z) is richer in material “a” and its relative concentration
Figure 4. Schematic showing manifold A and slit channel C1 which has a decreasing gap, h(z) with increasing z.
decreases along the z direction. The material in the mixing chamber with the varying composition of “a” and “b” in the z direction is mixed uniformly by a rotating mixer blade D1 while the varying blend composition is maintained in the z direction. If the refractive index of material “a” is higher than that of material “b”, the refractive index of the blended material in the mixing chamber D will decrease continuously in the z direction. While the flow in the GDB is driven by a pressure gradient, z-directional axial mixing in the mixing chamber is minimal because the pressure gradient in the z direction in the mixing chamber is insignificant. Therefore, a polymer blend with a continuously varying refractive index along the z direction can be prepared in mixing chamber D. The homogeneous blend prepared in mixing chamber D then flows through slit channel E to conical feed section F where a rotating cone, F1, is placed. The material flowing to conical feed section F at a location with a smaller value of z, which is richer in material “a”, is positioned closer to the surface of rotating cone F1. As that material flows along the z direction in conical feed section F, it is coated by the incoming lower refractive index material at larger z. This flow situation is depicted schematically in Figure 5. While the material flows downstream in the axial direction, rotating cone F1 distributes the material uniformly in the circumferential direction. Because of the high viscosity of polymers, a laminar flow is maintained and the circumferential distribution of the material by the rotating cone converts the axial-directional refractive index profile achieved in the mixing chamber to the radial-directional profile. Consequently, the material leaving circular exit hole G has a refractive index profile which decreases in the radial direction. When this material is stretched as in a fiber-spinning process, a GI-POF is finally obtained. The refractive index profile of the GI-POFs fabricated by this method is determined mainly by the axial profile (i.e., z-directional profile) of the blend composition in mixing chamber D, which is determined by the dimension of slit channels C1 and C2. Once the rheological properties of optical polymers “a” and “b” are known, the dimensions of slit channels C1 and C2 can be determined accordingly to achieve a predetermined refractive index profile in the mixing chamber. In
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Figure 5. Schematic flow patterns in the conical feed section (The helical motion of the fluid by the rotating cone has not been depicted in this figure for brevity.)
addition, a minor adjustment of the refractive index profile can be achieved by adjusting the z-directional flow rate profile in slit channel E. This minor tailoring of the refractive index profile is achieved by flow restricter E1 which controls the gap of slit channel E. 3. Experimental Results and Discussion Design of the GI Die Block (GDB). The design of the GI die block depends on the properties of the material to be processed and the operating conditions. For the present study, the GDB is designed for a poly(methyl methacrylate) (PMMA) with an average molecular weight (Mw) of 2 × 106 and for a total flow rate of 1 kg/h at 200 °C. The shear viscosity of this material varied from 1.1 × 104 Pa s at a shear rate of 1 s-1 to 1.8 × 103 Pa s at 100 s-1, showing a shear thinning behavior. Appropriate overall dimensions for the prescribed conditions were determined to be 3-in. long (L), 2.5-in. wide (W), and 6-in. tall (H) (Figure 3). The dimensions of manifold A and channel C1 are determined in such a way that the flow rate of the prescribed PMMA through channel C1 decreased linearly with z (Figure 4). Because the shear rate variation for the flow in the channel is rather small, from about 5 s-1 to 11 s-1, the shear viscosity of the material is assumed to be following the power-law model in determining the channel dimension. For the flow rate to be linear in z, the channel gap should vary nonlinearly with z. This, however, will make manufacturing (or machining) of the die very difficult. Thus, as a compromise, the channel gap is made to vary linearly in two segments: h(z) decreases linearly from 0.057 to 0.047 in. from z ) 0 to the midpoint (i.e., z ) 1.5 in.) and subsequently, it varies from 0.047 to 0.025 in. linearly. The length of the channel (or the land length l) and the diameter of the manifold A were 0.56 and 0.125in., respectively. This dimension provides a linearly varying flow rate in the z direction within 3% error. Manifold B and channel C2 are mirror images of B and C1 (Figure 2). But the gap of channel C2 increases with z. The vertical channel which combines the flow from C1 and C2 and leads to the mixing chamber D is 0.75-in. long with a 0.1-in. gap. The diameter of the mixing chamber is 1.5 in., which has been determined to make the residence time of the material in that region to be about 2 min to provide good mixing. The center of the conical feed section is located 2.25 in. below the center of the mixing chamber, and its diameter varies linearly from 1.1 to 0.54-in. Channel E connecting the mixing chamber and the conical feed section has a gap of 0.1 in. There are 11 flow restricters (E1) which are 0.125 in. in diameter and positioned 0.25 in. apart from neighboring ones. The standard position of these flow restricters are set in a way to make their faces be flushed with the face of channel E, and only a very minor adjustment of these restricters is intended.
Fabrication of GI-POF. The two materials which are to be used for the new fabrication methods (i.e., materials “a” and “b” in Figure 2) should be miscible when they are melt-blended. In addition, there should be a difference in their refractive index, typically in the range of about 0.01-0.02 to make GI fibers for communications. There can be a variety of material combinations which satisfy these conditions. For example, material “a” in Figure 2 can be a random copolymer of benzyl methacrylate (BMA) and methyl methacrylate (MMA) with the BMA content of 65 mol %. The refractive index of this copolymer is measured to be 1.538. Material “b” can also be a copolymer of BMA and MMA, but with a different BMA content. When the BMA content is 45 mol %, the refractive index of the BMA/ MMA copolymer becomes 1.525. Thus, the difference in the refractive index for this material combination is 0.013. Recently, we conducted an extensive study on the blend compatibility with BMA-MMA copolymers with different monomer compositions, and the results indicated that the prescribed copolymers with the BMA content of 65 and 45 mol %, respectively, are miscible without showing any evidence of phase separation up to a temperature of 250 °C which is much higher than the normal processing temperature. Detailed results of the study on the blend compatibility will be reported in our subsequent paper. One easy way to ensure the blend compatibility of the two materials to be used for the present process is to use an additive which raises or lowers the refractive index of an optical polymer when the additive is dissolved into it. For the present study, PMMA with dissolved benzophenone was used as the material with a higher refractive index (i.e., material “a” in Figure 2), whereas PMMA with triethyl phosphate was used as the other (i.e., material “b”). Benzophenone raises the refractive index of PMMA to 1.501 when it is added at 10 wt % and triethyl phosphate lowers the index to 1.483 when it is added at 10 wt %. It should be noted that the diffusion of the additive in the polymer should be insignificant during the processing time from the mixing chamber to the exit hole (D and G in Figure 2). Otherwise, the graded index profile which results from the radial variation of the additive concentration will be lost. Thus, the additives with low diffusivity should be selected for this process. The model for the refractive index profile of a GI optical fiber normally considered is that of a power-law index variation:10
[
(Rr ) ]
n(r) ) n1 1 - 2∆ n(r) ) n2
g 1/2
for r e R
for r > R
(1a) (1b)
Here, r is the radial distance from the fiber axis, R is the radius of the fiber beyond which the refractive index
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different settings of the restricters (E1 in Figure 2) are shown where the vertical axis is ∆n ) n(r) - n2. The average range of the data points is 0.0007 and is shown as an error bar in the figure. Also shown in Figure 6 are the theoretical profiles described by eq 1a with a g value of 2 (i.e., parabolic law) and an additional value of g for comparison. These g values do not necessarily represent the best fit of the data to eq 1a because they were chosen graphically to provide a reasonable fit. In fitting the data, the cutoff radius where ∆n became zero was first chosen, which was 200 and 180 µm for Figures 6a and 6b, respectively. The value of g was then chosen to give a reasonable fit to the data graphically. While the solid line for g ) 1.44 appears to be a better fit than the dotted line for g ) 2.0 in Figure 6a, the curve for g ) 1.76 appears to be no better than the one for g ) 2.0 in Figure 6b. The restricters (E1 in Figure 2) for the data in Figure 6a were at the standard positions (i.e., flushfaced with the surface of channel E, whereas the five restricters near the exit hole G were pushed in by 0.015 in. for the data in Figure 6b; 0.015 in. corresponds to a half-turn of each restricter screw. In Figure 6c, the two data sets with different restricter settings are overlaid. Although the two data sets are not very different considering the error bound indicated in the figure, the restricters appear to have some influence in altering the refractive index profile slightly. The refractive index profile of the fiber made by the GI die block was expected to vary over the entire radius of the fiber. However, the measured profiles (Figures 6a and 6b) showed a flat profile beyond a certain cutoff radius. Although the reason for this result is not clearly understood, it is likely to be due to the changes in the rheological properties of the material when the additives were added. The dimensions of channel C1 and C2 (Figure 2) described previously depend on the rheological property of the material and may have the most significant influence in determining the refractive index profile of the fiber. 4. Summary Figure 6. Refractive index profiles of a GI-POF fabricated by the new method using the GI die block with two different restricter settings (∆n ) n(r) - n2: The solid line is a theoretical fit to the experimental data with (a) g ) 1.44 and (b) g ) 1.76. The dotted curve for both figures is for g ) 2.0).
does not vary any further, n1 and n2 are the refractive indices at r ) 0 and r ) R, respectively. 2∆ ) (n12 n22)/n12 and parameter g controls the index profile as a function of radial position. The typical value of ∆ for optical fibers for communications is about 0.01, and the data transmission rate of the fiber is known to be sensitive to the value of g. In the particular case where g ) 2, the power law is called a parabolic law which is the case close to, but not exactly optimal, for the maximum data transmission rate. PMMA containing benzophenone at 10 wt % and PMMA containing triethyl phosphate at 10 wt % were extruded through the GI die block using a 1/2- and 3/ -in. extruder, respectively, to fabricate GI-POF of 1 4 mm in diameter. The melt temperature was set at 160 and 175 °C, respectively. The fiber radius was measured to be uniform with a variation less than 3%. The refractive index profile was measured three times at 100-m intervals and found to be stable. In Figure 6, the measured refractive index profiles obtained with two
A new method for the fabrication of GI-POFs has been introduced, which is a continuous extrusion process using an innovative die. Unlike other methods to fabricate GI-POFs, this new method is capable of controlling the refractive index profile by mechanical means. While the GI die block (GDB) is a new concept, part of its major elements are reminiscent of existing extrusion technologies. The flow in the manifolds and the connecting slit channels is similar to that in a slit die which is often used in a flat film-casting process. In addition, the mixing chamber resembles the static kneading mixers for polymer melt blending. Thus, the well-established design concepts for slit dies or static mixers can be directly applied to the design of GDB. Although the GDB has been developed mainly for the fabrication of GI-POFs, it can be applied to the general areas of producing cylindrical objects with radially varying properties including the functionally gradient materials (FGMs) in powder metallurgy and ceramics area. Acknowledgment The authors wish to thank Dr. Jacob Tymianski and Mr. Jonathan Couch of Nanoptics, Inc. for their assistance in material preparation and extrusion, and Mr.
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L. Blyler of Lucent Technologies for the measurements of the refractive index profile. Literature Cited (1) Koike, Y. High-Bandwidth Graded-Index Polymer Optical Fibre. Polymer 1991, 32, 1737. (2) Koike, Y.; Nihei, E. Method of Manufacturing a Graded Optical Transmission Medium Made of Synthetic Resin. U.S. Patent 5,253,323, 1993. (3) Koike, Y.; Nihei, E. Method of Manufacturing Optical Transmission Medium from Synthetic Resin. U.S. Patent 5,382,448, 1995. (4) Koike, Y.; Ishigure, T.; Nihei, E. High-Bandwidth GradedIndex Polymer Optical Fiber. J. Lightwave Technol. 1995, 13, 1475. (5) Ishigure, T.; Nihei, E.; Koike, Y. Graded-Index Polymer Optical Fiber for High-Speed Data Communication. Appl. Opt. 1994, 33, 4261. (6) Ishigure, T.; Nihei, E.; Koike, Y. Optimization of the Refractive-Index Distribution of High-Bandwidth GI Polymer
Optical Fiber Based on Both Modal and Material Dispersions. Polym. J. 1996, 28, 272. (7) Ishigure, T.; Satoh, M.; Takanashi, O.; Nihei, E.; Nyu, T.; Yamazaki, S.; Koike, Y. Formation of the Refractive Index Profile in the Graded Index Polymer Optical Fiber for Gigabit Data Transmission. J. Lightwave Technol. 1997, 15, 2095. (8) Ho, B. C.; Chen, J. H.; Chen, W. C.; Chang, Y. H.; Yang, S. Y.; Chen, J. J.; Tseng, T. W. Graded-Index Polymer Fibers Prepared by Extrusion. Polym. J. 1995, 27, 310. (9) Koike, Y.; Nihei, R. Method of Manufacturing Plastic Optical Transmission Medium. U.S. Patent 5,593,621, 1997. (10) Halley, P. Fiber Optic Systems; John Wiley & Sons: New York, 1987.
Received for review April 8, 1999 Revised manuscript received October 18, 1999 Accepted October 21, 1999 IE9902582
