Ind. Eng. Chem. Prod. Res. Dev., Vol. 17, No. 4, 1978 363
The Combined Packing of Rods and Spheres in Reinforcing Plastics J. V. Milewski’ Exxon Research and Engineering, Linden, New Jersey 07036
This paper introduces some of the basic principles of the combined packing of rods and spheres and illustrates how the ratio of sphere to fiber diameter affects void volume, which is resin demand. It also points out how minimum packing parameters change with respect to fiber length to diameter ratio and how choosing size combinations can optimize benefits from packing. I t is believed that these concepts can be applied to other aspects of the reinforced plastics business.
Introduction The plastic industry has made use of fillers and fibers for many years. However, it is only recently that some attention has been given to the synergistic effect that results from the use of selected combinations of fillers and fibers in plastic composites. These combinations can help to improve economics by reducing raw material cost, processing cost, wear on equipment, and produce better products. These are goals worth striving for, and it is believed that they are attainable through the application of a little more understanding of the principle of micro packing. This article will discuss the packing of fibers and spheres (or the science of micro packing) and present convincing indications that there are very few applications using short fiber reinforcements that will not perform better with the proper substitution of 25 to 75% of the fibers with a spherical filler or near-spherical shaped filler. There have been some commercial attempts to combine fillers and fibers. Almost every case investigated indicated a lack of study and understanding of the principle of micro packing. Materials were selected at random or from what was readily available and not optimum size for good micro packing. To make an effective packed mixture of fibers and spheres, the size diameter ratio of the sphere to the fiber must be known and how the optimum ratio changes with the fiber L I D (length to diameter ratio). An analysis made of most commercial glass bead-glass fiber products on the market today shows that they all fall short of their true economic potential because of poor packing fit of the two components. This will be illustrated in more detail later, but first a review is given of some principles of particle packing. Review Of Packing A. Fiber Packing. The packing combinations that were studied in a thesis by Milewski (1973) are illustrated in Figure 1 as (a) fiber packing at various LID’S, (b) fibers packed into fibers, (c) fibers packed into spheres, and (d) spheres packed into fibers. The experiments were run on two scales. The larger scale experiment used wooden rods and the smaller scale experiment used glass fibers. Figures 2 and 3 visually illustrate that bulk density varies with L I D . The date obtained in measuring the relative bulk volume for known LID’S of both wooden rods and glass fibers are plotted in Figure 4 and show very good volume packing agreement between the exact LID’S of wooden rods and the numerical average LID’S for glass fibers. The significance of this relationship is that it has been found that three-dimensional random packing values of Los Alamos Scientific Laboratory, Los Alamos, N.M. 87545. 0019-7890/78/1217-0363$01.00/0
fiber varies with the L I D and can be predicted from the above curve. Thus, with this relationship the average fiber L I D S can be determined from the bulk volume data of the fiber, without the time-consuming expense of photographing, counting, and averaging hundreds of fibers to obtain a statistically significant sample of the fiber LID. B. Review of Bimodal Packing Theory. Before studying the packing of fibers and spheres, the bimodal packing of spheres will be reviewed so that the detailed concept can be more easily understood. C. Theoretical Maximum Density Boundary. Conditions for Sphere-Sphere Packing. Figure 5 illustrates the densification that occurs when small spheres are added to large spheres. Maximum density is obtained when the small spheres are packed to their maximum density within the voids of the larger spheres. In Figure 5A and B, each illustration represents the same volume of solid material; thus the relative bulk volume is shown decreasing as densification occurs. In Figure 5A, this results because in each step toward greater density, a large sphere is removed and the same amount of solid material is replaced as small spheres within the voids of the remaining large spheres. Figure 5B illustrates how densification occurs by the opposite process, in which a number of small spheres and their associated voids are removed and the same amount of material is replaced as one large solid sphere. The solid line in Figure 6 is a theoretical packing curve for an infinite size ratio R = m. For this example the ratio R is the diameter of the large sphere divided by the diameter of the small spheres. The maximum density point represents the condition illustrated in Figure 5A and B at the extreme right. In Figure 6, the composition of the mixture is shown by the horizontal scale, X,being the volume fraction of the large spheres and Y , the volume fraction of the small spheres, for a total volume of unity. The left-hand ordinate is the relative bulk volume and is defined such that 1.0 is equal to 100% solid material (100 divided by the percent theoretical density). A material with a relative bulk volume of 1.5 would be 62.5% theoretically dense. Thus, C gives the experimentally determined packed volume of the large spheres, and M gives that of the small spheres. By using relative bulk volume rather than percent theoretical density, the packing curve for the infinite size ratio becomes two straight lines. When the size ratio R is less than infinity, maximum density is not attained because the small spheres begin to dilate the packing of the larger spheres before all the voids are filled. This concept is graphically illustrated in Figure 7, which shows curves for several R values. At an R value of 1,the two spheres are identical and obviously no packing advantage is seen. In this case the packing of the right 0 1978 American Chemical Society
364
Ind. Eng. Chem. Prod. Res. Dev., VoI. 17,No. 4, 1978 ADDITION OF SMALL SPHERES TO LARGE
A FIBERS ONLY SPHERES
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Varioui L / d rmbinalionr, E r a c l and Diatribvlionr
Figure 1. Packing combinations.
6
ADDITION OF LARGE SPHERES TO SMALL
0.0 LARGE 1.0 SMALL DENSllY b2.5%
0.33 LARGE 0.67 SMALL DENSITY 72.0%
0.72 LARGE 0.28 SMALL DENSITY 85,077 MAX.
Figure 5. A, Addition of small spheres to large. B, Addition of large spheres to small.
Figure 2. Wooden rods.
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Figure 4. Packing of various LID fibers.
component with the left follows the law of mixtures, that is, a straight line connecting the two components. This is of no consequence when the two components are spheres, but when one component is of different shape, such as a fiber, the straight line defines the worst possible packing conditions, also defining zero packing efficiency. Packing efficiency data were developed in a spherefiher system between the limits of R = 1and R = by Milewski in his 1974 S.P.I. paper. The curves were developed by
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 17, No. 4, 1978
365
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Figure 8. Packing of glass fibers and beads at constant L I D .
Figure 1 I . Location of minima in packing curves. 14
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Figure 12. Relationship between L I D and R a t minimum packing efficiency.
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Figure 10. The calculation of packing efficiency.
packing of fibers and spheres over a wide range of R values ( R now defined as sphere diameter divided by the fiber diameter) while varying the L I D of the fiber component. The results were viewed in two basic ways illustrated in Figure 8 at constant L I D and in Figure 9 a t constant R.
The concept of packing efficiency is defined as the maximum deviation of the bulk volume from the mixture line H,,, divided by the theoretical maximum deviation H m (see Figure 10). Experimental Minimum Packing Efficiency for Fiber-Sphere Systems Using the concept for packing efficiency, the bulk of the experimental packing work with fibers and spheres can be viewed in a single graph (Figure 11). Each fiber of different L I D exhibits a minimum packing efficiency. The long fibers show the minimum at higher R, as can be seen by the minimum in the 3711 L I D curve at R = 13.5 compared to the minimization between R = 1 and 2 for the 411 L I D fiber. The packing efficiency increases on either side of the minimum, and eventually reaches 100% as R approaches infinity or zero as defined by the system (Figure 10). Although the maximum packing density or minimum bulk volume for either very large or very small "R" could have been predicted, the exact location of the minimum conditions for the different L I D fibers must be located by experiment.
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Ind. Eng. Chem. Prod. Res. Dev.,
VoI. 17. No. 4, 1978 .
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ALL CVLiNDERS eDhT4lN WE S U E VOLUME OF SOLIDS 3 WRTS SPnERES PlNO iPARTFiBERSATI51ILID
Figure 13. Illustration of good packing at R = 0.5 and poor packing at R = 4.0. From Figure 11the " R values at the minimum packing conditions were determined for each fiber L I D and this relationship is illustrated in Figure 12. The curve is of importance to future investigators in that it points out what R values are to he avoided if good packing is desired or at what R values lowest packing density can he ohtained within the range of fiber L I D studied. By utilizing the above information, the density of packing of various fiber-sphere compositions can he calculated, and the void volume or resin demand can he determined. This also permits the economics of any chosen combination of fiber-sphere system to he calculated for
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wide ranees of fiber loading. LID. R. and resin and fiber cost. A clear example of how effective good packing comhinations are is illustrated in Figure 13. This photograph depicts four cylinders, all containing the same solid volume of fiher and spheres at two different R values. The two cylinders on the left are in the unmixed condition with the fiher and sphere completely fitting the cylinders. The two cylinders on the right are in the mixed condition and illustrate no packing advantage a t R = 4 and a significant packing advantage a t an R = 0.5 value, where the void volume or resin demand was reduced from 50% to 35%. It is believed that these packing concepts of replacing some of the fihers with spheres and reducing resin demand can he applied profitahly to many aspects of the reinforced plastic business in such areas as thermoplastic molding compound, BMC, SMC, casting resin, tooling resins, floor coating, furniture casting, reinforced foams, etc., or almost any composition where fillers are used and more strength is needed or where reinforcements are used and less cost and improved processing efficiencies are desired. I
,
.
Literature Cited MilewSki. J. V., Ph.D. Thesis. Rutgers University,
1973.
Miiewski, J. V., "Identification of Maximum Packing Conditions in the Bimodal Packing of Fibers and Spheres". 2% Annual Technical CDnlerenCe of S.P.I. Reinforced Piastic Division Feb 1974.
Received fur reuiew June 19, 1978 Accepted August 25,1978
This paper was presented at the Division of Organic Coatings and Plastics Chemistry, 175th National Meeting of the American Chemical Society, Anaheim, Calif., March 1978.
Stabilization of Hydrocracked Lubricating Oils Tsoung-Yuan Yan Mobil Research and Development Corporation, Central Research Division, Princeton, New Jersey 08540
A method for stabilization of hydrocracked lube oil against light instability involves reacting the oils with olefins over acidic catalysts. Both the sludge precursors were deactivated and the base oil was improved in solubility for the oxidized products by alkylation with olefins. Higher olefins are more effective. Good results are obtained with olefin concentrations of 5% or higher, space velocity of 'I, and temperature ranges of 100-120 'C and 200 OC for acid resins and inorganic acidic catalysts, respectively.
Introduction The manufacture of lubricating oil by hydrocracking or severe hydrotreating is not new, hut the process is not commercially useful. Improved hydroprocessing technology and dwindling choices of crudes has renewed interest in hydrocracking in the past 15 years (Gilbert and Walker, 1971). The hydroprocessing technology for lube oil production has been reviewed by several authors (Gilbert and Walker, 1971; Vlugter and Van't Spijker, 1971; Steinmetz and Reif, 1973). In contrast to solvent refining processes, hydrocracking alters the molecular structure and molecular weight of the feed by a combination of reactions. The important reactions involved are hydrogenation of aromatics, ring 0019-789017811217-0366501.0010
opening, isomerization, cracking, desulfurization, denitrogenation, and dealkylation. Through these reactions, the feed is converted to lower viscosity, hut high viscosity index (VI) lubricating oil. It is noted that small amounts of aromatic and heterocyclic compounds in the feed that contain nitrogen and sulfur are either unconverted or converted to partially hydrogenated species in the hydrocracking process. The quality of lubricating oil produced from hydrocracking has been well characterized (Gilbert and Walker, 1971; Bryer and Didot, 1973; Assef, 1970). By use of a hydrocracking process, lubricating oil of high viscosity index (which cannot he attained via conventional solvent refining processes) can he produced from most feed stocks. 0 1978 Ajierican Chemical Society
