Grinding and dispersing nanoparticles.Over the past few years we have observed an increase in the desire to use bead bead
Small object, usually pierced for stringing. It may be made of virtually any material—wood, shell, bone, seed, nut, metal, stone, glass, or plastic—and is worn or affixed to another object for decorative or, in some cultures, magical purposes. mills for grinding grinding, process by which surface material is removed from an object, usually metal, by the abrasive action of a rotating wheel or a moving belt that contains abrasive grains. and dispersion dispersion, in chemistry
dispersion, in chemistry, mixture in which fine particles of one substance are scattered throughout another substance. A dispersion is classed as a suspension, colloid, or solution. of "nanoscale At nanometer size. Any device only a few nanometers in size is nanoscale. See nanotechnology and nanometer. " particles. The objective of this paper is a general discussion of how this process works in a bead mill, the parameters required to successfully produce these nanoscale dispersions, and some experience in grinding or particle size Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. reduction of solids to the nanoscale.
According to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. a report released by the National Science and Technology Council The National Science and Technology Council (NSTC) was established in the US by Executive Order on November 23 1993. This Cabinet-level Council is the principal means within the executive branch to coordinate science and technology policy across the diverse entities that make up (NSTC See NTSC. ), "Nanoscience and Nanotechnology generally refer to the world as it works on the nanometer scale, say, from one nanometer to several hundred nanometers." (1) If we interpret this to mean that the particle size referred to as a nanoparticle means something that ranges from a few nanometers up to 700 nanometers, most of the components currently processed on a bead mill fall into the area of nanotechnology.
Most pigments used in inks and coatings, for example, have primary particle size from at least 0.02 [micro]m or 20 nanometers up to 200 nanometers. With the particle size analysis technology available today, we can easily learn that many operators of bead mills are grinding and dispersing their pigments into this range. Theodore Vernardakis establishes this point in his enlightening en·light·en
tr.v. en·light·ened, en·light·en·ing, en·light·ens
1. To give spiritual or intellectual insight to: discussion of pigment pigment, substance that imparts color to other materials. In paint, the pigment is a powdered substance which, when mixed in the liquid vehicle, imparts color to a painted surface. dispersion in the Coatings Technology Handbook. (2) This section contains several electron micrographs electron micrograph
A micrograph made by an electron microscope. of pigments, along with particle size analysis showing materials with mean particle size around 100-200 nanometers. For the sake of discussion, we will assume that the nanoparticles desired are less than 200-300 nanometers.
There are now and have been for some time materials available that are essentially nanoparticles. However these nanoparticles, like carbon black or ultrafine titanium titanium (tītā`nēəm, tĭ–) [from Titan], metallic chemical element; symbol Ti; at. no. 22; at. wt. 47.88; m.p. 1,675°C;; b.p. 3,260°C;; sp. gr. 4.54 at 20°C;; valence +2, +3, or +4. dioxide, are agglomerated agglomerated
of particles, compacted together into a mass.
particulated feeds compacted or extruded into pellets and similar forms. just by the nature of the manufacturing process or storage. The goal is to disperse disperse /dis·perse/ (dis-pers´) to scatter the component parts, as of a tumor or the fine particles in a colloid system; also, the particles so dispersed.
1. these particles to their primary particle size. We will address the required operating conditions for a bead mill to grind 1. GRIND - GRaphical INterpretive Display.
A graphics input language for the PDP-9.
["GRIND: A Language and Translator for Computer Graphics", A.P. Conn, Dartmouth, June 1969].
2. and disperse particles to less than 200 nanometers and the requirements for grinding large particles to a nanometer range.
PARTICLE SIZE CONTROL
The particle size achieved from a bead mill is a direct function of the media size used for the grinding process. The average particle size that can be achieved quickly in a bead mill is about 1/1000 the size of the grinding media. Figure 1 illustrates this point. In this experiment we processed limestone using two different media sizes: 0.4-0.6 mm zirconia-silica grinding media (SAZ) and 1.6-2.5 mm SAZ. We can see that rapid particle size reduction occurs and the curve plateaus at around 0.5 [micro]m for the 0.5 nominal media and the curve starts to plateau around 1.5 to 2 [micro]m for the 2 mm nominal media. Many other examples could be given, but this simple curve suffices to demonstrate the idea.
CURRENT INDUSTRIAL APPLICATIONS
The smallest bead size regularly used on a commercial basis is 200-300 [micro]m. The applications of this media are primarily in the pigment manufacturing and ink industry for fine grinding and dispersion of pigments such as phthalocyanine phthal·o·cy·a·nine
Any of several stable, light-fast, blue or green organic pigments used in enamels and plastics. blue and green and carbon black. The uses for these inks are in the ink jet See inkjet printer. market, textile inks, etc. As will be seen, there should be more interest in the coatings industry to quickly achieve maximum color development and trans-parency. Some other applications are pharmaceutical materials, ceramic materials for electronics applications, and dyes. Most of the work in this area is proprietary, but a lot of information can be obtained by searching patents. For example, U.S. patent 5,500,331 discusses the use of media less than 100 [micro]m to grind various dyes. (3) In this example, various bead sizes are used to grind a dye to nanometer particle size. At least in this case, using beads smaller than 50 [micro]m does not have as great an effect on the particle size reduction as the 50- and 75-[micro]m beads. This indicates that at some point media size and feed particle size become important points. This is true for any bead milling application. Normally for efficient grinding and dispersion, the feed particle size should have a [d.sub.90] (90% of the particles are less than) 1/10 the media size. For example, for 100-[micro]m beads, the [d.sub.90] should be about 10 microns (see Table 1).
[FIGURE 1 OMITTED]
In these markets in North America North America, third largest continent (1990 est. pop. 365,000,000), c.9,400,000 sq mi (24,346,000 sq km), the northern of the two continents of the Western Hemisphere. , we know of at least 50 Netzsch bead mills operating with the 200-[micro]m media in either steel or ceramic material. Certainly other manufacturers are supplying machines into this field or trying to at least on the lab scale. These machines range from lab equipment up to 300 horsepower horsepower, unit of power in the English system of units. It is equal to 33,000 foot-pounds per minute or 550 foot-pounds per second or approximately 746 watts. machines. Worldwide, we can probably double this figure again. This is a significant amount of capacity for this small media and this type of process. And this application will continue to grow. But how does it work, and what does a bead mill manufacturer need to consider for more efficient design?
BEAD SEPARATION PARAMETERS
What is the most important aspect of using small media? Getting the beads out of the slurry slurry,
n a thin mixture of insoluble material floating in liquid.
solids in suspension. Used as a method of feeding pigs—slurry is pumped through fixed lines and delivered to troughs by hoses equipped with gasoline pump fittings. . It is fine to say that using very small beads grinds or disperses a particle to a very fine particle size, but after the grinding process, how do you separate such a fine particle from the slurry? How do you do this on a continuous basis? In the case of the modern bead mill, this process is achieved by centrifugal centrifugal /cen·trif·u·gal/ (sen-trif´ah-gal) efferent (1).
1. Moving or directed away from a center or axis.
2. separation of the beads from the slurry.
Figure 2 shows a horizontal disc mill with a classifying rotor rotor: see generator; motor, electric. for separating the beads from the slurry. The beads are retained to the left, separation occurs at the discharge end of the machine by centrifugal force centrifugal force
Fictitious force, peculiar to circular motion, that is equal but opposite to the centripetal force that keeps a particle on a circular path (see centripetal acceleration). . This concept is covered in U.S. patent 4,620,673. (4) If we were to rely on the classic bead mill design of filtering the beads from a slurry using some type of screen inserted into the chamber or mounted in the end or wall of the chamber, the immediate problem that will occur is the screen or filter will block with layer upon layer of media until the entire surface is completely blocked. At this point the pressure in the vessel will increase to an unacceptable level and the mill will shut down on the over pressure safety device.
[FIGURE 2 OMITTED]
The principle of efficient bead separation is based on centrifuging the media out of the slurry. This allows continuous operation of the mill, not a batch process. Centrifugal force is calculated by multiplying the square of the peripheral velocity of the rotor by the mass of the object at hand and dividing by the radius of the rotor. However, we also have to consider the mass flow rate of the product through the mill, i.e., there is balance that must occur, separation force by the centrifuging of the rotor must be greater than the flow force of the product travelling through the mill. The factors that affect the bead separation curve are:
* Product viscosity
* Product mass flow
* Product density
* Bead density
* Bead size and bead charge
* Rotor peripheral speed and geometry
* Separation system geometry
In practice the smallest bead size that can currently be separated on lab scale equipment is 30 [micro]m. The limitations on separating grinding media by centrifuge centrifuge (sĕn`trəfyj), device using centrifugal force to separate two or more substances of different density, e.g., two liquids or a liquid and a solid. force are:
(1) PRODUCT VISCOSITY -- If the material is very viscous viscous /vis·cous/ (vis´kus) sticky or gummy; having a high degree of viscosity.
1. Having relatively high resistance to flow.
2. Viscid. two things happen to limit the separation. First, the power required to rotate the shaft is very high, or in other words Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently , the power needed to agitate the media is high, limiting the speed of the mill, therefore limiting the separation system speed. The viscosity inside a bead mill is much higher than the apparent viscosity of the slurry being fed to the mill because of the addition of the grinding media as part of the slurry. Second, the high viscosity forces the media toward the discharge screen. The answer is simply to apply more power to the mill volume. However, this also requires some mechanical considerations; there is a limit to how much power can be applied to an existing shaft design.
(2) PRODUCT FLOW RATE -- If the flow velocity In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of the fluid. Definition
The flow velocity of a fluid is a vector field
(3) PRODUCT DENSITY -- If a high slurry density is processed, this also has a counter effect to the centrifugal force of the separator.
(4) Bead Size and Density -- Centrifugal force is a function of the mass multiplied by the square of the velocity. For example, if we use a 1-mm bead that has a density of 2.6 grams per cubic centimeter cu·bic centimeter
Abbr. cc A unit of volume equal to one thousandth (10-3) of a liter or to one milliliter. like glass media and a constant rotor speed we can more than double the separation force by using an yttrium yttrium (ĭt`rēəm) [for Ytterby, a town in Sweden], metallic chemical element; symbol Y; at. no. 39; at. wt. 88.9059; m.p. about 1,522°C;; b.p. 3,338°C;; sp. gr. about 4.45; valence +3. Yttrium is a highly crystalline iron-gray metal. stabilized sta·bi·lize
v. sta·bi·lized, sta·bi·liz·ing, sta·bi·liz·es
1. To make stable or steadfast.
2. zirconium zirconium (zərkō`nēəm), metallic chemical element; symbol Zr; at. no. 40; at. wt. 91.22; m.p. about 1,852°C;; b.p. 4,377°C;; sp. gr. 6.5 at 20°C;; valence +2, +3, or +4. oxide (YTZP) grinding media that has a density of 6 or quadruple quad·ru·ple
1. Consisting of four parts or members.
2. Four times as much in size, strength, number, or amount.
3. Music Having four beats to the measure.
n. the separation force by using a tungsten carbide tungsten carbide
An extremely hard, fine gray powder whose composition is WC, used in tools, dies, wear-resistant machine parts, and abrasives. (WC) media with a density of 14. This is why we recommend using high-density beads in high viscosity slurries. We need the mass of the bead to increase the centrifuging force to overcome the drag force of the product flow. Now if we decrease the bead size the mass of the bead decreases as well by a factor of 8. So if we are using a 0.6-mm glass bead, calculations show this bead weighs around 2.3 milligrams. If we decide that 0.4-mm beads are going to grind better, we might want to consider using steel beads, because 0.4-mm steel weighs about 2 milligrams.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
(5) BEAD CHARGE AND POROSITY porosity /po·ros·i·ty/ (por-os´it-e) the condition of being porous; a pore.
1. The state or property of being porous.
2. -- This is an important consideration when we think about some of the other operational aspects of a bead mill. Figure 3 shows the calculated interstitial space Interstitial space
The fluid filled areas that surround the cells of a given tissue; also known as tissue space.
Mentioned in: Lymphedema between the grinding media at various charge levels. For example, if a 2-mm bead is used at 60% bead charge, the calculated space is around 400 [micro]m. If we use 100 [micro]m beads at a 95% bead charge the space is about 1.5 [micro]m. What we have to consider for bead separation and flow is the effect of the hydraulic pressure due to resistance to flow created by the tighter spacing or filtering effect of the smaller grinding media and higher charge.
(6) AGITATOR ag·i·ta·tor
1. One who agitates, especially one who engages in political agitation.
2. An apparatus that shakes or stirs, as in a washing machine.
Noun 1. SPEED -- A fast rotor speed, or peripheral speed, increases the centrifugal force, but there are limitations to how fast the rotor can turn. These considerations are the installed power, wear, and the mechanical seal. These are all areas that can be addressed through engineering modifications, but these changes have engineering costs.
(7) DIMENSIONS OF THE SEPARATION SYSTEM -- This includes the distance between the screen and rotor and the length of the screen. The design of the screen is critical; normal screen designs do not have the open surface area necessary to allow flow through the mill without creating a high velocity through the screen slots. High velocities at the screen slot usually result in poor bead separation and eventually screen blocking. The slots have to be precise in this application, otherwise they are blocked.
SELECTING A BEAD MILL FOR SMALL MEDIA
Considering the above points, how do we select the right mill design? There are essentially two types of bead mill that can use small media: a disc mill and a high-energy pin mill. Our view is that the better machine for using small media is the high-energy pin mill.
Horizontal disc mills, which have been the predominant type of mill used in industry in the past few years, have a limitation in this application due to the large volume of media required in the mill. The large volume of media requires tremendous power at high rotor speeds. This is a function of the viscosity of the bead/slurry dispersion in the mill. The high contamination and cost associated with a large media volume have to be considered. If the product has to pass through a large media volume, this increases the likelihood of contamination. To charge a 20-liter mill with 125 micron micron: see micrometer.
One micrometer, which is one millionth of a meter or approximately 1/25,000 of an inch. The tiny elements that make up a transistor on a chip are measured in micrometers and nanometers. See process technology. YTZP beads would cost around $43,000, about the same price as the mill.
Figure 4 shows a comparison between a horizontal disc mill and a high-energy pin mill. If we imagine the flow pattern through the disc mill, we can see that the long length or high length to diameter ratio would result in high resistance to flow. Disc mills typically have a length to diameter ratio of around 3:1.
The high volume of media required also results in a high filtration effect, and therefore, a high drag force to the separation system. The size of the separation system is designed for using larger media, 0.6 mm and above. The open surface area available and the diameter of the rotor are not optimized for very small beads. Basically what happens is that the flow velocity through the mill compacts the beads to the separation system, resulting in a slow process (20 or 30 min) of accumulating beads onto the screen. The mill then shuts down. The way to overcome this problem is to run slow flow rate. However this is a waste of efficiency and increases the contamination rate of the product with media.
[FIGURE 5 OMITTED]
The high-energy mill shown in Figure 4 has a lower length to diameter ratio, typically about 1.5:1, a larger diameter rotor, and larger separation system. The grinding zone is more defined by the use of the larger diameter rotor and the installation of shaft pegs or pins for media agitation agitation /ag·i·ta·tion/ (aj?i-ta´shun) excessive, purposeless cognitive and motor activity or restlessness, usually associated with a state of tension or anxiety. Called also psychomotor a. . Approximately 2/3 of the shaft length is used for bead separation. The product flow enters from the bearing housing end, flows through the grinding zone around the end of the shaft, and enters the screen area. The slots cut into the shaft centrifuge the beads out of the slurry. This separation flow of the grinding media results in a higher compression of the beads in the grinding zone. This means the packing of the media is much higher, and uniform through the grinding zone, than can be achieved in a disc agitator design. In a disc agitator design, the compression of the media in each grinding zone is a function of the rotor speed and the area near the edge of a disc.
An important consideration between these two machines is the fact that they both have the same installed horsepower, i.e., a 20-liter disc mill has 25 or 30 hp, while a 10-liter pin mill also has 25 or 30 hp. The higher energy input available on the pin mill means that we have the capability of running the machine at higher tip speeds required in the discussion on bead separation above. Also in the pin mill the higher tip speed increases the centrifugal compression of the media, decreasing the gaps between the beads, increasing the filtration effect, and therefore, resulting in tighter, finer particle size distribution The particle size distribution ("PSD") of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amounts of particles present, sorted according to size. .
[FIGURE 6 OMITTED]
Figure 5 illustrates the increase in grinding efficiency and bead compression. This is grinding phthalo blue pigment for ink. In this case we are processing the same slurry, using 250-[micro]m steel grinding media in a disc mill and a pin mill. Three passes through the disc mill at a total residence time of 11.7 min, a specific energy consumption ([E.sub.spec]) of 406 kilowatt-hours per ton does not produce as fine a particle size as circulation grinding on a pin mill at 4.3 min of residence time, 256 kW-hr/ton [E.sub.spec].
Because of the larger size of the separation system, we can have much higher flow rates through the pin mill versus the disc mill. This results in higher grinding efficiency, higher energy efficiency. We will not go into the benefits of high flow multiple pass grinding here; the theory and benefits of fast flow rates and multiple passes are well documented. Suffice it to say that high flow rates result in close to plug flow through the mill and therefore uniform particle size reduction.
Screen open surface area is another area for examination. For example, A 20-liter mill using a 100-[micro]m screen has about 12 [cm.sup.2] screen open surface area, about the same open surface area as 1 1/2 in. pipe. But the 10-liter pin mill has about 30 [cm.sup.2] open surface area, or about the same area as a 2 1/2 in. pipe. Remember this is spread over a large number of 100-[micro]m slots. The velocity through these slots is very high, so to reduce the velocity we need more slots--thus the requirement for a larger open surface area screen. The problem encountered with using even smaller media is the further reduction in open surface area, i.e., even higher velocity though the slots. A 100-[micro]m wedgewire screen has an open surface area of about 7%; reducing to a 50-[micro]m wedgewire screen basically reduces the open surface area to about 3.5%. Also the best tolerance the wedgewire screen manufacturer can provide is about 25 [micro]m, so we have large slots up to 75 [micro]m to 25 [micro]m. We have found a source for screens that have greater open surface area for 100- and 60-[micro]m slots, up to about 10-14%. The slots are precisely made to 60 and 100 [micro]m. This has been one of the key solutions to this process. These screens are commercially available and have been for many years.
Scale up parameters are always very important. The advantage that we have in selecting a high energy pin mill for this application is that as the machines are scaled up the important parameters like constant energy input to mill volume is linear, the geometry of the agitator rotor and separation system are constant. A further point for reflection is that as the mills become larger, the rotor tip speed available is faster. This is due to certain mechanical limitations on small machines, but what we can say is that the larger machines are capable of running faster tip speeds than the lab mills. Fundamentally, it is clear why this must occur--the tip speed scale up consideration historically used may not provide the required speed to utilize the full power available on the production mill. Looking at various factors such as centrifugal force for separation and equivalent kinetic energy kinetic energy: see energy.
Form of energy that an object has by reason of its motion. The kind of motion may be translation (motion along a path from one place to another), rotation about an axis, vibration, or any combination of may provide a more accurate method to determine the correct tip speed for operating the production size mill.
To summarize sum·ma·rize
intr. & tr.v. sum·ma·rized, sum·ma·riz·ing, sum·ma·riz·es
To make a summary or make a summary of.
sum the mill selection points we need the following features:
(1) Low mill volume with high energy input -- Low volume of media required -- High energy for high rotor speed (2) Large separation system -- High centrifugal force -- Greater screen open surface area for reduction in flow through velocity (3) Low length to diameter ratio -- Reduction in hydraulic compression -- Lower drag force on media
These features are currently available in high-energy pin mill design. So the question becomes, does this process work?
EXAMPLES OF BEAD MILLING WITH SMALL MEDIA
Figure 6 shows titanium dioxide dispersion. In this example the difference between 0.5-mm zircon zircon
Silicate mineral, zirconium silicate, ZrSiO4, the principal source of zirconium. Zircon is widespread as an accessory mineral in acid igneous rocks; it also occurs in metamorphic rocks and, fairly often, in detrital deposits. beads and 0.1-mm tungsten carbide (WC) beads is shown. A coarser feed slurry is passed through the discs mill, and some particle size reduction occurs which is apparently good enough because this is used as the final product for manufacturing Ti[O.sub.2]. We then take this slurry and pass it once through a pin mill with 100-[micro]m WC spheres. We can see dramatic difference in the particle size reduction compared to the larger beads in a disc mill, down to a mean size around 0.2 [micro]m, which is about the desired range for Ti[O.sub.2]. When we processed longer by circulating cir·cu·late
v. cir·cu·lat·ed, cir·cu·lat·ing, cir·cu·lates
1. To move in or flow through a circle or circuit: blood circulating through the body.
2. , we saw further reduction, down to around 0.15 [micro]m. This test was run to evaluate claims in patent 5,407,464 (5) in which it is claimed that using WC beads will grind Ti[O.sub.2] and various other mineral and organic powders to 100% less than 100 nanometers very rapidly. In comparison to the test described in the patent, the bead milling is much higher energy and more efficient. Although still not below 100 nanometers, there is significant particle size reduction. The process is much more efficient than using larger beads.
Figure 7 illustrates a test to grind a biocide biocide (bī`əsīd'), synonym for pesticide. to a nanometer size. We can see again in a typical grinding curve rapid reduction to a 75 nanometer [d.sub.50], about 1/2000 the size of the grinding media, 0.15-0.25 mm SAZ in this case. Ninety micron glass beads appear to have slightly greater efficiency, producing at 65-nanometer [d.sub.50].
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
Figure 8 shows dispersion of a fairly hard grinding synthetic organic pigment. (We cannot discuss the pigment type or application in this case.) Product specifications were roughly 35% solids, viscosity was around 500 centipoise cen·ti·poise
A unit in the centimeter-gram-second system that is of dynamic viscosity equal to one hundredth (10-2) of a poise. , with 6% dispersant dis·per·sant
A liquid or gas added to a mixture to promote dispersion or to maintain dispersed particles in suspension. on pigment solids. Flow-through rate on the bead mill was about a one-minute residence time. Particle size reduction is again very rapid down to the primary particle size of the pigment, but no significant reduction occurs at this point, i.e., we are not grinding the primary pigment particle, at least according to our particle size analysis. This could be a positive or negative point depending on the goal of the particle size distribution.
Figure 9 shows dispersion of alumina alumina (əl`mĭnə) or aluminum oxide, Al2O3, chemical compound with m.p. about 2,000°C; and sp. gr. about 4.0. using 300-400-[micro]m zircon beads and 125-[micro]m YTZP beads. The mill was operated at tip speed of about 11 meters per second. Flow rate was 0.6 liter liter, abbr. l, unit of volume in the metric system, defined since 1964 as equal to 0.001 cubic meters, or 1 cubic decimeter. A cube that has each of its edges equal to 10 centimeters has a volume of 1 liter. The liter is equal to 1.057 liquid quarts, 0. per minute. We can see in this case that grinding the alumina to a 100-nanometer particle size occurs rapidly, and the ultimate particle size was 87 nanometers ([d.sub.50]).
We could show more data to the same effect, but the conclusion is that the particle size reduction is a function of the material properties. If the material is soft and easily friable friable /fri·a·ble/ (fri´ah-b'l) easily pulverized or crumbled.
1. Readily crumbled; brittle.
2. Relating to a dry, brittle growth of bacteria. , then particle size reduction to sub 100-nanometer size is possible. If it is a harder material, further particle size reduction may not occur. Each application becomes very product specific. Laboratory testing is required to determine whether the material can be processed.
Grinding with very small media is possible, and process parameters have been developed for using less than 200 [micro]m grinding media. We have demonstrated that it is possible to operate a bead mill with 100-micron beads at least on a lab scale.
At this point the best available media is zircon and YTZP beads. Tungsten carbide beads are experimental, and using this media on certain materials of construction can cause severe wear. Zircon media is relatively inexpensive compared to YTZP, but the contamination rate is higher. Typically products that are to be produced in this size range are high value materials, and contamination is a concern.
The practicality of the process must be considered. Is the saving in time from using 200-micron beads, which are currently used in a significantly increasing number of processes, worth the order of magnitude A change in quantity or volume as measured by the decimal point. For example, from tens to hundreds is one order of magnitude. Tens to thousands is two orders of magnitude; tens to millions is three orders of magnitude, etc. of cost and potential difficulty versus the time saving? For example, if we demonstrate that we can make the product on a 10-liter mill in one-fourth the time, but with a potentially more difficult process condition and higher cost for media versus using a 60-liter mill to make the same production, is this the most practical choice?
Table 1 -- Particle Size Related to Bead Diameter Particle Size Bead Size (nanometers) No media 92.4 5 [micro]m 86.4 25 [micro]m 90.2 50 [micro]m 56.5 75 [micro]m 63.7 450 [micro]m 80.6
ACKNOWLEDGMENT acknowledgment, in law, formal declaration or admission by a person who executed an instrument (e.g., a will or a deed) that the instrument is his. The acknowledgment is made before a court, a notary public, or any other authorized person.
I would like to thank my colleagues Gerhard Kolb and George Scherer of Netzsch Feinmahltechnik GmbH, Selb, Bavaria, Germany, for their invaluable information on the focus of bead separation.
(1) "Nanotechnology: Shaping the World Atom atom [Gr.,=uncuttable (indivisible)], basic unit of matter; more properly, the smallest unit of a chemical element having the properties of that element. Structure of the Atom
by Atom," National Science and Technology Council literature, not dated.
(2) Vernardakis, T.G., "Pigment Dispersion," Coatings Technology Handbook, pg. 529-550, Marcel Dekker Marcel Dekker is a well-known encyclopedia publishing company with editorial boards found in New York, New York. They are part of the Taylor and Francis publishing group.
Initially a textbook publisher, they went to encyclopedia publishing in the late 1990's. , 1991.
(3) Czekai, D.A., U.S. Patent 5,500,331 (March 19, 1996); Eastman Kodak Company.
(4) U.S. Patent 4,620,673.
(5) Kaliski, A.F., U.S. Patent 5,407,464 (April 18, 1995); Industrial Progress, Inc.
by Henry W. Way
*119 Pickering Way, Exton, PA, 19341.