Chemical instrumentation S. Z. LEWIN,
N e w York University, Washington Square, N e w York
3, N. Y.
a t least, when comparing different makes of centrifuges. I t will be worthwhile to eonelude this brief discussion of tho theory of oentrifuge design by oonsidcring the role of time of centrifuging. For spherical particles that are not falling too rapidly in a fluid medium, Stokes' Isw is obeyed, via.;
T h i s rwies o j articles presents a survey aj' the basic principles, characteristics, and limitations of those instruments whichsnd impwtant applications i n chemical work, running the gamut from bolances and burets to seruomechanism and specbomtters. The emphasis is on con~merciallyavailable equipment; approximate prices are yuoted to indicate the order of magnitude of cost of the various types of design.
F
=
3mDu
where n is the viscosity, v is the rate of fall, F is the force producing the motion, and D is a constant. This means thitt the effect of the centrifugal force d l be to cause the particles to settle with a velocity that is proportional to the CF. That is: Centrifugal farce has been used in a practical way in many of mankind's activities for several centuries. The centrifuge, which is a term applied to any device that utilizes the centrifugal farce acting on x body moving in a circle to hasten the process of sedimentation or stratification, has a long and distinguished history in chemical and biological laboratory vork. The list of applications runs the gamut from the researches of T. W. Richards to those of T. Svedberg; from the removal of bacteria in air to the anelysis of butter fat in milk. The nature and characteristics of modern laboratory centrifuges are not as well understood by the average experimenter as they should be, and because of this, they are less widely and profitably used than is warranted. It may be categorically asserted that, with the single exception of the collection of a precipitate in the final step of a gravimetric analysis just prior to ignition to constant weight, there is no laboratory procedure involving filtration or extraction that cannot be improved by the use of a, centrifuge. Centrifuges are invaluable in the modern laboratory when dealing with precipitates, fractionating specimens, breaking dorm emulsions, and increasing the efficiency of extractions. A centrifuge is basically a very simple device. In principle, it need consist of nothing mare than s. source of motive force and a means of attaching the sample to it. I n fact, fifty years ago a common laboratory expedient was to tie a &ring around the neck of a test tube, and by means of the experimenter's extended arm, to whirl the test tuberapidly about. Modern instrument design has had the object of making it possible to whirl the specimen a t very high speeds under reproducible conditions and in perfect safety. The significance of speed, radius of gyration, and duration of centrifugation may be appreciated from the follou"ng considerations. The centrifugal force (CF), in dynes, acting outward d o n g the radius (r), in centimeters, of s. circular path in a.hich a particle of effective mass (m), in grams,
is moving with a speed (or frequency) of rotation (I),in revolutions per second, is given hy:
where o is the angular velocity in radians per second. The effective mass is the actual mans of the particle minus the huoyant force of the medium in which it is suspended. Thus, the force a n the particle depends on its distance from the sxis of rotat,ion as well as on the number of revolutions it makes per second. If a ver.v large C F is desired, it may be achieved by employing a large distance between the specimen and the axis of rotation, by adopting s large speed of rotation, or both. However, if the radius of gyration is made large, the specimen holder (i.e., the rotor or head, or howl of the centrifuge) must be large and heavy, and it becomes impractical t o attempt to whirl thin a t great speeds. Furthermore, the C F increases only as the first power of r, hut as the second power of the speed of rotation. Hence, the highest centrifugal forces are obtained in practice by keeping the radius of gyration relatively small, and using high speed motors. The force of gravity acting a n a freely falling hody is mg. The ratio of the eentrifngalforee to the force the object would feel if it were falling freely is called the relaliue cenl~ifugalforce (RCF), and is given by: war
RCF = 9 = (1.11
x
I O - ~ ) ~ 2 ~
where n is the number of revolutions per minute (rpm), and r i~ in centimeters. It is common practice to express the R C F in the units " X 6,"or "gravities," signifying that this number shows how many times greater than the force of gravity is the force acting on the hody being centrifuged. I t should be clear that the R C F of a eentrifuge has experimental significance, whereas the rpm alone has very little relevance-
" = k.fi But the C F and therefore v, depends on 1, and increases (at constant f ) as the particle moves outward, away from the axis of rotation. Since u=dr/dt, it is easy t o show that the distance of the particle from the axis of rotstion a t any t,ime, t, will he given by:
whwe ro is the position of the particle rut the start of the run. The nature of this equation is illustrated in Figure 1. I t is
Figure 1 . Variation of the position of a porti& or o function of the duration of centrifugetian.
evident that the rate of settling increases with time, for as the particles move away from the sxis of rotation, they move in the direction of increasing RCF. Therefore, extending the duration of centrifugation for a. relstively short time can mstwislly improve an incompletely sedimented speeimen. Also, where reproducible results with slowly sedimenting particles in a. high-speed centrifuge are important, as in t h fractionation ~ of mi~eromolecular dis(Continued on page AB70)
Volume 36, Number 5, Moy 1959
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Chemical Instrumentation persions, precise control of the duration of the run is esaentiitl. However, increasing the 8peed oi rotation or the time of centrifuging are not unmitigated advantages, for they create certain conditions that may work against efficient sedimentation unless cognizance is taken of these factors in the design of the instrument. At high speeds the effeot of air friction in heating the centrifuge head and it8 contents e m be considershlc, particularly in runs lasting aeverd minutes. This is known as "uindage," and its heating effect can cause convection currents to he set up in the tubes that will work against the desired ~edimentstion. In addition, the heat generated in the motor contributes to the heating of the tubes. Many high speed centrifuges provide for forced circulation of air through the inst,rument t o carry away most of the windage and motor heat. I n such a centrifuge, the temperature tends to reach a. steady state value during a run, as illustrated in Figure 2.
TIME
IN
MINUTES
Figure 2. Idealized representation of the temperature rise occurring in o rotor due to windage and motor heat. Curve eventually levels off when forced-air circvlotian carrier heat away at some rate ar it is generated.
When a specimen is being whirled a t high speeds to aehievo sedimentation of slowly settling particles, any vibration of the centrifuge will also tend to stir up the ~ediment. Similarly, the coming to rest of t,he rotor after cutting the power to t,he motor must he smooth and uniiorm to avoid vitiating the run. Thus, i t can be appreciated that the greater the RCF required, the mare exaeting are the demands made an the design and construction of the centrifuge; and, of course, the more expensive the instrument will be. Three broad categories of commercial laboratory centrifuges have come to be generally recognized. These can bc roughly claasified as follons: 1 . Ordinary centrifuacs-RCF's u~ to aboui 10,000 X-G (2) "Super" or "Super-speed" centrifuges-between nhout 10,000 and 50,OW X G
.
A270
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Journal of Chemical Education
Chemical Instrumentation (3) "Ultra" eentrifugesgreater then about 50,000 X G. The following sections will describe the characteristios of representatives of these various types of instruments. First, however, it will be well to start with some general considerations concerning the eomponent parts of a typical laboratory centrifuge.
Component Parts The important component parts of s genoreliaed form of laboratory centrifuge me illustrated schematically in Figure 3. Not every model of the commercial instruments will have all of these features; generally the smaller, inexpensive units dispense with the timer and the tachometer. Also, many instruments have features not shown in the figure, such as temperature control and forced-air circulation. The figure depicts an angle-head type of rotor; 11.m. arc srvrrnl utl.cr wmmon ndor drsi~u.. (\mnwn.iul irt.+trt~rnt.tltrulr
