RELATIVE CENTRIFUGAL FORCE

 
Figure F.2. Nomogram for R.C.F.

Modern day ultracentrifuges can generate forces in excess of 300,000 times that of gravity, forces sufficient to overcome the very cohesion of most molecules (including the metal of the rotor). The force is usually given as some value times that of gravity.

The centrifugal force is dependent upon the radius of the rotation of the rotor, the speed at which it rotates, and the design of the rotor itself (fixed angle, vs swinging bucket). Rotor speed and design can be held constant, but the radius will vary from the top of a centrifuge tube to the bottom. If a measurement for the radius is taken as the mid-point, or as an average radius, and all forces are mathematically related to gravity, then one obtains a relative centrifugal force, labeled as xg. Centrifugation procedures are given as xg measures, since RPM and other parameters will vary with the particular instrument and rotor used. Relative Centrifugal Force is a constant that is independent of the apparatus used.

Figure F.2 presents a Nomogram for calculation of R.C.F. for a given radius and RPM. A simple formula for calculating this value is:

RCF = 1.12r (RPM/1000)
where r = radius in millimeters
RPM = revolutions per minute

The difficulty with using the formula is establishing the value for r. Typically, there are three r values given (by the manufacturer) for a rotor: the maximum, minimum and average r. These correspond to the distances from the center of rotation to the bottom, top and middle of the sample tube.

If the density and viscosity of the medium are known, as well as the density of a given particle, then the time needed to completely sediement a particle can be determined by the formula:

T = ((D-L)/(D+L))*(N/(d(g-p)S))
where T = time in minutes
D = radial distance in cm for r
L = radial distance to meniscus
N = viscosity of the fluid medium
g = density of the fluid medium
p = density of the particle to sediment
d = diameter of the particle in cms.
S = rotational velocity in RPM

ROTOR COMPARISONS

When separating a particle, it is convenient to be able to compare one rotor's design characteristics with those of a differing rotor. A procedure may be given as centrifuging for 20 minutes at 15,000 RPM in a Sorvall SS34 rotor. The problem then becomes one of how do you equate that to a Beckman JA-20 rotor?

Working with the maximum RCF for each rotor, the conversion can be made with the following equation:

t = (t x RCF) / RCF
where t = run time needed for the Beckman rotor t = run time specified in the procedure
RCF = RCF of JA-20 rotor at maximum speed
RCF = RCF specified in the procedure
(calculated if procedure in RPM)

This equation can be altered somewhat to be even more useful. The efficiency of rotors can be compared for any given task. Each rotor is given a value for k (the clearing constant, or clearing factor), which is an estimate of the time (in hours) required to pellet a particle of known sedimentation coefficient at the maximum speed of the rotor. 4 The lower the value of k, the shorter the time required to sediment a given particle. The relationship is given by

t = k / s ¸
k = clearing factor expressed in hour-Svedbergs
s  ¸ = Sedimentation Coefficient in water at 20 ° C
expressed in Svedbergs

It is possible to compute k, but it is easiest to use the manufacturers values, which can be looked up in tables such as those in Table F.1.

k =(253,300)[ln(r/r)]/(Rotor angular velocity/1000)

Using tabulated k values, however, the comparison of rotors is even easier, as the equation above becomes

t = kt / k 
where the t and k values are the time and k factor for each rotor.

By substituting this equation, you can also determine the time of centrifugation for any change in rotor speed. 5

For a Sorvall SS-34, for example, at 20,000 RPM (k=402), the time required to sediment a particle of100 S, in water at 20 ° C is calculated by:

t = 402/100or 4.02 hours (4 hrs, 1 min)

Table F.2 presents the k values for the Sorvall SS-34 rotor and for the Sorvall GSA rotor. Since these two rotors will be used throughout the remainder of the course, reference should be made to this table in any future centrifugation work, when another rotor is substituted.

ROTOR SAFETY

There are a number of safety precautions that must be adhered to when using any centrifuge and rotor.

Rotor Failure:

All rotors are subject to stress and with time will undergo metal fatigue. This is a given, and consequently, a detailed history of the rotor use should be kept. This is usually not done with clinical centrifuges, but is an absolute for an ultracentrifuge rotor.

EVERY USE OF AN ULTRACENTRIFUGE ROTOR MUST BE RECORDED IN THE CENTRIFUGE LOG. ABSOSLUTELY NO EXCEPTIONS!

After a period of use, each rotor will in turn be derated , that is its maximum RPM will be lowered. The Beckman rotors may contain optical speed control rings at their base - be sure they are present, and clean before use. These devices will strobiscopically monitor the maximum speed that a rotor can be used at. They are replaced as the rotor is derated.

By far the most common cause of rotor failure is corrosion stress. Salts, highly alkaline detergents and of course corrosive acids and alkali's will cause decomposition of the coatings on aluminum rotors, which in turn will concentrate stress and eventually result in cracks and total rotor failure. Titanium rotors are more corrosion resistant, but more expensive. Ultracentrifuge rotors are expensive (in excess of $6,000 each on average) and can be potentially hazardous. At the forces generated in an ultracentrifuge, a rotor failure is the equivalent of a small bomb.

THEREFORE THE FOLLOWING RULES MUST BE OBSERVED.

1. Before running a centrifuge, check the classification decal on the centrifuge to ensure that the rotor is safe to use in the centrifuge at hand.

   
   

2. Never use an alkali detergent on a rotor (most are highly alkaline - be sure to check before use).

   
   

3. Always clean and completely dry the rotor after every use. Any spilled materials, especially salts and corrosive solvents must be removed immediately with running water. Fixed angle rotors are stored upside down, to drain after thorough cleaning and rinsing. Swinging buckets have only the buckets cleaned and dried, and stored inverted and with the caps removed. NEVER immerse the rotor portion of a swinging bucket rotor. Inevitably the linkage pins will rust, as it is virtually impossible to remove all fluids from them.

   
   

4. Be especially careful not to scratch the surface of a rotor or bucket. Use plastic brushes only. Normal wire brushes will scratch the anodized surface of aluminum rotors which will increase the likelihood of corrosion. The anodized layer is extremely thin and is the main defense against corrosion of an aluminum rotor.

   
   

5. Always use the proper centrifuge tube. Glass tubes are used in clinical centrifuges only. High Speed Corex tubes can be used up to 15,000 RPM (in SS34 rotor) IF there are no scratches or imperfections in the glass, and if the proper rubber or plastic adapter is employed. All ultracentrifugation use employs nitrocellulose or polyallomer tubes. Nitrocellulose ages and will collapse in a strong centrifugal field if old.

   
   

6. Always fill the centrifuge tubes to the proper level. (usually full to within 1/2 inch of the top). The tubes are thin walled and will collapse if improperly filled.

   
   

7. Always balance the rotor properly. Use a precision scale for most work. Always balance the tube with a medium that is identical to that being centrifuged, i.e. do not balance an alcohol solution with water, or a dense sucrose solution with water only -- the distribution of the densities will be incorrect. For swinging buckets, be sure the buckets are weighed with their caps in place, that the seals are intact and that the caps are secure. Be careful in the placement of tubes within a rotor to ensure proper balance - check the manufacturers guides for complex rotors that hold multiple tubes.

   
   

8. Ensure that the rotor is properly seated within the centrifuge. For swinging buckets, ensure that they are hanging properly - Double or Triple check! For preparative rotors, be sure the rotor cover is in place and properly screwed down, where appropriate. NEVER use a rotor without its lid, when one is supplied - the screw actually holds the rotor to the motor shaft.

   
   

9. Check that the centrifuge chamber is clean, defrosted and that all membranes or measuring devices are intact and functional (Beckman speed and temperature controls) and that the lid is securely closed.

   
   

10. Adjust acceleration rates, deceleration rates, temperature and RPM controls as appropriate. Set brake on or off as appropriate and check vacuum level where appropriate.

    
    

11. Start the centrifuge and set the timer. Do not attempt to open the centrifuge until the rotor has come to a complete stop.

    
    

12. Before opening the centrifuge, record the appropriate information in the centrifuge log.

Note: If properly balanced and used, the rotor should accelerate smoothly and with a constant change in the pitch of the motor sound. Any vibrations, or unusual sounds should cause the cessation of operation IMMEDIATELY by the operator. NEVER leave the centrifuge until you are certain that it has reached its operating speed and is functioning properly. All rotors go through a minor vibration phase when they first start. There will be a minor flutter when the rotor reaches this vibration point - do not confuse this with a serious vibration caused by imbalance. If in doubt, halt the centrifuge and get assistance.