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Vacuum Pumps

Figure 1 : Schematic diagram of a Varian VHS oil diffusion pump.

be essentially the same as the speed of the pump. However, as is oſt en the case, when the pump is connected to the vacuum chamber through a manifold, which may consist of a length of tubing, a valve, and possibly a liquid nitrogen trap, then these components tend to impede the fl ow of gas from the chamber to the pump and tend to reduce the speed of evacuation to a value considerably less than the speed of the pump. T e ease with which gas molecules can fl ow through such components is called their conductance (the reciprocal of their impedance). For tubes with a circular cross section, the conductance can be calculated with suffi cient accuracy for the present purpose using the equation

(7)

where D is the tube diameter in millimeters and L is its length in meters. [T is equation becomes C tube = 78 D 3 / (12 L + 1.33 D ) if D is measured in inches and L in feet.] T us, a tube one meter long and 100 millimeters in diameter would have a conductance of a little more than 100 liters per second. Conductance values for valves, traps, and other components of pumping lines are more diffi cult to calculate but are usually furnished by their manufacturers. Well-designed valves usually do not impede the fl ow of gas appreciably, but traps and baffl es do. T e important point here is that the conductance C of the pumping line between the vacuum chamber and the pump can cause a very serious reduction in the speed of evacuation S evac :

(8) second.

where all quantities are expressed in units of liters per Figure 3 is a plot based on this equation, which shows

the strong eff ect that the conductance of the line between the pump and the vacuum chamber has in reducing the speed of evacuation below that of the pump. For example, if the conduc- tance of the pumping line is one-half the speed of the pump ( C/S p = 0.5), the speed of evacuation will be only about one-third

2017 July • www.microscopy-today.com

Figure 2 : Variation of pumping speed with pressure for different types of high-vacuum pumps 200 mm (8”) in diameter.

31

the speed of the pump ( S e /S p ~ 0.3). If the conductance equals the speed of the pump, the speed of evacuation will be half the speed of the pump. Even if the conductance could be three times the speed of the pump, the speed of evacuation would still be only three-quarters that of the pump. For example, if a 160 mm (6”) turbomolecular pump with a rated speed of 500 liters per second is attached to a vacuum chamber through a valve of negligible impedance and a one-meter length of 160 mm diameter tubing ( C = 407 l/s, C/S p = 0.8), the speed of evacuation will be a little less than one-half the speed of the pump or about 225 l/s. If the length of the tubing is reduced to one-half meter ( C = 695 l/s, C/S p = 1.4) the speed of evacuation will increase to about six-tenths the speed of the pump, or about 300 liters per second. A further reduction in the length of the pumping line will produce a further increase in speed of evacuation, and mounting the pump directly onto the vacuum chamber (again, through a well-designed valve) will increase the speed of evacuation to essentially that of the pump.

How Big Should the Pump Be? Now the question oſt en arises as to just how large of a pump a vacuum system should have. T e answer is quite interesting, although somewhat complicated and diffi cult to specify exactly. Consider a bell jar 18” (460 mm) in diameter and 30” (760 mm) high, about the largest size commonly available, whose volume would be about 125 liters. Also assume the evacuation system consists of a ridiculously small oil diff usion pump with a diameter of 63 mm and a rated speed of 150 l/sec that is connected to this bell jar through a valve and a tube 63 mm in diameter and one-half meter long ( C = 52 l / sec). As shown in Figure 2 , oil diff usion pumps start to make signifi cant contri- bution to the evacuation process when the roughing pump reduces the pressure in the system P s to about one Pascal. At

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