Some Interesting Facts About Vacuum Pumps and Rate of Evacuation

Wilbur C. Bigelow Materials Engineering , 2911 Whittier Court , University of Michigan , Ann Arbor , MI 48109-2136 *

Abstract: Two important characteristics of a vacuum system, insofar as the user is concerned, are the rate at which it pumps down to an operating vacuum and the ultimate vacuum attainable. This article reviews the interplay of various factors, such as pump design, system design, and system cleanliness, that determine these characteristics. Pumping speeds and ultimate attainable pressures are discussed for oil diffusion, turbomolecular, and ion pumps.

Introduction While recently going through my fi les, I came across an article

I wrote for Microscopy Today several years ago describing how the desorption of water molecules from surfaces inside a vacuum system is the major factor causing it to take such long times to pump down to an operating vacuum [ 1 ]. Upon re-reading this article it occurred to me that it did not describe some fundamental aspects of the speed of evacuation that also might be of interest to readers of Microscopy Today. Hence, the present article.

The Atmosphere

To begin with, it will be useful to review some character- istics of our atmosphere, the gas most prominently involved in evacuation processes. T e kinetic molecular theor y combined two classical laws, Boyle’s Law and Charles’s Law, to produce the Ideal Gas Equation as follows:


where n is the number of moles (one mole = 6.023 × 10 23 molecules) of gas contained in a volume V (liters) at a pressure P (Pascal) and at a temperature T (Kelvin) (K = °C + 273). T e constant R has a value of 8314.4 (or 62.36 for pressures in Torr). Using this equation it is possible to calculate the number of gas molecules in a unit volume, N, a very interesting and important property of our atmosphere. T e result for the atmosphere at ambient temperature (298 K = 25°C = 77°F) is


(the constant becomes 3.2 × 10 19 for pressure in Torr). T e order of magnitude in Equation 2 indicates that the number is very large. To emphasize this more strongly, Table 1 lists the values for the number of air molecules per cubic centimeter (not a very large volume) for a range of pressures. At atmospheric pressure (10 5 Pa) there are twenty-fi ve billion-billion molecules in each cubic centimeter. At 10 -6 Pa, the bottom of the high vacuum range, there are two hundred and fi ſt y million molecules per cc, and even at 10 -8 Pa, which is well into the ultra-high vacuum range and about the best vacuum attainable in modern electron microscopes, there are still more than two million molecules per cc. So you can pump as long and as hard as you wish, but never get down to a really insignifi cant concentration of air molecules in your vacuum system.


at ambient temperature. T is is a rather interesting result, for contrary to what one might intuitively expect, the pressure cancels out. Whereas the data in Table 1 show that the number of gas molecules striking a unit area per unit time is a linear function of pressure, these calculations show that the volume of gas molecules doing so is independent of pressure. T e pumping speed of the pump serving a given vacuum system is a primary factor determining the speed of evacuation and the time required to achieve an operating vacuum. Now it is useful to remember that vacuum pumps do not suck, pull, draw, or attract gas molecules out of a vacuum system. Instead, they capture (as best they can) the gas molecules that wander into their inlet ports, under their own thermally activated motion, and return them to the surrounding atmosphere. Since the maximum number of molecules that can enter the inlet

doi: 10.1017/S1551929517000591 • 2017 July

T e kinetic molecular theory yields another very interesting and important equation, this time giving the number of molecules striking a unit area of surface at various values of temperature and pressure. For air at ambient temperature and diff erent pressures (Pa), the equation simplifi es to


(the constant becomes 3.8 × 10 18 for pressures in Torr). T e numbers here are truly staggering. Each second every square millimeter of our bodies is being bombarded by nearly three thousand-billion-billion air molecules (and we are totally unaware of it). At 10 -6 Pa each square millimeter of surface inside a vacuum system is struck by nearly thirty billion molecules per second, and the number is still a substantial three hundred million at 10 -8 Pa. Air molecules are almost unimag- inably small and incredibly numerous.

The Theoretical Maximum Pumping Speed In addition to providing this interesting insight into the properties of our atmosphere, Equation 3 can be used to calculate the theoretical maximum pumping speed that a vacuum pump can develop. To aid in doing this, suppose there is a material that might be called molecular quicksand that captures every molecule that strikes it with 100 percent effi ciency. T en according to this equation the number of gas molecules captured each second by a bed of this material with an area of A square millimeters will be N cap = A (2.8 × 10 16 P ). Dividing by Avogadro’s number ( N A = 6.023 × 10 23 molecules per mole) will give the number of moles of gas captured per second n cap = (4.7 × 10 -8 ) AP . T en using the ideal gas equation, the volume captured per second is found to be


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