ACCURATE MEASUREMENT OF THE STICKING TIME AND STICKING PROBABILITY OF Rb ATOMS ON A POLYDIMETHYLSILOXANE COATING
S. N. Atutov* A. I. Plekhanov
Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences
630090, Novosibirsk, Russia
Novosibirsk State University 630090, Novosibirsk, Russia
Received June 14, 2014
We present the results of a systematic study of Knudsen's flow of Rb atoms in cylindrical capillary cells coated with a polydimethylsiloxane (PDMS) compound. The purpose of the investigation is to determine the characterization of the coating in terms of the sticking probability and sticking time of Rb on the two types of coating of high and medium viscosities. We report the measurement of the sticking probability of an Rb atom to the coating equal to 4.3 • lCT', which corresponds to the number of bounces 2.3 • 104 at room temperature. These parameters are the same for the two kinds of PDMS used. We find that at room temperature, the respective sticking times for high-viscosity and medium-viscosity PDMS are 22 ± 3 ps and 49 ± 6 ps. These sticking times are about million times larger than the sticking time derived from the surface Rb atom adsorption energy and temperature of the coating. A tentative explanation of this surprising result is proposed based on the bulk diffusion of the atoms that collide with the surface and penetrate inside the coating. The results can be important in many resonance cell experiments, such as the efficient magneto-optical trapping of rare elements or radioactive isotopes and in experiments on the light-induced drift effect.
The major technical difficulty in many resonance cell experiments, such as cooling and trapping shortlived radioactive isotopes using a magneto-optical trap (MOT) fl 10] or experiments on light-induced drift (LID) fll 19], lies in the atomic vapor interaction with the inner wall of the resonance cell.
Since short-lived radioactive isotopes are available only in limited quantities, an efficient optical trapping process is of great importance to the possibility to create large samples of these elements. In this kind of experiment, atoms that are injected into the cell stick to the wall of the cell due to physical adsorption for a period of a characteristic sticking (dwell) time and return to the vapor. Obviously, to ensure efficient trapping of these short-lived radioactive isotopes, the sticking time of the atoms to the cell wall must be shorter than
their radioactive lifetime. Low trapping efficiency can also be attributed to a large loss through high chemical sorption, when the atoms react chemically with the wall and are irreversibly removed from the vapor.
The interaction of the vapor with a cell wall is also a serious problem in experiments on the LID effect. In this kind of experiment, resonance atoms can be pushed or pulled either inside or outside a capillary-cell by light. When the atoms inside the capillary are pushed by light, they stick to the wall as soon they arrive. When the dwell time is long, the fraction of the incoming atoms absorbed to the wall is much higher than in the vapor phase. As a result, it takes far too long time to saturate the wall with a relatively weak flux of incoming atoms that are pushed by light. The opposite is also true: when the atoms are pulled out of the saturated capillary by light, it takes a rather long time to clean the adsorbed atoms off the wall by pulling them out of the capillary using LID. Thus, the long sticking time leads to long time to achieve a steady-state distribution of atoms in the cell. This masks the manifestation of the LID effect to a considerable extent.
Table 1. The results of the measurements of the adsorption energy and sticking time for lib
Surface materials E, eV Ts, s Reference
Paraffin coated pyrex 0.1 4-10-10 
Paraffin coated pyrex - (1.8 ±0.2) • 10-® 
Tetracontane coated glass 0.06 lo-11 
Tetracontane coated pyrex 0.062 lo-11 
Oct adecy It richlorosilane coated pyrex (T = 103 °C) 0.19 ±0.03 (0.53 ±0.03) • 10-® 
Oct adecy It richlorosilane coated pyrex (T = 72 °C) - (0.9 ±0.1) • 10-® 
It is known that as atoms collide with the surface, they undergo an attractive potential whose range depends on the electronic and atomic structures of both the surface and the atoms. Therefore, a fraction of the atoms is physadsorbed in the attractive potential well at the surface. It is generally assumed that physical adsorption is characterized by an adsorption energy E that determines the sticking time
where to ~ 10-12 s is the period of vibration of the adsorbed atom in the wall potential, k is the Boltzmann constant, and T is the absolute temperature .
Presently, many publications are dealing with studies of different sorts of nonstick coatings with a view to minimize the sticking time. Wieman et al. performed the first direct measurement of the sticking time of Cs with a dry-film coating on Pyrex to make an efficient atom collection in vapor cell magneto-optical traps. In the experiment, adsorption energy of (0.40 ± 0.03 eV) and sticking time with the upper limit of 35 //s were measured . The results of the measurements of the adsorption energy and sticking time for Rb achieved by-other authors are summarized in Table 1.
The work described in this article is focused on measuring the sticking probability and sticking time of Rb atoms on a film made of a polydimethylsilox-ane (PDMS) compound. We measured these quantities using Knudsen's flow of Rb atoms in capillary-cells. We demonstrate in what follows that the proposed method is simple and allows accurately measuring both the sticking probability and the sticking time. We use cells with a capillary coated with two different types of PDMS coatings of different viscosities. The experimental studies are preceded by a discussion of a
model of atoms in Knudsen's flow in a capillary and by a definition of the relevant parameters. We note that the developed method can be effectively used for the study of many others atoms and molecules on a wide class of coatings.
2. EXPERIMENTAL SETUP
A sketch of the setup is shown in Fig. 1.
The Rb vapor density was measured through the detection of the intensity of atomic fluorescence by a fast, movable photodiode connected to a data acquisition (DAQ) system. The fluorescence was excited by a free-running diode laser with the frequency tuned to an Rb atom resonant transition of 780 11111. The fluorescent signals were processed by a digital oscilloscope connected to a computer. The DAQ system allows collecting data with a 0.1 ms resolution in time as well as measuring the variation in the Rb vapor over a wide range. The temperature of the cell walls was measured by a digital thermometer. The absolute Rb vapor density at the origin of the capillary and the Rb source is estimated from the temperature of the of Rb metal drop .
In the experiment, we used two groups of three glass capillaries with diameters of 16 mm, 5 mm, and 2 mm in each group. The inner surface of the cell area close to the Rb source and one group of three capillaries were covered by a nonstick coating prepared from a 3 % solution of commercial polydimethylsiloxane (PDMS, M,,,.92.400, 11000 mm-2 -s-1 viscosity) in ether. Three more capillaries were coated with a different compound (PDMS, M,,,..182.600, 410000 mm"2-s"1 viscosity). We call the first type of PDMS with a medium viscosity, the mvPDMS, and the second type with a higher viscosity, the hvPDMS. Both types of PDMS were bought from
Fig. 1. Experimental setup: 1 — laser; 2 — turbo pump; 3 — cell; photodiode; 7—data acquisition system (DAQ); S, 9 — gauges; 10 —
4 — source of lib vapor; 5 - photographic flash lamp; 11 -
- glass capillary; 6 -■ source of Na vapor
the Aldrich Chemical Company Inc. The cell preparation is described, for example, in Ref. . The chosen capillary is held inside the cell by two aluminum perforated disks, which allow the whole cell to be easily-pumped but, because of the absence of the coating between these disks, prevent any penetration of the des-orbed atoms around the capillary.
The turbo pump provides a vacuum of up to 10~' mbar in the cell. The rest gas pressure is measured by two vacuum gauges: one attached to the cell area close to the Rb source and the vacuum pump, and the other attached to the entrance of the cell where the probe laser beam enters the cell. We assume that a steady-state vacuum is obtained when both gauge readings are stable and the gauge that is kept away from the pump shows a bit less vacuum than that near the Rb source and the vacuum pump. The steady-state level of the vacuum in a cell with any capillaries inside is usually reached after one week of continuous pumping. This was verified by an RF discharge switched on inside the capillary. The RF voltage is then applied to two gauges that are disconnected from their monitors. The indicator that the steady-state vacuum is achieved is that the discharge luminescence is weak, stable, and uniform along the length of the capillary.
3. THEORETICAL CONSIDERATIONS
We consider the diffusion of atoms in the evacuated capillary in detail and assume that the atoms collide
with the wall only. These atoms move from the initial position along the distance
(a one-dimensional shift along the capillary axis). The mean quadratic shift is
= N(z?) = -u2
where t is time, and u2 and r are the mean quadratic elementary shift and the mean elementary time between two collisions. On the other hand, we know that
<c2) = 2 Dt. (4)
where D is the diffusion coefficient, and we can write
The time r between two collisions consists of the time needed by the atoms to fly between the walls (the mean pass time 17) and the sticking time rs:
T = Tf + Ts. (6)
Therefore, the diffusion coefficient D can be written as D=(7)
Tf + Ts
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