Cold ion–polar-molecule reactions studied with a combined Stark-velocity-filter–ion-trap apparatus

We have developed a combined Stark-velocity-filter–ion-trap apparatus for the purpose of reaction-rate measurements between cold trapped ions and slow polar molecules under ultrahigh vacuum conditions. The prerequisite steps such as the characterization of velocity-selected polar molecules (PM), namely ND${}_3$, H${}_2$CO, and CH${}_3$CN, were performed using time-of-flight (TOF) measurements. We confirmed the generation of slow ND${}_3$, H${}_2$CO, and CH${}_3$CN molecules having thermal energies of a few Kelvin. Additionally, the number densities of the slow velocity-filtered polar molecules were determined to be in the range of $n={10}^4$ to 10${}^6$ cm${}^{-3}$ by calibrating the TOF signals. In a first experiment, the Stark velocity filter was connected to a cryogenic linear Paul trap and reaction-rate measurements between laser-cooled Ca${}^{+}$ Coulomb crystals and velocity-selected polar molecules were carried out. The observed reaction rates are of the order of 10${}^{-5}$ s${}^{-1}$, which are much slower than typical reaction rates of molecular ion–polar-molecule reactions at low temperatures. The present results confirm that reaction-rate measurements between velocity-selected polar molecules and sympathetically cooled molecular ions cooled by a laser-cooled Ca${}^{+}$ Coulomb crystal can be performed. Next we measured the reaction rates between sympathetically cooled nonfluorescent stored ion molecules namely N${}_2$H${}^{+}$ ions and velocity-selected CH${}_3$CN molecules at the average reaction energy of about 3 K. The measured reaction rate of 2.0(2)$\times$10${}^{-3}$ s${}^{-1}$ is much faster than those of the Ca${}^{+}$+PM reactions. This is strong evidence that the velocity-selected polar molecules undergo reactive collisions. We also confirmed that the present reaction-rate constant of CH${}_3$CN+N${}_2$H${}^{+}$ $\to$ CH${}_3$CNH${}^{+}$+N${}_2$ is consistent with the estimated values from the room temperature results and the trajectory-scaling formula of Su et al. In the future, the present velocity-filter combined cryogenic trap apparatus will enable us to perform systematic measurements of cold ion–polar-molecule reactions, which are important problems from a fundamental viewpoint and also contribute to astrochemistry.

Figure 1

(a) Schematic drawing of the experimental setup. (b) A photograph of the vacuum chamber enclosing the Stark velocity filter. The vacuum chamber is made of aluminum alloy and is divided into two chambers to establish a differential pumped system. (c) Details of the gas nozzle assembly. The nozzle with a diameter of 1.5 mm is made of a ceramic material to avoid a discharge between the nozzle and the quadrupole electrodes. For thermalization of an introduced polar gas, the stainless steel pipe with a 3 mm diameter is plugged in a copper block, which is thermally contacted to the cold head of the 10 K cryocooler. A silicon-diode sensor is mounted on the nozzle to monitor the gas-nozzle temperature. (d) A photograph of a detection vacuum chamber containing a cryogenic linear Paul trap.

Figure 2

(a) Time-of-flight (TOF) signals of guided polar molecules at different guiding voltages. The solid lines show the fitted curve of the Gompertz function to the experimental data points. (b) The velocity distributions derived from the TOF signals. The representative errors are shown at the peak positions. In these experiments, room temperature polar gases were introduced. The nozzle pressures of CH${}_3$CN, ND${}_3$ and H${}_2$CO are set to 32, 40, and 41 mTorr, respectively.

Figure 3

(a) The TOF signals of the velocity-selected ND${}_3$ molecules measured at the different nozzle temperatures of 295 and 236 K. The guiding voltages and the nozzle pressure are $\pm$3.0 kV and 41 mTorr, respectively. (b) A plot of the integrated intensity ratio $I\left(T\right)/I\left(295\mathrm{K}\right)$ of slow velocity components in the Maxwell-Boltzmann velocity distribution as a function of temperature. $I\left(T\right)$ is obtained by integrating the velocity distribution from $v=$ 0 to 150 m/s.

Figure 4

(a) Nozzle pressure dependence of the guided ND${}_3$ signal intensity measured by the TOF method. In this experiment, the guiding voltages of $V_G=\pm 2.4$ kV are applied. The nozzle temperature is set to 251 K. The error bar of each point is within the mark. (b) A plot of the peak velocity as a function of nozzle pressure. The peak velocity gradually increases with increasing the pressure.

Figure 5

(a) Examples of correlation plots for the number density ($n$) of polar molecules as a function of the ion-count signal ($I_{\mathrm{QMS}}$) detected by the quadrupole mass spectrometer (QMS). The position of the ring filament in the ionization cage of the QMS was adjusted to 33 mm as measured from the beam-guide exit, which corresponds to the distance from the center of the linear Paul trap. We repeated the same measurement six to ten times in order to obtain the conversion factors from $I_{\mathrm{QMS}}$ to $n$ (see the text). (b) A plot of the number density of the velocity-selected polar molecules as a function of the guiding voltage. The data points are calculated by Eq. (2) and the solid curve is the fitted function which is proportional to $|V_G{|}^2$ [10].

Figure 6

(a) The geometry of the quadrupole beam guide for the Monte Carlo simulation. The polar molecules randomly enter into the beam guide from the bottom ($x=-30,z=12.5$). The initial positions of molecules within the diameter of 1.0 mm on the $yz$ plane are determined by generating uniform random numbers. The initial velocities were randomly set according to the Maxwell-Boltzmann distribution at a given temperature. (b) An enlarged view of the first bent section of the beam guide for the simulation. The radius of the curvature is $R=12.5$ mm. The electric potential on the $y^{\prime }{z}^{\prime }$ plane at an angle $\theta$ is expressed by $\varphi (x,y,z)=V_G\{{(z^{\prime }-R)}^2-y^{\prime 2}\}/r_0^2$, where $y^{\prime }=-z\sin \theta +x\cos \theta$, $z^{\prime }=z\cos \theta +x\sin \theta$.

Figure 7

Results of the Monte Carlo simulation of the velocity-selected CH${}_3$CN. The maximum rotational levels considered is $J_{\max }=50$, and the trial number of the input molecules is 4 $\times$ 10${}^3$ for each rotational level of $|J,K,M\rangle$, where $J$, $K$, and $M$ are rotational quantum number, quantum number of component of angular momentum along molecular axis, and projection of $\mathbf{J}$ on the fixed axis, respectively. The temperature of the polar gas source is assumed to be 295 K. (a) The longitudinal velocity ($v_z$) distribution at the center of the ion trap. The dashed line shows the experimental result at $V_G=\pm 3.0$ kV, which is displayed in Fig. 2b. The solid line is the result of the least-square fit of the one-dimensional thermal velocity distribution function to the simulation result. The most probable velocity of the fitted function is 51(1) m/s. The peak velocity is good agreement with the experimental result. (b) Simulated transverse velocity distribution. The solid curve shows the fitted Gaussian function to the simulated data points. The most probable velocity is 8.5(0.2) m/s, which corresponds to the thermal energy of 178(8) mK. (c) The rotational $J$-state distribution of velocity-selected CH${}_3$CN. (d) Rotational energy distributions of the velocity-selected CH${}_3$CN and the source gas. In the spectrum of the velocity-selected CH${}_3$CN, the population of the lower energy part is relatively high in comparison to that of the room temperature gas.

Figure 8

Numerically calculated normalized geometric factor $\alpha =\kappa \left(z_i\right)/{\kappa }_0$ near the beam-guide exit. At $z=0$ mm the beam guide is terminated. The solid curve represents the fitted function of Eq. (5) to the calculated points, where we divided two regions of $-2\le z\le 0.17$ mm and $0.17\le z\le 5$ mm for the least-square fitting.

Figure 9

Schematics of the geometry of the beam-guide exit and the ion trap, and the simulation images of velocity-selected CH${}_3$CN molecules near the ion trap center. The simulation parameters are the same as Fig. 7.

Figure 10

A plot of the integrated intensity of the CH${}_3$CN molecules within a 2 mm $\times$ 1 mm square at the center as a function of the distance $L$ between the beam-guide exit and the detection plane. The trap center is designed to at $L=33$ mm and the expected uncertainty is $\pm 1$ mm. The error of the number density of the velocity-selected CH${}_3$CN by the beam-divergence effect was estimated to be 10$\%$.

Figure 11

Energy diagrams of (a) Ca${}^{+}$-CH${}_3$CN and (b) Ca${}^{+}$-ND${}_3$ reaction systems calculated by the quantum chemical calculation packages (gaussian 03) [26]. The geometry optimization of molecular ions and calculations of zero-point energies were performed by B3LYP/6-31G(d). The ground-state energies were calculated using B3LYP/6-311+(3${df}$ , 3${pd}$ ) in the optimized geometries. The excited state energy of the association product ion was calculated by the CI-Singles method for the optimized geometry.

Figure 12

Examples of the reaction-rate measurements between a Ca${}^{+}$ Coulomb crystal and the velocity-selected polar molecules (CH${}_3$CN and ND${}_3$). The average collision energy of these measurements is estimated to be lower than 10 K. This is indicated by both the results of the velocity distributions of the polar molecules and the molecular dynamics simulation of the Ca${}^{+}$ Coulomb crystals [14, 15]. The graphs show a plot of the relative number of Ca${}^{+}$ ions in the Coulomb crystal, which was determined by the size of the observed fluorescence image shown in the left part. (a) A result of the decay rate measurement in a large Ca${}^{+}$ Coulomb crystal without the velocity-selected polar molecules at a vacuum of 10${}^{-8}$ Pa. The ion-molecule reactions between the background H${}_2$ molecules and the laser-excited Ca${}^{+}$(${}^2{P}_{1/2}$) ions cause the slow decay of the number of Ca${}^{+}$ ions [25]. (b) A plot of the relative number of the Ca${}^{+}$ in a small crystal as a function of time when irradiating with velocity-selected CH${}_3$CN molecules. The guiding voltage is set to $\pm$3 kV and the nozzle pressure is 32 mTorr at room temperature. (c) A plot of the relative number of the Ca${}^{+}$ as a function of time when irradiating with velocity-selected ND${}_3$ molecules. The guiding voltage is set to $\pm$3 kV and the nozzle pressure is 40 mTorr at room temperature.

Figure 13

Energy diagram of the N${}_2$H${}^{+}$-CH${}_3$CN reaction system calculated by the same method in Fig. 11. The only the exothermic reaction path is proton-transfer reaction, that is, CH${}_3$CN+N${}_2$H${}^{+}$ $\to$ CH${}_3$CNH${}^{+}$+N${}_2$. Although there are other possible endothermic paths, only the lowest endothermic path is depicted.

Figure 14

The production process of cold N${}_2$H${}^{+}$ ions. (a) Initial state of a Ca${}^{+}$ Coulomb crystal. The number of Ca${}^{+}$ is estimated to be about 4 $\times$ 10${}^3$. A nitrogen molecular gas of about 1 $\times$ 10${}^{-7}$ Pa is introduced into the vacuum chamber and the electron beam is incident to the ion trap in order to produce nitrogen molecular ions by electron impact ionization. The electron beam energy is set to 250 eV. (b) A two-species Coulomb crystal containing Ca${}^{+}$ and N${}_2^{+}$ ions. (c) The LIF image of the two-species Coulomb crystal during the production process of N${}_2$H${}^{+}$ ions. A hydrogen molecular gas of about 6 $\times$ 10${}^{-6}$ Pa is introduced into the vacuum chamber. The ion molecule reactions of N${}_2^{+}$+H${}_2$ $\to$ N${}_2$H${}^{+}$+H necessarily produce cold N${}_2$H${}^{+}$ ions [30]. The image of the two-species Coulomb crystal becomes smeared out because the H${}_2$ collisions heat the Ca${}^{+}$ ions. (d) The final state of the N${}_2$H${}^{+}$ production process is reached after four minutes. No significant loss of the molecular ions was observed for this time period.

Figure 15

Sequential LIF images of the two-species Coulomb crystal containing Ca${}^{+}$ and N${}_2$H${}^{+}$ during CH${}_3$CN+N${}_2$H${}^{+}$ $\to$ CH${}_3$CNH${}^{+}$+N${}_2$ reactions. The dark area progressively decreases with increasing reaction time. This means that the cold ion-molecule reaction proceeded. As the reactions proceed, the sparse dark area due to the product ions also appears in the outer peripheral region of the Ca${}^{+}$ Coulomb crystal.

Figure 16

(a) Simulation images of two-species Coulomb crystal containing 4000 Ca${}^{+}$ ions and several hundred of N${}_2$H${}^{+}$ ions. The dark area of the Ca${}^{+}$ Coulomb crystal is caused by the existence of sympathetically cooled N${}_2$H${}^{+}$ ions. The simulation method is explained in Refs. [14, 15]. The temperature of the virtual light atoms for cooling of Ca${}^{+}$ is set to 10 mK and the other trapping parameters are set to the same values as the present experimental conditions. (b) A plot of the calculated volume of the dark area as a function of the number of N${}_2$H${}^{+}$ ions. Each data point is obtained by the square of the averaged horizontal width of the dark area in the simulation images. The error is estimated by the uncertainty of the horizontal width of dark area. The correlation coefficient $r$ is about 0.98. A good correlation is obtained between the volumes and the number of N${}_2$H${}^{+}$ ions at least in this range.

Figure 17

A plot of the relative number of N${}_2$H${}^{+}$ ions as a function of the reaction time in CH${}_3$CN+N${}_2$H${}^{+}$ $\to$ CH${}_3$CNH${}^{+}$+N${}_2$. The average reaction energy is estimated to be about 3 K.