DOI: 10.1007/s00340-007-2595-9 Appl. Phys. B 87, 355–362 (2007) Lasers and Optics Applied Physics B j.h. rohling 1 j. shen 1, ✉ c. wang 2 j. zhou 1 c.e. gu 1 Determination of binary diffusion coefficients of gases using photothermal deflection technique 1 National Research Council of Canada, Institute for Fuel Cell Innovation, 4250 Wesbrook, Vancouver, British Columbia V6T 1W5, Canada 2 Institute of Modern Optical Technologies, Suzhou University, Suzhou, Jiangsu 215006, P.R. China Received: 25 September 2006/ Revised version: 22 January 2007 Published online: 24 March 2007 • © Springer-Verlag 2007 ABSTRACT A photothermal deflection (PD) technique was ap- plied to measure the binary diffusion coefficients of various gases (CO 2 –N 2 , CO 2 –O 2 ,N 2 –He, O 2 –He, and CO 2 –He). With an in-house-made Loschmidt diffusion cell, a transverse PD system was employed to measure the time-resolved PD signal associated with the variation of the thermal diffusivity and the temperature coefficient of the refractive index of the gas mix- ture during the diffusion. The concentration evolution of the gas mixture was deduced from the PD amplitude and phase signals based on our diffraction PD model and was processed using two mass-diffusion models explored in this work for both short- and long-time diffusions to find the diffusion coefficient. An optical fiber oxygen sensor was also used to measure the con- centration changes of the mixtures with oxygen. Experimental results demonstrated that the binary diffusion coefficients pre- cisely measured with the PD technique were in agreement with the literature values. Moreover, the PD technique can meas- ure the diffusion coefficients of various gas mixtures with both short- and long-time diffusions. In contrast, the oxygen sensor is only suitable for the long-time diffusion measurements of the gas mixtures with oxygen. PACS 78.20.Nv; 51.20.+d 1 Introduction Photothermal techniques are measurement schemes that monitor the thermal effects of incident radia- tion [1, 2]. While processes such as photochemical transform- ation and reemission of radiation may compete for a share of the excitation energy, a portion of the incident energy is converted into heat in the illuminated substance by a nonradia- tive deexcitation process. The heating can cause a number of different effects, which provide the detection mechanisms, in- cluding temperature rise, surface deformation, infrared emis- sion, and gradients of optical refractive index. Photothermal deflection (PD) techniques measure the in- fluence of the temperature change on the optical refractive index of the medium in contact with an illuminated solid sub- stance (solid sample) or on the optical refractive index of the ✉ Fax: +1-604-221-3001, E-mail: jun.shen@nrc.gc.ca solid sample itself. For instance, in a transverse PD scheme, a gradient of the optical refractive index (mirage region) in the medium is induced by a temperature gradient from the sam- ple surface to the medium, due to the absorbed excitation laser energy by the solid sample. A Gaussian probe beam, parallel to the solid sample with a distance x between the solid sam- ple surface and the probe-beam axis, probes the gradient of the optical refractive index in the medium, resulting in the deflec- tion and the diffraction of the probe beam [3]. Henceforth, the medium is named a deflecting medium. Since the first reported work in 1980 [4], the PD tech- niques have been widely employed for nondestructive char- acterization of solid materials, because of the high sensitivity, versatility, and remote (noncontact to its detection system) na- ture of the PD techniques [1–3, 5–9]. The deflection of the probe beam is not only sensitive to the optical and thermo- physical properties of the solid sample, but also dependent on these properties of the deflecting medium. As a result, the PD techniques have also been employed in the study of gases as deflecting media in PD experiments, such as trace-gas de- tection [10], in situ environmental monitoring and chemical analysis [11], species-selective detection in gas chromatog- raphy [12], the observations of laser cooling by resonant energy transfer in CO 2 –N 2 mixtures [13], and the measure- ments of the thermal diffusivities of gases and binary gas mix- tures [14–16]. After a precise determination of the distance x between the solid sample and the probe beam in a transverse PD experimental setup, we recently measured the values of the thermal diffusivity α g and the temperature coefficient of the refractive index d n/ d T of three pure gases (O 2 , N 2 , and CO 2 ). We also investigated the dependence of α g and d n/ d T of a binary gas mixture, i.e. CO 2 –N 2 or CO 2 –O 2 , on the gas concentration of O 2 or N 2 [16]. We found that the values of α g and d n/ d T changing with concentration could be explained by thermodynamic theory and the Lorentz–Lorenz formula, respectively. Therefore, the PD amplitude and phase signals could be expressed in terms of the composition of the binary gas mixture. This concentration dependence might be used for the real-time monitoring of the gas concentration in a bi- nary gas mixture for various applications. One of the possible applications could be the determination of a binary diffusion coefficient of a gas. Reliable data on binary diffusion coefficients of gases is of great interest for engineering, environmental, and theoret- ical applications [17–20]. For example, a gas diffusion layer