Schmid Michael, Parkinson Gareth S, Diebold Ulrike
Institute of Applied Physics, TU Wien, 1040Vienna, Austria.
ACS Phys Chem Au. 2022 Nov 15;3(1):44-62. doi: 10.1021/acsphyschemau.2c00031. eCollection 2023 Jan 25.
Temperature-programmed desorption (TPD) experiments in surface science are usually analyzed using the Polanyi-Wigner equation and/or transition-state theory. These methods are far from straightforward, and the determination of the pre-exponential factor is often problematic. We present a different method based on equilibrium thermodynamics, which builds on an approach previously used for TPD by Kreuzer et al. ( ). Equations for the desorption rate are presented for three different types of surface-adsorbate interactions: (i) a 2D ideal hard-sphere gas with a negligible diffusion barrier, (ii) an ideal lattice gas, that is, fixed adsorption sites without interaction between the adsorbates, and (iii) a lattice gas with a distribution of (site-dependent) adsorption energies. We show that the coverage dependence of the sticking coefficient for adsorption at the desorption temperature determines whether the desorption process can be described by first- or second-order kinetics. The sticking coefficient at the desorption temperature must also be known for a quantitative determination of the adsorption energy, but it has a rather weak influence (like the pre-exponential factor in a traditional TPD analysis). Quantitative analysis is also influenced by the vibrational contributions to the energy and entropy. For the case of a single adsorption energy, we provide equations to directly convert peak temperatures into adsorption energies. These equations also provide an approximation of the desorption energy in cases that cannot be described by a fixed pre-exponential factor. For the case of a distribution of adsorption energies, the desorption spectra cannot be considered a superposition of desorption spectra corresponding to the different energies. Nevertheless, we present a method to extract the distribution of adsorption energies from TPD spectra, and we rationalize the energy resolution of TPD experiments. The analytical results are complemented by a program for simulation and analysis of TPD data.
表面科学中的程序升温脱附（TPD）实验通常使用波兰尼 - 维格纳方程和/或过渡态理论进行分析。这些方法远非直接明了，而且预指数因子的确定常常存在问题。我们提出了一种基于平衡热力学的不同方法，该方法建立在Kreuzer等人（ ）先前用于TPD的方法之上。针对三种不同类型的表面 - 吸附质相互作用给出了解吸速率方程：（i）扩散势垒可忽略不计的二维理想硬球气体，（ii）理想晶格气体，即吸附位点固定且吸附质之间无相互作用，以及（iii）具有（位点依赖）吸附能分布的晶格气体。我们表明，在脱附温度下吸附的 sticking 系数对覆盖度的依赖性决定了解吸过程是可以用一级动力学还是二级动力学来描述。为了定量确定吸附能，还必须知道脱附温度下的 sticking 系数，但它的影响相当微弱（就像传统TPD分析中的预指数因子一样）。定量分析还受到能量和熵的振动贡献的影响。对于单一吸附能的情况，我们提供了直接将峰值温度转换为吸附能的方程。在无法用固定的预指数因子描述的情况下，这些方程也提供了脱附能的近似值。对于吸附能分布的情况，脱附光谱不能被视为对应于不同能量的脱附光谱的叠加。尽管如此，我们提出了一种从TPD光谱中提取吸附能分布的方法，并对TPD实验的能量分辨率进行了合理说明。分析结果辅以一个用于TPD数据模拟和分析的程序。
