Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA.
J Phys Chem A. 2013 May 16;117(19):3887-901. doi: 10.1021/jp312432z. Epub 2013 Apr 3.
Ion/electrical mobility measurements of nanoparticles and polyatomic ions are typically linked to particle/ion physical properties through either application of the Stokes-Millikan relationship or comparison to mobilities predicted from polyatomic models, which assume that gas molecules scatter specularly and elastically from rigid structural models. However, there is a discrepancy between these approaches; when specular, elastic scattering models (i.e., elastic-hard-sphere scattering, EHSS) are applied to polyatomic models of nanometer-scale ions with finite-sized impinging gas molecules, predictions are in substantial disagreement with the Stokes-Millikan equation. To rectify this discrepancy, we developed and tested a new approach for mobility calculations using polyatomic models in which non-specular (diffuse) and inelastic gas-molecule scattering is considered. Two distinct semiempirical models of gas-molecule scattering from particle surfaces were considered. In the first, which has been traditionally invoked in the study of aerosol nanoparticles, 91% of collisions are diffuse and thermally accommodating, and 9% are specular and elastic. In the second, all collisions are considered to be diffuse and accommodating, but the average speed of the gas molecules reemitted from a particle surface is 8% lower than the mean thermal speed at the particle temperature. Both scattering models attempt to mimic exchange between translational, vibrational, and rotational modes of energy during collision, as would be expected during collision between a nonmonoatomic gas molecule and a nonfrozen particle surface. The mobility calculation procedure was applied considering both hard-sphere potentials between gas molecules and the atoms within a particle and the long-range ion-induced dipole (polarization) potential. Predictions were compared to previous measurements in air near room temperature of multiply charged poly(ethylene glycol) (PEG) ions, which range in morphology from compact to highly linear, and singly charged tetraalkylammonium cations. It was found that both non-specular, inelastic scattering rules lead to excellent agreement between predictions and experimental mobility measurements (within 5% of each other) and that polarization potentials must be considered to make correct predictions for high-mobility particles/ions. Conversely, traditional specular, elastic scattering models were found to substantially overestimate the mobilities of both types of ions.
纳米颗粒和多原子离子的离子/电迁移率测量通常通过应用斯托克斯-密立根关系或与多原子模型预测的迁移率进行比较来与颗粒/离子物理性质相关联，这些模型假设气体分子从刚性结构模型上进行镜面和弹性散射。然而，这些方法之间存在差异；当应用于具有有限大小的撞击气体分子的纳米级离子的镜面、弹性散射模型（即弹性硬球散射，EHSS）时，预测与斯托克斯-密立根方程存在很大差异。为了纠正这种差异，我们开发并测试了一种新的多原子模型迁移率计算方法，其中考虑了非镜面（漫反射）和非弹性气体分子散射。考虑了两种不同的气体分子从颗粒表面散射的半经验模型。在第一种模型中，它在气溶胶纳米颗粒的研究中一直被传统地调用，91%的碰撞是漫反射和热容纳的，9%的碰撞是镜面和弹性的。在第二种模型中，所有的碰撞都被认为是漫反射和容纳的，但从颗粒表面重新发射的气体分子的平均速度比颗粒温度下的平均热速度低 8%。这两种散射模型都试图模拟碰撞过程中平移、振动和旋转模式能量之间的交换，这在非单原子气体分子与非冻结颗粒表面之间的碰撞中是可以预期的。在考虑气体分子之间的硬球势以及颗粒内原子与长程离子诱导偶极（极化）势的情况下，应用了迁移率计算程序。预测结果与在室温附近的空气中对多种电荷的聚乙二醇（PEG）离子和单价四烷基铵阳离子进行的先前测量结果进行了比较，这些离子的形态从紧凑到高度线性。结果发现，非镜面、非弹性散射规则都导致预测与实验迁移率测量值之间非常好的一致性（彼此相差 5%以内），并且必须考虑极化势才能对高迁移率的颗粒/离子进行正确预测。相反，传统的镜面、弹性散射模型被发现大大高估了这两种离子的迁移率。
