Mingdong Li

Electrospray-differential mobility analysis of bionanoparticles

Electrospray-differential mobility analysis (ES-DMA) is a versatile technique used to aerosolize bionanoparticles and measure their electrical mobility at ambient conditions. ES-DMA is similar to electrospray-mass spectrometry (ES-MS), but measures the effective particle size, rather than mass. It has a wide range of applications and nominally can be used to characterize biomolecules and nanoparticles ranging in size from a few nanometers (~3 nm) to several hundred nanometers, to obtain multimodal size distributions in minutes. Although both the ES and the DMA are mature technologies, they are finding increased use in combination to characterize particles in liquids. In this paper, we review ES-DMA, and how it has recently been used to characterize bionanoparticles such as polymers, proteins, viruses, bacteriophages and nanoparticle-biomolecule conjugates.

Method for determining the absolute number concentration of nanoparticles from electrospray sources.

We have developed a simple, fast, and accurate method to measure the absolute number concentration of nanoparticles in solution. The method combines electrospray differential mobility analysis (ES-DMA) with a statistical analysis of droplet-induced oligomer formation. A key feature of the method is that it allows determination of the absolute number concentration of particles by knowing only the droplet size generated from a particular ES source, thereby eliminating the need for sample-specific calibration standards or detailed analysis of transport losses. The approach was validated by comparing the total number concentration of monodispersed Au nanoparticles determined by ES-DMA with UV/vis measurements. We also show that this approach is valid for protein molecules by quantifying the absolute number concentration of Rituxan monoclonal antibody in solution. The methodology is applicable for quantification of any electrospray process coupled to an analytical tool that can distinguish monomers from higher order oligomers. The only requirement is that the droplet size distribution be evaluated. For users only interested in implementation of the theory, we provide a section that summarizes the relevant formulas. This method eliminates the need for sample-specific calibration standards or detailed analysis of transport losses.

Quantification and Compensation of Nonspecific Analyte Aggregation in Electrospray Sampling

Electrospray (ES) sources are commonly used to introduce nonvolatile materials (e.g., nanoparticles, proteins, etc.) to the gas phase for characterization by mass spectrometry or ion mobility. Recent studies in our group using ES ion mobility to characterize protein aggregation in solution have raised the question as to whether the ES itself induces aggregation and thus corrupts the results. In this article, we develop a statistical model to determine the extent to which the ES process induces the formation of dimers and higher-order aggregates. The model is validated through ES differential mobility experiments using gold nanoparticles. The results show that the extent of droplet-induced aggregation is quite severe and previously reported cutoff criterion is inadequate. We use the model in conjunction with experiment to show the true dimer concentration in a protein solution as a function of concentration. The model is extendable to any ES source analytical system and to higher aggregation states. For users only interested in implementation of the theory, we provide a section that summarizes the relevant formulas.

The Effect of Orientation on the Mobility and Dynamic Shape Factor of Charged Axially Symmetric Particles in an Electric Field

The mobility of a nonspherical particle is a function of both particle shape and orientation. Thus, unlike spherical particles, the mobility, through its orientation, depends on the magnitude of the electric field. In this work, we develop a general theory, based on an extension of the work of Happel and Brenner (1965), for the orientation-averaged mobility applicable to any axially symmetric particle for which the friction tensor and the polarization energy are known. By using a Boltzmann probability distribution for the orientation, we employ a tensor formulation for computing the orientation-averaged mobility rather than a scalar analysis previously employed by Kim et al. (2007) for nanowires. The resulting equation for the average electrical mobility is much simpler than the expression based on the scalar approach, and can be applied to any axially symmetric structures such as rods, ellipsoids, and touching spheres. The theory is applied to the specific case of nanowires and the experimental results on the mobility of carbon nanotubes (CNT). A set of working formulas of additional mobility expressions for nanorods and prolate spheroids in the free molecular, continuum, and transition regimes are also presented. Finally, we examine the expression of dynamic shape factor common in the literature, and propose a clearer definition based on the tensor approach. Mathematica codes for the electrical mobility evaluations for five cases are provided in the Supplemental Information. Copyright 2012 American Association for Aerosol Research

Evaluating the Mobility of Nanorods in Electric Fields

The mobility of a nonspherical particle is a function of both particle shape and orientation. In turn, the higher magnitude of electric field causes nonspherical particles to align more along the field direction, increasing their mobility or decreasing their mobility diameter. In previous works, Li et al. developed a general theory for the orientation-averaged mobility and the dynamic shape factor applicable to any axially symmetric particles in an electric field, and applied it to the specific cases of nanowires and doublets of spheres. In this work, the theory for a nanowire is compared with experimental results of gold nanorods with known shape determined by TEM images. We compare the experimental measured mobility sizes with the theoretical predicted mobility in the continuum, free molecular, and the transition regime. The mobility size shift trends in the electric fields based on our model, expressed both in the free molecular regime and in the transition regime, are in good agreement with the experimental results. For rods of dimension: width dr = 17 nm and length Lr = 270 nm, where one length scale is smaller than the mean free path and one larger, the results clearly show that the flow regime of a slender rod is mostly controlled by the diameter of the rod (i.e., the smallest dimension). In this case, the free molecule transport properties best represented our nanorod. Combining both theory and experiment we show how, by evaluating the mobility as a function of applied electric field, we can extract both rod length and diameter. Copyright 2013 American Association for Aerosol Research

Development of a Pulsed-Field Differential Mobility Analyzer: A Method for Measuring Shape Parameters for Nonspherical Particles

For a nonspherical particle, a standard differential mobility analyzer (DMA) measurement yields a mobility-equivalent spherical diameter, but provides no information about the degree of sphericity. However, given that the electrical mobility for nonspheres is orientation-dependent, and that orientation can be manipulated using electric fields of varying strength, one can, in principle, extract some type of shape information through a systematic measurement of mobility as a function of particle orientation. Here, we describe the development of a pulsed-field differential mobility analyzer (PFDMA) which enables one to change the peak E-field experienced by the particle to induce orientation, while still maintaining the same time-averaged field strength as a standard DMA experiment. The instrument is validated with polystyrene latex (PSL) spheres with accurately known size, and gold rods with dimensions accurately determined by transmission electron microscopy (TEM). We demonstrate how the instrument can be used for particle separation and extraction of shape information. In particular, we show how one can extract both length and diameter information for rod-like particles. This generic approach can be used to obtain dynamic shape factors or other multivariate dimensional information (e.g., length and diameter). Copyright 2014 American Association for Aerosol Research

Bionanoparticles as candidate reference materials for mobility analysis of nanoparticles.

We propose bionanoparticles as a candidate reference material for determining the mobility of nanoparticles over the range of 6 × 10(-8)-5 × 10(-6) m(2)V(-1)s(-1). Using an electrospray differential mobility analyzer (ES-DMA), we measured the empirical distribution of several bionanoparticles. All of them show monomodal distributions that are more than two times narrower than the currently used calibration particles for mobility larger than 6 × 10(-8) m(2)V(-1)s(-1) (diameters less than 60 nm). We also present a numerical method to calculate corrected distributions of bionanoparticles by separating the contribution of the diffusive transfer function. The corrected distribution is about 20% narrower than the empirical distributions. Even with the correction, the reduced width of the mobility distribution is about a factor of 2 larger than the diffusive transfer function. The additional broadening could result from the nonuniform conformation of bionanoparticles and from the presence of volatile impurities or solvent adducts. The mobilities of these investigated bionanoparticle are stable over a range of buffer concentration and molarity, with no evidence of temporal degradation over several weeks.

Rotational Diffusion Coefficient (or Rotational Mobility) of a Nanorod in the Free-Molecular Regime

The corrected rotational diffusion coefficient for a rod in the free molecular regime is given in this work and a simplified derivation using the differential drag forces for a rotating rod in the free molecular regime is presented to explain the difference between our result and the one from Kims approach. Finally, we compare the rotational diffusion coefficient between a rod and an ellipsoid with the same aspect ratio and the same volume. Copyright 2014 American Association for Aerosol Research

The effect of alignment on the electric mobility of soot

ABSTRACT The effect of an aligning electric field on the mobility of both flame generated smoke and smolder generated smoke was studied. A pulsed differential mobility analyzer was used to study the alignment without changing the DMA flows. No detectable change in the mobility was observed for the smolder smoke, while a small but detectable effect of up to 5% decrease in the mobility diameter with increasing field was observed for the largest aggregates with a mobility diameter of 200 nm. We modeled the friction coefficient tensor of soot fractal aggregates as an equivalent prolate spheroid to obtain the field induced mobility as a function of aspect ratio. The alignment probability distribution function was determined by computing the polarizability tensor for simulated fractal aggregates. One interesting result was the smallness of the prolate sphere aspect ratio of 1.2 to 1.3 compared to the much larger aspect ratio from TEM analysis and from the polarizability ratio. An explanation for the low value based on the contribution to the friction coefficient from the individual spheres for a fractal is given. Another interesting observation is the broadening of the mobility size distribution with decreasing field. This is shown to be related to the polydispersity of the aspect ratio. The fact that all three aggregate sizes appear to fit the same spheroid aspect ratio is interesting, and offers a first-order approach to describing transport properties of aggregates. An estimate of the rotation relaxation time of the fractal aggregate was made to verify that the rotation time was much shorter than the duration of the zero electric field period during each cycle. Copyright

Absolute quantification method for protein concentration.

A fast and accurate assay to determine the absolute concentration of proteins is described based on direct measurement of droplet entrapped oligomer formation in electrospray. Here we demonstrate the approach using electrospray differential mobility analysis (ES-DMA), which can distinguish monomers and dimers from higher order oligomers. A key feature of the method is that it allows determination of the absolute number concentration of proteins eliminating the need for protein-specific calibration. The method was demonstrated by measuring the concentration of a NIST Standard Reference Material 927e (bovine serum albumin), a high-purity immunoglobulin G 1κ, and a formulated Rituximab. The method may be applied to any electrospray source, regardless of diagnostic tool (e.g., MS or ion-mobility, etc.), provided the electrospray is operated in a droplet-fission mode.