Anal. Chem. 2005, 77, 7084-7089
Molar Mass and Molar Mass Distribution of Polystyrene Particle Size Standards Wen-Ping Peng, Yi-Chang Yang, Chung-Wei Lin, and Huan-Cheng Chang*
Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-116, Taipei, Taiwan 106, R.O.C.
Monodisperse polystyrene microspheres and nanospheres are often used as particle size standards for calibration of size-measuring instruments. They are potentially useful as the mass standards for particle mass spectrometry as well. We demonstrated in this work that it is possible to achieve high-precision mass determination for single polystyrene spheres using a quadrupole ion trap. We introduced the particles into the trap by laser-induced acoustic desorption and probed them with light scattering. Mass-to-charge ratios of the individual particles were determined from applied trap-driving frequencies, voltage amplitudes and the observed starlike oscillatory trajectories projected on the radial plane. Creation of one-electron differentials through charge-state changes by electron bombardment allowed determination for the absolute mass of a single trapped particle to a precision better than 0.1%. Both molar mass and molar mass distribution were deduced from a large number of measurements for NIST polystyrene particle size standards (SRMs 1690 and 1691). Our results are in excellent agreement with the size measurement for the 0.895-µm spheres (NIST SRM 1690), but a small discrepancy (4%) in number-average mass was found for the 0.269-µm spheres (NIST SRM 1691). In recent years, mass spectrometry (MS) has developed into an imperative tool for characterization of synthetic polymers. Both molar masses and molar mass distributions of polymer molecular weight standards and high molecular weight polydisperse polymer samples have been determined with high precision.1-4 Absolute mass determination has been achieved by matrix-assisted laser desorption/ionization (MALDI) time-of-flight (TOF) MS for polystyrene, in particular, with a mass approaching 1.5 MDa.2 To go beyond this limit, the determination is primarily restricted by the low efficiency of the ionization-based detector such as the * To whom correspondence should be addressed. E-mail: hcchang@ po.iams.sinica.edu.tw. (1) Nielen, M. W. F. Mass Spectrom. Rev. 1999, 18, 309-344. (2) Schriemer, D. C.; Li, L. Anal. Chem. 1996, 68, 2721-2725. Whittal, R. M.; Schriemer, D. C.; Li, L. Anal. Chem. 1997, 69, 2734-2741. (3) Domin, M.; Moreea, R.; Lazaro, M. J.; Herod, A. A.; Kandiyoti, R. Rapid Commun. Mass Spectrom. 1997, 11, 1845-1852. (4) Guttman, C. M.; Wetzel, S. J.; Blair, W. R.; Fanconi, B. M.; Girard, J. E.; Goldschmidt, R. J.; Wallace, W. E.; VanderHart, D. L. Anal. Chem. 2001, 73, 1252-1262.
7084 Analytical Chemistry, Vol. 77, No. 21, November 1, 2005
multichannel plate. We have previously shown5 that it is possible to obtain mass spectra of multiply charged, monodisperse polystyrene microspheres (molar mass on the order of 1011 Da) ejected from a quadrupole ion trap by elastic light scattering. These microspheres often serve as the particle size standards for calibration of flow cytometers, optical microscopes, electron microscopes, and other size-measuring instruments.6-8 They also serve as the mass standards in quantitative scanning/transmission electron microscopy of biological samples.9 However, to our knowledge, their masses have not yet been characterized accurately at a level comparable to that obtained by MALDI-TOF MS for polymeric molecules. This paper reports an effort to determine the molar mass and molar mass distribution of these monodisperse spheres accurately and individually with a quadrupole ion trap. The samples used to prove the principle are polystyrene particle size standards with nominal diameters of 1 and 0.3 µm from the National Institute of Standards and Technology (NIST). These spheres have an average deviation from sphericity of only 0.6%.10 Efforts to measure the masses of NISTtraceable polystyrene spheres have been previously made by Fuerstenau and Benner11 with an electrospray ionization chargesensitive detection TOF mass spectrometer. The use of quadrupole ion traps as an electrodynamic balance for absolute mass determination of single micrometer-sized particles was first demonstrated in the 1980s. Arnold and coworkers12 measured the mass-to-charge ratio (m/Ze) of a single aerosol based on the dc voltages applied to the end-cap electrodes of an ion trap to balance the gravitational force. Creation of oneelectron differentials in the charge state by UV light followed, enabling them to determine separately the charge number (Z) and mass (m) of the particle. For a single poly(vinyltoluene) aerosol of 2.35 µm in diameter, they obtained a weight of 6.84 pg with an uncertainty of (1.5%, derived mainly from the difficulty (5) Cai, Y.; Peng, W.-P.; Kuo, S.-J.; Lee, Y. T.; Chang, H.-C. Anal. Chem. 2002, 74, 232-238. Cai, Y.; Peng, W.-P.; Kuo, S.-J.; Chang, H.-C. Int. J. Mass Spectrom. 2002, 214, 63-73. (6) Mulholland, G. W.; Lettieri, T.; Hartman, A.; Hembree, G.; Marx, E. Aerosol Sci. Technol. 1983, 2, 233-233. Mulholland, G. W.; Bryner, N. P.; Croarkin, C. Aerosol Sci. Technol. 1999, 31, 39-55. (7) Li, Y.; Lindsay, S. M. Rev. Sci. Instrum. 1991, 62, 2630-2633. (8) Wyatt, P. J.; Villapando, D. N. Langmuir 1997, 13, 3913-3914. (9) Bahr, G. F.; Zeitler, E. H. J. Appl. Phys. 1962, 33, 847-853. Bahr, G. F.; Foster, W. D.; Peters, D.; Zeitler, E. H. Biophys. J. 1980, 29, 305-314. (10) Certificates of analysis for NIST Standard Reference Materials 1690 and 1691. (11) Fuerstenau, S. D.; Benner, W. H. Rapid Commun. Mass Spectrom. 1995, 9, 1528-1538. (12) Arnold, S. J. Aerosol Sci. 1979, 10, 49-53. Philip, M. A.; Gelbard, F.; Arnold, S. J. Colloid Interface Sci. 1983, 91, 507-515. 10.1021/ac050795y CCC: $30.25
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of finding the trap center and the necessity of performing the experiment at atmospheric pressure. A more accurate way to determine m/Ze is to measure the oscillation frequency of the single particle inside the ion trap in vacuo.13-15 Gerlich and coworkers15 demonstrated the feasibility with a sophisticated Paultype ion trap and precisely determined the mass-to-charge ratios of a single SiO2 particle subjected to electron stepping using a fast Fourier transform method. Mass measurement precision on the order of 10-3 or better was attained for a single 500-nm sphere weighing 130 fg. The experiment described herein follows that of Hars and Tass,14 who conducted similar m/Ze measurements by monitoring the starlike oscillatory trajectory of a single trapped particle in the radial coordinate and analyzed the result based on a pseudopotential approximation. However, due to particle clumping upon injection of the sample solution into the ion trap with a syringe, no effort was made to determine the absolute mass of the individual particles. In this work, we extended their theoretical treatment to go beyond the adiabatic approximation and introduced the polystyrene spheres to the ion trap by laser-induced acoustic desorption (LIAD).16-18 Compared to MALDI used in our previous work,19 LIAD offers the advantage that no coarse particles20,21 are produced as the background signals due to laser ablation of the matrix. The feature is critically important when determining the mass of 0.3-µm or smaller spheres. Although LIAD is less efficient than MALDI in producing charged particles, it is well-suited for the present study because only one particle is needed in each mass measurement. EXPERIMENTAL SECTION Materials. The samples, SRM 1690 and SRM 1691 polystyrene particle size standards, were obtained from the National Institute of Standards and Technology of the United States. They both consisted of colloidal suspensions containing 0.5% (w/v) monodisperse polystyrene spheres and 50 ppm sodium azides as biocides. The certified number-average diameter for SRM 1690 is 0.895 µm (with an uncertainty of (0.008 µm), determined by measuring the intensity of scattered He-Ne laser light as a function of scattering angle and fitting the experimental data to the Mie light scattering theory using the refractive index n(λexc ) 632.99 nm) ) 1.588 for polystyrene. For the SRM 1691 spheres, (13) Wuerker, R. F.; Shelton, H.; Langmuir, R. V. J. Appl. Phys. 1959, 30, 342349. (14) Hars, G.; Tass, Z. J. Appl. Phys. 1995, 77, 4245-4250. (15) Schlemmer, S.; Illemann, J.; Wellert, S.; Gerlich, D. J. Appl. Phys. 2001, 90, 5410-5418. Schlemmer, S.; Wellert, S.; Windisch, F.; Grimm, M.; Barth, S.; Gerlich, D. Appl. Phys. A 2004, 78, 629-636. (16) Lindner, B.; Seydel, U. Anal. Chem. 1985, 57, 895-899. Lindner, B. Int. J. Mass Spectrom. Ion Processes 1991, 103, 203-218. (17) Golovlev, V. V.; Allman, S. L.; Garrett, W. R.; Chen, C. H. Appl. Phys. Lett. 1997, 71, 852-854. Golovlev, V. V.; Allman, S. L.; Garrett, W. R.; Taranenko, N. I.; Chen, C. H. Int. J. Mass Spectrom. Ion Processes 1997, 169, 69-78. (18) Perez, J.; Ramirez-Arizmendi, L. E.; Petzold, C. J.; Guler, L. P.; Nelson, E. D.; Kenttamaa, H. I. Int. J. Mass Spectrom. 2000, 198, 173-188. Petzold, C. J.; Ramirez-Arizmendi, L. E.; Heidbrink, J. L.; Perez, J.; Kenttamaa, H. I. J. Am. Soc. Mass Spectrom. 2002, 13, 192-194. (19) Peng, W.-P.; Yang, Y.-C.; Kang, M.-W.; Lee, Y. T.; Chang, H.-C. J. Am. Chem. Soc. 2004, 126, 11766-11767. Peng, W.-P.; Lee, Y. T.; Ting, J. W.; Chang, H.-C. Rev. Sci. Instrum. 2005, 76, 023108. (20) Alves, S.; Kalberer, M.; Zenobi, R. Rapid Commun. Mass Spectrom. 2003, 17, 2034-2038. (21) Jackson, S. N.; Mishra, S.; Murray, K. K. J. Phys. Chem. B 2003, 107, 13106-13110.
Figure 1. Schematic of the experimental setup consisting of a quadrupole ion trap (Jordan C-1251), a pulsed Nd:YAG laser (Continuum Surelite III-10), a continuous-wave Ar ion laser (Coherent Innova 90C), an electron gun (Jordan C-950), an electron multiplier CCD camera (e2v Technologies L3Vision). Note that the charged particles were introduced into the ion trap through the gap between the ring and end-cap electrodes.
the certified number-average diameter is 0.269 µm (with an uncertainty of (0.007 µm), determined by transmission electron microscopy using SRM 1690 to set the dimensional scale. The number of outliners (particles with diameters not on the main peak) in both samples is less than 1%, and the standard deviation in size distribution is ∼0.009 µm for SRM 1690 and
