Absolute Mass and Size Measurement of Monodisperse Particles Using a Modified Millikan's Method: Part II—Application of Electro-Gravitational Aerosol Balance to Polystyrene Latex Particles of 100 nm to 1 μm in Average Diameter

Figures & data

FIG. 1 Electrodes used for the electro-gravitational aerosol balance experiment.

FIG. 2 Setup for the electro-gravitational aerosol balance experiment.

FIG. 3 Photograph of 100 nm PSL particles immersed in density reference liquids after settling for 30 days.

TABLE 1 Summary of mass and diameter measurements of PSL particles

Particle species	Nominal/certified diameter (measurement method)	Date of measurement (year/month)	Use of DMA ^a	Survival function type in data analysis	Holding time, t h	Particle density, ρp	Number average diameter, D pa	Particle mass, m a ^b	Standard uncertainty of D pa
NIST SRM 1963	100.7 nm (DMA)	1998/12	Yes	Diffusing	14 h	1.065 g/cm^3	100.8 nm	0.5714 fg	0.33 nm
JSR SC-011-S	100 nm (TEM)	1996/8	No	Diffusing	14 h	1.057 g/cm^3	109.9 nm	0.7339 fg	0.29 nm
JSR SC-021-S	208 nm (TEM)	1996/8	No	Diffusing	6 h	1.054 g/cm^3	210.5 nm	5.146 fg	0.20 nm
		2004/2	Yes	Diffusing	3 h	1.054 g/cm^3	211.1 nm	5.195 fg	0.24 nm
NIST SRM 1691	269 nm (TEM)	1997/9	No	Diffusing	2.5 h	(1.055 g/cm^3) ^d	(267.7 nm) ^e	10.60 fg ^f	(0.16 nm) ^g
JSR SC-048-S	479 nm (TEM)	1998/12	Yes	Nondiffusing	45 min	1.054 g/cm^3	473.1 nm	58.43 fg	1.0 nm
NIST SRM 1690	895 nm (LS ^c )	2002/11	No	Nondiffusing	30 min	(1.055 g/cm^3) ^d	(895.1 nm) ^e	396.6 fg ^f	(0.51 nm) ^g
JSR SC-101-S	1001 nm (TEM)	1996/4	No	Nondiffusing	20 min	1.058 g/cm^3	982.7 nm	525.7 fg	0.89 nm

FIG. 4 Survival rate spectrum obtained (a) for NIST SRM 1963; (b) for JSR SC-011-S. The data indicated by the empty diamonds were not included in the least squares fitting; (c) for JSR SC-021-S under two different conditions: t _h = 6 h and t _h = 3 h. Note that the two data sets are plotted on different scales; (d) for NIST SRM 1691. The data indicated by the empty diamonds were not included in the least squares fitting; (e) for JSR SC-048-S; (f) for NIST SRM 1690; (g) for JSR SC-101-S.

TABLE 2 Summary of uncertainty analysis of D _pa for NIST SRM 1963

Input quantity	Standard uncertainty	Contribution to u(D pa)/D pa	Remarks
ρp	u(ρ p ) = 6.4× 10^− 4 g/cm^3		ρp = 1.065 g/cm^3
V 0	u(V 0) = 3.6× 10^− 4 V		V 0 = 350 mV
H	u(H) = 2.9 μ m		H = 10.0 mm
g	u(g) = 4.4× 10^− 5 m/s^2		The effect of electrode inclination is included in u(g)
S i (i = 1, 2, …, 11)	u(S i ) = 5.1× 10^− 4		The uncertainty u(S i ) represents the random variation in S i
Relative combined standard uncertainty of D pa: = 3.3× 10^− 3			D pa = 100.8 nm u(D pa) = 0.33 nm

TABLE 3 List of possible uncertainty sources not included in the uncertainty analysis

Possible uncertainty source	Remarks
Nonvolatile impurities in PSL particle suspensions	See Appendix B
Distortion of the electrostatic field	Assumed to be negligible
Difference in work function between the electrode surfaces	Assumed to be negligible
Air convection	Will not contribute to a bias in m a and D pa
Particle coagulation	Will not contribute to a bias in m a and D pa
Space charge	Will not contribute to a bias in m a and D pa
Thermophoresis	See Appendix C
Existence of multiply charged multiplet particles	Assumed to be negligible
Nonuniformity in size distributions and densities within a batch or bottle of PSL particles	Assumed to be negligible

FIG. 5 Effect of the choice of ρ _p on D _pa and m _a for NIST SRM 1691.

FIG. 6 Reproducibility of D _pa obtained for JSR SC-021-S. The confidence interval for each of the data indicates the expanded uncertainty with a coverage factor of 2.

FIG. A1 Examples of temperature drift during the holding time on the back faces of the upper and lower electrodes. In the measurement of the No. 1 and No. 2 curves, thermistors A and B were used for the lower and upper electrodes, respectively, while in the measurements of the No. 3 and No. 4 curves, the two thermistors were exchanged.