1730
Anal. Chem. 1981, 53, 1730-1736
Time-Delayed Exponential Field-Programmed Sedimentation Field Flow Fractionation for Particle-Size-Distribution Analyses J. J. Kirkland,” S. W. Rementer, and W. W. Yau E.
I. du Pont de Nemours &
Company, Central Research and Development Department, Experimental Station, Wilmington, Delaware 19898
Partlcle-sire-distrlbutlon analyses have been carried out on a wlde varlety of suspended organic and inorganic particulates uslng a new technique of tlmedelayed exponentlal force-field sedlmentatlon field flow fractionation (TDE-SFFF). Analyses for partlcles In the ""
and d, = particle diameter (em), tR= retention time of sample components (min), T = the time constant and the delay-decay of the exponential-decay field programming (min), k = Boltvnann constant (1.38 X (g cm2)/(s "C), T = absolute temperature (Kelvin), e = 2.71828, to = retention time of solvent peak or any unretained sample compOnent (mid, Go = initial sedimentation force field (cm/s2), W = channel thickness (cm), and Ap = density difference between sample component and carrier mobile phase, respectively (g/cms). Equations 1 and 2 were specifically derived for retained components whose peaks are significantly separated from the channel void-volume peak, V,. At a constant mobile phase flow rate (F, cm3/min), Vo = Fto. In TDE-SFFF, the flow of liquid mobile phase is initiated after the completion of sample injection and relaxation (equilibration) under a high force field. The initial force field Go which is applied during sample injection and relaxation is then continued with the mobile phase flowing for a time equal to T , which is also the exponential-decay time constant. After time 7 passes, the force field is reduced exponentially with the same time constant T. The resultant particle retention time follows a log-linear relationship, as illustrated in Figure 5 for a series of polystyrene latex standards. The data in Figure 5 also illustrate the effect of changing the time constant T on the slope of the log-linear plot. As predicted hy eq 1,increasing the decay time constant T decreases the slope of the plot and increases the resolution between different partide sizes hut with an attendant increase in separation time. As predicted hy eq 1 and previous TDE-SFFFstudies (5). variations in the initial force field, Gh channel thickness, W,and flow rate, F, change the intercept hut not the slope of the log-linear SFFF relationship. Constant relative peak spacings are maintained when these parameters are varied, and this results in parallel hut displaced log-linear calibration plots. Constant Force-Field Relationshio. Accordine to Giddings et al. (1-3). in constant force-fieid SFFF, sample mo-
1732
ANALYTICAL CHEMISTRY, VOL. 53, NO. 12, OCTOBER 1981 IL
1 t
,
I
T
e-
I
:3.57
I
I
MIN
i
4
tR*
xtR&
dt
where, MWF is a molecular weight conversion factor, tR* represents the expected retention time for a constant force field, and Go is the field strength at times less than T min. For particle-size determination, a spherical particle is generally assumed and the desired particle diameter can be computed as
d, = PDF*(6t,*
1
- 2t0) ‘ I 3
(11)
where the particle-diameter conversion factor (PDF) is
0.01
I
PDF =
t
[ (:)(
$-)MWF]1’3
(12)
and No= Avogadros number (6.0238 X
RETENTION TIME t ~ MINUTES ,
Figure 5. Effect of exponential decay and delay time constant, T : polystyrenelatex standards; channel, 57 X 2.54 X 0.0125 cm; mobile phase, 0.1% FL-70, 0.01% NaN3;flow rate, 3.00 cm3/min; lnitlal rotor speed, 10000 rpm; relaxation, 1.0 min; exponential decay and delay time constant 7,as shown: detector, UV, 254 nm; sample, 0.09% 0.091 pm, 0.04% 0.178, 0.220, 0.312 pm, 0.05% 0.418 pm, 10 pL.
lecular weight is accurately related to retention time of particles according to the relationship
mol-’). Detector Responle Transformation. Our SFFF equipment uses a commercial UV-visible spectrophotometer detector (Variscan-Varian Instruments, Walnut Creek, CA) whose response approximates that of a turbidimetric detector. (This turbidimetric measurement is not exact because the optics were not specifically designed for turbidimetry.) In the absence of multiple light scattering, detector response DT is proportional to the turbidity of a colloidal suspension or a solution of macromolecules according to
DT a
suspension turbidity =
with
A=
ROTP, MG WAp
or (4)
where X = a dimensionless retention parameter, R = the retention ratio, Ro = gas constant (8.31 X lo7 (g cm2)/(s2“C mol)), p e = sample density (g/cmS),M = molecular weight of the sample, and G = constant sedimentation force field (cm/s2). All other symbols have been defined for eq 1 and 2. The force field is related to rotor speed according to
G=
(2):
(5)
where w = rotor speed in rpm and r = rotor radius (cm). In developing the data-handling algorithm for TDE-SFFF in this work, the approach was to describe retention on a time basis in terms of decreasing field strength. Other operating parameters were grouped into a constant term for mathematical convenience. It can be shown that for well-retained peaks, a polynomial approximation of eq 3 yields X
’( ”)3 - R 2
= to/(6tR- 2to)
Substituting for X in eq 4 and rearranging
TDE-SFFF Relationship. In TDE-SFFF the strength of the force field is a function of time, i.e., G = G(t), and the desired particle or molecular weight values can be computed via an integral function of the force field M = M w F . ( 6 t ~ *- 2to) (8) with
DT NKd;
cK/d,
(14)
where b = optical pathlength (cm), Io = incident light intensity, I = transmitted light intensity, N = particle number concentration ( ~ m - ~K) , = extinction coefficient, and c = particle weight concentration (g/cm3). The extinction coefficient K for nonabsorbing particles, related only to particle scattering efficiency in this case, can be estimated according to the light scattering theory for spheres by the Mie theory (6,7) 2 ” K = - C (2n a2 n=l
+ l)(lxnI2+ lynI2)(Mie scattering)
(15)
where a = ad,/Xo; Xo = wavelength of analytical light beam in the medium, and x,, y, = complex variables which are a function of a and m, where m = the ratio of the refractive indices of the particle and the medium. A convenient computer subroutine was obtained and used in this work for carrying out x, and yn calculations in this Mie correction routine (8). The Rayleigh scattering region is a narrow, limited part of the scattering phenomenon described by the Mie theory. Rayleigh scattering specifically involves small particles, long light wavelengths, and small refractive index differences between particles and medium, where, in this case, K = dp” and
DT 0: cd,3
(Rayleigh scattering)
(16)
Since particle sizes vary with SFFF retention time over the duration of a fractogram,the dependence of detector response on particle size must be accounted for in the transformation of a “raw” SFFF fractogram to a sample particle-size-distribution plot. The raw fractogram is a detector-response DT
ANALYTICAL CHEMISTRY, VOL. 53, NO. 12, OCTOBER 1981 /w0
A: Oll91pm
= 12,000 r p m
l-7
1733
,176pm ,312pm
%
’ 40I
W
0
3
2
1
6oti
AVERAGE PARTICLE DIAMETER (pml OF POLYSTYRENE LATEX MIXTURE TYPE OF AVERAGING SEE €L&!XLL Number 0092 0096 Surface 0 094 0 099 0 110 0 117 Specific Surface Weight 0 137 0 148 Volume 0 099 0 105 Turbidily 0 I81 0 193
4
RETENTION TIME I R , MINUTES
3
Figure 6. TDE-SFFF fractogram: real-time CRT display: polyst rene latex standards;conditions of Figure 1, except flow rate, 10.0 cm /min; initial rotor speed, 12 000 rpm; exponential decay and delay time, T = 0.8 min; sample, 0.14% 0.091 pm, 0.04% 0.176 and 0.312 pm,
Y
25 pL.
01
02 03 PARTICLE DIAMETER, p n
i
-1
04
Figure 8. Cumuhttve particle-size distributlon plot: CRT display. From data of Figure 6; expected values for mixture also listed.
01
‘\
02
C 4
j
03
-
L
-
04
PARTICLE DIAMETER, pm
Figure 7. Differentml particle-size distribution: CRT display. From data of Figure 6.
profile over the separation retention time span. On the other hand, the desired particle-size distribution curve is a plot of true particle concentration c as a function of particle diameter. I
RESULTS Known mixtures of narrow particle-size-distribution polystyrene latex standards have been fractionated to obtain data that confirm the quantitative aspects of SFFF-TDIS particle-size-distribution analysis and verify the effectiveness of the computer data-handling software. Details of this work will be presented in a future publication. Figure 6 shows the fractionation of a mixture of three polystyrene latex stamdards as presented on the real-time CRT display. A profile of the rotor-speed exponential decay is also displayed. These three latex standards were completely separated in about 4 min, using a 0.0125 cm thick channel and an iinitial rotor speed wo of 12000 rpm. Figure 7 shows the CRT plot of the differential particle-size distribution of this polystyrene latex mixture. This plot was obtained by transforming the “raw” LIV-turbidimetric detector signal from Figure 6 to a relative weight-fractionresponse, in this case, using the Mie scattering relationship. Figure 8 shows the corresponding cumulative particle-size-distribution plot as seen on the CRT. Also given on this plot are calculations of average particle diameters for the sample particles. Several types of averaging are included to meet specific application needs. For example, the turbidity average for a particle is related to the hiding power of a pigment. These statistical averages have previously been defined (5). Values listed in Figure 8 also show that tlne expected particle diameter values closely correspond to those measured for this known mixture. Further improvements in the accuracy of the particle-size determination are anticipated with the use of
40
1
?12
24
16 8 RETENTION TIME I R , MINUTES
I
0
Figure 9. TDE-SFFF fractograms of polychloroprene latex samples: channel, 57 X 2.54 X 0.0254 cm; mobile phase, 0.1 % FL-70, 0.01 % NaN,; flow rate, 1.O cm’/min; inkiil rotor speed, 10000 rpm; relaxatlon, 5.0 min; exponential decay and delay time constant 7 = 5.95 fmln; detector, UV, 254 nm; sample, 1 %, 10 pL.
-
optimum detectors. It has been observed that small errors occur because the UV detector does not respond exactly as a true turbidimeter.
APPLICATIONS Polychloroprene Latices. TDE-SFFF has proved to be an effective approaclh to characterizing a variety of polymer latices. For example, Figure 9 shows the TDE-SFFF fractograms of four polychloroprene latex samples prepared under different conditions. While these “raw” fractograms appear to be somewhat similar, the differential particle-size-distribution plots in Figure 10 show bimodal particle size distributions after transformation of detector signal. Figure 11 shows the cumulative particle-size distribution plots for these polychloroprene samples. In Table I the SFFF particle-size data for the polychloroprene latices are compared with those measured by transmission electron microscopy (TEM) and line-broadening laser light scattering (LLS) analysis (9). In general, the SFFF data compare well with TEM measurements. However, the SFFF analysis was carried out in less than 30 min, while several days of elapsed time is required for tedious TEM
1734 I
ANALYTICAL CHEMISTRY, VOL. 53, NO. 12, OCTOBER 1981 I
I
I
I
I
,
1
PARTICLE DIAMETER,prn
Figure 10. Differentialparticle-sizedistributkm of polychloroprenelatex samples. From data of Figure 9.
q 70
*’,
cull
I
I
I
PARTICLE DIAMETER, prn
Flgure 11. Cumulative particle-size distribution of polychloroprenelatex samples. From data of Figure 9.
Table I. Particle Size Data on Polychloroprene Latices samdp,w, fim ples TEMa SFFF LLSb 1 2 3 4
0.076 0.081 0.090 0.086
0.075 0.079 0.082 0.085
0.084 0.091 0.099 0.097
TEM”
fim SFFF
0.058 0.062 0.071 0.070
0.061 0.062 0.061 0.058
dp,N,
a TEM = transmission electron microscopy. laser light scattering (line broadening).
LLS =
characterization. The difference between SFFF and TEM data for sample 3 is believed to be real, since this difference is much larger than the usual experimental uncertainties of SFFF. The LLS data in Table I show a weight-average particle diameter that is somewhat higher than both TEM and SFFF values. This may reflect the fact that, under the conditions of the particular experimental approach used and the sample particle-size distribution present, the physical averaging of particle size in the LLS technique is of a higher statistical averaging order. However, the LLS technique is capable of producing only a single value for particle size, or at best only
PARTICLE DIAMETER, prn
Flgure 13. Differential and cumulative particle-slze distribution plots for poly(methy1 methacrylate)latex. From data of Figure 12.
a crude histogram of a particle-size distribution; it does not supply a continuous particle-size distribution as does SFFF. Poly(methy1 methacrylate) Latices. A wide variety of organic polymer latices can be readily characterized by TDE-SFFF. Figure 12 is a fractogram of an experimental poly(methy1 methacrylate) latex exhibiting bimodal particle-size distribution characteristics. Figure 13 shows the differential and cumulative particle-size distribution plots for this latex sample. These latter curves show approximately equal amounts of about 0.095 and 0.19 ym particles, while in the “raw” fractogram of Figure 12, the population of smaller particles appears less because of the lower response of the UV-turbidimetric detector. The transformation of the data from Figure 12 to Figure 13 is the result of scattering corrections applied to the turbidimetric detector response. Water-Based Titania Dispersions. The particle-size distribution of inorganic particulate suspensions can also be
ANALYTICAL CHEMISTRY, VOL. 53, NO. 12, OCTOBER 1981
L
0
01
L
,
113
02
I
I
I
I
I
04
05
05
07
08
1735
JIO
1 -
09
PARTICLE DIAMETER, pm
30
24 20 16 12 RETENTIONTIME 1 ~ MINUTES ,
28
4
8
Figure 14. TDE-SFFF fractograms of water-based titania dispersion; effect of field strength. Conditions are the same as for Figure 12, except initial rotor speeds as shown; exponential decay and dielay time constant, 7 = 2.38 min.
Flgure 16. Cumulative particle-size distribution of water-based titania dispersion. From data of Figure 14.
........ 3500 rpm ---5000 -7000
rpm rpm
d 0
01
02
03
04 05 06 PARTICLE DIAMETEP, pm
07
OB
09
10
Figure 15. Differential particle-size distribution of water-based titania dispersion. From data of Figure 14.
accurately characterized by the TDE-SFFF method. For example, Figure 14 shows fractogramsof w water-basedtitania dispersion a t three different initial rotor speeds, wo. These separations with different wo values were carried out to demonstrate the reproducibility of TDE-SFFF particle-size determinations under varying experimental conditions. Note that the unretained channel dead volume peaks of Voelute at thn
aamn
I 'Y 023
0075 0052 0035 PARTICLE DIAMETER, prn
0 I1
016
.r,
,I"
,i
0022
-.__L-i 0
n
RETENTION TIME 1 8 , MINUTES
Figure 17. TDE-SFFF iiractogram of carbon black dispersion. Conditions are the same as Figure 12, except initial rotor speed, 12000 rpm; exponential decay and delay time constant, T = 7.14 min.
timn uihiln thn rntnntinn timna nf thn titania
sample increase with increasing force field. As predicted by eq 1and 2, particles elute later at higher initial rotor sipeeds. Figures 15 and 16 show the differential and cumulative particle-size distribution plots, respectively, for these runs at different force fields. These data indicate that TDE-SFFF is capable of excellent particle-size analysis reproducibility and high analytical precision under varied operating conditions. The less than rt2% variation in the data for the cumulative plot in Figure 16 represents significantly smaller errors compared to other particle-size methods, even when different TDE-SFFF operating conditions are used. Other Application. Various other particulate samples have been examined by TDE-SFFF; an example is a carbon black dispersion in Figure 17. A qualitative particle-sizie scale is shown in the abscissa of this fractogram,but no quantitative particle-size distribution data are presented. This fractogram clearly shows that this sample contains a broad distribution of particle sizes. The average particle diameter of this carbon black dispersion is about 0.06 pm. However, significant
* I
d
40
Oh5 Ob2 0'10 PARTICLE DIAMETER, p m L
I
32 24 16 RETENTION TIME t ~ MINUTES ,
-A-
0047
-
A
8
Figure 18. TDE-SFFF friactogram of phthalocyanine blue. Conditions are the same as Figure 12, except exponential decay and delay time constant, T = 3.57 min.
amounts of particles as small as 0.01 pm also are apparent. Such small particles would be difficult to characterize by other
1736
ANALYTICAL CHEMISTRY, VOL. 53, NO. 12, OCTOBER 1981
samples such as this often can be quickly measured for detecting important differences.
CQNCLUSIQNS Particle retention time in TDE-SFFF correlates simply and accurately with the logarithm of particle size (diameter or mass). This relationship significantly simplifies the data handling for convenient and accurate particle-size distribution analysis. Relative to constant-field SFFF, TDE-SFFF provides the advantages of decreased analysis time and enhanced detection sensitivity, while maintaining adequate resolution. Quantitative particle-size-distribution analyses in the
