Anal. Chem. 1989, 61, 1934-1937
1934
Density Determination of Low-Density Polymer Latexes by Sedimentation Field-Flow Fractionation D. J. Nagy Air Products and Chemicals, Inc., Corporate Research Services, 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195
Particle density must be accurately known to characterize particle slze distributlons of polymeric latexes by sedimentation field-flow fractionation (SFFF). I n this work, it Is demonstrated that SFFF can be used to determine in M u density of copolymer latexes in the range from 1.00 to 1.02 g/cms. To perform these measurements the density of the SFFF mobile phase Is decreased to less than 1.00 g/cms with the use of methanol as an eluant modifier. Retention data are measwed for the latexes by Using several lowdensity mobile phase solutions. This method is feasible for lowdensity polymers s h e particle retention time by SFFF is directly related to the d e d t y dmerence between the parlldes and the mobile phase. This technique has been successfully appiled to narrow distribution styrene-butadiene and to narrow and broad partlcle size distribution vinyl acetate-acrylic copdymer latexes.
INTRODUCTION Sedimentation field-flow fractionation (SFFF) is a subtechnique of field-flow fractionation (FFF) used to characterize mixtures of high molecular weight polymers, emulsions, latexes, and other suspensions. SFFF technology combines the principles of single-phase chromatography and centrifugation to separate submicrometer-sized particles according to size (1,2). The size separation occurs in a circular channel of a spinning, continuous-flow centrifuge rotor. An imposed centrifugal force applied perpendicular to the laminar flow in the channel causes particulates heavier than the liquid mobile phase to sediment radially outward against the channel wall. This buildup of particles near the wall is resisted by normal diffusion in the opposite direction. The particles establish a steady-state concentration zone whose mean concentration is a t a height, 1, which is dependent on the force field and diffusion coefficient of the particles away from this wall. Particles of different masses reach sedimentation equilibrium with different characteristic layer thicknesses. This results in different mean distances from the wall and is shown in Figure 1 for mean distances l A and lB (3). The average particle velocity will increase or decrease depending on the degree of zonal compression. Heavier and bigger particles are intercepted by slower moving flow streamlines near the channel wall and will elute from the channel after the smaller particles. This order of elution is the basis for size separation by SFFF and has been used successfully for a variety of submicrometer-sized materials (3-5). Particle density must be known accurately to determine quantitative particle size distribution information from SFFF turbidity-time fractograms. However, if the particle density is unknown, it is still possible to determine the density from SFFF measurements. Kirkland and Yau demonstrated the usefulness of this approach to determine densities of polymer latexes from 1.05 g/cm3 (polystyrene) to 1.22 g/cm3 (polychloroprene), utilizing glycerine as a mobile phase modifier (3). This method is feasible since particle retention by SFFF 0003-2700/89/0361-1934$01.50/0
is directly related to the density difference between the particles and the mobile phase. The use of SFFF under nonaqueous conditions has also been described by Yonker et al. (6). Binary mixtures of ethanol and 1,1,2-trichlorotrifluoroethane were used to measure the density of silica particles. Many commercial latex products are copolymers whose densities are less than that of polystyrene (1.05 g/cm3). Classical methods for density measurement such as densitometry and weight per gallon exhibit poor accuracy and precision for low density polymer latexes. This is due to the fact that the dispersed polymer phase is at or near the density of the continuous aqueous phase. The presence of residual monomer, surfactant, salt, and/or initiators complicates the situation. SFFF, by providing an alternative means to examine in situ polymer density, circumvents these types of problems. In addition, SFFF provides the capability to examine polymer density homogeneity. This is not possible with the methods mentioned above. For particle size calculations of copolymers which exhibit suspected bimodal or broad distributions, it is important to establish that separation is by size alone and not the result of polymer compositional heterogeneity. In this paper, we wish to show the usefulness of SFFF for in situ density characterization of low-density copolymers in the range from approximately 1.00 to 1.02 g/cm3. For these low-density polymers, we used methanol-modified mobile phases with densities less than 1.00 g/cm3. As in the case for higher density polymers and related materials, SFFF is equally well suited for low-density polymer characterization. This will be shown for styrene-butadiene and vinyl acetate-acrylic copolymers.
BACKGROUND Kirkland and Yau have shown that under normal operating conditions (where the particles are more dense than the mobile phase), the mobile phase density, po, can be expressed as (3) where ps is the density of the particle (g/cm3), ps,o is an assumed particle density, Dp,ois the calculated particle diameter value based on the assumed ph0 value for particle density, and D, is the true average particle diameter of the same statistical averaging type. To determine particle density by SFFF, a plot of po values versus the quantity ( P , , ~- p0)Dp,03is constructed, with the intercept at the density axis ( x axis), to be that of the density of the particle in question (i.e., where ps,o = po). The validity of the above equation is based on the fact that the fundamental SFFF separation parameter is the effective particle mass, which is directly proportional to the product (Ap.D:), where AP = IPS
- Pol
This (ApD;) value always appears as an inseparable quantity in all SFFF retention equations. Each retention time on an SFFF elution fractogram is in direct correspondence with a single value for (Ap.Dp3). The value of this quantity remains 63 1989
American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 17, SEPTEMBER 1, 1989
Table 11. SFFF Operating Conditions
SEDIMENTATION FIELD
CHANNEL
polystyrene latex
PARABOLIC FLOW PROFILE
..
A
0.330 wm
-
e ..
1935
initial rpm field decay constant, min equilibration time, min decay delay time. min
.*e
.P
1
I
Flgure 1. SFFF separation process.
Table I. Latexes Used for Density Determination
latex B
latex C
latex D
12000 12000 12000 12000
5000 4
6
4
4
8
5
5
5
5
10
4
6
4
4
8
4.0 0
latex code
polymer type
particle size type
A B C D
styrene-butadiene (T,= -6 " C ) styrene-butadiene (T = +1 "C) vinyl acetate-acrylic [T,= -40 " C ) vinyl acetate-acrylic (T,= -40 " C )
narrow narrow narrow broad
PARTICLE DIAMETER AT PEAK MAXIMUM
the same regardless of different Ap values in the SFFF particle size calculations (3). Thus, for an assumed particle density, Po, MOBILE PHASE DENSITY, g/cm3 P8,O
(Ado =
IPs,o
- Pol
(3)
and (4) A rearrangement of eq 4 gives
Dp,o=
1-
Ps - Po Ps,o - Po
113
DP
(5)
The importance of eq 5 above is as follows: the effect of using an assumed density instead of the accurate particle density in the particle size calculation causes the calculated Dp,ovalues to differ from the true D, values by a simple factor containing the density term. For particles of homogeneous density p s , the ratio between the D , , and D, values is expected to be constant for all particle sizes a t every retention time on the SFFF fractogram. The average values for Dp should also differ by a constant factor
which is the basis for eq 1 for determining in situ particle densities by SFFF. Theory for density determination by SFFF has been described previously in greater detail (3, 7,8). Experimentally, SFFF measurements are made on an unknown sample by using four or five different mobile phase densities. The sample is analyzed under identical SFFF operating conditions for each density. A reasonable value of ps,o is then assumed. This value is used with the known p o values for the various mobile phases employed, to calculate the D,,,value of the sample for any statistical particle size average (number, weight, turbidity, peak maximum, etc.). In this investigation, methanol-modified aqueous mobile phases were used to lower the mobile phase density to values less than 1.00 g/cm3 (at 25 "C). This was necessary to keep the mobile phase density less than that of the polymer latexes studied.
EXPERIMENTAL SECTION Polymer Latexes. The polymer latexes used in this study are all free-radical polymerized, commercially available copolymers. The properties of the latexes are summarized in Table I. A monodisperse 0.330-pm polystyrene latex (Duke Scientific) was also used in this study. Polystyrene has a well-known polymer density of 1.05 g/cm3 (3, 9).
Figure 2. Density plot for polyslyene latex standard, 0.330-pm particle size. Mobile phase densities used: 0.9973, 0.9795, 0.9715, and 0.9633 g/cm3.
Instrumentation. AU measurementa were made on a Du Pont Model 1000 SFFF (Du Pont Instrument Systems) with a Hewlett-Packard 9000/216 data processing system. The standard SFFF aqueous mobile phase contained 0.1% Aerosol-OT emulWater sifier (Fisher Scientific) in HPLC-equivalent water (Milli-Q Systems). All measurements were performed on the SFFF system at 25 "C with a flow rate of 2.00 mL/min. Latex samples were prepared by dilution in the mobile phase to approximately 0.5-1.0% (by weight) and prefiltered through an 8.0-pm Teflon Millipore membrane to remove any aggregates or other particulate debris prior to injection into the SFFF channel. Samples were injected immediately after preparation in the appropriate mobile phase. Injection volumes were 50-pL. Detection was by turbidity at 254 nm. Operating Procedures. The SFFF operating conditions for the latex copolymers and the polystyrene standard are summarized in Table 11. The same conditions were employed for each mobile phase and each individual sample. Time delayed, field-decay programming was used in all cases. The methanol-modified mobile phases were prepared by adding a known amount of HPLC methanol (Fisher Scientific) to the standard aqueous mobile phase and degassing under house vacuum for 1-2 min. Actual densities of the methanol-modified mobile phases were determined on a Mettler/Parr DMA-55 density meter. Methanol-modified mobile phases at 25 "C were of the following densities: 0.9633, 0.9715, 0.9795, and 0.9882 g/cm3. The density of the standard 0.1% Aerosol-OT mobile phase was 0.9973 g/cm3 at 25 "C. Normal laboratory safety precautions were applied for the above procedures.
RESULTS AND DISCUSSION The usefulness of determining polymer density with methanol-modified mobile phases was first verified by using a 0.330-pm polystyrene latex standard. Experience in our laboratory has shown that polystyrene and latexes of the type used for this study do not exhibit swelling in aqueous solutions of methanol. Methanol is an excellent mobile phase modifier even for mobile phase densities as low as 0.9633 g/cm3, the lowest density solution we used. The SFFF density plot for polystyrene is shown in Figure 2, where the x intercept indicates a density of 1.053 g/cm3. This value compares favorably with the generally accepted density value of 1.05 g/cm3 for polystyrene. For this measurement the 95% confidence limit for the x intercept is 1.030-1.114 g/cm3. The linear regression R square value is
1936
ANALYTICAL CHEMISTRY, VOL. 61, NO. 17, SEPTEMBER 1, 1989 0
uz 0. 0 -
-
PARTICLE DIAMETER AT PEAK MAXIMUM
3.0
2'01
1Z\
0
X-INTERCEPT = 1.002 g i c m 3
I II
Table 111. Latex Particle Size Data from in Situ SFFF Density Determination latex
DWsa w
Dmb w
D, f D,c
A B C D
0.205 0.110 0.175 0.375
0.175 0.105 0.150 0.160
1.2 1.1 1.2 2.3
vi 1.0
3
I 0.98
0
0.96
I W I
I
1.00
1.02
I
I
"D,,weight average. bDn,number average. persity index.
I
1.04
1.06
polydis-
p 0 , MOBILE PHASE DENSITY, g i c m 3
Figure 3. Density plot for latex A. 0.9882, 0.9795, 0.9715, and 0.9633
Mobile phase densities used: g/cm3.
AT PEAK MAXIMUM 0
6.0
I
n
0.0 I l l 0.96 0.96
I
'
1.00
1.02
1.04
1.06
p0, MOBILE PHASE DENSITY, g / c m 3
TIME (MIN.)
Figure 5. Density plot for Latex 8. Mobile 0.9973, 0.9882. 0.9795, 0.9715, and 0.9633
fractograms for latex A using standard mobile phase of 0.1 % Aerosol-OT (solid line; density = 0.9973 g/cm3)and methanoknodified mobile phase (broken line; density = 0.9882 g/cm3).
phase densities used: g/cm3.
Figure 4. Turbidity-time
AT PEAK MAXIMUM r
0.979. The assumed density used for the calculations was 1.100 g/cm3. It should be noted that the wide range for the 95% tolerance limit is due to the fact that the data were taken for mobile phase densities less then 1.00 g/cm3. This requires a lengthy extrapolation of the data to the x axis. The use of glycerine-modified mobile phases for polystyrene, where 1.00 I po < 1.05, yields better precision as shown by Kirkland and Yau (3). The particle diameter used in Figure 2 (and in the data that follow) was the peak maximum diameter of the turbidityelution time fractogram. Any one of the normally reported diameter averages such as number, weight, volume, or turbidity could be used in the calculations and subsequent plot of density versus ( P , , ~- p0)Bp,03. The density plot for latex A (styrenebutadiene copolymer) is shown in Figure 3. The density of the polymer as given by the x intercept is 1.002 g/cm3. The 95% confidence limit for the n intercept is 0.997-1.009 g/cm3 and the linear regression R square value is 0.996. The assumed density used for the calculations was 1.080 g/cm3. Initially, this low polymer density was qualitatively verified when an attempt was made to sediment the latex by using the normal mobile phase of the SFFF (density = 0.9973 g/cm3). With a speed of 15OOO rpm, the fractogram indicated that the sample did not effectively sediment due to a lack of significant difference between the sample and mobile phase density. This is shown in Figure 4. Excellent sedimentation and separation were achieved for this sample by using a methanol-modified mobile phase of 0.9882 g/cm3. Note that for the case where poor sedimentation occurred using the standard mobile phase, most of the sample eluted near Vo (the channel void volume). Particle size averages for latex A (and latex B, C, and D to follow) were calculated by using the particle density value determined from the density plot and are summarized in Table 111. Latex B (styrene-butadiene copolymer) exhibited a higher density value determined by the x intercept of ita density plot, as shown in Figure 5. The density of latex B was found to be 1.019 g/cm3, with a 95% confidence limit of the x intercept from 1.009 to 1.036 g/cm3, and a linear regression R square
:1
3.0
2.0 X-INTERCEPT = 1.019 g i c m
vi 1.0
4
0.96
0.96
1.00
1.02
1.04
Po, MOBILE PHASE DENSITY,
1 16
g/crn3
Density plot for latex C. Mobile phase densities same as in Figure 5. Figure 6.
2.00 0
PARTICLE DIAMETER AT PEAK #l MAXIMUM PEAK #2 MAXIMUM
0
'2 1.00
X-INTERCEPT = 1.008 gicm3
0
a
'$
3
0,501
0.0 0.96
0.98
P,,
-10.50
\iX;~;~;~;m~
I
1.00
1.02
0
1.04
2 a
0.0
1.06
MOBILEPHASE DENSITY, g i c m 3
Density plot for latex D. Mobile phase densities same as in Figure 5. Flgure 7.
value of 0.973. The assumed density used for the calculations was 1.080 g/cm3. As expected, this latex sedimented adequately and was well-resolved by using the standard mobile phase density. It was determined by DSC analysis that the Tgof latex A was -6 "C and the Tg of latex B was +1 O C (measured at onset of the Tgtransition). The slightly higher Tgof latex B, presumably due to lower butadiene content, would account for the higher polymer density of latex A compared to latex B. The density plots for latex C and latex D (vinyl acetateacrylic copolymers) are shown in Figures 6 and 7, respectively. Latex C was known to be a narrow particle size distribution material, while latex D was known to be bimodal in character. The measured density for latex C was found to be 1.019 g/cm3,
Anal. Chem. 1989, 6 1 , 1937-1941 0.40 I
I
1937
of sample density enables accurate particle size distribution characterization of broad distribution latexes of this type.
CONCLUSION
0
18
54 TIME (MIN.)
36
72
90
F w e 8. Turbdi-time fractograms for latex D using standard mobile phase of 0.1 % Aerosol-OT (solid line; density = 0.9973 g/cm3) and methanoCmodifkd mobile phase (broken line; density
= 0.9882 g/cm3).
with a 95% confidence limit of the x intercept from 1.014 to 1.025 g/cm3. The linear R square value was 0.995. An assumed particle density value of 1.080 g/cm3 was used for latex C. For latex D, the density was measured by using the calculated particle size at the maximum of each of the two peaks in the fractogram shown in Figure 8. An assumed particle density value of 1.080 g/cm3 was used. Fractograms are shown for the standard mobile phase and the methanol-modified mobile phase of 0.9882 g/cm3. As expected, the fractograms are unchanged in shape and character for the two mobile phases. The sample in the methanol-modified mobile phase elutes approximately 7 min later than that of the one in the standard mobile phase. The densities of peaks 1and 2 for latex D in the fractogram are statistically equal, with measured values of 1.012 and 1.009 g/cm3, respectively. The 95% confidence limits of the x intercept for peak 1 are 1.003-1.032 g/cm3 and for peak 2, 1.009-1.019 g/cm3. The linear R square values are 0.980 and 0.960, respectively. This result demonstrates that for this particular vinyl acetate-acrylic latex, the copolymer composition is constant over the entire particle size distribution, although a distinct bimodal character is indicated. The lack of particle heterogeneity coupled with in situ determination
The use of methanol-modified mobile phases with SFFF expands the utility of this technique for characterizing densities of copolymer latexes with values near 1.00 g/cm3. Mobile phase densities from approximately 0.96-1.00 g/cm3 have been successfully used for characterization of these types of polymers. For particle size calculations of copolymers that exhibit suspected bimodal or broad distributions, it is important to establish that separation is by size alone and not due to polymer density heterogeneity.
ACKNOWLEDGMENT The author wishes to express his appreciation to S. C. Voth for assistance in these experiments and W. F. Tiedge and J. V. Martinez for helpful discussions. Registry No. Polystyrene, 9003-53-6; (styrene)(butadiene) (copolymer),9003-55-8.
LITERATURE CITED (1) Yang, F. J.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1974, 4 6 , 1924. (2) Giddings, J. C.; Caidwell. K. D.; Fisher, S. R.; Myers, M. N. Methods Biochem. Anal. 1980, 26, 79. (3) Kirkland, J. J.; Yau, W. W. Anal. Chem. 1983, 55, 2165. (4) Levy, G. B. Amer. Lab. 1987, 19, 84. (5) Kirkland, J. J.; Yau, W. W. Science 1982, 218, 121. (6) Yonker, C. R.; Jones, H. K.; Robertson, D. M. Anal. Chem. 1987, 59, 2574. (7) Giddings, J. C.; Karaiskakis, G.; Caldwell, K. D. S e p . Sci. Techno/. 1981, 16, 607. (8) Yau, W. W.; Kirkland, J. J. S e p . Sci. Techno/. 1981, 16, 577. (9) Po&mer Handbook; Brandrup, J., Irnmergut, E. H., Eds.; John Wiley 8 Sons: New York, 1967.
RECEIVED for review March 13,1989. Accepted May 23,1989. This work was presented in part at the First International Symposium on Field-Flow Fractionation, June 15, 1989, Park City, UT.
A Different Perspective on the Theoretical Plate in Equilibrium Chromatography Paul J. Karol Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
The differential rate model for equlllbrlum chromatography Is used to derlve both the continuous (Martin and Synge) plate model and the stepwlse (Cralg) plate model. The latter have previously been regarded as severely deflclent because of the ad hoc manner In whlch the plate height Is related to the chemistry and physlcs of the chromatographic process. However, It Is demonstrated that the “height equivalent to a theoretical plate” arises naturally from a finite different approach to solvlng the rate equatlon. I t Is also argued that the much mallgned step model Is a phenomenologically valld approximation to the continuous plate model and also to the rate model.
INTRODUCTION
of view, we will try to demonstrate that the plate concept is a phenomenologically and mathematically sound approximation to the chromatographic process and that its use is partially exonerated. After separately reviewing the differential rate model and the plate model, the link between them will be discussed. In so doing, it will be argued that the literature on this topic (1-7) routinely handicaps the plate model by prematurely invoking a unidirectional transport restraint in deriving chromatogram equations. It is that act which is the source of discord with the current procedure.
THEORY The (simplified) rate model for continuous flow equilibrium chromatography ( I ) , ignoring velocity profiles, usually starts with a differential rate equation such as
For the past 25 years the theoretical plate model has been viewed as failing to describe the physical and molecular events occurring in chromatography ( 1 ) . In contrast to this point 0003-2700/89/0361-1937$01.50/0
0 1989 American Chemical Society
