2271
Anal. Chem. 1965, 57, 2271-2275
Though the solubility of bismuth and tin(1V) in the eluting agent is higher than that in aqueous 0.5 M hydrochloric acid and considerably higher than that in acid of lower concentrations, it is nevertheless still limited and presents a problem which needs to be watched. Tests showed that 100 mL of the eluting agent will dissolve about 1g of bismuth and tin(1V); but to be on the safe side and to avoid side effects due to hydrolysis, adsorption of 1 g amounts of these elements was carried out from 200 mL of solution. Another problem is due to possible background contamination when very low amounts of lead have to be determined. Glassware has to be cleaned carefully and good AR purity reagents have to be used in measured amounts. A typical series of blank runs (triplicate) gave a value of 0.74 f 0.03 pg of lead. This relatively good reproducibility of the blank runs contributed significantly to the reproducibility and sensitivity of the method. The results obtained for actual samples (Table 11) show an excellent reproducibility, while results obtained for synthetic
mixtures (Table I) seem to indicate that the reproducibility is matched by an absolute accuracy almost as good. When relatively large samples are taken as for cadmium chloride (4 g), the sensitivity of the method is less than 0.05 pg of Pb per gram of sample. Registry No. Pb, 7439-92-1; Bi, 7440-69-9; Sn, 7440-31-5; Cd, 7440-43-9; In, 7440-74-6.
LITERATURE CITED (1) Strelow, Franz W. E.: van der Walt, Tjaart N. Anal. Chem. 1981, 53, 1637-1640. (2) van der Walt, TJaart N.; Strelow, Franz W. E.: Haasbroek, Floors, J. I n t . J. Appl. Radiat. Isot. 1982, 33, 301-303. (3) Fritz, James S.; Garralda, Barbara G. Anal. Chem. 1962, 34, 102-1 06. (4) Strelow, Franz W. E. Anal. Chem. 1984, 56, 1053-1056. (5) Strelow, Franz W. E. Anal. Chim. Acta 1984, 160, 31-45. (6) Strelow, Franz W. E. Anal. Chlm. Acta 1981, 127, 63-70. (7) Strelow, Franz W. E. Anal. Chem. 1978, 50, 1359-1361.
RECEIVED for review April 2, 1985. Accepted May 28, 1985.
Effect of Particle Conformation on Retention in Sedimentation Field Flow Fractionation J. J. Kirkland,* L. E. Schallinger,' and W. W. Yau E. I. d u Pont de Nemours and Company, Central Research and Development Department, Experimental Station, Wilmington, Delaware 19898
Basic concepts in sedimentatlon fleid flow fractlonatlon (SFFF) retention assume that particle shape or conformatlon Is not a factor and that retentlon Is a direct function only of particle mass. Unexpected results wlth blomacromoiecules of very hlgh aspect have led to a study on the effect of various partlcle shapes on SFFF retentlon. The effect of conformation on retentlon was tested for partlcles conslstlng of spheres, Irregulars, rods, and piates In a range of operating condltlons. Results show that particle shape has llttle or no effect on SFFF retention until the aspect ratio becomes qulte large (>50-100). Only wlth extremely hlgh aspect ratios can retention errors become large, and In these cases, very small moblle phase veloclties can be used io obtain correct retention and accurate calculated partlcle sires or molecular weights.
The utility of sedimentation field flow fractionation (SFFF) for characterizing the size distributions of a wide range of particulates has been clearly established (1-5). The latest SFFF equipment and techniques permit the handling of particles in the 0.005-2 pm range (6).Soluble macromolecules with molecular weights of about 5 X lo5 to lo8 also can be separated, isolated, and characterized (7-11). In SFFF the particulates or soluble macromolecules are introduced into an open channel formed by parallel plates that are shaped like a ribbon or belt and suspended in a centrifuge. The channel is then rotated without mobile phase flow for a relaxation or 'Present address: 3M Center, Analytical and Properties Research, St. Paul, MN 55144.
preequilibration step, causing particles to be forced toward the wall regions of the channel. Sample particles that have an effective mass greater than the mobile phase are forced toward the outer wall. Diffusional force in opposition to this external centrifugal force causes the particles to establish a specific layer thickness near the wall as a function of effective particle mass. Liquid mobile phase is then caused to flow continuously through the channel with a characteristic laminar flow profile. Smaller particles that are less influenced by the external force field are engaged by regions of faster flow and elute from the channel first, followed by particles of increasing mass that are closer to the wall and intercepted by slower flow streams. The resulting elution pattern or fractogram provides information on the masses of sample constituents as a result of the quantitative relationships describing SFFF retention (1,8). The basic concepts in SFFF retention assume that particle conformation is not a factor and that retention for particles of equal density is a direct function of particle mass. However, preliminary experiments with very long, linear biomacromolecules indicated a significant change in calculated particle mass with changes in mobile phase flow rate. Since this unexpected phenomenon was not anticipated in view of basic SFFF concepts, a study was carried out on the effect of various particle shapes on SFFF retention.
THEORY In SFFF when equilibrium is established with particles as a result of the force generated by the external force field and the normal particle diffusion, the species is distributed across the channel as an exponential concentration function (1)
c = coe-r/l
0003-2700/85/0357-227 1$01.50/0 0 1965 American Chemlcal Society
(1)
2272
ANALYTICAL CHEMISTRY, VOL. 57, NO. 12, OCTOBER 1985
where c is the solute concentration at distance x from the analytical wall, co is the concentration at the wall, where x = 0, and 1 is the distance characteristic of the mean concentration of the particle distribution profile. Parameter 1 can be characterized by the expression ( I )
1 =D/U where D is the solute diffusion coefficient and U is the mean particle velocity that is induced by the external force field. Thus, the external force field tends to compress the layer thickness, I , and particle diffusion tends to increase this layer thickness. The dimensionless ratio term X determines the magnitude of both particle retention and bandwidth ( I )
h = 1/W = D / U W
(3)
where W is the thickness of the channel. Now, the particle diffusion coefficient D can be described by
D = kT/f
(4)
where k is the Boltzmann constant, T is the absolute temperature (Kelvin), and f is the frictional force coefficient of the particle in the liquid. The mean velocity of the particle that is induced by the external force field can be expressed as
U = ma/f
(5)
where m is the effective particle mass and a is the acceleration of the particle caused by the force field. Substituting eq 4 and 5 in eq 2 produces the relationship
I=
D ma/(kT/D)
= -kT ma
Note that in eq 6 the shape-dependent diffusion coefficient of the particle cancels out, leaving the mass of the particle m and its acceleration a caused by the external force field as the prime determinants of parameter 1 describing retention. Thus, the basic theory of SFFF retention predicts that particle conformation should not have an effect on the retention process. A specific retention expression for SFFF has been derived by expressing the characteristic thickness 1 in terms of relevant experimental parameters (I)
(7) where Ro is the gas constant (8.31 X lo7 g-cm2/(s2.deg-mol)),
M is the molecular weight (g/mol), w is the centrifuge speed (rad/s), r is the radial distance from the centrifuge rotating axis to the SFFF channel (cm), Ap is the density difference between the sample component and the mobile phase (g/cm3), and p s is the density of the sample component (g/cm3). Retention in SFFF also can be related to particle diameter. For spherical particles
mol-l), and d, where No is Avogadro’s number (6.022 X = particle diameter (cm). Combining eq 7 and 8 produces A =
6kT rd,3u2rWAp
where k is Boltzmann’s constant (1.38 x g-cm2/(s2.deg)). Note that the relationships in eq 7 and 9 predict that retention (or calculated molecular weight or particle diameter dpvalues) is independent of the mobile phase flow rate F which does
Table I. Effect of Flow Rate on A-DNAasb flow rate, rotor speed, mL/min rpm
A
apparent calcd mol wt polydispersityC (Xl09 (Mw/Mn)
2.0 1.0 0.5 0.25 0.12
8 500 8 500 8 500 8 500 8 500
0.036 0.033 0.028 0.018 0.012
10.0 12.0 14.1 20.7 32.4
1.16 1.14 1.10 1.10 1.06
2.0 1.0 0.5 0.25
10 000 10 000 10 000 10 000
0.033 0.026 0.019 0.012
4.5 11.5 15.8 24.5
1.19 1.12 1.11 1.09
1.0 0.5
12000 12 000
0.017 0.013
11.8 15.0
NCd NCd
A-DNA mol wt is 33 X lo6. *Conditionswere as follow: Channel thickness, 0.024 cm; rotor speed, constant,as shown; relaxation, 10 min; detector, UV at 260 nm; sample, 6 fig in 100 rL of mobile phase; mobile phase, 0.01 M Tris-0.1 M NaCl, pH 7.6. CNocorrections for instrumental band broadening were made. d NC, not calculated; very broad peak. not appear as a variable in the retention equation. Previous studies have suggested that the retention relationships given in eq 7 and 9 appear to be valid for a wide range of particle types. On the other hand, specific information on the effect of various particle shapes in SFFF has not been described.
EXPERIMENTAL SECTION Apparatus. Data reported in this study were obtained on a research SFFF instrument constructed in a Sorvall Model RC-5 Superspeed centrifuge (Du Pont Biomedical Products, Wilmington, DE) with a “floating”plastic rotor containing the SFFF channel (6). The 0.0240 cm thick channel had a span of 2.54 cm and a length of 43.6 cm. The remainder of the equipment used in the separations has been described previously ( 4 , 5 ) . A MINC 023 computer (Digital Equipment Corp., Maynard, MA) was used to control the speed of the rotor, collect elution data, and calculate sample molecular weights or particle sizes. General procedures for equipment operation including sample injection,relaxation, and other features have been previously reported (4,5,12). A mobile phase of 0.001 M ammonium hydroxide was used for the silica-based particles. Studies with quinacridone were carried out with 0.1% Aerosol OT anionic surfactant (Fisher Scientific Co., Pittsburgh, PA) as the mobile phase. Data for A-DNA (Bethesda Research Laboratories, Bethesda, MD) were obtained by using a mobile phase of 0.01 M Tris, 0.1 M sodium chloride, pH 7.6. The silica sol sample, silica-coated attapulgite rods, and sodium polysilicate plates were kindly supplied by R. K. Iler (Wilmington, DE). Other materials were obtained within Du Pont.
RESULTS AND DISCUSSION Although the shape of a molecule affects its behavior in processes such as diffusion, viscosity, and sedimentation velocity, particle conformation was not expected to influence retention in SFFF. The theoretical considerations of eq 4 to 6 predict that any contribution of particle shape on retention as a result of the external force field and opposing particle diffusion would be entirely compensating. The possible effect of particle conformation on SFFF retention first came to light while studying the behavior of A-DNA in SFFF (IO). As indicated by the data in Table I, we found unexpectedly that the dimensionless retention factor A increased and the calculated molecular weight of A-DNA decreased with increasing flow rate. Concurrently, the apparent sample polydispersity (ratio of weight-average to number-average molecular weight) of this single molecular weight compound apparently increased with increased flow rate. The data in Table I show that the molecular weight and polydispersity of A-DNA only ap-
ANALYTICAL CHEMISTRY, VOL. 57, NO. 12, OCTOBER 1985
2273
Table 11. Effect of Flow Rate on Retention and Particle Size of Various Particles
particle type
rotor speed, rpm
flow rate, mL/min
exptl hb
apparent polydispersity”
particle diameter, pm dPm dPW dPn
dpw/dpn
spheres (silica sol)
5000
8 4 2 1
0.030 0.026 0.026 0.029
0.0409 0.0393 0.0402 0.0393
0.0443 0.0424 0.0427 0.0416
0.0380 0.0369 0.0382 0.0378
1.17 1.15 1.12 1.10
irregular (quinacridone)
6000
8 6 4 2 1
0.032 0.028 0.030 0.027 0.027
0.0470 0.0485 0.0475 0.0471 0.0480
0.0498 0.0516 0.0502 0.0488 0.0492
0.0441 0.0454 0.0447 0.0442 0.0450
1.13 1.14 1.12 1.10 1.09
rods (attapulgite)
5000
8 4 2 1 0.5
0.020 0.016 0.014 0.011 0.014
0.0447 0.0463 0.0479 0.0497 0.0484
0.0480 0.0488 0.0494 0.0506 0.0496
0.0424 0.0437 0.0449 0.0470 0.0460
1.13 1.12 1.10 1.08 1.08
200
8 4 2 1 0.5
0.017 0.014 0.011 0.010 0.007
0.405 0.421 0.434 0.457 0.479
0.407 0.423 0.434 0.456 0.476
0.393 0.412 0.423 0.446 0.456
1.04 1.03 1.03 1.02 1.04
plates (sodium polysilicate)
h a No corrections for instrumental band broadening were made. d m = number average diameter.
proached the theoretical values (molecular weight = 33 X lo6; polydispersity N 1.0) at relatively low flow rates. Higher flow rates resulted in early elution of A-DNA,with a much broader peak than that predicted for a single molecular weight. As illustrated by the data in Table I, the effect of flow rate on calculated molecular weight was increasingly magnified at higher rotor speeds that resulted in smaller I values for the A-DNA. Similar data to that for A-DNA was obtained with adenovirus DNA (23 X lo6 mol wt). Both of these materials have extremely long, narrow conformations and very high aspect (length/width) ratios. Steric effects (13)apparently do not significantly contribute to changes in calculated molecular weight values in Table I, as evidenced by the fact that results with increasing rotor speeds at the same flow rate (e.g., 1.0 mL/min) are constant within experimental error. If steric effects were prominent, it would be expected that the calculated molecular weight values would decrease with increasing rotor speed. From these initial experiments with linear DNA’s that act as extended semirigid rods in solution, it was apparent that such materials behave differently in actual SFFF experiments than predicted by the theory of eq 7 and 9. The fact that the large aspect ratio of the linear A-DNA and adenovirus DNA molecules does not behave as expected suggested that further studies on particle conformation were needed to define the influence of large particle shape differences on retention. To eliminate the possibility that the semirigid state of organic molecules might complicate an understanding because of possible shape changes in solution, rigid inorganic model particles of varying shapes were obtained for study. The basic approach used in this study was to determine the influence of flow rate on retention. From these observed retention values, mean particle diameters dpm were calculated in each experiment for various flow rates according to the procedures described in ref 4. These experiments utilized turbidimetric detection and conversion of this detector output to concentration vs. particle size plots using the Mie scattering theory (4). To test the effect of conformation, rigid particles in the shape of spheres (a silica sol), irregular particles (quinacridone), rods (attapulgite), and plates (sodium polysilicate plates) were studied. Table I1 shows the data obtained in these
V0/6VR; dpm = median diameter; dpw = weight average diameter;
I
I
I
I
,
,
PARTICLE SILICA SOL QUINACRIDONE
0
0
,
,
SHAPE SPHERE IRREGULAR
i
0030
1
2
3
4
5
6
7
8
MOBILE PHASE FLOWRATE, MLIMIN
Flgure 1. Effect of particle shape on SFFF retention as a function of moblle phase flow rate: channel, 0.024 cm. Silica sol conditions are rotor speed, 5000 rpm; as follows: mobile phase, 0.001 M “,OH; sample, 100 pL, 1 . 2 % ; detector, UV, 250 nm; relaxation, 5.0 min. Quinacridone conditions are as follows: mobile phase, 0.1 % Aerosol-OT; rotor speed, 6000 rpm; sample 100 pL, 1 %; detector, UV, 625 nm; relaxation, 5.0 min. Attapulgite conditions are the same as those for sllica sol above. Sodium polysilicate conditions are the same as those for silica sol above, except detection was at 260 nm and relaxation was 2.0 mln.
-
studies, and Figure 1shows the calculated particle diameter vs. mobile phase flow rate plots that were obtained on each of these materials. A discussion of the effects suggested by the data in Table I and Figure 1 follows. Spheres. Spheres in the form of silica sols were selected for study to verify the theory of eq 7 and 9, which suggest that a flow rate change should not have an effect on the retention of regular-shaped particles. In this case a sample was chosen
2274
ANALYTICAL CHEMISTRY, VOL. 57. NO. 12, OCTOBER 1985
Flgure 2. Transimlasion electron photomicrographs of particles: (a) spheres, silica sob (b) irregular particles. quinacridone; (c) rods. sillca-modifled attapulglte: (d) plates. sodium poiysilicate.
that exhibited a particle size range of 0.034.08 pm as determined by transmission electron micmmpy, with an average particle size of roughly 0.04 pm being indicated (Figure 2a). Data for the silica sol sample in Figure 1 (open circles) and Table I1 show, within experimental error, the expected constant A value and a constant mean particle size of about 0.04 pm for these spheres. Also shown in Table I1 are the calculated polydispersities (dpw/dpn) of the silica sol sample calculated a t the various flow rates. The apparent polydispersity of this sample increases with flow rate increase, suggesting an increase in instrumental band broadening at higher flow velocities. To ensure that no errors occurred as a result of deleterious concentration effects a t the 1.2% solids level, several separations also were carried out a t a sample concentration of 0.3%. Similar results were obtained, indicating that concentration effects were not significant at the level studied. Therefore, data obtained a t the 1.2% sample level was used for consideration, since particle diameter calculations at this concentration were more precise hecause of better signal-tonoise response of the detector. Irregular Particles. To test the effect of irregularly shaped particles, a sample of a finely pulverized pigment, quinacridone, was utilized. A transmission electron micrograph of this sample is shown in Figure 2b. These particles are mostly irregular, with aspect ratios of about 2 to 3. The data in Table I1 and the plot in Figure 1 (open hexagon) show that no change in calculated particle diameter is found when the flow rate is varied; the theory of eq 7 and 9 is confumed. Again,there is an increase in the calculated polydispersity for the particles of this irregularly shaped sample, probably due to the increase in hand broadeniw - due to mass transfer effecta a t high flow rates. The silica sol and quinacridone data in Figure 1and Table I1 verify the concepts on which eq 7 and 9 are based; namely, retention and calculated particle size are independent of flow rate for spherical particles and even irregular particles with appreciable aspect ratios. Rods. Attapulgite, a hydrated aluminum magnesium silicate clay, is a needlelike rigid particle typically about 1.0 pm in length and 0.01 fim in thickness. To ensure that the
chemical effects of such a particle would he comparable to that for the spherical silica sol discussed above, a sample of attapulgite particles was obtained in which the surface was completely covered with a skin of silica. Thus, the surface charge of the modified attapulgite was the same as silica sol particles and sodium silicate plates. A transmission electron micrograph of these particles is shown in Figure 2c. The aspect ratio of this mdlike structure is typically about 5&100. The plot in Figure 1for this modified attapulgite sample (solid triangles) clearly shows progressively smaller calculated particle sizes with increasing flow rates. At lower flow rates (e.g.,
