Langmuir 1996,11, 2399-2404
2399
Accurate Measurement of Density of Colloidal Latex Particles by Sedimentation Field-Flow Fractionation J. Calvin Giddings" and John Ho Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 Received July 25, 1994. I n Final Form: March 15, 1995@ In this study the density of colloidal latex particles was determined to four figure accuracy by subjecting the colloid to a series of sedimentation field-flow fractionation runs in which the density of the aqueous carrier solution was systematicallyvaned. Accuracy was gained by using high-field strengths which made possible the use of carriers with densities only 0.0005-0.05 g/cm3 removed from the isopycnic particle density. Both positive and negative density differences were used, yielding independent measurements of particle densities that differed on average by only 0.0003 g/cm3. At the high accuracy level achieved, a trend was discerned in w,fich the apparent or isopycnic density of polystyrene latex particles increases systematicallywith size, gaining -0.002 g/cm3over the diameter range 0.26-0.46pm. This trend is likely attributable to interfacial effects, particularly to an interfacial volume increment generated by structural rearrangements relative to the bulk phases at the particle-aqueous interface. A comparison of the data with theory yields, after correcting for Young-Lapacg particle compression, a specific interfacial volume (volumeincrement per unit area of interface) of -1.7 A and an ambient bulk polystyrene density of 1.0530 f 0.0003g/cm3. Suggestions are made for improving the work and extending it to the measurement of small second-ordereffects associated with adsorption,swelling, and polymer relaxation in the glassy state.
Introduction Sedimentation field-flow fractionation (SdFFF) is a chromatographic-like technique used to separate colloids and particles in the 0.01-100;um size range based on mass, size, or density differences.1-6 Separation occurs in a curved ribbonlike flow channel embedded in a rotor. The particle mass, diameter, density, and related parameters of the fractionated components can be determined by the time required for their elution from the rotating channel. This has made possible the accurate characterization of colloidal particles and distributions of particles and emulsions using SdFFF.5,7 In practical terms, the measurement of the particle size and size distribution of colloidal particles of known (or assumed) density has been the most prominent use of SdFFF.4-6,8-23 The SdFFF technique has been less
* Address correspondence to this author. *Abstract published in Advance A C S Abstracts, J u n e 1, 1995. (1)Giddings, J. C.; Yang, F. J . F.; Myers, M. N. Anal. Chem. 1974, 46, 1917-1924. (2) Giddings, J. C.; Caldwell, K. D. In Ph~sicalMethodsofChemistry; Rossiter, B. W., Hamilton, J. F., Eds.; Wiley: New York, 1989;Vol. 3B; pp 867-938. (3) Caldwell, K. D. Anal. Chem. 1988, 60, 959A-971A. (4) Giddings, J. C.; Myers, M. N.; Moon, M. H.; Barman, B. N. In Particle Size Distribution II:Assessment and Characterization;Provder, T., Ed.; ACS Symposium Series 472; American Chemical Society: Washington, DC, 1991; pp 198-216. ( 5 ) Giddings, J. C. Science 1993,260, 1456-1465. (6) Beckett,R.;Hotchin, D. M.; Hart, B. T. InEnuironmental Particles; BufTle, J., van Leeuwen, H. P., Eds.; CRC Press: Boca Raton, FL, 1993; Vol. 2, pp 157-195. (7) Giddings, J . C.; Karaiskakis, G.; Caldwell, K. D.; Myers, M. N. J. Colloid Interface Sci. 1983, 92, 66-80. (8)Giddings, J. C.; Myers, M. N.; Yang, F. J. F.; Smith, L. K. In Colloid and Interface Science; Kerker, M., Ed.; Academic Press: New York, 1976; Vol. W ,pp 381-398. (9) Kirkland, J . J.; Yau, W. W. Science 1982,218, 121-127. (10)Yang, F.-S.; Caldwell, K. D.; Giddings, J. C. J.Colloid Interface Sci. 1983,92, 81-91. (11)Martin, M. In Particle Size Analysis 1985; Lloyd, P. J., Ed.; Wiley: New York, 1987; pp 65-85. (12) Giddings, J. C.; Caldwell, K. D.; Jones, H. K. In Particle Size Distribution: Assessment and Characterization;Provder, T., Ed.; ACS Symposium Series 332: American Chemical Society: Washington, DC, 1987; Chapter 15. (13) Beckett, R.; Nicholson, G.; Hart, B. T.; Hansen, M.; Giddings, J. C. Water Res. 1988,22, 1535-1545. 0743-746319512411-2399$09.00/0
frequently used to measure particle density, although the potential accuracy of measurement is very high.24 Nonetheless, reports from a number of research groups suggest that density measurements by SdFFF have a n important role to play in colloid characterization, with applications to latex particle^,^^-^^ v i r ~ s e s ,diesel ~ ~ , soot,16 ~ ~ liposomes,32 and silica.33 In the original publication on density measurements by SdFFF, a method was developed in which the density of polystyrene latex particles was determined by a series of runs using carrier (suspending) liquids of different densities.24 The density was controlled by the addition of sucrose. A plotting procedure was devised that allowed the simultaneous measurement of both particle size and (14) Oppenheimer, L. E.; Smith, G. A. J. Chromatogr. 1989, 461, 103-110. (15) Caldwell, K. D.; Li, J . J. Colloid Interface Sci. 1989,132,256268. (16) Kirkland, J. J.; Liebald, W.; Unger, K. K. J. Chromatogr. Sci. 1990,28, 374-378. (17) Levin, S. Isr. J. Chem. 1990, 30, 257-262. (18) Koch, L.; Koch, T.; Widmer, H. M. J. Chromatogr. 1990,517, 395-403. (19)Hansen, M. E.; Short, D. C. J.Chromatogr. 1990,517,333-344. (20) Chittleborough, D. J.; Hotchin, D. M.; Beckett, R. Soil Sci. 1992, 153,341-348. (21) Beckett, R.; Nicholson, G.; Hotchin, D. M.; Hart, B. T. Hydrobiologia 1992,2351236, 697-710. (22) Barman, B. N.; Giddings, J. C. In Chromatography ofPolymers: Characterization by SEC and F F F Provder, T., Ed.; ACS Symposium Series 521; American Chemical Society: Washington, DC, 1993; pp 30-46. (23) Giddings, J. C.; Williams, P. S. A m . Lab. 1993,25, 88-95. (24) Giddings, J. C.; Karaiskakis, G.; Caldwell, K. D. Sep. Sci. Technol. 1981,16, 607-618. (25) Kirkland, J. J.;Yau, W. W. Anal. Chem. 1983,55,2165-2170. (26)Nagy, D. J. Anal. Chem. 1989, 61, 1934-1937. (27) Jones, H. K.; Giddings, J. C. Anal. Chem. 1989,61, 741-745. (28) Koliadima, A,; Dalas, E.; Karaiskakis, G . J. High Resolut. Chromatogr. Commun. 1990,13, 338-342. (29) Blanda, M.; Reschiglian, P.; Dondi, P.; Beckett, R. Polym. Int. 1994. ~ _ _, 33. - - ,61-69. -~ - (30) Caldwell, K. D.; Karaiskakis, G.; Giddings, J. C. J. Chromatogr. 1981,215, 323-332. (31) Yonker, C. R.; Caldwell, K. D.; Giddings, J. C.; van Etten, J . L. J . Virol. Methods 1985, 11, 145-160. (32) Caldwell, K. D.; Karaiskakis, G.; Giddings, J. C. Colloids Surf. 1981,3, 233-238. (33)Yonker, C. R.; Jones, H. K.; Robertson, D. M.Anal. Chem. 1987,59, 2573-2579. ~
0 1995 American Chemical Society
2400 Langmuir, Vol. 11, No. 7, 1995 density. The plotting procedure was later modified to accommodate runs made a t different field strengths (different r p m ~ ) . ~ ' In the plotting procedure referred to above, the carrier density is plotted against experimental retention and field strength data such that a straight line is generated. The slope of the line yields particle diameter. In order to determine particle density, the line must be extrapolated to the point of neutral buoyancy or the isopycnic point. It is important to understand that the particle behavior is never measured under isopycnic conditions; in fact, there is no retention a t the isopycnic point and thus no precise data can be generated at that point. As a result, the isopycnic condition is found by extrapolation. As with most extrapolations, accuracy increases for data sets that lie close to the point sought by extrapolation. One object of this work is to bring the data set close to the isopycnic point to improve accuracy. Thus for our experiments the difference he between the carrier density and the isopycnic density lies in the range 0.0005-0.05 g/cm3. The accuracy of density measurement near the isopycnic point is very high because here the particle retention is extremely sensitive to small variations in carrier or particle density (see next section). The SdFFF method is particularly convenient for most aqueous colloidal latex suspensions with particles having densities near that of water. It is then simple to modify the aqueous carrier density upward or downward to approach the colloid density using additives such as sucrose, glycerol, methanol, and various salt^.^^^^^ For particles having a density more distant from water's density, one must (a) use higher additive concentrations, (b)use nonaqueous carriers,34or (c)rely on amore extended extrapolation. The latter procedure, while reducing accuracy, has the advantage that for fragile species such as some bioparticles, the aqueous carrier need not be modified to such a degree that the particle is damaged or disrupted by the high concentration of additive a t the isopycnic point. Thus SdFFF has been applied to the measurement of virus densities using dilute solutions that remain far below isopycnic d e n ~ i t i e s . ~ ~ , ~ ~ The purpose of the present paper is to use the modified plotting technique in conjunction with relatively highfield SdFFF operation and more accurate control and measurement of the carrier density to closely approach the isopycnic point of some colloidal latex particles and thus obtain highly accurate density measurements. We are particularly interested in small shifts in density with changes in particle size as a possible reflection of interfacial effects.
Theory The retention timet, of a monodisperse colloidal sample in FFF is expressed by2,34,35
where to is the void time (the retention time of a nonretained component) and A is the retention parameter, which is given by
In this equation k is the Boltzmann constant, T is temperature, w is channel thickness, and F is the (34)Giddings, J. C. Sep. Sci. Technol. 1984,19, 831-847. (35)Giddings, J. C. Unified Separation Science; Wiley: New York, 1991.
Giddings and Ho transverse driving force exerted by the field on a single particle. For a sedimentation field F is expressed by36,37
F = mG(1 - QD)
(3)
where m is particle mass, G is the field strength expressed as acceleration, e is the carrier density, and D is the partial specific volume of the colloidal sample. Force F can be positive or negative, for sinking and floating particles, respectively. By measuring t,, values of F (and the physicochemical properties on which F depends) can be subjected to measurement down to extremely low levels, F 10-l6 N.5 Partial Specific Volume. When particle dimensions greatly exceed molecular dimensions such that interfacial effects are small, ii may generally be replaced by I/&, where @b is the bulk density of the particle. However, for measurements made near the isopycnic point (where eii = 11,F i s extremely sensitive to ii. Here small differences between D and 1/@bcan become experimentally significant. Considering that typical colloid dimensions exceed the dimensions of molecules (or molecular segments) by only -102-103, it is important to account for D more completely to obtain a valid F close to isopycnic conditions. The partial specific volume D is defined by38
-
=
(s)Tp
(4)
where V is the volume of the colloidal suspension a t temperature Tand external pressurep and m+is the mass of suspended colloid. As colloidal mass is added to the carrier suspension, the volume V of the latter changes because the liquid is displaced (in the absence of solvation) from the physical volume of the intruding particle mass without regard for the new interfaces generated and new particle-liquid interfaces are created that may lead to either an expansion or contraction of volume depending upon molecular configuration around the interface. These two effects give rise to the two respective terms (at constant T and p ) on the right side of the expression =
(z)A (3,+-g+ +
which reduces to
where @ b is the bulk density of the material composing the particle, A is the interfacial area, and Di = (8V/aA),+. The term iii, representing the change in volume per unit gain in interfacial area, can be termed the specific interfacial volume. By way of elaboration, the two terms on the right of eqs 5 and 6 can be visualized as those arising when (a) a macroscopic mass of solid is introduced into a large volume of suspending liquid and (b) the mass is subdivided into particles and the interfacial area is generated. However, subdivision into particles also leads to particle compression via the Young-Lapace effect (see eq 12). This effect can be accounted for by assuming that the density @b of the mass introduced in (a) is the postcompression density. Returning to eq 6, for spheres of diameter d the final term becomes (36)Shaw, D.J.Introduction to Colloid and Surface Chemistry; 3rd ed.; Buttenvorths: London, 1980;Chapter 2. (37)Hunter, R.J.Foundations of Colloid Science; Oxford University Press: New York, 1987;Vol. I, Chapter 3. (38)Freifelder, D. Physical Biochemistry, 2nd ed.; W. H. Freeman: San Francsico, 1982;Chapter 12.
Density of Colloidal Latex Particles
Langmuir, Vol. 11, No. 7, 1995 2401
aA - 68 an+ @bd
(7)
where 8 is a surface roughness factor. Equation 7 can be used for nonspherical particles of effective spherical diameter d providing 8 accounts for the increased interfacial area of such bodies relative to spheres. Equations 3, 6 , and 7 can be combined to yield
F = m G [1 - :(l+
T)]
Clearly the last term in the inner brackets has diminishing importance for inp-easing particle diameter d . If 8Di = 1 A and d = 3000 A, the final term is only 0.002 with 8 = 1, a negligible term compared to unity. However if Q = 0 . 9 9 5 ~and ~ d = 3000 A, as representative of some of the experiments reported here, then the presence or absence of 88i = 1 A would cause a 40% shift in F and thus also in A and in the measured retention time t,. Particle Density. When particle mass m in eq 8 is replaced by diameter d using m = .nd3@b/6and eq 8 is substituted into eq 2, rearrangement gives
where w = GkT/.nw. The (+) and (-1 signs apply when the particles float and sink, respectively. Either case provides viable FFF operation. For any given experiment, field strength G and carrier density Q are fixed and A is determined from eq 1 based on the measured retention time t,. A plot of Q versus VAG for a series of experiments at different carrier densities should, based on eq 9, yield a straight line for which the intercept and slope are
(10) S=
fw d 3 ( l 66Ui/d)
+
(14) When 68Dild
