J. Calvin Giddings Department of Chemistry University of Utah Salt Lake City, Utah 841 12
Future Pathways for Analytical Separations Separations employ such a variety of physical and chemictalforces, flows, phases, and geometrical designs that we can imagine a near infinity of pathways toward future technology. Yet, only a handful of techniques has become useful in present-day analytical chemistry, despite long and intensive effort. Optimistically, there are many important developments yet to be made, but obviously not each conceivable pathway will be productive. How do we choose the open pathways and avoid those that are dead ends? I t is this author’s opinion that the search for future separation technology can be both inspired and streamlined by going t? the roots of separative processes: finding out how and why these processes work, the parameters that limit them, and the measures that allow them to be compared. One source of perspelctive and guidance is the study of separation systematics-how separations, in general, originate and relate. Historically, different separation methods have been developed and refined by different cadres of scientists iwho rarely talked to one another to share insights and progress. By and large, methods have evolved independently (1).A shining exception is high performance liquid Chromatography (HPLC), which was initiated by extrapolating the theory of optimization of gas chromatography ( 2 4 ) .Without this extrapolation, it might have taken HPLC another decade to evolve, a t a great loss to science. Such relationships ought to be the rule, not the exception. Based on the talk, “New Directions in Separation Science,” presented at the symlposium, “New Directions in Analytical Chemistry,” at the 1981 Pittshur h Conference on Analytical Chemistry and Appyied Spectroscopy, Atlantic City, N.J., March 9,1981.
The search for future separation technology can be both inspired and streamlined by going to the roots of separative processes.
In a more specific vein, studies of GC and LC have shown that there are ceilings to separation performance that depend on certain physicochemical parameters such as viscosity and diffusivity, and operating limits such as the maximum pressure drop (5-8). Subsequent studies have similarly shown ceilings for electrophoresis and sedimentation (9, IO),isoelectric focusing and isopycnic sedimentation (10, l l ) ,and field-flow fractionation (12). Taking a systematic point of view, we conclude that the search for new areas of technological achievement in separations requires: pushing closer to the ceilings by careful experimental design, pushing back the ceilings by extending the limiting parameters, and finding new approaches with new ceilings beneath which new kinds of separations can be achieved. Opportunities and Constraints Imposed by Systematics There are some universal underpinnings of separations that bear on any global view. The treatment below borrows liberally from the author’s previous work (1,10). To start with, the act of separation requires that different components be
pulled apart, so there must always be a physical displacement through space. Therefore, transport processes underlie separations. The transport must, of course, have some elements that make it differential. There are two classes of displacement: bulk or flow displacement, in which components are carried along in their medium, and relative displacement through the surrounding medium. These displacement processes complement one another: The first is powerful but nonselective while the second is relatively weak in displacement power but provides selectivity. Since transport must be differential for sep’aration, relative displacement is needed in all separation processes. By contrast, flow displacement is optional. (Transport through evacuated chambers is a displacement class not considered here.) Focusing first on the key process of relative displacement, we note that the transport rate J per unit area along axis x is given by the expression (9):
0003-2700/81/035 1-945A$01.OO/O
0 1981 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
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b
Flgure 1. The three types of chemical potential @*) profiles underlying the relative displacement of separation processes
where c is concentration, p* is the chemical potential driving transport (at least in isothermal systems), f is the friction coefficient, R is the gas constant, and T is the absolute temperature. The friction coefficient measures the drag force on molecules or particles undergoing relative transport through a medium. Our first global concltision stems directly from this equation. We see that relative transport rates are inversely proportional to the friction eoefficient f. Therefore, the time scale for any desired level of relative transport is proportional to f. Since the relative transport described by Equation 1underlies all separations, the time scale of separation is universally linked to the magnitude off. Separation speed, on the other hand, is inversely related to f, a point we shall illustrate in the next section. According to Stokes's law, f is directly proportional to viscosity ( 9 ) and particle radius ( a ) : f = 6rqa (2) Where this law is applicable, a reduction in carrier viscosity will hasten separation. This conclusion is almost universal in separations. Changes in the medium or in the temperature can be used to this end (IO). We note that friction coefficient f and diffusion coefficient D are inversely related hy the Planck-Einstein equation f = RTID (3) Hence, the time scale of separation, linked directly with f, is inversely related to D. Separation speed almost always increases with D . The chemical potential ( p * ) profile has two elements: a continuous (c) part resulting from the application of an external field, and a discontinuous (d) component resulting from the abrupt partitioning forces acting across an interface. Therefore, the p* S46A
Relative Displacement
I
I
Figure 2. Orientations and conditions of flow with respect to the relative displacement axis in separation systems. S = static. F = flow
Table 1. Grouping of Separation Methods In the Nine Categorles Based on Flow and Relative Displacement
sc S
(static)
Electrophoresis lscelectric focuslng Rata-zonal sedimentation lwpycnic sedimentation
sd Batch extraction Batch adsorption Batch uystallizatlon Batch sublimation Batch ion exchange Dialysis
Scd
ElecircdeposRion Electrostatic precipitation Electrolytic refining Electrodialysis Equilibrium
sedimentation
F(=) (parallel
flow)
R=)C Elubiation Countercurrent electrophoresis
F(+N F(+)
perpendlcular
flow
profile can assume three forms depending on the components employed (IO):c = continuous p* profile; d = discontinuous p* profile; and cd = combination p* profile. The three profiles outlined above are shown in Figure 1. (In an earlier classification, only two profiles were distinguished (I)). Since flow is optional in separation systems, we can have either static (S) systems or flow (F) systems. Furthermore, flow systems can be physically
ANALYTICAL CHEMISTRY, VOC. 53, NO. 8. JULY 1981
F(=)d
F(=)Cd
Filtration Ultrafiltration Reverse osmosis Pressure dialysis Zone mening
ForcBd-flow electrophoresis
F(+W
W)Cd
Chromatography Field-flow Countercurrent fractionation distribution Thermcgravitational Fractional distillation separation Adsorptive bubble separation
arranged such that the flow displacement is essentially perpendicular (+) to the relative displacement, or parallel (=) to it. The former, for example, is represented by chromatography, while the latter includes filtration techniques. The relationship of the three flow conditions (S, F(+), F(=)) to the relative displacement vector is shown in Figure 2. The systematic approach above leads us to the conclusion that there are nine ways in which relative dis-
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
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Table II. Performance Ceilings for Various Multicomponent
Separation Methods ssparating POW. N (no ~ l a l e s l "(peak caOacnY1
M e w and ties
kodp2AP
LC (Ilquid
~
chromatography) *?''IDrn
sopratkm S p e d hvt (OlaI%j/llrrm)
(M"2In v, 4
The equations show the magnitude of
Dm Ddp2(1 K )
+
Vnd"
potential gains stemming
F(+)d
from the stretching of limiting operating parameters, such as pressure or voltage. L
-
FFF (Iield-flow fractionation) F(+)cd
dG8't
ZrpV 28RT
Electrophoresis sc
Rate-zonal sedlmentatlon sc
M(l
Thermal diliusion
sc
- Vp)w2AP 48R
[
M(t
- ?pP)O2AP 648RT
]
~2
D M(1
%[
- Vp)w* RT
01 AT -
28 T
Isoelectric focusing
x
I-wmk sedlmentatlon sc Symbols: dD = particle diameter D = molecular diffusion mffi-
cient Dm = dibion mefficient in mobile phase E = electric field strength f = frictioncoefficient H = plate height 'h = capacity factor k, = permeability/dP2 8 = mean layer thickness L = channel length M = molecular weight P, = inlet pressure Po = outlet pressure r = radius in centrifuge R = gas constant
948A
+
T = temperature V = voltage drop V,, = maximum elution volume
V,," = minimum elution volume z;r = molar charge a = thermal diffusion factor Ar2 = r22
-
r,2
AT = temperaturedrop
y = obstruction factor q = viscosity w = radians& D = red& mass transfer term fw stationary phase 8 = dispersion cmfflcient =
8' = HIH (ideal) p = carrier density U = partial specific volume
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8. JULY 1981
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placement and flow displacement (or the lack of it) can be combined. These nine categories are shown in Table I, along with the distribution of some common separation methods among the nine categories. There are some important associations in Tahle I that are not commonly recognized. For example, cone melting is grouped in the F(=)d category with ultrafiltration. despite their considerahle differences in materials and applications. Nonetheless, when we examine the phenomenological nature and theory of zone melting and ultrafiltration. we find them to he almost identical. Understanding one should help in understanding the other. In general, the relationships suggested by Tables I and I1 should be invaluable in comparing methods, encouraging technological transfer between methodologies, and in suggesting new approaches. The ahove is merely an example of how systematic comparisons can provide useful relationships among methods. Relationships among steady-state separation methods (surh as isoelectric focusing) have been described elsewhere (13).
Opportunities and Constraints imposed by SpecificTheory The general mass transport process descrihed hy Equation 1, along with the thermodynamirs that determines the form of p ' , can be developed into sperific equations describing most multiromponent techniques. These equations provide the reilings noted earlier for separative performance in terms of physicochemical parameters and operating limits. These equations can he used M point out gaps between theoretical ceilings and prartical per. formance. Each significant gap represents an opportunity for inrreaaed
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ieparative performance, hinging on thoughtful experimental design. The equations also show the magnitude of potential gains stemming from the 3tretching of limiting operating parameters, such as pressure or voltage. Furthermore, the equations show where little progress is to be expected, thus helping close off unproductive pathways. Table I1 shows performance ceilings for a group of contrasting techniques. Equations are shown for both separating power and speed. Separating power is expressed in terms of number of theoretical plates N (applicable even to electrophoresis (9)).and in terms of peak capacity n,the latter more generally useful because the plate concept does not extend well to such steady-state methods as isoelectric focusing (IO). Ceilings for separation speed are expressed as number of plates per unit time, Nlt. Table I1 has, of course, been simplified in the interest of clarity. and doea not begin to explain how each equation is to be used or the nature of any qualifications. But it captures the essence if not the details of each method's potential. The equations have been collected from the previously cited literature ( 5 7 - 1 1 ). Even casual inspection shows that there are many similarities among the equations in any of the columns of Table 11. This reflects the underlying systematics of separation, but space permits only a few points in this regard. We note that the terms 0 and P r e p resent the extent to which any dispersive process increases zone spreading. Ideally, 8 z 8' z 1. Parameter y plays the same role in the chromatographic equations, but is usually less than unity due to tortuous diffusion in packed columns. N is always inversely proportional to one of these parameters, while n is always inversely proportional to the square root of one of them. Reducing 8 or 8' is therefore a general goal for separations. Of significance, we note that every equation for separation speed Nlt is inversely proportional to friction coefficient f , or proportional to diffusivity D, which is one and the same thing according to Equation 3. This illustrates the validity of our earlier general conclusion that separation time is scaled with f and separation speed inversely with f and directly with D. (No separation speed equations are available for the steady-state methods where zones form by an unusual mechanism (11)).
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ANALYTICAL CHEMISTRY, VOL. 53. NO. 8. JVLY 1981
We note also that peak capacities are almost the same in the two complementary pairs: electrophoresis-isoelectric focusing and rate zonal sedimentation-isopycnic sedimentation
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pathways toward future separation methods.
(IO,11).Therefore, in trying to expand separation technology in these directions, one should not waste time looking for the intrinsically superior system, hut should look for specific advantages in experimental design, selectivity, e k . More specifically now, the number of plates in electrophoresis has a ceiling proportional to voltage drop V (9, 10). With 0 1and V 2 lo4 volts, electrophoresis shows a potential for several million theoretical plates (10). This ceiling is difficult to approach because of the heating effect of the electrical current, which leads to uneven migration and thus to 0 >> 1. There are important opportunities here. In chromatography, N is limited by maximum pressure drop, as has been long understood. However, ceiling N values are so high (-107) that increasing speed N l t is a more practical goal. Although overall optimization is complex ( 8 ) ,this mainly involves reducing particle size d p In field-flow fractionation (FFF), ceilings on both N and N l t are determined by minimum possible solute layer thickness 1. Some of the limiting factors on 1 have been discussed (12). In theory, one ought to he able to use the thermal diffusion phenomenon in a static (S)mode, using temperature drop AT just like electrophoresis uses voltage drop V. Perhaps this is an overlooked opportunity. Therefore, an N equatibn is s h o w in Table I1 to assess the possibilities (10).When we plug in known values of a (usually
