Report J. Calvin Giddings Department of Chemistry University of Utah Salt Lake City, Utah 84112
Future Pathways for Analytical Separations Separations employ such a variety of physical and chemical forces, flows, phases, and geometrical designs that we can imagine a near infinity of path ways toward future technology. Yet, only a handful of techniques has be come 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 conceiv able pathway will be productive. How do we choose the open pathways and avoid those that are dead ends? It is this author's opinion that the search for future separation technolo gy can be both inspired and stream lined by going to the roots of separa tive processes: finding out how and why these processes work, the param eters that limit them, and the mea sures that allow them to be compared. One source of perspective and guid ance is the study of separation sys tematica—how separations, in gener al, originate and relate. Historically, different separation methods have been developed and refined by differ ent cadres of scientists who 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 chro matography (2-4). Without this ex trapolation, it might have taken HPLC another decade to evolve, at a great loss to science. Such relation ships ought to be the rule, not the ex ception. Based on the talk, "New Directions in Separation Science," presented at the symposium, "New Di rections in Analytical Chemistry," at the 1981 Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlantic City, N.J., March 9,1981. 0003-2700/81/0351-945A$01.00/0 © 1981 American Chemical Society
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 (9,10), isoelectric fo cusing and isopycnic sedimentation (10,11), and field-flow fractionation (12). Taking a systematic point of view, we conclude that the search for new areas of technological achieve ment in separations requires: • pushing closer to the ceilings by careful experimental design, • pushing back the ceilings by extend ing 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 under pinnings 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 displace ment: • bulk or flow displacement, in which components are carried along in their medium, and • relative displacement through the surrounding medium. These displacement processes comple ment one another: The first is power ful 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 need ed in all separation processes. By con trast, flow displacement is optional. (Transport through evacuated cham bers is a displacement class not con sidered here.) Focusing first on the key process of relative displacement, we note that the transport rate J per unit area along axis χ is given by the expression (9): J =
οάμ* RTdc ' f dx _^^_f dx
(1)
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981 • 945 A
c Profile
d Profile
cd Profile
Perpendicular: F(+)
Parallel: F(=)
Relative Displacement
Distance Figure 1. The three types of chemical potential (μ*) profiles underlying the relative displacement of separation processes
where c is concentration, μ* is the chemical potential driving transport (at least in isothermal systems), / is the friction coefficient, R is the gas constant, and Τ is the absolute tem perature. The friction coefficient mea sures the drag force on molecules or particles undergoing relative transport through a medium. Our first global conclusion stems di rectly from this equation. We see that relative transport rates are inversely proportional to the friction coefficient /. Therefore, the time scale for any de sired level of relative transport is pro portional to /. Since the relative trans port described by Equation 1 under lies all separations, the time scale of separation is universally linked to the magnitude of/. Separation speed, on the other hand, is inversely related to /, a point we shall illustrate in the next section. According to Stokes's law, / is di rectly proportional to viscosity (η) and particle radius (a): / = βπηα
(2)
Where this law is applicable, a reduc tion 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 (10). We note that friction coefficient / and diffusion coefficient D are in versely related by the Planck-Einstein equation / = RT/D
(3)
Hence, the time scale of separation, linked directly with /, is inversely re lated to D. Separation speed almost always increases with D. The chemical potential (μ*) 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 μ*
Figure 2. Orientations and conditions of flow with respect to the relative displacement axis in separation systems. S = static, F = flow
Table I. Grouping of Separation Methods in the Nine Categories Based on Flow and Relative Displacement Flow Condition
S (static)
f(") (parallel flow)
c (continuous)
cd (combination)
Se Electrophoresis Isoelectric focusing Rate-zonal sedimentation Isopycnic sedimentation
Sd Batch extraction Batch adsorption Batch crystallization Batch sublimation Batch ion exchange Dialysis
Scd Electrodeposition Electrostatic precipitation Electrolytic refining Electrodialysis Equilibrium sedimentation
F(=)c Elutriation Countercurrent electrophoresis
F(=)d Filtration Ultrafiltration Reverse osmosis Pressure dialysis Zone melting
F(=)ccl Forced-flow electrophoresis
F(+)c F(+) perpendicular flow
profile can assume three forms de pending on the components employed (10): c = continuous μ* profile; d = discontinuous μ* profile; and cd = combination μ* profile. The three profiles outlined above are shown in Figure 1. (In an earlier classification, only two profiles were distinguished (1)). Since flow is optional in separation systems, we can have either static (S) systems or flow (F) systems. Further more, flow systems can be physically
946 A • ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
μ' Profile d (discontinuous)
F(+)cd F(+)d Field-flow Chromatography fractionation Countercurrent Thermogravitational distribution Fractional distillatior ι separation Adsorptive bubble separation
arranged such that the flow displace ment is essentially perpendicular (+) to the relative displacement, or paral lel (=) 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-
Table II. Performance Ceilings for Various Multicomponent Separation Methods Separating power Ν (no. plates) η (peak capacity)
Method and class
LC (liquid chromatography)
k0dp2AP 2
(AQ 1/2 | n Va** 4 Vmln
1 D
T / m
Separation speed N/t (plates/time)
The equations show the magnitude of
Ωα(ρ2(1 + k")
potential gains stemming
F(+)d
from the stretching of 2
GC (gas chromatography) F(+)d
KA, P, 4
a
(AQ 1 / Z , V,max In
7^0mPo
Vmln
3D m P 0 2ftd p 2 (1 + k')Pl
limiting operating parameters, such as pressure or voltage.
Ρ
FFF (field-flow fractionation)
RT
4^2 ~ 4 ^ 2 f
V -i^17 *
F(+)cd
zSfV
Electrophoresis Sc
Rate-zonal sedimentation Sc
z
vp)o) 2 Ar a
Thermal diffusion Sc
4
^
R
r
α AT — — 2θ Τ
Isoelectric focusing Sc
Isopycnic sedimentation Sc Symbols: dp = particle diameter D = molecular diffusion coeffi cient Dm = diffusion coefficient in mobile phase Ε = electric field strength f = friction coefficient Η = plate height k" = capacity factor k0 = permeability/dp 2 £ = mean layer thickness i. = channel length M = molecular weight P) = inlet pressure P0 = outlet pressure r = radius in centrifuge R = gas constant
2θ\ητ}
320R7J
20RT
M(1 -
yv\i/2
/ftf(1 -
vp)wzAr2Y^
640RF
D //W(1 - - νρ)ω 2 Αϋ 20
Rf
|
320 r]
/ z5?V
[320R7J
M(1 νρ)ω2ΑΛ^2 640R Τ J
Τ = temperature V = voltage drop Vmax = maximum elution volume Vmtn — minimum elution volume zi? = molar charge α = thermal diffusion factor
Δ/·2 = r22 - r? AT = temperature drop y = obstruction factor t\ — viscosity ω = radians/s Ω = reduced mass transfer term for stationary phase 0
=
dispersion
coefficient
DT/D Θ' m H/H (ideal) ρ = carrier density ν = partial specific volume
948 A • ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
=
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 associa tions in Table I that are not commonly recognized. For example, zone melting is grouped in the F(=)d category with ultrafiltration, despite their consider able differences in materials and ap plications. Nonetheless, when we ex amine the phenomenological nature and theory of zone melting and ultra filtration, we find them to be almost identical. Understanding one should help in understanding the other. In general, the relationships suggested by Tables I and II should be invaluable in comparing methods, encouraging technological transfer between meth odologies, and in suggesting new ap proaches. The above is merely an example of how systematic comparisons can pro vide useful relationships among meth ods. Relationships among steady-state separation methods (such as isoelec tric focusing) have been described elsewhere (13). Opportunities and Constraints Imposed by Specific Theory The general mass transport process described by Equation 1, along with the thermodynamics that determines the form of μ*, can be developed into specific equations describing most multicomponent techniques. These equations provide the ceilings noted earlier for separative performance in terms of physicochemical parameters and operating limits. These equations can be used to point out gaps between theoretical ceilings and practical per formance. Each significant gap repre sents an opportunity for increased
[••$31 B L U E M J
Where The Choice Is Yours OVER 1000 MODELS
OVENS
Blue M has anticipated your every oven need with a choice of over 1000 models . . . ranging from a $200 lab oven on up to a $20,000 fully automated inert gas chamber with microprocessing control. Mechanical and gravity . . . sizes to 96 cu. ft. . . . temperatures to +704°C. Batch . . . Life-Test . . . Utility . . . Burn-In . . . Drawer . . . High-Powered . . . Vacuum . . . Drying — even FRICTION-AIRE* the patented electric chambers with no heating elements. Most have Blue M control systems for superior performance - plus such other standard features as welded stainless interiors, elapsed time meters, overtemperature protection. It's easily America's finest, most complete line. Choice. With Blue M it does mean selection. And with Blue M, choice also means highest quality. We offer you both. Is anything less worth your time? Where the choice is yours: Blue M Electric Company; Corporate Head quarters; Blue Island, Illinois 60406; Telephone: (312) 385-9000.
e£ BLUE M CIRCLE 27 ON READER SERVICE CARD
INTRODUCING UNISEAL® PRESSURE MEASURING SYSTEM An innovation that counts UN1SE AL ' sets n e w standards ot accuracy and s i m p l i c i t y , upens up n e w h u n z o n s lor non invasive p r e s s u r e m e a s u r e m e n t s in c l o s e d s y s t e m s by external contact only " U N I S E A L » adds a vital d i m e n s i o n 10 your e x p e r i m e n t a l evaluations by obtaining absolute values of pressure w i t h Uniseal'5 Pressure Measuring System.
> HIGHLIGHTS :
• Se'f c o n t a i n e d c l o s e d s y s t e m simple s e a l i n g no leakage p r o b l e m s · Pressure values by e x t e r n a l surface contact only · No pressure St Π MM t U be i n s e r t e d into reactor . hence; no v o l u m e c h a n g e / no volume* corrections/ no c o n t a m i n a t i o n uf s p e c i m e n / no pressure se.isor lo damage · Reliable pressure data at t e m p é r a t u r e s up to 180° C • Ideal lor c o r r o s i v e s y s t e m s · S i m p l e to operate APPLICATIONS : Analytical chemistry Explosives • Energy calculations » Sitmplt? weigh ι optimization Organic Chemistry • Vapour pressure Studies by pressure determination • Bio applications • Critical pressures • Operational siitcty evaluation • Clinical applications • Chemical equilibrium • protem hydrolysis • Pressure characteristics υΐ studies • Carnoiiyl complexes unknown samples • Oxidation • reduction • Organo-meiallic compounds Chemical Engineering equilibria • Polymerization studies Inorganic Chemistry • Solubility studies • Ceramics Physical and Theoretical • Solubility products and Chemistry • Fertilizers precipitation • Reaction kinetics • Geochemistry Propel lantt • Caseous reactions - rate • Glasses studies • Metallurgy • Noble gas reactions • Refractories
*..-.·.---.·..
UNISEAL DECOMPOSITION VESSELS LTD. PO.Bux lJ
t
HAIFA jloy4 ISRAEL · Tel 04-244990 · ΓβΙβχ Available in USA and Canada from
BXHA M. 4f>400 EXI 8610
COLUMBIA ORGANIC CHEMICALS CO., INC. Ρ Ο Box 9096.
Columbia. S C 29290.
Phone
(803)770 4990
CIRCLE 210 ON READER SERVICE CARD
950 A • ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
5
separative performance, hinging on thoughtful experimental design. The equations also show the magnitude of potential gains stemming from the stretching of limiting operating pa rameters, such as pressure or voltage. Furthermore, the equations show where little progress is to be expected, thus helping close off unproductive pathways. Table II shows performance ceilings for a group of contrasting techniques. Equations are shown for both separat ing power and speed. Separating power is expressed in terms of number of theoretical plates Ν (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 isoelec tric focusing (10). Ceilings for separation speed are ex pressed as number of plates per unit time, N/t. Table II has, of course, been simpli fied in the interest of clarity, and does not begin to explain how each equa tion is to be used or the nature of any qualifications. But it captures the es sence if not the details of each meth od's potential. The equations have been collected from the previously cited literature (5, 7-11). Even casual inspection shows that there are many similarities among the equations in any of the columns of Table II. This reflects the underlying systematics of separation, but space permits only a few points in this regard. We note that the terms θ and Θ' rep resent the extent to which any disper sive process increases zone spreading. Ideally, θ at 0* at 1. Parameter y plays the same role in the chromatographic equations, but is usually less than unity due to tortuous diffusion in packed columns. Ν is always inversely proportional to one of these parame ters, while η is always inversely pro portional to the square root of one of them. Reducing θ or Θ' is therefore a general goal for separations. Of significance, we note that every equation for separation speed N/t is inversely proportional to friction coef ficient /, or proportional to diffusivity D, which is one and the same thing ac cording to Equation 3. This illustrates the validity of our earlier general con clusion that separation time is scaled with / and separation speed inversely with / and directly with D. (No sepa ration speed equations are available for the steady-state methods where zones form by an unusual mechanism
(ID). We note also that peak capacities are almost the same in the two com plementary pairs: electrophoresis-iso electric focusing and rate zonal sedimentation-isopyenic sedimentation
COMMON PROBLEMS IN CHROMATOGRAPHY # 9 When You Install a New Column, Do You Install a Solution . . . or a Problem? Most chromatographers know the frus tration of installing a new column only to f i n d out that the chromatograms are terrible. Where do you start?
7 *
1s your column OK? Is the trouble somewhere in the instrument? . . . or Are your connections leaking?
It is often difficult to isolate the actual problem, and it's extremely frustrating when you determine that the problem is your new column. You might eventu ally f i n d that the column you just in stalled is perfectly good, but is just not suited to your application. There is a way you can avoid this experience — buy and use packings which have been tested and approved specifically for your particular application. The tech nical staff at Supelco continually de signs and tests packings for a wide range of sample analyses, and publishes technical information on performing these analyses. (Remember, custom packings made to your specifications are not usually tested by any com pany.) General purpose packings are tested by our O.C staff, however they are tested for general purpose applica tions and may not do the job for your application. When you use packings pretested for your applications, you know that the column is going to do the job for y o u , so why should you buy one which might only cause problems?
If you cannot find a packing which has been tested for your analysis, let us know. Our technical staff thrives on challenges, and is waiting to solve your problem. Supelco has just introduced a new troubleshooting guide which will sim plify life in your GC lab. If your chromatograms just don't measure up, there's probably a reason. Send to day for your copy of our new trouble shooting guide. It can save you t i m e , money, and frustrations . . . and it's FREE!
§ SUPELCO, INC. SUPELCO PARK. BELLEFONTE, PA 16823 TELE: 814 359-2732/TWX: 510-670-3600
Theory shows many of the open and closed pathways toward future separation methods.
(10,11). T h e r e f o r e , in t r y i n g t o ex p a n d s e p a r a t i o n technology in t h e s e d i r e c t i o n s , one s h o u l d n o t w a s t e t i m e looking for t h e intrinsically s u p e r i o r s y s t e m , b u t s h o u l d look for specific a d v a n t a g e s in e x p e r i m e n t a l design, se lectivity, e t c . M o r e specifically now, t h e n u m b e r of p l a t e s in electrophoresis h a s a ceil ing p r o p o r t i o n a l t o voltage d r o p V (9, 10). W i t h θ ~ 1 a n d V > 10 4 volts, electrophoresis shows a p o t e n t i a l for several million t h e o r e t i c a l p l a t e s (10). T h i s ceiling is difficult t o a p p r o a c h b e c a u s e of t h e h e a t i n g effect of t h e electrical c u r r e n t , which l e a d s t o u n even m i g r a t i o n a n d t h u s t o θ » 1. There are important opportunities here. In c h r o m a t o g r a p h y , Ν is l i m i t e d b y m a x i m u m p r e s s u r e d r o p , as h a s b e e n long u n d e r s t o o d . However, ceiling Ν values a r e so high (~10 7 ) t h a t increas ing s p e e d N/t is a m o r e practical goal. A l t h o u g h overall o p t i m i z a t i o n is com plex (8), t h i s m a i n l y involves r e d u c i n g p a r t i c l e size dp. I n field-flow fractionation ( F F F ) , ceilings on b o t h Ν a n d N/t a r e d e t e r m i n e d b y m i n i m u m possible solute layer t h i c k n e s s /. S o m e of t h e limiting factors on I h a v e b e e n discussed (12). In t h e o r y , one o u g h t t o be able t o use t h e t h e r m a l diffusion p h e n o m e n o n in a s t a t i c (S) m o d e , using t e m p e r a t u r e d r o p AT j u s t like electrophoresis uses voltage d r o p V. P e r h a p s t h i s is an overlooked o p p o r t u n i t y . T h e r e f o r e , an Ν e q u a t i o n is s h o w n in T a b l e II t o as sess t h e possibilities (10). W h e n we plug in k n o w n values of a (usually < 1 0 b u t ~ 1 0 2 for s o m e p o l y m e r s ) , we find a ceiling of 10 2 or less for N. T h i s is i m p r a c t i c a l l y low. T h u s , developing a s t a t i c t h e r m a l diffusion m e t h o d is a closed p a t h w a y w i t h c o n v e n t i o n a l so l u t e s a n d solvents, b u t is a t least con ceivable for exotic solutions. Specific t h e o r y in t h i s case h a s told u s w h e r e we m u s t search if we wish t o p u r s u e this concept. In conclusion, t h e o r y , a p p l i e d b o t h s y s t e m a t i c a l l y a n d specifically, shows m a n y of t h e o p e n a n d closed p a t h w a y s toward future separation methods. It s h o u l d greatly simplify t h e search for b e t t e r s e p a r a t i o n s , s p e e d t h e i r realiza tion, a n d lead a r o u n d costly d e a d ends. G e n e r a l t h e o r y s h o u l d , in t h i s a u t h o r ' s opinion, b e i n c l u d e d in every g r a d u a t e c u r r i c u l u m in analytical
CIRCLE 201 ON READER SERVICE CARD 952 A • ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
c h e m i s t r y b e c a u s e of its s h o r t - a n d l o n g - t e r m ability t o p r e d i c t , r e l a t e , a s sess, a n d i m p r o v e s e p a r a t i o n m e t h o d ology, a n d avoid pitfalls in f u t u r e d e velopments.
Literature Cited (1) J. C. Giddings, Sep. Sci. Technol., 13, 3 (1978). (2) J. F. K. Huber, in "75 Years of Chro matography—A Historical Dialogue," L. S. Ettre and A. Zlatkis, Eds., Elsevier, Amsterdam, 1979, ρ 160. (3) J. C. Giddings, in "75 Years of Chro matography—A Historical Dialogue," L. S. Ettre and A. Zlatkis, Eds., Elsevier, Amsterdam, 1979, pp 96-97. (4) L. R. Snyder and J. J. Kirland, "Intro duction to Modern Liquid Chromatogra phy," Wiley, New York, 1974, Chapter 1. (5) J. C. Giddings, Anal. Chem., 36,1890 (1964). (6) J. C. Giddings, J. Chromatogr., 18, 221 (1965). (7) J. C. Giddings, Anal. Chem., 37,60 (1965). (8) G. Guiochon, Anal. Chem., 52, 2002 (1980). (9) J. C. Giddings, Sep. Sci., 4,181 (1969). (10) J. C. Giddings in "Treatise on Analyt ical Chemistry," 2nd éd., I. M. Kolthoff, P. J. Elving, and E. Grushka, Eds., Wiley, New York, in press, Vol. 5. (11) J. C. Giddings and K. Dahlgren, Sep. Sci., 6, 345(1971). (12) J. C. Giddings, Sep. Sci., 8, 567 (1973). (13) J. C. Giddings, Sep. Sci. Technol., 14, 875 (1979). This project was supported by NIGMS Grant 10851-24, National Institutes of Health.
J. Calvin Giddings is professor of chemistry at the University of Utah, where he earned his PhD in 1954. His research interests include field-flow fractionation, macromolecular separations, the theory of separations, high pressure chromatography, the theory of chromatography, environmental science, and world population.
