Zone Melting Considered as a Chromatographic Separation Technique W,. G. PFANN Bell Telephone labortrtories, Inc., Murray Hill,
b Zone melting can be adapted to perform separatioris of the kind achieved in chromat’ography. A mixture of solutes is placed a t a point in a long column of solid solvent, and molten zones are passed in one direction. The solutes separate into bands, each of which travels at a rate determined by the distribution coefficient of the solute. Idealized theory shows that the solute distribution in a band has the forni of a modified Poisson distribution, and that the n’umber of zone-passes required to separate two solutes depends only on the ratio of their distribution coefficients. Typically, some hundreds of zonepasses, and columns hundreds of zonelengths long, are required. Since the permissible rate of zone-travel is relatively low, prcictical realization of zone chromatography requires techniques for producing very short and very closely-spaced molten zones.
A
of zone melting (6, 8) that has received little attention is its potential as a chromatographic separation technique. If a mixture of solutes is introducedl a t a point in a long charge, or coluni.n, of solid solvent,, and if molten zones are passed along the colunin in one direction, the coniponents of the mixture will become separated into individual “bands.” IT-e denote this technique “zone chromatography,” or ZC, with the reminder to the reader that ZC is a technique of zone-melting, not of chromatography, a main difference from conventional zone refining being that longer charges and more zone-passes are required in ZC than in convent,ional zone refining. In this paper we present elementary theory for ZC, compare it with theory for gas liquid chromatography (GLC), indicate requirements for the apparatus, and discuss variants of the basic technique. I t appears, despite the relative slowness of ZC, tha.t it has a useful place alongside conventional chromatographic techniques. K e are not aware of an)- extensive experimentation with ZC; it is hoped that the present paper will lead to such effort. In GLC ( 1 , 3) there is a column, or tube, of solid particles, coated with a N ASPECT
N. J.
liquid--the stationary phase. A sample of components to be separated is inserted at the beginning of the column. .\n inert gas, in which the coniponents have a sensible vapor pressure, is passed through the column. I3y continuous repeated equilibrations of vapor and liquid, the components migrate along the column in bands, which travel at different rates, the component that most prefers the vapor traveling fastest. The rate of travel and the sharpness of a band depend on the vapor-liquid equilibrium constant and on features of the column, such as rate of gas flow, particle size, ratio of gas volume to liquid volume, dimensions and compositions of gas channels and liquid layers, diffusivities in gas and liquid. In ZC, there is a column of solid solvent. -1sample of components to be separated (soluble in the solid solvent) is introduced at the beginning of the column, or preferably, in certain cases, a t a point’ farther along the column. .I number of very short, closely-spaced, molten zones are caused t,o traverse the column. -1s in GLC, components migrate along the column in bands that
Rp 008-
0 00 -
i
0.04-
0.02 ~
0 0
4
6
12
9
I6
20
v
Figure 1 . Poisson distribution in time, for gas liquid chromatography, showing relative solute concentration, R,, a t pth plate, as a function of the number, v, of relative plate volumes of carrier gas that have passed plate P
t,rarel a t different rates. Components that prefer the liquid travel forward, a t a rate in accord with their preference for the liquid; components that prefer the solid travel backward, at a rate in accord with their preference for the solid. The latter effect is why it may be approi)riate to introduce the sample some dijtance along the column. The rate of travel and the sharpness of the bands depend on liquid-solid equilibrium constants, zone-length, zone-speed, zone-strirring, and little else. THEORY
G a s Liquid Chromatography. I n this subsection we present an essential expression for the movement of a solute in ideal gas liquid chromatography. The expression presented represents plate theory, rather than differential theory. Khile we recognize that the latter may be regarded as more accurate, we nevertheless adhere to the former, because it is simpler in concept, because it is well known to chromatographers, and because exact expressions of identical forni hold for ZC. Following Keulemans ( I ) , the ratio, R,, of the solute concentration in the vapor at the pth plate to that a t the first plate is
where 2’ is the number of effective plate volumes of carrier gas introduced. Equation 1 represents a Poisson distribution, some important features of which are illustrated in Figure 1, which is a plot of R, against u for p = 9. Xote that Figure 1 is not a distribution in space. Rather, it is a plot of the concentration at plate p as a function of u, the number of effective plate volumes of gas that have passed plate p . It should be emphasized that, for a given volume of gas, 2: is different for each solute. In fact,, this difference is the basis of the separating mechanism of the column. Zone Chromatography. The basic equation underlying zone chromatography was derived by Reiss and Helfand (Q), at the writer’s suggestion. Their derivation is rigorous within the usual siniplifying assumptions; namely that the distribution coefficient! k , deVOL. 36, NO. 12, NOVEMBER 1964
* 2231
Then, for z 2 E - nl, Reiss and Helfand (9) showed that C,(z) is given by:
t In the remainder of this section we simplify Equation 5, show that it represents a Poisson distribution, and develop from it equations useful for the practice of zone chromatography. Let the delta function be centered a t = 1, and let m = n - 1. Then Equation 5 becomes:
Figure 2. Poisson distribution in space, for zone-chromatography,showing relative solute concentration, after rn zone-posses, as a function of reduced distance from the initial position of the solute
fined as the ratio of the solute concentration in the just-freezing solid to that in the molten zone, is constant; that there is no diffusion in the solid; and that there is infinitely rapid mixing in the liquid. The last assumption is not realized in practice, but this can be accounted for by using an effective value of k which is consistent with the freezing conditions (8). Concentrations may be in weight-fraction or atomfraction, in which case the density change on freezing can be ignored, provided that the zone-length, I , is the length of solid that was melted to form the zone ( 5 ) . If concentrations are expressed on a volume basis, then it is assumed that the density does not change on freezing. Consider an infinite column of solid solvent extending in the z-direction from z = --m t o z = +m. The differential equation determining the distribution of solute in the solid after the nth pass is
where 1: denotes the position of the trailing end of the zone, C,(z) denotes the concentration in the solid, and the zone moves in the (+z) direction. Let the initial distribution of solute C&) be a delta (6) function centered at z = E :
2232
ANALYTICAL CHEMISTRY
where C, = K/1 = the concentration in the zone a t z = 0 in the first zone passLe., when the front of the zone has just reached the delta function of solute at z = 1. Equation 6 is a modified Poisson distribution. If m is held constant, it can be regarded as a true Poisson distribution. Even though mathematically similar Poisson distributions are obtained in both GLC and ZC, the distributions are physically different and the comparable parameters have different physical meanings. Thus, by comparing Equations 1 and 6, it can be seen that a location, p , in GLC corresponds to a number, m, of zone-passes in ZC, and that a number, v , of plate volumes of inert gas in GLC corresponds to a location, k[(z,’l) m], in ZC. By differentiating Equation 6 and setting d(C,(z)/kC,),’dz equal to zero, the maximum of the distribution is found to lie at:
+
which, by Stirling’s approximation, reduces to :
The Poisson distribution defined by Equation 6 is plotted in Figure 2 for the value m = 9. The ordinates are in units of relative concentration, as in Figure 1. The abscissas are in units of 2 = k [ ( z l l ) m]. The curve of Figure 2, in contrast with that of Figure 1, is a distribution in space. I t represents the distribution of solute along the column after n = m + l zone-passes. The peak width, in units of Z, is 4~‘;. Figure 2 is a universal curve, representing the distributions of all solutes after 10 zone-
I
lk
0.12,
I
I
II I”,.
Figure 3. Schematic representation of height, location, and width of solute bands in zone chromatography, for various values of the distribution coefficient, k, after m = 25, 50, and 196 zone-passes
passes, As such, it does not readily ipdicate the separating power of the column that arises from differences in k . For this, a plot having abscissas in units of (211) is more useful. Such plots are shown in Figure 3 for various k’s and for m = 25, 50, and 196. For simplicity, instead of the Poissoncurve for each k-value, triangles similar to d c in Figure 2 are plotted. Figure 3 illustrates the more rapid movement and more rapid increase of peak width with decrease in k , the stationary maximum for k = 1, and the reverse movement for k > 1. It is useful to ask how many znnepasses, n* = m*+l are required to separate two solutes. d useful approximate criterion for separation is that point a of triangle abc of the leading solute coincide with point b of triangle abc of the trailing solute. An expression for m* is obtained as follows. On the Z-scale, let the coordinate of point a be 2, = m* 1 - 2 and of point b be Zb= m* 1 2 d/m*.Let solute 2 be the faster moving, which means, for k’s < 1, that kz < kl. We require that, on the (z/&scale, point a for solute 2 coincide with point b for solute 1, in other words, that:
+
(r).
=
a,
+ +
Icz
Z, - m*
=
+
m*
+ 1+2 kl
4 2
- m*,
(11)
RADIATION
m-
MOVING MASK
METAL COOLANT
MOLTEN ZONE
SOLID
Figure 6. Schematic cross section of an apparatus for producing short molten zones for zone chromatography
1.0
u D
0
0.1
0.2
0.3
0.4
0.5
0.4
0.7
0.8
0.9
k,,/k,
Equation 7 , for Z,* to approach infinity as kz approaches zero. The essentially constant regions to the left of bands as a function of the ratio, kz = 1.0, occur in the range of k-values &z/&l, of the distribution coefficients for which the solutes move in opposite of the solutes directions. The rapid rise to the right of k2 = 1.0 corresponds to both solutes moving backward. The calculations of L* ignore the half peak-width beyond the maximum of the Solving Equations 10, 11, and 12 for leading solute. This width can be m* results in: quite large if k2 is small. However, it is ignored because the solute will be "piled up" at the end of the column by the well-known zone refining effect; Thus, the number of passes required and this effect is strongest for the very depends only on the ratio of distribution range of k in which the half peak-width coefficients. Equation 13 is illustrated is large. In fact, a potentially useful in Figure 4. It is seen that m* apvariant of ZC, once a solute band has proaches infinity as (k2/kl) approaches been isolated, is to concentrate the unity. solute by a series of zone refining passes I t is also useful to have a feeling for over the width of the band. For such the length, I,*, of column required to concentrating action to be effective, k separate two solutes, for this determines must differ substantially from unity. the size of the column and the time for JTe are now in a position to consider the separation. -1 rough measure of an important parameter in ZC, namely L* is the value of (r,I),, for the faster the time, t , required for a given separamoving solute after vi* passes, given by tion. The time required to pass a Equation 7 , or, if kl > 1 and kz < 1, the series of n zones, of spacing, d , between difference between thle values of ( Z / I ) ~ ~ zone ~ fronts, through a charge of length for the two solutes. In Figure 5 ) L* is L is ( 7 ) : plotted against k2 with Ak as a paL (n - l)d rameter. Clearly L* depends on many t = (14) factors. The rise of all curves a t small 0, k2 reflects the tendmcy, apparent in w-here v, is the velocity of the zones. Setting aside for the moment the value of v, and the length of a zone, the primary consideration is the value of: Figure 4. The numbler of zone- passes, m*, required to separate two solute
+
/ I
Ah=O.l
0
0.2
0.1
0.6
3.8
1.0
1.2
L*
1.4
+ (n* - 1 ) d = L* + m*d
Two cases are considered in Table I, for d = 2. Despite the convolutions of the curves of Figure 5 , it is clear from Table I , for Ak constant, that the separation time steadily decreases as k decreases. This, of course, is pertinent to selection of the inert solid solvent material of the column.
k.?
Figure 5. The length of column, L * , in zone-lengths, required to separate two solute bands ~ Y S a function of k2, the smaller distribution coefficient, with ilk as a parameter
EXPERIMENTAL
Apparatus. One form that apparatus for zone chromatography might take is shown schematically in section in Figure 6. The charge,
+
Table I. Relative Time, ( I * 2m*), Required to Separate Two Solutes Having Different &-Values. Ak
kz
m*
010 0 10 0 10 040 040 0 40
0 1 0 5
34 480 1760
10
0 1 0 5 10
7
47 144
I>* 306 480 176 62 48
41
L*
+
2m*
370 1440 3700 76 140 330
or column, is a long thin slab, perhaps -0.1 cm. X 2.0 cm. X 50 cm., of a suitable solvent substance of fairly low7 melting point. I t is contained between a clear glass or fused silica slide and a metal plate, which is cooled from the out,side. ;ibove the charge is a grid-like mask. Radiant energy from a projection lamp passes through the openings in the mask, and, by absorption in the charge or in the surface of the metal plate, heats the charge and forms a molten zone. The mask is moved at the desired zone velocity with either steady or reciprocating motion. At this m-riting a zone-length, I , of 0.1 cm. appears quite feasible. 11 representative L* may be -500, which would mean a column 50 cm. long. d typical zone velocity, v,, may be -2 cm.jhr.; and a t,ypiral value of (L* 2m*) may be -1000 zone lengths. The t,ime. t : m-ould be -50 hours for these values.
+
RESULTS
There are two ways in which reducing 1 can reduce the time. The first is by reducing the column length for a given value of (LA* 2m*). The second is by permitting a greater zone velocity. If diffusion is the only mixing mechanism (as is likely in very short zones), v , should be not more than --Dl'2, where -D is diffusivity. Typically, D s3 X cm.2,!sec. Therefore, if I could be reduced to -0.03 cm., v, could be cm.,'sec., or -3.6 cm.;' hr. For the above values of L* and (L* 2rn*), t h e cvlumn would be -15 cm. long and t would be -4 hours. At this writing, however, it remains to be shoivn that 1 as small as -0.03 em. i3 feasible.
+
+
VOL. 36, NO. 12, NOVEMBER 1964
2233
-\major difference between ZC, in its simple form described above, and other cthroinatographic techniques, as described b>- Keulemans ( I ) is that no material mores through the colunmthere is no “percolation.” In its fundamental aspect, however, the separation of solutes into bands, ZC resembles chromatography. Moreover, simulated or actual percolation of the solid solvent can be realized in ZC. If each time a molten zone is at one or the other end of the column it is removed and replaced by pure solvent, the effect, will be to remove solutes just as in conventional chromatography, even though there is not a net flow of solvent through the column. Allso,by using techniques of matter transport described in connection with continuous zone refining, (8) bulk flow of mat’erial along the column can be realized simultaneously with the zone-travels. Anot 1 in the solvent, or more properly, in the multicomponent solution. example of the former is benzene as a solvent for polystyrene. .\ wide range of k’s < 1 was found for certain growth conditions in this system by Loconti and Cahill ( 2 ) . An example of the latter is xylene as a solvent for polyethylene. Bands of solutes having k’s < 1 move forward, as mentioned above, and generally move more rapidly and spread out more rapidly than solutes having k’s > 1. The latter move backward and tend to be more concentrated. I t is also possible to select a solvent that will separate a mixture of solutes into two groups of bands, one moving forward, the other backward. The only published experiments the writer is aware of that might fall in the class of ZC are those of Peaker and Robb (4) on the partial fractionation of polystyrene in naphthalene and those of Loconti and Cahill ( 2 ) on polystyrene in benzene. Because the distributions of k-values for their systems were continuous, and because short columns and few zone-passes were used, imited
separations were achieved. Application of ZC to groups of distinct compounds, in apparatus utilizing an orderof-magnitude-greater number of zonelengths per column and more zonepasses can be expected to result in the kind of separations associated with conventional chromatography. T h i l e ZC is much slower than GLC, although perhaps comparable with some of the slower liquid-liquid chromatographic separations, it can be used for solutes of low volatility. It exploits a phase transformation hitherto unused for chromatography, and hence it may find application for entirely new classes of materials. ACKNOWLEDGMENT
The writer is indebted to E. Helfand; H. L. Frisch, K. A. Jackson, and P. R. Story for helpful discussions. LITERATURE CITED
I. M.,“Gas Chromatography,” Reinhold, 2nd Ed., New York 1959. (2) Loconti, J. D., Cahill, J. W., J . Polymer Sci. A , 1, 3163 (1963). (3) Martin, A. J. P., Synge, R. L. M., Biochem. J . 35, 1358 (1941). ( 4 ) Peaker, F. W., Robb, J. C., Nature No. 4649, 1591, (December 6, 1958). (5) Pfann, W. G., J . A p p l . Phys. 35, 258 (1964). (6) Pfann, W. G., Trans. A I M E 194, 747 (1) Keulemans, A.
f1052). \ - - - - ,
(7) Zbid., 197, 1441 (1953). (8) Pfann, W. G., “Zone Melting,” Wiley, Sew York, 1958. (9) Reiss, H.. Helfand., E.,. J . A d . Phys. 32, 228 (1961). L
.
RECEIVEDfor review April 23, 1964. Accepted August 25, 1964.
Gradient Loaded Columns in Gas Chromatography DAVID C. LOCKE’ and CLIFTON E. MELOAN Department of Chemistry, Kansas State University, Manhattan, Kan,
b The use of gradient loaded columns in gas chromatography is a new technique involving the systematic variation of the partition ratio, k, during the course of an analysis by varying the liquid loading from the beginning to the end of the column. The case of a continuous linear decrease in k down the column is considered theoretically and experimentally. Equations are derived describing solute retention behavior, column efficiency, and solute resolution on columns with a linear gradient in k. Good agreement is obtained between the theoretical predictions and the experimental results on a 16-stage step-wise approximation to a continuous linear gradient column. For linear gradient columns, the partition ratio i s reduced to 50% of that which it would be on a regular 2234
ANALYTICAL CHEMISTRY
column of liquid loading corresponding to the initial k on the gradient column. Column efficiency is improved for solutes of low or intermediate partition ratio on the gradient column. The combination of these effects results in resolution of solutes of low retention which is superior to that which could be obtained on a regular column.
S
EVERAL
CHROMATOGRAPHIC
TECH-
have been developed which involve the systematic variation of a critical parameter during an analysis. Programmed temperature gas chromatography has provided a simple method for the analysis of wide-boiling mixtures in a minimum of time while enhancing resolution. Gradient elution liquid chromatography ( I ) , which involves an NIQUES
increase in the eluting power of the mobile phase during the course of an analysis, has offered similar advantages to the column rhromatographer. Porath (14) has described a step-graded adsorption column constructed of six sections, each successive section down the column containing charcoal deactivated with stearic acid to a lesser extent than the preceeding section. Satisfactory results were claimed for the analysis of pea-root exudate. I t has been suggested, notably by Purnell ( 1 5 ) ,that a gas chromatographic column in which the partition ratio, k , was varied down the column, might exhibit capabilities similar to those Present address, Department of Chemistry, Stevens Institute of Technology, Hoboken, PI’. J.
