726
L. W. NICHOL,A. G. OGSTON, AND D. J. WINZOR
CH30H.12 The compounds (CH30)2SiH2and (CH30)3SiH were prepared by the base-catalyzed condensation of CH30SiH3.l 3 The compounds (SiH30)2SiH2 and (SiH30)3SiHwere obtained by the base-catalyzed condensation of (SiH3)20.13The nmr spectra of SiHBr3 and SiH13 were measured using a Perkin-Elmer HRlO spectrometer operating at 60 Alc/sec. The dimethylaminosilanes were recorded using a Varian Associates V4300B spectrometer operating at 40 Mc/sec; and the methoxy- and siloxysilanes were measured with a
Varian Associates HR60 spectrometer, Model 4300D, with flux stabilizer, operated at 60 Mc/sec. Acknowledgment. H. J. C.-F. wishes to acknowledge the receipt of a maintenance grant from the D.S.I.R. during the time that these experiments were being performed. (12) G. S. Weiss and E. R. Nixon, Spectrochim. Acta, 21, 903 (1965). (13) T. Yoshioka and A. G. MacDiarmid, Abstracts of 149th National Meeting, American Chemical Society, Detroit, Mich., Sept 1964, p 5M.
Reaction Boundaries and Elution Profiles in Column Chromatography
by L. W. Nichol, A. G. Ogston, and D. J. Winzor Russell Grimwade School of Biochemistry, University of Melbourne, Victoria, Australia, Department of Physical Biochemistry, J o h n Curtin School of Medical Research, Australian National University, Canberra, Australian Capital Territory, Australia, and C.S.I.R.O. Wheat Research U n i t , North Ryde, N e w South Wales, Australia (Receised June 37, 1966)
The relationships between the forms of migration boundaries within a chromatographic column and the forms of the elution profiles are examined by a method which makes use of constituent concepts of concentration and velocity of migration. The treatment applies to any procedure of column chromatography in which a plateau of all solute concentrations is ensured throughout the experiment. It is shown that the constituent concentration of any solute species in the effluent fluid is at any moment identical with that in the mobile solution within the column which reaches the exit plane at that time. I n addition, equations are derived in both differential and integrated form describing essential features of the elution profiles obtained with systems affected by chemical or physical interaction. It is concluded that the equations are formally identical with those obtained previously to describe migration patterns obtained in moving boundary experiments not involving a stationary phase, provided elution volumes are substituted directly for velocity terms. The conclusion is in agreement with other workers who considered the case of chemically reacting systems subjected to column chromatography.
Theoretical discussion of the forms of migration boundaries in interacting systems has been along two lines. Gilbert’s2 and Gilbert and Jenkins3 did Dioneer work in describing boundaries in freely migrating, chemically interacting systems ; Ackers and Thompson4 their method to the behavior Of a have merizing system in gel filtration. A later alternative T h e Journal of Physical Chemistry
approach uses “constituent” concepts of velocity and c o n ~ e n t r a t i o n :this ~ ~ ~approach has been developed in (1) G. A. Gilbert, Discussions Faraday Sac., 20, 68 (1955). (2) G. A. Gilbert, PTOC. Roy. SOC.(London), A250, 377 (1959). (3) G. A. Gilbert and R. C. L. Jenkins, ibid., A253, 420 (1959). (4) G. K.Ackers and T. E. Thompson, Proc. Natl. Acad. Sci. U.S., 53,342 (1965).
REACTION BOTJNDARIES AND ELUTION PROFILES IN COLUMN CHROMATOGRAPHY
detail for freely migrating and has certain advantages.” It has also been applied (in one form) both theoretically and experimentally to gel filtrat i ~ n . ’ - ~Recently Gilbert12 has examined the relationships of velocities and concentrations within a gel filtration column to the elution volumes and concentrations in the eluate; he pointed out an error made by Nichol and W i n z ~ r(who ~ ~ ~used the constituent approach) through simply replacing velocities in the column by reciprocal elution volumes in their version of the Johnston-Ogston equationg~l3 and the moving-boundary equation6 applied to a hypersharp boundary.3,8 Although we agree with Gilbert’s conclusions,l 2 we have undertaken a further and more general examination of the application of the constituent approach to column chromatography, hoping to eliminate any confusion caused by his use of constituent quantities, as well as to establish more clearly the relationship between the effluent profile and the situation within the column. To conflate the treatment of freely migrating with that of chromatographic systems, we choose to regard the latter as a special aspect of the former. Special Features of Chyoinatographic Migration. Chromatographic systems differ from freely migrating systems in the following ways. (i) I n addition to the mobile components (solvent and solutes), the chromatographic system contains a component or phase (which we term G), which is uniformly distributed between two limiting planes which define the ends of the column. The velocity of G is zero, and it vanishes across a sharp boundary at each limiting plane. (ii) When a solution is applied to the column, which was originally filled with solvent, a sharp initial boundary of all mobile solutes is formed at the entry plane. This houndary then migrates down the column as an “ascending” boundary system, followed by a plateau of unlform composition. After establishment of the plateau, replacement of inflowing solution by solvent similarly creates an initially sharp “descending” boundary at the entry plane. (iii) Both the solvent (S) and solutes (X = A, B, etc.) interact with G. These interactions may be represented by
without specifying the natures of the interactions; they could, for example, be partitions, adsorptions, or chemical interactions. Components SG and all XG have
727
zero velocity; the constituent velocities of S and each X are therefore determined by the positions of the equilibria represented by eq 1. (iv) Interactions between mobile solutes in solution of the type
A+B,’C
(2)
may also occur. Although all components A, B, and C migrate at the same velocity as that of free solvent, the constituent velocities of A and B are not identical, since interactions of the type expressed in eq 2 affect the interactions with G (eq 1). (v) Although it is convenient in the first place to describe migration in terms of concentrations and velocities within the column, the experimental observation is a relationship between composition and volume of eluate. Assumptions, Definitions, and Symbols. As we assume that all equilibria (of both types represented by eq 1 and 2 ) are established at rates infinitely great compared with that of migration, and that diffusion is negligible. The positions of the equilibria represented by eq 1 are defined by px, the fraction of each X which is free. The values of px will always depend on the nature of X and G and on the amount of G per unit volume of column. According to the nature of the interactions, they may be dependent on or independent of composition with respect to mobile components. Equilibria in free solution (eq 2 ) are assumed to be governed by the simple mass action law. The column is of unit total cross-sectional area; a fraction, 4, is occupied by mobile solvent or solution and a fraction x by G itself; the remaining fraction is occupied by immobile S and X (in states represented by SG and XG). Concentrations are defined as follows: (i) cx is the concentration of X and EX its constituent concentration in the mobile solution in the column; (ii) CX’ and EX’ are (5) A. Tiselius, Sova Acta Regiae SOC.Sci., Upsaliensis, 7, No. 4, 1 (1930). (6) L. G. Longsworth in ”Electrophoresis, Theory, Methods and Applications,” M.Bier, Ed., Academic Press Inc., New York, N. Y., 1959, p 91. (7) L. W. Nichol and D. J. Winzor, J . Phys. Chem., 68, 2455 (1964). (8) L. W.Nichol and D. J. Winzor, Biochim. Biophys. Acta, 94,591 (1965). (9) D. J. Winzor and L. W.Nichol, ibid., 104, 1 (1965). (10) L. W. Nichol and A. G. Ogston, J . Phys. Chem., 69, 1754 ( 1965). (11) L. W.Nichol and A. G. Ogston, Proc. Roy. S O C (London), . B163, 343 (1965). (12) G . A. Gilbert, Nature, 210, 299 (1966). (13) J. P. Johnston and A. G. Ogston, Trans. Faraday Soc., 42, 789 (1946).
Volume 71, ivumber S February 1967
L.W. NICHOL, A. G. OGSTON,AND D. J. WINZOR
728
the corresponding quantities in the inflowing solution. I n addition to these definitions it is also convenient to define (iii) EX' as the constituent concentration of X itself within the column (i.e., including forms X and XG but not including products of X resulting from chemical equilibria in the mobile solution) and (iv) & as the constituent concentration of X in all forms within the column (in the absence of chemical equilibria in the mobile solution ?XI and CX are identical). The following relationships for the system A B F? C (X = A, B, and C) follow from these definitions
+
cc
cc'
CACB -
K
(4)
to traverse the column is l/v and the volume that has flowed during this time is
vo = V l / v = I+
(8)
which is the void volume of the column. Similarly, a lamina moving a t velocity u emerges after a volume flow
v, = V l / u
(9)
There is thus a reciprocal relationship between velocities within the column and corresponding elution volumes. Consider now the conservation of constituent X across the entry plane of the column; this demands that _ _
VEX' =
(10)
EXEX
Since the velocity of XG is zero, we may write cx
I:
=+-+-
[e:
From eq 7, 10, and 11 it follows that
Ex e Ex'
(Of the definitions given :A corresponds with Gilbert's12
W ; it is not clear to us whether his w represents EA or CA.)
v is the linear velocity of solvent within the column. The values of' ux (the linear velocity of mobile X) and of tjx (the constituent velocity of X in the mobile phase) are necessarily the same as u. tjx' and SX are constituent velocities corresponding to the definitions of EX' and &. u is the linear velocity, within the reaction boundary system in the column, of a lamina of constant composition, all forms of all components being taken into consideration.11 zix is the median velocity of a boundary of constituent X between two neighboring plateaus. V is the rate of inflow of solvent or solution, 1 is the length of the column between limiting planes, Vu is the volume that has flowed into (or out of) the column between the time of establishment of a sharp initial boundary at the entry plane and the time at which a lamina of velocity u reaches the exit plane, and Vo is the volume of mobile solution between entry and exit planes. Relationships between Velocities, Volumes, and Concentrations. From the definitions given, it is immediately obvious that
V
=
+v
(7)
The time taken for a lamina moving with velocity v The Journal of Physical Chemistrzl
cx
(12)
Equation 12 applies to each constituent (X = A, B, C). Moreover, the same conservation equations apply across the exit plane, and it therefore follows that all constituent concentrations in the effluent fluid are at any moment identical with those in the mobile solution which reaches the exit plane at that time. Since the same conditions of chemical equilibrium hold for both, the two fluids are at every moment identical in all respects. The profile of composition of the effluent therefore exactly reproduces the profile of composition in the mobile phase of a moving-boundary system; it does not reproduce, through it corresponds to, the profile of composition of the boundary as a whole; neglect of this fact was responsible for the mistaken use of the reciprocals of elution volumes by Nichol and W i n ~ o r , * * ~ to which reference has been made. Relationships beticeen the Equations for Boundary and Elution Projiles. The equations of conservation, which lead to the boundary equations, may be stated generally in terms of the inclusive constituent quantities E and G. One such equation can be written for each constituent. I n differential form these equations are
u = d(&&)/dcx
(13)
In principle, solution of this set of equations describes uniquely the whole reaction boundary profile in terms of the relationship between u and the various concentrations. Hourever, to arrive at practical solutions it is necessary to specify each 6x as a function of composition,
REACTION BOUNDARIES AND ELUTION PROFILES IN COLUMN CHROMATOGRAPHY
which in the type of case considered requires definition both of the equilibria occurring in solution and their equilibrium const'ants, and of the composition dependence of each PX. By use of eq 8, 9, and 11, eq 13 can be rewritten in terms of elution volumes instead of velocit'ies
and solution of this set of equations gives, with the same limitations, a description of the elution profile. The correspondence between eq 13 and 14 may be illustrated by simplified examples. (i) With no interactions in solution, EX and & can be replaced by cx and CX', respectively, and, from eq 5 , eq 14 becomes
which is the analog, in our terms, of Gi1bert'sl2 eq 3. The boundary and elution profiles depend on the composition dependence of PX. If these are independent of composition, eq 15 reduces to v u
=
VdPX
729
which is the integrated form of the Johnston-Ogston equation. Integration of eq 14 likewise gives
It should be noted that the values of a and P for different constituents are in general not identical, but each corresponds to the medianlo of the boundary with respect to a particular constituent. Again, we apply this to two cases: (i) There is no chemical interaction in solution. If integration is performed between two phases CY and P across a boundary where X does not vanish, by use of eq 4,5, and 6c, eq 19 becomes
which is Winzor and SicholJsgequation, as corrected by Gilbert,I2 with X = B and V0/pxa and VO/PX' replacing Vxaand V x S ,respectively. (ii) PX is composition independent, but there is an equilibrium A B C in solution. Equation 19 can be written for (say) the A constituent, with the use of eq 4 and 6c
+
(16)
showing that there is an independent, sharp elution front for each component of the solution. (ii) PX is composition independent, but there is an equilibrium -4 B e C in solution. From eq 4 and 6c eq 14 can be written, for constituents A and B
+
Equation 21 may be rearranged to give an expression similar to eq 20, but with elution volume and concentration terms written as constituent quantities. I n this form it is recognized as the moving boundary (or flux) equation used by Nichol and Winzor to determine K for migrating systems of the type A B Fr-f- C in which both sharp7 and hypersharps boundaries are predicted theoretically (cf. Figure l a and 2b of ref 11). However, in the latter treatmenta eq 21 was incorrectly applied in that reciprocals of elution volumes were employed; the corrected data have been presented by Gilbert.12
+
These equations are of exactly the same forms as eq 21a and 21b of Sichol and Ogstonl' for free migration of the system A B Ft C, with replacement of u, oA, OB, and vc in the latter equations by Vu, V o / p ~ , V o / p g J and Vo/w,respectively; they can be handled in exactly the same way. Integral Forms of Equations for Elution Projiles. Integration of each eq 13 across a boundary between two adjacent plateaus gives
+
Discussion In summary, it may be concluded that eq 16, 17a, 17b, 20, and 21 find direct analogs with equations presented earlier to describe the effects of physicall1,13 or ~ h e m i c a l ~interactions ~!~ on migration patterns obtained by moving-boundary methods not involving a stationary phase. The relationship between the constituent concentration of any solute species in the effluent from a chromatographic column and mobile phase within the column shown in the discussion of eq 12 and the recognition that elution volumes Volume 71, .&-umber 8
FebTWTy 1967
M. J. D. Low AND N. RAMASUBRAMANIAN
730
must replace velocity terms in earlier e q u a t i o n ~ l ~ , are ~ ~ determined by the dependence of constituent velocities of each constituent species on total composition permit direct application of previous theory to the chromatographic case. Ackers and Thompson4 and may lead to a clearer understanding of elution profiles obtained in frontal analysis and affected by either Gilbert12 in their treatments of chemically reacting chemical or physical interaction. systems have also stressed the necessity of direct subAcknowledgment. We are grateful to Dr. G. A. stitution of elution volumes for velocity terms. It is Gilbert for drawing our attention to the error menhoped that the generalized approach based on the tioned, in advance of the publication of his paper.12 concept that essential features of migration patterns
The Dehydration of Porous Glass
by M. J. D. Low and
N. Ramasubramanian
School of Chemistry, Rutgers, The State Unitersity, New Brunswick, Yew Jersey
(Rereiced August 23,1966)
A microbalance was used to follow the kinetics of dehydration of porous glass in vacuo a t constant temperatures from 25 to 800". The kinetics of water sorption and desorption by the degassed surfaces was measured. Infrared spectra of degassed specimens were obtained. Physically adsorbed water as well as some tightly bound water could be removed at 25". Degassing above 600" produces surfaces containing isolated hydroxyls. The amount of water retained after a sorption-desorption cycle is a maximum with samples degassed near 300". It is proposed that geminal hydroxyls responsible for this maximum are destroyed. The percentage of the sorbed water which is retained increases with samples degassed above 600". This effect is produced by boron migrating to the surface of the glass.
Recent infrared spectroscopic studies of the dehydration and hydration of porous glass surfaces provided evidence for the existence of B-OH structures on the surface of highly degassed specimens. 1--3 The intensity of the absorption band at 3703 cm-l attributed to B-OH groups was higher than would be expected if the boron were evenly distributed, the results indicating the boron concentration to be higher a t the surface than within the bulk of the glass. However, it was not possible to detect surface B-OH groups on specimens which had been degassed under mild conditions. These effects thus raised some doubt about the stability of the surface of these adsorbents, because it was not clear if the boron enrichment a t the surface occurred during the manufacture of the glass or came about as a The Journal of Physical Chemistry
result of the high-temperature degassing. The present experiments were performed to provide some information on this topic as well as on dehydration and rehydration of porous glass surfaces. Experimental Section The general procedures described elsewhere were employed.2 Pressures of approximately torr were produced with conventional high-vacuum systems. Spectroscopic measurements were made with a Perkin(1) M. J. D. Low and N. Ramasubramanian, Chern. Commun., in press. (2) M. 5. D. Low and N. Ramasubramanian, J . Phys. Chem., 70, 2740 (1966).
(3) N. Ramasubramanian and M. J. D. Low, submitted.
