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Gas-liquid partition chromatography
130
ANALYTICACHIMICAAGTA
GAS-LIQUID COLLMN CRITERIA
PARTITION
CHROMATOGRAPHY
BEHAVIOR AND FOR FAVORABLE 13UDDHAI~EV
ITS REPRODUCTION COLUMN BEHAVIOR* SEN
CortlesClremrcal LaDovatortes,Loztzszunu Slate Univcrszly, Ruton Rouge, Lu. (U S A .)
(Rcccwcd July goth, rgsg)
In the present paper an attempt has been made to explain the movement and the distribution of a solute in a gas-liquid partition chromatographic (GLPC) column from probability considerations. It has been shown that the mechanism of movement ‘of the solute is analogous to a BERNOULLI trial system. Repeated independent trials are known as BERNOULLI trials if there are only two possible outcomes for each trial and their probabilities remain the same throughout 1. If b(k, 72,p) be the probability that ti BERNOULLI trialswith probabilities$ for success and q(= I - +) for failure resultin k successes and rt-4 failures, then
w,
n* P) -
(;)
p*q”-k
. . . . . . . .
. .
. .
. .
(I)
It is possible to attribute a “probability of success”~~term and a total number of “trials” term to any column-solute combination, The magnitude of these two terms, however, depends upon the operating conditions of the column and the nature of the solute. Once these two terms are specified, the “behavior” of the column is exactly defined. When these two terms are reproduced, the column behavior is also reproduced. It should be noted that the emphasis is laid upon reproducing the column “behavior” instead of duplicating the operating conditions individually. Conditions responsible for producing the most favorable column behavior for normal types of solutes have also been discussed from the viewpoint of the equilibrium distribution. The compounds having moderate polarities and heats of vaporization (obeying TROUTON’S relation) arc considered as normal solutes. Favorable column behavior is considered to be that one which is most suitable for the separation of certain specified groups of compounds. Colic9rtnbehaviov It is now well establishedz-G that whatever may be the approach to explain the mechanism in the GLPC column &using the!distribution of a solute, the distribution can always be expressed by one of the conventional covergent series like the binominal, POISSON, or GAUSSIAN. ---_-* Prcscnted bclorc the Analytical Dlvlsion of the 136111National Mcctlng of the American Chexnical Society at Atlantic City, N.J , Sept. 13-18, xgsg. Anal. Ghrm. Ada,
22
(1960)
x30-142
GX&FEIQUIDPARTITIONCHROMATOGRAPHY
131
During the chromatographic analysis the three parameters of the distribution of the solute measured are (I) the emergence time or volume, (2) the width of the distribution curve at the point of inflection, and (3) the height of the peak. It will be seen shortly that the emergence time Z& = f(n, V, p, F) and w = g(%, v, p, I;) of the same set of variables. In the two foregoing equations, n is the number of theoretical plates which corresponds to the number of trials in a BERNOULLI system; v is the plate dimension, p is the probability of success and F is the flow rate. In this particular case, the proba’ bility of success means the probability of finding a solute molecule in the gas phase: the event of entrance or exit of a solute molecule into or out of% plate corresponds to a trial. Thus the two fundamental conditions of the BERNOULLI theoremI, (i) that there are only two possible outcomes for each trial and (ii) that all the trials are identical and independent, are fulflllcd. The solute fraction, fi, stays m the gas phase and moves and is successful. The fraction, q (q = I*), stays in the stationary phase and is unsuccessful. When it is made large, using LAPLACE’S appro_ximation. the distribution can be cxpresscd by a GAUSSIAN function and the width of the distribution curve depends on u, the standard deviation. When p bccomcs infinitesimally small, i.e. by letting p --z o and q -> 1, and n IS very large so that ?tp is of moderate magnitude, tlic distribution becomes a POISSON function. In the case of GLPC, p is very small. In all the thiec types of distributions mentioned above, the height of the mean is the highest ordinate. Its value corresponds to the probability of finding the largest number of molecules at the particular trial, plate, or stage. The situation in GLPC is a cast of alternative probability (mutually exclusive events)a due to the constant value of partition coefficient. Mutually exclusive events mean that only one of them can happen and the happening of which automatically prevents the happening of the other. Due to the constancy of \hc partition coefficient, the presence of any one molecule in gas phase automatically prevents the presence of any other molecule, although the different molecules are indistinguishable. When a. quantity m is introduced into the column, let p be the probability of a molecule being present in the gas phase; when introduced into the column, all the different identical molecules will have the same probability $ of being present in the vapor phase, thctr the probability that any molecule will bc in the gas phase is given by P-P-+-p-l-P-t..
. .
. . . . . . .
, .
.
.
(2)
depending upon how many molecules have been introduced into the column. In other words, the largest number of probable molecules to be found at a definite stage will be double, triple, quadruple, etc., corresponding to the multiples of nt introduced into the column. Therefore, it follows that the height of the mean in the distribution curve is proportional to the quantity of solute introduced into the column. That this relation (z) is true can be proved by means of a simple analogy. Suppose one is to find out the probability of throwing an even number with an ordinary sixsided die. The events to be considered are the throwing of a 2, a 4, or a 6, each of which has a probability of I/G. These events are mutually exclusive, that is, the appearance of any one of these automatically prevents the appearance of any others. The probability of at least one of these numbers, that is, of an even number to show,up, is 116 + 116 + 116 = I 12; and therefore
B.SEN
I32
Let us now assume the following: I. The column is composccl of a large number, B, (say ti = IOO) of equivalent plates serially numbered o, I, 2 . . . . . . PZ. 2. Each plate consists of a stationary phase of volume V, and agaseousphase of volume V ,nI 3. One unit mass of the solute is introduced into the plate numbered zero within a very short time and the solute has a distributron coefficient * . . . . .
. . .
. I..
. -
(3)
whcrc C. and C,,, arc the concentrations in the stationary and the mobile phases. 4, Subsequent portrons of thcgaseous phase introduced into the plate zero in installments of V,,, are solute free and move from o to n plate. 5. At each operation (trial) V,,, volume of movable phase is passed onto the next plate. The fraction #Jof the solute that moves out of each plate at each operation is given by
p=
I’,,, cm
I’L.3
v’nrc,,, iVW
-
vnr + =I-
KV.
vm
. . . . .
.
V
. *
.
(4)
a.*
lhc quantity, V = V/,” + KV,, is the effective plate volume. The fraction, q = I-+ stays in the plate. The probability Pkn of finding a solute molecule in the gas phase after FZoperations (trials) at the plate number k (the (K + r)th. plate) is
= b(/r, n, p)
.
.
.
.
.
. .
.
.
.
.
.
.
.
* .
(5)
where o < k < rt. This means that as a result of n trials the solute fraction had k successes and moved to the plate number 18.The expansion of the above gives the fraction of the solute in different stages. After n operations, the mean location, i.e. the location of the largest number of molecules on the column in terms of plate units, is given by cr =rrp
.
. . . . .
. .
* . . .
At each operation, a volume V “, of the gaseous phase is introduced so the volume throughput at the peak emergcncc is given by I(,, = XV, =uvp
Lf the volumetric
VI; m Martin’s
(.
.
.
.
,
.
.
.
. * .
(6)
into the column,
equations) .
.
.
.
.
.
.
* .
.
.
(7)
flow rate is I; per unit time, then the peak emergence time is given by Anal.
Chit%
ACfa,
22
(1960)
130-142
GAS--LIQUID PARTITION CHROMATOGRAPHY *V,
units of trme
/Le=-FnvP
s---e
133
.
Rt
F
..a...
.
*
Thus the statement made earlier, RF = f(n, v, +, F), is correct. In binominal distribution, the mean, that is the value of greatest probability, and the standard deviation is given by Mean,
Standard
When n is very large, distribution
p =
np
dcwatlon,
n =
. . .
. . . . . . .
d$Gj
*.
these values can be substituted
.
.
in the equation
. . .
.
.
(9)
(10)
for normal
and becomes pm
=
--d
1
%ilp?
e-(A-nPhw~
.
.
.
.
.
.
.
_
,
(11)
So the distribution is a continuous function of the plate number, k, corresponding to the probability of finding the largest number of fractions. This is LAPLACE’S approximation. We have already expressed the emcrgencc time in terms of the plate number, it, the probability jh, the effective plate volume, v, and the volumetric flow rate, F. Similarly, the standard deviation, a, can be expressed m terms of the above factors. If uV be the standard deviation in terms of effluent volume, then uv -
L,v
(12) P because the solute in the mobile phase travels I ffi times faster than in the stationary phase. In units of time _- __ . vt/ “P4 unhs of tlmo . . . . . . . . . . . . . . (13) cr; = N)
=
q/-q.
.
.
*
F
Letting p + o, q + 1, and n -> cc whereas ~9 = constant and is of moderate magnitude, the equation (5) becomes a POISSON function. This situation approximates the type of mechanism operating in GLPC columns, whereas binominal distribution is true for GRAIG’S machine’. It is quite obvious from the equations 5,8, II, 12 and 13 that the values of ,u and u completely define the distribution curve or the macroscopic behavior of the column. Also and
#UC = f(% P, v, F)
(cf. eqn. 8)
UC= I!?(%P. VI F)
(cf. eqn. 13) . . .
,
.
. . * (14) .
. . (15)
Whe shall make some u @iovi assumptions here which are substantiated by our subsequent determinations. Macroscopically and microscopically, the equations 14 and 15 are true ; however, the value of p and v will be affected by such microscopic effects as the film thickness, 6, of the coating liquid, particle diameter, dp, of the solid support, Anat.
Chit?L Acta,
22 (1960)
1’30-142
B. SEN
134
density and the nonuniformity of the packing. When a column is repacked it is hardly possible that such microscopic factors can be reproduced. Yet it is quite possible to compensate for the slight change in v and p by suitable adjustment of F. Sometimes even a slight variation in temperature accomplishes the desired effect because K and consequently p is temperature dependent. With proper adjustment of the variables it is possible to reproduce the probability and distribution of successes. Once the distribution is reproduced, the macroscopic column behavior is also reproduced. In actual practice, one has to select a particular solute as standard (criteria for the selection of the standard are discussed later), inject it from time to time or when the column is repacked and measure the values of ,uuvor ,u: and the width (a measure of uV or it). These two parameters define the distribution curve. The adjustable variables are changed until the original values of the 1~” or pt and the width are reproduced. When the column behavior is thus reproduced for the standard, it is also repro’auced for the other solutes. This has been verified for over a hundred compounds, for which the substrate to support ratio was varied between j-s%. From the values of pt and u( it is possible to calculate the number of hypothetical plates of the columna. The number of plates required for a separation has been discussed by VAN DEEMTER el al.4 and GLUIXKAUF”. Using the same pressure differential and applying a pressure gradient correction to the apparent retention volume Vn does not insure that the same corrected retention volume Vk will be obtained”el0. Because Vk = f I’,< ‘c/i=
corrected
retention
volume,
f =
v; +
KV.
.
.
.
pressure gradient
.
.
.
.
.
.
.
.
.
. (IO)
correction
3(PclP0J)2- 1 2 (Pc/P#-1
V ,1 = apparent retention volume, V; = gas hold up volume, K = partition coeffir cient, Pi = inlet pressure, P, = outlet pressure. V, is an explicit function of Vi and KV,. It may not be possible to reproduce Vi and KV, when the column is repacked. On operating for a long time, V, may change slightly due to evaporation from the column. The operator generally finds it necessary to change the flow rate (pressure differential) in order to obtain the same retention volumes. It has been shown earlier that the effects of shght changes of the microscopic parameters can be corrected by varying the adlustable parameters, The operator is interested in knowing that he is operating with a column of identical behavior rather than knowing the different values of Vi due to intrinsically changed columns. In the foregoing discussion, the transportation of material has been assumed to be entirely due to the movement of the mobile phase. In the rate theory+“, the contributions of the eddy diffusion and the molecular diffusion in both the phases towards the movement of the material have also been considered. It was decided to study the contribution of the diffusional terms of the equation for the height equivalent of a theoretical plate (H) deduced by VAN DEEMTIZR et ~1.4.1~. Anal.
Chm.
Acla,
22
(1960)
130-142
GAS-LIQUID
H
==ddp
PARTITION
+
CHROMATOGRAPHY
I35
2y
value of I, where y = correction for the tortuosity of the ch%.nnels andM*limiting a measure of packing irregularity and dependence upon p$+icle diameter, i3= D o= molecular diffusion in gas phase, d p= particle diameter, If= liquid film thickness, liquid phase e U = linear velocity; DZ = molecular diffusion in liquid phase. K’ = K gas phase If one wants to calculate the value of H from this equation, a rather large number of assumption have to be made in computing the various terms of the equation which in itself is not a very desirable situation 13. Therefore, it was decided to find experimentally the contribution of the diffusional terms under the chromatographic flow condition (flow rates > 20 ml/min). In the first series of experiments the column packing material was completely removed from the column, or in other words an empty tube was used. The tube was maintwned at 80’ and helium was flowing through it. Different types of solutes were introduced into the tL,be by momentarily stopping the helium flow. Figs. I to 3 show the distribution of the various solutes under a virtual
Fig. I. Dlstrlbutlon of concentration of solutes in an empty tube at dlffcrcnt helium flow rates. Length of flow tube: I mctcr; tempcraturc of flow tube* 8o”; volume of organic samples 2 pl. volume of inorganic samples: 1 ml at 50’ and 1 atm. a. carbon tetrachlorlde; b. sulfur dloxldc.
Fig 2 L)istrlbution of concentration of diffcrcnt solutes in an empty tube under iclcntical conditions of temperature and hehum flow rate. Length of flow tube. 1 mctcr; tcmpcraturc . 8o”; helium flow* IO ml/mm; volume of the orgamc snmplc 2 ~1: volume of the inorganic samples: x ml at 5o” and I atm.
coefficient of diffusivity. This type of distribution was expected from TAYLOR’S studyla- 16 of the spread of the particles in a turbulent constant flow. Without going into the details of TAYLOR’S calculations, a number of conclusions may be drawn from the experimental cures: (I) Under identical conditions of flow rate and temperature, distributions are more or less the s;une for all the compounds so far as their spread and the time of arrival at the exit of the tube are concerned. (2) At higher or chromatographic volumetric flow rates the virtual coefficient of diffusivity was negligible there was nocspregd an’d all the solutes compared to the linear velocity. A f cur-it came out as plugs and at the same time. The time correspnikd to the holding time
B. SEN
136
of the tube which depended upon the length of the tube. This means the signal was the same as that produced by a permanent gas in gas-liquid chromatography. (3) The effect of temperature is less important. In the second series of experiments the tube was packed with sand, the distribution curves dne to varrous solutes are shown in Fig. 4. Conclusions from these experiments arc identical with those from the empty tube. Thus it appears that at the chromatographic flow rates the contribution of the first two terms of VAN DEEMTEK’S equation are ncgligrble or at the most they may be substituted by a suitable constant.
KJo*c 80-c
so
20
IO
6
FLOW RATE pig. 3 ‘rhc cffcct of tcmpcraturc cm the cllstrlbutlon of conccntratlon of a solute In an empty tube unilcr dcntb2,LI flow rates Length of flow tubI meter, hcllirm flow ~oml/ni~n;s;in~~~lc~z~Iofctlrbontctrilclilor~tlc
Criteria
/OY favorable
colatmn
I_ b
R
50 ml/min
6
IO
Distnbutlon of conccntratmn of F1g 4 solutes rn a sand pack4 tube at dlffcrcnt hellurn flow rAtcs Length of sand column: go cm, %rccn fraction of sand * 40180 mesh fractmn, tcmpcraturc of the sand packed tub2 80’ a 2 pl carbon tctrachlord2; b 2 pl ofa mlxturc ofcqual volumes of ally1 chlorrde, acctonc, set butyl chlorltlc. n-amyl chlorrde, carbon tctrachlor~tlc and chloroform
behnviov
A number of investigators have found that straight lines are obtained when logs of time are plotted against the boiling points of the solutes. Similar straight lines arc obtained when logs of retention time are plotted against the ratio of the boiling points of the solutes and the column temperature. TENNEY~O studied solutes like n-paraffins, z-methylparaffins, cyclopentanes, cyclohexanes, I-olefins, z-methylolefins, cycle-olefins, diolefins, alkylbenzenes, acetylenes, primary n-alcohols, secondary alcohols, tertiary alcohols, aldehydcs, ketones, formates, acetates, ethers and acetals on columns treated with such different types of solvants as convoil-20, squalane, b, ,9’-oxydipropronitrile, z-ethyl hexyl sebacate, convachlor-so. With only a few exceptions he obtained straight lines for boiling points vs. log rctcntion times plots. Strarght lines arc also obtained when logs of partition coefficients obtained by chromatographic methods are plotted against the ratio of the boiling point of the solute to the column temperature (cf. Figs. 5 and 6). This is expected because the retention time changes linearly with partition coefficients (cf. eqns. 4, 7 and 8). It was expected and also found that similar straight line plots are obtained when the latent heats of vaporization are plotted against logs of partition coefficients (cf. Figs. 7 and 8). The above conclusrons are true only for the compounds of the same family, Cyclopentane, being a compound of another family, did not fall in the straight line (cf. Figs. s-8). It is also interesting to note that column temperature higher than the critical temperature of the solutes were never used.
’ retention
Anal. Chn.
Ada,
22
(1960)
130-142
GAS-LIQUID
PARTITION
137
CHROMATOGRAPHY
3-MbPENfANE
?I-MbPENTANE I.10
2-?Ae PENTAHE
I IO
O.?bDIYeBUTAUE
2.3-DlM@BUT
ANE
c .
c?>
0
~.~-O’M*B’JTANE
c’
CYCLOPEHIANE
2,2-OlMrBUTA0
P
/
P 1.0t
CYCLOPENTANE
1.05
IO5
n-PENTANE
I 20
K
1
l
30
40
too
1
n-PENTANE , I
L
80
I
200
FIN. 5 Change of log partition coefflclcnt with the ratio of bolllng pomt to column tCmperatin% Tb(Ol<) = b p ; T(OIC) = cd from ~i&u~iShl~Ns~~ I’)ilta taken tcmp Column D~metl~ylsu1folanc Note Cyclopcntanc chd not fall in llnc with the chain hydrocarbon
I
300
6
400
500
Fig 6 Change of log partltron cocfflclcnt with the ratlo of boiling point to column temperatlirc ?‘b(OI<) 3 b p ; T(Ol<) = cd #I-Hcxadccanc Data taken temp. Column from ICP,uL&xANs12 Note. In this cast cyclopentnnc is cloacr to the llnc because of the low polarity of the substrrrtc.
7.80
7.50
n-HEXANE
3-M,PENTANE
3-MbPENTANE 2-MaPENTANE T.00
700 =
2,3-OlMe
BUT
ANE
x” CYCLOPENTANEO
OCYCLOPENTANE
f 2.2.DIMI
BUTANE
2.2-OIMeBUTANC
6.80
6.50
6.20
8.20
0 20
K
30
40
50
1
IQg 7 Change of log yartrtlon ctxfflclent with the molar heat of vaporization at constant prcusurc. Partition cocfftcient data taken from l
/
“_- PENTANE I
I
I
400 500 K 300 Ftg 8 Cllangc of log partltmn cocfflclcnt with the molar heat of vaporization at constant pressure Partltlon cocfflclcnt data tnkcn from KEULIZMANS~~ and heat of vaporization (at 25’) tlats taken from Chcmlcal Englnccrs’ Handbook Colllmn pa-Hcxadccanc. 200
sulfolanc
16 reveals yet anotlrerinteresting feature Examination of data obtained by TENNEY (cf. Fig. 2 of ref.10). The intercept of the log retention time VS.boiling point curve is practically independent of temperature even for a temperature differential of 50”.
/id.~Ghim;~
Acta.
22
(I@O)jZ36+142
B. SEN
138 Xl
PI1
nv
p/v
=-=-.
K
eL’ln*
. . . .
. . . . .
. . .
(18)
where K = partition coefficient, nt = moles of solute per unit volume of the condensed phase, 9~0= moles of solute per unit volume of the vapor phase, P/r = partition function of the solute in the condensed phase, P/* = partition function of the solute in the vapor phase, Li = mean potential energy difference per mole of solute in condensed phase and vapor phase (lmearly related to the molar heat of vaporization of the pure solute at constant volume), R = gas constant, T = temperature of the system. For an one component system Pft/Pf ,, tends to become unity. It can be shown that the PfJPf” is practically independent of temperature for very low concentrations of the solute. Li in equation (18) may bc substituted by LeIRT, where Le is the mean potential energy diffcrencc at constant pressure (Le is liucarly related to molar heat of vaporization of the solute at constant pressure) and the equation (18) becomes I< = ~‘~(I.cfllT)--l = _4c1,r/nr
. . .
. . . . .
* * (fS1
Because the plot of log K against TtJT (Tb = boiling point in “K) produces straight lines (cf. Figs. 5 and G), it may be expected that a relation similar to TROUTON'S rule exists between Tb and Lc in the cast of dilute solutions and the equation (19) may be written as IC = rl #t’bl1lT where
. . .
a..
.a,.
*
(20)
*
Le/?‘b =
time or retention Tt has been shown earlier that the relation between retention volume and K is linear (cf. cqns. 7, 8, and x.6), so the equation (20) may be modified to give an expression for retention time or retention volume, hence RL - fi< = /%?aT,/n’r.
. .
. . . . . . .
. . . (21)
I?, = retention time B = a constant for homologous compounds and the same substrate Ttic equations (19-21) may bc written as
wherc
In K =
In A -I- Le/RT
In
Xc
In
In
R;
=
=
In
A -+- CLTb/RT B +
u ‘I’b/RT
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . .
. . . .
.
.
.
.
.
.
.
.
.
. (23)
.
. . . . (24)
(22)
We can draw a number of conclusions from the equations (19-24). I, The partition coefficient or the retention time will change expontentially with the change of the ratio LEE or Tb/T. It is expected that for Tb/T ratio higher than unity Rt will increase very rapidly. Fig. g illustrates a plot nJnv against Tb/r assuming A = I and a = 23 (one component two phase system). At lower Tbr ratios (when T >, critical temperature), nt/rro will be constant at constant pressure and the above relations are not strictly applicable. In other words, it may be safely concluded that at column tem-
GAS-LIQUID PARTITION CHROMATOGRAPHY
139
peratures much lower thaD the boiling point of the solute (Tbr $ I) most of the molecules will remain in the stationary (condensed) phase for most of the time and there will be fewer exchanges between the two phases, i.e. the column will be inefficient. At column temperatures much higher than the boiling point of the solute (say Tbr < 0.6 ;
Fig. 9 Change of the rntlo of number moles/untt volume of the hqud
volume of the vapor In equllibrlum at tcmpcrnturc T’K cqulhbrium temperature. ‘f b= b p (Of<) I ‘f = cqulhbrlum
to number of molcs/umt with the rat-lo of the boding point to the tcmperaturc = column tcmpcraturc (OK).
for pure compounds the ratio of boiling and critical temperature is approximately equal to 0.6) most of the molecules will remain in the vapor phase for most of the time and the column will be inefficient. However, the actual optimum temperature range will be determined by the slope and the intercept of the log RI zrs.T&r plot. 2. A plot of In K or In RI against Le, or Le/T, or Tb or Tb/T will be a straight line and will make an intercept which will be constant and independent of temperature at least for modcrate temperature ranges. This expectation has been verified by our results as well as by TENNEY’S~~ data. 3. It is also expected that the slopes of the plots for different types of compounds will not be very different (cf. Figs. 5-S and TENNEY~~). 4. Combination of equations (7) and (16) and (23) should enable us to determine K and its temperature dependence in a very straight-forward manner. Recommendalim for determining the oplimfrm column conditions The choice of temperature of the column is the first parameter to be decided. It should be realized from the preceding discussion that any one column tcmperaturc cannot be suitable for all the solutes. The column temperature will t\a determined by the boiling point of the lowest boiling solute in a mixture. The optimum column temperature is given by a value of the T b/T ratio between I and 0.92. The compounds boiling between the column temperature and 0.92 times the .column temperature will be very nicely resolved. (cf. Fig, IO). Ad.‘CMm,.AcfU,:22
(1960)
X30-142
B.
r4o
SEN
After the column temperature has been fixed, a standard solute is selected, boiling as close possible to the column temperature, preferably slightly below the column temperature. This compound should not be highly polar and should have normal heat of vaporization (L.e/Z’bm 23). A volume of this solute, less than the plate volume, should be injected into the column at different flow rates until the flow rate corresponding to the maximum number of plates is obtained. The optimum temperature and the flow rate are thus determined. The condition of the column can be checked 140 0
N 1200
1.2- C2HqC12
IA C2HClf
c Cl4
Osaa.
1000
WllCl
600
0 ..c.c41i+lr
0
0
C4HgCI
C3lyr
CHC13
I-C3H,lw
0
400 LO4
I.00
096 ?,/
0.92
0.80
0.84
T
Pig. IO. Variation of the number of plates with bollmg potnt of the solutes Column. zoo/u trl-m-tolyl phosphate on 30/60 cchte ; column length : z meter; column tcmpcraturc: 93O; Hc flow rates: 52 ml/mm Widely varymg types of halogenatcd hydrocarbons wcrc dehberatcly chosen to omphasrze the lmportanco of the bolhng point, even when the compounds do not strmtly belong to tho samu famrly.
Fig.
I I.
efficiency.
Effect of borlmg point, (Compare with TableI)
length
heat of vapormatron and diclcctrm constant on the column Column: 20% tri-m-tolyl phosphate on 30/6o ccl&; column . z meter ; column temperature’ g3O. ~tld.
ChZ#l.
htU,
22
(1960)
130-142
GA!+LIQUID
I’ARTITION
CHROMATOGRAPHY
141
every nowand then by injecting the standard, and the overall column behavior maintained uniform by adjusting the flow rate and, very rarely, the temperature. The reason that a solute having a boiling point near the column temperature is selected is that the slightest change in column condition is reflected in the number of plates. When the column is repacked with the same material, the same plate number is reproduced by-adjusting the flow rate and the column temperature. The retention times may be easily expressed in terms of the standard. It was also found that for the same column, optimum flow rate was the same irrespective of Tb/T ratio, although the absolute efficiency of the column was different depending on the value of TO/T ratio, the dielectric constant and the heat of vaporization (cf. Fig. II and Table I). TABLE I EPPECTOPBOlLlNGPOlNT,HEATOFVADORIZATION,ANDDIlLLECfRICCONSTANTONCOtUMN EFFICIENCY (Compare wrth plate number In Frg. I I) Column: 2oy0 trr-m-tolyl pliosphatc on 30/6o cclrte; column length 2 mctcr, column tempcraturc g3O
Acetonitrite (7) rsopropyl alcohol (6) Cyclohcxane (2) Bcnzenc (I) Carbon tctrachloride (5) n-Hexane (9) Zsopropyl ether (3) Methanol (IO) Chloroform (4) Acetone (8)
o 97 o 97 o 97 o 965 o 955 o-935 o 93 0915 0.91 5
o 90
38 8 IS 9 20 23 22 r9 32 6 44 *r 4
84 7 05 72
ACKNOWLEDGEMENT
author wishes to thank Professor PHILIP W. WEST for providing the facilities his lahoratories and his constant encouragement in the author’s work. Dr.
The of
ROBERT
V.
NAUMAN,
Dr.
SEAN P.
MCGLYN
and
Professor
PAUL
DELAHAY
made
valuable suggestions and criticism. Dr. B. R. SANT helped in numerous ways during the preparation of the manuscript. Partial financial assistance from the Research Grant S-43 of the Study Section of Sanitary Engineering and Occupational Health, Division of Research Grants, Public Health Service, is being acknowledged. SUMMARY The drstributron of a solute in a gas-liquid chromatographrc column hau been d~scusscd from the probabrlrty view pomt and its analogy to the BEBNOULLI trral system has been shown It has been shown that the rcproductwn of column behavior IS possrblo by rcproducmg the probabrlrty The crrterron for the optimum column temperature has also been discussed Rccommcndatrons have hean made for dctcrmming the optimum column condrtrons and its rcproductron. L’auteur a cffcctub unc Gtudc, B I’ardc du calcul dcs probabilrtds, sur Ic comportcmcnt d’unc substance dans uno colonnc chromatographrquc gaz-hqutdc. On a ddtcrmmd 6galcmcnt les condrtrons optimales ct la reproductrbrfitd. ZUSAMAMENFASSUNG Es wurde veniucht, dre Bcwegung unrl Verterlung einer Substanz rn cincr gas-fltissig Chromatogrephre-Kolonne mit Hilfe der Wahrschernlichkertsrechnung zu erkltlren. Drc Krrterrcn fur die And..Chim.
Acta, 22 (1960) 130-142
B. SEN
142
optimale Kolonnentemperatur werden diskutvxt und Vorschllge optimalcn Kolonnen-Bedingungen und dcrcn Reproduznxbarkeit.
gemacht
zur Bestimmung
der
REFERENCES 1
2 3
4 5 6 7 8 0 10 11 12 la 14 1G 16 17
w FELLISR, ‘*An Introductzon to Probabalzly Theory and Ifs Applacatsons,” Vol. I, John Wdey and Sons, Inc., New York 1956, pp. 13542. A. J. P. MARTIN AND R. L. M. SYNGE, Bzochem J., 35 (194x) 1358. A. J P MARTIN AND A. T. JAMES, Biochsm J ,50 (195x) 679. J. J.VAN DEEMTER,F.S.ZUIDERWEGAND A KLINKENBURG, Chem Eng Scz.,5 (rg56)271. A KLINKENBURGAND F.SJENITZER,C/~~~ Bng. Set , 5 (r956)258. M. C. HOLMBS, “An Outltne of Probab&fy and Zfs Uses,” Burgess Publishing Co , Mmncapolis ~93% P. 7 L. c, CRAIG, J. Bzol. Chem , 155 (x944) 5x9_ A. I. M. KEULRMANS, “Gas Chromatography,” Rcmhold Publishing Corp , New York 1957, pp. 1 I I-1 13. . E. GLU~C~AUP, Trans. Faraday Sot., 51 (1955) 35 D. AMBROSE, A I. M KEULEMANS AND J. H. PURNOLL, An&. C/rem ,30 (x958) 1582. L. LAPIDUS ANDN. R. AMYNDSDN,J. Phys. Chem ,56(x955) 34. A. I. M. KEULEMANS, “Gas Chromatography,” Rcmhold Pubhshmg Corp , New York 1957, pp. I x9-27. A. I. M. KEIJLEMANS, “Gas Ciwomatogvapiry,” Remhold Pubhshmg Corp., New York 1957, PP. 179-83. G. TAYLOR, Proc Roy. Sot. London, A219 (x953) 186. G TAYLOR, Proc. Roy Sot. London, A225 (x954) 473. H. M TENNEY, Anal. Chem., 30 (rg58) 2 Press, Oxford Umversity G. S. RUSHBROOKE, “Ixtvoduclron to Sta&sficaZ Thernrodynamics,” London 1949, Chapter XIII and XIV. Anal.
CHROMATOGRAPHIC
SEPARATION
Chrm. Acta, 22 (1960) 130-142
OF SOME
ALKALI
METALS
E. C. MARTIN Scirool
of Applred
Chemistry,
The University of NS
W.,
Sydney (Australia)
(Reccivcd June aznd. 1959)
Numerous papers have been publishedl-8 on the separation of the group I metals possibly none more successful than that of L~NSTEAD~, all however, suffer from the difficulty of identifying the position of the metal ions after development. As these metals travel as ions it occurred to the author that a combination of LINSTEAD methanol solvent to which some aqueous ammonia was added and using an acid base indicator as detector would prove simple and effective. This proved to be the case. EXPERIMENTAL l’lre solvenl Pure methanol was used in early trials but redistilled commercial mathenol proved successful in later experiments. To this was added one to ten percent of 15 N aqueous ammonia. Solvents based on ethanol +proponal and n-butanol were used with less success. Anal.
Chm.
Acta, 22 (19th)
x42-144
ANALYTICACHIMICAAGTA
GAS-LIQUID COLLMN CRITERIA
PARTITION
CHROMATOGRAPHY
BEHAVIOR AND FOR FAVORABLE 13UDDHAI~EV
ITS REPRODUCTION COLUMN BEHAVIOR* SEN
CortlesClremrcal LaDovatortes,Loztzszunu Slate Univcrszly, Ruton Rouge, Lu. (U S A .)
(Rcccwcd July goth, rgsg)
In the present paper an attempt has been made to explain the movement and the distribution of a solute in a gas-liquid partition chromatographic (GLPC) column from probability considerations. It has been shown that the mechanism of movement ‘of the solute is analogous to a BERNOULLI trial system. Repeated independent trials are known as BERNOULLI trials if there are only two possible outcomes for each trial and their probabilities remain the same throughout 1. If b(k, 72,p) be the probability that ti BERNOULLI trialswith probabilities$ for success and q(= I - +) for failure resultin k successes and rt-4 failures, then
w,
n* P) -
(;)
p*q”-k
. . . . . . . .
. .
. .
. .
(I)
It is possible to attribute a “probability of success”~~term and a total number of “trials” term to any column-solute combination, The magnitude of these two terms, however, depends upon the operating conditions of the column and the nature of the solute. Once these two terms are specified, the “behavior” of the column is exactly defined. When these two terms are reproduced, the column behavior is also reproduced. It should be noted that the emphasis is laid upon reproducing the column “behavior” instead of duplicating the operating conditions individually. Conditions responsible for producing the most favorable column behavior for normal types of solutes have also been discussed from the viewpoint of the equilibrium distribution. The compounds having moderate polarities and heats of vaporization (obeying TROUTON’S relation) arc considered as normal solutes. Favorable column behavior is considered to be that one which is most suitable for the separation of certain specified groups of compounds. Colic9rtnbehaviov It is now well establishedz-G that whatever may be the approach to explain the mechanism in the GLPC column &using the!distribution of a solute, the distribution can always be expressed by one of the conventional covergent series like the binominal, POISSON, or GAUSSIAN. ---_-* Prcscnted bclorc the Analytical Dlvlsion of the 136111National Mcctlng of the American Chexnical Society at Atlantic City, N.J , Sept. 13-18, xgsg. Anal. Ghrm. Ada,
22
(1960)
x30-142
GX&FEIQUIDPARTITIONCHROMATOGRAPHY
131
During the chromatographic analysis the three parameters of the distribution of the solute measured are (I) the emergence time or volume, (2) the width of the distribution curve at the point of inflection, and (3) the height of the peak. It will be seen shortly that the emergence time Z& = f(n, V, p, F) and w = g(%, v, p, I;) of the same set of variables. In the two foregoing equations, n is the number of theoretical plates which corresponds to the number of trials in a BERNOULLI system; v is the plate dimension, p is the probability of success and F is the flow rate. In this particular case, the proba’ bility of success means the probability of finding a solute molecule in the gas phase: the event of entrance or exit of a solute molecule into or out of% plate corresponds to a trial. Thus the two fundamental conditions of the BERNOULLI theoremI, (i) that there are only two possible outcomes for each trial and (ii) that all the trials are identical and independent, are fulflllcd. The solute fraction, fi, stays m the gas phase and moves and is successful. The fraction, q (q = I*), stays in the stationary phase and is unsuccessful. When it is made large, using LAPLACE’S appro_ximation. the distribution can be cxpresscd by a GAUSSIAN function and the width of the distribution curve depends on u, the standard deviation. When p bccomcs infinitesimally small, i.e. by letting p --z o and q -> 1, and n IS very large so that ?tp is of moderate magnitude, tlic distribution becomes a POISSON function. In the case of GLPC, p is very small. In all the thiec types of distributions mentioned above, the height of the mean is the highest ordinate. Its value corresponds to the probability of finding the largest number of molecules at the particular trial, plate, or stage. The situation in GLPC is a cast of alternative probability (mutually exclusive events)a due to the constant value of partition coefficient. Mutually exclusive events mean that only one of them can happen and the happening of which automatically prevents the happening of the other. Due to the constancy of \hc partition coefficient, the presence of any one molecule in gas phase automatically prevents the presence of any other molecule, although the different molecules are indistinguishable. When a. quantity m is introduced into the column, let p be the probability of a molecule being present in the gas phase; when introduced into the column, all the different identical molecules will have the same probability $ of being present in the vapor phase, thctr the probability that any molecule will bc in the gas phase is given by P-P-+-p-l-P-t..
. .
. . . . . . .
, .
.
.
(2)
depending upon how many molecules have been introduced into the column. In other words, the largest number of probable molecules to be found at a definite stage will be double, triple, quadruple, etc., corresponding to the multiples of nt introduced into the column. Therefore, it follows that the height of the mean in the distribution curve is proportional to the quantity of solute introduced into the column. That this relation (z) is true can be proved by means of a simple analogy. Suppose one is to find out the probability of throwing an even number with an ordinary sixsided die. The events to be considered are the throwing of a 2, a 4, or a 6, each of which has a probability of I/G. These events are mutually exclusive, that is, the appearance of any one of these automatically prevents the appearance of any others. The probability of at least one of these numbers, that is, of an even number to show,up, is 116 + 116 + 116 = I 12; and therefore
B.SEN
I32
Let us now assume the following: I. The column is composccl of a large number, B, (say ti = IOO) of equivalent plates serially numbered o, I, 2 . . . . . . PZ. 2. Each plate consists of a stationary phase of volume V, and agaseousphase of volume V ,nI 3. One unit mass of the solute is introduced into the plate numbered zero within a very short time and the solute has a distributron coefficient * . . . . .
. . .
. I..
. -
(3)
whcrc C. and C,,, arc the concentrations in the stationary and the mobile phases. 4, Subsequent portrons of thcgaseous phase introduced into the plate zero in installments of V,,, are solute free and move from o to n plate. 5. At each operation (trial) V,,, volume of movable phase is passed onto the next plate. The fraction #Jof the solute that moves out of each plate at each operation is given by
p=
I’,,, cm
I’L.3
v’nrc,,, iVW
-
vnr + =I-
KV.
vm
. . . . .
.
V
. *
.
(4)
a.*
lhc quantity, V = V/,” + KV,, is the effective plate volume. The fraction, q = I-+ stays in the plate. The probability Pkn of finding a solute molecule in the gas phase after FZoperations (trials) at the plate number k (the (K + r)th. plate) is
= b(/r, n, p)
.
.
.
.
.
. .
.
.
.
.
.
.
.
* .
(5)
where o < k < rt. This means that as a result of n trials the solute fraction had k successes and moved to the plate number 18.The expansion of the above gives the fraction of the solute in different stages. After n operations, the mean location, i.e. the location of the largest number of molecules on the column in terms of plate units, is given by cr =rrp
.
. . . . .
. .
* . . .
At each operation, a volume V “, of the gaseous phase is introduced so the volume throughput at the peak emergcncc is given by I(,, = XV, =uvp
Lf the volumetric
VI; m Martin’s
(.
.
.
.
,
.
.
.
. * .
(6)
into the column,
equations) .
.
.
.
.
.
.
* .
.
.
(7)
flow rate is I; per unit time, then the peak emergence time is given by Anal.
Chit%
ACfa,
22
(1960)
130-142
GAS--LIQUID PARTITION CHROMATOGRAPHY *V,
units of trme
/Le=-FnvP
s---e
133
.
Rt
F
..a...
.
*
Thus the statement made earlier, RF = f(n, v, +, F), is correct. In binominal distribution, the mean, that is the value of greatest probability, and the standard deviation is given by Mean,
Standard
When n is very large, distribution
p =
np
dcwatlon,
n =
. . .
. . . . . . .
d$Gj
*.
these values can be substituted
.
.
in the equation
. . .
.
.
(9)
(10)
for normal
and becomes pm
=
--d
1
%ilp?
e-(A-nPhw~
.
.
.
.
.
.
.
_
,
(11)
So the distribution is a continuous function of the plate number, k, corresponding to the probability of finding the largest number of fractions. This is LAPLACE’S approximation. We have already expressed the emcrgencc time in terms of the plate number, it, the probability jh, the effective plate volume, v, and the volumetric flow rate, F. Similarly, the standard deviation, a, can be expressed m terms of the above factors. If uV be the standard deviation in terms of effluent volume, then uv -
L,v
(12) P because the solute in the mobile phase travels I ffi times faster than in the stationary phase. In units of time _- __ . vt/ “P4 unhs of tlmo . . . . . . . . . . . . . . (13) cr; = N)
=
q/-q.
.
.
*
F
Letting p + o, q + 1, and n -> cc whereas ~9 = constant and is of moderate magnitude, the equation (5) becomes a POISSON function. This situation approximates the type of mechanism operating in GLPC columns, whereas binominal distribution is true for GRAIG’S machine’. It is quite obvious from the equations 5,8, II, 12 and 13 that the values of ,u and u completely define the distribution curve or the macroscopic behavior of the column. Also and
#UC = f(% P, v, F)
(cf. eqn. 8)
UC= I!?(%P. VI F)
(cf. eqn. 13) . . .
,
.
. . * (14) .
. . (15)
Whe shall make some u @iovi assumptions here which are substantiated by our subsequent determinations. Macroscopically and microscopically, the equations 14 and 15 are true ; however, the value of p and v will be affected by such microscopic effects as the film thickness, 6, of the coating liquid, particle diameter, dp, of the solid support, Anat.
Chit?L Acta,
22 (1960)
1’30-142
B. SEN
134
density and the nonuniformity of the packing. When a column is repacked it is hardly possible that such microscopic factors can be reproduced. Yet it is quite possible to compensate for the slight change in v and p by suitable adjustment of F. Sometimes even a slight variation in temperature accomplishes the desired effect because K and consequently p is temperature dependent. With proper adjustment of the variables it is possible to reproduce the probability and distribution of successes. Once the distribution is reproduced, the macroscopic column behavior is also reproduced. In actual practice, one has to select a particular solute as standard (criteria for the selection of the standard are discussed later), inject it from time to time or when the column is repacked and measure the values of ,uuvor ,u: and the width (a measure of uV or it). These two parameters define the distribution curve. The adjustable variables are changed until the original values of the 1~” or pt and the width are reproduced. When the column behavior is thus reproduced for the standard, it is also repro’auced for the other solutes. This has been verified for over a hundred compounds, for which the substrate to support ratio was varied between j-s%. From the values of pt and u( it is possible to calculate the number of hypothetical plates of the columna. The number of plates required for a separation has been discussed by VAN DEEMTER el al.4 and GLUIXKAUF”. Using the same pressure differential and applying a pressure gradient correction to the apparent retention volume Vn does not insure that the same corrected retention volume Vk will be obtained”el0. Because Vk = f I’,< ‘c/i=
corrected
retention
volume,
f =
v; +
KV.
.
.
.
pressure gradient
.
.
.
.
.
.
.
.
.
. (IO)
correction
3(PclP0J)2- 1 2 (Pc/P#-1
V ,1 = apparent retention volume, V; = gas hold up volume, K = partition coeffir cient, Pi = inlet pressure, P, = outlet pressure. V, is an explicit function of Vi and KV,. It may not be possible to reproduce Vi and KV, when the column is repacked. On operating for a long time, V, may change slightly due to evaporation from the column. The operator generally finds it necessary to change the flow rate (pressure differential) in order to obtain the same retention volumes. It has been shown earlier that the effects of shght changes of the microscopic parameters can be corrected by varying the adlustable parameters, The operator is interested in knowing that he is operating with a column of identical behavior rather than knowing the different values of Vi due to intrinsically changed columns. In the foregoing discussion, the transportation of material has been assumed to be entirely due to the movement of the mobile phase. In the rate theory+“, the contributions of the eddy diffusion and the molecular diffusion in both the phases towards the movement of the material have also been considered. It was decided to study the contribution of the diffusional terms of the equation for the height equivalent of a theoretical plate (H) deduced by VAN DEEMTIZR et ~1.4.1~. Anal.
Chm.
Acla,
22
(1960)
130-142
GAS-LIQUID
H
==ddp
PARTITION
+
CHROMATOGRAPHY
I35
2y
value of I, where y = correction for the tortuosity of the ch%.nnels andM*limiting a measure of packing irregularity and dependence upon p$+icle diameter, i3= D o= molecular diffusion in gas phase, d p= particle diameter, If= liquid film thickness, liquid phase e U = linear velocity; DZ = molecular diffusion in liquid phase. K’ = K gas phase If one wants to calculate the value of H from this equation, a rather large number of assumption have to be made in computing the various terms of the equation which in itself is not a very desirable situation 13. Therefore, it was decided to find experimentally the contribution of the diffusional terms under the chromatographic flow condition (flow rates > 20 ml/min). In the first series of experiments the column packing material was completely removed from the column, or in other words an empty tube was used. The tube was maintwned at 80’ and helium was flowing through it. Different types of solutes were introduced into the tL,be by momentarily stopping the helium flow. Figs. I to 3 show the distribution of the various solutes under a virtual
Fig. I. Dlstrlbutlon of concentration of solutes in an empty tube at dlffcrcnt helium flow rates. Length of flow tube: I mctcr; tempcraturc of flow tube* 8o”; volume of organic samples 2 pl. volume of inorganic samples: 1 ml at 50’ and 1 atm. a. carbon tetrachlorlde; b. sulfur dloxldc.
Fig 2 L)istrlbution of concentration of diffcrcnt solutes in an empty tube under iclcntical conditions of temperature and hehum flow rate. Length of flow tube. 1 mctcr; tcmpcraturc . 8o”; helium flow* IO ml/mm; volume of the orgamc snmplc 2 ~1: volume of the inorganic samples: x ml at 5o” and I atm.
coefficient of diffusivity. This type of distribution was expected from TAYLOR’S studyla- 16 of the spread of the particles in a turbulent constant flow. Without going into the details of TAYLOR’S calculations, a number of conclusions may be drawn from the experimental cures: (I) Under identical conditions of flow rate and temperature, distributions are more or less the s;une for all the compounds so far as their spread and the time of arrival at the exit of the tube are concerned. (2) At higher or chromatographic volumetric flow rates the virtual coefficient of diffusivity was negligible there was nocspregd an’d all the solutes compared to the linear velocity. A f cur-it came out as plugs and at the same time. The time correspnikd to the holding time
B. SEN
136
of the tube which depended upon the length of the tube. This means the signal was the same as that produced by a permanent gas in gas-liquid chromatography. (3) The effect of temperature is less important. In the second series of experiments the tube was packed with sand, the distribution curves dne to varrous solutes are shown in Fig. 4. Conclusions from these experiments arc identical with those from the empty tube. Thus it appears that at the chromatographic flow rates the contribution of the first two terms of VAN DEEMTEK’S equation are ncgligrble or at the most they may be substituted by a suitable constant.
KJo*c 80-c
so
20
IO
6
FLOW RATE pig. 3 ‘rhc cffcct of tcmpcraturc cm the cllstrlbutlon of conccntratlon of a solute In an empty tube unilcr dcntb2,LI flow rates Length of flow tubI meter, hcllirm flow ~oml/ni~n;s;in~~~lc~z~Iofctlrbontctrilclilor~tlc
Criteria
/OY favorable
colatmn
I_ b
R
50 ml/min
6
IO
Distnbutlon of conccntratmn of F1g 4 solutes rn a sand pack4 tube at dlffcrcnt hellurn flow rAtcs Length of sand column: go cm, %rccn fraction of sand * 40180 mesh fractmn, tcmpcraturc of the sand packed tub2 80’ a 2 pl carbon tctrachlord2; b 2 pl ofa mlxturc ofcqual volumes of ally1 chlorrde, acctonc, set butyl chlorltlc. n-amyl chlorrde, carbon tctrachlor~tlc and chloroform
behnviov
A number of investigators have found that straight lines are obtained when logs of time are plotted against the boiling points of the solutes. Similar straight lines arc obtained when logs of retention time are plotted against the ratio of the boiling points of the solutes and the column temperature. TENNEY~O studied solutes like n-paraffins, z-methylparaffins, cyclopentanes, cyclohexanes, I-olefins, z-methylolefins, cycle-olefins, diolefins, alkylbenzenes, acetylenes, primary n-alcohols, secondary alcohols, tertiary alcohols, aldehydcs, ketones, formates, acetates, ethers and acetals on columns treated with such different types of solvants as convoil-20, squalane, b, ,9’-oxydipropronitrile, z-ethyl hexyl sebacate, convachlor-so. With only a few exceptions he obtained straight lines for boiling points vs. log rctcntion times plots. Strarght lines arc also obtained when logs of partition coefficients obtained by chromatographic methods are plotted against the ratio of the boiling point of the solute to the column temperature (cf. Figs. 5 and 6). This is expected because the retention time changes linearly with partition coefficients (cf. eqns. 4, 7 and 8). It was expected and also found that similar straight line plots are obtained when the latent heats of vaporization are plotted against logs of partition coefficients (cf. Figs. 7 and 8). The above conclusrons are true only for the compounds of the same family, Cyclopentane, being a compound of another family, did not fall in the straight line (cf. Figs. s-8). It is also interesting to note that column temperature higher than the critical temperature of the solutes were never used.
’ retention
Anal. Chn.
Ada,
22
(1960)
130-142
GAS-LIQUID
PARTITION
137
CHROMATOGRAPHY
3-MbPENfANE
?I-MbPENTANE I.10
2-?Ae PENTAHE
I IO
O.?bDIYeBUTAUE
2.3-DlM@BUT
ANE
c .
c?>
0
~.~-O’M*B’JTANE
c’
CYCLOPEHIANE
2,2-OlMrBUTA0
P
/
P 1.0t
CYCLOPENTANE
1.05
IO5
n-PENTANE
I 20
K
1
l
30
40
too
1
n-PENTANE , I
L
80
I
200
FIN. 5 Change of log partition coefflclcnt with the ratio of bolllng pomt to column tCmperatin% Tb(Ol<) = b p ; T(OIC) = cd from ~i&u~iShl~Ns~~ I’)ilta taken tcmp Column D~metl~ylsu1folanc Note Cyclopcntanc chd not fall in llnc with the chain hydrocarbon
I
300
6
400
500
Fig 6 Change of log partltron cocfflclcnt with the ratlo of boiling point to column temperatlirc ?‘b(OI<) 3 b p ; T(Ol<) = cd #I-Hcxadccanc Data taken temp. Column from ICP,uL&xANs12 Note. In this cast cyclopentnnc is cloacr to the llnc because of the low polarity of the substrrrtc.
7.80
7.50
n-HEXANE
3-M,PENTANE
3-MbPENTANE 2-MaPENTANE T.00
700 =
2,3-OlMe
BUT
ANE
x” CYCLOPENTANEO
OCYCLOPENTANE
f 2.2.DIMI
BUTANE
2.2-OIMeBUTANC
6.80
6.50
6.20
8.20
0 20
K
30
40
50
1
IQg 7 Change of log yartrtlon ctxfflclent with the molar heat of vaporization at constant prcusurc. Partition cocfftcient data taken from l
/
“_- PENTANE I
I
I
400 500 K 300 Ftg 8 Cllangc of log partltmn cocfflclcnt with the molar heat of vaporization at constant pressure Partltlon cocfflclcnt data tnkcn from KEULIZMANS~~ and heat of vaporization (at 25’) tlats taken from Chcmlcal Englnccrs’ Handbook Colllmn pa-Hcxadccanc. 200
sulfolanc
16 reveals yet anotlrerinteresting feature Examination of data obtained by TENNEY (cf. Fig. 2 of ref.10). The intercept of the log retention time VS.boiling point curve is practically independent of temperature even for a temperature differential of 50”.
/id.~Ghim;~
Acta.
22
(I@O)jZ36+142
B. SEN
138 Xl
PI1
nv
p/v
=-=-.
K
eL’ln*
. . . .
. . . . .
. . .
(18)
where K = partition coefficient, nt = moles of solute per unit volume of the condensed phase, 9~0= moles of solute per unit volume of the vapor phase, P/r = partition function of the solute in the condensed phase, P/* = partition function of the solute in the vapor phase, Li = mean potential energy difference per mole of solute in condensed phase and vapor phase (lmearly related to the molar heat of vaporization of the pure solute at constant volume), R = gas constant, T = temperature of the system. For an one component system Pft/Pf ,, tends to become unity. It can be shown that the PfJPf” is practically independent of temperature for very low concentrations of the solute. Li in equation (18) may bc substituted by LeIRT, where Le is the mean potential energy diffcrencc at constant pressure (Le is liucarly related to molar heat of vaporization of the solute at constant pressure) and the equation (18) becomes I< = ~‘~(I.cfllT)--l = _4c1,r/nr
. . .
. . . . .
* * (fS1
Because the plot of log K against TtJT (Tb = boiling point in “K) produces straight lines (cf. Figs. 5 and G), it may be expected that a relation similar to TROUTON'S rule exists between Tb and Lc in the cast of dilute solutions and the equation (19) may be written as IC = rl #t’bl1lT where
. . .
a..
.a,.
*
(20)
*
Le/?‘b =
time or retention Tt has been shown earlier that the relation between retention volume and K is linear (cf. cqns. 7, 8, and x.6), so the equation (20) may be modified to give an expression for retention time or retention volume, hence RL - fi< = /%?aT,/n’r.
. .
. . . . . . .
. . . (21)
I?, = retention time B = a constant for homologous compounds and the same substrate Ttic equations (19-21) may bc written as
wherc
In K =
In A -I- Le/RT
In
Xc
In
In
R;
=
=
In
A -+- CLTb/RT B +
u ‘I’b/RT
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . .
. . . .
.
.
.
.
.
.
.
.
.
. (23)
.
. . . . (24)
(22)
We can draw a number of conclusions from the equations (19-24). I, The partition coefficient or the retention time will change expontentially with the change of the ratio LEE or Tb/T. It is expected that for Tb/T ratio higher than unity Rt will increase very rapidly. Fig. g illustrates a plot nJnv against Tb/r assuming A = I and a = 23 (one component two phase system). At lower Tbr ratios (when T >, critical temperature), nt/rro will be constant at constant pressure and the above relations are not strictly applicable. In other words, it may be safely concluded that at column tem-
GAS-LIQUID PARTITION CHROMATOGRAPHY
139
peratures much lower thaD the boiling point of the solute (Tbr $ I) most of the molecules will remain in the stationary (condensed) phase for most of the time and there will be fewer exchanges between the two phases, i.e. the column will be inefficient. At column temperatures much higher than the boiling point of the solute (say Tbr < 0.6 ;
Fig. 9 Change of the rntlo of number moles/untt volume of the hqud
volume of the vapor In equllibrlum at tcmpcrnturc T’K cqulhbrium temperature. ‘f b= b p (Of<) I ‘f = cqulhbrlum
to number of molcs/umt with the rat-lo of the boding point to the tcmperaturc = column tcmpcraturc (OK).
for pure compounds the ratio of boiling and critical temperature is approximately equal to 0.6) most of the molecules will remain in the vapor phase for most of the time and the column will be inefficient. However, the actual optimum temperature range will be determined by the slope and the intercept of the log RI zrs.T&r plot. 2. A plot of In K or In RI against Le, or Le/T, or Tb or Tb/T will be a straight line and will make an intercept which will be constant and independent of temperature at least for modcrate temperature ranges. This expectation has been verified by our results as well as by TENNEY’S~~ data. 3. It is also expected that the slopes of the plots for different types of compounds will not be very different (cf. Figs. 5-S and TENNEY~~). 4. Combination of equations (7) and (16) and (23) should enable us to determine K and its temperature dependence in a very straight-forward manner. Recommendalim for determining the oplimfrm column conditions The choice of temperature of the column is the first parameter to be decided. It should be realized from the preceding discussion that any one column tcmperaturc cannot be suitable for all the solutes. The column temperature will t\a determined by the boiling point of the lowest boiling solute in a mixture. The optimum column temperature is given by a value of the T b/T ratio between I and 0.92. The compounds boiling between the column temperature and 0.92 times the .column temperature will be very nicely resolved. (cf. Fig, IO). Ad.‘CMm,.AcfU,:22
(1960)
X30-142
B.
r4o
SEN
After the column temperature has been fixed, a standard solute is selected, boiling as close possible to the column temperature, preferably slightly below the column temperature. This compound should not be highly polar and should have normal heat of vaporization (L.e/Z’bm 23). A volume of this solute, less than the plate volume, should be injected into the column at different flow rates until the flow rate corresponding to the maximum number of plates is obtained. The optimum temperature and the flow rate are thus determined. The condition of the column can be checked 140 0
N 1200
1.2- C2HqC12
IA C2HClf
c Cl4
Osaa.
1000
WllCl
600
0 ..c.c41i+lr
0
0
C4HgCI
C3lyr
CHC13
I-C3H,lw
0
400 LO4
I.00
096 ?,/
0.92
0.80
0.84
T
Pig. IO. Variation of the number of plates with bollmg potnt of the solutes Column. zoo/u trl-m-tolyl phosphate on 30/60 cchte ; column length : z meter; column tcmpcraturc: 93O; Hc flow rates: 52 ml/mm Widely varymg types of halogenatcd hydrocarbons wcrc dehberatcly chosen to omphasrze the lmportanco of the bolhng point, even when the compounds do not strmtly belong to tho samu famrly.
Fig.
I I.
efficiency.
Effect of borlmg point, (Compare with TableI)
length
heat of vapormatron and diclcctrm constant on the column Column: 20% tri-m-tolyl phosphate on 30/6o ccl&; column . z meter ; column temperature’ g3O. ~tld.
ChZ#l.
htU,
22
(1960)
130-142
GA!+LIQUID
I’ARTITION
CHROMATOGRAPHY
141
every nowand then by injecting the standard, and the overall column behavior maintained uniform by adjusting the flow rate and, very rarely, the temperature. The reason that a solute having a boiling point near the column temperature is selected is that the slightest change in column condition is reflected in the number of plates. When the column is repacked with the same material, the same plate number is reproduced by-adjusting the flow rate and the column temperature. The retention times may be easily expressed in terms of the standard. It was also found that for the same column, optimum flow rate was the same irrespective of Tb/T ratio, although the absolute efficiency of the column was different depending on the value of TO/T ratio, the dielectric constant and the heat of vaporization (cf. Fig. II and Table I). TABLE I EPPECTOPBOlLlNGPOlNT,HEATOFVADORIZATION,ANDDIlLLECfRICCONSTANTONCOtUMN EFFICIENCY (Compare wrth plate number In Frg. I I) Column: 2oy0 trr-m-tolyl pliosphatc on 30/6o cclrte; column length 2 mctcr, column tempcraturc g3O
Acetonitrite (7) rsopropyl alcohol (6) Cyclohcxane (2) Bcnzenc (I) Carbon tctrachloride (5) n-Hexane (9) Zsopropyl ether (3) Methanol (IO) Chloroform (4) Acetone (8)
o 97 o 97 o 97 o 965 o 955 o-935 o 93 0915 0.91 5
o 90
38 8 IS 9 20 23 22 r9 32 6 44 *r 4
84 7 05 72
ACKNOWLEDGEMENT
author wishes to thank Professor PHILIP W. WEST for providing the facilities his lahoratories and his constant encouragement in the author’s work. Dr.
The of
ROBERT
V.
NAUMAN,
Dr.
SEAN P.
MCGLYN
and
Professor
PAUL
DELAHAY
made
valuable suggestions and criticism. Dr. B. R. SANT helped in numerous ways during the preparation of the manuscript. Partial financial assistance from the Research Grant S-43 of the Study Section of Sanitary Engineering and Occupational Health, Division of Research Grants, Public Health Service, is being acknowledged. SUMMARY The drstributron of a solute in a gas-liquid chromatographrc column hau been d~scusscd from the probabrlrty view pomt and its analogy to the BEBNOULLI trral system has been shown It has been shown that the rcproductwn of column behavior IS possrblo by rcproducmg the probabrlrty The crrterron for the optimum column temperature has also been discussed Rccommcndatrons have hean made for dctcrmming the optimum column condrtrons and its rcproductron. L’auteur a cffcctub unc Gtudc, B I’ardc du calcul dcs probabilrtds, sur Ic comportcmcnt d’unc substance dans uno colonnc chromatographrquc gaz-hqutdc. On a ddtcrmmd 6galcmcnt les condrtrons optimales ct la reproductrbrfitd. ZUSAMAMENFASSUNG Es wurde veniucht, dre Bcwegung unrl Verterlung einer Substanz rn cincr gas-fltissig Chromatogrephre-Kolonne mit Hilfe der Wahrschernlichkertsrechnung zu erkltlren. Drc Krrterrcn fur die And..Chim.
Acta, 22 (1960) 130-142
B. SEN
142
optimale Kolonnentemperatur werden diskutvxt und Vorschllge optimalcn Kolonnen-Bedingungen und dcrcn Reproduznxbarkeit.
gemacht
zur Bestimmung
der
REFERENCES 1
2 3
4 5 6 7 8 0 10 11 12 la 14 1G 16 17
w FELLISR, ‘*An Introductzon to Probabalzly Theory and Ifs Applacatsons,” Vol. I, John Wdey and Sons, Inc., New York 1956, pp. 13542. A. J. P. MARTIN AND R. L. M. SYNGE, Bzochem J., 35 (194x) 1358. A. J P MARTIN AND A. T. JAMES, Biochsm J ,50 (195x) 679. J. J.VAN DEEMTER,F.S.ZUIDERWEGAND A KLINKENBURG, Chem Eng Scz.,5 (rg56)271. A KLINKENBURGAND F.SJENITZER,C/~~~ Bng. Set , 5 (r956)258. M. C. HOLMBS, “An Outltne of Probab&fy and Zfs Uses,” Burgess Publishing Co , Mmncapolis ~93% P. 7 L. c, CRAIG, J. Bzol. Chem , 155 (x944) 5x9_ A. I. M. KEULRMANS, “Gas Chromatography,” Rcmhold Publishing Corp , New York 1957, pp. 1 I I-1 13. . E. GLU~C~AUP, Trans. Faraday Sot., 51 (1955) 35 D. AMBROSE, A I. M KEULEMANS AND J. H. PURNOLL, An&. C/rem ,30 (x958) 1582. L. LAPIDUS ANDN. R. AMYNDSDN,J. Phys. Chem ,56(x955) 34. A. I. M. KEULEMANS, “Gas Chromatography,” Rcmhold Pubhshmg Corp , New York 1957, pp. I x9-27. A. I. M. KEIJLEMANS, “Gas Ciwomatogvapiry,” Remhold Pubhshmg Corp., New York 1957, PP. 179-83. G. TAYLOR, Proc Roy. Sot. London, A219 (x953) 186. G TAYLOR, Proc. Roy Sot. London, A225 (x954) 473. H. M TENNEY, Anal. Chem., 30 (rg58) 2 Press, Oxford Umversity G. S. RUSHBROOKE, “Ixtvoduclron to Sta&sficaZ Thernrodynamics,” London 1949, Chapter XIII and XIV. Anal.
CHROMATOGRAPHIC
SEPARATION
Chrm. Acta, 22 (1960) 130-142
OF SOME
ALKALI
METALS
E. C. MARTIN Scirool
of Applred
Chemistry,
The University of NS
W.,
Sydney (Australia)
(Reccivcd June aznd. 1959)
Numerous papers have been publishedl-8 on the separation of the group I metals possibly none more successful than that of L~NSTEAD~, all however, suffer from the difficulty of identifying the position of the metal ions after development. As these metals travel as ions it occurred to the author that a combination of LINSTEAD methanol solvent to which some aqueous ammonia was added and using an acid base indicator as detector would prove simple and effective. This proved to be the case. EXPERIMENTAL l’lre solvenl Pure methanol was used in early trials but redistilled commercial mathenol proved successful in later experiments. To this was added one to ten percent of 15 N aqueous ammonia. Solvents based on ethanol +proponal and n-butanol were used with less success. Anal.
Chm.
Acta, 22 (19th)
x42-144