ystems Exhibitin P. F. McCrea' and J. H. Deparement of Chemistry, Unioersity College of Swansea, Swansea, Wales, U.K. ovel gas c ~ r o m a t o ~ r a p h isystems c manifest temrature independence of solute retention over cerin temperature ranges, achieved through use of a c o n ~ ~ n ~ i o nsohent al in conjunction with a solvent whose sorbing power for vapors increases with temis behavior is characteristic of systems hase changes or other transitions over emperature. The theory of and its validity and the practicality of the technique are established by detailed ics of oleic acid-stearic acid ~ i x ~used ~ ralone ~ sand in combination with squalane. Temperature-independent retention is achieved with in the test solute mixtures over spans of up to lQo region 45O to 65 O C . Extension of the method to incorporate the use of a wide variety of transition sorbents, and to achieve wider spans of compensation, i s discussed, and areas of obvious application are
THETEMPERATURE DEPENDENCE of solute retention is a determining feature in the performance of gas chromatographic systems. Temperature fluctuations of only a few degrees, whether from thermostat inadequacies or the evolution or absorption of heat of sorption, are undesirable. There is interest in and advantage to be derived from the use of columns whose power to sorb vapors is constant, even if only over short temperature ranges. This possibility had never been considered, even in theory, prior to our earlier publications on the subject (1-3). The present paper presents the theory underlying the development of such systems, the practical realization of such behavior, and the chromatographic characteristics of a model system.
A
DO 4 '4
II T
Figure 1. Forms of log for a solute
+ ajT
(1
where a and b are constants and, since a is generally negative, dVgT/dTis correspondingly negative. The combination of such a conventional column with one for which dVgTJdTwas positive would lead to a situation wherein dVoTJdTwas zero. Solvents or adsorbents which are likely to give dVgTJdTgreater than zero include any substances which undergo a phase or chemical transition over an extended range of temperature. Figure 1, A-D, shows the various kinds of retention temperature dependence to be anticipated. Only D of Figure 1, B-D, is of interest, and for convenience we designate a 1
Present address, The Foxboro Co., Foxboro, Mass. 02035
(1) J. H. Purnell, Brit. Patent Application 51851/67 (1967). (2) P. F. McCrea and J. H. Purnell, Nature (London), 219, 261
(1968).
(3) P. F. McCrea and J. H. Purnell, in "Gas Chromatography 1968," C. L. A. Narbourn, Ed., Institute of Petroleum, London, 1969, p 446.
1322
e
against T-1 plot
strate with retention greater at higher temperatures
solvent or adsorbent exhibiting such behavior as a transition sorbent. The temperature dependence of retention volume in the transition region may be approximated by Equation 2, log VgT(2)= d
The temperature dependence of the specific retention volume, VoT,of a solute in GLC or CSC over moderate ranges of temperature is well described by the approximate equation :
V,T
A . Conventional GLC or GSC substrate B , C. Sharp phase or other transition of substrate D. Extended temperature range transition of sub-
THEORY
log VgT(I)= b
B
+ c/T
whence, for conventional and transition columns in series, the total retention is VxT(172)=
VeT(1)
+ wz
VpT(2)
(3)
where w1 and w 2are the respective weights of conventional and transition sorbent. The condition that VXT(1 ,2) is temperature-independent leads readily to the equation
which is an expression for the relative weight of conventional to transition sorbent required for temperature-independent retention over the transition region. Constants a to d are obtained in preliminary experiments on the respective substrates, and corrections to the weight ratio to allow for carrier gas compressibility and viscosity changes can be made later. Figure 2 illustrates graphically the principle of temperatureindependent columns. The apparent temperature dependence of wl/wz is of no consequence, as shown later, and the temperature term is best assigned the value corresponding to the central temperature, Tm, of the compensation span [(TI T2)'2)/2] in Figure 2. This study employed a single mixture to investigate all aspects of the compensation concept and the behavior of
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
+
I
I50
/BENZENE
100
t
1
I I/T
6
(OK")
Figure 2. Illustration of temperature-compensating concept a. Conventional sorbent plot for some solute b. Analog of Figure 1, D ,for same solute c. Anticipated plot for solute if sorbents a and b are properly combined
2.90
2.95
103/T
3.00
(OK")
Figure 3. Log VgT as a function of T-1 for benzene, n-hexane, and n-pentane eluted from stearic acid column (25% w/w on Silocel) between about 60" and 80°C
column systems. This mixture, varying proportions of oleic acid in stearic acid, was chosen because it gives substantial thaw-melt ranges (4), and because the retention characteristics of stearic acid (5) and of stearate mixtures (6) were encouraging. EXPERIMENTAL
Retention data were obtained on a laboratory-constructed chromatograph which maintained column temperatures constant to within 0.05 OC. A pneumatically actuated sampling value (Foxboro Q100D-67) admitted a 53O-pl vapor sample, about 3.8 pmoles of total hydrocarbon, to the column inlet. Dry hydrogen was employed both as carrier gas and as diluent for the solute vapor. Eluting components were detected with a dual thermistor thermal conductivity unit (Carle, Model 100) in conjunction with a I-mv potentiometric recorder (Leeds & Northrup Speedomax W). A precision mercury manometer and barometer were used to record column inlet and outlet pressures. Carrier flow rates were measured with a thermostated soap bubble flowmeter and a stopwatch. A thermometer encased within the flowmeter water jacket facilitated corrections for the measurement temperature of the gas and for the vapor pressure of water. The copper-constantan thermocouple used to measure column temperatures had been calibrated against an NPL-certified mercury thermometer. The solid support used in this investigation was sieved 60-80-mesh (ASTM) Silocel C-22 firebrick obtained from Phase Separations, Ltd., and was subsequently washed and fluidized to remove fines. The squalane was May and Baker Embaphase brand for gas chromatography. Oleic acid and stearic acid (pure) were obtained from British Drug Houses, Ltd. These stationary phases were used as supplied. With the exception of n-pentane, which contained a 5 % isopentane (2-methylbutane) impurity (fully resolved (4) J. C. Smith, J. Chem. SOC.,1939,974. ( 5 ) C. G ; Scott, in "Gas Chromatography 1962," M. van Sway, Ed., Butterworths, London, 1962, p 36. (6) J. H. Purnell, S. P. Wasik, and R. S . Juvet, Acta Chim. Acud. Sci. Hung., 80, 201 (1966).
on all columns investigated), all hydrocarbon solutes were reagent grade. A rotary evaporator was employed to coat the solid support from a slurry with 80" to 100 "C reagent grade petroleum ether at temperatures in excess of the stationary phase melting range. No crystal formation or support size degradation was observed with slow rotational speeds. Solvent loading was in the range 20 to 25 w/w (solvent-Silocel) for all columns. Solvent-support weight ratios of coated support were determined in a Soxhlet apparatus using 80" to 100 "C petroleum ether as the extracting medium. Repetitive analysis of identical coated supports were reproducible to rtO.2 %, and the extraction of uncoated support resulted in a negligible weight loss (0.05 %). Columns of 0.25-inch 0.d. stainless steel were packed before bending because the tubing possessed sufficient wall thickness to be bent to the desired configuration without constricting the bore. Columns were conditioned for 12 hours with a 30 ml per minute hydrogen flow and at 15 "C above the melting range of the stationary phase. The accuracy of retention volume measurement was estimated to be 1%, and the precision to be better than 0.5 Differential thermal analysis data were obtained with a Linseis instrument (L73 combination with L61 DTA head), modified to provide reference to the ice point. The lowest rate of heating commensurate with adequate sensitivity was used, usually 1.4 "C min-1. The sample thermocouple was compared against the same copper-constantan thermocouple used to determine chromatographic column temperatures, and agreement to *0.1 "C was observed over a 20" to 100 OC range. Measurement head geometry consisted of two vertically arrayed alumina rods, each supporting thermocouples and platinum foil cylinders. Measurement of transition temperatures of stationary phases in situ-i.e., analysis of coated support-appeared to be the most satisfactory means of comparing thermal and chromatographic transition temperatures, as substrate effects should affect each method equally. Uncoated Silocel was used as the reference material. The sample quantity was 200 mg, corresponding to 40 mg of thermally active GC solvent. Since the changing
z
ANALYTICAL CHEMISTRY, VOL, 41, NO. 14, DECEMBER 19S9
z.
e
1923
2.0
-
-
50
60
70
40
BO
50
60
SOLID
70
A. Stearic acid B. 25 mole oleic acid-stearic acid C . 60.6 mole oleic ~ c ~ ~ - acid ~ ~ ~ a ~ i c D. 60 mole % oleis acid-stearic acid All distributed at 25 % w./w. on SiEocel, Heating rate, 1.4 deg/min-J. Sample weight (as acid), 40 mg
x
temperature monitored by the instrument was that at the center of the sample, the maximum of the peak was taken as the transition temperature. Endothermal melting transitions showed no dependence on heating rate and all values determined were reproducible to AO.1 "C. ESULTS
ention ~ ~ ~ r a c ~ eofr ~Stearic s ~ ~ Acid. s s Data obtained e solutes, benzene, n-hexane, and rz-pentane, with stearic acid columns are shown in Figure 3 in the form of plots of log VqTagainst T-I. The form of the three curves is identical and complete melting is taken to correspond to the sharp break in the plots at 68.7 "C as confirmed by differential thermal analysis (DTA) of the coated support, which yielded the fairly sharp endothermal peak a t 68.5 "C shown in Figure 4, A . Figure 3 establishes that this sample of stearic acid, because of either impurity or solid phase changes near the melting point, exhibits the positive temperature dependence of retention required of a transition sorbent by the theory, but the available span is too small bo be useful. The latter suggestion, which is supported by other unpublished findings, indicates that gas chromatographic sorption characteristics might be useful diagnostically in the study of solid-state phase changes. Asid MixRetention Characteristics of leie Ac~dlStear~c tures. The phase diagram far oleic acid-stearic acid mixtures (on Silocel solid support) for the range 0 to 80 mole % oleic acid was determined by DTA, some of the DTA curves being shown in Figure 4, B-D. The derived transition temperature data, along with those of Smith ( 4 ) for the range 63 to 100 mole %, are used to construct Figure 5. The agreement between the two sets of data must be regarded as reasonable, since Smith's material had undergone rigorous purifica-
0
10
20
40
30
50
60
70
80
90
Figure 5. Phase diagram for oleic acid-stearic acid mixtures 0 Thiswork
A Smith(4)
tion and was used in the absence of extraneous solid. The phase diagram is of a broad eutectic (monotectic) form, and this, along with the evidently extended melting span (cf. Figure 4, A and B to D),establishes the suitability of this system for our present purposes. Columns containing 25 mole oleic acid-stearic acid mixtures, at about 25% w/w on solid support, were wed to determine the dependence of log YoTon T-l for the several solutes. The results are plotted in Figure 6 and the vastly greater span of positive temperature dependence attained with the mixture than with stearic acid alone is evident from a comparison with Figure 3. The results of more detailed studies, confined to the range 53" to 66 "C and the solutes, benzene and acetone, are illustrated in Figure 7, which includes the corresponding plots for elution of benzene and acetone from a 20 % w/w squalane-Silocel column. These plots allow computation of the constants of Equations 1 and 2 and, hence, via Equation 4, of w1/w2 for compensation between squalane
200
I
I50 IO0
30
Table 1. Constants of Equations 1 and 2 for Elutfon of enzene and Acetone from Approximately 20% w/w Columns, ~ o n ~ a Squalane ~ ~ ~ n or g 25 Mole % Oleis AcidStearic Acid Mixture, in Temperature Range 53" to 66 "G w,/wZ calculated for midpoint of temperature range (Tm-l = 3.005 X 10-9 Squalane Acid mixture IO-% --b -lo-% d WllW2 Benzene 1.500 2.178 2.949 11.015 1.31 Acetone 1.223 1.745 3.015 10.638 1.10
1924
e
100
MOLE % OLEIC ACID IN STEARIC ACID
15
3.00
3.IO
3.20
TPK-~ Figure 6. Log VgT as a function of T-' for elution of benzene, n-hexane, and n-pentane from 25 mole oleic acid-stearic acid column
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
600 500 400 300 200
G-
100
90 80
-
100
(mb-') *o:
70 60
60 50 -
50
40
n- PENTANE
-
40
30 30
60 3.00
2.95
K$/T
(OK-'
Figure 7. Log VoTas a function of T-1 for elution of benzene (upper four plots) and acetone (lower four plots) from columns A, squalane;
0,25 mole
55
50
45
40
35
3.10
3.15
3.20
3.29
3'05
oleic acid-stearic acid; 0,
series combination with W I / W Z = 1.29. - Curves for series combination computed via Equation 3.
--
and the mixture. These latter data, calculated for the median temperature, Tm, of the indicated compensation span, are listed in Table I. To test the theory, a series column pair with a solvent weight ratio [squalane-mixture] = 1.29 was constructed and V,' data for benzene and other solutes, eluted from the composite system, were obtained. The data obtained are also plotted in Figure 7, along with the "theoretical" curve calculated via Equation 3 for the appropriate values of wl and wz; their agreement is seen to be better than 2%. The temperatureindependent span achieved is substantial ; even if temperature independence of retention is defined as closely as +=OS%, some 6' around 60 "C is available, while at the =k2%level close to a 10" span is achieved. In the experiments described, column lengths and flow rates were adjusted so that compressibility corrections to V,' were not excessive. In practice this would almost certainly be unacceptable and the calculations would require the use of the usual gas compressibility correction. This offers no real difficulty, since it merely requires introduction of a small factor to modify the value of wI/w2. The fact that good compensation is observed for acetone, although w1/wz is far removed from the "theoretical" value (cf. Table I),is surprising at first but has a straightforward explanation. The data simultaneously establish the viability of series operation of compensating columns and the validity of the theory. Self-compensation. It is apparent from Figure 4 that both the span and the central temperature of compensation are functions of the transition column composition. Thus, adjustment of these, via composition change, is possible and this adds a useful variable to the technique. The system under study, however, exhibits the property that, at high oleic acid content (ca. go%), the plot of log V,' against T-1 is virtually linear over the whole range, solid + solid liquid -+ liquid. Such a possibility has been envisaged earlier (2). Thus, at some composition intermediate between 25 and 90
+
3.00
3.05
io3/ W K - ~ ) Figure 8. Comparison of log V J dependence on T-1 for elution of benzene, n-hexane, and n-pentane from columns
A,80; 0,6Q;
a,50.6 mole % oleic acid In stearic acid
mole %, an oleic acid-stearic acid mixture should yield a column packing which would be self-compensated over some temperature range. Figure 8 shows plots, for the solutes benzene, n-hexane, and n-pentane, of log V,' against T - 1 data for three columns containing, respectively, 50.6, 60, and 80 mole of oleic acid-stearic acid mixtures (approximately, 25% w/w on Silocel). The plots for the last of these, as for 90 mole oleic acid, are almost linear over the whole range from solid through liquid, while, for both the other columns, the predicted spans of temperature independence of retention are observed. With the 60 mole column, for example, this range, at the i1 retention variation level, covers 43" to 53 T. In the region of complete liquefaction, vJ' appears to be essentially independent of the oleic acid-stearic acid ratio of the several columns. There may obviously be many similar examples of self-compensation, and search for these could be rewarding. Alternative Configurations. The series configuration is, of course, only one of three basically similar ways of combining conventional and transition packings on inert solid support to achieve temperature independence of retention. The second method is to construct a single column of alternating, short slugs of each packing-Le., a multiple series system, a configuration which we describe as striated. This arrangement has the potentially substantial advantage over the series arrangement that carrier gas compressibility corrections to calculated W : / W Z ratios are not required if more than three or four striations are used. The characteristics of such columns are excellent and the retention data are identical with those presented earlier for series columns. The third approach, which does not need compressibility corrections, is to construct a column with a single, mixed packing of the conventional and transition sorbent either by (a) prior mixing of the separate liquids with solid support and then combining these packings or (h)mixing the liquids prior to dispersion on solid support. We describe here experiments
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969 o 1925
t
300
200
-
1
I-
UPC) 0.0
c
I
60
1
I
50
40
Mgure 30. DTA curves for blended squalane, 25 mole % oleic acid-stearic acid packings (each 25% wjw on Silocel)
. . . Immediately after blending - - - After brief heating to 80 'C Figure 9. Comparison of behavior of squalane, 25 mole % oleic m i -stearic acid-compensated column systems 0 Series A Blended configurations w1/w2
w1+
= w2
1.28 = 1.396 g
carried out with columns blended as in mode a, since the findings are relevant to use of mode b. A pair of column packings identical with those used for the series experiments described earlier (wl/w2 = 1.29) was made up and first used in series column arrangement to determine VgTdata for benzene, acetone, and n-pentane over the chosen temperature range (Figure 9). Subsequently, the column packings were removed and carefully mixed before repacking in a single column. Overnight conditioning of this column at a temperature above the melting point of the oleic acid-stearic acid mixture (ca. 80 "C)preceded the retention measurement experiments, the results of which are also shown in Figure 9. It is immediately obvious that, while a wide span of temperature independence of retention is achieved with the blended column, the center of the compensation range is shifted t o lower temperature with respect to that for the corresponding series and striated systems. This is not, of course, surprising, since we now potentially have a threecomponent liquid-solid system with its own characteristic TA studies of a blended packing, identical with the above, establish the course of events, as Figure 10 shows. The dotted curve represents the transition peak for the blended material immediately following mixing and is obviously identical with that of Figure 4, B, for the acid mixture; the broken line shows that, after brief conditioning at about 80 "C,there is undoubted change in the physical state of the system while, after 12 hours (full line), a new and entirely reproducible transition, shifted some 12" toward lower temperature than the initial one, is seen. The shift is identical with that of the center of the chromatographic compensating range from that of the series system, as may be deduced from Figure 9. The characteristic of blended packings constructed in mode b are identical with those of mode a packings after conditioning, provided the solvents do not interact appreciably. We thus see that blended columns offer a practicable approach but that the theory developed is only approximate in 1926
B
_.After
12 hours at 80 "C
these circumstances. This inconvenience is, however, substantially redressed by the finding that a DTA survey, which can be carried out very rapidly, provides most of the required information for an empirical adjustment to wl/wz as calculated by theoretical first approximation. Efficiency and Selectivity of Compensated Systems. For efficiency studies, theoretical plate height H was measured as a function of carrier gas out!et velocity, ue0,defined by H
=
&5
and
($)2
uso = L tlzj
where L is the packed column length, b the peak width at half height, tR' the total retention time, ta the air peak retention time, and j the carrier gas compressibility correction factor. However, since the objective was a comparison of conventional and compensated column systems, the precise method of definition of velocity and plate height is not critical. Figure 11 shows plots of N against ueofor the elution of benzene by hydrogen at 61 "C from 25% w/w columns of squalane, 25 mole oleic acid-stearic acid and the striated packings 2.0
1.5
H (mm) I .o
0.9 0.8
0.7L
0
'
I
'
' '
5
:U
.~
' I'O ' (cm sec") I
' '
I
'
15
' ' '
Figure 11. Column efficiency (van Deemter) plots for elution of benzene by hydrogen at 61 "c from columns
ANALYTICAL CHEMISTRY, VQL. 41, NO. 14, DECEMBER 1969
0 Squalane
025 mole
oleic acid-stearic acid A Striated squalane-mixed acids
Table 11. Relative Retentions for Solutes Eluted from Squalane, Oleic Acid-Stearic Acid, and Series and Blended Columns of Both All columns approximately 25 w/w solvent on Sil-0-Cel
Elution temp, "C
Solute n-Pentane n-Hexane Benzene Acetone Benzene
50
60
Column 50 mole
zoleic-stearic
acid (self-compensatinid Series, squalane -t 25 mole oleic-stearic acids. W J W Z = 1.29
z
Column
ff
1 2.70 6.10 1 3.2
+
Blended, squalane 25 mole oleicstearic acids. W I / W Z =
Column
ff
Squalane
01
1 2.70 4.33
Squalane
1 3.2
1 3.1
1.28.
I 1.3
'
1.2
Figure 12. Minimum theoretical plate height as a function of temperature for elution of benzene by hydrogen at 61°C from columns A . Squalene B. 25 mole ,% oleic acid-stearic acid C. Series and striated combinations of A and B packings
(precisely the same curve is obtained for the corresponding series column; the data are therefore omitted for clarity). The minimum H achieved with the striated column is virtually identical with that for the squalane column but the corresponding value of ue0is shifted to higher velocity. Since the operating temperature was chosen to be at the center of the compensating range, when the acid mixture is only partially liquefied, a greater net mass transfer coefficient would be expected for the composite system than for the squalane column and this would explain the observed shift of minimum plate height velocity. Figure 12 shows plots of minimum H a s a function of temperature for the columns described and operated as above. The minimum plate heights of the several columns in the region of 65 'C, when complete liquefaction of the acid mixtures has occurred, are identical. There is a small, and totally acceptable, loss of efficiency in the compensating region. As temperatures are lowered below the point of acid solidification, predictably, N for the composite column increases considerably. Figure 12, inter alia, suggests that the theoretical plate height of the composite system at any temperature is approximately an additive function of the values for the component column packings. The above findings establish that the efficiencies attainable with column systems exhibiting temperature-independent retention characteristics can be as good as those achieved with conventional GLC columns. Selectivity is also excellent, as is illustrated by consideration of the relative net retentions, cy, for several solutes and columns listed in Table 11. Obviously, the compensating systems are at least as selective as squalane and, in one instance, more so.
59*50c
;I
64.3OC
I)
'I
l1 I
5
c Figure 13. Chromatograms of representative mixture obtained at 59.5" and 64.3 OC with series Combination of squalane and 25 mole % oleic acid-stearic acid columns (wI/w3 = 1.29)
Solute identification. 1. Air 2. Isopentane 3. n-Pentane 4. .4cetone 5. Benzene Corrected flow rates at outlet 59.5' run, 33.95 ml min-l; 64.3OC run, 33.45 ml min-' The results presented establish that limited ranges of temperature independence of retention are attained without loss of column effectiveness, as judged by any of the usual gas chromatographic standards. This is brought out in Figure 13, which illustrates chromatograms obtained over a 5 "Cspan with a series pair of squalane and 25 mole oleic acid-stearic acid columns. There is no measurable shift of any peak although, with squalane alone, this retention shift would be close to 2075. DISCUSSION
The strong temperature dependence of wl/w2 indicated by Equation 4 is illustrated by inserting the values of coefficients a to d for benzene eluted from both squalane and from 25 mole 75 oleic acid-stearic acid columns (cf. Table I). Over
ANALYTICAL C H E M I S T R Y , VOL. 41, NO. 14, D E C E M B E R 1969 * 1927
300 250 260 240
220
200 L
180 -
2.95
(OK"
-
140
-
3.05
3.00
IO3/ T
160
120 -
)
Figure 14. Comparison of predicted log VgT against T-1 plots
1
~
0.7
~
5.5
~
8.9
~
9.0
1
*
9.1
IO6/ T' (" K"2
Computed via Equation 4, for solvent weight ratios (wl/wz). A , 1.78 (T2); B, L29 ( T m ) ; C,1.03 (Ti)
,
92
~
-
.
9.3
1
Figure 15. Plots of VQT against T-2 for elution of benzene from columns A . Squalane
the anticipated compensation range (ca. 55" to 65 "C)the value of w1/w2 ranges from about 1 to 2, depending on the temperature chosen. On the face of it, such a change would entirely negate the basic propositions of this work, since the optimum weight ratio would appear to be critially temperature-dependent, even over very short ranges. The results of the experiments clearly prove otherwise. This finding becomes understandable on recognition of the fact that there is built-in compensation in the product w-V, which determines VR. This view can be quantitatively developed as follows. The total retention volume of any solute eluted at temperature Tfrom a compensated system is
VET
= w1 V E T (1)
+
W?
V,T (2)
(5)
while, in the present computation and method, the ratio w1/w2is fixed by the median temperature, Tm,so that
B. 25 mole
oleic acid-stearic acid Broken line on B illustrates trivial extent of deviation of experimental curve from linearity in transition region
and it is clear that the most satisfactory compensation span is achieved when T = T,. Thus, the intuitive choice of the median temperature, made earlier, is justified. It is, however, clear that, even at T = T I ,the system performs well and this emphasizes our view that choice of w1/w2is not very critical. The success of the theoretical method employed here is now completely intelligible and forms a sound basis for future elaboration of practice or of theory, although, in the light of the above discussion, this does not seem particularly important. There would thus seem to be little reason to seek for alternatives. However, we have found, empirically, that an equation suggested (7) by the Bertrand form of vapor pressure equation gives excellent representation of retention volume dependence upon temperature over ranges at least as great as those which are of interest here. The form of equation for conventional and transition sorbents is
VgT = b'
+ a'/T2
(8)
V,T
+ c'/T2
(9)
and
(7) If now we substitute into this equation the values of a to d quoted in Table I we find that over the compensation span of about 10' around 60 "C,the change in VRTis less than h 2 . 4 ml deg-1 and so is within experimental error. This establishes that retention volumes with the composite system are only marginally temperature-dependent over the range of compensation and that the choice of wI/wz is not as critical as might have been expected. Obviously, however, there is a best value and it remains only t s determine how, on a routine basis, this should be calculated. Using the same example as above we deduce that the values of w,/w, corresponding to the choice of T = T I , Tz, or T, in Equation 4 are, respectively, 1.03, 1.78, and 1.29. Figure 14 illustrates the "theoretical" plots of log VBTagainst T-l, calculated via Equation 3, corresponding to each of these values 1928
e
=
d'
where, as before, a' to d' Eire constants. Figure 15 shows plots of data for benzene elution from squalane and from 25 mole oleic acid-stearic acid columns according to these equations and these illustrate the excellent linearity of representation. The singular advantage of this finding is that, following the earlier procedure, we derive from these equations the compensating condition, w1/wn
= -c'/a'
(10)
an equation far easier to handle than 4. Evaluation of c' and a' from Figure 15 yields the value wl/wz = 1.28, in re(7) J. R. Partington, "Advanced Treatise on Physical Chemistry," Vol. 2, "Properties of Liquids," Longmans Green, London, 1951, p 274.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
*
.
markable agreement with what has now been established as the optimum value derivable via Equation 4, that corresponding to Tm,quoted in Table I. Obviously, the present method represents an alternative approximation to those employed earlier, and one which offers much empirical convenience. The work establishes the viability of the concept of temperature-independent solute retention and the validity of the theory offered. Compensation spans up to lo”, which are substantial, have been achieved with the present systems. The attainment of wider spans is evidently possible, but must ultimately be limited by rate of phase or species change. No adequate theory exists and so it is possible only to speculate on eventual limits. It would obviously be very desirable to devise a system spanning 30’ around room temperature since, then, for the many separations carried out in these conditions, no thermostat would be required. There is no reason to suppose, at this time, that such a span is unattainable. Compensation systems can be constructed and, as shown, operated successfully in any of the four configurations tested. An obvious alternative to the use of a separate conventional GLC or GSC packing is to replace the inactive solid support by an active GSC solid and coat this with compensating substrate. This procedure is successful but introduces a number of theoretical and handling difficulties. It will, therefore, be discussed separately in a future publication. Compensating systems other than simple solid solutions, eutectics, etc., have been used with success and their characteristics will also be discussed elsewhere. The systems described here have a number of immediate areas of application. In isothermaI analytical work, there is clearly potential for the reduction of sophistication and extent of temperature control, with attendant simplification of operation and reduction of capital cost. In temperature programming the use of column systems of the type we have developed could offer the double advantage of operating at low
temperature as a GSC system and, with increasing temperature converting to GLC, while giving a “built-in” isothermal arrest, or indeed, arrests designed to facilitate specially desired resolutions. Thermal effects in large scale G C arise because of evolution or absorption of heat during the sorption-desorption process and/or poor heat transfer characteristics of the whole or part of the thermostated system. A theoretical assessment of the former has been given by Scott (8) and detailed studies have been carried out on several occasions (9, IO). Peters and Euston (9), for example, have shown that in the normal mode of preparative scale operation of a I-inch column, radial temperatures differ by at least h6” around the apparent mean, during solute passage. Even this degree of excursion causes retention changes and very marked peak distortion. Clearly, such systems as described here could cope with temperature fluctuations of this order, whatever their origin, with no loss of column effectiveness. With broader columns such as are now under construction for industrial scale usage, the thermal problems are substantially increased and it appears to us that systems such as described here may be of great value in this area. ACKNOWLEDGMENT
The authors thank The Foxboro Go., Foxboro, Mass., for provision of a fellowship (P. F. M.) and financial support for the work. RECEIVED for review July 11, 1969. Accepted September 25, 1969. (8) R. P. W. Scott, ANAL.CHEM., 35, 481 (1963). (9) J. Peters and C . B. Euston, ibid.,37,657 (1965). (10) A. Rose, D. J. Royer, and R. S. Henly, Separation Sci., 2, (2), 229 (1967).
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
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