ANALYTICAL CHEMISTRY
408 standpoint. The effect of abrupt discontinuities and the ability to predict them may be the key to speeding up chromatographic separations. Indeed, the earlier technique of recording chromatograms during their development (1 ) owed its speed and resolution largely to the use of constricted paraffin channels on the paper. As shown there, detectable separations became apparent in 10 or 20 seconds and complete separations of some binary systems were achieved in a minute or less. The present studies have shown how relative diffusion rates are predictably affected by shape factors. From both this information and the earlier practical application one can say that within
the limits of flooding, geometric or shape factors can be applied to advantage in speeding up the chromatographic process. It now remains to be shown how the diffusion rate in a given paper structure is influenced by its previous history and the physical properties of the eluting liquid. This is discussed in the following paper. LITERATURE CITED
(1) Muller, R. H., and Clegg, D. L., ANAL.CREM.,21, 1123 (1949). (2) Ibid.. p. 1429. RECEIVED August 30,19.50.
Kinetic Studies
T
HE present study is concerned with the previous history of
the paper and the physical properties of liquids, from which it is possible to predict relative diffusion coefficients for a given system. Previous work (2, 3 ) has shown that all the data for the rate of rise of liquids can be fitted to an empirical square law well within the experimental error. This is of the form: h2 = Dt - b
where h
=
(1)
Several conclusions may be stated a t once. In the Rutter disk technique (2, 3, 6) where flow is in a horizontal plane, the simple square law is adequate. Indeed, this has been found to hold, not only for the motion of solvent, but for the colored components carried by it ( 4 ) . For the rise in vertical strips, the square law will be adequate for moderate distances and elapsed times. Returning to Equation 2, if we assume that
height in millimeters
h, =
t = timeinminutes
b = constant and equivalent to an hi term D = constant for a given paper and liquid
and represent this by a, then the integrated form will be: kt In ( a - h) = -
A logical explanation of the phenomenon required that the rate of rise should be proportional to the surface tension of the liquid and inversely proportional to its viscosity. As accurate data became available, this was found to be the case. It was not possible to ignore the density of the liquid, and i t became evident that the diffusion coefficient, D , was proportional to y/qd. Now, although Equation 1 represents the data with high precision, it leads to infinite height a t infinite time, so that for the ascent of liquids in a vertical strip, it must break down for very large values of t. In all measurements here reported, the distance traversed was too small to make this limitation apparent, and this equation has been retained for its simplicity and precision ( 8 ) . The following equation eliminates this difficulty, if one assumes that the rate of rise is a t all times proportional to the difference between the height and the maximum height attained when t = m . Hence:
where k equals a constant and it is assumed that the rate is also inversely proportional to the viscosity. Now, when dhldt = 0-Le., a t infinite time
27 COS e wh
11
+ In a
2006
1500
a
1000
h = h,
and, as shown by Washburn (6),this should be equal to: h,
=
2-, COS e vd
500
which is the maximum height to which a liquid rises in a capillary in infinite time. Washburn also shows that, in horizontal capillaries, where the gravitational factor is absent, the rate of capillary flow is given by: 39 ry - =-
t
cos e 211
This is precisely of the form of Equation 1 which is satisfactory for all data herein reported, and also indicates the respective roles of surface tension and viscosity.
0
I
I
I
2
4
6
1 8
X’?ld
Figure 1. Relation between Diffusion Coefficient and y/qd
V O L U M E 23, NO. 3, M A R C H 1 9 5 1
409
The data fit this equation equally well, but i t is extremely awkward for plotting or computing, in that suitable values for a must be assumed. Not only is this true mathematically for an equation of this sort, but from the nature of a it will be seen that several factors cannot be ascertained directly. As in most cases where surface tension is concerned, e is assumed to be zero and the cos 6 term is neglected. The real difficulty is presented by T , the capillary radius, and it is hard t o imagine a more complex case than that presented by a mat of cellulose fibers. That Equation 2 is of suitable form may be shov n by assuming any arbitrary value for the maximum height, h,, and plotting the data semilogarithmically. A straight line results Ivith the intercept for t = 0 equal to h,. No data have been plotted in this form, for the simple reason that a much more direct and useful correlation may be obtained by relating the diffusion coefficient value, D , to y/?d for various liquids and papers. A recent symposium, published in Dzscussions of the Faraday Society (I), contains a large number of papers devoted to the diffusion of liquids through porous media, few of which are directly applicable to these studies, but which confirm and support the general conclusions arrived a t in this study
necessary to get the information a t the desired temperature. From these the values of y/?d were computed. The graphs shown in Figure 1 are the observed diffusion coefficients D as measured in the three papers. The upper or steepest line is for 601, the next for 598 W, and the lowest for 598 ST. Though not identified on the graph, the highest value for y/qd represents water and the smallest that for amyl alcohol.
Table I.
Surface Tension, Viscosity, and Density Values d
Substance
250
Water 71.97 Methanol 22.17 Ethyl alcohol 21.83 1-Butanol 22.18 Amyl alcohol 23.40 a hlp. represents millipoise.
8.949 5,631 10.829 25.740 42.660
c.
0,9971 0.7868 0.78.506 0.8061 0.8050
8.065 5.054
2.568 1.165 0.678
The lines drawn through the points can be represented in each case by an equation of the form:
D
=
ay/?d
+- b
and they are, respectively:
74 1.5 1.4 1.3
1.2 1.1
1 .o
20
25
Figure 2.
35
20 TEMFERATURE
For 601 D = 238y/qd For 598 W D = 163r/qd For 598 ST D = 97.ly/?d
++ 115 167 + 68
Table I1 shows the observed and calculated values of D and the individual and average errors. From these results, it may be seen that one can predict the diffusion rates through a given paper to about 3 to 6% on the basis of literature values of surface tension, viscosity, and density. This is very useful and eonvenient, but if detailed and exact measurements, particularly of surface tension, are made in the system a t the time of measurement, much more accurate values can be obtained. Of greater significance is the wide range over which this relationship holds, for the rate for Tvater is many times greater than that for the higher alcohols. The rates for ethyl ether and benzene were predicted to be high from their y/?d values; indeed, ether is considerably higher than water, but in both cases very considerable difficulty XTas encountered in maintaining adequate vapor saturation, so that no very accurate measures of their diffuPion coefficients tvere obtainable.
40
TEMPERATURE EFFECTS
C.
Effect of Temperature
A . Surface tension of water B. Reciprocal viscosity (fluidity) of water C. Reciprocal density of water r/sd of water r/qd of water, calculated f r o m diffusion rate i n paper
In order to measure the influence of temperature on the diffusion process, many measurements were made a t five different
Table 11. Observed and Calculated Diffusion Coefficients r/qd
A direct check on the assumption made above is afforded by the data shown in Figure 1, wherein the diffusion coefficients, D , for three different papers have been plotted against y/qd for five different liquids. The papers were Schleicher & Schull, Sos. 601, 598 W, and 598 ST. From a great variety of papers, these three were selected primarily on the basis of speed of diffusion, 601 being very fast and 598 ST relatively slow, with 598 W intermediate. The liquids examined in this case were distilled water, methanol, ethyl alcohol, butyl alcohol, and amyl alcohol. In this and all other systems, the liquids &-erechecked repeatedly in a thermostated Abbe refractometer. All measurements were made a t 25' * 0.02" C. The surface tension, viscosity, and density values were taken from the International Critical Tables as noted in Table I. As usual, with information from this source, considerable cross plotting or computation from empirical equations was frequently
Deslod.
Error
Dobad.
% Paper 598 ST
Water Methanol E t h y l alcohol Butanol Amvl alcohol
Paper 601 8.065 2086 5.094 1379 2.568 778 1.165 444 0.678 328
2086 1370 824 416 328
Water Methanol E t h y l alcohol Butanol Amyl alcohol
Paper 598 W 8.065 1427 5.094 944 2.568 533 1,165 305 0.678 226
1427 952 463 293 250
Av.
3.3
Av.
0.00 0.66 5.58 6.73 3.53 3.3
Av.
0.00 0.84 15.10 4.10 9,60 5.9
ANALYTICAL CHEMISTRY
410
temperatures. For each of these the thermostat was carefully set for 20 O, 25 O , 30 ', 35 O , and 40 O C. At each of these temperatures, the diffusion of pure water was measured. Several other systems were measured, but the values for water are given here because there seems to be little uncertainty about the exact values of surface tension, viscosity, and density over this range of temperatures. The observed values are given in Table 111 and are plotted in Figure 2.
Table 111. hlm.2/hlin. 696 770 840 89 1 963
O
Ethyl Ilcohol,
Effect of Temperature
t,
Dobad.,
Table V.
C. y * 0.05 7, M.P. 20 72.75 10.050 8.937 25 71.97 8.007 30 71.18 35 70.38 7.226 40 69.56 6.560
d 0.99823 0,99707 0,99567 0,99406 0.99224
Composition of >lixtures
wt.
%
Surface Tension
I'iscosity, hlp.
0 10 20 30 40 50 60 70 80 90 100
71.97 47.5 37.7 32.4 29.63 27,90 26.60 25.40 24.3 23.4 22.03
8.94 13.2 18.0 22.0 23.7 23.6 22.3 20.2 17.3 14.2 11.0
Density 0.9971 0.98043 0.96639 0.96067 0.93148 0.90985 0,88699 0.86340 0.83911 0.81362 0.78506
r/nd 8.065 3.648 2.158 1.547 1.340 1.295 1.344 1.452 1.666 2.023 2.549
rid 7.252 8.077 8.928 9.799 10.687
The manner of plotting the results in Figure 2 is thought to emphasize more clearly the contribution of each variable. The abscissas represent temperature in degrees centigrade and, beginning a t the top, are the viscosity of water, next the reciprocal viscosity or fluidity, and next the reciprocal density. From these three, it is seen that, although surface tension decreases with increasing temperature, the reciprocals of viscosity and density increase. The net effect, y/qd, which is of special interest here, is Been to rise slightly with increasing temperature and very nearly linearly. The dots superimposed on this function are calculated from the observations of the rate of diffusion of water through the paper. The agreement is very good; indeed, as shown in Table IV, they may be computed to about 1%.
The surface tension of the solution was carefully measured by the capillary rise method. Changes in viscosity and density were neglected, inasmuch as the solution is very dilute. A new value of y/qd was then computed to see if the decreased rate of diffusion could be predicted. The results were very disappointing and as much as 20% in error, although in the right direction. As a routine check on the surface tension some of the liquid from the diffusion chamber was remeasured after the diffusion run. Its surface tension had increased, and when this second value of y was used to compute y/qd, the predicted rate ww in excellent agreement with the observations. This w m confirmed for three different papers and the resulte are shown in Table VI. The calculation in each case uses constants in the equation which were obtained from the rates for four alcohols and water (Figure 1).
7
-$d Table IV. Calculation of D for Water in 598 ST From D = 8.17 r / i d 100 %
CALCULATED FROM OBSERVED
+
1,o
c.
20 25 30 35 40
r/d
Doaled.
Dobsd.
7.252 8.077 8.928 9,799 10.687
692 768 830 901 973
696 770 840 891 963
6
Error 0.6 0.3 1.2 1.1 1.0 Av. 0.84
~d
DIFFUSION RATES IN PAPER
5
3
These results indicate that although the temperature coefficient is small, it can be predicted on the basis of the temperature variation of y/qd.
FOR ETIIANOL-U'ATER MIXTURES
4
\
3
ETHYL ALCOHOGWATER MIXTURES
An additional check on the utility of y/qd as a means of predicting diffusion rates in paper was obtained by measuring several ethyl alcohol-aater mixtures over the entire range of composition. Table V gives the composition of the various mixtures and the calculated values of y/sd. These are plotted in Figure 3, in which the solid line represents y/qd as a function of composition and the solid dots are y/qd values recalculated from the measured values of D. The general form of the curve is followed faithfully, but the precision is inferior to those observed for pure water. The combined results of Figures 1,2, and 3 leave no doubt that y/qd is a reliable index of the diffusion rates. A few additional results indicate how the precision of these results may be greatly affected by minor factors. When it was decided that a critical test of these results would be given by adding a surface tension depressant, some rates were measured on pure water saturated with caprylic alcohol. This is notoriously effective and is commonly used to suppress foaming in aqueous solutions.
2
l
I 20
Figure 3.
I
I
I
40 60 80 WEIGH?' PERCENT ETHANOL Calculated Values of y / d
I 100
There is little doubt that, in this case, some caprylic alcohol was adsorbed in the chamber, or otherwise lost to the system, and the correct value of y is that actually exhibited by the liquid as it enters the paper. As all compilations of surface tension emphasize, there is considerable discrepancy among the values recorded in the litera-
V O L U M E 2 3 , N O . 3, M A R C H 1 9 5 1
41 1
tule. Furthermore, it is a property notoriously influenced bjtiaces of impurities. Because there is ample evidence in this woik that y/vd as computed from literature values is a fairly prwise means of predicting diffusion rates, this is itself of great potential use to the chromatographer. The latter experiments also indicate that considerable precision can be obtained if one mcwures the surface tension of the liquid after it has been in cont:ic*t nith the system. R E P E 4 T E D DIFFUSIOY 1Y SAME PAPER
In alternative approach to checking surface active substances ii
to meaeure the diffusion rate and then dry the strip in situ and
rt yeat the diffusion measurements with more of the same liquid.
Within limits, this can lie repeated indefinitely, although the phvsical texture of the paper may gradually change if this is done too oftcan When this was tried with water, followed by careful, N :Lini-air drying, the rate increased and after several runs ctnrted to decrease very slightly. The increase \I as undoubtedly cliic to the washing out of residual impurities by the fiist, and less l ) the ~ ~Gecond runs. h small decrease could arise from ncw impurities picked up, but much more likely from structural changes i n the fibers or their orientation. Inasmuch as texture and physical structure have an enormous influence, it is prohably too much t o expect to secure a final equilibrium condition. These results are entirely in accord mith qome limited obseivations of 1,e Strange in this laboratory. In measurements on the electrolytic conductance of paper strips through which solutions or pure liquide were diffusing, he never failed to observe a strong wave of increawd conductance as the solvent crossed the electrodes. This alwaye subsided as morc liquid came along and, therefore, indicated some conducting material in the advancing liquid front. Obvioubly, this technique would respond only to ionic species, n h e r c a ~ in . general, a n r solute might well alter the curface tenuion.
of time and, although rapid i n the beginning. several days were required before equilibrium was attained. I n another instance, a strip of paper was clamped between two electrodes in a conipletely vapor-t,ight enclosure. The resistance of the strip WBP about 1000 megohms initially and reached an equilibrium valur. of about 30 megohms in several days.
The results by the two methods w r e very similar and indicate that. whereas a steady state for the diffusion of liquid is attained after ahout 30 minutes of vapor presaturation, this xrtually iqwcscnts ahout half the total amount of water vapor which the paper can absorb from the saturated atmosphere. This affords strong evidence that the accommodation of moisture in the fiber mass is a comples mattei, and bears no simple relationship to the suhsequent diffusion of the liquid phaw through it. Many more experiments would l i e Lequircd t.o understand this phenomenon. Table \ 11.
Influence
d
Tlnlr of ratiiration I I i n ,
Saturation
Time
011
1)ifTiisiotr
D , 31111' / 3 I i n Paper 601
10 20
408
40
482
60
485
470
Th(, effects of vapor saturation, pwvious preparation of thr paper, and surface active impurities might well seem to presrnt insuperahle difficulties in this work. .ktuaIIy, one must recognize the compromise which the chromatographrr must make. The properties of filter paper are not "constants of nature" hut rharacteristics of a complex system. I n pr:rctical work, ronditions arc so chosen that there is a constnnt intrrcornparison hetween solvent and solute motion, and thr v:irious factors may he expected to compensate somewhat. Enough has been estahlished on thr kinetics of solvent, motion to cnal)k one to evaluate different papers. However, as this i p hut a part' of the rhroniatoglaphic technique, the automatic recording of solvent and solute, motion should furriisli one with all the desired information bout a given paprr. SU~131.4RU
6.02 1600 8.07 737 3.82 398 W 8.07 6.52 6.02 ,598 ST 8.07 a Rrnirarrireti after contact with sgsteui. ti0 I
1643 734 637
2.62 0.41
0.76
Pretreatment of paper, such as washing and drying, has been recommended in the literature of chromatography. In some instances the presence of ultramicro traces of substances, such as copper, has profound efferts, hut usually for chemical reasons. INFLUENCE O F VAPOR SATURATIOY
all chromatographic. work, it is essential to keep the paper in an environment saturated with the vapor of the eluting liquid. In this work, vapor saturation was very carefully controlled; indeed, this was indispensahle for securing good checks and reproducitjle results. However, it may be shown that the attainment of equilibrium conditions requires considerable time. Table VI1 shone the progressive increase in diffusion rate as a function of time of saturation. The rate becomes constant after 30 minutes, hut t,he paper of itself continues to ahsorh vapor for a much longer time. Two series of measurements, the details of whirh are not repeated here, confirm this conclusion. 111
In one case a strip of paper was suspended from one arm of a chainomatic balance in a nearly vapor-tight tube saturated with water v ~ p o r . The inrrease of weight was followed as a function
Heniiautomatic methods for recording the diffusion ratrs of liquids through paper yield values which follow a square law with high precision. The diffusion coefficients so obtained are n simple funct.ion of y/vd of the liquid. This is strikingly illustrated for the binary system, ethyl alcohol-water, which obeys the relationship over the entire composition range. The positive temperature coefficient is completelh- mplained by the temperature coefficient of the quantity y/qd. -4s it is known that, both solutes and solvent follow the square law, a knowledge of the laws governing solvcnt behavior is an important, though inromplete criterion, of chromatographic separat ion. The complete inforniatiori will he obt,ained when the motion of both solvent and solute are followed simultaneousl~-,and automatic methods are in the process of development for this purpose. ' On the basis of such methods, one may hope to attain a rapid and distinctive criterion of papers suited for any- chromatographic separation. LITERATURE CITED (1) Discussions F a r a d a y Soc., S o . 3, 1948.
( 2 ) Muller, R. H., and Clegg. D. L.. Asar.. C H m f . , 21, 192 (1949,. (3) Ihid., p. 1123. ( 4 ) I b i d . , p. 1429. (5) Rutter, L . , S a t f c r e , 161,435 ( 1 9 4 8 ) . ( 6 ) Washburn, Phua. Ref,.,17,276 (1921). RECEIVED hugiist 28, 1950
