Investigation of Paper Chromatography Flow of Fluid i n Filter Paper H.4ROLD G . CASSIDY Sterling C h e m i s t r y L a b o r a t o r y , Y a l e I‘niversity, .Vew Hacen, Conn.
Paper chromatography has become such an important analytical tool that it seemed desirable to make a fundamental study of the factors that control its effectiveness. These factors are of three kinds: those which affect flow of liquid, those which influence RF values, and those which influence definition of zones. These classes of factors are not mutually exclusive. This paper deals with the first class of factors, analyzing the factors in terms of bulk properties of paper and fluid, and of molecular properties of paper and fluid. The major influential factors of the first kind are porosity of the medium and viscosity of the fluid. Those of the second kind are more numerous and are examined. The value of this analysis lies in presenting the active worker with an insight into the complexity of the problem, with a brief survey of what has been done. It serves as a framework for subsequent reports on the influence of various factors on choice of solvents for paper chromatography.
S
ONE time ago it seemed desirable to begin a fundanieiital study of the factors which operate in the process of paper
chromatography. The f i s t communication ( 4 0 ) reported the results of an examination of some 75 filter papers, in which their suitabilities for the separation of amino acid mixtures were judged on six counts, using a number of solvent mixtures. It seemed desirable to report an analysis of the problem, as a frameMork for further reports on experimental findings, and to call attention to a large amount of work which has been done in fields intimately related to paper chromatography but which, because it was done with veiy different points of view, is reported in a variety of jouinals not often available to chromatographers. In paper chromatography, a developer flows through a paper strip or sheet, down%-ard(19, 28), upward (35, 47, S Z ) , or horizontally (69). Mediated by the flow of liquid, and oning to the differential countercurrent nature of the process ( 1 7 ) ,a mixture of substances may be separated. Paper chromatography resembles chromatography in that the separation depends on a process of distribution between phases which are brought into differential countercurrent contact. A marked difference between the two methods is that the former usually relies on capillary forces to set, an “outer” boundary to the moving phase, while the latter uses a glass, or other, tube as a container. The developer and mixture may be applied to the paper in one of several ways. In capillary analysis the strip of paper is dipped into the mixture, which rises up it, the components being separated because some rise less rapidly (are more strongly adsorbed and retarded) than others. This is the essence of Tiselius’ frontal analysis (87). The classical capillary analysis method of Schonbein ( 7 8 ) and Goppelsroeder ( 9 7 ) is essentially frontal analysis. In this method there is no development of the chromatogram in the sense descriged by Tswett (88)and applied by Liesegang ( 4 7 ) , and by Consden, Gordon, Martin, and Synge*(19, 28). The same principle is also utilized when mixtures are analyzed by placing drops on blotting or filter paper (72). In another method, more closely related to classical chromatography, the mixture is placed on the paper as a spot, or streak, and developed chromatographically with a developer liquid (47). The development may be carried out by any of the processes known as development analysis (19, 28,47), elution analysis (62, 6 3 ) ,or displacement analysis (55). It is an essential part of the method that the fluid developer move along the paper. Movement of the developer does not alone guarantee separation, but a sufficient difference in rate of
movement of the components of the mixture must also occur, together with adequate definition of the zones. There are, therefore, a t least three groups of linked factors v-hich operate in the process of paper chromatography: those which affect the flow of fluid in the paper, those which affect the Rr values which are exhibited by the components of the mixture, and those which affect the definition of the zones. This paper deals with the first of these. A certain arbitrariness is necessary in classifying the varisubous factors so as t o make their discussion manageable. TWO headings have been chosen: the properties of filter paper and the properties of the fluid. The scheme of discussion is shon-n in Table I. BULK-PHASE PROPERTIES OF SUPPORTING MEDlUM
Filter paper is a mat formed by interlaced and to some extent bonded purified cellulose fibers. The optical microscope shows a mat structure, and the electron microscope shows (in mechanically disintegrated Whatman KO.0 filter paper) ( 2 ) a brush-heap structure of what appear to be ribbonlike filaments. Ordinary filter paper is a simple paper in which the fibers have been matted to produce a given porosity, and in which the amount of impurity has been kept under a specified limit. It is this kind of simple filter paper which is now commonly used in paper chromatography, though many other kinds of “papers” of natural and synthetic fibers, glass, and quartz are becoming available. Two classes of properties of filter paper are of importance t o this discussion: the properties of the paper as a porous body, and the properties of the fibers and smaller units, as cellulosic material (and possibly as porous bodies). These classes need to be distinguished because, for example, in speaking of the porosity of filter paper, as paper, one speaks of a phenomenon very different from v hat has been termed the “porosity” of cellulose fibers. h distinction between the roles played by the paper structure and the fiber structure may not be possible in certain experimental observations, but this only introduces an added complication which should be recognized. This distinction appears in Table I as that betn een bulk properties and niolccular properties. A convenient way of characterizing the paper as a structure is in terms of its volumetric composition (1, 49, 60, 62, 7’5): the fractional volumes of solid matter, of air, and of liquid (if any) in a sheet. The dimensional, total, volume of the paper is determined by lining up a known number of sheets of the same size and shape one above the other to form a pad. This is pressed between glass plates, and the thickness and area of the pad are measured. From
1415
A N A L Y T I C A L CHEMISTRY
1416 Table I.
Factors That Operate in Paper Chromatography
I
I
I
i
Factors that influence movement of fluid
Factors that influence RF value
Factors that influence definition of zones
Bulk-phase properties
I
Molecular urooerties
Of the fluid Type of flow, inertial effects: in liquid, in displaced gas
Of the paper Porosity: Number of capillaries, distribution of lengths, distribution of widths, uniformity in properties
1
i
Of the paper Chemical nature, presence of impurities, uniformity of properties I
Of the fluid Chemical atructure as it influences: density, viscosity, surface te sion
~
I
~
I
I
Of the system Utilization of driving force
in overcoming friction, in changing dimensions, in affecting viscosity
these measurements and the number of sheets the volume of one sheet can be calculated. The fractional volume of solid can be obtained by immersing the dried evacuated paper in a known volume of a fluid R-hich fills the pores of the paper but does not swell the fibers, and measuring the increase in volume. The volume of solid fraction may be difficult to determine because of difficulties also found in determining the density of the fibers. These have to do with swelling of the fiber during immersion, complete removal of water, etc. This problem has been discussed by Hermans and Vermaas (32, 33). The fractional volume of liquid can be obtained approximately from the loss in weight on drying, and the density of the volatile material. The liquid fraction which is removed on eshaustive drying, and which may be largely water, may not actually represent the fraction that exists as liquid in the paper, but a portion of it may be a “part” of the fiber in the sense that it is chemically bound to the fiber ($0). The fractional volume of air can usually be obtained by difference. Obviously, in making measurements such as these the size of sample taken must be large enough that the results no longer depend on the size of the sample. Only then will one be measuring the properties of the paper. The attempt to measure these quantities n i t h a sample consisting of a few fibers would in general yield values not a t all characteristic of the sheet of paper. The physical picture one gets a t present of the total filter paper complex is of a mat of fibers, the pores between which interconnect to form a system of anastomosed capillaries. The fibers which form the mat themselves contain “pores,” but of submicroscopic or even molecular dimensions. Because of the nature of filter paper it is difficult to give a sharp picture of the capillary structure: of the number of capillaries and
Of the system Interactions that influence capillarity, interactions that influence porosity, swelling, changes in dimensions, plugging of capillaries
of their length and width distributions. Instead, the paper is characterized by various parameters such as “porosity,” “average,” or “equivalent” pore size, and pore size distribution. These quantities must not, however, be thought to have necessarily the same meaning as the same terms used in connection with glass capillaries, metal tubes and pipes, or even beds of sand. The entire physical structure of filter paper must be considered in analyzing the flow of liquids through the paper. Though the pores in filter paper probably can run in any direction relative to the surface of the paper, there is none the less not complete iandomness of arrangement. (Carman, 16, suggests that in the path of liquid through granular beds the flow is equivalent to that in a helically wound capillary, the diameter of the helix being approximately 1.5 times the diameter of the capillary.) The paper usually differs in structure along the two dimensions of its surface. These dimensions are defined as the machine direction, parallel to its forward movement in the paper-making machine, and the cross direction, a t right angles to the machine direction. The ’ tIvo are distinguished by tests which rely on: 1. Ease of bending. A paper strip cut in the machine direction tends to bend less easily than one cut in the cross direction. 2. Tendency to curl. If pieces of paper are floated on water, or, if very absorbent, are exposed to water for a few seconds, the paper tends to curl. with the axis of curl parallel to the machine direction (85). 3. Cs illarity. Water usually rises faster up a strip cut in the machine &-ection. A drop of xater placed on a sheet may spread to an oval, with the longer avis parallel to the machine direction (4). (There are some commercial filter papers in which machine direction cannot be determined by f l o of ~ solvent.) These properties are consistent uith a preferential lining up of the fibers in the machine direction as the paper is laid down.
V O L U M E 2 4 , N O . 9, S E P T E M B E R 1 9 5 2 Handmade papers may bho\v increased orientation of the fibers in one direction. Foote (22) found by application of Lucas’ method (see below) that the calculated pore diameter of several papers (not filter papers) n-as l a r g c ~in the machine than in the cross direction. Manegold ( 5 2 ) reported that a dried filter paper showed a specific weight (not including the empty space) of 1 3 . The specific weight’including the empty space was 0.46. After the paper had &ood 8 days in a desiccator over sulfuric acid its thickness was 1.42 X em., and the yolume of empty space per cubic centimeter was 0.71. After 8 days in a water-saturated at.mosphere the thickness was 1.92 X lo-? em., and the volume of empty space was 0.79. Thus. swelling increased the thickness and the fractional volume of empty space in the paper. Stamm and Millet’t (80)distinguish two kinds of internal surface in filter paper: the eurfaw of the microscopically visible tubular lumen in natural organized cellulose walls, and of the interfiber spaces; and the surface of “transient capillaries within the (.ell walls of all types of cellulosic material that exists only in t’he presence of a swelling agent.” These authors found the area of the first kind of surface in a filter paper, determined by adsorption of stearic acid from benzene, to be 2.7 X 103 sq. em. per g r a m The surface areas obtained in cellulosic systems in which the cell walls are swollen are of the order of 3 X 106 sy. em. per gram. BULK PROPERTIES O F THE FLUID
Analyies of the fact,ors influencing rate of flow of fluids (gaws or liquids) through or in filter paper show, as described in a later section, that the properties of the fluid which have a major effect on rate of flow are its viscosity, density, and (Tl-ith liquids) surface tension. These are niorc conveniently discussed in connection with molecular properties. h further point, of more interest, perhaps, in a discussion of fipI is the observation of Krulla ( $3)that the amount of liquid per unit area of the paper decreases u p the strip to the advancing front of the liquid. BULK PROPERTlES OF THE SYSTEM
In measuring the rate of filtration of a liquid through filter paper ( 7 , 30, Yd, 78, 79) or in general the permeability of a paper normal to the surface ( 7 5 ) ,a fluid may be forced through the paper under an external pressure, the effect of which is large compared with that of the capillary forces present. Under these conditions an empirical treatment of the rate of movement of the fLuid through the paper may be made through the application of Darcy’s law. This law states that the rate of flow, Q, of a given liquid through a porous bed is directly proportional to the area of the bed, A , and the driving pressure, P (the pressure difference through the porous bed), and inversely proportional t o the thickness of the bed, L. This is stated in the following equation, K lieing a constant of proportionality:
Q
=
KAPjL
The equation is valid for laminar (viscous) flow. The constant Ii is characteristic of the given liquid and porous body. I n the measurement of rate of filtration, L would be the thickness of t’he sheet of filter paper, and papers would be compared by using a given fluid and comparing the values of K so obtained, “without t~iiquiringinto the size, shape, number, distribution, or orientation of the actual channels through which the flow takes place” (36).
\Then Darcy’s law ie applied to the capillary penetration of liquids into filter paper, it becomes necessary to invoke the theory of capillarity t.0 define and estimate the driving pressure, P . One then must inquire into the size, shape, number, and orientation of the pores in the paper. In applying the theory of capillarity, there are also opened up for consideration the molecular properties oE the fluid as manifested iri surface tension, viscositl-, and density.
1417 MOLECULAR PROPERTIES OF THE SUPPORTING MEDIUM
An approach similar to that used to the paper as a whole has been t,aken to the fibers themselves: The fibers also have been characterized volumetrically as consisting of a certain volume fraction of cellulose, a fraction of water, and a fraction of empty space (33). The fibers are very narron- ribbons which seem to be composed of layers that can be dissected still further ( 6 7 ) . The intimate structure of the fibers is still under investigation, but it seems that they show many properties typical of macromolecular systems. Glucose residues are linked together to form long chains, the cellulose molecules. These are hound together into larger bodies which eventually constitute the fiber. HOTever, the arrangement appears not to be uniform along the fiber, but to yield submicroscopic crystalline regions, in which a regular repeated alignment of the chains is present, alternating with amorphous regions in n-hich the chains are more or less randomly kinked and unaligned, the regions shading off the one into thv other. The empt,y space in t,he fibers may consist of pores of various sizes, some with dimensions large as compared n-ith the molecules of common liquids. Into such pores liquids might penetrate by a process called porous imbibibion. I n porous imbibition the liquid seems to be taken up by already existing pores and the porous body does not necessarily change its dimensions. This is distinguished from swelling, in which p r e formed pores are not necessarily present, and the process is accompanied by dimensional change in the porous body (s8j. 4ccording to Hermans ( 3 2 ) , the amorphous parts of the cellulose, structure are the regions where imbibition leading t o swelling may occur. The fraction of water which may be present in the fibers may be made u p of several parts. Some of the moleculeEi nisy be present in such a form and stoichiometry that they may be considered as hydrate water molecules. Ot,hers may be more loosely bound and classified as sorbed miter molecules. Some modern ideas on this subject have been summarized (76). It is in any case evident t h a t in filter paper we deal wit’han extremely complicated system and many variables. It is probable that the volume fraction of water in paper, as measured, is a summation of the water fraction of the fibers, and of any water which may be held by sorption between the fibers. Cellulose. Chemically speaking, t’he solid fraction of filter paper consists largely of cellulose. This material in filter paper can usually be separated into three fractions on t’he following practical basis (45, 84). Alpha-cellulose is insoluble in strong sodium hydroxide solution. From that part which is soluble, mineral acid precipitates 6-cellulose. The part which still remains soluble is ~-cellulose. I t was found that’ a good analytical paper contains at least 96% a-cellulose (86). Reducing substances are present in the paper, probably largely as part ot the degraded, soluble fract’ion. These are determined as a copper number, the number of grams of copper in the cuprous oside resulting from the reduction of copper sulfate by 100 grams of paper fibers (85). A good filter paper is found to have a copper number of 0.4, or less. The acidity of a good paper is found to he of the order of pH 6 (86). Cellulose shows a slight solubility in water. Strachan ( 8 1 ) found that a carefully purified cotton cellulose gave up a small quantity of material, 13 t,o 21 parts per million, even after 50 extractions with water. This material on hydrolysis shoived some reducing action. Turner (89)found that when a highly purified cotton fabric was dipped into conductivity water a brown line formed where the r a t e r evaporated. It could be reformed a t lower and lower levels on the same piece of fabric with undiminished intensity. This indicated some chemical change in the cellulose lvhich converted it into a water-soluble material. The brown material was alcohol-soluble and showed reducing power. Filter paper cont’ains some “ash,” and many effect’s of its capillary behavior are laid to the inorganic content (39, 82). In filter papers which are not *‘filled”with noncellulosic materials,
1418
ANALYTICAL CHEMISTRY
the inorganic material may be present as inorganic substances incorporated in the cellulose by the living plant, as adsorbed salts, or as cations held by the weakly acid groups present in the paper. Kullgren (44) reports that in the better grades of filter paper the ash-forming materials are mostly of the latter type-that is, cations held through the cation-exchanging ability (largely laid to carboxylic acid groups) of the cellulose fibers. These cations, even though present only in traces, may be of considerable importance in chromatography through their catalytic effects (19).
Some filter papers contain additives introduced for special purposea. Thus, some papers are treated with melamine or other substances, to give increased wet strength. Papers are sometimes filled with filtration aids, such as fuller’s earth or charcoal. Black papers for use with white precipitates are made. Cellulose fibers are swelled by water and many other liquids. Kress and Bialkowsky ( 4 2 ) ranked liquids in decreasing order of swelling ability thus: formamide > > water, slightly greater than ethylene glycol > methyl alcohol > furfuryl alcohol > ethyl alcohol > furfural, slightly greater than propyl alcohol, slightly greater than n-butyl alcohol, slightly greater than fuel oil (a mixture of hydrocarbons slightly heavier than kerosene). These authors state that liquids with hydroxyl or potential hydroxyl groups and with high dielectric constants show a high rate of swelling of cellulose. Liquids with low dielectric constants did not show much swelling ability. Cellulose is also swollen by acids and bases within certain concentration ranges. The phenomenon is an exceedingly complicated one, upon which a great deal of work has been done (29,34,61,71). FLOW OF FLUID IN FlLTER PAPER
If a strip of filter paper (or any paper which has some porosity) is dipped into a liquid which wets it, the liquid is observed to rise up the paper. In the first few seconds after the filter paper is dipped into the liquid, the liquid seems to enter the paper with a very turbulent motion (46). The rate of rise, a t first relatively rapid, slows down gradually as the liquid rises higher in the paper. The rise of liquids in filter paper has been studied by a large number of workers who have been interested in characterizing the properties of the filter paper, or evaluating the penetrating power of the liquid, or relating physical t o chemical properties of the system. Two types of experiments are reported. In one type of experiment the liquid rises up the paper (or flows down it) in an enclosed space saturated with the vapors of the liquid. No evaporation can occur, and the liquid can under these conditions move rather far. The length of ordinary filter paper sheets limits the observable distances moved, but long rolls couId be obtained. In packed sand a column of paraffin oil wm still moving after a year, the height attained being two to three times that attained in the first 24 hours (31). In the other type the liquid moves along the paper (blotting or filter paper) in an open space, so that free evaporation can occur. Under these circumstances the liquid reaches a certain level a t which evaporation just balances availability of liquid. The first type of experiment describes the way in which paper chromatography is usually carried out-that is, in a saturated atmosphere. The earliest studies of the factors which control rate of flow of liquids in filter or blotting paper were qualitative. The first quantitative and semitheoretical study seems to have been made by Cameron and Bell (5,f4)in connection with an investigation of the movement of soil water. An independent empirical investigation by Ostwald (60) supported Cameron and Bell. I t remained for Lucaa (48) in an analysis similar to that of Cameron and Bell, but more profound, to clarify the relation between height risen, h, by a liquid in a vertical strip of paper and time of rise, t. He
showed that with the aid of the Poiseuille law, made manageable through suitable assumptions, the relation between h and t could be derived from theory in the form:
where y is the surface tension of the liquid (assumed t o wet the paper completely), 7 is the viscosity, and T is a radius of a capillary which would act in the same way as was observed. On applying this equation to a large number of data obtained with various liquids and papers, Lucas found what he felt was good agreement, considering the simplifying assumptions which had to be made. For example, the exponents of h fell between 2 and 2.5. The Lucas relation has been used by paper chemists for estimating the pore sizes of papers ( 3 6 ) . Lucas realized that his equation implied that the liquid would continue to rise indefinitely. He showed how this could be corrected for. He also mentioned the possible effects of sn~elling(see below). Peek and McLean (64)in connection with work on the impregnation of papers, studied the height of rise of liquids in glass capillaries and filter paper. Their analysis of the problem was much like that of Lucas. Recently, very precise measurements were made by Muller and Clegg (57) on the rise of water, methyl, ethyl, butyl, and amy1 alcohols, and ethyl alcohol-water mixtures in three Schleicher and Schull papers Nos. 598-ST and 598-\V (for spot analysis) and 601. The authors fitted their data with an equation:
h2 = Dt
-b
(2)
in which D and b are constants; D is a “diffusion coefficient,” related to surface tension, viscosity, and density, d of the liquid by the relation:
D = ay/qd
+b
(3)
where a and b are constants for a given paper. Here also the simple equation fits the data over the ordinary range of measurement, so that the equation corrected for maximum height of rise need not be used. The expressions which apply Poiseuille’s law are derived from equations for the f l o ~of liquids through cylindrical capillaries under known limiting conditions. The exact extension of these ideas t o filter paper (21, 25, 36, 48, 57, 7 7 ) would require modifications of the theory t o deal with capillaries which branch, and vary in cross-sectional area and shape. Some such studies have been made, for example, for capillaries with square, or elliptical, or in general noncircular cross section (15, 49-51), and for capillaries which branch (61-53). Yet even if the mathematics mere manageable, the extension to filter paper would break down from a lack of knowledge of the detailed capillary structure of the paper. The difficulty was met by Peek and McLean (64) by assuming a model for the capillary system of the paper. This model “is one involving a set of capillaries in parallel alternating in series with larger capillaries, each capillary whether small or large varying in radius along its length, and therefore similar in its viscous resistance to a set of shorter capillaries in series.” Each group of capillaries in series is “replaced by single capillaries having the same resistance to viscous flow.” The capillaries are assumed t o vary in size in the model, as in the medium, and, setting up a distribution function to describe this variation, Peek and McLean arrive a t an equation which, for practical purposes may be written: (4)
The derivation is not given because the paper is readily accessible. Here “ A and B are dependent only on the distribution of pore sizes in the medium and are therefore constants for a given
V O L U M E 24, NO. 9, S E P T E M B E R 1 9 5 2 medium.” g is the acceleration due to gravity. The paper strip is required to have constant width and thickness, in order that the measurement of the volume of liquid rising per unit time may reasonably be transformed to a measurement of length, or height, The plot of the rate of rise dhldt versus l / h should give a straight line. This was verified a t several temperatures with benzene, carbon tetrachloride, ethyl alcohol, ethylbenzene, ethylene dichloride, and methyl alcohol rising up strips of filter paper in an atmosphere saturated with the solvent. For a given filter paper the intercepts of the straight lines obtained with different liquids should be proportional to d/7, and the values of B (87/dg times the intercept) should be the same, since they depend only on the medium and not on the liquid. This also was verified with various liquids. The slopes of the straight lines are proportional to ~ / 7 ,and from the slopes relative values of y can be calculated. A-y is 47 times the slope. Taking a given liquid as having a relative y of 1, the surface tensions of the other liquids can be calculated. Good agreement was found between calculated and accepted values of relative surface tension for these liquids. Peek and McLean showed how a range of pore sizes for the medium could be estimated, and showed that the estimate for the filter paper which they used gave a reasonable value. In all these equations relating h and t, there are tn o classes of quantities (apart from 9 ) : those which are properties of the liquid, such as y , d and 7 ; and those which are propeities either of the capillary, as r is, or of the porous system, as are ,4 and B . In the latter case, the net effect in fitting the theory derived from the model to the experimental data is that an adjustable parameter is present in the capillary dimensions: the “pore size” or the “pore size range.” Quantities r , A, and B . The detailed lengths and cross sections of the capillaries, or rather the “effective” lengths and cross sections, since the “length of the capillary” depends upon the distance from the inlet a t which flow becomes steady, and the distance from the outlet a t which the flow ceases to be steady and laminar, are difficult to estimate. However, the front of rising liquid in a strip of filter paper is usually regular in appearance: the variations iyhich are visible are small, and are averaged out over-all in the dynamic system. This makes the treatment of Peek and bicLean applicable, as they point out. The equation for flow in the capillaries makes no alloxyance for end effects. I t is k n o m that the shape of the end of a capillary xi11 affect the rate of flow of a liquid through it. At the entrance to the capillary there may be a certain distance over r-ihich the flow of liquid is turbulent. The initial turbulent region is shorter the smaller the capillary and the less the driving pressure ( 9 I ) , so the effect is probably not important with filter paper. In capillaries of irregular shape the measurement of length may be open to meniscus errors because the meniscus does not rise evenly all around its perimeter, particularly if sharp angles, or cracks, are present (15). This error is of course included in the general error of not allowing for the mass of liquid above the bottom of the meniscus in reading h . Changes in effective radius of the capillaries-that is, in porosity-might be brought about by the adsorption of colloidal particles along the ~ - a l l sof the capillaries, or by filtering out of dispersed material which might block some of the pores, Thus, it was found (9) that rate of rise of colloid suspensions varied inversely with the extent of adsorption to the paper of the colloid. This was influenced by the presence of electrolytes. Entrapment of air (15,56,18) due to imperfect \vetting (S) may alter porosity. Bartell and Greager (3)studied the wetting of poxders (which are porous masses) by liquids and found that when liquids with large contact angles to the material of the powder were absorbed (penetrated the powder) air tended to be entrapped. The larger the contact angle, the more air was entrapped, and the less the amount of liquid held by the powder. The greatest volume absorption of liquid was likely to be observed with liquids giving zero
1419 contact angle with the solid, especially if, in addition, the adhesion tension were low. Liquids with high adhesion tension tended to draw the particle together, leaving less capillary volume available for holding liquid. [The adhesion tension A(Ls),was defined by Freundlich by the relation: A ( L S )= ?(OS) - ~ ( L s ) ,where ~ ( G s is ) the “surface tension” of the solid, and y ( ~ s is)the interfacial tension of the liquid-solid interface.] Release of gas by the liquid ( 7 , 5 6 ) may be another of the causes of change in porosity when different liquids are compared The effect of swelling is not sufficiently well understood (84). It is sometimes assumed ( 2 2 , S O ) that swelling of paper by, say, water, would tend t o make the capillary spaces smaller. Holyever, several studies have shown that this is not necessarily so. Manegold ( 5 2 ) found (the data are given above) that filter paper after standing in a water-saturated atmosphere was thicker than the dried paper, and showed about 10% more empty space volume. In agreement Rith this is the observation of Bogaty and Carson ( 7 ) ,based on air permeability studies of filter papers, that the spaces betn-een fibers probably become larger as a result of swelling in the structure following wetting with water. I t is not likely that this increased permeability iyould occur only perpendicular t o and not parallel to the paper surface. In the swelling process the cellulose fiber gains in thickness, but apparently not greatly in length. h sloning of filtration rate is sometimes observed when water and other fluids are filtered through paper ( 7 , SO, 7 8 ) [or through glass, porcelain, or quartz filters (78), for that matter]. Prefiltering the water usually diminished the slowing ( 7 , 7 8 ) . The forces due t o change in momentum of the liquid rising in the capillary are not accounted for in the equation. They appear t o be very small, especially for capillaries of small radius (8). Other factors which have been found to play a role in the flow of fluid through capillaries or porous bodies, are roughness of the capillary walls ( 5 9 ) ,slippage along the wall ( 4 6 ) , and electroosmotic Pack pressure ( 1 1 , I S ) . I t has been suggested ( 7 0 ) that the streaming potential generated in chromatography may affect the movement of some substances. However, Martin ( 5 4 ) states that this is unlikely, though the zeta potential may affect the distribution of a charged solute betneen the phases. These factors may not be very important in influencing the rise of liquid in filter paper. Many of them must be swallowed up in the adjustable parameters, A and B , of Equation 4. Some may operate in opposite ways and so to some extent cancel each other. It must be evident, however, that filter paper is not a simple porous body. The walls of the capillaries are flexible, and capable of s~velling,and the possibility exists that many still unknown factors are present. If they are, however, it would seem that their net influence on the flow of the liquid is small. Quantities y , 7, and d. The liquid would not rise by capillarity in the paper if it did not wet the paper to some extent This, of course, is why there is the y term (replaced by y cos 0 for liquids which make a contact angle e with the paper) in Equations l, 3, and 4. In the derivation of the equation relating h and t (Equation 4),it is assumed that the liquid wets the surface of the capillary with a contact angle of zero. Brown ( I O ) has pointed out that zero contact angle must not be considered a special case similar to that represented by a given finite value of the contact angle (e), but as being characteristic of the class of circumstances in which when a liquid of surface free energy Y L wets a solid with the resulting free surface energy Y L ( S ) ,the relation is: YL
k - YL(S)
What this means is that there is a field of force outside of the (inextensible) solid surface reaching to the maximum range of attraction of the solid molecules, and directed inward perpendicularly t o the surface. When a liquid comes into contact with such a surface, the attraction by the molecules of the solid will oppose the inward attraction of the molecules in the surface of the
1420 liquid which normally manifests itself in y ~ .The condition for zero contact angle is that the molecules of the solid attract those of the liquid to an extent equal to, or greater, than that to which the liquid molecules attract each other. If the attraction is greater, then there is a tangential pressure in the surface layer which tends to cause spreading. If the surface is not inext,ensible, but, can, for example, be swelled by the liquid, the energy relations can be changed, but a zero contact angle can still remain (10).
CONTACT ANGLE. The contact angle of importance in measurements of rate of penetration of liquids is the advancing contact angle (18); that of a liquid moving on to a fresh surface. (Receding contact angles, observed on withdrawing liquid from a wetted surface, appear t o be unstable, and not to have a unique value.) The presence of pores tends to increase the contact angle. Thus, surfaces of porous clothing may show an apparent contact angle of about 150°, when the fibers of which the material is woven show an angle of about 90" (18). However, where the contact angle on a material is zero, it is unlikely that mere macroscopic porosity could increase it to a large value, for a zero contact angle liquid spreads as a very thin film, probably as a monolayer, and should easily enter such pores. It seems that most organic liquids do wet paper in a manner which implies a zero contact angle (23). Rideal (66) has raised the point that in measuring the contact angle the alteration of the radius of curvature is observed and measured a t some point distant from the line of contact with the tube wall, and not at the contact "line" itself, and he suggests that the angles of wetting (of glass capillaries j given in the literature are probably fictitious. Surface tension may change with change in the velocity of' flow of the fluid (14). The surface tension of the liquid may also be altered (usually lowered) on contact with the paper, either t'hrough the dissolution of surface-active impurit,ies ( 3 7 , 6 7 ) or through a change in pH. Thus, in contact with solutions of alkaloidal salts, the filter paper binds acid; this raisp the pH and alters the degree of hydrolysis of the salt in the direction of increasing the relative amount of free base. This produces a fi!ll in surface tension (37); for the free base is more surface active than the soluble salt. If the liquid wets the paper and thus penetrates it, the rate will be dependent on viscosity of the fluid. Thus, if fluids of essentially the same surface tension but widely different viscosities are allowed to penetrate paper, the amount of penetration is inversely related to the viscosity. This was shown by Vincent (go), who used as his penetrants aqueous polyvinyl acetate solutions. Viscosity. The presence of the viscosity term in the equations implies, or is related to, the condition of laminar or viscous flow in the capillaries of the paper, for if the flow were turbulent the viscosit,y term \vould disappear. That the flow becomes laminar after the iiiitial rushing in of liquid is indicated by analogy to other porouq bodies such as beds of sand (36). The viscosity of the fluid is Assumed constant, but this assumption may be invalidated if the liquid shows structural viscosity change (65). Bulkley (fa)found for some capillaries and fluids a departure from the Poiseuille law. The viscosity coefficient may in these cases be a structure-dependent quantity and vary with rate of flow (51). The assumption may also be invalidated: if the liquid shows plastic flow, or is thixotropic; if it is a mixture containing components of different viscosities, one component of which is adsorbed more strongly than another; if the liquid contains large molecules which change their average orientation with change in rate of flow; if the liquid contains charged colloidal particles which are adsorbed along the capillary walls or which can be discharged under the influence of electromotive forces generated by the flowing liquid (48);or if the liquid contains dispersed material (even bacteria, 23) which is filtered out. The effect of slipping along the walls may be of importance in t.he contribution to the frictional force due to viscosity ( 4 6 ) . Density. The density of the liquid enters the equations as
ANALYTICAL CHEMISTRY part of the term for the force opposing capillary rise: the hydrostatic head of liquid, which is TPLdg. g is a constant, but d may change if the fluid is a mixture of substances of very different, densities, one of which is strongly adsorbed. This eventualit,y is not likely to arise as a serious factor in the application of the equation. Cameron and Bell ( 1 4 ) found the same relation between h and t for blotting paper whether it was in the horizontal or in the vertical position, which led them to conclude that the capillary forces were much greater than the gravitational when the dktance risen was small compared to that to which the water might ultimately rise (penetrate). Berthier (6) ana yzed the forces operating in the rise of a liquid in a porous body, and the descent of the liquid. She concluded that only the term for the work clone against gravity is affected, being positive in the first, and negative in the second, case. -41~0,if u' is the speed of descent a t the distance h, and v is the speed of rise at a height h, the function h ( u v') varies linearly with h. The case where the porous substance dissolves in the liquid being absorbed was esamined by Russenberger ( 6 8 )using devives i n which t'he weight of the rising liquid is continually counterbalanced. If an esperiment lasts too long when the developer is arid (or becomes acid for any reason) the behavior of the paper may be affected. Murray ( 5 8 ) found that adsorption of acid by filter paper decreases after the paper has been in contact with the arid for some days. Muller and Clegg ( 6 7 ) found changes in rate of rise of water in paper on repeated alternating testing followed by careful drying of the paper. ?VJorsTmE. The effect of moisture has been studied quantitatively by Muller and Clegg (57). They found that filter paper exposed to an atmosphere saturated Tyith water vapor showed an increased rate of rise with increased time of exposure t,o the vapors. The maximum rate was found after about 30 minute?' exposure, though the paper continued to take up water for several days. This seems to indicate, as a f i s t approximation, that it is the water of porous imbibition which affects rate of rise and that any effect as a result of the much slower imbibition due to s i d l i n g is not marked. If the paper hangs in a very small quantity of liquid, the lowering in height of the liquid level may affect the rate of rise of the liquid. TEMPERATURE. Change in teniperat'uremay affect rate of rise. Increase in temperature reduces viscosity and surface tension, and these tend to cancel in their effects on the rate of rise (26). Lucas calculated the ratio ( y ~ o o / y o o ) / ( q 2 0 0 / ~ ofor o ) ethyl alcohol to be 1.4. The ratio should be independent of the porosity of the paper, and was found for two papers of different porosities to be 1.48 and 1.48 from rate of rise experiments (48). The effect of temperature has also been investigated by others (57, 6 4 ) with the conclusion that the temperature coefficient of the rate of rise is relatively small. The effects calculat,ed when the temperature coefficient,s of y, q , and d are known, agree with esperiment to within about 1% in precise work ( 6 7 ) . These conclusions c:~n be stated only for pure liquids at the present time. n'hen a volatile liquid is allowed to rise in filter paper in an open spare so that evaporation may occur freely, the liquid ceases t'o rise a t that height a t which the amount of liquid rising into the paper is just balanced by the amount which evaporates. Garner (25,26)has derived an espression for the effect of evaporation on the rate of climb of liquid under these conditions. An experimental test indicated that the theoretical equations were not entirely satisfactory (26). This case is not of importance t o paper chromatography at present. Esplicit in the discussion so far has been the requirement' t'h:it the strips or sheets of paper along which the liquid moves have constant width and thickness. The shape of a strip will obviously influence the linear rate of penetration of liquid into it. Thus, if the point of a triangular strip dips into a liquid which in rising
+
V O L U M E 2 4 , NO. 9, S E P T E M B E R 1 9 5 2 must spread over a greater and greater area for each unit of distance risen, even though the available volume may obey the equations for du/dt (Equation 5), the rate of rise will not obey the dh/dt equation (Equation 4) derived on the basis that, since width and thickness remain constant, each increase in volume will sweep out the same increase in height. Quantitative and theoretical studies of the effects of shape on rate of rise have been made by Muller and Clegg ( 5 7 ) . Some effects of shape of the strip on Rp have been reported ( 4 1 ) . 4CKYOWLEDGMEhT
The author is indebted t o George N. Kowkabany and to Chester A. Hargreaves, 2nd, for valuable discussions of this work. He also wishes t o thank the referee for his comments on commercial filter papers, LITERATURE CITED
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