MOLECULAR DIFFUSION INTO WOOD' L. C. CADY
Department o j Chemistry, University o j Idaho, Moscow, Idaho AND
J. W. WILLIAMS
Laboratory of Colloid Chemistry, University of Wisconsin, Madison, Wisconsin Received June 1.6, 1934 I. STATEMENT O F PROBLEM
One of the purposes of the study of molecular diffusion into a gel has been to obtain information about the structure of the gel. Thus, in spite of the fact that eariy investigators had assumed the gel to have no effect on the diffusion, it is now a matter of record that mechanical blocking, wall friction, and viscosity effects do modify the rate at which a simple solute molecule can diffuse across an interface and into such a solid. It appeared possible to us that the methods which have been successful in the study of gels could be extended to the porous solids. Therefore it was decided to measure the rate of diffusion, from dilute aqueous solutions, of the neutral molecules urea, glycerol, and lactose into wood samples, with the expectation that these diffusion data could be used to estimate the effective mechanical blocking. Wood samples were chosen because through the efforts of the scientists a t the U. S. Forest Products Laboratory and elsewhere the capillary dimensions for certain species are quite accurately known. This report describes the results obtained in a somewhat extended series of experiments and discusses their significance. A number of interesting experiments have followed the successful analyses by March and Weaver (8) and by Langer (7) of the mathematical problem involved in a diffusion experiment in which the process is allowed to take place across the interface formed by a stirred liquid in contact with a gel or porous solid. As a result of experiments based upon this analysis Friedman and Kraemer (3) have been able to make observations of the diffusion of non-electrolytes into gelatin gels, Friedman (2) and Klemm and Friedman (4) have been able to extend the work to agar and cellulose 1 A more complete account of this work is to be found in the thesis of L. C. Cady, presented to the Faculty of the University of Wisconsin in partial fulfillment of the requirements for the degree of Doctor of Philosophy and filed in the Library of the University of Wisconsin in August, 1934. 87
88
L. C. CADY A N D J. W. WILLIAMS
acetate gels, and Wolkowa (14) has obtained data for the diffusion of glucose into silica gels. I n all these cases the diffusion into the gel is slower than it is into pure water a t the same temperature. Friedman and Kraemer considered three causes for the retarded diffusion: a mechanical blocking by the gel substance, an additional resistance due to the proximity of the diffusing molecule to the capillary walls, and an increased viscosity of the dispersion medium due to the solution in it of a certain amount of the gel substance. Correction for these effects was made by the use of an equation of the form,
D,
=
D,(1 + T ) (1 + 2.4 r/R) (1 + CY)
I n this equation, D, is the diffusion coefficient of the substance into water, D, is the diffusion coefficient of the substance into the gel or porous solid, ir is the correction factor for mechanical blocking, r is the radius of the diffusing molecule, R is the radius of the pore through which the diffusion is taking place, and CY is the correction factor for changed viscosity. In the treatment of our experimental data we shall prefer to make use of another equation, as follows:
D, (1 -
T)
=
D, A
=
D,(1 + 2.4 r / R ) (1 + CY)
(2)
Our work has been done with wood samples, and R is now to be interpreted as the effective radius of the pit membrane pores. Since mechanical blocking serves to reduce the unit area through which the diffusion can take place, it has seemed logical to compare D,and D, for a process taking place across equal areas. This necessitates the adjustment of D, to the reduced open cross-sectional area of the porous substance. Thus, the mechanical blocking may be taken into account by multiplying D, by a factor A , which is the fraction of the area unobstructed by the solid substance. Then differences between D, values which have been adjusted in this way for reduced cross-sectional area and D,are due to other factors, including the anisotropic character of the wood. Aside from microscopic measurements with extremely thin sections there is no direct method by which the amount of open area in a given surface can be evaluated. The method of attack most frequently used is based upon a determination of the partial pore volume of a sample, using densiity measurements. If the partial pore volume is represented by S, then S = 1 - g/d. I n this definition, g is the weight of the gel or porous solid per cubic centimeter, and d is the density of the solid material forming the structure.
MOLECULAR DIFFUSION INTO WOOD
89
Thus, the problem becomes one of expressing the factor A in terms of X. There are two conditions which any equation relating A and S should fulfil. When the partial pore volume is zero the substance is solid throughout, the area is completely blocked, and the factor A becomes zero. Likewise, when the partial pore volume is unity there is no mechanical blocking, none of the area is obstructed, and A becomes unity. The mechanical blocking factor has been obtained in different ways by interested investigators. I n order to collect in one place a few of the results, table 1 and figure 1 have been prepared. Buckingham’s equation was based upon his observations of the resistance experienced by carbon dioxide and oxygen diffusing through soil. The Dimanski expression resulted from an attempt to calculate by theory the area in a single plane of the sections of spherical molecules forming the disperse phase. It was applied by Dumanski to the correction of both electrical conductivity and diffusion data for gels. To correct conductivity data which were obtained with samples of wood, Stamm modified TABLE 1 Evaluation o j mechanical blocking factor A VALUE OF
A
S2
1 - (1 -
S
S)2‘3
REFERENCE
INVESTIGATOR
Buc kingham
U. S. Department of Agriculture, Bur.
Dumanski Stamm
Soils, Bulletin No. 25 (1904) Kolloid-Z. 3, 210 (1908) J. Phys. Chem. 36, 312 (1932)
the equation, because in this case the structural units are elongated rather than spherical in shape. The diffusion problem was not considered by the latter investigator. Since Friedman and his associates have adopted the Dumanski relationship for their work it may be remarked that their use of equation 1 is equivalent to a definition of the mechanical blocking factor such that,
A=
1
1
+ (1-
S)2’3
This equation does not meet the condition that A must be zero when the partial pore volume is zero, therefore it cannot have any general validity. The reason why its use with gel systems which have very large values of partial pore volume has not led to apparent difficulties is evident from an inspection of figure 1. The correction t o be made for the increased frictional resistance to the movement of a molecule in the neighborhood of a wall has been studied a t some length by Ladenburg (6), Arnold (l),and many others. The correc-
90
L. C. CADY AND J. W. WILLIAMS
tion used in the diffusion equations (1,2) is that of Ladenburg. The effect of the proximity of the wall surface on spheres falling in cylindrical glass vessels was measured, and 8tokes' law of fall was modified to take it into account. Arnold confirmed the Ladenburg correction and showed that it is independent of the viscosity of the liquid in which the molecule or particle is moving.
a
I
I n order to correct the law of Stokes the viscosity was multiplied by the factors (1 + 2.4 r / R ) and (1 3.3 r/h). In these factors h is the length of the capillary, and r and R have the significance already assigned them. The second factor becomes appreciable in the case of short tubes with closed ends and may be disregarded in the gel and wood problems. For wood, h would be twice the diameter of a lumen which is about one thousand times the value of r. Obviously the additional resistance to motion caused by the proximity of the wall will manifest itself for a limited range of values of r/R. When
+
MOLECULAR DIFFUSION INTO WOOD
91
r/R is large, one is dealing with a condition approaching ultrafiltration, but when r / R is very small, the wall is so far removed that the condition is one of free fall, or in the case of a diffusion, one of free diffusion. The data of Ladenburg indicate that this ratio should have values between 1/90 and 1/11 if the first factor is to be applicable without modification. Arnold’s curves place the lower limit in the neighborhood of 1/100, with the upper limit a t about 1/10. The correction factor a for increased viscosity of dispersion medium is obtained from the difference between D,a t zero concentration of solid and D,. Since there is only one “concentration” of wood substance when the voids or capillaries are filled with water, it is not possible to estimate a by an extrapolation of the kind resorted to when synthetic gels are being considered. For reasons which cannot be given a t this time it seems reasonable to conclude that the factor a can be considered to be negligible in our work with wood sections. If this correction factor for increased viscosity of medium can be neglected, diffusion experiments of the type to be reported here can give considerable information with regard to the magnitude of the mechanical blocking effects, because the radii of the diffusing molecules and the average radii of the pores of the pit membranes are known with some degree of accuracy. Stamm (13) has summarized the results for R obtained by using several independent methods. I n this way it should be possible to differentiate between the several equations proposed to calculate the magnitude of the mechanical blocking coefficient. In addition, differences between observed values and values obtained by calculation with the equation adjudged to be most nearly correct can be ascribed to the anisotropic character of the capillary spaces and to the presence of lumen pores without outlet. It might be assumed that diffusion studies of the kind we are to report would make possible an estimate of an average radius of the pit membrane pores in wood sections, but when it is realized that the principal cause of the reduction of diffusion is the mechanical blocking, the difficulties involved become apparent. We have little exact information about several factors which determine the effective area available for the diffusion. Furthermore, since the effects due to mechanical blocking are very large compared to those which result from the additional frictional resistance to motion due to the proximity of the walls, small errors in the A factor would lead to large errors in the determination of the ratio r/R, and therefore in the effective capillary area of the pores of the pit membranes. 11. MATHEMATICAL FORMULATION AND EXPERIMENTAL PROCEDURE
The coefficient of diffusion or diffusion constant is defined as the quantity of matter which in unit time moves through a unit of cross section
92
L.
C. CADY AND
J. W. WILLIAMS
under unit concentration gradient. I n this work it was required to determine the constant for various solute molecules, moving across the interface formed by the stirred solution in contact with a wood section, from observations of the decrease in concentration of the solution with time. March and Weaver showed that the diffusion constant, D,,of a solute moving into the solution contained in a porous solid is given by the expression
D,= a2T t
(3)
I n this equation D,is the diffusion constant expressed in cma2per second, and a is the thickness of the solid and also the depth of the solution above the solid. The value of T is found from the equation, 1 V = - - (0.327e-4."7T+ 0.0766e-24.'4T+ 0.0306e-63.6sT 2
+ 0.0160e-'23T + 0.0100e-200T+ 0.0067e-2eaT+
.)
I n this expression V is the fraction of the total amount of solute which has diffused into the void spaces of the solid. I n our experiments this quantity was found by determining the concentration of the solution above the block of wood with an immersion refractometer. At any time, t ,
Here Ra is the reading of the refractometer for the solution a t time, t = 0, R t is the reading a t time t, and R, is the reading for the solution originally filling the void spaces of the solid. I n order that equation 3 be exact it is required that the depth of solution and thickness of the solid be the same, and that the solution be maintained at uniform concentration throughout. I n order to use equation 4 in the form given, it is necessary to assume the concentration of solute to be directly proportional to the refractive index of the solution. I n practice, values of T were assumed and the corresponding values of V were calculated. A plot of V versus T was then made and values of T for any experimentally determined value of V were read from the curve. I n an experiment a block of wood was saturated with water and fitted into a thermostated brass diffusion chamber. The solution containing nearly spherical solute molecules was placed in contact with the block, and the change of concentration with time, as the solute diffused into the block of wood, was observed. Samples of cedar and white fir were obtained from freshly felled trees
93
MOLECULAR DIFFUSION INTO WOOD
about 15 in. in diameter. The sample of white pine was a kiln-dried piece, and results with it were obtained largely while developing the technique
FIQ. 2. LOCATION OF SAMPLES TAKEN FROM
TREE
a
3 FIG. 3. EVACUATION CELL
of the method. The Western hemlock sample was furnished by the U. S. Forest Products Laboratory. Sections taken from these were numbered
94
L. C. CADY AND J. W. WILLIAMS
as shown in figure 2. All samples were turned to the required size in a lathe and the ends were coated with paraffin to prevent drying and checking. T o lower the humidity to a sufficient extent to avoid growth of molds, the samples were kept over a saturated solution of barium chloride. The turned wood samples were cut into cylindrical blocks of the desired length, which varied from 1.5 to 4.0 cm. The exact thickness was measured with a micrometer caliper. The samples were placed in a n evacuation cell whose cpnstruction is indicated by figure 3. This cell was a brass
I
A
5
a FIG.4. DIFFUSION CELL cylinder 5 in. long and 2 in. in diameter. Cover and bottom, provided with brass stopcocks, were arranged so that they could be clamped to the cylinder. The upper stopcock was connected to a vacuum pump and the lower one was attached to a mercury manometer. Rubber gaskets between the cylinder and the cover and bottom sealed the apparatus. The cylinder, with block in place, was maintained for about twenty-four hours a t a pressure of 4 to 5 mm. of mercury. Water was introduced through the lower stopcock of the cell in order to fill the evacuated void spaces in
MOLECULAR DIFFUSION INTO WOOD
95
the block of wood, The sample was then kept for four weeks or longer in a vacuum desiccator filled with water, from which the air was exhausted a t intervals. The diffusion apparatus proper is shown in figure 4. It resembled the evacuation cell in form except that it had no stopcocks and the cover piece was provided with a stirrer and tapped hole to permit removal of the sample. Since diffusion was to take place only across the upper surface of the block, it was necessary to make it impossible for the solution to come into contact with the sides and bottom of the block. This was accomplished by painting the block on these faces with an aluminum-glyptal paint, and then coating them with a layer of paraffin to such a thickness that the block would not quite slip into the cylinder. The cylinder was then warmed and the paraffined block forced into it. On cooling, the block was firmly imbedded in the paraffin. The apparatus wag tested for tightness by allowing it to stand full of water overnight. Any seepage of water along the sides of the block could be detected in this way. After inversion to remove the excess water, the cell was clamped firmly to a brass frame by means of which it was possible to lower the cell in fixed position into the thermostat. The temperature chosen for the experiments was 25°C. To start an experiment an amount of the solution, such that its height in the cell was equal to the height of the wood block, was introduced into the diffusion cell. The choice of solute molecule was restricted for several reasons. The molecule should be nearly spherical in shape and of such radius that the ratio r / R falls within the limits mentioned in the previous section. The refractive index of the aqueous solution should be such that it varies linearly with the concentration of the solute. The solution should not cause change in any of the constituents of the wood. The molecules urea, lactose, and glycerol met these requirements fairly well. The concentration of the glycerol solution used was 4 per cent, while that of the urea and lactose was 5 per cent, by weight. The concentrations were kept as low as possible in order to avoid a “solute hindered” diffusion, but a t the same time the concentration was great enough to allow a difference of reading of 15 to 20 immersion refractometer units between the solution and water a t the beginning of the experiment. Refractometer readings were taken a t the beginning of the experiment and a t intervals of from twelve to twenty-four hours. The diffusion was allowed to continue until successive readings indicated that equilibrium had been reached. Six to twelve values of the diffusion constant were determined for each block. I n this way it was possible to obtain a representative value provided the variations between individual figures were not excessive. Preliminary experiments showed that there was no change T E E JOURNAL OF PHYSICAL CHEMISTRY, VOL.
39, NO. 1
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L. C. CADY AND J. W. WILLIAMS
of refractometer reading due to leakage, seepage, oil from the stirrer, or solution of material from the cylinder or paraffin. Further, no measurable sorption of solute by the wood substance was found. Before the start of all experiments the blocks were saturated as nearly as could be determined by weighing a t intervals to constant weight. The rate of stirring was so adjusted that the solution was kept a t uniform concentration without producing a vortex effect above the block. A stirrer speed of 275 R.P.M. was maintained. The initial refractive index of the water saturating the block depended upon the amount of material extracted from the block and varied with the species of wood. It was assumed that the solution filling the void spaces of the wood and the solution covering the block had reached equilibrium during the time that the block was in the vacuum desiccator. The refractometer reading, R,, was taken as the value obtained for the solution in which the block was saturated. 111. EXPERIMENTAL RESULTS
Data obtained in a typical diffusion measurement are presented in table 2. The values of D,in this table check each other unusually well, but in practically all cases the mean deviation from the average value is less than 0.01. The length of the block which could be used was fixed within definite limits by the dimensions of the diffusion cell, the amount of solution that could be stirred adequately, and the effect of sample removal upon the concentration of the remaining solution, It is evident from table 3 that the length of the block may be changed by 100 per cent without changing the diffusion coefficient to an appreciable extent. Additional experiments were made in which the wood was saturated with the solution so that a diffusion of the solute into water above the block took place. When glycerol diffused into the seasoned heartwood of white was obtained. Reversing the experipine a value of D, = 0.66 X ment with glycerol diffusing into the water above the block the value D, = 0.63 X resulted. However, experiments in which the solute diffused out of the block into the water above it offered several difficulties and were not generally used. When the pore dimensions of the wood blocks were larger, the values for the diffusion constants increased. I n all, there could be distinguished: (1) hindered diffusion, in which the ratio r / R was not too small to be of significance; (2) free diffusion, in which the effective pores were small enough to prevent mixing of the water in the block with the solution, but large enough to allow practically unrestricted diffusion of the solute molecules; and (3) stirred diffusion, in which the pores were so large that mechanical mixing with the liquid in the pores of the wood block took place
97
MOLECULAR DIFFUSlON INTO WOOD
as the solution was stirred. There is involved a mechanical blocking in all three cases. Results of experiments typical of the three kinds of diffusion have been collected to form table 4. The solute used was urea, for which D, = 1.3 X lov6 at 25°C. There have been summarized in table 5 the data for diffusion studies made on wood sections cut in the transverse direction. I n the table heartwood is represented by the symbol Hw and sapwood is designated by Sw. Numbers in parenthesis after the kind of wood refer to the positions indicated by the chart, figure 2, which gives the location of the sample in the tree. The sample labeled 3a was taken next to the center but not conTABLE 2 Diffusion data for lactose into heartwood of white fir Length of block = 3.14 cn ; R , = 14.00; Ro = 31.50 HOUXS
Rt
22.8 46.8 70.8 94.8 119.8
29.00 28.10 27.48 27.00 26.55
I
Ro- Rt
V
T
D, X 106
2.50 3.40 4.02 4.50 4.95
0.143 0.194 0,228 0.257 0.282
0,0205 0,0414 0.0615 0.0828 0.1062
0.248 0.244 0.240 0.240 0.244
TABLE 3 Effect of length of block o n diffusion coejicient of glycerol into white fir heartwood (a) BLOCK LENGTH
I
D,
x 105
Cm.
1.35 1.38 1.41 2.09 3.14
0.46 0.45 0.46 0.44 0.44
centric with it. Each figure in the table represents the average value of from six to twelve diffusion coefficients obtained from experiments on two to six samples of wood. It may be concluded from these data t,hat a reproducible hindered or nearly free diffusion, of the type required for estimation of the mechanical blocking effect, results when observations are made on the heartwoods of pine, cedar, hemlock, and fir. It is also indicated that the structure of the sapwood in these species is too coarse to give consistent and reproducible diffusion constants. The above data have been obtained with wood samples cut in the trans-
98
L. C. CADY AND J. W. WILLIAMS
verse direction. Diffusion into radial sections was also investigated and much lower diffusion constants resulted. Space does not permit the
I
,
TIME INTERVAL
1
2 3 4
TABLE 4 Egect of pore size i n determination of type of digusion Figures given are diffusion constants for urea, D , WHITE PIR HBARTWOOD (2) APPROACHES F R E E DIFFUSION
WHITE FIR
HEARTWOOD (3) HINDERED DIFFULION
0.34 X 0.36 x 0.34 X 0.35 X
10-6 10-5
,
10-5 10-6
0.64 X 0.66 x 10-5 0.65 X 0.63 X
WHITE FIR SAPWOOD (1) STIRRED DIFFUSION (SLOW STIRRING)
1.38 X 1.34 X 1.31 X 1.19 x
WHITE FIR SAPWOOD (1) STIRRED DIPFUSION (RAPID STIRRINO)
1.66 x 1.61 x 1.55 x 1.38 x
10-6 10-6 10-6
10-5
10-5 10-6 10-5 10-6
TABLE 5 Digusion data for wood samples cut in transverse section SOLUTE
WOOD
SAMPLES
D* x
TYPE OF DIBPUSION
105
1
Cedar Sw ( l ) . . ...................... Cedar Sw (1)........................
Lactose Glycerol
6 3
0.85-2.4 0.76-1.2
Cedar Hw ( 2 ) . . ,.................... Cedar Hw (2) .......................
Glycerol Lactose
5 3
0.43 0.20
App. free App. free
( 3 4 ...................... (3) ....................... (3) ....................... (3) .......................
Lactose Glycerol Lactose Urea
3 2 6 3
0.13 0.25 0.12 0.38
Hindered Hindered Hindered Hindered
Western henilock Sw.. . . . . . . . . . . . . . . . Glycerol Western hemlock Hw. . . . . . . . . . . . . . . . Lactose Western hemlock Hw.. .. . . . . . . Glycerol
2 2 3
0.264.93 0.18 0.43
Stirred App. free App. free
Lactose Glycerol
3 3 6
0 ,86-1.55 0.52-1.51 0.40-0.63
Stirred Stirred Stirred
White fir Hvv ( 2 ) . . ,. . . . . . . . . . . . . . . . . Urea White fir Hw ( 2 ) , . ,. . . . . . . . . . . . . . . . . Glycerol White fir Hw (2). . . . . . . . . . . . . . . . . . . . Lactose
3 6 4
0.67 0.44 0.22
App. free App. free App. free
White fir Hw (3). .. White fir Hw (3). . . . . . . . . . . . . .
3 3
0.30 0.36
Hindered Hindered
Cedar Cedar Cedar Cedar
Hw Hw Hw Hw
. . . . . . . . . . . . . . . . Urea White fir Sw (1). ...... White fir Sw (1). ....................
.
Glycerol Urea
Stirred Stirred
presentation and discussion of these data a t the present time. Purely tangential sections of required length could not be cut from the trees
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MOLECULAR DIFFUSION INTO WOOD
from which the sample blocks were taken. Several experiments with semi-tangential sections also gave much lower diffusion constants. IV. DISCUSSION O F RESULTS
In the experiments in which a hindered or nearly free diffusion took place we assume D,to be smaller than D, for two reasons. The first and more important reason is the effect of the mechanical blocking, the second is the additional resistance to motion due to the proximity of the pit membrane pore walls to the diffusing solute molecule. Values of the fractional open area A have been calculated by the use of equation 2. I n these TABLE 6 Fractional open area of transverse heartwood sections SPECIES
Western cedar (3). .................... Western cedar (3). .................... Western cedar (3). ....................
SOLUTE
A 8 De TIR ---
Glycerol Lactose Urea
0.25 0.12 0.38
0.05 0.10 0.04
0.70
0.32 0.32 0.32
Western cedar (3a).................... Lactose
0.13
0.10
0.70
0.36
Western cedar (2). .................... Western cedar (2). ....................
Glycerol Lactose
0.43 0.20
0.03 0.10
0.72
0.56 0.54
Western hemlock (Hw). . . . . . . . . . . . . . . . Glycerol Western hemlock (Hw). . . . . . . . . . . . . . . . Lactose
0.43
0.05
0.71
0.18
0.08
0.55 0.48
White fir (3) ........................... White fir (3) ...........................
Glycerol Urea
0.30 0.36
0.03 0.02
0.77
0.36 0.30
White fir (2) ........................... White fir (2). .......................... White fir ( 2 ) , . . ........................
Glycerol Lactose Urea
0.44 0.22 0.67
0.03 0.05 0.02
0.77
0.54 0.54 0.54
calculations CY is assumed to be zero and the pit membrane pore radii, based on Stamm’s values, are for Western red cedar, 8 mp, for Western hemlock, 12 mp, and for white fir, 15 mp. The values of A have been collected to form table 6. These values are shown by the points on figure 1. The values of A fall into two regions, one a t about 0.35 and the other at about 0.55, depending upon the distance from the center of the tree at which the sample was taken. Samples of heartwood taken a t some distance from the center (region 2) give blocking coefficients which are but slightly below those required by the Dumanski equation. The differences between observed values and values obtained by calculation with the
100
L. C. CADY AND J. W. WILLIAMS
Dumanski equation are probably due, in large measure, to the anisotropic character of the capillary spaces in the wood, and to aspirated tori. These samples are representative of the major area of the heartwood. Samples of heartwood taken from the center (region 3) have A values lying much below the expectation based upon the use of the Dumanski equation, and even below that required by the Buckingham relation. These low values are not surprising when it is realized that the percentage of aspirated tori is high at the center of the tree. Furthermore, the actual effective value of the radii of the pores of the pit membranes is probably smaller than the value actually used in the calculations. A reduction of pit membrane pore radius for red cedar from 8 mp to 4 mp would cause an increase in blocking of 0.06 unit. Further, it must be recognized that the blocking factor changes more from the center to the periphery of the tree than would be expected from density measurements alone. It is worthy of note that the data of table 6 are not inconsistent with rough estimates of the relative amounts of open and closed area of a wood section as determined by running a planimeter over photomicrographs of transverse wood sections. These estimates, made on photomicrographs which have been reproduced in articles by Ritter (12), indicate a fractional open area varying from 0.35 td 0.40. The data obtained, therefore, may be considered to indicate the essential correctness of the theoretical deductions of Dumanski for the calculation of the mechanical blocking factor in a diffusion experiment involving a porous solid. We are not prepared to say as to whether or not the deviation between experiment and theory can be completely accounted for on the basis of the considerations presented above, because the apparent diffusion constants may be affected by the particle size and other factors not yet taken into account. The matter is deserving of further experimental work and theoretical analysis. Finally, the data of this article are not without interest in connection with recent studies of Northrup and Anson (11) and of McBain (9, lo), in which the diffusion process has been caused to occur across thin porous membranes of alundum or glass powders, the idea being that the process would be greatly accelerated owing to the maintenance of a high concentration gradient, and a t the same time, troublesome convection currents would be avoided. As Northrup and Anson point out, the pores must be small enough to prevent convection currents in the liquid held in them and large enough to allow free diffusion of the particles or molecules of the solute. It is evident from our table 4 that there is, between the two extremes, such a favorable capillary pore size in some wood sections for the diffusion of solute molecules of radius comparable to that of urea. It is only reasonable to suppose that there can be found other membranes having pore sizes to permit free diffusion of any given solute molecule and at the same time prevent convection currents.
MOLECULAR DlFFUSION INTO WOOD
101
I n the method of Northrup and Anson a membrane is standardized against some solution, the diffusion constant of which is known, much after the fashion of the determination of the constant of a conductance cell. When the membrane constant for the diffusion apparatus with a particular diaphragm has been determined, it is used to obtain the diffusion coefficient for unknown substances. I n this way any effects due to what we have termed mechanical blocking are eliminated. Among other things this determination of membrane constant assumes invariable effective area of the pores. It would seem, therefore, that there still remains some uncertainty as to what effect, if any, there will be when the radius of the diffusing molecule is varied over such wide limits as has been the case in the investigations which have been carried out in this manner. At the present time we are inclined to agree with Kraemer (5), who writes, “This technic, however, combines the theoretical complications of osmotic pressure and free diffusion so that results obtained in this way for D,if presumed to be quantitative, can only be accepted as provisional until independent confirmation is obtained.” SUMMARY
1. Diffusion experiments in which the process is allowed to take place across the interface formed by a stirred liquid in contact with a gel have been extended to porous solids. The coefficients of diffusion at 25°C. of urea, lactose, and glycerol from aqueous solution into transverse sections of samples of white fir, Western hemlock, and Western red cedar wood have been determined. 2. From the data obtained it has been possible to distinguish three kinds of diffusion. They have been described as hindered diffusion, free diffusion, and stirred diffusion. Attention has been called to results of experiments which are typical of each. These data are of interest in connection with recent methods which have been proposed for the determination of the diffusion coefficient of a solute from its rate of passage through a thin porous membrane. 3. Fractional open areas for heartwood sections have been calculated by using a modified theory, when it could be shown that the diffusion constant was not influenced by the rate of stirring. Comparisons of the experimentally observed mechanical blocking factors with those calculated by the theoretical and empirical equations already existent in the literature have been made. REFERENCES (1) ARNOLD: Phil. M a g . 22, 755 (1911).
(2) FRIEDMAN: J. Am.Chem. SOC.62, 1311 (1930). AND KRAEMER: J. Am. Chem SOC. 62, 1295 (1930). (3) FRIEDMAN
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