tion. The data show that fractions 1 and 2 are more associated in methylene chloride than in tetrahydrofuran. The molecular weight of fraction 3 appears to be unaffected by these two solvents. That is, the degree of association among the components of fraction 3 is not significantly altered by one solvent relative to the other solvent. In general, the molecular-weight data of Table I11 suggest that molecular association is responsible for the GPC separation of certain compound types. The carboxylic acids of fraction 2 illustrate the ability of a specific compound type to undergo molecular association. Fraction 2 had a molecular weight of 619 in methylene chloride and 474 in tetrahydrofuran. The molecular weights of 619 and 474 represent equilibrium mixtures of monomers and dimers. Furthermore, these two weights suggest that methylene chloride shifts the equilibrium toward dimers, while tetrahydrofuran shifts the equilibrium toward monomers. Model compound studies reported by Helm and Petersen (17) have shown that carboxylic acids are present as an equilibrium mixture of monomers and dimers in methylene chloride. The equilibrium ratio of monomers and dimers as determined by infrared spectrometry was found to be concentration dependent as well as solvent dependent. The osmometric molecular weight of the carboxylic acid fraction determined in tetrahydrofuran solvent, i.e., 474, indicated that some association is still present because mass spectrometric data show the average molecular weight to be approximately 370. Additional evidence suggests that dimerization of carboxylic acids in methylene chloride is responsible for the observed GPC separation. First, infrared analysis indicated that both dimeric and monomeric acids were present when fraction 2 was dissolved in methylene chloride. The carbonyl absorption band of a nonassociated acid was observed at 1730 cm-’, while the carbonyl absorption band of a dimeric acid was observed at 1710 cm-1. Second, methyl ester derivatives of fraction 2 carboxylic acids were prepared using diazomethane, and the elution volumes of the esters compared with those of (17) R. V. Helm and J. C . Petersen, ANAL.CHEM., 40, 1100 (1968).
the carboxylic acids. The esters had elution volumes greater than those of the carboxylic acids, indicating that the molecular volumes of the ester derivatives were smaller than those of the carboxylic acids. Although carboxylic acid monomers and dimers are known to be present as an equilibrium mixture in methylene chloride, the monomer-dimer ratio present in the GPC column is difficult to determine. Nevertheless, because the monomerdimer equilibrium is a dynamic process, a separation of carboxylic acids from other materials can take place. The average size of associated molecules in a monomer-dimer mixture would be larger than that of molecules which do not associate. CONCLUSIONS
Gel permeation chromatography has been found to be a useful tool for quickly separating the components of a petroleum acid concentrate. Molecular weight, infrared, and elution volume data indicate that molecular association of compound types is responsible for the separation. Carboxylic acids obtained using gel permeation chromatography are essentially free of phenolic and nitrogen-containing compounds. GPC may find general application as a method to be used for isolating compounds which selectively associate. ACKNOWLEDGMENT
The authors thank H. H. Oelert of the University of Clausthal, Clausthal-Zellerfeld, Germany, for his inspiration and ideas. RECEIVED for review October 5, 1970. Accepted February 3, 1971. Work presented in this report was done under a cooperative agreement between the Bureau of Mines, U. S. Department of the Interior, and the American Petroleum Institute as part of Research Project 60. Presented at the 160th National Meeting, American Chemical Society, Chicago, Ill., September 1970. Mention of specific brand names or models of equipment is made for identification only and does not imply endorsement by the Bureau of Mines.
Wet Weights of Ion Exchange Resin Beads by Centrifugation Gordon H. Fricke and Donald Rosenthal Department of Chemistry, and Institute of Colloid and Surface Science, Clarkson College of Technology, Potsdam, N . Y . 13676 George A. Welford Health and Safety Laboratory, U . S . Atomic Energy Commission, New York, N . Y . 10014
A centrifugation method of determining the wet weight of ion exchange resin beads without surface liquid i s proposed. The volume per cent of liquid remaining on the surface of the centrifuged beads at the plateau centrifugal force is found of volume per cent liquid to depend on the relative disDersion of the size distribution Of the beads. Surface sulfonated Copolymer beads were preparedm These beads and glass beads were employed to test this method.
beads if care is not taken when the beads are returned to their orieinal condition Therefore, it is desirable to have a method of determining the wet weight of ion exchange resin beads under the conditions in which they are used exDerimentallv. There are advantages to determining the wet rather &n just the dry weight. -The wet weight can be used to calculate the molality or molarity in the resin phase. In this study. surface sulfonated copolymer beads and - glass beads, materials with different surface characteristics, _
THEDRY WEIGHT of ion exchange resins is frequently used to express the exchange capacity or the concentration of species in the resin phase. The method of obtaining dry weights is time consuming and may lead to cracking of the 648
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
I
(I) Discussion with D. H. Freeman, National Bureau of Standards, Washington, D. C.
have been used to help determine wet weights of ion exchange resin beads. The procedure involves determination of the volume of liquid remaining on these materials following centrifugation to a constant weight. It is assumed that similar results will be obtained for ion exchange resin beads which have the same relative shape of the size distribution. After initial size distributions and density measurements have been made on a large batch of material, the centrifugation-weighing procedure may be performed relatively rapidly. Centrifuged wet weights are compared with the conventional dry weights to show the constancy of the procedure. Contrifugation of the wet ion exchange resin beads to a constant weight in a tube with a fritted disk has been suggested by a number of investigators (2-5). The present article extends the work of these authors to show that a plateau exists, for the various beads studied, when the volume or the volume per cent of liquid on the surface of glass and surface sulfonated copolymer beads is plotted US. centrifugal force. The liquid remaining on the beads, at this plateau of the curve, is a constant volume for a series of solutions which have different densities, viscosities, and surface tensions. It is shown that the liquid remaining on the surface of the beads is related to the spread of the size distribution of the beads and that the method of centrifugation can be used in place of vacuum drying as a rapid and accurate method of determining the weight of ion exchange resin beads. EXPERIMENTAL
Materials. Glass beads, which had a high degree of sphericity, were obtained from Microbeads Division, Cataphote Corporation. The 8 divinylbenzene-polystyrene copolymer beads were generously supplied by Dow Chemical Company. The 50-60 mesh copolymer beads were resieved to narrow the size distribution by first placing the beads in a 0.1M NaCl solution. The solution was immersed in an ultrasonic bath (Disontegrator, Ultrasonic Industries, Inc.). The beads were then separated using standard sieves and divinylbenzene-polystyrene codistilled water. The 8 polymer beads and sulfonated resin beads were obtained from Ionac Chemical Company. The other ion exchange materials used in this study were Dowex 50W-X8 beads reprocessed, sized, and supplied by Bio-Rad Laboratories. Surface Sulfonation of Copolymer Beads. The effect of sulfuric acid concentration upon the depth of sulfonation of 1W 200 mesh Dow copolymer beads in a 25 "C constant temperature box was determined initially. For these tests, 12 grams of the material were used with 100 ml of the appropriate concentration of sulfuric acid. The mixture was stirred with a magnetic stirrer for 48 hours in a flask which was covered with Parafilm. After the preliminary studies, 500 grams of the copolymer material were stirred with a magnetic stirrer in a 4-liter flask with 3 liters of 17.4M H2S04for 48 hours at 25°C. Another method has been described by Pepper, et. a1 (3), who suggested using sulfur trioxide vapor at 0 "C to surface sulfonate the copolymer beads. The method presented in this paper is simpler and less hazardous. To determine the exchange capacity of the surface sulfonated beads, the material, initially in the hydrogen form, was completely converted to the sodium form with a sodium
z
z
(2) H. P. Gregor, K. M. Held, and J. Bellin, ANAL.CHEM., 23, 620 (1951). (3) K. W. Pepper, D. Reichenberg, and D. K. Hale, J. Chem. SOC., 1952, 3129. (4) K. W. Pepper, J. Appl. Chem., 1, 124 (1951). (5) G. Scatchard and N. J. Anderson, J. Phys. Chem., 65, 1536 (1961).
hydroxide solution which contained sufficient sodium-22 to give approximately 105 counts per minute in a 10.0-ml aliquot. Radiochemical isotope dilution procedures were used to determine the capacity of the surface sulfonated beads from the measured activity before and after equilibration of the sodium hydroxide solution with the surface sulfonated copolymer beads. Blank samples were prepared with the sodium hydroxide solution containing the sodium-22 and unsulfonated copolymer beads. Centrifugation. Samples of each of the materials were placed in a special glass tube, 1.7 cm in diameter and 4.7 cm in height, with a fine porosity fritted disk sealed in the bottom. These tubes were supported by thick walled cylinders of glass and were placed inside high impact polyethylene centrifuge tubes. The centrifuge tubes were covered with Parafilm during the centrifugation. When the samples, initially wetted with an excess of liquid, are centrifuged, the liquid goes through the fritted disk and is collected in the bottom of the centrifuge tube. A study was made to determine the time of centrifugation which would give a minimum weight of liquid on the sample at any particular force. Samples were centrifuged from 5 minutes to 120 minutes in no particular order of time. Between each centrifugation, the samples were rewetted with an excess of liquid. For the 50-60 mesh beads, it was determined that a maximum of 10 minutes was necessary for constant weight down to approximately 100 G . As much as 30 minutes were needed for beads of 230-325 mesh. When the tubes were first used, it was found necessary to allow the fritted disk to be wetted and centrifuged a few times before the first weights were recorded. The materials used in this research were studied at centrifugal forces from 100 G to 1200 G. The samples were centrifuged in no particular order of forces and were rewetted with an excess of liquid between runs. The amount of liquid remaining on the fine porosity fritted disks was found to be constant for the range of centrifugal forces used in this study. Earlier investigations were conducted with medium and coarse porosity fritted disks. The amount of liquid remaining on these disks was found to be dependent on the centrifugal force. After a sample was centrifuged at a particular force, the amount of liquid on the glass beads or the surface sulfonated copolymer beads was obtained by weighing the sample in the tube and subtracting the weight of the dry tube, the weight of the dry sample, and the weight of the liquid on the fritted disk. Size Distribution. The various particles used in this research were photographed with a Nikon Model S microscope at a number of convenient magnifications using Kodak Panatomic-X film. The negatives were enlarged and printed on either a single weight Medalist F-4 paper or Kodak Polycontrast-N single weight paper using Contrast Filter No. 4. This procedure gives high contrast between the black and white features of the film. At irregular intervals on each film, a micrometer scale was photographed. The micrometer negatives were enlarged at the same time as the negatives of the beads and were used to determine the exact magnification. A Carl Zeiss Particle Size Analyzer TGZ-3 was used for determination of the sizes of the particles on 8- or 10-inch prints. This instrument has 48 categories of sizes into which the actual sizes of the particles on the photographs can be placed. The absolute sizes range from 1.22 mm to 27.71 mm with center intervals evenly spaced along the range. It is necessary to enlarge photographs of each particular material and the corresponding micrometer scales, in such a way that the largest particles on the prints d o not exceed 27.71 mm. The instrument is particularly well suited for spherical or circular particles since it uses an adjustable circular light beam to measure the size. Densities of Solid Particles. The densities of all beads are needed for the determination of the volume per cent of liquid ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
649
i1.50
B1,.
50 0
is the exchange capacity of a fully sulfonated bead in meq/g of dry material and mi is the exchange capacity of the surface sulfonated bead in meq/g of dry material then
where Vi is the volume of a spherical bead and vi is the volume of the shell which is assumed to be sulfonated. The volume of ui is calculated as
400
m 0
E 300 v)
0
a z
d 20 0
If it is assumed the material is surface sulfonated when the capacity is to times the capacity of the fully sulfonated material, then X
where and 7 are the mean squared and mean cubed radii of the beads and are calculated from -
rk = Z f i r t
(5)
where k = 2 or 3 and fi is the fraction of the number of beads having radius ri (actually r t - A to r i + A where A is one half the interval between ri and r,+J. Equations 1 to 4 were derived for a model which neglects the possibility that the copolymer beads may have pores which are exposed to the sulfuric acid and sulfonated, so that a uniform sheath would not be formed. If the model is appropriate, the depth of surface sulfonation may be calculated from Equation 4. Figure 1 gives the ratio of capacities (m/M> and depth of sulfonation in 48 hours at 25 “C for various concentrations of sulfuric acid on one batch of copolymer beads. Table I shows the depth of penetration of the sulfuric acid for a number of different samples using 17.4MHzS04at 25 OC for 48 hours. The difference in depth of sulfonation of the materials in Table I is of a similar magnitude to the differences observed when three samples of the 50-60 mesh copolymer beads were surface sulfonated simultan5ously (standard deviation for an individual sample was 9.0 A). Thus all of the beads sulfonate to approximately the same distance from the surface independent of the actual size of the particles. These results are consistant with the assumptions made in deriving Equation 4. The ratio of the capacities would be indicative of the total surface involved and would be expected to be less for the larger beads (smaller mesh size). This is observed for the 8 DVB materials. Pure metadivinylbenzene-polystyrene copolymer beads (8 crosslinked), obtained from Ionac Corporation, were surface sulfonated for the centrifuga-
Material 50-60 mesh resieved Dow polystyrene-8 DVB 100-200 mesh resieved Dow polystyrene-8 DVB 100-200 mesh resieved Dow polystyrene-8 DVB 100-200 mesh Ionac Polystyrene-8 m-DVB Re1 std dev,
x
z
Table I. Depth of Sulfonation 17.4M H2S04, 25 "C, 48 Hours Weight of meg per gram sample of dry beads sulfonated, Average bead radius ?,p in 48 hours grams 12 112 0.604 X loda
12
24.4
1.28 x 10-3
500
24.4
1.27 x 10-3
12
35.6
1.51 X 10-8
3
0.7
z
Ratio of capacities, mlM 1.14 x 10-4
x 2.39 x 2.85 x 2.42
Depth of sulfoqation, A
44
10-4
36
10-4
35
10-4
45 25
0.7
Table 11. Characteristics of Materials Investigated
Material Glass Glass Glass Ionac SSCb+ DOWSSCbsd
Designated Magnificamesh tion 60-80 79.2 120-170 113 230-325 246 100-200 115 50-60 90.8 Resieved 115 100-200 20-50 25.0 101-200 86.5 116 200-400 116 100-200
-
-
r9p
96.0 40.7 14.7 35.6 112
r* X P2
9.94 1.81 0.256 1.51 12.8
-
r3 x P8
106 8.45 0.502 7.16 148
Re1 std dev of the Vol % Ratio" = radius, liquid on dry weight/ Shape of distribution Equation 7 surface wet weight ... Bimodal 0.277 4.8Y 4.996 ... Bimodal 0.303 ... 5.3lC Bimodal 0.437 5.26~ ... Bimodal 0.437 ... 4. 316 Monomodal 0.183
Reverse J DOWSSCb,d 0.854 3.77 24.4 Dowex 50W-X8d Monomodal 104 3690 310 Monomodal Dowex 50W-X8d 3.86 25.4 61 . O Dowex 50W-X8d 8.46 Monomodal 1.86 42.4 9.50 Ionac 94.1 1.73 Bimodal 37.0 sulfonate& 100-200 1.41 6.97 Ionac 68.4 33.2 Bimodal 115 Sulfonated. 10.7 1.86 Bimoda1 Ionac 39.0 100-200 89.5 38.3 sulfonatedc 89.5 11.5 1.94 Ionac 25.3 Bimodal 100-200 39.0 sulfonatedc 4 0.2 4 3 Re1 std dev, a Resin beads in H+form. b SSC = surface sulfonated copolymer. Ionac materials are sulfonated poly(styrene-m-divinylbenzene); photographed in Na+ form in water. Dow materials are sulfonated poly(styrene-m and p-divinyl benzene). e Experimentally determined. Calculated by Equation 9.
x z x
x
tion studies. The fully sulfonated resin is known to have similar properties to the fully sulfonated Dowex 50W-X8 material as shown by Wiley et al. (7). Size Distributions. Table I1 gives the mean values calculated by Equation 5 for the materials presented in this report. All of these materials unless otherwise noted, were photographed in 0.10M NaC1. A minimum of 3000 particles was sized in each case. A typical particle size distribution is presented in Figure 2. The size of the sulfonated ion exchange resin beads changes when they are placed in contact with different concentrations of electrolyte solutions. Freeman and Scatchard (8) have investigated a number of resins in contact with various electrolyte solutions by accurately measuring the sizes of a few beads in different solutions. To test the sizing procedure used in this research, Dowex 50W-X8 (100-200 mesh) beads were photographed in solutions of different sodium chloride concentration. The experiment was repeated twice, eighteen (7) R. H. Wiley, J. K. Allen, S. P. Chang, K. E. Musselman, and T. K. Venkatachalam,J. Phys. Chem., 68,1776 (1964). (8) D. H. Freeman and G. Scatchard, ibid., 69, 70 (1965).
...
0.662 0.284 0.174 0.187 0.516
6.196 (4.79)f (4.39)f (4.43)' (5.64)f
0.525 0.525 0.523 0.480
0.522
( 5 .66)f
0.539
0.517
(5.64)'
0.754
0.528
(5.68)f
0.825
3
5
0.1
months apart. The sizing in each experiment was performed by a different worker. Figure 3 shows the volume of the particles in the salt solutions relative to the volume in water as a function of the sodium chloride concentration. Centrifugation. It was first established that the volume of liquid on the disks was constant over the entire range of forces used in this study for solutions which have different densities, viscosities, and surface tensions. Water, 3M NaC1, 5M NaCI, 3 M HCl, and 10M LiCl were centrifuged in the tubes. In each case approximately 0.12 ml of liquid remained after centrifugation. The 90% confidence limits for individual values of liquid centrifuged at forces corresponding to the plateau (100 G to 1200 G) was about 0.0008 ml. An estimate was made of the total volume of the pores in the fine porosity fritted disks by placing water on the eight disks until they appeared to be wet on the top and bottom. The tubes were then weighed. The value obtained for the total pore volume by this method was less than 3% above the volume of liquid on each disk as obtained by centrifugation with various liquids. Therefore, when an excess of liquid is placed on the fine porosity fritted disks and the tubes are centrifuged at any force used in this study, a constant ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
651
0.06
OQ5
0.04
85
0.03
a
L 0.02
0.01
0 "
I
0.00
20
't
I I 40 60 RADIUS IN MICRONS
100
80
Figure 2. Fraction of surface sulfonated Ionac pol styrene - rn divinylbenzene) copolymer beads in each of the size distribution categories of the Zeiss particle size analyzer us. the radius of the beads in microns
-
6213 beads sized,
7 =
35.6
p,
RSD r
=
200
600
400
800
1000
G
Figure 4. Volume liquid (0.10N NaCl) on glass beads, P, us. centrifugal force, G
0.437
0 60-80 mesh, average of four samples(use upper right hand
scale) 0 120-170 mesh, average of four samples (use lowerright hand scale) 0 230-325 mesh, average of six samples(use left hand scale)
1.000
beads is hydrophobic and the beads are not completely wetted. The amount of liquid remaining at any one force was found not to be constant. The volume per cent of liquid on the sample is calculated as
0 950
I .
R
0.900
where V Lis the volume of liquid remaining on the surface of the sample and Vs is the volume of the sample. This means that ( V L V s ) is the total volume of the material with the surface liquid. It may be convenient in some cases to determine the ratio VL/Vs directly instead of P (9). The volume per cent liquid on the surface of the glass beads and on the surface sulfonated copolymer beads is plotted us. the centrifugal force in Figure 4 and Figure 5, respectively. The volume of liquid on the surface of the ion exchange resin beads is not known; this is what will be determined. Therefore, in Figure 6 the weight fraction rather than volume per cent is plotted us. the centrifugal force. The weight fraction is the total weight of resin and the surface liquid at any point on the curve divided by the average total weight on the plateau. A loss of liquid is observed for the 20-50 mesh samples as the force is increased. No such loss is observed for the smaller beads at forces up to 1400 G. This is the maximum force which the glass tubes with fritted disks can withstand. At higher forces, a similar loss in weight for the smaller beads is to be expected. To show that the plotting of volume per cent is correct, four samples of surface sulfonated Ionac copolymer beads were centrifuged with six solutions (water, 0.1, 3, and 5M NaC1, 3M HC1, and 10M LiC1) which have different densities,
+
0.850
0 800
I
I
I
I
I
I
1
100
I00
200
300
400
500
600
MOLALITY OF NoCl
Figure 3. Volume of Dowex 5OW-X8 Resin (100-200 mesh) relative to volume in pure water, R, in various concentrations of NaCl solutions A Data from Freeman and Scatchard (9) 0 This study, first experiment 0 This study, second experiment
volume of liquid remains on the fritted disks. This is the volume which completely fills the pores of the disk. For the glass beads and the surface sulfonated copolymer beads, there was a region of forces over which the volume of liquid or volume per cent of liquid remaining on each sample was constant. The surface of the unsulfonated copolymer 652
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, M A Y 1971
(9) D. H. Freeman, J . Phys. Chem., 64, 1048 (1960).
As another means of evaluating the centrifugation procedure, the centrifuged wet weights at the plateau (Le., with the surface liquid) were compared with the dry weights obtained by drying the samples over PzOs under vacuum at 40 "C until a constant weight was obtained. It took a minimum of eight days to reach a constant dry weight. The average results of replicate experiments are given in Table 11. The Dowex resins and the first Ionac resin are fully sulfonated while the last three Ionac resins are partially sulfonated. The results of the replicate experiments agree to within a few parts per thousand. Thus, the ratio of dry weight to wet weight is constant for a particular batch of resin, but can be different for different resins. Attempts to dry the resin more rapidly at an elevated temperature (115 to 130 "C) resulted in additional weight loss for the hydrogen form of the resin. This is believed to be due to decomposition of the resin. If the resin is converted to the sodium form, the same dry weight was obtained by drying for eight days at 40 "C as was obtained in less than eight hours at 115 "C. Prolonged drying at 115 "C appeared to result in a small amount of decomposition of the sodium form of the resin.
90
! \ 70t \
-ZOO
400
800
600
i
30
1000
DISCUSSION When beads are centrifuged to the plateau region of volume per cent liquid US. force, it is believed that the major portion of the liquid remaining on the beads is in the capillaries created by the contacts of the beads. In genera1,the broader (or more disperse) the size distribution of the particles, the more small capillaries there would be since the smaller particles could fall into spaces which larger particles could not occupy. The narrower the size distribution, the fewer small capillaries there would be. The standard deviation and variance were calculated to represent the spread of the size distribution. To relate beads of one size to beads of another completely different size which might have the same relative spread of sizes, the relative standard deviation and the relative variance were used. These values are calculated from the size distribution data using Equations 7 and 8.
1200
G
Figure 5. Volume liquid (0.1N NaCI) on surface sulfonated copolymer beads, P,us. centrifugal force, G 0 100-200 mesh Ionac beads, average of three samples (use upper right hand scale) n 50-60 mesh resieved Dow beads, average of four samples (use lower right hand scale) 0 100-200 mesh Dow beads, average of three samples (use left hand scale)
viscosities, and surface tensions. In all cases, once the plateau was reached, the weight remained constant over a range of forces. When the statistical results obtained for each sample were compared with the results obtained for each solution, no pattern was observed. This suggests that the same volume per cent of liquid was obtained in water and each of the solutions to within the experimental uncertainty. The average value for the twenty-four experiments was 5.26%. The 90% confidence limits for the individual results were +0.14%. This is approximately 2% of the total volume per cent. This error can be explained by a one part per thousand error in the weight of the sample with the surface liquid.
1.030
Figure 6. Weight fraction of liquid (0.1N NaCl) on Dowex 50W-X8 resins, F, us. centrifugal force, G 1.020
0 20-50 mesh, average of four samples (use upper 0 0
right hand scale) 100-200 mesh, average of eight samples (use lower right hand scale) 200-400 mesh, average of four samples (use left hand scale)
F
1.010
1.000
I
I
I
I
I
I
I
200
400
600
800
1000
1200
1400
G
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
653
-
Table 111. Linear Least Squares Fitted Equations for Volume Per Cent, P, us. Various Factors, F F
P=u+bF b 3.658 1.664 0.984 4.137 1.020 0.386 - 8 . 8 8 1 X 10-6 -7.340 x 10-7 -0.404 -0.085
U
3.750 4.031 4.197 4.448 4.575 4.666 5.553 5.487 5.572 5.561
Re1 std dev r Re1 std dev r 2 Re1 std dev r3 Re1 variance r Re1 variance r z Re1 variance r3 rz r3
dK
PZ
T’
I
I
I
I
11
6.0
(SEE LEGEND)
SD, 0.114 0.125 0.130 0.114 0.121 0.133 0.246 0.232 0.363 0.358
SDb 0.277 0.166 0.115 0.526 0.156 0.071 3.681 X 10-6 3 . 1 1 8 X 10-7 0.244 0.051
SDP 0.104 0.136 0.159 0.171 0.203 0.240 0.443 0.450 0.565 0.565
presented in Table 111. Calculations which included errors in the abscissa values as well as errors in per cent liquid were performed (IO). SDp differed by less than 1 % from the results presented in Table 111. Examination of these results indicates that the dispersion factor of the size distribution which best represents the data in this research is the relative standard deviation of the radius.
P
=
3.75
+ 3.66 (RSD r)
(9)
where P is the volume per cent of liquid. The volume per cent of liquid does not correlate as well with and 3. r 2 is related to the surface area of the beads and 2 is related to the volume of the beads. The two standard shape estimators of a distribution, (measure of relative skewness), and p2(measure of relative kurtosis), which are calculated from the central moments of the distribution ( I I ) , were not linearly related to the volume per cent of liquid. Figure 7 shows the volume per cent of liquid on the six samples, P,us. the relative standard deviation of the radius. Each volume per cent plotted represents an average of at least twelve measurements. The wider the spread of the size distribution, the larger is the volume per cent of liquid held by the sample, presumably in the small capillaries. The size distributions for the materials corresponding to points E and F i n Figure 7 can be seen from Micrograph 1 and Micrograph 2. The first micrograph is the material with the widest spread of size distribution used in this research. Disregarding obvious sizing problems on this material, it can be seen that there is a very wide range of sizes of particles. The second micrograph is of a material which was specially resieved in this research to obtain a relatively narrow size distribution. Since the surface sulfonated copolymer beads and the glass beads are relatively impenetrable to liquid and have different surface properties and since all sizes and size distributions of these materials lie on the line of volume per cent us. relative standard deviation of the radius of the size distribution, then it is assumed that the ion exchange resin beads, which have surface properties similar to the surface sulfonated copolymer beads, also lie on the line. The size distribution of the ion exchange resin beads is obtained and the spread of the distribution is calculated in Equation 7 with k = 1. Then from Equation 9 the volume per cent of liquid on the surface of the beads, as centrifuged
>
5.5
P
dz
5.0
1
-= /
4.5
020
030
040 RSDr
050
060
Figure 7. Volume % of liquid at the plateau of centrifugation, P, us. relative standard deviation of the radius, RSD r. The open circles are the experimental average values A . 60-80 mesh glass beads B . 120-170 mesh glass beads C. 230-325 mesh glass beads
D. 100-200 mesh surface sulfonated Ionac copolymer beads E. 50-60 mesh surface sulfonated resieved Dow copolymer beads F. 100-200 mesh surface sulfonated Dow copolymer beads (as supplied) .E Range of errors for an individual measurement at the W % confidence level
where k = 1 , 2, or 3 and 7 is calculated from Equation 5. These quantities were calculated for each size distribution of each material used in the present study. P is the volume per cent of liquid on the surface of each of the six materials after centrifugation to the plateau region. The P values were fitted to equations linear in the quantities calculated from Equations 7 and 8. A least squares procedure which assumed no error in abscissa values was employed. The results are 654
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
(10) A. Madansky, “Journal of American Statistical Association,” Vol. 54, American Statistical Association, Washington, D. C., 1959, p 173. (11) G. J. Hahn and S. S. Shapiro, “Statistical Models in Engineering,” John Wiley and Sons, Inc., New York, N. Y.,1967.
- Micrograph 1. 100-200 mesh surface sulfonated Dow polystyrene4 % divinylhenzene copolymer heads i =
at the plateau, is determined. Table 11 gives the results for the Dowex 50W-X8 and Ionac ion exchange resin heads studied. It would be possible for the porous resin heads to contain capillaries which are larger than some of those created by the contacts of the beads. In this case, there would he a greater negative slope of the.line of volume per cent liquid >c---LL--"":
- , : ~ . . : J : .....I,-
Micrograph 2. 5 0 6 0 mesh resieved surface sulfonated D O ~ polystyrene-8 % divinylhenzene cop01 i=llZp,RSDr=I
24.4 p, RSD r = 0.66
~ ~ . *
~~
__^_ ^"
IA.oarn""
us. 1orceasrneuqluuisp~L.uiiuiir u ~ ~ s a u p u l r u A.
lLbLIB-LL,
Patel, and Bucbanan (12) mentioned that the decrease in weight of the 2% crosslinked resin observed by Scatchard and Anderson (5) above 650 G may possibly be due to a loss of internal liquid from the resin beads. There appears to be a greater loss of liquid from the 8% crosslinked resin beads than from the glass beads or from the surface sulfonated copolymer beads (see Fgures 4 and 6). I t is believed that at less than 1000 G the loss is not si@pnifcant. The loss could be somewhat greater for 2% cros!$linked resin which *,. *n would have larger pores. The loss of liqum n o m ma LG-JU mesh ion exchange - beads is believed to ht: due to the fact that these beads are quite large in cornpali s ,on with the other materials used and have larger capillarier1 at the contacts .PAL. L-->- . . . L : L a.,.*.. --_*.."+I 01 Lnc "CdUS WIILU, W V U l U GlL'IJLJ L,' fOLU,*. For the materials studied, the volume per cent of liquid on the beads is relatively independent of the electrolyte solution, ie., its nature and concentration. Also, if the method of determining volume per cent is to he generally applicable, the relative standard deviation of the radius must be independent of the electrolyte solution. Sice the size of the resin beads will be different at different electrolyte concentrations. the standard deviation of the radius must change pr,oportionately if the relative standard deviation is to remaiu1 constant. This was checked for 100-200 mesh :~~ _
