1777
Anal. Chem. 1984, 56, 1777-1781
syndiotactic and isotactic isomers (first two peaks in each oligomer packet of Figure 7) decrease steadily with increasing oligomer length, until only heterotactic isomers are observed in oligomers longer than decamer.
CONCLUSIONS The marked differences between localizing and nonlocalking B solvents can be applied to specific polymer problems. Molecular weight distributions can be obtained by using THF (as demonstrated in ref 10)or ethyl acetate gradients without complications arising from tadicity or end-group differences. Quantitation of molecular weight distributions must be approached cautiously, however, because large amounts of sample and steep solvent gradients may lead to incomplete sample elution. It is presumed that in both localizing-solvent examples, polystyrene oligomers do not have a preferred adsorption configuration because of the inability of aromatic rings to weakly localize. Preferred adsorption configuration with nonlocalizing solvents such as dichloromethane produces isomeric fine structure and effectively separates oligomers according to molecular weight, stereochemistry, and chemical compositional differences that may typically arise from endgroup differences or comonomers. This adsorption mode is best applied to oligomer problems that require more information than a molecular weight distribution. ACKNOWLEDGMENT We thank J. Uebel for his assistance in the characterization of stereoisomers by NMR and E. Otocka and D. Wonnacott for their helpful comments in the preparation of this manuscript. Registry No. Polystyrene (homopolymer),9003-53-6; n-hexane, 110-54-3; THF, 109-99-9; ethyl acetate, 141-78-6; dichloromethane, 75-09-2.
LITERATURE CITED (1) Sato, H.; Saito, K.; Miyashtta, K.; Tanaka, Y . Makromol. Chem. 1981, 782, 2259. (2) Fujishige, S.;Ando, I. Makromo/. Chem. 1978, 777, 2195. (3) Fujishige, S.; Ohguri, N. Makromol. Chem. 1975, 178, 233. (4) Kiesper, E.; Hartmann, W. J . Polym. Sci., Po/ym. Len. Ed. 1977, 75, 707. (5) Klesper, E.; Hartmann, W. J . Polym. Sci., Polym. Left. Ed. 1977, 75, 9. (6)Lewis, J. J.; Rogers, L. B.; Pauls. R. E. J. Chromatcgr. 1983, 284, 339. (7) Larmann, J. P.; DeStefano, J. J.; Goidberg, A. P.; Stout, R. W.; Snyder, L. R.; Stadalius, M. A. J. Chromatogr. 1983, 255, 183. (8) Lattimer, R. P.; Harmon, D. J.; Welch, K. R. Anal. Chem. 1979, 57, 1293. (9) Eigert, K. F.; Henschei, R.; Schorn, H.; Kosfeld, R. Polym. Bull. 1881, 4, 105. (10) Curtis, M. A.; Webb, J. W.; Warren, D. C.; Brandt, V. 0.; Gerberich, F. G.; Raut, K. B.; Rogers, L. 8. Sep. Sci. 1980, 75, 1413. (11) Sackett. P. H.; Hannah, R. W.; Slavin, W. Chromatographie 1978, 7 1 , 834. (12) Tennikov, M. 6.; Nefyedov, P. P. Polym. Sci. USSR (Engl. Trans/.) 1978, 22, 513. (13) Rosen, L., Pressure Chemicals, private communication, March 1982. (14) Snyder, L. R.; Giajch, J. L.; Kirkland, J. J. J. Chromatcgr. 1981, 278,
---.
9QQ
(15) Hara, S.;Fujii, M.; Hirasawa, M.; Miyamoto, S. J. Chromatogr. 1979, 749, 143. (16) Hara, S.; Ohsawa, A.; Dobashi, A. J . Liq. Chromatogr. 1981, 4 . 409. (17) Snyder, L. R.; Glajch, J. L. J . Chromatogr. 1982, 248, 165. (18) Snyder, L. R.; Kirkland, J. J. "Introduction to Modern Liquid Chromatography"; Wiley: New York, 1979; Chapter 16. (19) Snyder, L. R. J . Chromatogr. 1985, 20, 463. (20) Snyder, L. R. "Principles of Adsorption Chromatography"; Marcel Dekker: New York, 1968. (21) Snyder, L. R. J. Chromatogr. 1983, 7 7 , 195. (22) Snyder, L. R. J . Chromatogr. 1982, 245, 165. (23) Snyder, L. R. High-Perform. Llq. Chrom8togr. 1983, 3 , 157. (24) Snyder, L. R.; Giajch, J. L.; Kirkland, J. J. J . Chromatogr. 1981, 278, 299. (25) Jasse, B.; Laupretre, F.; Monnerie, L. Makromol. Chem. 1977, 178, 1987.
RECEIVED for review April 21,1983. Resubmitted February 6,1984. Accepted April 19,1984.
Liquid Chromatographic Retention of Polystyrene Oligomers Thomas H. Mourey Research Laboratories, Eastman Kodak Company, Rochester, New York 14650
The adsorption chromatography of anlonlcally and catlonlcally prepared polystyrene ollgomers was lnvestlgated on 8-nm porediameter, 5-pm slllca wlth n-hexane/dlchloromethane eluents. Endgroup dlfferences between the two samples produced slgntflcant differences In the retentlon of oligomers that are equlvalent In length. Measured adsorption energles and occupatlonal areas of ollgomers 2-14 lndlcate tilted repeat-unlt/adsorbent contact, whlch Is a result of chaln stlffness. Methylene backborn, carbon atoms In ollgomers longer than pentamer make only mlnor contrlbutlons to the adsorp tlon process, as demonstrated by greater adsorptlon energy per unlt of occupled adsorbent surface area for these ollgomers than Is calculated for planar solute Conformation on the slllca surface.
The solvent-displacement model, originally developed for the adsorption chromatography of small organic molecules (1-3), adequately explains the effects of solvents on the se0003-2700/84/0356-1777$01.50/0
lectivity of oligostyrene stereoisomer separations (4) without considering in detail the effects of oligomer length and structural complexity on the adsorption. This paper defines the fundamentals of a potentially practical approach to the separation and analysis of homologues such as polystyrene oligomers and testa the adsorption theory for small-molecule separations when applied to large molecules. It focuses, in particular, on the adsorbed solute conformation and its influence on chromatographic retention. A general expression for the chromatographic distribution coefficient K of a polystyrene oligomer can be written as log K = r
log
v, + 4CQ"r +
r &"e,
+ Q",, - d C a r + a,, + a,JI
(1) where Q".,Q",,, and Q",,are the standard adsorption potentials for adsorbed repeat units r and end groups e, and e2, respectively, 'ab is the mobile-phase solvent strength, and a,, a,,, and aszare the molecular areas of adsorption for adsorbed repeat units rand the oligomer end groups el and e2. Standard 0 1984 American Chemical Society
1778
ANALYTICAL CHEMISTRY, VOL. 56, NO. 11, SEPTEMBER 1984
Table I. Anionically Polymerized PS-800,Distribution Coefficients K for n -Hexane/Dichloromethane Isocratic Elution €ab
N
0.11
0.14
0.16
0.18
0.20
0.21
0.22
0.24
0.25
2 3 4 5 6 7 8 9 10 11 12 13 14
1.97 5.32 12.13 26.23
1.26 2.81 5.48 10.39 19.05 34.38
0.92 1.82 3.17 6.81 8.85 14.06 23.12 37.62
0.65 1.23 2.01 3.15 4.76 7.12 10.86 16.05 23.98 35.73 51.75
0.44 0.79 3.31 2.10 2.77 3.89 5.50 7.68 10.49 13.98 19.90
0.34 0.63 0.93 1.26 1.84 2.45 3.21 4.27 5.56 7.31 9.51 12.47 16.26
0.33 0.50 0.73 0.94 1.22 1.57 2.03 2.46 3.18 3.79 4.64 5.71 7.09
0.20 0.34 0.49 0.65 0.83 1.00 1.18 1.55 1.85 2.17 2.66 3.10 3.82
0.16 0.22 0.36 0.50 0.65 0.79 0.93 1.02 1.11 1.42 1.69 1.98 2.26
Table 11. Cationically Polymerized Oligomers, Distribution Coefficients K for n -Hexane/Dichloromethane Isocratic Elution %ab
N
0.11
0.14
0.16
0.18
0.20
0.21
0.22
0.24
0.25
2 3 4 5 6 7 8 9 10
2.80 7.86 18.44 42.82
1.95 4.56 9.08 17.98 35.15
1.14 2.73 4.84 8.54 14.21 23.72
1.05 1.86 3.13 4.85 7.46 11.25 17.32
0.76 1.56 2.08 3.02 4.34 6.13 8.62 12.26
0.64 1.04 1.54 2.14 2.93 4.04 5.41
0.53 0.80 1.11 1.49 1.95 2.54 3.18 4.10
0.43 0.66 0.83 1.09 1.34 1.51 2.05 2.51 3.05
0.37 0.54 0.65 0.83 0.97 1.25 1.45 1.72 2.06
adsorption potentials are dimensionless quantities, and molecular areas of occupation are in units of 8.5 A2. The distribution coefficient is defined as n,V,/n,W,, where n, and nuare the moles of adsorbed and unadsorbed solute, VI is the volume of the liquid phase, and W , is the weight of the stationary phase. V, is the adsorbent surface volume in mL/g, and CY is the adsorbent activity (2). No provisioqs are made for stereochemical influences on oligomer conformation. This model simply assumes additivity of the individual oligomer-unit adsorption potentials and a planar adsorption conformation for all contributing groups. The additivity approach has accurately predicted the retention of a variety of small molecules (2) and provides a starting point for the extension of adsorption chromatography to large, polyfunctional molecules. Equation 1 can be simplified to
containing LiChrosorb Si60 (E. Merck, 5-pm particle diameter) packed by the stirred-slurry method. The column was thermostated to 30.00 f 0.05 "C with a circulating-water jacket. The samples were isocratically eluted at 2.0 mL/min with various HPLC grade n-hexane/dichloromethane binary eluents delivered from two Waters Associates M6000A pumps controlled by a Model 660 solvent programmer. A Perkin-Elmer LC-55 variablewavelength detector monitored ultraviolet absorbance of the eluent at 265 nm. Column parameters CY = 0.54 and log V , = -0.43 were determined experimentallyfrom the elution of polycyclic aromatic hydrocarbons with n-hexane. The logarithm of the distribution coefficient for each polycyclic aromatic was plotted against a tabulated standard adsorption potential (2). Values of CY = 0.54 and log V, = -0.43 were calculated from the slope and the intercept of the resultant linear plot. Solvent strengths were calculated from the mole fraction of dichloromethane in each binary eluent examined and the adsorbent activity (5). The silica column was unpacked after completion of these experiments,and an adsorbent weight of 1.967 g was determined gravimetrically.
where individual contributions from end groups and repeat units are summed. A plot of log K vs. solvent strength is predicted to give a straight line with slope = -cYC'UL and intercept = log V , + CYCQ. If the adsorbent parameters a and log V, are known, standard adsorption potentials and molecular areas of occupation can be calculated for each oligomer. These values and the adsorption energy per unit of occupied adsorbent surface area, CiQi/Cca, = SOIA,, can then be used to elucidate the geometrical configuration of an oligomer on the adsorbent surface.
RESULTS AND DISCUSSION Polystyrene oligomer structures were determined by heated, dired-probe electron-impact mass spectrometry. Mass spectra of volatile oligomers at 30 "C incrementa between 120 and 300 "C allowed identification of the general structure of the anionically prepared oligomers: C H3 (CH,) 3(CH2CHPh),CH2CH2Ph. The cationically prepared sample contained predominantly unsaturated and methyl-terminated end groups: PhCH=CH (CHPhCH2),$HPhCH3. Smaller amounts of several additional saturated oligomers were also identified in the cationically polymerized sample. Figures 1 and 2 show typical isocratic chromatograms of both samples, obtained by using an n-hexaneldichloromethaneeluent with a solvent strength tab = 0.18. The number of units in each oligomer (noted above each peak) was confirmed by mass spectrometry on semipreparatively trapped fractions. Substantial f i e structure within each oligomer packet results from partial separation of stereochemical isomers (4). An average retention-volume measurement was taken from the weighted
EXPERIMENTAL SECTION Anionically polymerized, narrow:molecular-weight polystyrene, weight-averagemclecular weight M , = 800 and number-average molecular weight M, = 650, was obtained from Pressure Chemicals (Pittsburgh, PA). A cationically prepared oligomer sample, A-25, I$, = 370 and M, = 200, was obtained from Piccolastic Co. (sample and vendor no longer available). The samples were dissolved in the mobile phase at 2.5 and 1.25 mg/mL, respectively, and injected in a volume of 10 pL onto a 4.6 mm i.d. X 250 mm column
ANALYTICAL CHEMISTRY, VOL. 56, NO. 11, SEPTEMBER 1984 2s
1.c
1
I
I
,
I
I
I
I
I
1779
I
4
Log K N=2
C
b
I
~
I2
6
l
18
I
24
I
#
I
36
x)
I
I
42
~
48
1
1
~
,
~
54
Time (mini
Flgure 1. Anionically polymerized polystyrene oligomers, isocratlcally eluted from 4.6 X 250 mm LiChrosorb Si60 5-pm silica column, mobile phase 78/22 (v/v) n-hexane/dlchloromethane (cab = 0.18), 3O-pg sample injected in 10 pL, UV detection at 265 nm, 0.20 absorbance units full scale (AUFS).
-IS I
I
0.IO
2
I
I
I
0.14
OS8
0.22
Gab Flgure 3. log K vs. solvent strength tab for anlonically prepared polystyrene oligomers. Values above llnes correspond to total number N of oligomer units.
3
4
Table 111. So and A , for Anionically Polymerized PS-800
planar ads, calcd N 2 3 4 5 6 7 8 9 10 11 12 13 14
0
I
0.26
6
I2
18
Time (mid
14.51 20.01 25.51 31.01 36.51 42.01 47.51 53.01 58.51 64.01 69.51 75.01 80.51
S O
A,
r2
3.01 4.12 4.96 5.95 6.55 7.40 8.01 8.87 9.62 10.29 11.01 9.96 10.63
14.51 17.75 19.96 23.17 24.78 27.69 29.53 32.51 35.10 37.21 39.59 34.52 36.72
0.993 0.996 0.998 0.995 0.993 0.992 0.992 0.990 0.987 0.982 0.978 0.966 0.964
Table IV. So and A I for Cationically Polymerized Polystyrene
planar ads,
Flgure 2. Cationically polymerized polystyrene ollgomers, same conditions as in Figure 1, 12.5-pg sample Injected In 10 pL, 2.0 AUFS.
mean of the individual oligomer peak packets, as shown in the figures. Distribution coefficients calculated from the average retention volumes and void volume V,, using K = ( V , - Vm)/W, are given in Tables I and 11. Linear plots of log K as a function of solvent strength were obtained for all retention data of both the anionically and cationically prepared oligomers. Data for PS-800 shown in Figure 3 demonstrate that the distribution coefficient becomes more sensitive to changes in solvent strength with increasing total number of oligomer repeat units N . The progressive steepening of slopes in these plots with increasing oligomer length is completely consistent with the additivity of individual unit adsorption energies, as can be demonstrated by increasing the value of i in the summations of any values for Qiand a, in eq 2. Soand A, values calculated from slope and intercept data of log K vs. tab plots are given with linear regression coefficients rz in Tables I11 and IV. The use of average retention volumes produces an uncertainty of ~ 1 0 % in So and A, values.
3.01 4.47 5.93 7.39 8.85 10.31 11.77 13.23 14.69 16.15 17.61 19.07 20.53
exotl
exptl
calcd
N
So
As
So
A,
rz
2 3 4 5 6
2.96 4.42 5.88 7.34 8.80 10.26 11.72 13.18
11.94 17.44 22.94 28.44 33.94 39.44 44.94 50.44
2.96 4.15 5.23 6.25 7.11 7.60 8.20 8.80
11.94 15.55 19.33 22.82 25.68 26.91 28.65 30.43
0.997 0.990 0.996 0.994 0.990 0.992 0.985 0.969
7 8 9
Soand A , values were calculated for planar adsorption of oligomers by group additivity principles (2). End-group contributions for planar adsorption were approximated as the experimental So and A, dimer values for the anionically prepared samples, Q,, + Q,, = 3.01 and a,, + a,, = 14.51, and the cationically prepared values, Q,, + Q,, = 2.96 and a,, + a,, = 11.94. The repeat-unit adsorption energy, Q, = 1.46, was calculated from Table VIII-4 in ref 2. The occupational area of a repeat-unit aromatic ring is -3.7, as calculated from the difference between terphenyl (A, = 13.4) and biphenyl (A, =
1780
ANALYTICAL CHEMISTRY, VOL. 56, NO. 11, SEPTEMBER 1984
i
i
10
/I/'
Log K 0-
i
I
I
&'
b
- 1.0 0
5
N
IO
I5
Figure 4. log K vs. N at E,,, = 0.22 for (0)cationically prepared A-25 and (0)anionically prepared PS-800 and (- -) relationships predicted for planar adsorption.
-
+
9.71, using A, = 6 + 0.8(h- 6) 0.25(c - h) for unsubstituted hydrocarbons of any formula, where c and h are the numbers of carbon and hydrogen atoms. Addition of two methylene carbons gives a repeat unit area of a, = 5.5 (2). Theoretical So and A, values were obtained by summing the appropriate number of repeat-unit and end-group Q" and a parameters. The experimental standard adsorption potential ( S O ) and molecular areas of occupation (A,) in Tables I11 and IV are generally smaller than values calculated for planar adsorption. Cationically prepared oligomers are retained more strongly than anionically prepared oligomers of equivalent length. The constant difference in Figure 4 between log K values of the two samples is caused by stronger adsorption of methyl and unsaturated end groups in the cationically prepared sample. Linear relationships for planar adsorption were obtained by using eq 1 and are plotted in Figure 4. The planar model accurately predicts that the cationically prepared oligomers should have consistently larger distribution coefficients than the anionically prepared oligomers. Despite the calculation of So and A, values that are much larger than experimentally measured quantities (Tables I11 and IV) and a failure to fit the curvature of data points plotted in Figure 4, the planar adsorption model calculates adequately the magnitude of the distribution coefficients for most oligomers. This approximate agreement between predicted and experimental behavior is a result of simultaneous and fortuitous reductions in So and A, values of the repeat units, which effectively cancel changes in the solute and solvent terms of eq 2. Simple comparisons between experimental and calculated distribution coefficients without explicit knowledge of actual So and A, values are therefore of limited use and are often misleading for deducing solute adsorption geometry. The difference between measured So and A, values of oligomers differing in length by one unit gives an approximate measure of the adsorption energy Q, and the occupational area a, of a repeat unit in the longer oligomer. Average repeat unit Q, and a, values, calculated from the data in Tables I11 and IV, are plotted in Figure 5. Q, and a, values decrease with increasing oligomer length from their planar adsorption values of 1.46 and 5.5, respectively. These reductions are expected for tilted repeat-unit contact, which results from hindered chain rotation, and are analogous to rotational energy-barrier-induced reductions in phenyl arenes (6). Q, and a, values approach 0.65 and 2.0 in the longest oligomers examined, corresponding to 56 and 64% reductions from respective planar conformation values. Methylene carbon atoms make only a minor contribution
r
Figure 5. Average occupational areas, a, (O), and standard adsorption potentlais, 0,(0),for repeat units where r = N - 2.
I
-
0.30
+-T :
______-j t----.
0.25-
0.20-
I
0.15
I
1
5
1
10
N
i:4
be
Figure 6, SOIA, vs. N for (0)cationically prepared A-25 and (0) anionically prepared PS-800 and (- --) relatlonships predicted for planar adsorption.
to the total oligomer adsorption energy while significantly increasing the total occupational area; thus the value of a, for nonplanar adsorption conformation at r = 5 (heptamer) is reduced from the value of a, for planar adsorption conformation a t r = 0 (dimer) in Figure 5, while the change in Q, over the equivalent range of r is comparatively small. The contact area of the large but weakly adsorbed methylene groups decreases progressively as the chain stiffens with increasing oligomer length, but since the primary contributor to Q, is the aromatic ring, little is lost in total adsorption energy when the oligomer backbone is flexed away from the silica surface. This disproportionate reduction in a, and Q, values in oligomers smaller than heptamer is responsible for the curvature at low values of N in Figure 4. A consequence of the aliphatic oligomer backbone not contacting the adsorbent surface is greater adsorption energy per unit of occupied adsorbent surface area SOIA,. SOIA, ratios calculated from data in Tables I11 and IV are clearly greater than ratios plotted in Figure 6 for the planar adsorption of both anionically and cationically prepared samples. It may also be proposed that the difference between planar and experimental SOIA, values is potentially larger than can be justified from hindered-rotation arguments, particularly in long oligomers; competition between methylene groups and the stronger solvents needed to elute long oligomers with reasonable distribution coefficients may cause additional flexing of the chain
1781
Anal. Chem. 1984, 56, 1781-1785
backbone away from the adsorbent surface. The separation of oligostyrene stereoisomers in the chromatograms shown in Figures 1 and 2 may be qualitatively explained by the influence of chain tacticity on the planarity of the adsorbed repeat units. Simple geometric models, without the aid of detailed rotational isomeric state calculations, will show that planarity of the adsorbed aromatic rings increases in the order syndiotactic, isotactic, to heterotactic isomers, which parallels the elution order for oligostyrene stereoisomers observed in the previous work (4). Chain tertiary structure also contributes to the planarity of adsorbed units in oligomers longer than pentamer. At large values of N , energy must be expended for both the uncoiling of the oligomer chain and the rotation of repeat units to a conformation that maximizes collectively the planar adsorption of all oligomer units. The rapid decrease in Q, and a, repeat-unit values for r < 5 can be attributed to the rotational barriers of repeat units, The gradual decrease in these values in oligomers longer than heptamer ( r > 5) may reflect the increasing values of chain disorientation entropy. In polymeric chains, the entropy of disorientation is proportional to chain length and generally causes loop and train adsorption conformations, with only a fraction of the repeat units contacting the adsorbent surface ( 8 , 9 ) . There is no abrupt change in the Q, and a, values of oligomers with r between 5 and 12, or other obvious experimental evidence for the adsorption of only a fraction of the repeat units in the oligomers examined. The relatively constant reduction from planar values of Q, and a, in oligomers longer than heptamer (r > 5 ) does provide the possibility for simple adjustments that account for nonplanar adsorption. Typically, subtracting constant values that account for nonplanarity from the readily calculated planar adsorption energies and occupational areas is similar in ap-
proach to adjusting Q, and a, values for localizing solutes (1-3).
CONCLUSIONS Unique polymer characteristics that lead to nonplanar adsorption of oligostyrenes, such as hindered repeat-unit rotation, are observed in oligomers as small as trimer. The functional-group additivity principles used in the solventdisplacement model for small-molecule adsorption chromatography will not accurately explain all aspects of the adsorption behavior of oligomeric solutes, unless these factors that are unique to the sample are indirectly incorporated into the fundamental expressions for retention. ACKNOWLEDGMENT I thank G. A. Smith for his assistance. Discussions with E. P. Otocka, D. M. Wonnacott, and L. R. Snyder were helpful in the preparation of this manuscript. Registry No. Polystyrene (homopolymer),9003-53-6;silica, 7631-86-9. LITERATURE CITED (1) Snyder, L. R. Hlgh-Perform. Liq. Chromefogr. 1983, 3, 157. (2) Snyder, L. R. “Principles of Adsorption Chromatography”; Marcel Dekker: New York, 1966. (3) Snyder, L. R. J . Chromatogr. 1980, 784, 363. (4) Mourey, T. H.;Smith, Q. A.; Snyder, L. R. Anal. Chem., preceding paper In this issue. (5) Snyder, L. R.; Glajch, J. L. J . Chromatogr. 1981. 274, 1. (6) Snyder, L. R. J . Phys. Chem. 1983, 6 7 , 240. (7) Snyder, L. R.; Dale, H. J . Chromatogr. 1984, 13, 344. (8) DIMarzio, E. A,; Rubin, R. J. J . Chem. Phys. 1971, 55, 4318. (9) Lipatov, Yu. S.; Sergeeva, L. M. “Adsorption of Polymers”; Wiley: New York, 1974.
RECEIVED for review April 21,1983. Resubmitted February 6, 1984. Accepted April 19, 1984.
Static Exclusion Method for Determination of Specific Pore Volume Wei Cheng Beckman Instruments, Inc., 1716 Fourth Street, Berkeley, California 94710
A new method named the “statlc excluslon method” (SEM) has been developed to determine specific pore volume of porous materials. I t is based on sire exclusion of some polymer from pore volume in an appropriate solvent. This method has no restriction on particle sire, shape, and rigidity so that It can be applied io mlcroparticies such as catalysts and chromatographlc support materlals. I n addltion to that It provides a simple, rapid and accurate determination.
classical methods for determining specific pore volume of microporous particles are gas absorption and mercury porosimetry. Some other methods were reported such as sizeexclusion chromatography (2,3), centrifugal fiitration (4),and oil titration (5). However, these methods have considerable restriction because of the size and shape of particles and a low accuracy. A simple, rapid and accurate method for determination of specific pore volume, which has no restriction because of particle size and shape, is presented in this paper.
The specific pore volume is an important parameter to characterize a porous material. Porous materials for catalysis and chromatography, in general, have pore sizes in the range of 20-1000 A (diameter) and particle sizes in the range of 3-1000 fim (diameter or 6 times the ratio of apparent volume to external surface area). For particles larger than 1mm, the pore volume can be determined readily by the simple conventional method ( l ) in , which the apparent volume is measured after coating the particles by a thin layer of wax. The
PRINCIPLE OF THE STATIC EXCLUSION METHOD The present method is based on the complete exclusion of macromolecules added to a suspension of a porous material from a solvent contained in the pores; this exclusion produces a measurable concentration effect which can be used to calculate the pore volume. High molecular weight polymer possesses a large gyration radius, R,, and therefore would be expected to be excluded
0003-2700/84/0356-1781$01.50/0
0 1984 American Chemical Society
