Langmuir 1994,10, 1573-1579
1573
Analysis of the Surface Heterogeneity of Unmodified and Modified Silica by Capillary Inverse Gas-Solid Chromatography at Finite Dilution Marek Pyda, Brett J. Stanley, Minngao Xie, and Georges Guiochon' Department of Chemistry, University of Tennessee, Knoxville, Knoxville, Tennessee 37996-1501,and Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6120 Received December 7,1993. I n Final Form: March 14, 1994@ The adsorption energy distributions (AEDs) of several molecular probes on two silica samples were determined from their chromatographic retention data. Adsorption data were obtained using the elutionby-characteristic points (ECP) method of capillary inverse gas chromatography at finite dilution. The diffuse rear profiles of the bands obtained with samples of different sizes overlay consistently. The numerical expectation-maximization (EM) method has been applied to the calculation of the AEDs from the unfitted experimental adsorption isotherms, using the Langmuir model for the local adsorption isotherm. Two silica samples, both unmodified and reacted with trimethylchlorosilane,were used. Results were obtained with methanol, diethyl ether, 1-chlorobutane, dichloromethane, and toluene. Their AEDs exhibit two high-energy peaks, around 45-60 and 50-70 kJ/mol, respectively. The differences observed for the specific capacities of adsorptionand for the energy distributions of the unmodified and modified silicas are correlated with the chemical structure of the probe and the adsorbent surface.
Introduction Characteristic properties of solid surfaces may be derived from the study of the physical adsorption that occurs when they interact with gas molecules.lJ One of the important problems in the physical adsorption of gases on heterogeneous solid surfaces is concerned with the adsorption energy distribution, obtained as the solution of the fundamental equation
This equation relates the adsorption energy distribution, f(E),and the experimental adsorption isotherm, q@),with the solute partial pressure, p, the local adsorption isotherm, B(E,p),and the minimum and maximum values of the adsorption energy, Eminand E,, respectively. This general problem has been investigated a t length.14 An extensive review of existing methods for solving this equation has been presented by Rudzinski and Everett' and by Jaroniec and Madey.2 However, the complexity of the physical problem, which extends much beyond the mathematics of the solution of eq 1, is still insufficiently recognized. There are two possible approaches to derive adsorption energy distributions (AEDs) from gas chromatographic data. In the first method, the adsorption isotherm is derived from the retention data, then it is fitted to an analytical function, and the latter is used to determine the AED. Recently, Jagiello et ala6 and Roles and Guiochon7 have employed this approach to calculate the AED for silica and alumina samples, respectively. In the e Abstract published in Adoance ACS Abstracts, May 1, 1994.
(1)Rudzinski, W.; Everett, D. H. Adsorption of
Gases on Heterogen-
eous Surface;Academic Press: New York, 1992.
(2)Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, The Netherlands, 1988. ( 3 ) Adamson, A. W.; Ling, I. Adu. Chem. Ser. 1961, 33, 51. (4) House, W. A.; Jaycock, M. J. J . Colloid Polym. Sci. 1978,256, 52. (5)Boudreau, S.P.; Cooper, W. T. Anal. Chem. 1989,61, 41-47. (6) Jagiello, J.; Ligner, G.; Papirer, E. J. Colloid Interface Sci.1990, 131, 128. (7) Roles, J.; Guiochon, G. J. Phys. Chem. 1991, 95,4098. (8)Stanley, B.J.; Guiochon, G. J. Phys. Chem. 1993, 97,8098.
0743-7463/94/2410-1573$04.50/0
second method the AED is calculated directly from gas chromatography measurements as shown by Rudzinski et al.' and done by Boudreau and Cooper6 for different adsorbents. Since the functional dependence of neither the experimental isotherm nor the adsorption energy distribution is known, there are only advantages in not forcing an arbitrary model on them. The practice of premodeling the data can only generate artifacts. Stanley and Guiochons proposed the expectationmaximization method (EM) to calculate the adsorption energy distributions of probes from their raw adsorption isotherms, without any assumptions about the functional form of either this isotherm or the energy distribution. Only a model of the local adsorption isotherm is needed. The numerical estimation of AEDs with the EM method was described in detail.8 Briefly, the AED estimate is updated iteratively with the correction step
where qexp@j)is the experimental isotherm, qcd@j)is the isotherm calculated from the distribution parameters a t the kth iteration, AE is the grid spacing around Ei, and pminand p, are the minimum and maximum pressures observed experimentally. The method does not need smooth isotherm data, it is robust and accurate a t high iteration numbers, and it converges with high stability toward the maximum-likelihood estimate. The EM method is guaranteed to converge at every iteration to the maximum-likelihood estimate, negative values are prevented as positive multiplication is always applied, oscillatory behavior is not observed as long as a reasonable initial estimate is used, the solution is equivalent to the maximum entropy solution, and, finally, simulation studies have shown the method to be accurate when a t least 70% of the isotherm is sampled.8 The present work provides examples of application of the EM method for the determination of AEDs from experimental adsorption isotherm data on different but 0 1994 American Chemical Society
1574 Langmuir, Vol. 10, No. 5, 1994
related surfaces. The adsorption isotherms of several probes (methanol, diethyl ether, 1-chlorobutane, dichloromethane, and toluene) on two silica samples, before and after modification with trimethylchlorosilane, were measured. The isotherm measurements were performed with inverse gas chromatography (IGC) at finite concentration, using the ECP m e t h ~ d . ~ There are some important advantages in using open tubular columns in the IGC technique. The narrow capillary column allows the use of minimal amounts of adsorbent and adsorbate materials. More importantly, high chromatographic efficiency and low column pressure drop are observed with open tubular columns, as compared with conventional packed columns. This allows for more accurate measurements and permits the easy study of adsorbents available as very small particles. The low phase ratio allows reasonable retention times to be observed with high-energy adsorption. The disadvantages in using capillaries are the difficulty in measuring accurately the weight of stationary phase in the column and the fact that the low phase ratio causes low energy adsorption to yield retention times that may be too small. A disadvantage common to all elution techniques is their inability to carry out retention time measurements at high solute partial pressures. However, the major benefit of chromatographic techniques of isotherm determination (the ease and rapidity of the measurements and the possibility of extensive data accumulation), coupled with the advantages mentioned above, seem to outweigh the disadvantages and to warrant further study and experimentation. Solid-state silica matrices have enjoyed significant attention in many fields of science and technology, playing important roles as stationary phases in chromatography (both as adsorbents and as supports for other materials), in polymer matrices as fillers, in catalysis processes, in electronic and ceramic components, and others.lOJ1 In these applications the properties of the silica surface play a n important role. The adsorption properties of silica are related to the presence of two types of surface-active groups, silanols (Si-OH) and siloxanes (Si-0-Si), and to the geometry or pore structure controlling adsorbate accessibility to certain populations of these groups. In our work, we studied two porous silica samples-a chromatographic stationary phase and a Davisil sample, and the adsorbents obtained by trimethylsilane modifications of these samples.
Experimental Section Equipment. Measurements were performed with a PerkinElmer Model 8500 gas chromatograph (Norwalk,CT) fitted with
a flame ionization detector (FID). The analog signal from the FID is digitized and recorded on an IBM PC. The computer is interfaced to the chromatograph via an A/D board (Data Translations, Marlboro, CT). We have used the same modified instrument as in previous reports.12JS In short, the sample is split between a calibration column in parallel with the tested column. By design,the split ratio between these columns is constant. It is determined from the ratio of the gas flow rates through the two columns. The injected sample is also split to a vent, so that samples of large volumes may be injected, and high injector flow rates can be used to minimize (9) Conder, J. R.; Young, C. L. Physicochemical Measurements by Gas Chromatography; Wiley: New York, 1979. (10) Kiselev, A. V.; Yashin, Y. I. Gas-Adsorption Chromatography; Plenum Press: New York, 1969. (11) Unger, K.K.Porous Silica, Its Properties and Uses as a Support in Liquid Chromatography; Elsevier; The Netherlands, 1979; Vol. 16. (12) Roles, J.; Guiochon, G. J. Chromatogr. 1992, 591, 233-243. (13) Roles, J.; Guiochon, G. J. Chromatogr. 1992, 591, 245-265.
Pyda et al.
band spreading in the injection port. The calibration column is used to determine the detector response factor by passing an aliquot having a Gaussian profile through the FID. This calibration peak elutes after elution of the sample on the test column has occurred. The response of the FID is linear; its response factor is measured daily. The test column yields the nonlinear chromatogram from which the ECP analysis is performed to obtain the adsorption data. Hamilton syringes (1-5 pL and 5-20 pL, Reno, NV), equipped with a Chaneyadapter and a needlespacer,were used for injection of the probes. The calibration column (DB-5, 30 m long, 0.32 mm i.d.) was obtained from J&W Scientific (Folsan, CA). An analytical semimicro balance (Sartorius Corp., Bohemia, NY), accurate to within hO.01 mg, was used to measure the weight of the silica samples. More details about the equipment have been described in earlier publications.14-16 Materials. A sample of Davisil silica gel (specific surface area 480 m2/g, average particle size 6.0 pm, Aldrich, St. Louis, MO) and a sample of silica for liquid chromatography (IMPAQ RGlOlOSi, specific surface area 246 m2/g, particle diameter 8.9 pm, BTR Separations, Wilmington, DE) were used. Both were modified by reaction with trimethylchlorosilane (TMCS,Alltech, Deerfield, IL). Preparation of Modified Silicas. In a typical experiment, 10 g of silica was dispersed in 250 mL of an hexane solution of TMCS (3 g). The amount of trimethylchlorosilane was in slight excess of what would be needed for the formation of a complete monolayer of trimethylsilane on the silica surface. After evaporation of the solvent, the samples were heated at 150 "C for 24 h, then extracted with heptane to remove any ungrafted reagent. Finally, the samples were vacuum dried at 60 "C. The resulting unmodified and modified silicas are identified below as follows: SG, Davisil silica gel; SGM, modified Davisil silica gel; S, IMPAQ chromatographic silica; SM, modified IMPAQ chromatographic silica. Modification ratios, l / r (number of molecules per unit surface), were calculated from the results of elemental analysis. Probe Solutes. Methanol, diethyl ether, 1-chlorobutane, dichloromethane, and toluene (all HPLC grade from Aldrich) were used as received, as the probes for the determination of adsorption isotherms. Preparation of Capillary Columns. The empty capillary column (ca. 15 m long, 0.53 mm i.d., quartz tube from Polymicro Technologies, Phoenix, AZ) was washed with several column volumes of methanol and then conditioned in the gas chromatograph at 320 "C for 74 h under a stream of helium (inletpressure, Pi = 1.0 psi). The empty column was weighed, and a silica suspension in DMSO (dimethyl sulfoxide)was forced through it. The coating procedure described earliePJ4 was followed. For this work, a 5% (w/v) DMSO suspension was used for samples SG and SGM, and a 2 % (w/v)suspension for samples S and SM. After coating, the column was placed in the gas chromatograph and conditioned under a helium stream (Pi= 1.0 psi) for 72 h at 320 "C. After conditioning, the weight of silica was derived by difference of the initial and final column weights. Experimental Procedure for Adsorption Measurements. Measurements were made between 40 and 88 "C with helium as the carrier gas (Pi= 5 psi). The injector was operated at 250 "C and the FID at 350 "C with low and high detector sensitivities. All columnstested were operated in parallel with the calibration column,at an approximately1/10 split ratio. Detectorcalibration, flow rates, and inlet pressure measurements were previously described.13 The volumes of sample injected range from 0.5 to 20 pL. Under these conditions, the rear diffuse profiles of bands corresponding to different injection sizes overlay exactly in most of their range (Figures 1-3). This is due to the high efficiency of the columns used. In this case, an adsorption isotherm may be obtained simply from the largest peak available. The equilibrium adsorption isotherms of the probe compounds were calculated from high concentration band profiles using the (14) Halasz, I.; Horvath, Cs. Nature 1963, 197, 72. (15) Guan, H.; Stanley, B.; Guiochon, G. J. Chromatogr., in press. (16) Guiochon,G.;Guillemin,C. L. Quantitative Gas Chromatography, Elsevier; Amsterdam, The Netherlands, 1988.
Langmuir, Vol. 10, No. 5, 1994 1575
Analysis of Surface Heterogeneity Table 1. Grafting Ratios of the Modified Silicas
SamDle
c (%)
S SM SG SGM
Figure 2. Experimental band profiles of methanol on chromatographic silica (S)at 60 "C, at low sensitivity. Experimental conditions were as follows: column length, 1570.9 cm; mass of silica, 11.14 mg; column temperature, 60 "C; absolute inlet pressure, 1.319 atm; gas hold-up time, 0.533 min; column efficiency, around 20 OOO plates; injection volumes, 10,5,4pL. The experimental adsorption data were derived from eq 5, using the experimental band profiles recorded for methanol, diethyl ether, 1-chlorobutane,dichloromethane, and toluene. Figures 4 and 5 show the adsorption isotherms of methanol on the silica samples. The adsorption capacity of the silica surface seems to decrease slightly with increasing temperature (Figure 4). It also decreases markedly after modification (Figure 5 ) . This decrease and the lower adsorption capacity for methanol after chemical modification of the silica surface with TMCS are consistent with the replacement of most of the silanol groups by trimethylsilyl ether groups. However, it must be noted that in a few cases the adsorption isotherms were higher on the modified than on the unmodified silica. This is the case with diethyl ether on the IMPAQ silica.
The isotherms of methanol are much higher (Figures 4 and 5 ) and the monolayer capacity (qm)nearly twice larger (Tables 3 and 4) on the Davisil silicagel than on the IMPAQ silica, consistent with the ratio of the specific surface areas. Finally, we note that the adsorption data could not be measured at partial pressures of methanol in excess of 0.03-0.04 atm. In this pressure range, the isotherm still appears to be far from its saturation (Figures 4 and 5). 111. The Adsorption Energy Distributions. The results of the calculation of the adsorption energy distribution of the different probes on the four samples are reported in Figures 6-10 and summarized in Tables 3 and 4. q1 and 92 are the amounts adsorbed corresponding to the first and second peaks of increasing energy, respectively, not including the divergent low-E portion of the AED. q m is the amount adsorbed with respect to the entire AED. These estimates possess a large uncertainty of approximately *lo%, because of the uncertainty in the mass of stationary phase coated on the wall of the capillary columns. This mass is obtained by a ca. 0.02% weight difference of the capillary and cage with and without the silica present. Similarly, El and E2 are the mean adsorption energies corresponding to the first and second peaks
Langmuir, Vol. 10, No. 5, 1994 1577
Analysis of Surface Heterogeneity
Table 3. Characteristics of the Adsorption Energy Distribution of Several Probes on Unmodified (SG) and Modified (SGM) Silica Gel at Different Temperatures
T ("0
adsorbent
qm X
106 (mol/@
E1 (kJ/mol)
41 X
106 (mol/g)
Ez (kJ/mol)
q1 X
lo5 (mol/g)
Methanol
SG
50 60 70
22.6 19.7 19.5
SG SGM
40 40
14.5 9.88
49.9 52.1
SG SGM
70 70
8.04 11.6
54.3 59.4
SG
88
8.54
60.1
52.3 51.8 52.6
6.35 4.90 3.24
63.0 61.1 64.1
0.35 0.19 0.34
0.31 0.53
66.2
0.29 0.43
64.4 65.9
0.04 0.03
0.21
71.5
0.02
Dichloromethane l-Chlorobutane Toluene
Table 4. Characteristics of the Adsorption Energy Distribution of Several Probes on Unmodified (S) and Modified (SM) Chromatographic Silica at Different Temperatures
T ("0
adsorbent
qm X
lo5 (mol/g)
E1 (kJ/mol)
41 X lo5 (mol/@
Ez (kJ/mol)
1.15 1.23
65.0 60.6
0.08 0.09
1.81 2.17 1.07
53.3 58.3 60.6
0.50 0.20 0.13
qz X
106 (mol/g)
Methanol
S SM
60 60
11.91 7.24
53.8 52.6
S SM
50 50 60
1.66 6.93 6.52
469 47.9 50.0
Diethyl Ether
10
'e * 2
,K
o!
3
W
\
"2
u
W
v u-
O Y
ooc
001
cc2
003
c
A
Partiai pressure Catm) Figure 5. Adsorption isotherms of methanol on unmodified (solid line) and modified (dashed line) chromatographic silica, at 60 O C .
of increasing energy, respectively, not including the divergent low-E peak. These estimates are obtained from the first statistical moment of the peaks and possess an uncertainty of f2.0%. All the AEDs show an incomplete low energy band and two high-energy peaks (around 50-54 and 60-65 kJ/mol for methanol, Figures 6-8). The high-energy peaks represent a small fraction of the total adsorption isotherm, corresponding to the low partial pressure range. The lowenergy area was incompletely observed in our experiments. Undersampling of this region may cause artifacts to occur in the distribution function.8 In order to obtain the entire AED, measurements of the retention times of outlet partial pressures of methanol well in excess of 0.04 atm are required. It does not seem that the ECP method may allow this, however. The injection of the large size samples needed causes too much disruption in the steady-state distribution of temperatures and pressures in the injection
8 SO 60 73 Adsoration Enerqy (kJ,hoi)
Figure 6. Adsorption energy distribution of methanol on SG silica at 50 "C (dotted line), 60 O C (dashed line), and 70 O C (solid line).
port and along the column. Under the experimental limitations of this study, such high pressure was not possible. Thus, further improvements of the chromatographic IGC techniques and the study of alternate methods (e.g., FA and FACP) to carry out adsorption determinations in this region of partial pressures are warranted.18 As examples of the results obtained, Figure 6 shows the AEDs of methanol on IMPAQ silica derived from the isotherms in Figure 4, measured a t different temperatures; Figures 7 and 8 show the AED's of methanol in Davisil and IMPAQ silica and on modified and unmodified IMPAQ silica, respectively. In Figure 6, it appears that the shape and position of the high-energy peaks remain the same and that only the adsorption capacities decrease slightly with increasing temperature. This is expected, as the distribution of energies should not change with temperature, only the adsorption capacity. For IMPAQ
Pyda et al.
1578 Langmuir, Vol. 10, No. 5, 1994 (D
I
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F s
R 0
s 3: -c
W
r
,t f i
w
W 'c
L3
4c
d
-^
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-I-
0 0
8C
Ads3Fptio- Enerqy OCJ-~JI) Figure 7. Adsorption energy distribution of methanol on SG silica (dashed line) and S chromatographic silica (solid line), at 60 "C.
Adsorption Energy (kJ/md Figure 9. Adsorption energy distribution of diethyl ether on unmodified (S)(solid line) and modified (SM) (dotted line) chromatographic silica (SM) at 60 O C .
m
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*
I:
j
l i h
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Y
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-5c 6C Acsorptior ;i?rgy (
