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Elution Behavior of Chemically Different Probes on the Evaluation of Surface Properties of Cellulose by Inverse Gas Chromatography
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
194, 127–137 (1997)
CS975074
Elution Behavior of Chemically Different Probes on the Evaluation of Surface Properties of Cellulose by Inverse Gas Chromatography Grzegorz Czeremuszkin, 1 Prithu Mukhopadhyay, and Slawomir Sapieha Engineering Physics Department, E´cole Polytechnique, P.O. Box 6079, Station A, Montre´al, Que´bec H3C 3A7, Canada Received March 17, 1997; accepted July 9, 1997
The inverse gas chromatography (IGC) technique has been employed to examine adsorption behavior of cellulose surfaces from elution characteristics of chemically different adsorbates. The neutral probes were eluted completely during IGC measurements while acidic, amphoteric, and basic probe molecules were eluted incompletely. In this work, complete elution is defined by the flat postpeak FID signal within the noise limits of the detector. An understanding of incomplete elution is thereby reached by introducing a precisely controlled, very small quantity of individual probes into the column. A strong correlation is found between elution efficiency of vapors and their enthalpies of acid–base interactions. Delayed elution of acid–base vapors is interpreted as being due to nonequilibrium sorption process, and calculations have shown that diffusion into the bulk is unlikely under the measurement conditions. The chromatographic process is simulated and it is found that the contribution of nonequilibrium adsorption to the retention is responsible for observed peak tailing and thereby delayed elution of acid–base probes. Results of the study indicate that characterization of acid–base (electron acceptor–donor) type of stationary phase material surfaces by IGC needs careful attention and is an area for future work. q 1997 Academic Press Key Words: cellulose; inverse gas chromatography; acid–base interactions; elution yield; delayed elution; equilibrium and nonequilibrium adsorption.
INTRODUCTION
The popularity in the use of inverse gas chromatography (IGC) measurements applied to surface, interface, and bulk characterization of technologically important materials is due mainly to the technique’s flexibility and potential for yielding useful data in the wide range of physicochemical properties of materials. Except for the reversed role of solute probes and stationary phase packing materials, the principle and instrumentation of IGC measurements are similar to that of conventional gas chromatography (GC). The principle is based on the characteristic equilibrium partitioning of the vapor molecules (adsorbate) between the mobile and solid stationary phases (adsorbent). Schreiber and Lloyd (1) have 1
To whom correspondence should be addressed.
reviewed the method, its advantages, and limitations including areas of application. Several other reviews on this subject are also available (2–6). Essentially, the instrument monitors the residence time and shape of the elution curve for different probe adsorbates of known chemical structure and properties, which allow inferences concerning the characteristics of the column packing materials to be drawn, i.e., the solid adsorbent surfaces. The implications of IGC studies can be readily recognized from the fact that solids used in many industrially important formulations and/or processes are not utilized alone in its virgin state. Frequently, to achieve the level of performance desired in commercial applications, solid surfaces are modified and/or used in combination with other additives, thereby complicating the composition of solids’ interfaces and their interaction potential. It is therefore important to know both the nature and magnitude of solid surface free energy to generate products of desired properties and to optimize the process. Similarly, the relevance of studies involving diffusion of molecules into the system and the migration of components from the bulk to the surface are equally important. In many industrial processes, such as food packaging, controlled release technology, solvent devolatilization, and bulk polymerization, knowledge of small molecule diffusion is vital. Conventionally, diffusion studies are carried out by sorption experiments (7, 8). However, difficulties in comparing and interpreting experimental data on diffusion of solvent molecules in polymers have been observed by several researchers (9, 10). In recent years, diffusivity measurements in polymer–solvent systems by IGC have become a method of growing choice. Nevertheless, uncertainty concerning the accuracy of diffusion data obtained by IGC is evident from literature reports. While measuring diffusion coefficients in polymer–solvent systems, Hu et al. (11) observed that correct modeling of the stationary phase geometry in the column is a difficult task. Pawlisch et al. (12) argued that use of capillary columns instead of the packed column method can circumvent this difficulty because of the uniform distribution of the polymeric stationary phase. In this regard, Laurence and co-workers (12–15) studied extensively the diffusion of solvents including the size effects of penetrants in PMMA
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0021-9797/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
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and PVAc by capillary column IGC. Elsewhere, applying the same methodology and model, diffusion coefficient measurements of solvents in PS were carried out (16). These studies, however, raised a serious concern over the validity of the model used (17) which assumes no surface adsorption at the gas–polymer interface. Earlier, Smidsrod and Guillet (18) showed that, near the polymer Tg , surface effects and bulk diffusion coexist. Schreiber and Qin (17) further demonstrated that, by changing the carrier gas flow rate, surface adsorption and bulk diffusion coexist at temperatures above the polymer Tg . In that study, the stationary phase material was styrene/4-vinylpyridine. It becomes obvious from these studies that a greater familiarity of the surface adsorption process is necessary to better understand the issue of diffusion. Another important aspect of IGC investigation is associated with the analysis of resulted chromatogram. Frequently, the chromatographic retention volume, Vr (derived from the retention time, tr ), is considered as a fundamental datum characterizing the equilibrium partitioning of probe molecules between the gas and solid phases. While reproducible tr is obtained within the experimental error during IGC investigation, however, the data do not yield the true nature of the sorption phenomenon. Particularly, for vapors which are able to interact by acid–base forces in addition to Lifshitz– van der Waals (LW) forces. As a result, complete elution behavior of these probes remain unexplored. In this work, we attempted to analyze the incomplete elution of acid–base probes from their elution behavior by employing IGC technique. For this purpose, delayed elution of probe molecules through the stationary phase were analyzed quantitatively, and simultaneously the shapes of respective peaks were simulated by computer program. Further, this study addresses the issues of surface adsorption and bulk diffusion of chemically different probe molecules for a better knowledge of sorption process. We have chosen cellulose as the stationary phase material. Our attention toward cellulose fibers is drawn since its surface properties are becoming increasingly important as its application areas continue to broaden. These include increasing use of recycled fibers in newsprint production and surface and interfacial interactions between cellulose and other materials, such as fillers in paper, polymeric layers in laminates or inks in printing. The probe molecules were chosen on the basis of their propensity to participate in acid–base type interactions with the stationary phase. Our objective also constitutes chromatographic data handling procedures. It is hoped that the conclusions obtained in this work may provide clues to describe diffusion data by IGC more accurately. Concept of Delayed Elution Not infrequently, diffusion studies have encountered retention of specific probe molecules in the system for prolong
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period of time. Robertson reported (19) prolonged retention of organic liquids such as alcohols, ketones, ethers, esters, aldehydes, amines, and acids in cellulose fibers while conducting liquid phase immersion swelling tests. In fact, 21 out of 26 liquids employed in that study enhanced the weight of dry cellulose fibers. The study involved immersion of cellulose fibers in test liquids which was subsequently recovered by drying at 1057C for 16 h. The author attributed the prolonged retention of probe molecules as either entrapment of test liquids within the fiber structure or reaction with cellulose surfaces. However, entrapped liquids were released when dried cellulose were made to reswell in water or methanol after another drying procedure. It is known that IGC studies at infinite dilution employ probe molecules at very low concentration in gas phase contrary to the concentrations used in immersion swelling test. Presumably, one would not expect such an effect at infinite dilute condition. During the current investigation of cellulose at infinite dilution, we found that some probes were not eluted through the stationary phase. These probes such as alcohols or amines appeared to have interacted strongly with the packing material and were either permanently trapped by cellulose or their elution times were very long compared to the time span of measurements. Whereas, other probes (ethers, esters, ketones) were eluted, generating distinct chromatographic signals. Thus the term ‘‘delayed elution’’ refers to the prolonged trapping phenomenon or incomplete elution of probe molecules in the adsorbent which allows to distinguish the latter effect form typical retention behavior normally seen by IGC. Retention Process Simulation Computer simulations have proved their strength to the understanding of surface science (20–22). Indeed, several studies benefitted from the computer simulations of elution process to analyze the peak shape and retention behavior in gas chromatography. Among others, Hattam and Munk simulated the elution of probes by the IGC technique with the assumption that diffusion (23, 24) or equilibrium adsorption (23) takes place in the solute–polymer system. For the diffusion-controlled process, authors distinguished four types of chromatographic behavior which include instantaneous equilibrium, pseudoequilibrium, a transition region, and a marker-like region corresponding to the diminishing diffusion coefficient values. They noted that the probe amount had the influence on the maximum peak position and confirmed the validity of using moments method in IGC data analysis (25), whereas in this work retention of acid– base probes at infinite dilution conditions was simulated assuming two simultaneous processes (equilibrium and nonequilibrium) responsible for probe retention behavior. The kinetic model was utilized to describe aspects of delayed elution.
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MATERIALS AND METHODS FOR IGC STUDIES
Column Preparation Washed and nonwashed cellulose fibers, CF-1 (Whatman), were used in this study. The nonwashed variety was used as received, whereas the same fibers were washed with distilled water and dried in vacuum at 607C (washed fibers) before the investigation. Cellulose fibers (5 g of each washed and nonwashed separately) were packed in two different previously degreased, washed, and dried stainless steel tubings (4.4 mm i.d. and 1 m long). For the peak shape analysis purpose, short columns were also utilized (4.4 mm i.d., 6 cm long, containing 0.25 g of cellulose) employing the identical procedure. Before the measurements, packed columns (as well as the empty columns used to determine the reference data) were conditioned overnight at 1107C under the flow of carrier gas (helium, 20 ccm/min). The conditions were chosen to obtain a constant background signal of thermal conductivity detector (TCD) system. Column conditioning temperature was based on industrial practice of effectively removing water from cellulose fibers. Hydrocarbons and acid–base probes used in this work were all of analytical grades unless mentioned otherwise. The IGC measurements were performed using Varian 3400 gas chromatograph, equipped with flame ionization (FID) and thermal conductivity (TCD) detectors. Methane and air were used as the indirect and direct markers, respectively. In other words, retention times were determined with respect to air TCD peak and recalculated corresponding to methane FID peak. The average error in the evaluation of retention times (tr ) was below 0.5% for all probes except pentane and hexane where errors were 4% and 2.1%, respectively. Elution Efficiency In quantitative elution measurements precisely controlled amounts of molecular probes (10 011 –10 012 mol/injection) were introduced into the GC system using the following dosage procedure: Liquid probes (Fluka, Anachemia; diethyl ether and ethyl acetate previously dried and purified by dis˚ molecular sieves at 257C in tillation) were stored over 4 A glass, septum-sealed bottles. A known volume of probe vapor was sampled with Hamilton syringe and injected to the encapsulated glass ampule to obtain the required dilution. Special care was taken during sampling to avoid the increase of bottle temperature containing the liquid probe. Diluted vapor was subsequently sampled from the glass ampule prior to injection, thus reaching infinite dilute condition. The dilution, required to obtain FID signal at least one order of magnitude higher than its sensitivity threshold, was calculated on the basis of saturated vapor pressure of probe liquids and FID response factor (26). The calculated amount of diluted vapor was injected into
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FIG. 1. The percentage of probe molecules eluted (elution yield) through the column as compared to the amount of probes injected.
the column and the chromatographic peak area was computed by Varian system software. The elution efficiency ( b ) of each probe was calculated as the ratio b Å Ap /Ae ,
[1]
where Ap and Ae are the peak areas of equivalent amount of injected probe for packed and empty column, respectively. To minimize experimental error, Ap was determined from at least six injections and Ae was calculated from Ae Å FVin j ,
[2]
where Vin j is the volume of injected probe and F is the FID sensitivity factor. The value of F, defined as the peak area per unit volume of the probe injected to reference (empty) column was found as the slope in Ae vs Vin j dependence (for Vin j Å 0.05–1 ml). The average error of FID sensitivity factor remained below {10% and was higher only for pentane. The ultimate error of elution efficiency for each probe was calculated from its component errors, i.e., the errors from the FID sensitivity factor and the FID response for the packed column. Delayed Elution For analysis of peak shape in its tail region, where the probe elution rate becomes very low and the resulted signal fall below the detector sensitivity threshold, the short columns (0.25 g of cellulose) were used. This resulted in shorter retention times and brought the elution rate above the noise level of FID. Additional probes were also used, such as nonane, decane, undecane, dodecane, methanol, ethanol, and tert-butanol (Anachemia). RESULTS OF IGC STUDIES
The probe molecules which eluted through the column and gave measurable FID signals are shown in Fig. 1. These
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FIG. 2. Dependence of probes elution yield on the adsorption free free energy due to acid–base interactions, DH ab , between the cellulose surface and chemically different probes.
probes are commonly used to characterize the cellulose surface (27–30). However, injections of precisely measured amounts of these probes (10 011 –10 12 mol/injection) revealed incomplete elution during measurements. In spite of incomplete elution, they exhibited a flat postpeak FID signal within the noise limits, an indication of entire removal of adsorbates from the column. Delayed elution, as mentioned earlier, contributed significantly to their peak behavior and decreased the elution efficiency. Further, probe molecules like methanol, ethanol, pyridine, formamide, n-butylamine, and tert-butylamine did not yield peaks at the measurement conditions. The reason may be that at infinite dilute concentration, these probes were either permanently trapped by cellulose or desorbed at very slow rates, giving FID signals within the limits of detector noise. In the above noted figure, the percentage of probe molecules of each kind eluted through the column compared to the amount that were injected into the system is presented. The hydrocarbons which are able to interact via LW forces only gave elution yield close to the unity (within statistical error), whereas probes which can be involved in acid–base (acceptor–donor type) interactions in addition to LW forces were eluted incompletely. It is further observed that elution efficiency and retention time of individual probes did not correlate. For instance, at column temperature of 507C, tr values of octane and ethyl acetate were almost identical yet elution yields (E) for both vapors were 100% and 60%, respectively. The results indicate a possible link between acid–base characteristics of vapor probes and their corresponding E values. Earlier, Mukhopadhyay and Schreiber (31) suggested while studying the SBR polymer that vapors that can interact with the polymer by AB forces are more strongly retained by the surface above Tg than the hydrocarbon molecules of similar dimensions. Figure 2 tests the hypothesis in which T ! Tg and shows that the percentage of
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elution yield can be correlated with specific nature of the probes where E is plotted against the enthalpies of acid–base interactions ( DH ab ). It is evident that stronger the ability of probe vapors to enter into acid–base interactions with cellulose, the longer the dwelling time period, which in turn reduces the percentage of elution yield. This shows that acid–base (AB) interactions are related to incomplete and therefore, delayed elution phenomenon. In order to ascertain AB character of the injected probes with E values, the acceptor (AN) and donor number (DN) approach of Gutman was applied (32). As shown in Fig. 3, E gives a linear relationship with AN and DN numbers of adsorbates. We used the modified acceptor numbers due to Riddle and Fowkes (33). Apparent deviation from linearity can be understood from the fact that the solid surfaces under investigation is energetically heterogeneous. The modified AN numbers were derived by correcting the van der Waals contributions to the 31P NMR chemical shifts of Et3PO and the IR shifts for the —P|O stretching peaks using pure probe liquids on squalane, a liquid hydrocarbon that has no acidic or basic sites. In order to confirm the aspects of incomplete elution of acid–base probes in IGC studies, a finite amount of water was introduced into the column after basic and amphoteric probe injections. Probes of the latter category, such as THF, diethyl ether, acetone, and ethyl acetate, were chosen since the cellulose surface is predominantly acidic (28). Prior to water injections, zero FID response was reached to ensure no elution of AB probes that were previously put into the column. The column was then allowed to stabilize for another 30 min at the measurement temperature. Interestingly enough, subsequent water injections resulted in chromatographic peaks. This is shown in Fig. 4. The first injection of 1 ml of water, marked with an arrow in the figure, gave a small FID response. The observed response revealed the
FIG. 3. Plot showing a relationship between the probes elution yield and the donor (DN) and acceptor numbers (AN*) values for the probes adsorbed on cellulose surface.
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FIG. 4. Detector (FID) response for subsequent injections of liquid water to the column after multiple injections of probe vapors. The water injections are marked with arrows. FIG. 5. Shape of peak shoulder (one-step decay) for undecane (b, ---), dodecane (c, – – – ), and decane (a1–a3) with increasing concentration.
release of organic probes which had been trapped or retained in the column. This is obvious since the flame ionization detector is sensitive to carbon compounds only and gives no signal for water. Three consecutive injections of 5 ml of water yielded three significant peaks in order of decreasing intensity. Finally, the small yet broad FID signal showed the remaining of the stated organic adsorbates retained inside the column. It seems likely that the stronger affinity of water molecules toward cellulose due to stronger AB interactions has made water drive out organic probe molecules which were held by weaker AB forces onto the cellulose. If one were to assume that retention times of above mentioned vapors characterize the AB interactions potential of cellulose surface and describe the complete elution of adsorbates then the appearance of water-induced peaks prove otherwise. Rather specific probes were held onto the stationary phase inside the column by acid–base forces even after the postpeak FID signal was brought to the level of base line noise. The results, therefore, confirm earlier hypothesis of decreased elution efficiency due to acid–base nature of probes (Fig. 2). Figure 5 represents the shape of chromatographic signal decay for decane (n-C10), undecane (n-C11) and dodecane (n-C12) in ln(R) vs ln(t 0 tmax ) coordinates, where R denotes the FID response at time t and tmax is the position of respective peak maximum. These coordinates are useful as IGC peak shoulders decrease and allow observation of the short and long time trends of FID signals. All curves given in Fig. 5 are very similar, illustrating the decay type of FID signal and will be referred to henceforth as ‘‘one-step decay.’’ It is observed that the decay type is independent of probe concentration and of alkanes irrespective of their carbon chain length (n-C10, curves a1–a3; n-C11 and n-C12, curves b and c). When AB probes were introduced into the column the peak shoulders differed from those observed for alkanes. The deviation involved in a slower signal decrease at a longer period of time and characteristically depended on
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the adsorbates’ AB character. For acidic probes the deviation from one-step decay was small (Fig. 6, shown for CCl4 ), whereas the deviation was relatively profound for basic and amphoteric vapors (Fig. 7, shown for diethyl ether and acetone). The smaller deviation of acidic vapors can be attributed to the stationary phase AB properties. However, when the nature of IGC signal decay of basic and amphoteric probes was compared with those observed for alkanes, not only a type dependence but also a concentration dependence were found. A representative example of such dependencies utilizing basic probe tetrahydrofuran is shown in Fig. 8. Alcohols (Fig. 9), which are known to strongly interact with cellulose, gave an FID signal decay that can be compared to the above stated pattern. However, the contribution to one-step decay (alkane-like behavior) was very small for ethanol whereas it was distinct in case of tert-butanol which may be due to the tert-butyl group in the latter molecule.
FIG. 6. Shape of peak shoulder for carbon tetrachloride with increasing concentration (a–c).
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FIG. 7. Shape of peak shoulder for acetone (---) and diethyl ether ( – - – ).
The difference in shape of IGC peak shoulders detected for alkanes and acid–base probes can be ascribed to different adsorption phenomena which eventually accounted for their retention process and will be discussed in subsequent sections. Character of Retention Process In the first process, i.e., ‘‘one-step decay’’ of the FID signal, the stabilization of adsorption equilibrium was fast in comparison to gas–surface contact time. This can be seen from the shapes of hydrocarbon peaks, which exhibited the features of typical equilibrium retention process (23). Since direct correlation between the partition coefficient of equilibrium adsorption (K) and the retention time (tr ) exists, the process can be characterized by the IGC method. The second process was related to the peak tailing. This type of peak asymmetry is observed when the equilibrium
FIG. 8. Shape of peak shoulder for tetrahydrofuran (a–c) with increasing concentration.
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FIG. 9. Shape of peak shoulder for ethanol ( – – – ) and tert-butanol ( —).
of sorption is not attained during the measurement period. This interpretation is generally accepted in gas–solid chromatography (34). Whereas the decrease of retention volume with the probe amount as well as carrier gas flow rate is normally encountered for nonequilibrium sorption processes. In this work, however, the retention volumes were affected neither by the probe amount (in the range of 10 011 –10 012 mol/injection) nor by changing the flow rate (10–30 sccm/ min). This kind of phenomenon was previously reported for several glassy polymers below their Tg , when sufficiently small amount of probes designated as infinite dilution were injected (35). However, to the best of our knowledge the elution efficiency was never quantitatively analyzed in such cases. Contribution of Nonequilibrium Sorption Process to Delayed Elution In general, nonequilibrium sorption in gas chromatography is controlled by surface and/or by bulk kinetics. The contribution of slow kinetic process to the retention was studied (36), and the model that included two kinds of sorption sites with fast and slow time constants was analyzed (37). In case of IGC measurements applied to surface characterization of polymers, the presence of peak tails and large peak asymmetry is normally attributed to the bulk diffusion (24). At first sight, observed chromatographic peaks from this work may appear to have resulted from the bulk diffusion process. It is worth mentioning that diffusion of water or alcohols into the cellulose fibers by IGC have already been noted in the same temperature range (38). In that study, however, liquids or vapors were used at concentrations 5– 7 orders of magnitude higher than those we utilized in the current investigation. At infinite dilution IGC, the origin of peak broadening for polymers below Tg is still a matter of
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debate although the arguments exist that it cannot be caused by nonequilibrium diffusion (23). In this work, the remote possibility of diffusion effects at very low dilution and at significantly lower temperature region of investigation than the Tg of cellulosic materials (39) appears to be reasonable. Moreover, for semicrystalline polymers it is known that diffusion of molecules into amorphous phase about 130–2007C below polymer Tg is very limited (3). This can be further appreciated by way of rough calculations. The surface area of a typical probe molecule is of the ˚ 2 . For a 1 m column containing 5 g of order of Ç50 A cellulose of 1 m2 /g specific surface area, pentane and ethyl acetate presented two limiting values for peak half-width, which are 5 and 60 s, respectively, at 407C. This yields an estimated maximum surface coverage occupied by adsorbed molecules, in the order of 10 06 of the total accessible surface. At this low concentration it is very unlikely that adsorbate– adsorbate interactions or swelling-induced diffusion will occur. Further, if the diffusion were responsible for probe retention in this time scale then the average diffusion distance ˚ during one elemental act of sorp(x) would be below 50 A tion (x was calculated from x Å 2[Dt/ p] 1 / 2 , assuming a diffusion coefficient D Ç 10 8 cm2 /s) which is essentially the surface region. Due to the presence of functional groups on cellulose surfaces, preferential interactions between the cellulose and AB probes can be more likely, provided that the activation energy barrier is overcome. Such a process may not be controlled by thermodynamic equilibrium within the time scale of IGC experiment but may do so under kinetically controlled process. Therefore, the observed second decay type FID signal refers to the nonequilibrium adsorption responsible for the second process. In other words, the AB interactions seem to contribute to the second process causing a delayed elution and subsequently decreasing the elution efficiency. The implications are important since the contribution of delayed elution to the retention process increases with the concentration of adsorbate molecules. In particular, when comparing the results of IGC at infinite dilute concentration with the results of contact angle measurements or diffusion coefficients from sorption studies. To analyze the manifestation of proposed mechanism of nonequilibrium adsorption in IGC, we applied the method of computer simulation of probe elution. COMPUTER SIMULATIONS METHOD FOR PROBE ELUTION
The simulation is described schematically in Fig. 10. Chromatographic column was partitioned into L elements (cells) containing the mobile and stationary phases numbered as m. The initial step was to locate probe molecules [P0 ] in the first column element. Each subsequent simulation
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FIG. 10. Column partitioning for probe retention and a schematic presentation of simulation steps.
steps involved in the transfer of m- cell content (gas phase) to m / 1 cell followed by the calculation of number of molecules in mobile and stationary phases after a given contact time (t f ). The value of t f was the same for each calculation, which represented the constant flow rate of carrier gas in IGC experiment. The concentrations of molecules in mobile phase [P] and in stationary phase [S1 , S2 ] were calculated from the equations shown below. The content of the last cell [PM ] was equal to the number of molecules reaching the detector and was equivalent to the FID response (R). These values were collected as a function of the current step (n) which represented the simulated chromatogram in time domain as follows: [PM (n)] Å R(t);
t Å nt f
with
N @ L,
where N is the total number of simulation steps. In each case the elution yield was calculated as the percentage of probe molecules which passed through the detector area with respect to the number of molecules introduced. In IGC studies, determination of peak surface area is often calculated by the system software. The decisions where the peak starts and ends are done either automatically or by the operator, during the data acquisition procedure. These decisions are based on the value of signal amplitude, which increases significantly over the base line when the peak starts and returns to the base line level when the peak ends. At infinite dilution IGC, the probe amount injected into the column is very small and thus yields a very low detector response. The resulted signal, in fact, is close to the sensitivity threshold of the detector used. This brings up the issue of detector noise or ‘‘spreading’’ the base line which renders the decision on peak start and end positions more difficult. To mimic the real evaluation of chromatographic peak surface in our computer simulations, we set the peak start and peak end to the positions where signal amplitudes (Rstart
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and Rend , respectively) were the given fractions of peak maximum amplitude (Rmax ). We made the distinction between the small and large peaks, as their maxima exceed noise level (base line) by 10 and 100 times, respectively (this corresponds to Rstart /Rmax and Rend /Rmax values of 0.1 and 0.01). However, it was found from the simulations that the peak start position did not have a marked effect on the calculated peak area in the stated range. This was due to peak asymmetry making the area determination much more sensitive to the peak end position. The general scheme of the processes was considered as ka1
ka2
the purpose of GC studies in saturation conditions where nonlinear isotherms are involved or for multicomponent elution in preparative methods where axial dispersion and mass transfer effects influence the peak patterns. In IGC at infinite dilution such as here, some of these parameters can be neglected, such as the effect of column packing (which is the same for all probes in the series of measurements), the nonlinearity of adsorption isotherms, or the influence of probe amounts (which is negligible in the range of probe concentration õ 10 08 mol/l). Simulation Parameters
where P, S1 , and S2 denote the probe molecule in the gas phase, adsorbed within process 1 and adsorbed within process 2, respectively. The ka1 , kd1 and ka2 , kd2 are the rate constants for processes 1 and 2, respectively (indexes a and d denoting adsorption and desorption, respectively). Adsorption (1) was the nonequilibrium process in question, while adsorption (2) was always in equilibrium in simulations. This was achieved by using small and large values of the stated rate constants as related to the contact time between stationary and mobile phases in the column.
While calculating the elution in ion-exchange chromatography with large number of simulation steps, Sato and Watanabe (40) found that the simulation results occasionally produced inaccuracy. It was caused by the error accumulations in the calculation process even when the quadruple precision variables were used, giving significant uncertainty to the results. In order to avoid error accumulation, we used a low number of column cells (L Å 100) and simulation steps (N Å L / 1000 to L / 2500). This, however, may cause another uncertainty in the results related to the low column efficiency, i.e., small number of theoretical plates. For instance, most GC or LC measurements (26, 41) apply more than 1000 theoretical plates ( ú5000 in case of HLPC). In the case of IGC, where the column efficiency is usually not very large, lower values are acceptable (25).
Model
Procedure Verification
The kinetic model of adsorption is based on the assumptions of the Langmuir adsorption formula in Henry’s law approximation:
To evaluate the above procedure, a series of calculations with simple assumptions were performed.
S1 ` P ` S2 ,
0
kd1
kd2
1
2
[3]
d[P] Å ka1[P] 0 kd1[S1 ] / ka2[P] 0 kd2[S2 ] dt
[4]
Since process 2 is in thermodynamic equilibrium; the solution of Eq. [2] with ka2 /kd2 Å K2 (K2 being the surface partition coefficient) was used to calculate the amounts of probe on the surface and in the gas phase. For a nonequilibrium adsorption, higher and smaller values for both ka1 and kd1 described the faster and slower processes respectively. Rate constants of process 1 are related by, e.g., ka1 Å K1kd1 , where K1 is the partition coefficient of process 1 in hypothetical equilibrium. In the simulation, simultaneous contribution of two processes namely equilibrium and nonequilibrium was assumed while second one being controlled by kinetics. Several related parameters such as diffusion in the gas phase, pressure drop in the column, flow distribution, the effects of mass transfer through the interphase borders, and uniformity of column packing, were neglected. Many of them are frequently incorporated in advanced simulations programs for
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(A) When the probe transport through the column was assumed nondispersive, the d-Dirac FID response was obtained (ideal marker simulation). It was due to neglecting probe diffusion in the gas phase which showed that error accumulations in calculation process (42) is negligible even for the largest values of N and L parameters used. ( B ) Eluted peaks due to probes were always asymmetric, however, only feebly when a single equilibrium adsorption process was assumed. This is in agreement with the data reported for filled ( 12, 23 ) and capillary column IGC studies ( 25 ) . (C) When the equilibrium adsorption was assumed (simplification) the retention volumes were proportional to the assumed partition coefficients. The observations noted above confirm the validity of the assumptions made in the model and calculation procedure utilized in this work. RESULTS OF SIMULATIONS OF ELUTION PROCESSES
If immediate equilibrium was assumed for both the processes 1 and 2, obtained peaks were only slightly asymmetric
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second decay type is typical for experimentally determined retention of acidic, basic, and, in particular, amphoteric probes used in this work. Such results seem to confirm the interaction behavior of specific AB probes with cellulose in which a nonequilibrium adsorption process is involved. This further suggests that observed peak tailing can be caused not only by probe diffusion as normally cited in the literature but also by a surface nonequilibrium process. In this case, the elution yield was lower than 100% and depended strongly on the values of partition coefficients for both processes and the constant rates of process 1. The exemplary values of calculated elution yields are gathered in Table 1. Presented data show that incomplete elution of probe molecules can be related to the contribution of nonequilibrium adsorption process in retention phenomena where total elution yield decreases with the increasing partition coefficient of process 1. This indicates that smaller elution yield is due to the larger contribution of nonequilibrium process. The influence of partition coefficient of process 2 on elution yield is found to be more complex. Generally, elution yield decreases with partition coefficient of equilibrium process. This may be the manifestation of the competitive character of considered processes. Additionally, conformational behavior of AB probes (43) may have implications on nonequilibrium process. This, however, needs further studies. Higher values of FIG. 11. Shape of simulated peak (a) and decreasing peak shoulder in logarithmic coordinates (b) for equilibrium processes 1 and 2.
(Fig. 11a), similar to those obtained with the assumption of single equilibrium process. The simulated chromatogram revealed the features typical to those obtained in experiments for the retention of alkanes in cellulose packed column. When ln(R) is plotted against ln(t-tmax ) coordinates, FID signal (R) exhibited the presence of one-step decay as shown in Fig. 11b. In this case, probes were eluted close to 100% for relatively short observation time period. It seems that one-step decay of FID signal can be used to confirm the equilibrium character of the retention process in IGC measurements. Since the alkanes may be adsorbed by dispersive forces only, it is reasonable to assume that this type of chromatographic signals is related to dispersive interactions. However, the results differed markedly when the equilibrium and non-equilibrium processes were considered. When instantaneous equilibrium was assumed only for process 2 and nonequilibrium adsorption was for process 1, the decreasing shoulder of IGC peaks revealed different features than as noted above (Fig. 12a). The resulting decay of IGC signal described a slower decrease in the tail region where an additional feature along with the one-step decay is observed. This is evident in ln(R) vs ln(t-tmax ) coordinates (Fig. 12b). The deviation from one-step decay becomes more pronounced when larger contribution of nonequilibrium process is considered (Fig. 13b). The character of this
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FIG. 12. Shape of simulated peak (a) and decreasing peak shoulder in logarithmic coordinates (b) for equilibrium process 2 (K2 Å 2) and nonequilibrium process 1 (K1 Å 0.1).
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K1 have enhanced significantly the probe dispersion in the stationary phase and caused the elution yield to drop. Some deviations from this general behavior are due to the complex influence of K1 and K2 on peak shapes and are related to arbitrarily chosen Rend values of IGC peak. SUMMARY
This work has utilized the IGC measurement technique at infinitely dilute conditions to describe the sorption characteristics of probe molecules on solid surface. A major problem in the analysis of chromatographic results by IGC using retention time data was addressed. Elution yields of neutral and acid–base (AB) vapors from the cellulose fibers packed column were analyzed. The elution yield of probe molecules did not correlate with their retention time pattern but did correlate well with the enthalpies of specific adsorption of AB probes as well as acceptor and donor numbers of AB vapors. Although AB probes were eluted from the column incompletely, they did yield a flat postpeak FID signal indicating a complete elution. This incomplete elution phenomenon was ascribed to the nature of probes and their AB type of interactions with the stationary phase. Chromatographic retention process was described by two
TABLE 1 Values of Calculated Elution Yields (%) Process 1 Process 2 K2
Equilibrium conditions
K1 Å 0.1
K1 Å 1
K1 Å 2
0.02 0.1 1 2
98.2/99.9 98.1/99.9 98.3/99.8 98.1/99.90
97.2/98.9 97.0/98.8 96.4/98.5 95.8/97.6
87.8/90.2 87.9/89.6 81.5/87.1 77.0/—
80.2/81.5 78.9/80.4 67.8/88.3 61.7/—
processes: equilibrium and nonequilibrium sorption. The equilibrium adsorption gave normal, in-peak elution; however, the contribution of nonequilibrium surface adsorption is by no means to be discarded. The results seem to indicate that delayed elution of AB vapors is caused by kinetically controlled adsorption process. Depending on the time scale of IGC measurements, acid–base interactions can take part in both type of adsorption processes. It was proposed that delayed elution of AB probes was not attributed to the diffusion in the bulk. An attempt was made to confirm the presence of nonequilibrium adsorption process by computer simulations of retention. The simulation studies also have shown that effects of nonequilibrium process on retention time was negligible in the region controlled predominately by equilibrium adsorption. In other words, the former process cannot be studied by the IGC technique at infinite dilution condition on the basis of retention time measurements. Clearly, the implications are important if one were to predict interaction potential of materials on the basis of infinite dilution IGC studies. The significance of elution yield measurements is further justified. ACKNOWLEDGMENT We thankfully acknowledge financial support of this research by the Natural Sciences and Engineering Research Council, Canada.
REFERENCES
FIG. 13. Shape of simulated peak (a) and decreasing peak shoulder in logarithmic coordinates (b) for equilibrium process 2 (K2 Å 0.1) and nonequilibrium process 1 (K1 Å 2).
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1. Schreiber, H. P., and Lloyd, D. R., in ‘‘Inverse Gas Chromatography Characterization of Polymers and Other Materials’’ (D. R. Lloyd, T. C., Ward, and H. P. Schreiber, Eds.), p. 1. ACS Symposium Series 391, American Chemical Society, Washington, DC, 1989. 2. Braun, J. M., and Guillet, J. E., Adv. Polym. Sci. 21, 107 (1976). 3. Mandal, B. M., Bhattacharya, C., and Bhattacharya, S. N., J. Macromol. Sci. Chem. A 26, 175 (1989). 4. Berg, J. C., in ‘‘Wettability’’ (J. C. Berg, Ed.), p. 140. Marcel Dekker, New York, 1993. 5. Hegedus, C. R., and Kamel, I. L., J. Coat. Technol. 65, 23 (1993). 6. Mukhopadhyay, P., and Schreiber, H. P., Colloids Surf. A: Physicochem. Eng. Aspects 100, 47 (1995). 7. Crank, J., in ‘‘Diffusion in Polymers’’ (J. Crank and G. S. Park, Eds.). Academy Press, London, 1968.
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Ward, and H. P. Schreiber, Eds.), p. 33. ACS Symposium Series 391, American Chemical Society, Washington, DC, 1989. Wang, J.-Y., and Charlet, G., Macromolecules 22, 3781 (1989). Grob, R. L., ‘‘Modern Practice of Gas Chromatography.’’ Wiley-Interscience, New York, 1977. Felix, J. M., and Gatenholm, P., Nord. Pulp Pap. Res. J. 8, 200 (1993). Jacob, P. N., and Berg, J. C., Langmuir 10, 3086 (1994). Lee, H. L., and Luner, P., Nord. Pulp Pap. Res. J. 2, 164 (1989). Belgacem, M. N., Czeremuszkin, G., and Sapieha, S., Cellulose 2, 145 (1995). Mukhopadhyay, P., and Schreiber, H. P., Macromolecules 26, 6391 (1993). Gutmann, V., Steininger, A., Wychera, E., Monatsh. Chem. 97, 460 (1966). Riddle, F. L., and Fowkes, F. M., J. Am. Chem. Soc. 112, 3259 (1990). Conder, J. R., and Young, C. L., ‘‘Physicochemical Measurement by Gas Chromatography.’’ Wiley, Chichester, 1979. Glass, A. G., and Larsen, J. W., Macromolecules 26, 6354 (1993). Wasserman, B., Dresselhaus, M. S., Wolf, M., Wnek, G. E., and Woodhouse, J. D., J. Appl. Phys. 60, 668 (1986). Giddings, J. C., in ‘‘Dynamics of Chromatography,’’ Part 1, Vol. 1, p. 13. Marcel Dekker, New York, 1965. Brandrup, J., and Immergut, E. H., ‘‘Polymer Handbook.’’ Wiley-Interscience, New York, 1975. Rowland, S. P., and Howley, P. S., J. Polym. Sci., Part A: Polym. Chem. 26, 1769 (1988). Sato, H., and Watanabe, H., React. Polym. 17, 1 (1992). Hegedus, C. R., and Kamel, I. L., J. Coat. Technol. 65, 31 (1993). Frenkel, Z., Physik 26, 117 (1924). Mukhopadhyay, P., and Schreiber, H. P., J. Polym. Sci., Part B: Polym. Phys. 32, 1653 (1994).
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CS975074
Elution Behavior of Chemically Different Probes on the Evaluation of Surface Properties of Cellulose by Inverse Gas Chromatography Grzegorz Czeremuszkin, 1 Prithu Mukhopadhyay, and Slawomir Sapieha Engineering Physics Department, E´cole Polytechnique, P.O. Box 6079, Station A, Montre´al, Que´bec H3C 3A7, Canada Received March 17, 1997; accepted July 9, 1997
The inverse gas chromatography (IGC) technique has been employed to examine adsorption behavior of cellulose surfaces from elution characteristics of chemically different adsorbates. The neutral probes were eluted completely during IGC measurements while acidic, amphoteric, and basic probe molecules were eluted incompletely. In this work, complete elution is defined by the flat postpeak FID signal within the noise limits of the detector. An understanding of incomplete elution is thereby reached by introducing a precisely controlled, very small quantity of individual probes into the column. A strong correlation is found between elution efficiency of vapors and their enthalpies of acid–base interactions. Delayed elution of acid–base vapors is interpreted as being due to nonequilibrium sorption process, and calculations have shown that diffusion into the bulk is unlikely under the measurement conditions. The chromatographic process is simulated and it is found that the contribution of nonequilibrium adsorption to the retention is responsible for observed peak tailing and thereby delayed elution of acid–base probes. Results of the study indicate that characterization of acid–base (electron acceptor–donor) type of stationary phase material surfaces by IGC needs careful attention and is an area for future work. q 1997 Academic Press Key Words: cellulose; inverse gas chromatography; acid–base interactions; elution yield; delayed elution; equilibrium and nonequilibrium adsorption.
INTRODUCTION
The popularity in the use of inverse gas chromatography (IGC) measurements applied to surface, interface, and bulk characterization of technologically important materials is due mainly to the technique’s flexibility and potential for yielding useful data in the wide range of physicochemical properties of materials. Except for the reversed role of solute probes and stationary phase packing materials, the principle and instrumentation of IGC measurements are similar to that of conventional gas chromatography (GC). The principle is based on the characteristic equilibrium partitioning of the vapor molecules (adsorbate) between the mobile and solid stationary phases (adsorbent). Schreiber and Lloyd (1) have 1
To whom correspondence should be addressed.
reviewed the method, its advantages, and limitations including areas of application. Several other reviews on this subject are also available (2–6). Essentially, the instrument monitors the residence time and shape of the elution curve for different probe adsorbates of known chemical structure and properties, which allow inferences concerning the characteristics of the column packing materials to be drawn, i.e., the solid adsorbent surfaces. The implications of IGC studies can be readily recognized from the fact that solids used in many industrially important formulations and/or processes are not utilized alone in its virgin state. Frequently, to achieve the level of performance desired in commercial applications, solid surfaces are modified and/or used in combination with other additives, thereby complicating the composition of solids’ interfaces and their interaction potential. It is therefore important to know both the nature and magnitude of solid surface free energy to generate products of desired properties and to optimize the process. Similarly, the relevance of studies involving diffusion of molecules into the system and the migration of components from the bulk to the surface are equally important. In many industrial processes, such as food packaging, controlled release technology, solvent devolatilization, and bulk polymerization, knowledge of small molecule diffusion is vital. Conventionally, diffusion studies are carried out by sorption experiments (7, 8). However, difficulties in comparing and interpreting experimental data on diffusion of solvent molecules in polymers have been observed by several researchers (9, 10). In recent years, diffusivity measurements in polymer–solvent systems by IGC have become a method of growing choice. Nevertheless, uncertainty concerning the accuracy of diffusion data obtained by IGC is evident from literature reports. While measuring diffusion coefficients in polymer–solvent systems, Hu et al. (11) observed that correct modeling of the stationary phase geometry in the column is a difficult task. Pawlisch et al. (12) argued that use of capillary columns instead of the packed column method can circumvent this difficulty because of the uniform distribution of the polymeric stationary phase. In this regard, Laurence and co-workers (12–15) studied extensively the diffusion of solvents including the size effects of penetrants in PMMA
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0021-9797/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
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and PVAc by capillary column IGC. Elsewhere, applying the same methodology and model, diffusion coefficient measurements of solvents in PS were carried out (16). These studies, however, raised a serious concern over the validity of the model used (17) which assumes no surface adsorption at the gas–polymer interface. Earlier, Smidsrod and Guillet (18) showed that, near the polymer Tg , surface effects and bulk diffusion coexist. Schreiber and Qin (17) further demonstrated that, by changing the carrier gas flow rate, surface adsorption and bulk diffusion coexist at temperatures above the polymer Tg . In that study, the stationary phase material was styrene/4-vinylpyridine. It becomes obvious from these studies that a greater familiarity of the surface adsorption process is necessary to better understand the issue of diffusion. Another important aspect of IGC investigation is associated with the analysis of resulted chromatogram. Frequently, the chromatographic retention volume, Vr (derived from the retention time, tr ), is considered as a fundamental datum characterizing the equilibrium partitioning of probe molecules between the gas and solid phases. While reproducible tr is obtained within the experimental error during IGC investigation, however, the data do not yield the true nature of the sorption phenomenon. Particularly, for vapors which are able to interact by acid–base forces in addition to Lifshitz– van der Waals (LW) forces. As a result, complete elution behavior of these probes remain unexplored. In this work, we attempted to analyze the incomplete elution of acid–base probes from their elution behavior by employing IGC technique. For this purpose, delayed elution of probe molecules through the stationary phase were analyzed quantitatively, and simultaneously the shapes of respective peaks were simulated by computer program. Further, this study addresses the issues of surface adsorption and bulk diffusion of chemically different probe molecules for a better knowledge of sorption process. We have chosen cellulose as the stationary phase material. Our attention toward cellulose fibers is drawn since its surface properties are becoming increasingly important as its application areas continue to broaden. These include increasing use of recycled fibers in newsprint production and surface and interfacial interactions between cellulose and other materials, such as fillers in paper, polymeric layers in laminates or inks in printing. The probe molecules were chosen on the basis of their propensity to participate in acid–base type interactions with the stationary phase. Our objective also constitutes chromatographic data handling procedures. It is hoped that the conclusions obtained in this work may provide clues to describe diffusion data by IGC more accurately. Concept of Delayed Elution Not infrequently, diffusion studies have encountered retention of specific probe molecules in the system for prolong
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period of time. Robertson reported (19) prolonged retention of organic liquids such as alcohols, ketones, ethers, esters, aldehydes, amines, and acids in cellulose fibers while conducting liquid phase immersion swelling tests. In fact, 21 out of 26 liquids employed in that study enhanced the weight of dry cellulose fibers. The study involved immersion of cellulose fibers in test liquids which was subsequently recovered by drying at 1057C for 16 h. The author attributed the prolonged retention of probe molecules as either entrapment of test liquids within the fiber structure or reaction with cellulose surfaces. However, entrapped liquids were released when dried cellulose were made to reswell in water or methanol after another drying procedure. It is known that IGC studies at infinite dilution employ probe molecules at very low concentration in gas phase contrary to the concentrations used in immersion swelling test. Presumably, one would not expect such an effect at infinite dilute condition. During the current investigation of cellulose at infinite dilution, we found that some probes were not eluted through the stationary phase. These probes such as alcohols or amines appeared to have interacted strongly with the packing material and were either permanently trapped by cellulose or their elution times were very long compared to the time span of measurements. Whereas, other probes (ethers, esters, ketones) were eluted, generating distinct chromatographic signals. Thus the term ‘‘delayed elution’’ refers to the prolonged trapping phenomenon or incomplete elution of probe molecules in the adsorbent which allows to distinguish the latter effect form typical retention behavior normally seen by IGC. Retention Process Simulation Computer simulations have proved their strength to the understanding of surface science (20–22). Indeed, several studies benefitted from the computer simulations of elution process to analyze the peak shape and retention behavior in gas chromatography. Among others, Hattam and Munk simulated the elution of probes by the IGC technique with the assumption that diffusion (23, 24) or equilibrium adsorption (23) takes place in the solute–polymer system. For the diffusion-controlled process, authors distinguished four types of chromatographic behavior which include instantaneous equilibrium, pseudoequilibrium, a transition region, and a marker-like region corresponding to the diminishing diffusion coefficient values. They noted that the probe amount had the influence on the maximum peak position and confirmed the validity of using moments method in IGC data analysis (25), whereas in this work retention of acid– base probes at infinite dilution conditions was simulated assuming two simultaneous processes (equilibrium and nonequilibrium) responsible for probe retention behavior. The kinetic model was utilized to describe aspects of delayed elution.
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MATERIALS AND METHODS FOR IGC STUDIES
Column Preparation Washed and nonwashed cellulose fibers, CF-1 (Whatman), were used in this study. The nonwashed variety was used as received, whereas the same fibers were washed with distilled water and dried in vacuum at 607C (washed fibers) before the investigation. Cellulose fibers (5 g of each washed and nonwashed separately) were packed in two different previously degreased, washed, and dried stainless steel tubings (4.4 mm i.d. and 1 m long). For the peak shape analysis purpose, short columns were also utilized (4.4 mm i.d., 6 cm long, containing 0.25 g of cellulose) employing the identical procedure. Before the measurements, packed columns (as well as the empty columns used to determine the reference data) were conditioned overnight at 1107C under the flow of carrier gas (helium, 20 ccm/min). The conditions were chosen to obtain a constant background signal of thermal conductivity detector (TCD) system. Column conditioning temperature was based on industrial practice of effectively removing water from cellulose fibers. Hydrocarbons and acid–base probes used in this work were all of analytical grades unless mentioned otherwise. The IGC measurements were performed using Varian 3400 gas chromatograph, equipped with flame ionization (FID) and thermal conductivity (TCD) detectors. Methane and air were used as the indirect and direct markers, respectively. In other words, retention times were determined with respect to air TCD peak and recalculated corresponding to methane FID peak. The average error in the evaluation of retention times (tr ) was below 0.5% for all probes except pentane and hexane where errors were 4% and 2.1%, respectively. Elution Efficiency In quantitative elution measurements precisely controlled amounts of molecular probes (10 011 –10 012 mol/injection) were introduced into the GC system using the following dosage procedure: Liquid probes (Fluka, Anachemia; diethyl ether and ethyl acetate previously dried and purified by dis˚ molecular sieves at 257C in tillation) were stored over 4 A glass, septum-sealed bottles. A known volume of probe vapor was sampled with Hamilton syringe and injected to the encapsulated glass ampule to obtain the required dilution. Special care was taken during sampling to avoid the increase of bottle temperature containing the liquid probe. Diluted vapor was subsequently sampled from the glass ampule prior to injection, thus reaching infinite dilute condition. The dilution, required to obtain FID signal at least one order of magnitude higher than its sensitivity threshold, was calculated on the basis of saturated vapor pressure of probe liquids and FID response factor (26). The calculated amount of diluted vapor was injected into
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FIG. 1. The percentage of probe molecules eluted (elution yield) through the column as compared to the amount of probes injected.
the column and the chromatographic peak area was computed by Varian system software. The elution efficiency ( b ) of each probe was calculated as the ratio b Å Ap /Ae ,
[1]
where Ap and Ae are the peak areas of equivalent amount of injected probe for packed and empty column, respectively. To minimize experimental error, Ap was determined from at least six injections and Ae was calculated from Ae Å FVin j ,
[2]
where Vin j is the volume of injected probe and F is the FID sensitivity factor. The value of F, defined as the peak area per unit volume of the probe injected to reference (empty) column was found as the slope in Ae vs Vin j dependence (for Vin j Å 0.05–1 ml). The average error of FID sensitivity factor remained below {10% and was higher only for pentane. The ultimate error of elution efficiency for each probe was calculated from its component errors, i.e., the errors from the FID sensitivity factor and the FID response for the packed column. Delayed Elution For analysis of peak shape in its tail region, where the probe elution rate becomes very low and the resulted signal fall below the detector sensitivity threshold, the short columns (0.25 g of cellulose) were used. This resulted in shorter retention times and brought the elution rate above the noise level of FID. Additional probes were also used, such as nonane, decane, undecane, dodecane, methanol, ethanol, and tert-butanol (Anachemia). RESULTS OF IGC STUDIES
The probe molecules which eluted through the column and gave measurable FID signals are shown in Fig. 1. These
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FIG. 2. Dependence of probes elution yield on the adsorption free free energy due to acid–base interactions, DH ab , between the cellulose surface and chemically different probes.
probes are commonly used to characterize the cellulose surface (27–30). However, injections of precisely measured amounts of these probes (10 011 –10 12 mol/injection) revealed incomplete elution during measurements. In spite of incomplete elution, they exhibited a flat postpeak FID signal within the noise limits, an indication of entire removal of adsorbates from the column. Delayed elution, as mentioned earlier, contributed significantly to their peak behavior and decreased the elution efficiency. Further, probe molecules like methanol, ethanol, pyridine, formamide, n-butylamine, and tert-butylamine did not yield peaks at the measurement conditions. The reason may be that at infinite dilute concentration, these probes were either permanently trapped by cellulose or desorbed at very slow rates, giving FID signals within the limits of detector noise. In the above noted figure, the percentage of probe molecules of each kind eluted through the column compared to the amount that were injected into the system is presented. The hydrocarbons which are able to interact via LW forces only gave elution yield close to the unity (within statistical error), whereas probes which can be involved in acid–base (acceptor–donor type) interactions in addition to LW forces were eluted incompletely. It is further observed that elution efficiency and retention time of individual probes did not correlate. For instance, at column temperature of 507C, tr values of octane and ethyl acetate were almost identical yet elution yields (E) for both vapors were 100% and 60%, respectively. The results indicate a possible link between acid–base characteristics of vapor probes and their corresponding E values. Earlier, Mukhopadhyay and Schreiber (31) suggested while studying the SBR polymer that vapors that can interact with the polymer by AB forces are more strongly retained by the surface above Tg than the hydrocarbon molecules of similar dimensions. Figure 2 tests the hypothesis in which T ! Tg and shows that the percentage of
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elution yield can be correlated with specific nature of the probes where E is plotted against the enthalpies of acid–base interactions ( DH ab ). It is evident that stronger the ability of probe vapors to enter into acid–base interactions with cellulose, the longer the dwelling time period, which in turn reduces the percentage of elution yield. This shows that acid–base (AB) interactions are related to incomplete and therefore, delayed elution phenomenon. In order to ascertain AB character of the injected probes with E values, the acceptor (AN) and donor number (DN) approach of Gutman was applied (32). As shown in Fig. 3, E gives a linear relationship with AN and DN numbers of adsorbates. We used the modified acceptor numbers due to Riddle and Fowkes (33). Apparent deviation from linearity can be understood from the fact that the solid surfaces under investigation is energetically heterogeneous. The modified AN numbers were derived by correcting the van der Waals contributions to the 31P NMR chemical shifts of Et3PO and the IR shifts for the —P|O stretching peaks using pure probe liquids on squalane, a liquid hydrocarbon that has no acidic or basic sites. In order to confirm the aspects of incomplete elution of acid–base probes in IGC studies, a finite amount of water was introduced into the column after basic and amphoteric probe injections. Probes of the latter category, such as THF, diethyl ether, acetone, and ethyl acetate, were chosen since the cellulose surface is predominantly acidic (28). Prior to water injections, zero FID response was reached to ensure no elution of AB probes that were previously put into the column. The column was then allowed to stabilize for another 30 min at the measurement temperature. Interestingly enough, subsequent water injections resulted in chromatographic peaks. This is shown in Fig. 4. The first injection of 1 ml of water, marked with an arrow in the figure, gave a small FID response. The observed response revealed the
FIG. 3. Plot showing a relationship between the probes elution yield and the donor (DN) and acceptor numbers (AN*) values for the probes adsorbed on cellulose surface.
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FIG. 4. Detector (FID) response for subsequent injections of liquid water to the column after multiple injections of probe vapors. The water injections are marked with arrows. FIG. 5. Shape of peak shoulder (one-step decay) for undecane (b, ---), dodecane (c, – – – ), and decane (a1–a3) with increasing concentration.
release of organic probes which had been trapped or retained in the column. This is obvious since the flame ionization detector is sensitive to carbon compounds only and gives no signal for water. Three consecutive injections of 5 ml of water yielded three significant peaks in order of decreasing intensity. Finally, the small yet broad FID signal showed the remaining of the stated organic adsorbates retained inside the column. It seems likely that the stronger affinity of water molecules toward cellulose due to stronger AB interactions has made water drive out organic probe molecules which were held by weaker AB forces onto the cellulose. If one were to assume that retention times of above mentioned vapors characterize the AB interactions potential of cellulose surface and describe the complete elution of adsorbates then the appearance of water-induced peaks prove otherwise. Rather specific probes were held onto the stationary phase inside the column by acid–base forces even after the postpeak FID signal was brought to the level of base line noise. The results, therefore, confirm earlier hypothesis of decreased elution efficiency due to acid–base nature of probes (Fig. 2). Figure 5 represents the shape of chromatographic signal decay for decane (n-C10), undecane (n-C11) and dodecane (n-C12) in ln(R) vs ln(t 0 tmax ) coordinates, where R denotes the FID response at time t and tmax is the position of respective peak maximum. These coordinates are useful as IGC peak shoulders decrease and allow observation of the short and long time trends of FID signals. All curves given in Fig. 5 are very similar, illustrating the decay type of FID signal and will be referred to henceforth as ‘‘one-step decay.’’ It is observed that the decay type is independent of probe concentration and of alkanes irrespective of their carbon chain length (n-C10, curves a1–a3; n-C11 and n-C12, curves b and c). When AB probes were introduced into the column the peak shoulders differed from those observed for alkanes. The deviation involved in a slower signal decrease at a longer period of time and characteristically depended on
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the adsorbates’ AB character. For acidic probes the deviation from one-step decay was small (Fig. 6, shown for CCl4 ), whereas the deviation was relatively profound for basic and amphoteric vapors (Fig. 7, shown for diethyl ether and acetone). The smaller deviation of acidic vapors can be attributed to the stationary phase AB properties. However, when the nature of IGC signal decay of basic and amphoteric probes was compared with those observed for alkanes, not only a type dependence but also a concentration dependence were found. A representative example of such dependencies utilizing basic probe tetrahydrofuran is shown in Fig. 8. Alcohols (Fig. 9), which are known to strongly interact with cellulose, gave an FID signal decay that can be compared to the above stated pattern. However, the contribution to one-step decay (alkane-like behavior) was very small for ethanol whereas it was distinct in case of tert-butanol which may be due to the tert-butyl group in the latter molecule.
FIG. 6. Shape of peak shoulder for carbon tetrachloride with increasing concentration (a–c).
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FIG. 7. Shape of peak shoulder for acetone (---) and diethyl ether ( – - – ).
The difference in shape of IGC peak shoulders detected for alkanes and acid–base probes can be ascribed to different adsorption phenomena which eventually accounted for their retention process and will be discussed in subsequent sections. Character of Retention Process In the first process, i.e., ‘‘one-step decay’’ of the FID signal, the stabilization of adsorption equilibrium was fast in comparison to gas–surface contact time. This can be seen from the shapes of hydrocarbon peaks, which exhibited the features of typical equilibrium retention process (23). Since direct correlation between the partition coefficient of equilibrium adsorption (K) and the retention time (tr ) exists, the process can be characterized by the IGC method. The second process was related to the peak tailing. This type of peak asymmetry is observed when the equilibrium
FIG. 8. Shape of peak shoulder for tetrahydrofuran (a–c) with increasing concentration.
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FIG. 9. Shape of peak shoulder for ethanol ( – – – ) and tert-butanol ( —).
of sorption is not attained during the measurement period. This interpretation is generally accepted in gas–solid chromatography (34). Whereas the decrease of retention volume with the probe amount as well as carrier gas flow rate is normally encountered for nonequilibrium sorption processes. In this work, however, the retention volumes were affected neither by the probe amount (in the range of 10 011 –10 012 mol/injection) nor by changing the flow rate (10–30 sccm/ min). This kind of phenomenon was previously reported for several glassy polymers below their Tg , when sufficiently small amount of probes designated as infinite dilution were injected (35). However, to the best of our knowledge the elution efficiency was never quantitatively analyzed in such cases. Contribution of Nonequilibrium Sorption Process to Delayed Elution In general, nonequilibrium sorption in gas chromatography is controlled by surface and/or by bulk kinetics. The contribution of slow kinetic process to the retention was studied (36), and the model that included two kinds of sorption sites with fast and slow time constants was analyzed (37). In case of IGC measurements applied to surface characterization of polymers, the presence of peak tails and large peak asymmetry is normally attributed to the bulk diffusion (24). At first sight, observed chromatographic peaks from this work may appear to have resulted from the bulk diffusion process. It is worth mentioning that diffusion of water or alcohols into the cellulose fibers by IGC have already been noted in the same temperature range (38). In that study, however, liquids or vapors were used at concentrations 5– 7 orders of magnitude higher than those we utilized in the current investigation. At infinite dilution IGC, the origin of peak broadening for polymers below Tg is still a matter of
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debate although the arguments exist that it cannot be caused by nonequilibrium diffusion (23). In this work, the remote possibility of diffusion effects at very low dilution and at significantly lower temperature region of investigation than the Tg of cellulosic materials (39) appears to be reasonable. Moreover, for semicrystalline polymers it is known that diffusion of molecules into amorphous phase about 130–2007C below polymer Tg is very limited (3). This can be further appreciated by way of rough calculations. The surface area of a typical probe molecule is of the ˚ 2 . For a 1 m column containing 5 g of order of Ç50 A cellulose of 1 m2 /g specific surface area, pentane and ethyl acetate presented two limiting values for peak half-width, which are 5 and 60 s, respectively, at 407C. This yields an estimated maximum surface coverage occupied by adsorbed molecules, in the order of 10 06 of the total accessible surface. At this low concentration it is very unlikely that adsorbate– adsorbate interactions or swelling-induced diffusion will occur. Further, if the diffusion were responsible for probe retention in this time scale then the average diffusion distance ˚ during one elemental act of sorp(x) would be below 50 A tion (x was calculated from x Å 2[Dt/ p] 1 / 2 , assuming a diffusion coefficient D Ç 10 8 cm2 /s) which is essentially the surface region. Due to the presence of functional groups on cellulose surfaces, preferential interactions between the cellulose and AB probes can be more likely, provided that the activation energy barrier is overcome. Such a process may not be controlled by thermodynamic equilibrium within the time scale of IGC experiment but may do so under kinetically controlled process. Therefore, the observed second decay type FID signal refers to the nonequilibrium adsorption responsible for the second process. In other words, the AB interactions seem to contribute to the second process causing a delayed elution and subsequently decreasing the elution efficiency. The implications are important since the contribution of delayed elution to the retention process increases with the concentration of adsorbate molecules. In particular, when comparing the results of IGC at infinite dilute concentration with the results of contact angle measurements or diffusion coefficients from sorption studies. To analyze the manifestation of proposed mechanism of nonequilibrium adsorption in IGC, we applied the method of computer simulation of probe elution. COMPUTER SIMULATIONS METHOD FOR PROBE ELUTION
The simulation is described schematically in Fig. 10. Chromatographic column was partitioned into L elements (cells) containing the mobile and stationary phases numbered as m. The initial step was to locate probe molecules [P0 ] in the first column element. Each subsequent simulation
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FIG. 10. Column partitioning for probe retention and a schematic presentation of simulation steps.
steps involved in the transfer of m- cell content (gas phase) to m / 1 cell followed by the calculation of number of molecules in mobile and stationary phases after a given contact time (t f ). The value of t f was the same for each calculation, which represented the constant flow rate of carrier gas in IGC experiment. The concentrations of molecules in mobile phase [P] and in stationary phase [S1 , S2 ] were calculated from the equations shown below. The content of the last cell [PM ] was equal to the number of molecules reaching the detector and was equivalent to the FID response (R). These values were collected as a function of the current step (n) which represented the simulated chromatogram in time domain as follows: [PM (n)] Å R(t);
t Å nt f
with
N @ L,
where N is the total number of simulation steps. In each case the elution yield was calculated as the percentage of probe molecules which passed through the detector area with respect to the number of molecules introduced. In IGC studies, determination of peak surface area is often calculated by the system software. The decisions where the peak starts and ends are done either automatically or by the operator, during the data acquisition procedure. These decisions are based on the value of signal amplitude, which increases significantly over the base line when the peak starts and returns to the base line level when the peak ends. At infinite dilution IGC, the probe amount injected into the column is very small and thus yields a very low detector response. The resulted signal, in fact, is close to the sensitivity threshold of the detector used. This brings up the issue of detector noise or ‘‘spreading’’ the base line which renders the decision on peak start and end positions more difficult. To mimic the real evaluation of chromatographic peak surface in our computer simulations, we set the peak start and peak end to the positions where signal amplitudes (Rstart
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and Rend , respectively) were the given fractions of peak maximum amplitude (Rmax ). We made the distinction between the small and large peaks, as their maxima exceed noise level (base line) by 10 and 100 times, respectively (this corresponds to Rstart /Rmax and Rend /Rmax values of 0.1 and 0.01). However, it was found from the simulations that the peak start position did not have a marked effect on the calculated peak area in the stated range. This was due to peak asymmetry making the area determination much more sensitive to the peak end position. The general scheme of the processes was considered as ka1
ka2
the purpose of GC studies in saturation conditions where nonlinear isotherms are involved or for multicomponent elution in preparative methods where axial dispersion and mass transfer effects influence the peak patterns. In IGC at infinite dilution such as here, some of these parameters can be neglected, such as the effect of column packing (which is the same for all probes in the series of measurements), the nonlinearity of adsorption isotherms, or the influence of probe amounts (which is negligible in the range of probe concentration õ 10 08 mol/l). Simulation Parameters
where P, S1 , and S2 denote the probe molecule in the gas phase, adsorbed within process 1 and adsorbed within process 2, respectively. The ka1 , kd1 and ka2 , kd2 are the rate constants for processes 1 and 2, respectively (indexes a and d denoting adsorption and desorption, respectively). Adsorption (1) was the nonequilibrium process in question, while adsorption (2) was always in equilibrium in simulations. This was achieved by using small and large values of the stated rate constants as related to the contact time between stationary and mobile phases in the column.
While calculating the elution in ion-exchange chromatography with large number of simulation steps, Sato and Watanabe (40) found that the simulation results occasionally produced inaccuracy. It was caused by the error accumulations in the calculation process even when the quadruple precision variables were used, giving significant uncertainty to the results. In order to avoid error accumulation, we used a low number of column cells (L Å 100) and simulation steps (N Å L / 1000 to L / 2500). This, however, may cause another uncertainty in the results related to the low column efficiency, i.e., small number of theoretical plates. For instance, most GC or LC measurements (26, 41) apply more than 1000 theoretical plates ( ú5000 in case of HLPC). In the case of IGC, where the column efficiency is usually not very large, lower values are acceptable (25).
Model
Procedure Verification
The kinetic model of adsorption is based on the assumptions of the Langmuir adsorption formula in Henry’s law approximation:
To evaluate the above procedure, a series of calculations with simple assumptions were performed.
S1 ` P ` S2 ,
0
kd1
kd2
1
2
[3]
d[P] Å ka1[P] 0 kd1[S1 ] / ka2[P] 0 kd2[S2 ] dt
[4]
Since process 2 is in thermodynamic equilibrium; the solution of Eq. [2] with ka2 /kd2 Å K2 (K2 being the surface partition coefficient) was used to calculate the amounts of probe on the surface and in the gas phase. For a nonequilibrium adsorption, higher and smaller values for both ka1 and kd1 described the faster and slower processes respectively. Rate constants of process 1 are related by, e.g., ka1 Å K1kd1 , where K1 is the partition coefficient of process 1 in hypothetical equilibrium. In the simulation, simultaneous contribution of two processes namely equilibrium and nonequilibrium was assumed while second one being controlled by kinetics. Several related parameters such as diffusion in the gas phase, pressure drop in the column, flow distribution, the effects of mass transfer through the interphase borders, and uniformity of column packing, were neglected. Many of them are frequently incorporated in advanced simulations programs for
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(A) When the probe transport through the column was assumed nondispersive, the d-Dirac FID response was obtained (ideal marker simulation). It was due to neglecting probe diffusion in the gas phase which showed that error accumulations in calculation process (42) is negligible even for the largest values of N and L parameters used. ( B ) Eluted peaks due to probes were always asymmetric, however, only feebly when a single equilibrium adsorption process was assumed. This is in agreement with the data reported for filled ( 12, 23 ) and capillary column IGC studies ( 25 ) . (C) When the equilibrium adsorption was assumed (simplification) the retention volumes were proportional to the assumed partition coefficients. The observations noted above confirm the validity of the assumptions made in the model and calculation procedure utilized in this work. RESULTS OF SIMULATIONS OF ELUTION PROCESSES
If immediate equilibrium was assumed for both the processes 1 and 2, obtained peaks were only slightly asymmetric
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135
second decay type is typical for experimentally determined retention of acidic, basic, and, in particular, amphoteric probes used in this work. Such results seem to confirm the interaction behavior of specific AB probes with cellulose in which a nonequilibrium adsorption process is involved. This further suggests that observed peak tailing can be caused not only by probe diffusion as normally cited in the literature but also by a surface nonequilibrium process. In this case, the elution yield was lower than 100% and depended strongly on the values of partition coefficients for both processes and the constant rates of process 1. The exemplary values of calculated elution yields are gathered in Table 1. Presented data show that incomplete elution of probe molecules can be related to the contribution of nonequilibrium adsorption process in retention phenomena where total elution yield decreases with the increasing partition coefficient of process 1. This indicates that smaller elution yield is due to the larger contribution of nonequilibrium process. The influence of partition coefficient of process 2 on elution yield is found to be more complex. Generally, elution yield decreases with partition coefficient of equilibrium process. This may be the manifestation of the competitive character of considered processes. Additionally, conformational behavior of AB probes (43) may have implications on nonequilibrium process. This, however, needs further studies. Higher values of FIG. 11. Shape of simulated peak (a) and decreasing peak shoulder in logarithmic coordinates (b) for equilibrium processes 1 and 2.
(Fig. 11a), similar to those obtained with the assumption of single equilibrium process. The simulated chromatogram revealed the features typical to those obtained in experiments for the retention of alkanes in cellulose packed column. When ln(R) is plotted against ln(t-tmax ) coordinates, FID signal (R) exhibited the presence of one-step decay as shown in Fig. 11b. In this case, probes were eluted close to 100% for relatively short observation time period. It seems that one-step decay of FID signal can be used to confirm the equilibrium character of the retention process in IGC measurements. Since the alkanes may be adsorbed by dispersive forces only, it is reasonable to assume that this type of chromatographic signals is related to dispersive interactions. However, the results differed markedly when the equilibrium and non-equilibrium processes were considered. When instantaneous equilibrium was assumed only for process 2 and nonequilibrium adsorption was for process 1, the decreasing shoulder of IGC peaks revealed different features than as noted above (Fig. 12a). The resulting decay of IGC signal described a slower decrease in the tail region where an additional feature along with the one-step decay is observed. This is evident in ln(R) vs ln(t-tmax ) coordinates (Fig. 12b). The deviation from one-step decay becomes more pronounced when larger contribution of nonequilibrium process is considered (Fig. 13b). The character of this
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FIG. 12. Shape of simulated peak (a) and decreasing peak shoulder in logarithmic coordinates (b) for equilibrium process 2 (K2 Å 2) and nonequilibrium process 1 (K1 Å 0.1).
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K1 have enhanced significantly the probe dispersion in the stationary phase and caused the elution yield to drop. Some deviations from this general behavior are due to the complex influence of K1 and K2 on peak shapes and are related to arbitrarily chosen Rend values of IGC peak. SUMMARY
This work has utilized the IGC measurement technique at infinitely dilute conditions to describe the sorption characteristics of probe molecules on solid surface. A major problem in the analysis of chromatographic results by IGC using retention time data was addressed. Elution yields of neutral and acid–base (AB) vapors from the cellulose fibers packed column were analyzed. The elution yield of probe molecules did not correlate with their retention time pattern but did correlate well with the enthalpies of specific adsorption of AB probes as well as acceptor and donor numbers of AB vapors. Although AB probes were eluted from the column incompletely, they did yield a flat postpeak FID signal indicating a complete elution. This incomplete elution phenomenon was ascribed to the nature of probes and their AB type of interactions with the stationary phase. Chromatographic retention process was described by two
TABLE 1 Values of Calculated Elution Yields (%) Process 1 Process 2 K2
Equilibrium conditions
K1 Å 0.1
K1 Å 1
K1 Å 2
0.02 0.1 1 2
98.2/99.9 98.1/99.9 98.3/99.8 98.1/99.90
97.2/98.9 97.0/98.8 96.4/98.5 95.8/97.6
87.8/90.2 87.9/89.6 81.5/87.1 77.0/—
80.2/81.5 78.9/80.4 67.8/88.3 61.7/—
processes: equilibrium and nonequilibrium sorption. The equilibrium adsorption gave normal, in-peak elution; however, the contribution of nonequilibrium surface adsorption is by no means to be discarded. The results seem to indicate that delayed elution of AB vapors is caused by kinetically controlled adsorption process. Depending on the time scale of IGC measurements, acid–base interactions can take part in both type of adsorption processes. It was proposed that delayed elution of AB probes was not attributed to the diffusion in the bulk. An attempt was made to confirm the presence of nonequilibrium adsorption process by computer simulations of retention. The simulation studies also have shown that effects of nonequilibrium process on retention time was negligible in the region controlled predominately by equilibrium adsorption. In other words, the former process cannot be studied by the IGC technique at infinite dilution condition on the basis of retention time measurements. Clearly, the implications are important if one were to predict interaction potential of materials on the basis of infinite dilution IGC studies. The significance of elution yield measurements is further justified. ACKNOWLEDGMENT We thankfully acknowledge financial support of this research by the Natural Sciences and Engineering Research Council, Canada.
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FIG. 13. Shape of simulated peak (a) and decreasing peak shoulder in logarithmic coordinates (b) for equilibrium process 2 (K2 Å 0.1) and nonequilibrium process 1 (K1 Å 2).
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