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110th Anniversary: Commentary: Perspectives on Adsorption of Complex Mixtures Krista S. Walton Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b04243 • Publication Date (Web): 21 Aug 2019 Downloaded from pubs.acs.org on August 27, 2019

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Industrial & Engineering Chemistry Research

110th Anniversary: Commentary: Perspectives on Adsorption of Complex Mixtures Krista S. Walton* School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive NW, Atlanta, Georgia 30332, USA, [email protected]

ABSTRACT: The development of new adsorbents and/or new adsorption separation processes has the potential to bring enormous energy and cost savings to the chemical process industry. Achieving success in this area requires a detailed understanding of how a proposed adsorbent performs under realistic conditions, but most research studies focus on idealized process streams. This critical lack of data on adsorption of complex mixtures represents a major barrier to growth in the development of new separation systems. This commentary discusses the persistent nature of the mixture-adsorption knowledge gap, while providing some historical framework, and provides several strategies that researchers might adopt to move away from pure-component systems towards true multi-component adsorption studies.

Introduction The chemical process industry represents one of the largest and most important industries in the world. The US is the worldwide leader in the production of chemical products, with an estimated chemical output value of over $765 billion in 2017.1 A perception of the chemical industry may be one of a classic, well-established sector, but the US is currently undergoing a dramatic renaissance, with many billions of dollars being invested in new production facilities. The amount of energy consumed by the chemical process industry is large and growing. It is well known that the efficiency of chemical production largely tracks the efficiency of the separation and purification steps involved in the product supply chain. These chemical separations are energy intensive and, by some estimates, consume 10-15% of all energy produced in the US.2 Furthermore, much of this energy is produced from hydrocarbon sources, which results in a corresponding production of carbon dioxide. The majority of legacy separation systems are inherently energy inefficient. For example, distillation columns that have been highly optimized over decades for water purification still consume 50x more energy than necessary on a thermodynamic basis.3 A key aspect of most legacy separation processes (e.g. distillation) is that they rely on thermally-driven phase changes. Advanced separation units that make use of membranes or adsorption processes can offer a more efficient alternative to the existing separation systems, largely because many of these systems avoid the need to input thermal energy to achieve phase changes. Unfortunately, there are many issues that must be resolved before new non-thermal separations applications can be developed. A US Department of Energysponsored report on materials for separation technologies published over a decade ago4 highlights these barriers and subsequent opportunities in materials discovery for energy and emission reduction that are still relevant today. For example, to offer valid alternatives to legacy separation systems, separation materials are needed that provide high selectivity, high throughput, durability in complex, harsh industrial environments, and sufficient economies of scale. Additionally, fundamental information is needed to enable process design for these approaches, and in almost all industrially relevant situations, this information is lacking.

Much of the fundamental work on materials for use in adsorption separations focuses on idealized systems. For example, thousands of papers have been published on adsorption of pure gases. However, many of the environments in which adsorbents must function are chemically complex. For example, enormous reserves of natural gas exist that contain up to 50% of H2S in addition to moisture, CO2 and other hydrocarbons.5 Crude oil is a complex mixture of 104-105 distinct chemical species.6 Pipeline quality natural gas contains up to 10 ppm H2S, low levels of water vapor, and ppm levels of mercaptans that are added as odorants.7 Materials designed for capturing CO2 from coal-fired power plants will need to operate in the presence of ppm levels of SOx and NOx, even after treatment to address current emissions regulations, and high levels of moisture.8 Even ambient air in urban environments has been estimated to contain as many as 104 distinct VOC species.9 Developing new adsorbents and/or new adsorption separation processes could allow for enormous energy savings in chemical production. However, materials development for these real applications hinges on understanding industry needs, evaluating materials under complex and sometimes harsh environments, and predicting the adsorption behavior of complex mixtures with some degree of accuracy. These types of research projects often fall outside the typical fundamental research portfolio in academia, but are also not applied enough for industry to fully incorporate into their general R&D. As a result, this lack of mixture adsorption data represents an enormous knowledge gap that severely hinders the design or selection of high-performing adsorbents to enable next-generation chemical separations. As early as 1923, this journal published a study by Chaney, Ray, and St. John10 showing that silica gel adsorbs water preferentially over toluene. They attributed this behavior to differences in wetting action and further observed that these differences “reveal the operation of specific chemical or polar forces, which are not explicable on any mathematical concept as simple as relative capillary diameters.” Essentially, the case for mixture adsorption studies was being made 8+ years before Markham and Benton11 presented their derivation of the now-ubiquitous extended Langmuir model for predicting mixed gas adsorption equilibria, possibly the first model to ever do so.

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Some sixty years later in the late 90s, the challenges associated with fully describing mixture adsorption remained unsolved as Talu pointed out in his excellent review of the field at the time that “almost all applications of adsorption involve mixtures”, but very few papers on adsorption separations actually include mixture adsorption data.12 He discussed an urgent need for these measurements because we cannot predict accurately the adsorption behavior of even the simplest gas mixtures from pure-component data. The prevailing method for calculating mixture adsorption from pure-component data is the Ideal Adsorbed Solution Theory (IAST). IAST has been the benchmark theory for over 50 years, but the lack of mixture adsorption data means that the theory has not been frequently evaluated experimentally.12 A more recent review of the mixture adsorption literature by Wu and Sircar13 in 2016 further highlights this persistent knowledge gap. Their survey found that predictions of gas adsorption selectivity from IAST vary wildly, with errors ranging from small to large, and that no real trends can be determined due to the paucity of data in the literature. They recommended that such predictions must be verified experimentally to facilitate separations design. This year the US National Academies released a new report entitled A Research Agenda for Transforming Separation Science.14 The report highlights major gaps and challenges that plague separation science. In particular, understanding the behavior of complex mixtures in real separations is discussed as a critical challenge to the field. A typical separation problem almost always involves complex mixtures with multiple chemical components that can impact selectivity, capacity, and throughput in an unpredictable way. Nevertheless, the authors note that the field continues to lag behind in this area. The design of materials and processes for efficient adsorption separations hinges upon knowledge of mixture adsorption, and this issue has been identified again and again over the past century as one that must be prioritized to advance chemical separations. It is quite unusual for there to be such a mismatch between strong consensus on the importance of a particular scientific challenge and the relative attention being given to it. A natural question that arises then is why aren’t more researchers tackling the topic of mixture adsorption? I believe there are two main issues that have impeded progress in this area: resources (human and financial) and instrumentation. Fundamental adsorption science and even separations more broadly are perhaps perceived as slightly old-fashioned or solved research problems. As a result, the number of new investigators entering the field over the past few decades has been arguably small when compared to other more trending areas in nanotechnology and biotechnology. The recent National Academies report noted that since 1987 the number of academic chemists who include separation science as a major topic in their research portfolio has decreased by almost 40%. Similarly, top chemical engineering departments have seen their number of faculty who focus on separations research drop by 30%, in spite of the large overall growth in total faculty numbers. With such a steep decline in expertise, it is not surprising that the significant questions in adsorption science remain unanswered. The development of new materials has attracted some newcomers to the adsorption field over the years. This is driven in part by the funding landscape. For example, private industry and federal agencies have recognized the importance of CO2 capture over the past decade, and available funding levels reflect this. Much of the work in this field has focused largely on designing and synthesizing new adsorbents that exhibit high CO2 adsorption capacities. Real target mixtures are typically ignored, and publications tend to re-

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port results for idealized streams such as mixtures of CO2/N2. Adsorption selectivities are often reported as a ratio of the Henry’s constants for CO2 and N2 or calculated using IAST. If more complex mixtures are considered, then dynamic adsorption or breakthrough studies are typically performed; this technique gives a good indication of separation capability but presents issues unique to the system that will be discussed in the next section. Instruments for measuring pure-component gas adsorption are commercially available as push-button units. Thus, it is no surprise that pure adsorption data dominate the literature. A recent multilab, round-robin study organized by NIST highlights the challenges with ensuring repeatability of single-component adsorption data.15 However, investigators who are only casually interested in adsorption science through novel materials work can obtain high-quality data using these instruments if sufficient care is taken with the experiments. However, few turn-key systems exist for measuring true mixture adsorption equilibrium leaving researchers to construct their own systems. Thus, instrumentation poses a significant barrier for investigators who are interested in considering mixture adsorption but do not have the expertise or the means to construct their own instrument for the task. If the proper instrument is available, mixture measurements are still notoriously time-consuming and laborious. An entire purecomponent isotherm can be measured systematically by sequentially dosing the gas into the system and waiting for equilibrium to be achieved at each pressure point. However, once two or more components are present, weight change (gravimetric method) or pressure change (volumetric method) alone cannot be used to determine adsorption loadings. Further, determining a pure-component adsorption isotherm requires a single curve, but obtaining the same level of detail for a mixture requires sampling many more pressure and composition points to fully describe the adsorption space. Since mixture adsorption measurements are already difficult, the number of measurements necessary to describe the adsorption then compounds the problem. In a mixture adsorption system, the total system pressure at equilibrium can be used to calculate the total adsorption loading, but the individual adsorption loadings cannot be determined using total pressure alone. The head space surrounding the adsorbent must be analyzed to determine the gas-phase composition and then adsorbed-phase compositions can be calculated. Mixture adsorption studies can be accomplished several ways. Three of the more common methods are highlighted here. Volumetric Adsorption (Recirculation Method) A schematic for a closed volumetric system equipped with a gas chromatograph is shown in Fig. 1. In this system, a gas with known composition is pre-loaded into the sample cylinder (reference volume) to a desired pressure. The total number of moles for each gas can then be calculated from PVT relationships using the known volume of the sample cylinder. The valve between the sample cylinder and adsorbent loop is then used to inject the gas mixture, and a circulation pump is used to drive the equilibrium in the adsorbent bed. The new pressure of the sample cylinder is used to calculate the number of moles that were injected using a simple mass balance. Knowing the total number of moles of each component injected into the system, the adsorption loading of each component can then be calculated as the quantity that is “missing” from the gas phase. Inclusion of the pump in the instrument design is critical to obtaining high-quality data because without it, the approach to equilibrium can take days or weeks and due to concentration gradients in the system caused by early adsorption, the remaining gas phase will not be well mixed. A well-designed volumetric system will

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Industrial & Engineering Chemistry Research

Adsorption Loading, mol/kg

10

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Pure CO2

BCO2

CCO2

ACO2 1

Initial Loading

ACO 0.1

BCO CCO

Pure CO

Figure 1. Example of a volumetric adsorption unit used to measure mixture adsorption.

have accurately determined volumes, high-quality pressure transducers in the range of experimental interest, and a circulation pump to drive equilibrium. The concept is simple enough, but collecting data in a systematic way is a difficult challenge. In general, two different gas injection methods can be used for measuring mixture adsorption in a volumetric system. A mixture of constant composition can be injected into the volumetric system, but each injection will result in a different set of compositions for the adsorbed phase and gas phase. This strategy often requires a significant amount of time to reach equilibrium as well, even with a circulation pump. For a binary mixture, a second strategy is to load the adsorbent initially with one component and then add incrementally the second component. In this case, systematic measurements of binary adsorption data are easier if one of the components is strongly adsorbed. The “heavy” component can be pre-loaded onto the adsorbent. Once equilibrium is established at a particular loading, the second component is dosed into the system. The heavy component will not be displaced by the lighter component. Thus, an adsorption isotherm of the light component can be measured in the presence of a prescribed loading of the heavy species. Examples of this kind of binary mixture include hexane/methane, water vapor/CO2, and CO/CO2 and are of course dependent on the composition of the mixture. Figure 2 illustrates the binary adsorption behavior for the inverse case; the light component (CO) is loaded first and then the heavy component (CO2) is added sequentially.16 Pure CO is adsorbed into zeolite NaY at a pressure of ~ 101 kPa at 298 K. After the CO loading is at equilibrium, CO2 is then added to the system at a partial pressure of 10 kPa (ACO2). As shown in the figure, the CO2 adsorbs with equilibrium loadings that closely match its purecomponent isotherm. However, CO immediately is displaced, and the loading decreases (ACO). As more and more CO2 molecules are added to the system, the CO continues to desorb (indicated by decreasing loadings and increasing partial pressure). Thus, in a separation system for these molecules, the CO2 can be modeled as if it were a pure component, and CO can treated as a carrier gas if the operating pressure is high enough. For mixtures having components with similar adsorption capabilities, the composition of the gas phase changes in unpredictable ways during the adsorption process. For a ternary system, the best strategy is to pre-adsorb a particular loading of the more strongly adsorbed component. Then, the remaining 2 components will adsorb like a binary mixture in the presence of the third component. If the more strongly adsorbed component undergoes appreciable desorption when the other two components are added, then systematic data collection using this instrument will be difficult. In this

0.01 10

Pressure, kPa

100

Figure 2. Adsorption of CO and CO2 in NaY at 25C. Pure adsorption isotherms for CO2 and CO are plotted as black curves. The y-axis is the adsorption loading for each gas and the x-axis represents the partial pressure for each gas or total pressure in the case of the pure isotherms. The orange square (“Initial Loading”) denotes a single, pure CO adsorption measurement at approximately 101 kPa. Data points A, B, and C represent the binary adsorption loadings measured after injecting pure CO2 into the system pre-loading with CO. The CO data point labeled “ACO” indicates that the injection of CO2 (loading ACO2) causes significant desorption of CO. Upon further injection of pure CO2 (data points BCO2 and CCO2), CO is further desorbed as shown by the decreasing adsorption loadings and increasing pressure. (Data from Ref 16)

case, the best strategy for studying the adsorption equilibrium behavior is to conduct experiments specifically for the composition of interest in the target separation. The resulting data will provide important information such as adsorption selectivities that can be determined for the mixture. One could also characterize the target separation system by plotting selectivities vs. gas-phase composition. Desorption Methods Reich, Zeigler, and Rogers described a flow-through volumetric method (1980) that is better suited than the recirculation method for measurements of mixture adsorption when the components have similar adsorption capacities.17 This method requires saturating an adsorbent bed at a constant temperature, pressure, and gas composition by flowing the mixture through the bed until the inlet and outlet compositions are the same. The bed volume is then isolated, and the moles of each component in the gas phase are determined using the total pressure, temperature of the system, and gasphase composition. The bed is then heated to fully desorb the column into an evacuated calibrated volume. Thus, the total moles of each component can be calculated using pressure, temperature, and composition of the gas phase. The difference between the total moles and the originally calculated moles in the gas phase at equilibrium (before desorption) will give the adsorbed-phase composition. This method is advantageous over the recirculation method in that it is more conducive to performing systematic measurements for obtaining the x-y diagram (adsorbed-phase composition vs. gasphase composition). On the other hand, using this method is challenging because it depends on the full desorption of all adsorbed molecules and requires careful and accurate measurements of temperature, pressure, volume, and composition.



The gravimetric method can also be used to measure mixture adsorption using desorption to determine adsorbed-phase loadings. A flow system rather than static is better suited for these measurements to ensure true mixture equilibrium is reached in a reasonable amount of time. When the weight of the sample is no longer changing, desorption is then carried out to allow analysis of the composition of the adsorbed phase. Thus, the adsorption loadings are determined directly. The head space cannot be used in this case because the adsorbent is equilibrated by exposure to constant flowing gas that continually flushes the system; the gas phase composition will be equal to the feed composition and there is no “missing” amount to calculate as in the case of the volumetric method. On the other hand, the flow method enables one to collect mixture data at prescribed gas-phase compositions in a way that is not possible with the closed volumetric systems. Overall, the desorption method can be better than the recirculation method when it comes to systematic data collection, but limitations in sample size, extent of adsorption, and approach to equilibrium can hinder the effectiveness of this strategy. Particular attention should be given to sample size based on how much of each component is adsorbed. If the adsorption loadings are small, the desorbed amounts can be very small compared to the moles of each component in the gas phase. Thus the gas phase will overwhelm the adsorbed phase in the mole balance, lowering the accuracy of the adsorption measurement. Fixed-Bed Adsorbers and Chromatography A much simpler and oft-used method for obtaining mixture adsorption data is a fixed-bed adsorber or breakthrough system. These systems are less complicated to build compared to the volumetric or desorption systems described above and are used to approximate a separation process. A typical breakthrough system is equipped with mass flow controllers, a volume for fixing the adsorbent sample (the fixed bed), and an instrument at the outlet for analyzing the gas composition exiting the bed. A mass spectrometer or component-specific sensor is typically used for this purpose. The gas mixture is introduced into the fixed bed along with a carrier gas using mass flow controllers. The more weakly adsorbed gases will exit or break through the adsorbent bed with the carrier gas before the more strongly adsorbed components. The area above and behind the breakthrough curve (concentration of the gas phase vs. time) can be used to calculate the dynamic adsorption loading. While seemingly less complicated than the volumetric and desorption methods, obtaining an accurate calculation of the adsorption loadings of multiple components from breakthrough curves presents its own difficulties. For example, if the compositions of the components are large enough such that significant velocity variation occurs at the bed exit, then the flow rate at the exit must also be measured as a function of time. Then, the velocity of each component over time must be integrated rather than just the concentration curve to improve the accuracy of the mass balance. In addition to flow considerations, breakthrough adsorption measurements present other interesting operational challenges that are often underappreciated in the literature. The mixture CO2/H2O/N2 provides a good example of these challenges. Most adsorbents that exhibit good CO2 loadings will interact even more strongly with water vapor. Thus, during the beginning of a feed step, water will adsorb very strongly near the inlet of the fixed bed. CO2 will co-adsorb very little in this region of the bed, and its concentration front will move ahead of the water vapor and deeper into the bed. This means that at some distance from the inlet, CO2 is essentially adsorbing to a clean bed because the water vapor concentration front is lagging far behind it. Based on the observed breakthrough behavior, one might be tempted to determine that

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CO2 adsorption is unaffected by the presence of water vapor. However, this would be a mischaracterization of the adsorption behavior. A closer approximation to the mixture adsorption equilibrium behavior can be obtained by first equilibrating the fixed bed with water vapor in a carrier gas. Once the composition of the outlet stream matches the inlet, the CO2 can be added to the mixture. Thus, the CO2 breakthrough curve will be measured in the presence of water vapor that has been pre-loaded into the bed. It is also important to point out that many investigators tend to measure a single breakthrough curve and do not cycle the adsorbent. Concentration swing dynamics are important for understanding mixture adsorption, and reporting even a few cycles would add tremendous knowledge to the literature A packed column can also be used to study mixture adsorption behavior using the concentration pulse chromatographic method (CPM) of Van der Vlist and Van der Meijden (1973).18 The set up is relatively easy and cheap compared to the other mixture adsorption methods but is limited to binary systems. Harlick and Tezel improved upon the method (HT-CPM) and showed that it can be used to obtain binary adsorption data for components with large differences in their adsorption capacity.19 The experiment involves injecting a pulse of gas into a carrier stream that flows into the column. As in a typical breakthrough experiment, the gas concentration exiting the column is monitored as a function of time, and a model is applied to the pulse data to calculate the adsorption loading. The data obtained using this method has been found to compare favorably with binary adsorption data determined using a static method such as the volumetric system. The data reduction technique used to model the pulse will influence the binary adsorption results and is perhaps one reason that CPM has not found widespread use in spite of its simplicity of operation. Outlook The decreasing number of researchers working in separation science and the difficulties in adsorption instrumentation both underscore the challenges facing the field of adsorption – and by extension, chemical separations. With renewed focus on the importance of understanding competitive adsorption effects, highlighted by the National Academies report, researchers involved primarily on the materials side may be prompted to study adsorption fundamentals in search of applications for new materials. However, even with increased interest in the field, the current challenges with instrumentation are non-trivial and must be addressed for real progress to be achieved. Mixture adsorption measurement systems are typically custom built in-house, are labor intensive, and as a result, are not accessible to most researchers. Breakthrough systems provide a good balance in terms of ease of construction and operation for researchers interested in mixture adsorption, but special attention must be given to bed design and to dynamic capacity calculations. In the near term, researchers should focus on experimental measurements of mixture adsorption using breakthrough systems or desorption methods. These two methods are no less tedious than the recirculation method but provide a lower barrier for in-house construction. These instruments provide for determining important mixture information such as experimental selectivities that will enable the field to better evaluate the IAST. Overall, until access to commercial multicomponent adsorption systems is comparable to the pure-component instruments on the market, the knowledge gap on adsorption of complex mixtures is likely to persist. Acknowledgments The author gratefully acknowledges Prof. David Sholl (Georgia Tech), Prof. Ryan Lively (Georgia Tech), and Prof. Handan Tezel (U. Ottowa) for their invaluable critiques of early drafts of this


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Industrial & Engineering Chemistry Research manuscript. The author also owes a debt of gratitude to Prof. Jim Ritter (U. South Carolina) for his detailed critiques of the manuscript, fruitful discussions, and helpful suggestions on adsorption instrumentation and the state of field of mixture adsorption. References 1. U.S. Chemical Industry - Statistics & Facts | Statista. 2. Sholl, D. S.; Lively, R. P. Seven chemical separations to change the world. Nature 2016, 532, 435-437. 3. Lively, R. P.; Realff, M. J. On Thermodynamic Separation Efficiency: Adsorption Processes. AIChE J. 2016, 62, 3699-3705. 4. Materials for Separation Technologies. Energy and Emission Reduction Opportunities. United States: 2005. Web. doi:10.2172/1218755. 5. Taifan, W.; Baltrusaitis, J., Minireview: direct catalytic conversion of sour natural gas (CH4 + H2S + CO2) components to high value chemicals and fuels. Catal. Sci. Technol. 2017, 7 (14), 29192929. 6. Barman, B. N.; Cebolla, V. L.; Membrado, L., Chromatographic techniques for petroleum and related products. Critical Reviews in Analytical Chemistry 2000, 30 (2-3), 75-120. 7. Faramawy, S.; Zaki, T.; Sakr, A. A. E., Natural gas origin, composition, and processing: A review. J. Nat. Gas Sci. Eng. 2016, 34, 34-54. 8. Rezaei, F.; Jones, C. W., Stability of Supported Amine Adsorbents to SO2 and NOx in Postcombustion CO2 Capture. 1. SingleComponent Adsorption. Ind. Eng. Chem. Res. 2013, 52 (34), 12192-12201. 9. Kumar, A.; Viden, I., Volatile organic compounds: Sampling methods and their worldwide profile in ambient air. Environ. Monit. Assess. 2007, 131 (1-3), 301-321. 10. Chaney, N. K.; Ray, A. B.; St. John, A. Ind. Eng. Chem.1923, 15 (12) 1244-1255. 11. Markham, E. C.; Benton, A. F. The adsorption of gas mixtures by silica gel. J. Am. Chem. Soc. 1931 53(2) 497-507. 12. Talu, O. Adv. Coll. and Interface Science 1998 76, 227-269. 13. Walton, K. S.; Sholl, D. S. Predicting multicomponent adsorption: 50 years of the ideal adsorbed solution theory. AIChE J. 2015 61(9), 2757-2762. 14. Wu, C. W.; Sircar, S. Comments on binary and ternary gas adsorption selectivity. Sep. Purif. Tech. 2016 170, 453-461. 15. National Academies of Sciences, Engineering, and Medicine. 2019. A Research Agenda for Transforming Separation Science. Washington, DC: The National Academies Press. Doi: https://doi.org/10.17226/25421. 16. Nguyen, H. G. T., van Zee, R. D.; Thommes, M.; Toman, B.; Hudson, M. S. L.; Mangano, E.; Brandani, S.; Broom, D. P.; Benham, M. J.; Cychosz, K.; Bertier, P.; Yang, F.; Krooss, B. M.; Siegelman, R. L.; Hakuman, M.; Nakai, K.; Ebner, A. D.; Erden, L.; Ritter, J. A.; Moran, A.; Talu, O.; Huang, Y.; Walton, K. S.; Billemont, P.; De Weireld, G. A reference high-pressure CO2 adsorption isotherm for ammonium ZSM-5 zeolite: results of an interlaboratory study Adsorption. 2018 24(6) 531-539. 17. Walton, K. S.; LeVan, M. D. Sep. Sci. Tech. A novel adsorption cycle for CO2 recovery: Experimental and theoretical investigations of a temperature swing compression process. 2006 41(3), 485500. 18. Reich, R.; Ziegler, W. T.; Rogers, K. A. Adsorption of methane, ethane, and ethylene gases and their binary and ternary mixtures and carbon-dioxide on activated carbon at 212-301 K and pressures to 35 atmospheres. Ind. Eng. Chem. Process Des. Dev. 1980 19, 336-334.

19. Van der Vlist, E. and J. Van der Meijden, Determination of the adsorption isotherms of the components of binary gas mixtures by gas chromatography,” J. Chrom., 1973 79, 1–13. 20. Harlick, P. J. E.; Tezel, F. H. Use of concentration pulse chromatography for determining binary isotherms: comparison with statically determined binary isotherms. Adsorption. 2003 9 275– 286.



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