Adsorption of CO2-Containing Gas Mixtures over Amine-Bearing Pore

on CO2 adsorption capacity even at very low CO2 partial pressure, e.g. 400 ppm, without adverse effect on CO2 selectivity. ... Forgot ACS ID or Pa...
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Ind. Eng. Chem. Res. 2010, 49, 359–365

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Adsorption of CO2-Containing Gas Mixtures over Amine-Bearing Pore-Expanded MCM-41 Silica: Application for Gas Purification Youssef Belmabkhout, Rodrigo Serna-Guerrero, and Abdelhamid Sayari* Department of Chemistry and Department of Chemical Engineering, UniVersity of Ottawa, Ottawa, Ontario, K1N 6N5, Canada

Adsorption of CO2 on triamine-grafted pore-expanded mesoporous silica, TRI-PE-MCM-41, was investigated from very low pressure to 1 bar at four temperatures (298, 308, 318, 328 K) using gravimetric measurements. TRI-PE-MCM-41 exhibited one of the highest equilibrium capacities compared to other typical CO2 adsorbents such as zeolites, activated carbons, and metal-organic frameworks (MOFs). In contrast, under the same pressure and temperature conditions, TRI-PE-MCM-41 exhibited very small uptakes of N2, CH4, H2, and O2. Column-breakthrough measurements of CO2 in mixtures with other species showed exceedingly high selectivity of CO2 over N2, CH4, H2, and O2 even at very low CO2 concentrations, indicating that TRI-PE-MCM-41 is suitable adsorbent for gas purification applications. Moreover, water vapor was found to have a beneficial effect on CO2 adsorption capacity even at very low CO2 partial pressure, e.g. 400 ppm, without adverse effect on CO2 selectivity. Introduction With CO2 being one of the main contributors to global warming, there is increasing interest in removing CO2 from the air to combat the greenhouse gas effect.1,2 Moreover, low concentrations and traces of CO2 are also undesirable in some gas streams. This work deals with the removal of relatively small concentrations of CO2 from various mixtures with the purpose of gas purification. The following is a limited list of instances where the removal of CO2 for gas purification is of prime importance. (i) As the main feed stream for the cryogenic separation of nitrogen and oxygen, air has to be free from carbon dioxide to avoid any potential blockage of heat exchange equipment due to frozen CO2 during the liquefaction process.3,4 Carbon dioxide also can poison the catalyst used for ammonia production plants and should be removed from hydrogen. It may also contaminate adsorbents (e.g., zeolites) for oxygen production by pressure swing adsorption (PSA).5 Thus, in all these instances, traces of CO2 have to be removed. (ii) Oxygen and hydrogen used as feedstock for fuel cells also need to be CO2 free. Trace amounts of CO2 in oxygen degrade the electrolyte, particularly for alkali fuel cells (AFC), while high purity hydrogen is needed for AFC.6 (iii) Efficient removal of CO2 at low concentration is also key for the proper operation of closed-circuit breathing systems.7 Such systems are used in confined spaces such as submarines and aerospace shuttles,8 in mining as well as in rescue missions, diving,9 and also in medical applications.10 (iv) To be transported in pipelines, natural gas must meet strict specifications with respect to carbon dioxide content as CO2 must typically be removed to below 2%.6 Adsorption technology such as pressure swing or temperature swing adsorption (TSA) is widely used for purification and separation of gases.11 Adsorption is considered to be a competitive method for CO2 removal in comparison to other technologies, provided that highly selective adsorbents with high CO2 capacity are available.12 A large variety of CO2 solid sorbents have been reported in the literature including oxides,13 zeolites,14 * Corresponding author. E-mail: [email protected].

activated carbons,15 metal-organic frameworks (MOFs),16-18 and organo-silicas and surface-functionalized silicas, including the so-called molecular baskets.19-26 In previous contributions,19,27 our group reported that triamine-modified PE-MCM-41 (TRIPE-MCM-41) obtained by postsynthesis surface functionalization of pore-expanded MCM-41 silica showed promising properties in terms of CO2 uptake and rate of adsorption at low CO2 partial pressures. On the basis of pure CO2 and N2 adsorption data, TRI-PE-MCM-41 exhibited a high CO2/N2 selectivity ratio. In addition, these adsorbents are thermally stable and tolerant to water vapor. The current work is focused on CO2 removal over TRI-PE-MCM-41 as a potential method for purification of air, CH4, and H2. Adsorption isotherms of dry CO2 and other gases like CH4, H2, and carbon-free air (CFAir (N2:O2 ) 80:20)) at room temperature were determined up to 1 bar. To explore the effect of competition of other species against CO2, we investigated experimentally the selectivity of CO2 over N2, CH4, H2, and O2 at low CO2 concentrations using column breakthrough measurements. This contribution addresses the potential use of TRI-PE-MCM-41 in purification applications i.e. CO2 content below ca 5%. Separation applications of TRIPE-MCM-41 using CO2-rich feedstocks and its long-term operation stability will be reported in a separate paper. Experimental Section Materials. The detailed preparation procedure and structural characteristics of TRI-PE-MCM-41 may be found elsewhere.19,27 Briefly, MCM-41 type silica was synthesized at 100 °C using cetyltrimethylammonium bromide as a structure directing agent. Pore expansion was achieved through hydrothermal treatment of as-synthesized MCM-41 using dimethyldecylamine as swelling agent at 120 °C for 3 days. After removal of the surfactant template and expander agent by calcination, the obtained product was labeled PE-MCM-41. Incorporation of the amine functionality onto PE-MCM-41 was achieved via surface grafting. PEMCM-41 was loaded into a multineck glass flask containing 150 mL of toluene. Once a homogeneous mixture was obtained, 0.3 mL/g PE-MCM-41 of distilled deionized water was added and left stirring for 30 min. The glass flask was then submerged in a silicon oil bath set at 85 °C using a temperature-controlled

10.1021/ie900837t  2010 American Chemical Society Published on Web 11/13/2009

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Figure 1. Setup for column breakthrough measurements.

stirring hot plate. 2-[2-(3-Trimethoxysilylpropylamino)ethylamino]ethylamine (3 mL/g silica) was subsequently added to the mixture and left stirring overnight. The material was filtered and washed with copious amounts of toluene, then pentane. Finally, the recovered solid was dried at 100 °C in a natural convection oven for 1 h and was labeled TRI-PE-MCM-41. The BET surface area, pore volume, and pore size of TRIPE-MCM-41 were 367 m2/g, 0.87 cm3/g, and 9.4 nm, respectively. 13X zeolite (658 m2/g; 0.31 cm3/g) was supplied by Sigma-Aldrich. The typical amine loading of TRI-PE-MCM41 determined by TGA was 7.9 mmol amine/g. Carbon dioxide (99.99%), nitrogen (99.999%), helium (99.999), carbon dioxide (0.1; 1; 10; 20%) in nitrogen, methane (99.999%), hydrogen (99.999%), and carbon-free air (CFAir, N2:O2 ) 80: 20) (grade 0.1) were supplied by BOC Canada. Pure Gas Adsorption Measurements. Single gas adsorption equilibrium measurements for CO2, N2, CH4, H2, and CFAir were performed using a Rubotherm gravimetric-densimetric apparatus (Bochum, Germany) with an accuracy of 0.1 mg. More details about this experimental setup and procedure may be found elsewhere.27,28 Column-Breakthrough Measurements for CO2-Containing Binary Mixtures. The experimental setup used for dynamic beakthrough measurements is shown in Figure 1. The gas manifold consisted of three lines fitted with mass flow controllers of precision (1%. Line “A” is used to feed an inert gas, most commonly nitrogen, to activate the sample before each experiment. The other two lines, “B” and “C” feed a mixture of CO2 and other gases like N2, CH4, H2, and CFAir. Hence, gas mixtures with concentrations representative of different industrial gases may be prepared. Whenever required, gases flowing through lines B and C may be mixed before entering a column packed with 40-60 mesh particles of TRI-PE-MCM-41 using a four-way valve. The stainless steel column was 120 mm in length with 4.2 mm of inner (6.4 mm outer) diameter. The column downstream was monitored using a Pfeiffer Thermostar mass spectrometer. The lowest detection limit of CO2 was estimated to be 10 ppm. In a typical experiment, 0.4-1 g of adsorbent was treated at 423 K for 2 h under a nitrogen (or helium) flow of 100 mL/min and cooled to room temperature. The gas flow was then switched to the desired gas mixture at the same flow rate. Whenever required, the level of humidity was adjusted using distilled-deionized water in a temperaturecontrolled glass saturator. The complete breakthrough of CO2 and other species was indicated by the downstream gas composition reaching that of the feed gas.

Figure 2. CO2 adsorption isotherms for TRI-PE-MCM-41 at 298, 308, 318, and 328 K (a) up to 1 bar (b) up to 0.05 bar.

The adsorption capacity was estimated from the breakthrough curves using the following equation: nadsi ) FC0itni

(1)

where nadsi is the adsorption capacity of gas i, F is the total molar flow, C0i is the concentration of gas i entering the column, and tni is the stoichiometric time corresponding to gas i, which is calculated from the breakthrough profile according to eq 2: tni )

∫

t

0

(

1-

)

CAi dt C0i

(2)

where C0i and CAi are the concentrations of gas i upstream and downstream the column, respectively.29 The selectivity of CO2 over species i in the binary mixture of CO2 and species i is determined using the following equation: xCO2 SCO2/i )

xi yCO2

(3)

yi where x and y refer to the molar composition of the adsorbed phase and the gas phase, respectively. Results and Discussion Pure Gas Adsorption Measurements. Figure 2a and b shows the CO2 adsorption capacity of TRI-PE-MCM-41 up to 1 and 0.05 bar, respectively, at four temperatures (298, 308, 318, 328 K). All isotherms were of type I according to the IUPAC classification with a steep slope in the low pressure

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Figure 3. CO2 adsorption isotherm for TRI-PE-MCM-41 at 298 K compared to other adsorbents up to 0.6 bar.

range (0-0.05 bar). Although, the isosteric heat of adsorption calculated from the above isotherms was ca. 92 kJ/mol at very low CO2 loading, reflecting the strong chemical interaction of CO2 with amine groups,27 the TRI-PE-MCM-41 could be completely regenerated at moderate temperatures from 348 up to 423 K in the presence of N2 purge or vacuum.30 Figure 3 shows the adsorption isotherm of CO2 on TRI-PEMCM-41 at low pressure and room temperature compared to typical CO2 adsorbents such as zeolites,14,31 carbon-based materials,13 plain MCM-41 mesoporous silica,28 and MOFs.32 All the data but those obtained in the presence of TRI-PE-MCM41 were borrowed from the literature. Notice that literature data on CO2 adsorption over 13X zeolites under apparently the same conditions showed as much as 50% variations, mainly due to differences in 13X samples and measurement techniques.3,14,31 As seen in Figure 3, TRI-PE-MCM-41 outperformed 13X zeolites at low CO2 partial pressure, i.e., below ca. 0.05 bar, while the adsorption capacities for plain MCM-41, carbon-based materials, and MOFs were very small in the low pressure range compared to TRI-PE-MCM-41 and 13X. Figure 3 shows also that the lower the partial pressure of CO2, the higher the difference between CO2 capacity for TRI-PE-MCM-41 and all the other materials. By contrast to TRI-PE-MCM-41, the CO2 performance of 13X was strongly dependent on the high activation temperature (473-673 K) and also very sensitive to the presence of moisture.33-35 The adsorption capacity of organically modified mesoporous silicas at low CO2 concentrations was also investigated by others. Recently, Yue et al.38 reported a CO2 adsorption capacity of 4.54 mmol/g for tetraethylenepentamine impregnated MCM-41 at 5% CO2 and room temperature. However, this material suffered from amine loss as the adsorption capacity decreased by 8.6% after just 6 cycles by regeneration at 373 K. Satyapal et al.8 obtained adsorption capacity at 2% CO2 of 0.91 mmol/g for solid amine beads known as HSC+, a material consisting of a liquid amine bonded to a high surface area polymeric support. As shown in Figure 2, the equilibrium capacity for the TRI-PE-MCM-41 at 298 K 2% CO2 is 1.75 mmol/g. The adsorption isotherms of CO2, N2, CH4, H2, and CFAir onto TRI-PE-MCM-41 at 298 K and up to 1 bar are shown in Figure 4. At the same temperature and adsorbate concentration,

Figure 4. Adsorption isotherms of CO2, N2, CH4, H2, and CFAir on TRIPE-MCM-41 at 298 K up to 1 bar.

TRI-PE-MCM-41 exhibited very small N2, CH4, H2, and CFAir adsorption capacity compared to CO2 uptake. This finding is indicative of a strong affinity toward CO2 which is a highly desirable feature for applications where CO2-free gases and/or high purity CO2 are sought. At 1 bar of dry CO2 and 298 K, the molar selectivity ratios for CO2/CH4 and CO2/N2 over TRI-PE-MCM-41 were found to be 28 and 308, respectively,27 much larger than the corresponding values of 12 and 18 for 13X zeolite and 2 and 8 for carbons.36 Notice that the molar selectivity ratio used in this work was calculated based on single adsorption data, without any consideration of the effect of competition between adsorbates during multicomponent adsorption. Nevertheless, the molar selectivity is strongly indicative of the actual selectivity. Thus, it reflects the efficiency of the separation and removal of CO2 Column Breakthrough Adsorption Measurements for CO2-Containing Binary Mixtures. To assess the effect of competition between CO2 and other components in adsorption on TRI-PE-MCM-41 under representative CO2 concentration, breakthrough experiments were carried out using mixtures of CO2 with N2, CH4, H2, and CFAir with concentrations akin to different industrial gases.

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Figure 5. Breakthrough curves for CO2:CFAir ) 0.03:99.97% mixture at 298 K and 1 bar.

Figure 6. Breakthrough curves for CO2:N2:O2 ) 5:76:19 mixture at 298 K and 1 bar.

CO2-N2-O2 Mixture: Application to Air and Oxygen Purification. While the typical CO2 concentration in atmospheric air is 300-400 ppm, the requirements for CO2 levels in prepurified air and in pure oxygen for alkali fuel cells (AFC) are below 10 ppm. In terms of CO2 gas adsorption capacity, zeolite 13X is the most used adsorbent for prepurification of air, with a CO2 capacity of 0.5 mmol/g at 400 ppm and 295 K.1,2 As shown in Figure 3, the current TRI-PE-MCM-41 exhibited a CO2 capacity at ca. 400 ppm and 298 K of ca. 0.98 mmol/g, significantly higher than 13X. Moreover, the N2 and O2 uptake over TRI-PE-MCM-41 was very small, leading to the inference that the selectivity of CO2 over N2 and O2 is very high. Figure 5 shows the breakthrough curves of N2, O2, and CO2 in the presence of a CO2:CFAir ) 0.03:99.97 (CO2:N2:O2 ) 0.03:79.98:19.99) mixture on TRI-PE-MCM-41 at 298 K and a total pressure of 1 bar. As seen, O2 and N2 appeared in the column downstream almost immediately after the process has started, indicative of a small adsorption capacity for N2 and O2, if any. No release of CO2 (within an accuracy of 10 ppm) was observed downstream the column up to 167 min. The complete saturation of the packed column occurred after ca. 328 min, representing a final CO2 adsorption capacity of 0.9 ( 0.1 mmol/g. Hence, the CO2 dynamic adsorption capacity is in excellent agreement with the equilibrium capacity obtained by gravimetry (0.98 mmol/g) at the same partial pressure (Figure 2b). Consistent with single component adsorption data, the above findings show that the selectivity of CO2 over N2 and O2 is extremely high approaching infinite value. Sircar and Golden37 reported the CO2-N2 Henry law selectivity at 303 K to be 330.7 and 11.1 for 5A zeolite and BPL activated carbon, respectively. Thus, in the low pressure range, TRI-PE-MCM-41 outperforms zeolites, carbons, and MOFs in terms of both CO2 adsorption capacity and selectivity. It is inferred that TRI-PE-MCM-41 is a promising material for air and oxygen purification applications. CO2-N2-O2 Mixture: Application to Closed-Circuit Breathing Systems. Oxygen intake by humans is used at a rate of 25%, the rest being exhaled in an ca. 5% CO2-containing gas. If the exhaled gas is to be recycled using closed-circuit breathing systems (CCBSs), it is necessary to remove the carbon dioxide from the breathing loop to avoid its presence at concentrations considered hazardous to human health.38 According to the United States Occupational Safety and Health Administration, the threshold limit value (TLV) of CO2 is 0.5% and its short-term exposure limit (STEL) during 15 min is 3%. With these exposure limits in mind, a typical breathing system

using absorbent is considered to be exhausted when the concentration of CO2 downstream of the scrubber of a CCBS lies in the range of 0.1-0.5%.39,40 Figure 6 shows the breakthrough curves for CO2, N2, and O2 using a CO2:N2:O2 ) 5:76:19 mixture at 298 K and 1 bar total pressure. As can be seen, O2 and N2 were detected downstream the column immediately, suggesting that the adsorption capacity for both O2 and N2 is very small i.e., within the limit of accuracy of the experimental setup. It is thus inferred that the selectivity for CO2 over N2 and O2 is approaching infinite value. No CO2 (within an accuracy of 10 ppm) was observed downstream the column until the breakthrough time of 9 min. The downstream concentration of CO2 increased sharply to reach 80% of inlet CO2 content in few seconds. Complete saturation of the bed occurred after 19 min, representing a final CO2 dynamic adsorption capacity of 2.21 ( 0.2 mmol/g. This finding is in good agreement with the gravimetric capacity (2.1 mmol/g) obtained at similar partial pressure of CO2, as shown in Figure 2a. The selectivity toward CO2 in CO2-N2 and CO2-O2 mixtures using other organically modified silicas has also been reported in the literature, but only at high CO2 concentration. For example in the presence of polyethylenimine-containing MCM-41 silica, the CO2 selectivity over N2 and O2 in a CO2:N2:O2 ) 14.9: 80.85:4.25mixturewasfoundtobe>1000and180,respectively.41,42 Moreover, 3-aminopropyltriethoxysilane grafted MCM-48 exhibited a CO2 selectivity higher than 100 in the presence of an equimolar mixture of CO2 and N2 at a total pressure of 1 bar.43 Thus owing to its high CO2 adsorption capacity and selectivity over O2 and N2, compared to other materials, TRI-PE-MCM41 appears to be a promising material for CCBS applications. CO2-CH4 Mixture: Application to Natural Gas Purification. Carbon dioxide and other contaminants are often found in natural gas streams. When combined with water, CO2 generates carbonic acid which is corrosive. Generally, the CO2 specification for natural gas transportation in pipelines is below 2-3%.14,44 Thus, CO2 should be removed from natural gas. Figure 7 shows the breakthrough curves of CH4 and CO2 using a CO2:CH4 ) 1:99 mixture at 298 K and a total pressure of 1 bar over TRI-PE-MCM-41. As seen, CH4 appears at the column downstream immediately after the process has started, suggesting that the adsorption capacity for CH4 is very small and, hence, the selectivity of CO2 over CH4 is extremely high. No CO2 was detected downstream the column until the breakthrough time of 24 min. Figure 7 shows that the breakthrough curve of CO2 is very steep

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Figure 7. Breakthrough curve for CO2:CH4 ) 1:99 mixture at 298 K and 1 bar.

reaching 80% of upstream concentration in a few seconds. After 40 min, the bed was completely saturated corresponding to a final CO2 dynamic adsorption capacity of 1.89 ( 0.19 mmol/g. Figure 2b shows that the gravimetric capacity obtained at similar partial pressure was ca. 1.6 mmol/g in fairly good agreement with the dynamic adsorption capacity. The adsorption capacity of CO2 and CH4 as well as the selectivity toward CO2 over methane at low CO2 concentration were seldom reported in the literature for organically modified mesoporous silicas. Huang and Yang22 obtained a CO2 capacity of 1.14 mmol/g at 5% CO2 and small CH4 adsorption capacity on amine-grafted MCM48, but the CO2/CH4 selectivity was not reported. Sircar and Golden37 found the CO2/CH4 selectivity in the Henry law region at 303 K to be 195.6 and 2.5 for 5A zeolite and BPL activated carbon, respectively. A literature survey about CO2/CH4 selectivity data at high CO2 concentration on materials like zeolites, carbons, and periodic mesoporous silica was reported elsewhere.45 On the basis of the current findings, TRI-PE-MCM41 appears to be a viable material for CO2 removal from natural gas. CO2-H2 Mixture: Application to Hydrogen Purification. High purity hydrogen (99.99%) is needed for alkali fuel cells (AFC) and polymer electrolyte membrane fuel cells (PEMFC). Hydrogen of 98-99.99% purity produced from syngas contains CO2 as the predominant impurity.6 Depending on the primary bulk separation technology used (e.g., absorption, single, or multibed adsorption), a secondary purification process may be needed for further removal of CO2 impurities, from ca. 2% CO2 to less than 10 ppm. Indeed, in adsorption separation processes, the two key design and operating parameters, namely efficiency (product purity) and capacity are very interdependent. To increase the product yield, the general tendency is to shorten the adsorption cycles in the primary bulk PSA which often lead to a decrease of the product purity.46 Thus, the use of highly selective adsorbent toward CO2 in TSA or TPSA as a secondary purification stage, in addition to the first bulk separation, will promote both capacity and efficiency in the overall process. Figure 8 shows the breakthrough curves of H2 and CO2 using a CO2:H2 ) 1:99 mixture at 298 K and 1 bar on TRI-PE-MCM41. Hydrogen breakthrough occurs at the column downstream immediatly after the process has started. Figure 8 indicates that the H2 adsorption capacity over TRIPE-MCM-41 is also exceedingly small and that the selectivity of CO2 over H2 is very high. No release of CO2 within an accuracy of 10 ppm was observed downstream the column until the abrupt breakthrough of CO2 at 10 min. The complete

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Figure 8. Breakthrough curves for CO2:H2 ) 1:99 mixture at 298 K and 1 bar.

Figure 9. Breakthrough curves for a CO2:N2 ) 0.04:99.96 mixture at 298 K and 1 bar with and without the presence of moisture.

saturation of the bed was recorded after 104 min, representing a final CO2 dynamic adsorption capacity of 1.73 ( 0.17 mmol/ g. This finding is in excellent agreement with the gravimetric capacity of 1.6 mmol/g obtained at similar partial pressures of CO2 shown in Figure 2b. Literature data on the selectivity of CO2 over H2 at low CO2 concentration on other adsorbents are very scarce. Akten et al.47 reported a selectivity of CO2 over H2 of 70 at low CO2 partial pressure and 298 K over 4A zeolite. Sircar and Golden37 reported a CO2-H2 Henry law selectivity at 303 K of 7400 and 90.8 for 5A zeolite and BPL activated carbon, respectively. At high CO2 concentration, room temperature, and high pressure, the CO2 vs H2 selectivity was reported to be 35 for activated carbon,48 25 for MOFs-5 (IRMOF-1), and 60 for Cu-BTC.49 On the basis of CO2 adsorption capacity, its high selectivity toward CO2 in the presence of H2, and its tolerance to moisture,19,27,50 TRI-PE-MCM-41 may prove to be suitable for H2 purification from syngas. Effect of Moisture on CO2 Adsorption Capacity and Selectivity. In our previous contributions,19,27 it was shown using 5% CO2 in nitrogen, that the CO2 adsorption was enhanced in the presence of moisture. To verify if a similar effect applies at very low CO2 pressure, a series of column-breakthrough experiments were carried using a CO2:N2 ) 0.04:99.96 mixture in dry condition as well as with 27 and 64% relative humidity (RH), at 298 K and 1 bar (Figure 9). In all experiments, N2 appeared at the column downstream immediately after the process has started, suggesting that the adsorption capacity for

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N2 remains very small regardless of the occurrence of moisture. Hence, it is inferred that the selectivity of CO2 over N2 is also extremely high in the presence of moisture. The breakthrough time for water vapor was 22 and 24 min, and the water adsorption capacity was ca. 4.7 and 7.29 mmol/g for 27 and 64% RH, respectively. The breakthrough of CO2 was 154 and 262 min for mixtures with 26 and 64% RH, respectively, vs 130 min for the dry feed. The corresponding CO2 adsorption capacity was 32 and 56% higher than the capacity under dry conditions. This finding is also consistent with our earlier report on the effect of water vapor on CO2 adsorption on monoaminegrafted PE-MCM-41.50 The promoting effect of water vapor may be explained on the basis of the generally accepted reaction mechanisms between CO2 and amines, i.e., formation of carbamate under dry conditions and partial formation of bicarbonate in the presence of moisture.50 Conclusion Pure CO2, N2, CH4, CFAir, and H2 and multicomponent CO2/ N2/O2, CO2/CH4, and CO2/H2 adsorption experiments were carried on amine modified mesoporous silica TRI-PE-MCM41 at CO2 concentrations akin to many industrial gases with relatively low CO2 content. This material exhibited very high adsorption capacity at low CO2 concentration (