Parametric Study of CO2 Fixed Carrier Facilitated Transport through

894

Ind. Eng. Chem. Res. 2009, 48, 894–902

Parametric Study of CO2 Fixed Carrier Facilitated Transport through Swollen Chitosan Membranes Louei A. El-Azzami and Eric A. Grulke* Department of Chemical and Materials Engineering, UniVersity of Kentucky, Lexington, Kentucky 40506-0046

Swollen and dry chitosan membranes were used to separate carbon dioxide from a feed gas composed of 10% CO2, 10% H2, and 80% N2 in a temperature range of 20-150 °C for a feed pressure of 1.5 atm. Swelling increased CO2 permeabilities (barrers) of chitosan membranes from 0.381 to 213 at 20 °C, 9.50 to 482 at 110 °C, and 26.1 to 399 at 150 °C, accompanied with similar trends for the separation factors: CO2/H2 and CO2/ N2. The total water levels of the membranes were controlled to be the same at all temperature conditions by manipulating the relative humidities of the feed and sweep gases. This permitted direct comparison of the levels of bound and free water to carbon dioxide permeability and selectivity factors. CO2 transport in swollen chitosan membranes is mainly dominated by water-facilitated reactions of CO2 with primary amine groups of chitosan. Cussler’s model was modified to incorporate facilitated reactions caused by both free and bound water. The values of the model’s kinetic and transport parameters were consistent with the reaction chemistry of the facilitated process and the physical chemistry of the polymer. 1. Introduction The separation of carbon dioxide from mixed streams of hydrogen and nitrogen is critical to many industries such as hydrogen production, ammonia production, fuel cell technology, and flue gas purification. A number of researchers are working on facilitated transport membranes that use amines for enhanced carbon dioxide removal. These membranes would need to function over a range of temperatures, gas compositions (including variable water and carbon dioxide levels), and pressures. Membrane separations operating at elevated temperatures, e.g., above the boiling point of water, would be easier to integrate in these processes. However, as water is known to participate in complexation reactions between carbon dioxide and amines, better understanding of the state of water in such membranes and its effects could lead to improved membranes with better process control strategies. 1.1. Facilitated Transport Membranes and Models. Immobilized liquid membranes, swollen membranes, and fixed carrier membranes are the main three configurations of facilitated transport membranes. Models for immobilized liquid membranes have been extensively studied.1-9 This work focuses on a fixed carrier polymer membrane, which selectively complexes with penetrants via reactive groups of its repeating units. Recently, new facilitated transport membranes for carbon dioxide separations have been developed. Membranes have been developed with both fixed and mobile carriers based on amine functional groups,10 and with amine dendrimers,11-13 that use glycerol to broaden the range of humidities of the feed stream over which the membrane could operate. Previous transport models for ion-exchange membranes14-17 and fixed carrier membranes18,19 may provide a basis for interpretation of experimental results. 1.2. Models for Fixed Site Facilitated Transport Membranes. Noble’s model18 originates from the facilitated transport of mobile carriers and is extended to describe the fixed-site facilitated mechanism by the incorporation of the dual mode theory. On the other hand, Cussler’s model19 is based on the intermolecular jumps of the targeted penetrant from one fixed * To whom correspondence should be addressed. Tel.: +1 859 257 6097. Fax: +1 859 323 4922. E-mail address: [email protected].

site to another. Cussler’s model is more dependent on the lengths separating the fixed sites in the polymeric material and their ability to overlap for reactions to occur. This provides a physical explanation of the intermolecular interactions driving the separation. Both models for fixed carrier membranes do not account for the presence of water and have not been extended to accommodate facilitated transport mechanisms that are initiated by different forms of the swelling agent. 1.3. Carbon Dioxide Permeabilities in Chitosan Membranes. Chitosan membranes at dry conditions have been used in CO2 permeation tests and demonstrate low permeabilities.20-24 Water-swollen chitosan membranes have dramatically higher CO2 permeabilities.20-22,24,25 Ito et al.25 demonstrate that the humidification of the feed gas increases CO2 transport properties in the separation of CO2/N2 through chitosan membranes. Bae et al.22 is the only study that introduced a model for CO2 permeation through swollen chitosan by incorporating the equilibrium reaction of chitosan and CO2 into the free volume diffusion model. While the model has not been tested to prove its validity, both studies demonstrate that water plays a critical role in the transport of CO2 through chitosan. A comparison of the model to permeation data would need to include the amount and types of water in the chitosan membrane at separation conditions. 1.4. Objectives. Chitosan membranes were used to separate CO2 from H2 and N2 at high temperatures for a feed pressure of 1.5 atm. The feed and sweep gases were humidified to maintain a constant total water content (8.3 wt %) for all experimental temperatures over the range. 20-150 °C. The amounts of bound and free water were measured at each temperature. Cussler’s model for facilitated transport was modified to include terms for facilitated transport via bound and free water. Measurements of the membrane’s carbon dioxide permeability, carbon dioxide flux, and carbon dioxide selectivity with respect to nitrogen and hydrogen were interpreted using the modified model. The research objective was to link total water content, and the bound and free water fractions, to the facilitated transport mechanism for improved understanding of the case in which a mobile, diffusing species participates in the reactions leading to facilitated transport.

10.1021/ie7016916 CCC: $40.75  2009 American Chemical Society Published on Web 12/23/2008

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2. Background and Theory Two phenomena probably contribute to the increased flux of carbon dioxide through water-swollen chitosan membranes: (1) the potential for formation of carbamic acid and then carbamates between carbon dioxide and chitosan’s primary amines in the presence of water and (2) the presence of both bound and free water in the swollen polymer. This section describes relevant elements of prior work on amine reactions with carbon dioxide, prior measurements of bound and free water in chitosan, specifically, modeling of transport in swollen membranes, and modifications of Cussler’s model to extend it to facilitate transport by two types of water. 2.1. Amine Reactions with Carbon Dioxide. Chitosan’s repeating unit, a glucopyranose, has a primary amine group, a hydroxyl group on the β-carbon to the amine group, and a hydroxymethyl group on the opposite side of the ring. Carbon dioxide, a molecule that is generally unreactive, will react readily with amines. In the presence of water, primary amines react with CO2 in a two-step sequence, forming first a zwitterion, which then transfers a proton to an unionized amine, forming the corresponding carbamate.26,27 NMR studies have shown that water facilitates this reaction.27 The reaction scheme is H2O

R-NH2 + CO2 798 R-NH(CO)-OH + R′ -NH2T R-NH(CO)-O- · · · H3N+-R′ Carbamic acid, represented by R-NH(CO)-OH, is the intermediate product. The proton on the acid can transfer to an amine group on a nearby polymer chain segment, forming the corresponding carbamate (the bold dots indicate an ionic bond). Vibrational spectroscopy and ab initio studes of carbon dioxide reactions with secondary and tertiary alkylamino ethanol solutions28,29 show that four ions can be formed when water is present, compared to two ions in the absence of water. These ions can be stabilized in the liquid state by hydrogen bonds, including those with nearby hydroxyl groups of the alcohol moiety, resulting in preferred product conformations that have high stability. Carbamate salt formation is essentially an acid-base equilibrium between carbamic acid and a second amino group and is expected to be reversible. The rate of the reverse reaction of carbamate salts back to the amine increases with temperature. When carbon dioxide is removed from the system and heat is applied, the amines will reform26,27 Thus, chitosan’s chemical structure has some unique attributes for enhancing carbon dioxide reactions. The water in the membrane could help catalyze carbamic acid reactions, which can result in several stable ion species. Each primary amine group in its repeating unit could participate in the formation of carbamic acid or in protonating a carbamate. Either hydroxyl group of the repeating unit, i.e. the hydroxyl group on the ring near the primary amine or the hydroxymethyl group, could help stabilize the several carbamate-type ions formed in the presence of water (by hydrogen bonding) All of these groups could participate in various ways in the facilitated transport of carbon dioxide in swollen chitosan membranes. Stabilization of ion products by hydroxyalkyl groups could be an additional factor that leads to improved facilitated transport of carbon dioxide when glycerol is added to poly(amine) dendrimer membranes.13 While researchers often control the water in the membrane by controlling the humidities of the feed and sweep gases,10,30 the average amount of water in the membrane is often not reported. As water can help catalyze the reactions of carbon

dioxide with primary and secondary amines and is required for carbamate formation from tertiary amines,13 the actual amount of water in the membrane should affect the complexation reactions. The states of water in the membrane, either free or bound water, could also be important. 2.2. Two States of Water in Chitosan. The water in swollen three-dimensional polymer networks can exist in different states. Qu et al.31 proposed that, in chitosan, water can either be bound to the polymer via hydrogen bonding (bound water), can form secondary and tertiary “shells” or clusters around bound water (“freezing” bound water), or can be randomly dispersed with no freezing point depression (free water). In some hydrogels, water can also form “ice-cage” structures around hydrophobic groups.32 Polymers with phase-separated water (“capillary” water) would have porosity, which would not be helpful for selective separation of carbon dioxide. In practice, researchers can differentiate between bound water and free water either by freezing point depression or boiling point elevation type measurements. For example, differential scanning calorimetry (DSC) of water-swollen chitosan shows two distinct melting/freezing events.33 The melting peak area representing free water is centered near 0 °C, while the melting peak area representing bound water is centered several degrees C above this point. Thermogravimetric analysis (TGA) of these same samples showed two water loss peaks, one around 100 °C and the other near 150 °C. Khalid and co-workers evaluated the swelling behavior of chitosans for drug delivery and controlled release applications.34 TGA data showed that bound water (∼10 wt % in their sample) was only lost at temperatures greater than 140 °C. Both free and bound water would contribute to increases in the free volume of swollen chitosan. However, bound water is expected to hydrogen-bond to the chitosan and should contribute significantly to the several reactions and reaction products possible between carbon dioxide and the functional groups (primary amines plus hydroxyls) on chitosan repeating units. 2.3. Swollen Membrane Characteristics and Equations. Permeability (Pi) is a main parameter that characterizes the performance of gas transport through membranes. Permeabilities for gases at dry and humidified conditions are quantified from experimental techniques such as the time diffusion lag method. The gas permeability through free water is the product of the effective gas diffusivity (Deff) and the gas solubility (Si) as shown in eq 1. Pi ) DeffSi

(1)

The effective diffusivity is calculated by the product of the diffusivity obtained by the Wilke and Chang equation35 and the free water fraction, while the solubility data is obtained from the work of Schulze et al.36 This method has been implemented to explain water’s role in gas transport for swollen cellulose membranes.37 Equation 2 demonstrates that the total flux (JTi) is the product of the pressure driving force across the membrane and the ratio of the permeability and the membrane thickness (lm). JTi )

Pi (p x - ppyi) lm f i

(2)

The feed pressure, the sweep pressure, feed mole fraction of component i, and the sweep mole fraction of component i are represented by pf, pp, xi, and yi, respectively. In the case of a swollen membrane, where solution-diffusion and facilitated mechanisms occur, the total flux (JTi) can be equated to the sum of the fluxes of species through the following

896 Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009

mechanisms: transport through water (JWi), solution-diffusion (JSDi), and facilitated transport (JFi). Equation 3 represents the total flux of the above mechanisms. JTi ) JWi + JSDi + JFi

(3)

The total flux, JTi, measured in the experiments was that of carbon dioxide diffusing through swollen chitosan membranes. It was assumed that water did not phase-separate from the membrane material at these conditions, so no transport through capillary water occurred (no pores in the membrane). The solution-diffusion flux of carbon dioxide, JSDi, was measured directly by experiments with dry chitosan membranes without water humidification. The flux of carbon dioxide through free water in the membrane, JWi, was estimated by calculating the flux of carbon dioxide through water using the Wilke-Chang equation, the solubility of carbon dioxide in water, and the amount of free water in the swollen chitosan membrane. This is probably an upper bound for the contribution of JWi to the total flux of carbon dioxide. The total facilitated transport flux was taken to be the difference between JTi and the sum of JSDi and JWi. Another important parameter that verifies the separation efficiency of the membrane is the separation factor (Rij). The mathematical representation of the separation factor is composed of the ratio of the mole fractions of the key components in the permeate divided by the mole fraction ratio of the key components in the retentate. When the downstream pressure approaches zero, the separation factor becomes the ideal selectivity, R/ij, which is the ratio of the permeabilities of the targeted (Pi) and the untargeted species (Pj). Equations 4a and 4b represent the definition of the separation factor and the ideal selectivity. Rij )

yi/xi yj/xj

(4a)

Pi Pj

(4b)

R/ij )

where i and j are the gases involved in the separation, y is the mole fraction of the gas on the permeate side, and x is the mole fraction of the gas on the retentate side. 2.4. Modification of Cussler’s Model. Cussler et al.19 derived the facilitated flux in a reactive system where overlapping of the carrier occurs between two adjacent carriers throughout the membrane (l0 > l > l0/2). The carrier is arranged in a laminar structure with layers having thickness, l. The carrier functional group can only move a distance, l0, around its equilibrium position. The model assumptions include the following: the carrier exists only within the membrane, the solute can react rapidly and selectively with the carrier, and the interfacial concentrations are at equilibrium at each surface of the membrane. The conditions in a swollen chitosan membrane separating carbon dioxide from other gases are consistent with the model assumptions in the following ways. Water is the key mediator of the reaction between carbon dioxide and the primary amine groups on the chitosan repeating unit. This assumption is supported by the data for carbon dioxide permeability in dry and swollen chitosan membranes, as well as the known chemistry of carbamic acid reactions with water. Water in the membrane is characterized as free and bound water only, which can be determined independently and directly via evaporation experiments. The total carrier concentration (primary amine groups) is constant, and equal to the product of the fraction of

deacetylation, the polymer density and the molecular weight. It was assumed that the two hydroxyl groups in each chitosan repeating unit did not affect the forward reaction of carbon dioxide with the primary amines. However, they may have helped stabilized any ions or carbamic-type acids, thus reducing the rate of the reverse reaction. The facilitated flux (JF) for the fixed carrier membrane is represented by eq 5: JF )

(

)

DFCT KeqCA0 χ L 1 + KeqCA0

(5)

where DF is the facilitated diffusivity, CT is the total carrier concentration, L is the membrane thickness, Keq is the equilibrium constant, and CAo is the initial concentration of gas. The chain carrier correction factor, χ, includes the effects of chain mobility and Thiele modulus: χ)

[( )( )(

1 1 + cosh ψ l l l + 2-1 l0 l0 l0 2 ψ sinh ψ

)]

-1

(6)

where l is the thickness of the lamellar unit and l0 is the distance of chain carrier mobility. The Thiele modulus (ψ) is represented by the following equation: ψ)



2kCTl(l0 - l)2 l0DF

(7)

where k is the reaction constant and CT is the total carrier concentration. The total concentration is expressed by the following equation: CT )

1 l NA

(8)

3

where NA is Avogadro’s number. The total concentration is assumed to be constant as the reaction reaches steady state. The thickness of the lamellar unit is therefore constant according to eq 8. Equation 5 does not account for water being present in the system and only considers the occurrence of one reaction. Therefore, the equation can be modified to include both effects and is represented by eqs 9, 10a, and 10b: JF ) JFF + JFB

( (

(9)

) )

JFF ) φDF

KeqCA0 CT χFF 1 + KeqCA0 L

(10a)

JFB ) φDF

KeqCA0 CT χFB 1 + KeqCA0 L

(10b)

where φ is the water mole fraction (either bound or free), FF stands for facilitated reaction of CO2 occurring due to free water, and FB signifies the facilitated reaction of CO2 occurring due to bounded water. The bound and free water mole fractions have been determined experimentally at each temperature. The total concentration is replaced by eq 8. Model parameters were related to temperature by the following correlations:

( )

DF ) DF0 exp

-ED RT

(11)

where DF0 and ED are the pre-exponential factor and activation energy of the facilitated diffusion, respectively. The rate constant is

Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 897

( ) -Eact RT

k ) k0 exp

(12)

where k0 and Eact are the pre-exponential factor and activation energy of the reaction. The distance of chain carrier mobility is expressed in terms of temperature by:

( ) -El0 RT

l0 ) l/0 exp

(13)

where l0/ and El0 are the pre-exponential factor and activation energy of the distance for the chain carrier mobility, respectively. The product of the equilibrium constant (Keq) and the initial concentration (CA0) can be equated to a dimensionless equilibrium constant, K. This equilibrium constant can be represented in a similar manner to eq 11 by

( )

K ) K0 exp

-EK RT

(14)

where EK and K0 are the pre-exponential factor and activation energy of the dimensionless equilibrium constant. 2.5. Simulation. For the determination of the diffusive and reactive properties of the CO2 facilitated fluxes, the total concentration (CT) has a constant value of 1.3 × 10-5 mol/ cm3. Using eq 8, the value of thickness of the lamellar unit (l) is 5.0 × 10-7 cm. These values are used for the modeling of CO2 facilitated fluxes. Equations 6-8 were substituted in eqs 10a and 10b. For every value of l/l0 ranging from 0.5-1 with an incremental change of 0.1, large ranges of diffusivities, rate constants, and dimensionalized equilibrium constants were used to calculate the CO2 fluxes for free and bound water. Nonlinear regression (GraphPad Prism 4 and SYSTAT 11 software packages) was employed to find starting ranges of the above properties that would compute the CO2 fluxes near the experimental CO2 flux values. The parameter, l/l0, was optimized by decreasing the fitting error. The optimization toolbox and f-solve function featured by Matlab 7 were utilized to extract the parameters at their optimum values for eqs 11-14. The optimization processes was repeated until the problem converged for all studied temperatures. 3. Experimental Methods 3.1. Materials. High molecular weight chitosan flakes (batch number 14418LB; DDA ) 82%; Mw )89 192 g/mol; F ) 1.43 g/cm3), glacial acetic acid (99.99% pure), and deionized water were obtained from Aldrich Chemical Co., Milwaukee, WI. All chemicals, except for chitosan, were used without further purification. The purification of chitosan flakes from insoluble matter was performed through a series of dissolution-filtration-centrifugation-drying steps. Crude chitosan was dissolved in 1 vol % acetic acid aqueous (most typical solvent) for 48 h resulting in a 1 wt % solution. The solution was filtered through a Millipore membrane (5.0 µm) and degassed using a vacuum pump. The filtered solution was centrifuged for 30 min at a speed of 8500 rpm The chitosan was recovered and dried under vacuum overnight at 100 °C. The microporous Teflon (Tetratex) support (∼0.2 µm pore size and ∼80% porosity) with a Nomex fabric backing, was obtained from Tetratec PTFE Technologies, Feasterville, PA. The feed gas mixture composition was 10% hydrogen, 80% nitrogen, and 10% carbon dioxide. The carrier gas used for the GC and the sweep gas for the permeation process was ultra

Figure 1. Gas permeation unit for the separation of CO2 from N2 and H2.

high purity argon. All gases were obtained from Scott Gross Co. Inc., Lexington, KY. 3.2. Membrane Synthesis. Purified chitosan was dissolved in 1 vol % acetic acid and a 1 wt % solution was obtained then cast onto the microporous Teflon support backed with Nomex using a casting knife. Little of the active chitosan polymer penetrated the pores, as determined by examining cross-sections of the completed membrane. The cast membrane was first dried at room temperature for 72 h. The membrane was removed and placed in a temperature programmed vacuum oven where it was dried at the following conditions: (1) ramped at a rate of 1 °C/ min from 22 to 120 °C, (2) held for 6 h at 120 °C, (3) ramped at a rate of 1 °C/min from 120 to 150 °C, and (4) held for 6 h at 150 °C. This temperature was known to remove all bound water from the membranes. Finally, the oven was turned off and the chitosan membrane was cooled down to room temperature. The average final thickness of membrane, 65 µm, was measured by a micrometer. The effective membrane area was calculated to be 49 cm2. 3.3. Permeation Unit Operation. The gas permeation apparatus and method used were similar to those described by Tee et al.38 A simplified schematic of the gas permeation unit is shown in Figure 1. The permeation cell was housed in a temperature programmable Bemco oven (model FTU4.6, Simi Valey, CA), keeping the process at isothermal conditions. The temperature of the permeation process was varied from 20 to 150 °C. The feed mixture gas flowed at 200 cm3/min through a 1-way valve into a calibrated Brooks mass flow meter (Model 5850E, Hatfield, PA) and entered the permeation cell. Varian solvent delivery module pumps (Prostar 210, Walnut Creek, CA) delivered water to the bottom of the accumulators where the feed gas was humidified. The argon sweep gas flowed at 40 cm3/min into the accumulator along with water vapor. The humidified feed and sweep gases exited and flowed countercurrently to the permeation cell. The retentate pressure was maintained by the Tescom back-pressure regulator (Model ER3000, Elk River, MN), which was monitored and controlled by the software supplied by the manufacturer. The retentate pressure was varied from 7.35 to 58.8 psig. Water was removed from retentate and permeate streams by water knockouts. The relative humidities of the feed and sweep gases were determined via material balances of the gas and water flows. This method permitted control of the water content of the membrane at each temperature. Pumping rates for the feed and

898 Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 Table 1. Relative Humidities vs Temperature to Obtain 0.034 g Water/Membrane (8.3%) at pf ) 1.5 atm and ps ) 1 atm temperature (°C)

RHf (%) RHs (%)

20

40

50

65

75

85

100

110

120

125

130

140

150

97.5 75.9

82.4 75.5

61.6 57.5

38.5 36.5

36.5 35.2

34.4 33.6

30.8 30.3

28.6 28.3

26.4 26.2

24.4 24.2

22.6 22.4

18.1 17.9

14.6 14.5

sweep water flows were varied in order to achieve a constant partial pressure of water gradient across the membrane. The humidity levels to achieve 8.3 wt % water were determined via experiments. Pulses of both exiting streams were sent to the HewlettPackard (HP) 6890 network series GC system, equipped with a thermal conductivity detector (TCD), and the rest of the streams were vented off. Before entering the GC system, both the streams passed through drierite tube and a reducer-restrictor to remove any residual water. The streams entered the GC system in alternating fashion by using the valve system (switching valve and gas sampling valve each had four ports). The gas sampling valve had a loop volume of 1 mL and an injection time of 2 min. A Carboxen 1004 stainless steel micropacked column was used to analyze the gas streams, supplied by Supelco. The column mode was constant flow of 1.5-2.0 mL/min of argon as the carrier gas and the column pressure is maintained at ∼12 psi. The oven for the GC system was programmed at an isothermal temperature of 120 °C. The two gas streams were switched over the TCD’s filament 5 times per second, while the detector’s temperature was set at 200 °C. The makeup gas and reference gas flow rates were ∼2.5 and ∼20 mL/min of argon, respectively. Since, all gases had higher thermal conductivities than argon, they showed negative peaks. To make all the peaks positive, the negative polarity was switched on during the runs. Continuous analysis of these streams was done by running a sequence of runs alternating among runs of permeates, retentates, and calibrations on the Agilent ChemStation v9 software (Wilmington, DE). Total, free, and bound water were determined for the membranes at each operating condition by the following procedure. After the membranes were dried at 150 °C, they were weighed to determine their “dried” weight. After gas permeation, the membrane was weighed again to determine the total water fraction (free + bound) in the membrane. The membrane was heated at 100 °C in a vacuum oven equipped with a condensate trap. The membrane was then reweighed (residual water at this condition was bound water). As shown in prior work on bound water in chitosan,33,34 heating the membrane to 140 °C released all water from the membranes. The weight measurements to determine total, bound, and free water in the membrane were consistent with the measurements of water in the condensate trap after the various drying operations. 4. Results and Discussion 4.1. Water Content in the Membranes. For all the experiments, the temperatures studies ranged from 20 to 150 °C, while the feed pressure and sweep pressure were maintained at 1.5 and 1 atm. The relative humidities of the feed and sweep gases were determined for each temperature to obtain, approximately, the same percentage of water (8.3 wt % or 0.8 moles of water per mole of chitosan repeating units) in the swollen chitosan membrane as shown in Table 1. Assuming that water would preferentially hydrogen bond with the amines, not all amines would have a closely associated water molecule. At this level of water, the membrane was mechanically sound and facilitated transport of carbon dioxide was known to occur. The chitosan membranes were used at a constant weight percent water for

Figure 2. Effect of temperature on bound and free water in swollen chitosan membrane at pf ) 1.5 atm and ps ) 1 atm.

the sole purpose of this modeling study. Note that the relative humidity of the feed at the lowest temperature is near saturation, Higher amounts of water in the membrane are possible at high temperatures, but the 8.3 wt % level was the best achievable experimentally over the entire temperature range. This approach permitted a direct comparison of the fractions of bound and free water at each temperature condition, as the total water in the membrane was the same for all trials. Figure 2 shows the effect of temperature on the mole fractions of free water and bound water. The mole fraction of the free water decreases to depletion at temperatures greater than 110 °C, where the saturated vapor pressure of water exceeds the total pressure of the feed stream. As temperature increases, more bound water exists in the membrane when the total water fraction is held constant. 4.2. Carbon Dioxide Permeabilities and Selectivities. Table 2 lists CO2 permeabilities through dry chitosan membranes, free water, and swollen chitosan membranes at a temperature range of 20-150 °C and a feed pressure of 1.5 atm. The CO2 permeability through dry chitosan membrane increases with temperature, as expected. This is explained by the solutiondiffusion mechanism. Increasing temperature increases diffusivity, which greatly contributes to the increase in the permeability. This is observed in many glassy polymers, such as cellulose acetate, Kapton, and others.39 Swelling the chitosan membrane with water increases the CO2 permeability by 559fold at 20 °C. A similar result is observed for swollen cellulose.37 The CO2 permeability through water is 304 times that of the CO2 permeability through the dry chitosan membrane. The large differences suggest that water is not acting only as a swelling agent that increases the diffusivity of CO2 by plasticization. Water can bind with amino groups attached to chitosan or protonize them, resulting in facilitated CO2 transport. Increasing temperature to 110 °C increases CO2 permeability through the swollen chitosan membrane to 482 barrers, while CO2 permeability through water is 25 barrers. At this temperature, water’s key role is as a facilitator for carbon dioxide transport. Above 110 °C, only bound water exists in the chitosan membrane, and only bound water is responsible for fixed facilitated transport of CO2. At 150 °C, the bound water is essentially depleted and the carbon dioxide flux drops. The separation factors of carbon dioxide with respect to H2 and N2 through dry chitosan, water, and swollen chitosan are listed in Table 2. Table 2 illustrates the following: (1) the separation factors for the dry chitosan decrease continuously

Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009 899 Table 2. CO2 Transport Properties for Dry Chitosan, Water, and Swollen Chitosan at pf ) 1.5 atm and ps ) 1 atm T (°C)

20

40

50

0.4 116 213

0.9 86 262

1.3 78 307

3.1 10 19

2.8 7.7 23

2.6 7 27

19 40 69

13 34 95

65

75

2 63 356

3 56 397

85

100

110

4.3 50 422

7.1 38 471

9.5 25 482

120

125

130

140

150

permeability (barrers) dry watera swollen

12 0 449

14 0 439

16 0 436

21 0 409

26 0 399

CO2/H2 separation factor dry watera swollen

2.2 5.9 30

2.3 5.4 33

2.3 4.8 35

2.3 4.3 39

2.3 3.9 43

2.2 NA 39

2.2 NA 36

2.2 NA 34

1.9 NA 31

1.7 NA 29

8.4 28 142

8.2 26 164

7.7 24 180

6.9 21 216

6.3 NA 250

5.8 NA 232

5.5 NA 220

5.3 NA 213

4.9 NA 200

4.6 NA 194

CO2/N2 separation factor dry watera swollen a

12 32 117

Calculated by eq 1.

Figure 3. Effect of temperature on total and facilitated CO2 fluxes in swollen chitosan membrane at pf ) 1.5 atm and ps ) 1 atm.

as temperature increases, (2) the separation factors for the gas transport in water decrease continuously as temperature increases due to the loss of free water, and (3) separation factors for the swollen chitosan membrane go through maxima near 110 °C and then decrease beyond that temperature. For 20-110 °C, the separation factors, CO2/H2 and CO2/N2, increase from 19 to 43 and from 69 to 250, respectively. The increase in separation factor with rising temperature is due to the increase in CO2 facilitation. The loss of the separation factor beyond 110 °C is due to the depletion of free water and its contribution to CO2 facilitated transport. There is an enhancement of the solution-diffusion transport of H2 and N2, but it remains insignificant relative to facilitated transport of CO2. 4.3. Model Estimates of Facilitated Transport Fluxes. Figure 3 shows the effect of temperature on total CO2 flux (JT), total CO2 flux due to facilitated transport (JF), CO2 flux due to facilitated transport initiated by bound water (JFB), and CO2 flux due to facilitated transport initiated by free water (JFF). The fluxes for carbon dioxide transport through water (JWi) and for solution-diffusion (JSDi) are not shown. The JWi flux is a maximum at 20 °C (where it represents half of the total carbon dioxide flux) and declines to zero at 110 °C. The carbon dioxide flux due to solution-diffusion is insignificant at low temperatures and is only ∼10% of the total flux at 150 °C. The total flux increases as temperature increases from 20 to 110 °C and then starts to decrease beyond 110 °C. The facilitated transport of CO2 is the most dominant mechanism and follows a similar thermal trend to that of the total flux. The facilitated reaction initiated by free water contributes more to the carbon dioxide flux below 50 °C. Above 50 °C, the facilitated flux

Figure 4. CO2 facilitated flux initiated by free water as a function of l/l0 at different values of DF, k, and K at 20 °C (model ) dashed line; experimental ) (•) 1.5 × 10-6, 2 × 1012, 1; (0) 2 × 10-6, 2 × 1012, 1; (9) 1.5 × 10-6, 3 × 1012, 0.75) and 110 °C (model ) solid line; experimental ) (∆) 1.5 × 10-5, 3 × 1015, 1; (/) 1.5 × 10-5, 4 × 1015, 0.15; (×) 1.5 × 10-5, 2 × 1015, 0.15). Table 3. Range of Kinetic and Diffusive Parameters of the Facilitated Reaction Initiated by Free and Bound Water for l/l0 ) 0.5-0.8 at 20-150 °C, pf ) 1.5 atm, and ps ) 1 atm DF (10-6 cm2/s)

K (1012 cm3/(mol s))

K (10-4)

free water 20 °C 110 °C

1.5-2 15-16

20 °C 150 °C

1-2 30-40

2-3 3000-4000

0.75-1.0 0.1-0.15

bound water 1-2 104-2 × 105

2.0-3.0 0.045-0.15

initiated by bound water is the major contributor. Beyond 110 °C, no free water exists in the membrane and only bound water is available to initiate facilitated transport. This results in a decrease in the level of carbon dioxide in the chitosan membrane. Figure 4 compares experimental (points) and model (continuous curves) results for CO2 facilitated fluxes initiated by free water at 20 and 110 °C as a function of length ratio (l/l0). At 20 °C, all combinations of the values of the parameters in question (diffusivity, rate constant, and dimensionalized equilibrium constant) give a similar trend with respect to the length ratio (Table 3). In comparison to 20 °C, the values within the ranges of the diffusivity and the rate constant increase while the dimensionalized equilibrium constants decrease at 110 °C. The experimental fluxes lay within the simulated fluxes at different parameter combinations. This gives many possible

900 Ind. Eng. Chem. Res., Vol. 48, No. 2, 2009

Figure 5. CO2 facilitated flux initiated by bound water as a function of l/l0 at different values of DF, k, and K for 20 °C (model ) dashed line; experimental ) (•) 1 × 10-6, 1 × 1012, 3; (0) 2 × 10-6, 2 × 1012, 3; (9) 3 × 10-6, 2 × 1012, 2) and 150 °C (model ) solid line; experimental ) (∆) 3 × 10-5, 1 × 1016, 0.15; (/) 3 × 10-5, 1 × 1017, 0.045; (×) 4 × 10-5, 1 × 1017, 0.045).

Figure 7. Effect of temperature on rate constants initiated by free water and bound water at pf ) 1.5 atm and ps ) 1 atm.

Table 4. Arrhenius Parameters for Facilitated Transport Initiated by Free and Bound Water at pf ) 1.5 atm and ps ) 1 atm

ED (kJ/mol) Eact (kJ/mol) El0 (kJ/mol) EK (kJ/mol) DF0 (cm2/s) k0 (1026 cm3/(mol s)) l/0 (10-6 cm) K0 (10-4)

free water

bound water

22 ( 3 78 ( 15 4.5 ( 2.1 -19 ( 4 0.025 ( 6 1.4 ( 0.7 4 ( 1.2 3.21 ( 0.52

27 ( 8 92 ( 24 0.008 ( 0.003 -29 ( 6 0.059 ( 6 199 ( 52 1 ( 0.05 0.12 ( 0.02

Figure 6. Effect of temperature on facilitated diffusivities initiated by free water and bound water at pf ) 1.5 atm and ps ) 1 atm.

length ratios for the true values of the above parameters. To find the true length ratios at each temperature, the following constraints were set: (1) the diffusivity and the rate constant increase with temperature and (2) the dimensionalized equilibrium constant decreases with temperature. The length ratios are optimized and the corresponding parameter values are obtained. This optimization technique is performed for all the other temperatures within the studied temperature range. Figure 5 compares experimental (points) and model (continuous curves) results for CO2 facilitated fluxes initiated by bound water at 20 and 150 °C as a function of l/l0. The same optimization is used to obtain the diffusive and reaction properties at the appropriate length ratios. 4.4. Model Estimates of Arrhenius Parameters. The optimization results of the diffusivities, rate constants, l0, and dimensionalized equilibrium for CO2 facilitated transport initiated by free and bound water are used to obtain the Arrhenius parameters. The activation energies and pre-exponential factors and their average standard errors are listed in Table 4. Figure 6 shows the Arrhenius plot of the facilitated diffusivities of CO2 corresponding to free and bound water. As expected, activation

Figure 8. Effect of temperature on l0 for free water and bound water systems at pf ) 1.5 atm and ps ) 1 atm.

energy for diffusion of free water is lower than that of bound water (22.1 kJ/mol compared to 26.6 kJ/mol). Free water has more mobility within the membrane, which enhances successful equilibrium transitions from one site to another. As temperature increases, the difference in the above diffusivities decreases, and this is attributed to the larger pre-exponential factor of the facilitated diffusivity initiated by bound water. As temperature increases, free water content decreases, decreasing its contribution to the transport of CO2. Figure 7 shows the Arrhenius plot of the rate constants of CO2 corresponding to free and bound water. The rate constants describing the free and bound water reactions are near each other in magnitude. The activation energy of the free water (77.7 kJ/ mol) is lower than that of the bound water (91.8 kJ/mol), but the average standard errors associated with these parameters make the values similar. These apparent rate constants vary by ∼5 orders of magnitude over the temperature range, showing a large effect on the carbon dioxide reaction with the primary amines. Figure 8 shows the Arrhenius plot of the chain mobility distance (l0) corresponding to free and bound water. Increasing temperature increases l0 for the free water. This is due to the decrease of free water in the swollen chitosan membrane. For the bound water, l0 is essentially constant, consistent with the concept that hydrogen bonding constrains the mobility of the bound water. Figure 9 shows the Arrhenius plot of the dimensionalized equilibrium constants of the free water and bound water models. The dimensionalized equilibrium constants for both types of water decrease as temperature increases. This is consistent with prior reports that stripping carbon dioxide from carbamic acid solutions is more rapid at high temperatures.26,27 Over the temperature range where both types of water exist simultaneously, the dimensionalized equilibrium constant of the bound water is higher, suggesting that the reaction involving the bound water is more thermodynamically favorable. Another important factor is the initial concentration of CO2, which is part of the

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improved membranes, and controlling their separation performance in the field. Nomenclature

Figure 9. Effect of temperature on dimensionalized equilibrium constants for free water and bound water systems at pf ) 1.5 atm and ps ) 1 atm.

dimensionalized equilibrium constant. At low temperatures, the initial CO2 concentration is higher due to water presence and as the temperature is raised the initial concentration decreases. The coefficient set in Table 4 appears to be consistent with the facilitated transport mechanisms postulated for water-swollen chitosan membranes separating carbon dioxide. 5. Conclusions Gas permeation test were performed for dry and swollen chitosan membrane for the separation of CO2 from a mixture of CO2/H2/N2 at 20-150 °C and 1.5 atm. Dry chitosan membranes operated under the solution-diffusion mechanism, which is expected for a glassy polymer. Swelling the chitosan membrane improved CO2 transport properties dramatically because water acted as a mediator to facilitate CO2 from one amine site to another. Cussler’s model was modified to accommodate type of water, bound and free water, for facilitated transport of CO2.. A consistent set of model parameters were found using an optimization process. While each type of water participated in facilitated transport of CO2, bound water contributed more to the carbon dioxide flux, especially above the boiling point of water. Comparison of the facilitated transport model parameters for each type of water led to the following conclusions: (1) The apparent diffusivity for the free water initiated transport of carbon dioxide was higher than that of bound water initiated transport. As temperature increased, the transport facilitated by free water diminished because the free water content decreased. (2) The rate constants for both free and bound water increased with temperature. However, the total facilitated transport flux went through a maximum near the temperature where all free water was lost. (3) The length ratio describing the bound water facilitation was essentially constant over the temperature range, while that for the free water facilitation increased moderately with temperature. This is consistent with the constraining effects of hydrogen bonding. (4) While the dimensionalized equilibrium constant was required to decrease with temperature, the value associated with the bound water process was always higher than that for the free water process, suggesting that bound water is associated with more stable reaction products. Measurements of free and bound water in the membrane are consistent with the physical chemistry of chitosan. The facilitated transport model parameters are consistent with the known chemistry and responses of primary amine reactions with carbon dioxide. Together, these two elements could provide useful tools to interpreting permeability and selectivity results, for designing

CAo ) initial concentration of gas (mol/cm3) CT ) total carrier concentration (mol/cm3) D ) diffusivity (cm2/s) DF ) facilitated diffusivity (cm2/s) DF0 ) diffusion constant (cm2/s) DDA ) degree of deacetylation (%) Eact ) activation energy (kJ/mol) ED ) diffusion energy (kJ/mol) EK ) activation energy of the dimensionless equilibrium constant (kJ/mol) El0 ) energy barrier of the distance of the chained carrier mobility (kJ/mol) JSD ) solution-diffusion flux (mol/(cm2 s)) JF ) facilitated flux (mol/(cm2 s)) JFB ) facilitated flux initiated by bound water (mol/(cm2 s)) JFF ) facilitated flux initiated by free water (mol/(cm2 s)) JW ) flux through water (mol/(cm2 s)) JT ) total flux (mol/(cm2 s)) k ) reaction constant (cm3/(mol s)) K ) dimensionalized equilibrium constant k0 ) reaction rate constant (cm3/(mol s)) Keq ) equilibrium constant (cm3/mol) L, lm ) membrane thickness (cm) l ) thickness of the lamellar unit (cm) l0 ) distance of chain carrier mobility (cm) l0/ ) constant of the distance of the chain carrier mobility (cm) NA ) Avogadro’s number (atoms/mol) P ) permeability (barrer ) 10-10 cm3 (STP) cm/(cm2 cmHg s)) pf ) feed pressure (atm) pp ) permeate pressure (atm) ps ) sweep pressure (atm) R ) gas constant (J/(mol K)) S ) solubility (cm3 (STP)/(cm3 cmHg)) T ) temperature (°C) x ) feed mole fraction y ) sweep mole fraction Symbols Rij ) separation factor Rij/ ) ideal selectivity χ ) chain carrier correction factor φ ) water mole fraction, mole bound or free water per mole of all water F ) polymer density (g/cm2) ψ ) Thiele modulus Subscripts BW ) bound water FW ) free water i ) component i j ) component j

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ReceiVed for reView December 11, 2007 ReVised manuscript receiVed October 2, 2008 Accepted October 22, 2008 IE7016916