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Jun 5, 2013 - Fractionation of Organic Fuel Precursors from Electrolytes with. Membranes. Melissa Rickman,*. ,†. Robert H. Davis,. † and John Pell...
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Fractionation of Organic Fuel Precursors from Electrolytes with Membranes Melissa Rickman,*,† Robert H. Davis,† and John Pellegrino*,‡ †

Department of Chemical and Biological Engineering and ‡Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309-0596, United States S Supporting Information *

ABSTRACT: Efficient membrane fractionation of small, neutral organics from electrolytes could improve the sustainability of biofuel production from microorganisms, but the separations achieved are often insufficient. To rationally develop improved membrane materials for these fractionations, we need to better understand the mechanisms that govern solute transport through different types of materials. To this end, we have studied the transport properties of a variety of commercially available (that belong to major classes of polymeric materials) and some newly synthesized membranes. We determined that membranes belonging to a particular class have signature transport propertiesfor example, fully aromatic polyamides (FA-PA) are slightly more permeable to glycerol than NaCl, while the converse is true for semiaromatic polyamides (SA-PA)although all glycerol/ NaCl separation factors are near unity. Selected membranes were further probed with different reduced-carbon/electrolyte combinations. The cellulose−acetate (CA) membrane achieved the greatest separation between ethanol and electrolyte (NaCl, LiCl, Na2SO4), and the SA-PA membranes are better at fractionating larger reduced-carbons (glucose and sucrose) from the monovalent electrolytes. Meanwhile, an order-of-magnitude improvement in separation factor was found for the challenging glycerol/electrolyte fractionation with the SA-PA membranes when a divalent anion is used. The main transport mechanisms are interpreted based on Donnan exclusion and thermally activated transport through the polymer. The CA and FA-PA membranes appear to separate electrolytes through a predominantly steric-based mechanism, while the SA-PA membranes are more sensitive to anion valency. Furthermore, while solute size clearly plays a role in determining neutral solute transport, the relative roles of solubility (i.e., polymer-permeant interactions) versus polymer free-volume in the transport of small organics through the different materials remain unclear.

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INTRODUCTION Drioli and co-workers,1 along with other researchers, have pointed out the important role for membrane systems in process intensification, which is broadly used to describe innovative equipment and processing methods that can improve sustainability, efficiency, and environmental performance, in addition to life-cycle economic outcomes. For example, process intensification has recently improved outcomes for membrane integration in the fields of water desalination, agrofood, petrochemical, and biotech.1 In this work, we present results of a systematic study of the separation factors between model, small organic molecules and single salt electrolytes, in aqueous solutions, using pressure-driven filtration with several nanofiltration-type membranes. This study was motivated by the potential of a variety of biomass-based processes to produce energy fuel-precursors in aqueous electrolyte streams, and the dual requirements of concentrating a purified organic stream and recycling water (and electrolyte) to the upstream process. Relevant Biomass Processing Options. Microalgae are often cited as a sustainable source of energy and specialty products. However, the large material and energy inputs required to grow and process the cells using conventional methods make these processes infeasible from both economic and environmental perspectives. More recently, algal “milking” has been investigated as a more sustainable method to produce fuels2−4 and high-value products.5 Rather than dewater and then break open the cells, these processes continuously harvest © XXXX American Chemical Society

secreted products from the cell culture. This approach has the potential to reduce the inputs for nitrogen/phosphorus fertilizers and dewatering/lysing energy, both of which are major portions of the material and energy inputs to conventional systems.6 In general, the growth reactor is expected to contain four main components: (1) whole cells, (2) small colloidal species (cell debris/opportunistic bacteria/macromolecules), (3) secreted product, and (4) electrolyte (nutrients and possibly excess electrolyte to enhance product secretion). The cells and colloidal species can be fractionated from secreted product and electrolyte using sequential microfiltration and ultrafiltration.7 This process leaves the product to be fractionated from the electrolyte, such that the former can be further processed and the latter can be recycled to the growth reactor. Similar fractionations are required during production of lignocellulosic fuels, in which biomass is enzymatically hydrolyzed to produce glucose and other sugars that can be fermented into fuels such as ethanol and butanol, or processed in some other route.8−11 Thus, if fuels are to be sustainably produced by microSpecial Issue: Enrico Drioli Festschrift Received: March 19, 2013 Revised: June 4, 2013 Accepted: June 5, 2013

A

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with a YSI 2635 membrane. Before YSI measurements were performed, the sucrose solutions were hydrolyzed to glucose by adding 1 mg invertase enzyme (Sigma, grade VII, ≥300 units/ mg solid) to 1 mL samples and incubating at room temperature for 5 h. All measurements were calibrated to standard solutions. Membranes. Nine different membrane materials, including commercially available and some novel ones, were tested (Table 2). All error bars and ± values are 95% confidence intervals for two to five replicates.42 Description of Apparatus for Pressure-Driven Filtration Measurements. Experiments were performed in a unit that houses three membranes, each with a circular surface area of 9.6 cm2 and 2 mm channel height (Figure 1, additional schematic provided in the Supporting Information). All three membrane cells were fed from the same 2 L stainless steel feed reservoir, which was submerged in a cooling bath to maintain the temperature at 25 °C. The feed was delivered to the membranes with a rotary vane pump (Fluid-o-Tech). Transmembrane pressure was maintained with three back-pressure regulators (Swagelok) and monitored with three differentialpressure transducers (Omega) connected to a data-acquisition unit and logged in LabView (National Instruments). Boundary-layer, Mass-Transfer Calibration/Calculation. The film model is based on a mass balance over an element of the boundary layer and allows the concentration at the membrane surface to be calculated from the mass-transfer coefficient:

organisms, efficient methods to fractionate electrolytes from the small, neutral fuel precursors are desirable. Prior Studies on Small Organic Molecule Separations with Membranes. Since the development of cellulose-acetate (CA) reverse-osmosis (RO) membranes in the 1960s, many studies have been published on the fractionation of small organic molecules from electrolytes in aqueous solutions using RO- and nanofiltration (NF)-type membranes;12−38 however, a major drawback is that separation factors are often insufficient.39 These studies primarily feature membranes composed of CA, fully aromatic polyamide (FA-PA), and semiaromatic polyamide (SA-PA) materials, although additionaland often proprietarymaterial modifications are possible. However, most authors do not demonstrate how their results for a particular membrane are broadly applicable to a class of materials, or if such a generalization is even realistic. Mechanistic understanding of solute transport through these different types of materials is necessary to rationally design new materials that can accomplish difficult fractionations. Herein, we report fractionation figures-of-merit for a variety of membranes that fall within the three major material classes noted above (FA-PA, SA-PA, and CA). In addition, in the last 15 years there has been a burgeoning literature and application of new membranes for separations in organic solvents (OSNF). While this latter area is outside the main scope of the current report, we report some initial results for new structures with similar attributes as this class. We further evaluated selected membranes with different combinations of electrolyte and neutral solutes and report the characteristic transport properties of these membranes via separation factors. These results are used to interpret the transport mechanisms through the different materials on the basis of Donnan and steric exclusion.

Jv =

MATERIALS AND METHODS Materials. The electrolytes included NaCl (Fisher), LiCl (Fisher), and Na2SO4 (Macron Chemicals). The reducedcarbons were 200-proof ethanol (Decon), glycerol and glucose (Acros Organics), and sucrose (Fisher). The Stokes’ radii (i.e., the radius of an uncharged, rigid sphere that displays the same hydrodynamic properties as a solvated molecule in solution40) of these solutes are summarized in Table 1.27,41

Sh =

Table 1. Stokes’ Radii of Tested Solutes Stokes’ radius (Å)

Na+ Li+ Cl− SO42− ethanol glycerol glucose sucrose

1.8 2.4 1.2 2.3 2.0 2.6 3.7 4.7

(1)

where Jv is the total volumetric flux, Di is the diffusivity of solute i in water, δi is the thickness of the boundary layer, Ci,m is the concentration in solution at the feed-membrane interface, Ci,p is the permeate concentration, Ci,b is the bulk concentration, and ki is the mass-transfer coefficient.43 All Ci values refer to the concentration in solution. The mass-transfer coefficients were determined from the Sherwood correlation for laminar flow in a horizontal slit,

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solute

⎡ (C − Ci ,p) ⎤ Di ⎡ (Ci ,m − Ci ,p) ⎤ ⎥ = ki ln⎢ i ,m ⎥ ln⎢ ⎢⎣ (Ci ,b − Ci ,p) ⎥⎦ δi ⎢⎣ (Ci ,b − Ci ,p) ⎥⎦

⎛ d ⎞0.33 kidh = 1.86Re 0.33Sci 0.33⎜ h ⎟ ⎝L⎠ Di

(2)

where dh is the hydraulic diameter, Re is the Reynolds number, and Sc is the Schmidt number.44 Further information regarding the cell geometry, calculation of the mass-transfer coefficients, and propagation of uncertainty into the primary figures-of-merit is available in the Supporting Information. Experimental Design and Protocols. After installing three new membranes in the unit, they were conditioned with deionized (DI) water at 10 bar until the permeate flux did not change by more than 3% (∼2.5 h). Next, the pure water permeance (m/(s MPa)) was measured by determining the permeate flux at 0.5 and 1.0 MPa with DI water. All experiments were performed in full-recycle mode at constant transmembrane pressure. Crossflow velocity (∼0.28 m/s) was determined by a timed, periodic collection of retentate in a graduated cylinder. Permeate flux was measured by frequent timed weighings on a scale. For the initial membrane screening, three factors were varied: membrane, reduced-carbon composition, and transmembrane pressure. Electrolyte composition was held constant in these experiments (0.14 M NaCl). All nine membrane materials were

Analytical Methods. Electrolyte concentrations were measured with a conductivity meter (Denver Instrument). Glycerol concentration was measured using an enzymatic glycerol assay (BioAssay Systems). For the initial membrane screening, sucrose concentrations were measured with a hand-held refractometer (Atago). For the additional membrane studies, ethanol, glucose, and sucrose were measured with a YSI 2700 SELECT Biochemistry Analyzer. Ethanol was measured with a YSI 2786 membrane, and glucose and sucrose were measured B

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Table 2. Summary of Tested Membranes typea

membrane BR1

CA

BR2

CA

Osm CPA3

source

pure water permeance [× 10−8 m3/(m2 s MPa)]b

nominal rejectionc

6±1

90.6% NaCl rejection

6±1

93.4% NaCl rejection

CA TFC FA-PA

Bureau of Reclamation Bureau of Reclamation Osmotik Hydranautics

7±1 11 ± 2

ESPA1

TFC FA-PA

Hydranautics

13 ± 2

NF45 SR100 TFC NP

TFC SA-PA TFC SA-PA TFC PI without particles

10 ± 2 16 ± 3 6±5

TFC 1%

TFC PI with 1% silica particles

Dow Filmtec Koch synthesized in our lab synthesized in our lab

4±4

88.9% NaCl rejection 99.7% nominal salt rejection (1500 ppm NaCl at 1.55 MPa) 99.3% nominal salt rejection (1500 ppm NaCl at 1.05 MPa) 200 g/mol MWCO 200 g/mol MWCO N/A N/A

a TFC: thin-film composite. PA: polyamide. SA: semiaromatic (piperazine-based). FA: fully aromatic (1,3-benzenediamine-based). CA: cellulose acetate. PI: polyimide. bMeasurements taken in our lab. cNominal rejections as reported by manufacturers for commercial membranes and through personal communication with the Bureau of Reclamation for their cellulose acetate membranes.

Figure 1. Schematic of apparatus for pressure-driven filtration measurements.

tested. Reduced-carbon composition was either a “high” level of glycerol (1.8 g/L), a “low” level of glycerol (0.18 g/L), or sucrose (50 g/L). The relatively high concentration of sucrose was used due to the detection limits of the refractometer. The constant transmembrane pressure was either “high” (1.0 MPa, ∼twice the osmotic pressure of the feed) or “low” (0.5 MPa, ∼equal to the osmotic pressure of the feed). For each experiment, the system was allowed to equilibrate for 20 min before samples of the feed and permeates were collected to measure their electrolyte and reduced-carbon concentrations. For the additional membrane studies, four selected membranes (BR1, ESPA1, NF45, and SR100) were tested with different electrolyte/reduced-carbon combinations. The electrolyte was either NaCl, LiCl, or Na2SO4, all at the same ionic strength (0.14 M). The reduced carbons included ethanol, glycerol, glucose, and sucrose (5 g/L). It was possible to use a lower sucrose concentration than previously employed because we switched our characterization technique from the hand-held

refractometer to YSI, which had much more sensitive limits of detection. The transmembrane pressure was 1.0 MPa, and the filtrations were allowed to equilibrate for 30 min before taking a measurement. Each of the twelve electrolyte/reduced-carbon combinations was tested for three different coupons from the same membrane roll, and in a randomly selected order, for each membrane type. The system was flushed with DI water between each run. The pure-water permeance of each membrane was measured initially, and then again after six and twelve solutions were tested (Figure 2). The average purewater permeance decreased by 8%, 5%, and 5% of its initial value for ESPA1, BR1, and NF45, respectively, and increased by 7% for SR100. However, the change is only significant at 90% confidence for ESPA1 (p = 0.10). Note that we measured greater variance in the pure-water permeance of NF45 relative to the other membranes. The most logical rationale is that, since we cut samples from a larger sheet, there can be spatial C

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water permeance coefficient was redefined from its standard definition, such that it is normalized to the activity difference of water instead of the effective pressure drop. In other words, we define DwΦw/l as the new water permeance coefficient, rather than DwΦwCw,mvw/lRT.45 Using this newly defined transport property of water, the separation factor, αw/r = Pwater/ Preduced‑carbon, was calculated.

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RESULTS Membrane Screening with Glycerol or Sucrose and NaCl. The permeance coefficients for each of the three solutes tested during the initial, nine-membrane screening are presented in Figure 3. Analysis of variance of the data set Figure 2. Initial pure water permeance for four membranes, and after conducting six (“mid”) and twelve (“final”) fractionation experiments. The uncertainty bars represent the 95% confidence intervals for triplicate experiments with three fresh membranes.

variations along or across the sheet on the length scale of the diameter of our disks. Data Analysis Model and Methods. Solute transport from the bulk feed to the permeate involves four main steps: (1) transport through the concentration polarization boundary layer, (2) equilibrium partitioning of the solute into the membrane, (3) diffusion and/or convection of the solute across the membrane, and (4) equilibrium partitioning of the solute from the membrane to the permeate. The solution-diffusion model is widely used to describe solute transport through dense polymeric membranes with small pores, for which convective transport is negligible. For reverse-osmosis membranes, this model describes the flux of solute i as Ji =

⎛ −νiΔp ⎞⎤ Pi ⎡ ⎟⎥ ⎢Ci ,m − Ci ,pexp⎜ ⎝ RT ⎠⎦ l⎣

Figure 3. Permeance coefficients of three solutes (NaCl, glycerol, sucrose) through nine different membranes. The uncertainty bars represent the 95% confidence intervals for four to eight repeats.

indicates that the permeance coefficients for electrolyte and reduced-carbon do not deviate significantly from the mean as a function of low or high pressure, or low or high glycerol concentration. As such, permeance coefficients for NaCl (low/ high pressure, low glycerol/high glycerol/sucrose), glycerol (low/high pressure, low glycerol/high glycerol), and sucrose (low/high pressure, sucrose) were grouped together and are reported with 95% confidence intervals. All of the membranes tested are more permeable to NaCl than to sucrose. However, notable differences in NaCl and glycerol permeance are apparent for the different classes of membrane materials. For example, the CA and FA-PA membranes are slightly more permeable to glycerol than NaCl, while the SA-PA membranes are slightly more permeable to NaCl than glycerol. The PI membranes appear to be similarly permeable to both NaCl and glycerol. Figure 4 recasts the results of Figure 3 in terms of the log of the separation factor, αr/e = Preduced‑carbon/Pelectrolyte. When log(αr/e) = 0, there is no separation between solutes. When log(αr/e) > 0, the membrane is more permeable to the reducedcarbon. When log(αr/e) < 0, the membrane is more permeable to the electrolyte. Although little fractionation takes place between glycerol/NaCl for any of the membranes, the CA membranes retain the greatest amount of electrolyte relative to glycerol, while the SA-PA membranes retain the greatest amount of glycerol relative to electrolyte. Meanwhile, the SAPA membranes, which are more permeable to electrolyte compared to the other membrane materials, not surprisingly, also have the greatest fractionation between electrolyte and sucrose, a larger reduced-carbon.

(3)

where Pi = DiΦi is the permeability coefficient of solute i, Φi is the liquid-phase/membrane-phase sorption coefficient, l is the membrane thickness, νi is the permeant molar volume (assumed here to be the same in the liquid and membrane phases), Δp is the transmembrane pressure, R is the gas constant, and T is the absolute temperature.45 The term Pi/l was calculated for each experiment to describe the permeance of each membrane, as madeincluding the thin-film composite layers, to each solute under the given conditions.45 The ratio of permeability coefficients of the neutral and charged solutes (αr/e = Preduced‑carbon/Pelectrolyte) was then calculated to describe the fractionation performance for each membrane and condition, herein referred to as the separation factor. A separation factor equal to unity indicates that no fractionation has occurred; a separation factor greater than unity indicates that the membrane is more permeable to reduced-carbon than electrolyte; and a separation factor less than unity indicates that the membrane is more permeable to electrolyte than reduced carbon. Similarly, the water permeance coefficient (DwΦwCw,mvw/ lRT, often referred to as “A”) can be calculated from the solvent flux during reverse-osmosis: Jw =

Dw φw Cw,mvi lRT

(Δp − Δπ )

(4)

where Δπ is the osmotic pressure difference. However, to assess the transport of water on the same basis as the solute, the 45

D

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and membrane material on fractionation results. Analysis of variance indicated that reduced-carbon permeance coefficients do not differ significantly from the mean when the different electrolytes’ results are combined (p = 0.62) and likewise that electrolyte permeance coefficients do not differ significantly from the mean when the different reduced-carbon results are combined (p = 0.98). Intrinsic rejections (Rint = 1 − Cp/Cm) for each solute are reported in Table 3. Figure 6 shows the Table 3. Intrinsic Rejections and 95% Confidence Intervals for Each Solute/Membrane Combination Rint (%) ethanol glycerol glucose sucrose NaCl LiCl Na2SO4

Figure 4. Separation factors between glycerol/NaCl and sucrose/NaCl for nine tested membranes. The uncertainty bars represent the 95% confidence intervals for four to eight repeats.

Figure 5 presents the water/glycerol versus NaCl/glycerol separation factors for each of the screened membranes. The

BR1 10 66 96 98 78 79 93

± ± ± ± ± ± ±

ESPA1 1 3 1 0 1 1 1

29 87 99 99 92 93 95

± ± ± ± ± ± ±

3 2 0 0 1 0 0

NF45 13 42 92 99 31 28 93

± ± ± ± ± ± ±

3 3 1 0 3 2 2

SR100 18 65 98 99 54 47 92

± ± ± ± ± ± ±

3 2 0 0 3 1 2

Figure 6. Permeance coefficients of the reduced-carbons (ethanol, glycerol, glucose, sucrose) through four different membranes. The uncertainty bars represent the 95% confidence intervals for nine replicates.

Figure 5. Water/glycerol versus NaCl/glycerol separation factors for nine tested membranes. Uncertainty bars are 95% confidence intervals. The dotted reference line indicates the locus of equivalent water and electrolyte permeance.

permeance coefficients for each reduced-carbon/membrane combination, and Figure 7 shows the permeance coefficients for each electrolyte/membrane combination. ESPA1 is the least permeable to all solutes, while NF45 is the most permeable to

grouping of membranes on this plot appears to loosely correspond with particular material classes. Both the FA-PA and CA materials, for example, are slightly more permeable to NaCl than glycerol, but the FA-PA materials are significantly more permeable to water than glycerol, compared to the CA membranes. Meanwhile, the SA-PA materials are slightly more permeable to glycerol than NaCl and have lower water/glycerol separation factors than the FA-PA materials. Within the SA-PA classification, NF45 has notably lower αw/NaCl compared to SR100. The three CA membranes showed the least variation between separation factors for a given class of materials. All of the materials have at least an order-of-magnitude greater permeance to solute than water (on a concentration/activitynormalized basis), as indicated by their positions relative to the x-axis and the Pwater = Pelectrolyte reference line. However, the FAPA materials have over an order-of-magnitude greater relative water permeance compared to the PI materials and NF45, consistent with observation that the FA-PA materials have greater overall permeate productivity. Selected Membrane Testing. Four membranes were selected to further explore the effects of solution composition

Figure 7. Permeance coefficients of electrolytes (NaCl, LiCl, Na2SO4) through four different membranes. The uncertainty bars represent the 95% confidence intervals for twelve replicates. E

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glycerol, glucose, NaCl, and LiCl. As expected, a given membrane is more permeable to smaller neutral solutes than to nominally larger ones, in the order ethanol > glycerol > glucose > sucrose. However, although BR1 is less permeable to glycerol and glucose than is NF45, it is considerably more permeable to ethanol than is NF45. Meanwhile, each membrane has similar permeance to NaCl and LiCl but is significantly less permeable to electrolyte when the divalent anion is present. The difference in electrolyte permeance for the monovalent versus the divalent anion is much larger for the SA-PA membranes, compared to the CA and FA-PA membranes. The separation factor calculated for each membrane/ reduced-carbon/electrolyte combination is shown in Figure 8. Figure 9. Water/reduced-carbon versus NaCl/reduced-carbon separation factors for selected membrane materials. The marker shape indicates the membrane material, while the marker size indicates the reduced-carbon identity, from smallest to largest (ethanol < glycerol < glucose < sucrose). Uncertainty bars are 95% confidence intervals for three repeats.

increased exclusion of higher-valency anions is primarily ascribed to Donnan exclusion, which relates the electrochemical potential in the feed solution to that inside the membrane.22 We estimated the difference in Donnan partitioning (See the Supporting Information) between NaCl and Na2SO4 to be 2−3 orders of magnitude for our filtration conditions and with the nominal membrane charges reported in prior studies. Thus, the theory predicts that there could be even greater differences between monovalent and divalent anion permeances than we found in our experiments, if differences in NaCl and Na2SO4 diffusion coefficients within the active layer were within an order-of-magnitude to each other. The lower differences between our measures permeances compared to the theoretical estimates could result from a lower concentration of ionizable functional groups in our membranes than those measured for the FA-PA membranes used by Coronell et al.47 Indeed, NF45 has been reported to be an uncharged membrane,21,48 but measurements with NF45 show similar permeance of NaCl and LiCl, and much lower permeance of Na2SO4, despite the similar hydrated radii of Cl− and SO42− anions, and so charge exclusion certainly plays a role in these separations. While differences in membrane charge concentration in the various materials may play a limited role in the observed differences in electrolyte permeance, steric exclusion of electrolyte may be a more important mechanism in ESPA1 and BR1, relative to the SA-PA membranes, due to their tighter structure. Thus, increased Donnan exclusion results in slightly lower (less than an order of magnitude) Na2SO4 permeance in those former membranes relative to that observed for the monovalent electrolytes, but a much lower (over an order of magnitude) Na2SO4 permeance in the SA-PA membranes, which provide less steric inhibition to solute transport. Reduced-Carbon Permeation. Equation 5 was derived by Freeman49 to describe the permeability of gases with kinetic diameter di through dense polymer membranes, assuming that thermally activated motion of the polymer chain segments controls penetrant diffusion:

Figure 8. Separation factors for each combination of membrane/ reduced-carbon/electrolyte tested. The uncertainty bars represent the 95% confidence intervals for three repeats.

It is clear that the most challenging separation is that between glycerol and the monovalent electrolytes. However, switching to the divalent anion improves the glycerol/electrolyte separation factors for all membranes, with an order-ofmagnitude improvement for NF45. The SA-PA membranes, which are more permeable to the monovalent electrolytes than are the other membranes, also have the higher separation factors for the monovalent electrolytes versus glucose or sucrose. Meanwhile, BR1, which has the notably high ethanol permeance, also has improved ethanol/electrolyte separation factors compared to the SA-PA membranes. The ethanol/ electrolyte separation factors for the SA-PA membrane are comparable to those for BR1 when the divalent anion is used. Figure 9 plots the water/reduced-carbon separation factors versus the NaCl/reduced-carbon separation factors for each membrane. ESPA1 has consistently greater water/reducedcarbon separation factor compared to the other materials, and the converse is true for NF45.

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DISCUSSION We begin our discussion with an interpretation of the main transport mechanisms, including (1) electrolyte permeation based on Donnan exclusion and (2) reduced-carbon permeation based on thermally activated transport through polymers. Then, we present more detailed comparisons between our results and prior literature. Interpretations of Main Mechanisms. Electrolyte Permeation. Our electrolyte permeation results are consistent with a previous finding that the rejection of divalent ions with the same charge as the membrane is above 95%, while monovalent ion rejection can vary between 20 and 80%.46 The

⎛1 − a ⎞ 2 ⎛1 − a ⎞ ⎟cd + f ⎜ ⎟ − b + ln K ln Pi = −⎜ i ⎝ RT ⎠ i ⎝ RT ⎠ F

(5)

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where a is independent of polymer type and equal to 0.64, and b, c, and f are constants that depend on the viscoelastic properties of the polymer and all tend to be larger for glassier polymers. The first three terms on the right-hand side of the equation describe the solute diffusivity and are based on the assumption that the activation energy for diffusion is proportional to the volume of the “activated state,” which is in turn proportional to the square of the penetrant diameter multiplied by the penetrant jump length. Although the solubility term, ln Ki, is a function of polymer-permeant interactions, the analysis assumes these interactions to have the same magnitude for a variety of polymers and solutes but allows the solubility term to vary with the potential-energy well-depth parameter in the Lennard-Jones potential-energy function (which is more important for gas separations because the penetrant must first condense before mixing with the polymer). If the solubility term is the same for different solutes in a given polymer, then a plot of ln Pi vs di2 should yield a straight line with negative slope. The results from our experiments using Stokes’ diameters as the metric for uncharged penetrant size are shown in Figure 10.

0.90 for SA-PA, and 0.79 for CA and FA-PA), indicating that the solubility parameter could vary with solute in the latter materials. This difference could explain the high permeability that we observed for ethanol in these membranes compared to the larger solutes. On the other hand, solubility may play a lessimportant role in neutral solute transport through the SA-PA materials. Independent measurements of the solubility parameter can be used (in later studies) to clarify the role of solute/polymer sterics versus polymer−permeant interactions in the diffusive transport through the membrane. Previous attempts at rationalizing solute permeation using sorption measurements in similar materials have yielded mixed results.50,51 Prior Literature. Our survey of prior literature suggests two things: (i) our reported results are both quantitatively and qualitatively consistent with the trends of other studies and (ii) that it may not be possible to find an unambiguous correlation between reduced-carbon size and selectivity with the materials studied because they function via a solution−diffusion mechanism. That is, all the nuances of possible solute-induced local swelling and solute−solute coupling in both solubility and mobility appear to arise in explanations for reported results. Nonetheless, it appears that both SA-PA and CA membranes have higher mobility of polar organics than does the FA-PA materials, even when solubilities are similar. These observations are illustrated and discussed in the following sections. NF45 SA-PA Membrane. In our measuements, the NF45 membrane has a uniquely low pure water permeance coupled with a relatively high permeance to the tested solutes. Despite having one of the lowest water permeances, its glycerol permeance is higher than that of other membranes (Figure 6, note, it is ∼6-fold higher). This same trend is observed for glucose, NaCl, and LiCl. In general, membranes with lower permeance to water are expected to have higher solute rejection (and thus lower solute permeance),52 and so, our results for NF45 were somewhat unexpected. The separation results reported by different authors often use solute rejection as the figure-of-merit for a membrane, but rejection is not intrinsic to a given membrane/solution combination. Instead, it also depends on the permeate flux. Therefore, we have reformulated the results of other authors for selected membranes in terms of the solute’s permeance, in the cases where enough information has been reported to do so (see the Supporting Information). These results are in Table 4.

Figure 10. Correlation between Stokes’ diameters and permeabilities of reduced-carbons for four membrane materials.

The points are more linear for the SA-PA membranes than for CA and FA-PA (R2 values on the linear trendlines are 0.98 and

Table 4. Results from Selected Publications That Contain Sufficient Information to Reformulate in Terms of the Solution− Diffusion Model Permeance Constant ref

membranea

solute

concentration

mixed?

feed temp

log(P/l)b

% deviationc

25 25 25 24 24 24 24 24 21 21 21

NF NF NF NF45 NF45 NF45 NF45 NF45 NF45 NF45 NF45

glycerol glucose NaCl glycerol glucose sucrose NaCl Na2SO4 NaCl Na2SO4 PEG200d

1.5 g/L 1.5 g/L 0.1 M 0.1 g/L 0.2 g/L 0.1 g/L 0.1 M 0.01 M 0.02 M 0.02 M 0.7 g/L

1.5 g/L glucose 0.1 M NaCl no no 0.1 M NaCl no no no no no no

20 °C 20 °C 20 °C 32 °C 32 °C 32 °C 32 °C 32 °C 22−26 °C 22−26 °C 22−26 °C

−4.6 −5.8 −4.5 −4.6 −5.8 −6.8 −4.5 −6.0 −4.5 −6.0 −5.8

0% 0% −9% +12% +13% +18% +5% 0% −2% −1% +6%

a The membrane NF is Dow’s replacement for NF45. bValues obtained in the current study, in units of [log(m/s)]. cReported results are compared to our measurements for log(P/l) in the NF45 membrane. dCompared to glucose.

G

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rejection for the C6 alcohol, even though the CA’s pure-water permeance is over ten times lower than that for NF200. Likewise, phenol rejection increased (87−99%) with solute size for the FA-PA membrane, but not for the CA membrane, which had loweven negativephenol rejections. A hypothesis from the prior work that uses materials similar to those studied in this paper is that mobility selectivity appears to be different between these materials even when solubility selectivity appears to be similar. The FA-PA membrane used by Ben-David et al.50 appears to perform similarly to the PA membrane used by Schutte,51 and the same is true for the SAPA and CA membranes, respectively. However, the low rejections of ≤C5 alcohols by the SA-PA membrane and ≤C7 alcohols by the CA membrane are not explained in either paper, but can be due to differences in mobility due to local swelling. Some pertinent observations were made decades ago. For example, Matsuura et al.53 determined parameters related to the polar and nonpolar character of several CA and PA materials based on solute retention times in packed liquid chromatography columns. Despite scatter in the nonpolar term, the FAPA polymers are more hydrophobic (i.e., have a larger polar parameter) than the CA polymers, which supports the very low rejection of ethanol we observed in our tested CA membrane. On the other hand, it is perhaps unexpected that their tested piperazineamide polymer (i.e., SA-PA) has both polar and nonpolar terms that correspond precisely with those of the CA polymers. Perhaps these similar solubility characteristics of CA and SA-PA polymers can help explain their similar performance relative to FA-PA materials in previous studies.50,51 Consistent with the findings of Matsuura et al.,53 Fang et al.54 published a study of the separation properties of a large number of CA and PA membranes, which indeed found lowereven negative rejection of polar organics in the CA compared to the PA membranes. In general, perhaps, using reasoning drawn from the behavior of glassy polymers in mixed-gas separations,55 which often show penetrant-induced plasticization56,57 or blocking of freevolume by parts-per-million-level contaminants,58 could prove to be useful in future analysis of membrane materials’ effects on solute fractionation.

Overall, our solute permeance results with NF45 are within 10−20% of those reported in the open literature, when all are normalized with the solution−diffusion model. The greatest difference is versus Wang et al.24 who investigated NF45 with mixed-solute solutions. All of their permeances are slightly higher than ours, but so is their feed temperature and purewater permeance (a 7 °C higher temperature and ∼10% higher pure-water permeance). Note, that as Bargeman et al.25 increased NaCl concentration from 0.01 to 1.0 M, its permeance to NaCl increased by over an order of magnitude, emphasizing the importance of electrolyte ionic strength (which we hold constant in the present work) on the membrane’s separation properties. Indeed, glucose retention decreased (permeance increased) from ∼98% to ∼89% as the electrolyte (NaCl) was increased to 1.0 M. Researchers also reported that the NF membrane retains slightly more glycerol when glucose is also present, although glucose retention does not change in the presence of glycerol. Finally, our electrolyte permeances are very similar to those reported by Xu et al.,21 with their values only slightly lower than ours, and their PEG200 permeances were quite similar to our results with the similarly sized glucose. These previous studies with NF45, while supporting our findings, also indicate the importance of solute−membrane and solute−solute interactions in determining solute permeance. Sorption Results for Small, Neutral Organics in Similar Membranes. Ben-David et al.50 recently compared separation properties of ESPA1 (FA-PA) and NF200 (SA-PA). This study is very relevant to our work, as few others have made direct comparisons between the separation properties of the present material types against small organics (although the lower electrolyte retention by SA-PA compared to FA-PA was previously acknowledged52), and, to the best of our knowledge, none has done so in the context of fractionation. The authors used ATR-FTIR to attempt to resolve the influence of size and sorption of different solutes (n-alcohols and organics) on rejection in different materials. The results for ESPA1 (FA-PA) with the n-alcohols indicated that the larger alcohols have greater sorption (due to increased hydrophobicity that pushes them into the more hydrophobic membrane environment), but rejection of the larger alcohols is also higher, indicating that size’s effect on mobility was an important exclusion mechanism. On the other hand, while the sorption data show a similar trend of increase with larger carbon numbers in NF200 (SA-PA), rejection is relatively low (∼10%), and apparently independent of size for up to C5 alcohols. Surprisingly, although urea and methanol have similar Stokes’ radii and sorption, urea permeates more than methanol during filtration, for both the FA-PA and SA-PA membranes analyzed. The authors suggest this finding is due to urea breaking the structure of water: since urea forms strong associations with water, its sorption is low, but these strong hydrogen bonds cause it to get “dragged” through the membrane during filtration. Meanwhile, since methanol increases water structure, it has lower permeability. This hypothesis was not tested further. Schutte51 studied sorption and permeation (diffusion) using CA and FA-PA reverse-osmosis membranes using measurements on linear-alcohols and different-sized phenols. Similar to the results of Ben-David et al.50 with ESPA1 (FA-PA), Schutte51 found rejection of linear alcohols to increase with size for the FA-PA membrane, but not for the CA membrane. Instead, the CA membrane mimicks the behavior that BenDavid et al.50 observed for NF200 (SA-PA), with only 10%

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CONCLUDING REMARKS Our screening experiments for the separation of small organics and electrolytes using different nanofiltration membranes identified signature characteristics of major classes of membrane materials that are currently in commercial use or under development. For instance, while the FA-PA and CA membranes are all slightly more permeable to glycerol than NaCl, the converse is true for the SA-PA membranes. Differences between these classes were further probed with a variety of electrolytes and neutral solutes, and results indicate that the FA-PA and CA membranes rely on steric exclusion of electrolyte to a greater extent than do the SA-PA membranes, which are more sensitive to anion valency. Despite being the least permeable to water, the CA membrane is most permeable to the small polar solute, ethanol. Furthermore, the SA-PA membrane NF45 has surprisingly high permeance to NaCl, LiCl, glycerol, and glucose, considering its low water permeance. Electrolyte and neutral solute transport mechanisms were interpreted using some simple, benchmarking calculations. Of the membranes we tested, CA provides the most separation between ethanol and various electrolytes, while H

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(6) Lardon, L.; Helias, A.; Sialve, B.; Stayer, J. P.; Bernard, O. Lifecycle assessment of biodiesel production from microalgae. Environ. Sci. Technol. 2009, 43 (17), 6475−6481. (7) Rickman, M.; Davis, R. H.; Pellegrino, J. Fouling phenomena during membrane filtration of microalgae. J. Membr. Sci. 2012, 423− 424, 33−42. (8) Smith, B. T.; Knutsen, J. S.; Davis, R. H. Empirical evaluation of inhibitory product, substrate, and enzyme effects during the enzymatic saccharification of lignocellulosic biomass. Appl. Biochem. Biotechnol. 2010, 161 (1−8), 468−482. (9) Zheng, Y.; Yu, C.; Cheng, Y. S.; Lee, C.; Simmons, C. W.; Dooley, T. M.; Zhang, R.; Jenkins, B. M.; VanderGheynst, J. S. Integrating sugar beet pulp storage, hydrolysis and fermentation for fuel ethanol production. Appl. Energy 2012, 93, 168−175. (10) Sharma, D. K.; Tiwari, M.; Behara, B. K. A review of integrated processes to get value-added chemicals and fuels from petrocrops. Bioresour. Technol. 1994, 49 (1), 1−6. (11) Lutz, H.; Esuoso, K.; Kutubuddin, M.; Bayer, E. Low temperature conversion of sugar-cane by-products. Biomass Bioenergy 1998, 15 (2), 155−162. (12) Freeman, S.; Stocker, T. Comparison of two thin-film composite membranes: low pressure FT-30 to very low pressure NF40HF. Desalination 1987, 62, 183−191. (13) Ikeda, K.; Nakano, T.; Ito, H.; Kubota, T.; Yamamoto, S. New composite charged reverse osmosis membrane. Desalination 1988, 68, 109−119. (14) Schirg, P.; Widmer, F. Characterisation of nanofiltration membranes for the separation of aqueous dye-salt solutions. Desalination 1992, 89, 89−107. (15) Van der Horst, H. C.; Timmer, J. M. K.; Robbertsen, T.; Leenders, J. Use of nanofiltration for concentration and demineralization in the dairy industry: Model for mass transport. J. Membr. Sci. 1995, 104, 205−218. (16) Levenstein, R.; Hasson, D.; Semiat, R. Utilization of the Donnan effect for improving electrolyte separation with nanofiltration membranes. J. Membr. Sci. 1996, 116, 77−92. (17) Bowen, W. R.; Mohammad, A. W.; Hilal, N. Characterisation of nanofiltration membranes for predictive purposes - use of salts, uncharged solutes and atomic force microscopy. J. Membr. Sci. 1997, 126, 91−105. (18) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. The electrostatic and steric-hindrance model for the transport of charged solutes through nanofiltration membranes. J. Membr. Sci. 1997, 135, 19−32. (19) Vellenga, E.; Tragardh, G. Nanofiltration of combined salt and sugar solutions: coupling between retentions. Desalination 1998, 120, 211−220. (20) Van der Bruggen, B.; Schaep, J.; Wilms, D.; Vandecasteele, C. Influence of molecular size, polarity and charge on the retention of organic molecules by nanofiltration. J. Membr. Sci. 1999, 156, 29−41. (21) Xu, Y.; Lebrun, R. Comparison of nanofiltration properties of two membranes using electrolyte and non-electrolyte solutes. Desalination 1999, 122, 95−106. (22) Bowen, W.; Welfoot, J. Modelling the performance of membrane nanofiltration - critical assessment and model development. Chem. Eng. Sci. 2002, 57, 1121−1137. (23) Straatsma, J.; Bargeman, G.; van der Horst, H. C.; Wesselingh, J. A. Can nanofiltration be fully predicted by a model? J. Membr. Sci. 2002, 198 (2), 273−284. (24) Wang, X. L.; Zhang, C.; Ouyang, P. The possibility of separating saccharides from a NaCl solution by using nanofiltration in diafiltration mode. J. Membr. Sci. 2002, 204, 271−281. (25) Bargeman, G.; Vollenbroek, J. M.; Straatsma, J.; Schroen, C. G. P. H.; Boom, R. M. Nanofiltration of multi-component feeds: Interactions between neutral and charged components and their effect on retention. J. Membr. Sci. 2005, 247 (1−2), 11−20. (26) Bouchoux, A.; Balmann, H. R.; Lutin, F. Nanofiltration of glucose and sodium lactate solutions: Variations of retention between single- and mixed-solute solutions. J. Membr. Sci. 2005, 258 (1−2), 123−132.

SA-PA has the best performance for larger solutes (glucose and sucrose) mixed with monovalent electrolytes. The most challenging separation (i.e., separation factors near unity) for all of the tested membranes is that between glycerol and monovalent electrolyte. However, separation factors are improved by about an order of magnitude when a divalent electrolyte is used with the SA-PA membranes. Thus, from a separations perspective, we suggest that sulfate may be the preferred, dominant background anion in growth media as opposed to chloride. Of course, the biological feasibility of such a scenario must be determined for a given microbial system. Although our limited review spans several decades of the available literature regarding neutral solute transport through various PA and CA polymers, the more recent studies highlight our still-limited understanding of the role of solute size, solute polarity, and nature of the membrane material (in terms of chemistry and free volume) in determining the mechanism for solute transport. Furthermore, a systematic assessment of how these mechanisms figure into the optimal material properties to achieve solute fractionation is lacking. Future work should focus on refining our fundamental understanding of the mechanisms that govern these processes, to guide development of improved membrane materials for fractionation.

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ASSOCIATED CONTENT

S Supporting Information *

Further data as mentioned in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +1-303-7184542 (M.R.). E-mail: [email protected]. Tel.: +1303-735-2631 (J.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Phillips66 for sponsoring this research, Chevron for providing a graduate research fellowship to Melissa Rickman through the Colorado Center for Biorefining and Biofuels (C2B2), Saied Delagah for providing the CA membranes, Koch Membrane Systems for providing the SR100 membrane, Ann Greco for facilitating YSI measurements, and Dhinakar Kompala for access to YSI equipment.

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REFERENCES

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