WO2023225514A2

WO2023225514A2 - Membranes and membrane systems for sorpvection

Info

Publication number: WO2023225514A2
Application number: PCT/US2023/067065
Authority: WO
Inventors: Haley Danielle WHITE; Ryan P. LIVELY; Young Hee Yoon; William J. Koros
Original assignee: Georgia Tech Research Corporation
Priority date: 2022-05-16
Filing date: 2023-05-16
Publication date: 2023-11-23
Also published as: WO2023225514A3

Abstract

Disclosed herein are membrane systems comprising a feed stream comprising at least a sorpvection agent and a sorpvected species, the sorpvected species having a first chemical potential; a permeate stream wherein the sorpvected species has a second chemical potential numerically greater than the first chemical potential; and a membrane separating the feed stream from the permeate stream, the membrane configured such that a mass fraction of the sorpvected species is 0.06 or greater, based on a total weight of adsorbed material in the membrane, and a flux of the sorpvection agent is greater than a flux of the sorpvected species by a factor of 7 or more.

Description

MEMBRANES AND MEMBRANE SYSTEMS FOR SORPVECTION

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Application No. 63/342,316, filed on 16 May 2022, and the entire contents and substance of each is incorporated herein by reference in its entirety as if fully set forth below.

FIELD OF THE DISCLOSURE

[0002] The present disclosure relates generally to membranes and membrane system for sorpvection. Particularly, embodiments of the present disclosure relate to membranes for conveying a sorpvected species having a high mass fraction in the membrane with a sorpvection agent having a high transmembrane flux.

BACKGROUND

[0003] Emerging organic contaminants of concern are ubiquitous to surface waters due to influx from industrial, municipal, and agricultural waste streams. Such contaminants are typically small and neutrally charged, making them difficult to remove with traditional nonthermal water treatment processes. Thermally-driven processes, such as distillation, drying, and evaporation, are effective for the removal of organics from aqueous waste streams. While these technologies are commonly used in industrial settings, they are also significant energy consumers. Importantly, the energy required to concentrate the organic from these streams increases exponentially as the organic becomes more dilute, highlighting the need for low- energy pre-concentration and separation processes. Highly selective membrane separations represent one energy-efficient and widely applicable technology for both the removal of organics from wastewater and the pre-concentration of organics in biochemical and pharmaceutical applications, among others.

[0004] Complex multi-component permeation through novel selective membranes can result in unusual nonidealities in terms of transport driving forces and transport modalities. For instance, when removing trace phenol from a CO2 stream, phenol can be concentrated in the permeate stream and move “up” a concentration gradient due to a behavior called “sorpvection”. Similar non-idealities have been discussed in the separation of complex organic feeds, the transient movement of ideal gases up concentration gradients, ionic species moving up concentration gradients via coupling to mobile or fixed carrier agents within a membrane, and other liquids traveling up concentration gradients. Indeed, many organophilic pervaporation membranes are capable of concentrating an organic on the permeate side of the membrane, but this is achieved via an energy-intensive vaporization process to provide strongly “downhill” chemical potential gradients across the selective layer of the membrane (i.e., the penetrant is permeating from a state of high chemical potential to a state of low chemical potential). A diagram representing classical membrane transport and an example of the non- classical transport phenomena observed in this work are shown in FIGs. 1 A and IB.

[0005] What is needed, therefore, are membrane systems for sorpvection that can transport fluids up a concentration gradient without the energy-intensive requirements of previous methods. Embodiments of the present disclosure address this need as well as other needs that will become apparent upon reading the description below in conjunction with the drawings.

BRIEF SUMMARY OF THE DISCLOSURE

[0006] The present disclosure relates generally to membranes and membrane system for sorpvection. Particularly, embodiments of the present disclosure relate to membranes for conveying a sorpvected species having a high mass fraction in the membrane with a sorpvection agent having a high transmembrane flux.

[0007] An exemplary embodiment of the present disclosure can provide a membrane system comprising: a feed stream comprising at least a sorpvection agent and a sorpvected species, the sorpvected species having a first chemical potential; a permeate stream wherein the sorpvected species has a second chemical potential numerically greater than the first chemical potential; and a membrane separating the feed stream from the permeate stream, the membrane configured such that a mass fraction of the sorpvected species is 0.06 or greater, based on a total weight of adsorbed material in the membrane, and a flux of the sorpvection agent is greater than a flux of the sorpvected species by a factor of 7 or more.

[0008] In any of the embodiments disclosed herein, the concentration of the sorpvected species in the permeate stream can be greater than the concentration of the sorpvected species in the feed stream.

[0009] In any of the embodiments disclosed herein, the mass flux of the sorpvection agent through the membrane can be greater than the mass flux of the sorpvected species through the membrane.

[0010] In any of the embodiments disclosed herein, the flux of the sorpvection agent can be greater than the flux of the sorpvected species by a factor of 10 or more. [0011] In any of the embodiments disclosed herein, the sorpvected species can have a negative transmembrane fugacity gradient and the sorpvection agent can have a positive transmembrane fugacity gradient, wherein the absolute value of the positive transmembrane fugacity gradient is greater than the absolute value of the negative transmembrane fugacity gradient.

[0012] In any of the embodiments disclosed herein, the membrane can further have a first uptake with the sorpvection agent and a second uptake with the sorpvected species, the second uptake being greater than the first uptake.

[0013] In any of the embodiments disclosed herein, the feed stream can be in an aqueous state and one or more of the sorpvected species or the sorpvection agent can be in a liquid state.

[0014] In any of the embodiments disclosed herein, the sorpvected species can be capable of hydrogen bonding with the sorpvection agent.

[0015] In any of the embodiments disclosed herein, the sorpvected species can be an organic molecule.

[0016] In any of the embodiments disclosed herein, the membrane can comprise a hollow fiber membrane.

[0017] In any of the embodiments disclosed herein, the membrane system can be configured to operate at steady-state conditions.

[0018] Another embodiment of the present disclosure can provide a membrane having a sorpvected species mass fraction when in contact with a sorpvected species, the mass fraction being 0.6 or greater, based on a total weight of the of adsorbed material in the membrane; and a sorpvected agent mass fraction when in contact with a sorpvection agent, the sorpvected species mass fraction being greater than the sorpvected agent mass fraction, wherein a flux of the sorpvection agent is greater than a flux of the sorpvected species by a factor of 7 or more, and wherein the sorpvected species has a negative transmembrane chemical potential.

[0019] In any of the embodiments disclosed herein, the concentration of the sorpvected species in a permeate side of the membrane can be greater than the concentration of the sorpvected species in a feed side of the membrane.

[0020] In any of the embodiments disclosed herein, the mass flux of the sorpvection agent through the membrane can be greater than the flux of the sorpvected species through the membrane.

[0021] In any of the embodiments disclosed herein, the mass flux of the sorpvection agent can be greater than the mass flux of the sorpvected species by a factor of 10 or more. [0022] In any of the embodiments disclosed herein, the sorpvected species can have a negative transmembrane fugacity gradient and the sorpvection agent can have a positive transmembrane fugacity gradient, wherein the absolute value of the positive transmembrane fugacity gradient is greater than the absolute value of the negative transmembrane fugacity gradient.

[0023] In any of the embodiments disclosed herein, the membrane can further have a first uptake with the sorpvection agent and a second uptake with the sorpvected species, the second uptake being greater than the first uptake.

[0024] In any of the embodiments disclosed herein, one or more of the sorpvected species or the sorpvection agent can be in a liquid state.

[0025] In any of the embodiments disclosed herein, the sorpvected species can be capable of hydrogen bonding with the sorpvection agent.

[0026] In any of the embodiments disclosed herein, the sorpvected species can be an organic molecule.

[0027] In any of the embodiments disclosed herein, the membrane can comprise a hollow fiber membrane.

[0028] In any of the embodiments disclosed herein, the membrane system can be configured to operate at steady-state conditions.

[0029] These and other aspects of the present disclosure are described in the Detailed Description below and the accompanying figures. Other aspects and features of embodiments of the present disclosure will become apparent to those of ordinary skill in the art upon reviewing the following description of specific, exemplary embodiments of the present invention in concert with the figures. While features of the present disclosure may be discussed relative to certain embodiments and figures, all embodiments of the present disclosure can include one or more of the features discussed herein. Further, while one or more embodiments may be discussed as having certain advantageous features, one or more of such features may also be used with the various embodiments of the invention discussed herein. In similar fashion, while exemplary embodiments may be discussed below as device, system, or method embodiments, it is to be understood that such exemplary embodiments can be implemented in various devices, systems, and methods of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate multiple embodiments of the presently disclosed subject matter and serve to explain the principles of the presently disclosed subject matter. The drawings are not intended to limit the scope of the presently disclosed subject matter in any manner.

[0031] FIG. 1A is a diagram representing classical membrane transport mechanisms as used in the prior art.

[0032] FIG. IB is a diagram representing membrane transport mechanisms in accordance with the present disclosure.

[0033] FIG. 2 illustrates a representative structure of a membrane, in accordance with some examples of the present disclosure.

[0034] FIGs. 3A and 3B are scanning electron microscopy (SEM) images of a membrane, in accordance with some examples of the present disclosure.

[0035] FIGs. 4A and 4B are plots of pore size distribution for a membrane, in accordance with some examples of the present disclosure.

[0036] FIG. 5 illustrates plots of flux, weight percentages, and transmembrane fugacity gradients for a membrane, in accordance with some examples of the present disclosure.

[0037] FIGs. 6A and 6B are plots of sorpvected species fugacity gradient and sorpvection agent mass flux, respectively, against sorpvected species mass flux for a membrane, in accordance with some examples of the present disclosure.

[0038] FIGs. 7A and 7B are plots of sorpvection agent fugacity gradient and sorpvected species feed composition, respectively, against separation factor for a membrane, in accordance with some examples of the present disclosure.

[0039] FIG. 8 illustrates plots of flux, weight percentages, and transmembrane fugacity gradients for a membrane, in accordance with some examples of the present disclosure.

[0040] FIGs. 9A and 9B are plots of adsorption and diffusion behavior, respectively, for a membrane, in accordance with some examples of the present disclosure.

[0041] FIG. 10A is a diagram representing membrane transport mechanisms in accordance with the present disclosure.

[0042] FIGs. 10B and 10C illustrate plots of sorpvected species separation factor and permeance, respectively, in a membrane, in accordance with the present disclosure.

DETAILED DESCRIPTION

[0043] The need for energy-efficient recovery of organic solutes from aqueous streams is becoming more urgent as chemical manufacturing transitions towards nonconventional and bio-based feedstocks and processes. In addition to this, many aqueous waste streams contain recalcitrant organic contaminants, such as pharmaceuticals, industrial solvents, and personal care products that must be removed prior to reuse. The present disclosure can provide examples of rigid carbon membrane materials that can remove and concentrate organic contaminants via an unusual liquid phase membrane permeation modality. Surprisingly, detailed thermodynamic calculations on the chemical potential of the organic contaminant reveal that the organic species has a higher chemical potential on the permeate side of the membrane than on the feed side of the membrane. This unusual observation challenges conventional membrane transport theory that posits that all permeating species move from high chemical potential states to lower chemical potential states. Based on experimental measurements, the present disclosure can illustrate that the organic can be concentrated in the membrane relative to water via favorable binding interactions between the organic and the carbon membrane. The concentrated organic can then be swept through the membrane via the bulk flow of water in a modality known as “sorpvection”. The present disclosure can include, via simplified nonequilibrium thermodynamic models, that this “uphill” chemical potential permeation of the organic does not result in second law violations and can be deduced via measurements of the organic and water sorption and diffusion rates into the carbon membrane. Moreover, this disclosure identifies the need to consider such nonidealities when incorporating novel, rigid materials for the separations of aqueous waste streams.

[0044] There has been a growing need for separation systems capable of removing or concentrating organic molecules from aqueous streams. The present disclosure can provide for carbon-based membranes that can enable this important pre- concentration or removal step. The transport of the organic through the membrane can occur despite the presence of an unfavorable chemical potential driving force. The experimental observation of steady-state uphill chemical potential permeation without fixed or mobile carriers is novel and challenges conventional membrane transport theories. This observation is reconciled by coupling continuity expressions to models derived for diffusive transport of guests in membrane materials. This new membrane separation modality can provide a potentially low-energy method to pre-concentrate organic species from an organic-aqueous mixture before further purification via existing technologies. [0045] Although certain embodiments of the disclosure are explained in detail, it is to be understood that other embodiments are contemplated. Accordingly, it is not intended that the disclosure is limited in its scope to the details of construction and arrangement of components set forth in the following description or illustrated in the drawings. Other embodiments of the disclosure are capable of being practiced or carried out in various ways. Also, in describing the embodiments, specific terminology will be resorted to for the sake of clarity. It is intended that each term contemplates its broadest meaning as understood by those skilled in the art and includes all technical equivalents which operate in a similar manner to accomplish a similar purpose.

[0046] Herein, the use of terms such as “having,” “has,” “including,” or “includes” are open- ended and are intended to have the same meaning as terms such as “comprising” or “comprises” and not preclude the presence of other structure, material, or acts. Similarly, though the use of terms such as “can” or “may” are intended to be open-ended and to reflect that structure, material, or acts are not necessary, the failure to use such terms is not intended to reflect that structure, material, or acts are essential. To the extent that structure, material, or acts are presently considered to be essential, they are identified as such.

[0047] By “comprising” or “containing” or “including” is meant that at least the named compound, element, particle, or method step is present in the composition or article or method, but does not exclude the presence of other compounds, materials, particles, method steps, even if the other such compounds, material, particles, method steps have the same function as what is named.

[0048] It is also to be understood that the mention of one or more method steps does not preclude the presence of additional method steps or intervening method steps between those steps expressly identified.

[0049] The components described hereinafter as making up various elements of the disclosure are intended to be illustrative and not restrictive. Many suitable components that would perform the same or similar functions as the components described herein are intended to be embraced within the scope of the disclosure. Such other components not described herein can include, but are not limited to, for example, similar components that are developed after development of the presently disclosed subject matter.

[0050] As used herein, a sorpvection agent can be a component that moves from a relatively higher chemical potential to a relatively lower chemical potential side of a membrane. A sorpvected species can be a component that moves from a lower chemical potential to a higher chemical potential side of a membrane. In other words, the sorpvected species can move “uphill.” The bulk flow of the sorpvection agent can assist in moving the sorpvected species from a lower chemical potential to a higher chemical potential side of a membrane. In such a manner, the sorpvection agent can cause a mass flux of the sorpvected species in the same direction as the sorpvection agent which can exceed the reverse diffusional flux of the sorpvected species. Hence, the “uphill” flow of the sorpvected species. Such a mechanism can be implemented if the product of the average sorpvected species weight fraction in the membrane and the sorpvection agent mass flux exceeds the diffusional flux of the sorpvected species. In such a manner, the sorpvected species can flow from a lower chemical potential to a higher chemical potential side of a membrane.

[0051] In terms of chemical potentials, the potentials of the sorpvection agent and the sorpvected species can be measured according to transmembrane chemical potential. The total transmembrane chemical potential is positive (i.e., greater than 0). Further, the transmembrane chemical potential of the sorpvected species can be positive, zero, or notably, negative (e.g., less than zero) so long as the total transmembrane chemical potential is positive. In such a manner, the limiting case for the presently disclosed membranes can be where n_SVDA = jsVDA + ^ωSVDA (ⁿtotal) ~ ^ωSVDA (ⁿSVNA) •

[0052] The enhancement for the sorpvected species can also be determined by the product of the sorpvection agent flux (whether achieved by high sorption or high diffusion contribution, or both types of contributions) times the mass fraction of the sorpvected species in the membrane. On this basis, it can be preferable to have the ratio of sorpvected species mass fraction to sorpvection agent mass fraction in the membrane be high. However, it is not necessary. For example, if the sorpvection agent is similar to water in a hydrophilic medium that rejects the sorpvected species sorption in the membrane, if the water mass flux were super high, it still could enhance the sorpvected species across the membrane.

[0053] Certain embodiments and implementations of the disclosed technology are described above with reference to block and flow diagrams of systems and methods and/or computer program products according to example embodiments or implementations of the disclosed technology. It will be understood that one or more blocks of the block diagrams and flow diagrams, and combinations of blocks in the block diagrams and flow diagrams, respectively, can be implemented by computer-executable program instructions. Likewise, some blocks of the block diagrams and flow diagrams may not necessarily need to be performed in the order presented, may be repeated, or may not necessarily need to be performed at all, according to some embodiments or implementations of the disclosed technology.

Examples [0054] The following examples are provided by way of illustration but not by way of limitation. By way of illustration, and not limitation, water can be a sorpvection agent and DMF can be the sorpvected species.

[0055] Examples of the present disclosure can utilize PIM- 1 -derived carbon hollow fiber membranes to separate aqueous streams containing trace amounts of organics using pressure- driven liquid permeation. Very few examples exist of the application of selective carbon membranes developed for water and wastewater treatment. PIM- 1 hollow fiber membranes can be fabricated using a dual-layer spinning technique. Membranes can be pyrolyzed with a refined thermal technique; chemical and structural characteristics can be probed with X-ray photoelectron spectroscopy, CO2 and N2 physisorption, scanning electron microscopy, gravimetric sorption, and liquid phase sorption experiments. Simulated waste streams containing 2.5-14.5 wt% n, n-dimethylformamide (DMF) in DI water can be separated with a custom-made bench-scale crossflow permeation system, and samples can be characterized with HPLC. In liquid phase permeation experiments, the disclosed membranes and membrane systems can present non-ideal behavior such as permeation of the organic against a chemical potential gradient (i.e., the organic is permeating uphill from a state of low chemical potential to a state of higher chemical potential). As used herein, fugacity is simply a mathematical manipulation of the chemical potential and is easier to calculate using modem thermodynamic models, and thus the present examples use fugacities throughout instead of the chemical potential. The present disclosure can provide a phenomenological description for the water and organic transport that rationalizes this unusual permeation observation in addition to second law and nonequilibrium thermodynamic analyses.

[0056] PIM-1 can be synthesized using a polycondensation method. Tetrafhioroterephthalonitrile (TFTPN) and 5,5’6,6’-tetrahydroxy-3,3,3’,3’-tetramethyll,l’- spirobisindante (TTSBI) can both be purified and subsequently dissolved with anhydrous DMF in a 1 : 1 M ratio. Once dissolution was achieved, anhydrous potassium carbonate that was finely ground can be added to initiate polymerization. The polymerization reaction can be allowed to stir continuously for 72 hours, while under a nitrogen atmosphere at 65 °C. Then the reaction mixture can be allowed to cool to room temperature, and DI water can be added to quench the reaction and precipitate PIM-1. PIM-1 can be removed from the solution with vacuum filtration; DI water can be used to wash away excess salts from the polymer. Iterative reprecipitation from chloroform can be used to remove low molecular weight oligomers. An average MW of 155,000 g/mol can be determined from gel permeation chromatography. Prior to casting, PIM-1 can be dried in a vacuum oven for 24 h at 80 °C.

[0057] Asymmetric PIM-1 hollow fiber membranes can be fabricated using a dry-jet wet- quench method. Three layers of fluids can be extruded from a triple orifice spinneret. A polymer solution dope with solvent and non-solvent [15 wt% PIM-1, 69.5 wt% THF, 13.25 wt% DMAC, and 2.25 wt% ethanol] dope fluid can be extruded through the core flow, and a solvent mixture (45 wt% THF, 46.75 wt% DMAc, 8.25 wt% ethanol) that does not precipitate the polymer can be extruded through the inner channel bore flow to keep the fibers hollow. The third layer of THF and 1 -butanol [82.5 wt% butanol, 17.5 wt% THF] can be used as a sheath layer surrounding the outside of the polymer hollow fiber; this can cause reduced THF evaporation rates, allowing for better tailoring of the membrane surface. Syringe pumps can be used to extrude all 3 layers of fluids (1000D for sheath and core, 500D bore fluid, Teledyne Isco). The air gap can be set at 1.5 cm, and the flow rates for bore, core, and sheath layers can be 90/120/65 mL/h, respectively. The dope temperature from pump to spinneret can be kept at room temperature, which is around 22 °C, while the water quench bath can be kept between 48 °C and 50 °C. Drum take up rate can be 1.5 m/min. After phase inversion, the fibers can be collected on a rolling drum in a separate water bath. The fibers can remain on this drum for at least 45 min before removal to a separate DI water bath, which can be replaced every day for three days; subsequently, fibers can undergo three methanol washes for 20 minutes each, followed by three more 20-minute washes in hexane. Finally, fibers can be dried in ambient conditions for an hour before being placed in a 60 °C vacuum oven (-29 in. Hg) overnight.

[0058] PIM-1 membranes can be soaked in methanol for 2 hours and then dried at least overnight (>15 h) in a hood to remove any residual methanol. Fibers can be secured to a stainless-steel mesh plate and then placed in a quartz tube, along with thermal insulation blocks to better maintain temperature, and this set up can be placed in a three-zone furnace (OTF- 1200X-III-S-UL, MTI Corporation). To ensure an oxygen-free atmosphere, the pyrolysis set up can be purged with 4% H2 in Ar balance. The maximum temperature of pyrolysis can be 900 °C, 1000 °C, or 1100 °C. The ramp rate at each temperature can be one of two choices: (1) 50 °C to T_max at 5 °C/min followed by 120 min hold at Tmax (denoted as amorphous carbon or AmC here) (2) 50 °C to 250 °C at 10 °C/min, 250 °C to T_max -15 °C at 3.85 °C/min, T_max -15 °C to T_max at 0.25 °C/min, and no hold at T_max (denoted as disrupted carbon molecular sieves or dCMS here). Cool carbon hollow fiber membranes can be soaked in methanol for at least 2 h; after this time, they can be removed from methanol and stored in a hood under ambient conditions to allow residual methanol to evaporate for at least 24 h. Single hollow fibers can be then used to make membrane modules to be assessed in crossflow permeation experiments. [0059] Permeation experiments can be conducted at a feed flowrate of 7 ml/min under a constant pressure of 20 bar and at ambient temperatures (22 °C) with concentrations ranging from 2.5 to 14.5 wt/wt% DMF in DI water balance. Stage cuts can be < 1 %. Throughout the permeation experiment, pressure can be maintained at 20 bar with a flow rate of 7 ml/min, under ambient temperatures. Once an initial permeance for each module is estimated, the time necessary to permeate 10 downstream volumes can be calculated, and the module can be allowed to permeate for at least this time period, with the exception of modules that had especially low permeances (< 1 x 10-2 LMH bar-1 total permeance), prior to collecting permeate samples. Permeate can be collected over a certain time period, which can vary between samples based on their productivity. Typically, samples can be allowed to permeate for several days before taking permeate samples. Membranes that demonstrated very low permeances can be allowed to circulate for at least 14 days prior to collecting permeate samples. Permeate and retentate samples can be analyzed with high performance liquid chromatography. Control experiments can be run to understand the ambient rate of water evaporation out of the collection vials to rule out this as a mechanism for concentration of the DMF in the permeate; this evaporation rate is found to be orders of magnitude lower than the water flowrates from even the lowest permeance membranes.

[0060] Carbon membranes can be characterized with X-ray photoelectron spectroscopy (XPS) to understand carbon bonding and elemental analysis. First, the elemental composition of carbon samples, both before and after soaking in methanol, can be measured. Methanol soaking can be tested to observe the effect of controlling the surface chemistry of carbons on water and DMF transport. After soaking in methanol for 2 hours, the average carbon and nitrogen compositions can decrease, while oxygen content can increase. The elemental composition of samples can also be compared for samples that were fabricated with a dCMS pyrolysis protocol versus an AmC protocol (5 °C/min and 2-h hold at Tmax). In general, as pyrolysis time increases, the AmC carbon composition can increase. As the pyrolysis temperature increases, the relative amount of carbon-carbon bonds can increase, while carbon-oxygen, and carbon-nitrogen bonds can decrease. Additionally, samples that were exposed to methanol can have lower amounts of carbon-carbon bonds and increased amounts of carbon-oxygen bonds relative to samples that were not soaked in methanol. This collection of data can be used to construct a representative structure that reflects the average composition and bonding of carbons (FIG. 2). [0061] Scanning Electron Microscopy (SEM) images can be obtained of the cross-sections of each of the carbon samples (FIG. 3 A). While the skin layer thickness of PIM-1 hollow fibers can vary based on the spinning parameters, the present disclosure finds that the skin layer thickness can largely be unaffected by the pyrolysis conditions, consistent with standard PIM- 1 hollow fiber CMS formation. A cross section of a hollow fiber and an example of a skin layer of a carbon membrane are shown in FIG. 3B.

[0062] Nitrogen and carbon dioxide physisorption experiments carried out at 77 K and 273 K, respectively, can be used to better understand the pore size distribution and pore volumes of dCMS and AmC samples. Typical CMS materials have a bimodal pore size distributioncomprised of ultramicropores (diameter < 7 A) and micropores (diameters between 7 A and 20 A). The traditional bimodal CMS pore size distribution is due to the slow and methodical temperature ramp rate followed by soaking at a max temperature for an extended period of time, which allows for increased ordering of carbon plates. Here, the present disclosure can utilize two pyrolysis protocols that are distinct from traditional CMS protocols to create AmC or dCMS materials: (1) 5 °C/min from 50 °C to Tmax with 2 h hold at Tmax to create AmC and (2) 50 °C to 250 °C at 10 °C/min, 250 °C to T_max -15 °C at 3.85 °C/min, T_max -15 °C to T_max at 0.25 °C/min, and no hold at T_max) to create dCMS. AmC and dCMS can be made using three different maximum temperatures (900 °C, 1000 °C, and 1100 °C). The reasoning behind the creation of the two types of carbon membranes (AmC and dCMS) can be to probe the relationship between pyrolysis protocol and liquid phase fluxes and selectivities. All materials can be pyrolyzed in 4% H2 in Ar balance, as this atmosphere can improve flux and increase pore volumes in PIM- 1 -derived CMS materials.

[0063] The pore size distributions of all carbons, as derived from the nitrogen isotherms at 77K using two-dimensional nonlocal density functional theory (2D-NLDFT) method, are shown in FIG. 4A. Regardless of pyrolysis protocol, the pore size distribution for the AmC and dCMS materials is not bimodal, unlike conventional CMS materials. Samples pyrolyzed at 900 °C have the largest pore volumes in the ultramicroporous and microporous ranges, and the sample pyrolyzed at 900 °C with a constant ramp rate can have a less refined pore size distribution with larger pore volumes. Without wishing to be bound by any particular scientific theory, this can result from arresting the carbonaceous structure during the relatively rapid thermal ramp, which can provide insufficient time for the carbon plates to organize into the microcellular structure found in traditional CMS materials. Samples pyrolyzed at 1000 °C can have the lowest N₂ uptake capacity due to lower pore volumes, regardless of thermal technique, likely as a result pore collapse at this specific pyrolysis temperature. Ultramicropore size distributions found with CO2 sorption at 273 K are also shown in FIG. 4B. Regardless of pyrolysis technique, the PSD can be similar, with primary pore volumes at 4.2 and 6 Å. Interestingly, all dCMS samples show an ultramicropore at 3.6 Å, whereas only AmC samples pyro lyzed at 1100 °C exhibit this 3.6 Å ultramicropore in addition to a 7.5 A micropore.

[0064] The carbon hollow fiber membranes can be incorporated into membrane modules for use in liquid phase H2O/DMF permeation experiments

⁼ 0-025 — 0.145 g/ g ,

T=22°C, ΔP_membrane = 20 bar). The permeation results from this experimental campaign are highlighted in FIGs. 5-8. The membrane can selectively permeate DMF such that DMF is found to be concentrated in the permeate stream relative to the feed stream. FIG. 5 shows the fluxes, permeate weight fractions, and transmembrane fugacity gradients of water and DMF for the most selective membranes (dCMS pyrolyzed at 900 °C). These membranes can yield a DMF/water separation factor of 3.94 (+/- 0.43). Importantly, both the flux and permeate concentration of water can be significantly larger than that of DMF. However, the transmembrane fugacity gradient of water is positive (i.e., while that

of DMF is negative (i.e., implying that DMF can be transported

against a fugacity (or chemical potential) gradient during the membrane separation process, which is contrary to traditional Fickian transport processes. There is a minimal correlation between increasing DMF flux and increasing DMF fugacity gradient (FIG. 6A). Importantly, FIG. 6B shows there can be almost a linear correlation between the DMF and water fluxes in permeation experiments; moreover, the separation factor for DMF over H2O can scale nearly linearly with the water transmembrane fugacity gradient (FIG. 7A). Standard thin-film composite reverse osmosis membranes with an active polyamide layer and support polysulfone layer (Dow Filmtec SW30HRLE) can be measured in permeation experiments as a control. Traditional RO membranes can be employed to (1) ensure the permeation system is providing accurate results and (2) compare this unique transport modality shown with carbon membranes with results shown with typical RO separations. In contrast with the carbonaceous membranes tested here, DMF can be rejected with 82.4 ± 5.8 % effectiveness (i.e., it is retained on the feed side of the membrane), which is consistent with the expected performance and transport modality for traditional RO membranes.

[0065] While permeation against transmembrane concentration gradients can be used in other examples (e.g., water in seawater reverse osmosis), the observation of permeation against a chemical potential (or fugacity) gradient is unusual and unexpected, especially in steady-state systems without chemical carriers. In dissipative systems, such as membranes, single component transport up a chemical potential gradient is not possible; however, in multi- component transport systems, such a scenario could be possible. Equation 1 shows a simplified non-equilibrium thermodynamic analysis of coupled driving forces. Here, J_DMF represents the flux of DMF through the membrane, while L_DMF-DMF and LDMF-H20 are Onsager’s phenomenological coefficients. R is the universal gas constant and T is the absolute temperature. and

are the transmembrane fugacity gradients of DMF and water.

f_DMF and F_H20 are the fugacities of DMF and water in the membrane. Importantly, this non- equilibrium approach highlights that the flux of DMF can be positive in the presence of a negative DMF fugacity gradient since both (1) the Onsager coefficients are positive and (2) the absolute value of the positive water fugacity gradient is significantly larger than the absolute value of the negative DMF fugacity gradient.

[0066] The present disclosure can also highlight via second law analyses that the sorpvection transport modality with uphill solvent permeation is (i) a net consumer of work (i.e., W_in > W_out), and (ii) is a net entropy producer. These analyses reveal that this sorpvection modality can likely be useful as a pre-concentration step within a multi-unit separation system, and that this modality can be unlikely to operate beyond -15% stage cut in realistic applications.

[0067] To investigate the impact of feed concentration on separation factor, the most selective membranes (900 °C dCMS) can be used to separate feed streams containing 2.5, 7.3, and 14.5 wt% DMF. At a lower DMF feed concentration, the separation factor can be -3.25, while at higher feed concentrations, the separation factor can decrease to -1.5 (FIG. 7B). As the concentration of DMF in the feed stream increases, this can limit the separation factor that can be achieved. A series of pervaporation experiments can also be conducted to remove many of the nonidealities associated with liquid phase permeation (i.e., the transmembrane fugacities for both H₂O and DMF are both positive in pervaporation due to the purge gas sweep on the downstream membrane surface). These experiments can yield essentially pure water as a product, as the DMF was not detectable with gas chromatography (FIG. 8).

[0068] Without wishing to be bound by any particular scientific theory, the DMF and H2O are hypothesized to transport through the membrane via a sorption-diffusion mechanism (i.e., IP = where IP represents the guest permeability, D is the guest diffusivity, and is the guest

sorption coefficient). The present disclosure includes a series of single component diffusion and sorption experiments to better understand the unusual concentration of DMF in the liquid phase permeation experiments shown in FIGs. 5-8. Dynamic vapor sorption experiments can be conducted with PIM- 1 -derived AmC powders and hollow fibers that were pyro lyzed at 1000 °C to assess isotherm behaviors and maximum uptake capacity at 25 °C with water and DMF. The DMF isotherm exhibits strong IUPAC Type 1 , or Langmuir, behavior, while water exhibits Type 4 sorption behavior (FIGs. 9A and 9B). Due to the very low vapor pressures of DMF, it is experimentally challenging to confirm that DMF has reached equilibrium at each partial pressure, especially at low activities. At relative saturations of 0 to 0.2, the DMF uptake (on a mass basis) can be larger than that of water, while at higher activities of 0.3 to 0.8, the water uptake can be greater than DMF. To further understand the sorption behavior of DMF in the condensed phase, a liquid isotherm can be measured, and showed excess uptake of DMF up to a value of approximately 3 wt %. The liquid-phase isotherm can reveal a maximum DMF sorption of 0.17 gDMF/g-membrane at unit activity. Kinetic uptake analysis on the carbon films can provide estimates of the diffusion coefficients of water (1.58 x 10-8 cm²/s) and DMF (1.42 x 10-12 cm²/s). This highlights a strong diffusion selectivity (-10000) for water over DMF, while the carbon membrane can exhibit some sorption selectivity (approximately 8-30 based on the somewhat low accuracy of the isotherm measurements) within the composition ranges investigated here.

[0069] The concentration of DMF in the permeate stream is an unexpected observation, since the hydrolyzed diameter of DMF is much greater than that of water, which likely improves upon the already-impressive diffusion selectivity of these membranes. Molecular modeling indicates that three water molecules can hydrogen bond with DMF, creating a larger hydrated radius than pure DMF. Additionally, such hydrated amides can show somewhat broad radial distributions when estimated with molecular dynamics. The apparent larger size of DMF and the significant disparity in diffusivities highlights that the concentration of DMF is unlikely to be achieved via any diffusive transport mechanism. Competitive sorption alone is also not likely to be the cause of this transport behavior, as the magnitudes of the sorption selectivity are completely mismatched with those of the diffusion selectivity (i.e.,

Indeed, classical sorption-diffusion analyses suggest highly selective water

permeation based on the water and DMF sorption/ diffusion coefficients alone.

[0070] Without wishing to be bound by any particular scientific theory, the present disclosure can provide for the combined effects of DMF-selective sorption and water-driven bulk flow via a large water fugacity gradient to drive the uphill permeation of DMF through the carbon membranes. Specifically, the positive flux of DMF can derive from bulk flow effects that are opposed by negative diffusive fluxes, viz.,

where is the total flux of DMF in the membrane, j_i is the diffusive flux of DMF (estimated from the sorption-diffusion model), ω _i is the mass fraction of DMF in the membrane, and n_total is the total flux through the membrane.

[0071] Here, the negative transmembrane fugacity for DMF can yield a negative DMF diffusive flux that is strongly overcome by a positive bulk flow flux (i.e., ω_DMF(n _total) > jDMF and JDMF < 0). Moreover, as DMF has a meaningful sorption selectivity over water, the bulk flow term results in concentration of DMF relative to the feed concentration. The concentration of the DMF via sorpvection is contingent on both (1) significant sorption selectivity favoring DMF and (2) high water fluxes of water through the membrane.

where x_i and x_j are the local mole fraction of i and j, respectively, within the membrane,

is the chemical potential gradient of i within the membrane, u_i and u_j are the velocities of i and j within the membrane, respectively, and is the mutual diffusion coefficient between

components i and j (where i or j can include the membrane).

[0072] Using Equation 3, the present disclosure can include an approximate expression for the diffusive flux by assuming linear fugacity gradients, a constant average guest loading across the membrane, and no frictional interactions between i and j. The simplified expression is as follows:

where J_i is the molar diffusive flux of component i, is the “thermodynamically corrected”

diffusivity of component i in the membrane (as determined from experimental values), p is the density of the membrane, is the saturation loading of component i in the membrane at unit

activity, is the average fractional occupancy of guest i in the membrane, is the

transmembrane fugacity across the membrane,

is the average fugacity of component i within the membrane (which is easily estimated when linear fugacity gradients are assumed), and is the membrane thickness. In this expression,

can be thought of as a simplified sorption coefficient in the sorption-diffusion model. The molar diffusive fluxes calculated with Equation 4 can then be converted to a mass diffusive flux (j_i) and used to estimate the total flux of each species via the Lightfoot expression shown in Equation 2.

[0073] FIG. 10A provides a schematic representation of the unusual uphill permeation modality observed in these experiments calculated with the fugacity gradient based on the differences in concentrations between feed and permeate samples. The model (based on single component diffusivities and sorption isotherm data shown in FIGs. 5-8) can effectively capture the DMF/H2O separation factor (FIG. 10B) and DMF permeances (FIG. 10C) using reasonable ranges of the sorption selectivity (sorption selectivities of 30 can be predicted by the model to yield the experimental permeation separation factors; the experimental sorption selectivity can be estimated to be between 8 and 30). The experimental water permeances for the membrane system that was modeled can be found to be 3.5x10-3 L/m²-h-bar, which compares favorably with the model predictions of 2.0x10-3 L/m²-h-bar. These simplified transport equations can also provide insight into a pervaporative separation of DMF and H2O. These calculations highlight that DMF can likely still be effectively concentrated into the permeate via the sorpvection mechanism but is diluted below the detection limit into the sweep stream on the permeate side of the membrane.

[0074] From a mechanistic perspective, the present disclosure indicates that there can be three primary steps occurring in the sorpvection-style separations presented herein. The first is that DMF and water can sorb into the upstream membrane surface based on their respective partition coefficients. Secondly, both water and DMF can then diffuse with net motion driven by their thermodynamic driving forces. DMF can be concentrated in the upstream side of the membrane due to sorption. Concurrently, high water fluxes can “sweep” DMF downstream, thus capturing the concentrated DMF product in the permeate. The negative transmembrane chemical potential gradient for DMF can provide a backwards diffusive flux that reduces the effectiveness of the sorption-induced concentration of DMF; however, due to the low diffusivities of DMF in both dCMS and AmC membranes, this backwards diffusion can have a minimal effect on the overall DMF flux. This also reconciles why the sorpvection separation can be most effective in the dilute regime (for the organic): at higher organic concentrations, water’s contribution to bulk flow can be reduced, leading to reduced fluxes for DMF. As a result, this type of separation is likely possible and effective with dilute streams as the favorable partitioning for the organic relative to water is likely to be lost in more concentrated systems. [0075] Therefore, disclosed in the present example are carbon hollow fiber membranes derived from a polymer of intrinsic microporosity (PIM)- 1. Carbon membranes can be characterized with X-ray photoelectron spectroscopy, nitrogen physisorption, scanning electron microscopy, and gravimetric sorption. Separation performance of the carbons can be investigated with permeation experiments, using simulated waste streams containing both water and DMF. In liquid permeation experiments, DMF can be surprisingly concentrated in the permeate stream due to a transport phenomenon called sorpvection, where the high sorption of the organic phase heavily impacts the separation performance as a result of bulk flow of water through the membrane. While this result is unanticipated, this supports the notion that sorption can play a more significant role when using microporous materials for liquid phase separations. It is also worth noting that transport against chemical potential gradients in membranes have previously been thought to be insufficient. “Chemical pumping” membranes that rely on fixed or mobile carriers have been shown to concentrate ionic species from low to high concentrations across a membrane. However, these chemical pumping membranes typically require a continuous supply of a co-reactant to supply the “uphill” driving force, which is distinct from the simple transmembrane pressure applied in the present disclosure.

[0076] While the present disclosure has been described in connection with a plurality of exemplary aspects, as illustrated in the various figures and discussed above, it is understood that other similar aspects can be used, or modifications and additions can be made to the described aspects for performing the same function of the present disclosure without deviating therefrom. For example, in various aspects of the disclosure, methods and compositions were described according to aspects of the presently disclosed subject matter. However, other equivalent methods or composition to these described aspects are also contemplated by the teachings herein. Therefore, the present disclosure should not be limited to any single aspect, but rather construed in breadth and scope in accordance with the appended claims.

Claims

CLAIMS What is claimed is:

1. A membrane system comprising: a feed stream comprising at least a sorpvection agent and a sorpvected species, the sorpvected species having a first chemical potential; a permeate stream wherein the sorpvected species has a second chemical potential numerically greater than the first chemical potential; and a membrane separating the feed stream from the permeate stream, the membrane configured such that a mass fraction of the sorpvected species is 0.6 or greater, based on a total weight of adsorbed material in the membrane, and a flux of the sorpvection agent is greater than a flux of the sorpvected species by a factor of 7 or more.

2. The membrane system of Claim 1, wherein the concentration of the sorpvected species in the permeate stream is greater than the concentration of the sorpvected species in the feed stream.

3. The membrane system of Claim 1, wherein the mass flux of the sorpvection agent through the membrane is greater than the mass flux of the sorpvected species through the membrane.

4. The membrane system of Claim 3, wherein the flux of the sorpvection agent is greater than the flux of the sorpvected species by a factor of 10 or more.

5. The membrane system of Claim 1, wherein the sorpvected species has a negative transmembrane fugacity gradient and the sorpvection agent has a positive transmembrane fugacity gradient, wherein the absolute value of the positive transmembrane fugacity gradient is greater than the absolute value of the negative transmembrane fugacity gradient.

6. The membrane system of Claim 1, wherein the membrane further has a first uptake with the sorpvection agent and a second uptake with the sorpvected species, the second uptake being greater than the first uptake.

7. The membrane system of Claim 1, wherein the feed stream is in an aqueous state and one or more of the sorpvected species or the sorpvection agent is in a liquid state.

8. The membrane system of Claim 1, wherein the sorpvected species is capable of hydrogen bonding with the sorpvection agent.

9. The membrane system of Claim 1, wherein the sorpvected species is an organic molecule.

10. The membrane system of Claim 1, wherein the membrane comprises a hollow fiber membrane.

11. The membrane system of Claim 1 , wherein the membrane system is configured to operate at steady-state conditions.

12. A membrane having: a sorpvected species mass fraction when in contact with a sorpvected species, the sorpvected species mass fraction being 0.6 or greater, based on a total weight of adsorbed material in the membrane; and a sorpvected agent mass fraction when in contact with a sorpvection agent, the sorpvected species mass fraction being greater than the sorpvected agent mass fraction, wherein a flux of the sorpvection agent is greater than a flux of the sorpvected species by a factor of 7 or more, and wherein the sorpvected species has a negative transmembrane chemical potential.

13. The membrane of Claim 12, wherein the concentration of the sorpvected species in a permeate side of the membrane is greater than the concentration of the sorpvected species in a feed side of the membrane.

14. The membrane of Claim 12, wherein the mass flux of the sorpvection agent through the membrane is greater than the flux of the sorpvected species through the membrane.

15. The membrane of Claim 14, wherein the mass flux of the sorpvection agent is greater than the mass flux of the sorpvected species by a factor of 10 or more.

16. The membrane of Claim 12, wherein the sorpvected species has a negative transmembrane fugacity gradient and the sorpvection agent has a positive transmembrane fugacity gradient, wherein the absolute value of the positive transmembrane fugacity gradient is greater than the absolute value of the negative transmembrane fugacity gradient.

17. The membrane of Claim 12, wherein the membrane further has a first uptake with the sorpvection agent and a second uptake with the sorpvected species, the second uptake being greater than the first uptake.

18. The membrane of Claim 12, wherein one or more of the sorpvected species or the sorpvection agent is in a liquid state.

19. The membrane of Claim 12, wherein the sorpvected species is capable of hydrogen bonding with the sorpvection agent.

20. The membrane of Claim 12, wherein the sorpvected species is an organic molecule.

21. The membrane of Claim 12, wherein the membrane comprises a hollow fiber membrane.

22. The membrane of Claim 12, wherein the membrane is configured to operate at steadystate conditions.