Solid with infused reactive liquid (SWIRL): A novel liquid-based separation approach for effective CO2 capture

Economical CO2 capture demands low-energy separation strategies. We use a liquid-infused surface (LIS) approach to immobilize reactive liquids, such as amines, on a textured and thermally conductive solid substrate with high surface-area to volume ratio (A/V) continuum geometry. The infused, micrometer-thick liquid retains that high A/V and directly contacts the gas phase, alleviating mass transport resistance typically encountered in mesoporous solid adsorbents. We name this LIS class “solid with infused reactive liquid” (SWIRL). SWIRL-amine requires no water dilution or costly mixing unlike the current liquid-based commercial approach. SWIRL–tetraethylenepentamine (TEPA) shows stable, high capture capacities at power plant CO2 concentrations near flue gas temperatures, preventing energy-intensive temperature swings needed for other approaches. Water vapor increases CO2 capacity of SWIRL-TEPA without compromising stability.

printed in a vertical orientation and were removed from the base plate after excess powder was removed from the part internals.

General thermodynamic criteria for liquid immobilization on textured surfaces
Consider an arbitrarily rough surface of actual area, . The surface when projected onto a 2D plane has a projected area, . There are three possible states of liquid immobilization on this surface (Fig. S9a-c): 1) The surface is non-wetting to the liquid of choice. In this dry state, the energy of the system is where is the solid-vapor surface energy.
2) The liquid is immobilized in the texture, but only fills to the brim. In this infused state, the energy of the system is = + + (2) where and are the solid-liquid and liquid-vapor surface energies, respectively. , and are the solid-liquid, solid-vapor and liquid-vapor surface energies in the infused state, respectively.
3) The liquid is immobilized in the texture and also fully encapsulates it. In the encapsulated state, the energy of the system is Firstly, for the infused scenario to be energetically favored over the dry state, the following criterion must be satisfied − < 0 (4) Substituting (1) and (2) into (4) + − + < 0 Then if the spreading coefficient, S, is defined as Equation (6) can be rewritten as − − + < 0 (8) or > − 1 ≡ (9) Equation (9) identifies a critical spreading coefficient ( ) above which the infused state is preferred. The value of is dictated purely by the texture geometry and the liquid-vapor surface energy. We note that since < (Fig. S9d), has a negative value. Now, for the encapsulated scenario to be energetically favored over the infused state, the following criterion must be satisfied − < 0 (10) Substituting (2) and (3) into (10) − + − − < 0 Using (7), Equation (12) can be rewritten as Equation (14) identifies a critical spreading coefficient ( ) above which the encapsulated state is preferred. The value of is dictated by the texture geometry and the liquid-vapor surface energy. Now we identify conditions for to be greater than . From (9) and (14) we have − > Rearranging we get Let , ! , and " be the areas of the bottom, side-walls, and top of the asperity, respectively. Therefore = + ! + " , = + ! , and = − " .
From Fig. S9, (16) can be expressed  (9) and (14)). However, the magnitude of this difference is dependent on the substrate curvature relative to the local curvature imposed by the microstructure.
To illustrate this point in quantitative terms we pick a grooved texture of lattice spacing w, wall thickness t and height h (see Fig. S10c). The curved substrate is a fiber of radius b. The derivation of the wetting criteria for the dry to infused transition on the fiber is identical to the flat substrate. For the grooved substrate the critical spreading coefficient on a flat substrate (of unit depth into the page) is For the grooved substrate the critical spreading coefficient on a fiber of radius b is The difference between these terms is plotted in Fig ) / + ℎ + 3 − ) − * / + ℎ / + ℎ * − 11 (23) where e is the thickness of the encapsulating liquid film. The difference between these terms is plotted in Fig. S10e for a range of w and b values at e = 1 µm, t = 20 µm and h = 30 µm, for water ( =72.8 mN/m). As is evident, However, this difference is only significant when the fiber radius approaches the asperity size. Since our fiber is significantly larger than the asperity size, we believe our approach to making S>0 is sufficient for the 3D printed filaments. We pick a grooved structure because here, the fiber's curvature is imposed on the entire liquid volume, which represents an extreme case. In a substrate with an arbitrarily rough surface, the local curvature will likely have a stronger effect than the underlying fiber curvature, which could relax the wetting criterion back to a flat surface case.

Modeling the diffusion of carbamate
We model the absorption of the CO2 in the amine as a pure diffusion problem. As outlined in the main text of the paper, the reaction between CO2 with the amine is nearly instantaneous and occurs kinetically with a high Damköhler number (i.e. the rate of the chemical reaction is much faster than the rate of diffusion). This is supported by the references noted in the main paper.
Therefore, a very good approximation for this reaction-diffusion process is to assume that the chemical reactions that generate the carbamate occur right at the interface between the amine and the CO2, and this generated carbamate then diffuses downward into the bulk amine. This means that there are few to no CO2 molecules in the bulk amine, having all been consumed at the surface, and no further reactions taking place in the bulk. Under this picture, we can simplify the problem to that of pure diffusion of carbamate generated at the interface into the bulk amine.
Under the conditions of the experiments conducted in the capillary tube (see Fig. 3A-B of the main paper) and over the timescale of the experiment the capillary tube can effectively be considered to be infinitely long. In other words, the diffusion process is so slow that the carbamate effectively never sees the end of the capillary tube. This assumption is supported by the fact that the Damköhler number is of order 10 4 making diffusion much smaller than the reaction.
where C, C K , C L are the viscosities of the mixture, component A, and component B, respectively, and J is the mole fraction of component A. In our notation, species A is the carbamate and species B is the amine. Although Eq. (13) states that the viscosity of the mixture (and hence the diffusion coefficient) is a function of the concentration, in the above analysis solving for 4 6, * , we have made the approximation that this dependence on concentration is small, given the 1/3 power dependence. This implies that the diffusion coefficient is assumed to be a constant in the differential equation.
To be more accurate we should solve the full non-linear equation accounting for the spatially varying diffusion coefficient, which is beyond the scope of this paper. However, as we show below, our approximate model captures the measured data closely.
Substituting Eq. (13) into Eq. (22), and noting that the mole fraction J = 4 6, * (assuming the units of concentration is mole fraction), we have Here N G = DC K G/I , N 0 = DC L G/I , and F are fitting constants. Because species A is the carbamate, which is much more viscous than species B (the amine), we expect to have N To test the results of Eq. (24) against data, we run the following experiment: We first fill a capillary tube with amine mixed with a small concentration of molecular rotor. At time * = 0, the tube is exposed to CO2 at a fixed temperature, leading to the interaction of CO2 with amine to generate carbamate. This carbamate has a higher viscosity than the amine, and hence the molecular rotor displays a larger fluorescent intensity. In Fig. 3C we show the result of measuring the fluorescent intensity along the tube, at three different temperatures, after the absorption process has proceeded for * = 28 minutes.
The symbols correspond to data collected at different temperatures, while the black lines are fits of Eq. (24) to the data. While performing the fits, we held F = 0.75 which was obtained from an independent experiment that measured the viscosity of the amine-molecular rotor mixture at various temperatures against the corresponding fluorescent intensity at those temperatures. The fitting parameters were the diffusion coefficient 9 and the ratio of the viscosity of the carbamate to the amine C K /C L . In all cases the fits of Eq. (24) to the data are good, signifying that the simple model of assuming all carbamate generation occurs at the gas liquid interface is a good physical model for the more complicated process of reaction-diffusion. The values of the diffusion coefficient and the ratio of the carbamate viscosity to the amine viscosity is presented in Table S1. We note that the diffusion coefficient increases with temperature, because viscosity decreases with increasing temperature which speeds up diffusion. This also leads to our experimental observation of increasing absorption capacity with increasing temperature at a fixed time of absorption.
These diffusion coefficients are in the correct range of values that we would estimate from the Stokes-Einstein relationship. This relationship states that where U L is the Boltzmann constant, V is the temperature, C is the viscosity of the medium, and O is the molecular size of the diffusing species. Using the values of V = 300 K, C = 0.01 Pa s, O = 1 nm, we find that 9 = 2.2 × 10 GG m 2 s -1 . This estimated value is close to the values measured through the above analysis shown in Table S1.

Reactive Molecular Dynamics of CO2 in liquid amine
Before we provide details of the MEA-CO2 reaction process we need to ensure that our molecular modeling approach simulates the same mass transport mechanism as observed experimentally. As discussed above the mass transport is determined by the balance of diffusion and reaction rates, quantified by the Damköhler number 9\ = ]_`a 0 , with kr being the reaction rate in s -1 , D0 being the diffusion coefficient of reacting species, and L denoting a lengthscale over which the reaction takes place. The real system has an amine layer thickness of L ≈ 50 µm and the diffusion coefficient is on the order of 10 -11 m 2 /s or smaller (see above). Using a reaction rate of kr = 100 s -1 we obtain a Damköhler number 9\ ≈ 10 4 or larger. Our molecular simulation system needs to have a similar value to ensure the same diffusion-reaction balance. Since the diffusion coefficient cannot be varied in atomistic simulations (it is a system property solely based on the forcefield used), and the layer thickness is about 4 nm (half the liquid slab) we need to set the reaction rate to kr ≈ 10 7 s -1 = 100 ns -1 . The value does not need to be exact and is rather a guidance on how to choose the parameters in the reactive MD model to ensure that we can observe the reaction-diffusion mechanism on the molecular scale.
For MEA-CO2 reactions the following two-step reaction scheme was implemented (58) as follows: If during the simulation the distance between the nitrogen atom of an MEA molecule and the carbon atom of a CO2 molecule is within a predefined distance of 3.4 Å, a reaction is attempted and will be accepted with a probability of 0.5%. Once a reaction is accepted, the two atoms (N and C) are bonded and a carbamate anion generated. In this process a proton is released from the amine. In the second reaction step the released proton is bonded to another MEA if its nitrogen gets closer than 3.4 Å of the proton. Since this reaction is typically fast, the probability of accepting this bond was set to 100%. After each reaction a short energy minimization is performed to relax the system. With these settings we obtain reaction rates on the order of 100 ns -1 , as the above Damköhler number analysis requires. We ignore backward reactions since they are surpressed at high CO2 pressure (here 0.5 atm).
The MEA-CO2 reaction can now be observed on the molecular scale. The mechanism for this behavior can be explained by higher diffusion and mixing of amine molecules as temperature is increased. Fig. S14 shows the density profiles of all species as a function of the z coordinate, denoting the value of the normal vector of the liquid/gas interface.
Shown are results for 32 °C and 71 °C, both at a CO2 partial pressure of 0.5 atm. In the beginning -the first 20 ps -only amine is present corresponding to the initial liquid slab thickness of around 70 -80 Å. As time progresses carbamate is produced directly at the gas liquid interface. This is demonstrated by the occurrence of red peaks that have noticeably established within the first 0.5 ns. Those peaks are positioned at ~20 Å from the left interface and at ~80 Å from the right interface. At 71 °C, the peaks are slightly broader compared to the 32 °C case (at 0.5 ns). Juxtaposing the 2 ns data, one can clearly see that the carbamate peak has further broadened at higher temperature, indicating the carbamate diffused further into the bulk region. The inward diffusion of carbamate species entails an outward diffusion of bulk amine towards the interface, enabling more reactions with CO2. We note that CO2 molecules never reach the bulk amine region; in fact one can observe little enrichment of CO2 in the carbamate interface layer at 2 ns (small green peaks). This is an important result since it reveals a detail of the reaction-diffusion mechanism: due to the fast reaction MEA is only consumed at the interface, and not in the bulk liquid. The increased consumption of MEA at elevated temperature is promoted due to higher diffusion of carbamate and amine, enabling an increased exchange of carbamate produced at the interface with fresh amine from the bulk.

Pressure drop calculations
Pressure drop is an important parameter in absorption bed design. The geometry selected as the SWIRL solid substrate not only provides a high A/V but also has a high void volume fraction. This is particularly important to minimize the pressure drop throughout the absorption bed.
To estimate the pressure drop that occurs as the gas flow is driven through the SWIRL device, we approximate the flow through the SWIRLS's hexagonal Laves structure as a flow through an ordered porous medium (Fig. S15). Several approaches can be used to describe such a gas flow through porous media (e.g. Karmen-Kozeny relations for flow through packed beds).
Closer examination of the large scale (60x) mock-up model of the Laves structure shown in Fig.   1D, and also in Fig. S15, reveals that the gas flows mainly through parallel channels. From              printed Laves lattice, to highlight the channel structure in this ordered porous medium.   Table S1: Diffusion coefficient and relative viscosity of carbamate at various temperatures.
Carbamate diffusion coefficient and the ratio of viscosity of carbamate to amine at various temperatures Movie S1. Flow of fluorescent beads in bulk and within the texture and roughness of the solid structure. The flow of ~20-micrometer latex fluorescent beads demonstrates the existence of a thin layer of bulk liquid within the texture and roughness of the solid structure. See also Fig. 1 Movie S2. Experimental visualization of carbamate propagation in MEA during carbon capture. Propagation of carbamate in MEA containing CCVJ at 35 °C. The bright zone is the highviscosity area where carbamate molecules are present.