Two-dimensional dry ices with rich polymorphic and ...Two-dimensional dry ices with rich polymorphic and polyamorphic phase behavior Jaeil Baia, Joseph S. Franciscoa,1, and Xiao Cheng

Two-dimensional dry ices with rich polymorphic andpolyamorphic phase behaviorJaeil Baia, Joseph S. Franciscoa,1, and Xiao Cheng Zenga,b,1

aDepartment of Chemistry, University of Nebraska–Lincoln, Lincoln, NE 68588; and bBeijing Advanced Innovation Center for Soft Matter Science andEngineering, Beijing University of Chemical Technology, 100029 Beijing, China

Contributed by Joseph S. Francisco, August 22, 2018 (sent for review May 29, 2018; reviewed by Liem Dang and Ryoichi Yamamoto)

Both carbon dioxide (CO2) and water (H2O) are triatomic moleculesthat are ubiquitous in nature, and both are among the five mostabundant gases in the Earth’s atmosphere. At low temperatureand ambient pressure, both CO2 and H2O form molecular crys-tals––dry ice I and ice Ih. Because water possesses distinctive hy-drogen bonds, it exhibits intricate and highly pressure-dependentphase behavior, including at least 17 crystalline ice phases andthree amorphous ice phases. In contrast, due to its weak van derWaals intermolecular interactions, CO2 exhibits fewer crystallinephases except at extremely high pressures, where nonmolecularordered structures arise. Herein, we show the molecular dynamicssimulation results of numerous 2D polymorphs of CO2 molecules inslit nanopores. Unlike bulk polymorphs of CO2, 2D CO2 poly-morphs exhibit myriad crystalline and amorphous structures,showing remarkable polymorphism and polyamorphism. We alsoshow that depending on the thermodynamic path, 2D solid-to-solid phase transitions can give rise to previously unreportedstructures, e.g., wave-like amorphous CO2 structures. Our simula-tion also suggests intriguing structural connections between 2Dand 3D dry ice phases (e.g., Cmca and PA-3) and offers insightsinto CO2 polyamorphic transitions through intermediate liquid oramorphous phases.

two-dimensional dry ice | polymorphic transition | polyamorphictransition | slit nanopores | CO2 sequestration

Carbon dioxide and water found on the outer planets andasteroids are typically in solid forms, namely, dry ice and ice.

Both dry ice and ice may be viewed as relatively soft molecularcrystals due to their intrinsic nonbonding intermolecular inter-actions, i.e., hydrogen-bonding interactions in ice (1–4) and vander Waals (vdW) interactions in dry ice. To date, bulk CO2 dryice is found in seven crystalline forms, namely, CO2 I–VII, in-cluding CO2-V (with tetrahedral coordination), which is formedunder extremely high pressure (∼37 GPa) (5–14). In outer space,solid phases of CO2 often exist in mixtures with water ice and/orother molecular crystals. Depending on the ice-formation con-ditions, interstellar and planetary ice mixtures can exist inamorphous, hydrate, or layered forms with varying layercompositions (15–18).Gaseous CO2 is known to contribute to global warming on

Earth. Over the past century, human activities have considerablyincreased the amount of anthropogenic CO2 in the Earth’s at-mosphere. The capture and sequestration of CO2 in deep geo-logical reservoirs is considered a promising approach tomitigating the growing problem of global warming. However, thefeasibility of CO2 sequestration hinges on the ability to captureCO2 in a host porous structure, which is governed by the in-terfacial properties of CO2 and the confinement media. Ingeneral, interfacial and confined fluids exhibit microstructural,dynamical, and thermophysical behaviors that differ from thoseof their bulk counterparts (19–29). For water, nanoscale con-finement can result in a large number of 2D phases of ice andamorphous ice (22–30). A question that we aim to address in thisstudy is whether nanoscale confinement can also yield distinct2D phases of CO2. Here, we use molecular dynamics (MD)

simulations to explore the phase transitions and phase stability ofCO2 under nanoscale confinement. The identification of bulkCO2 polymorphs is known to be a challenging task due to thedifficulty of analyzing solid CO2 using spectroscopy alone. Forexample, the intermediate phase and phase boundary betweenCO2-I and CO2-III remain unclear (9, 31). Knowledge of 2DCO2 polymorphs may offer unique insights into the intermediatepolymorphs of bulk CO2.MD simulations (see Methods and SI Appendix, section E for

additional simulation details and results) are carried out for asystem consisting of a slit nanopore with width h = 8 Å and 400CO2 molecules. At 500 MPa and 260 K, the stable phase of CO2is a bilayer (BL) liquid. The BL CO2 liquid is then isothermallycompressed at 1 GPa of lateral pressure, and this simulation isperformed for 20 ns. The BL CO2 liquid undergoes a first-orderphase transition to a BL CO2 solid (Fig. 1A). Interestingly, theBL CO2 solid exhibits a herringbone-like structure with two out-of-registry herringbone layers. This BL CO2 solid exhibits PCCAsymmetry. We tentatively name this BL solid CO2 “BL dry ice I”(or BL-DI I). The computed diffusion coefficient of BL-DI at260 K and 1 GPa is ∼2 × 10−10 cm/s2. Additional structuralanalysis regarding the transition behavior of BL-DI I is given inSI Appendix, Figs. S1 and S2.Next, we perform another series of MD simulations with

various smaller slit widths: h = 6.5, 6.8 7.1, 7.4, and 7.8 Å. For h =7.4 and 7.8 Å, the resulting BL dry ice structure is likewise BL-DII. For h = 6.8 Å, however, the stable phase at 200 MPa and 250 Kis a stable monolayer (ML) CO2 liquid. After the ML CO2 liquidis cooled instantly to 120 K, an ML dry ice (named ML-DI I)

Significance

Bulk CO2 or dry ice has seven polymorphs, namely, CO2 I–VII.Here, we show molecular dynamics simulation evidence of 20+two-dimensional (2D) CO2 polymorphs and polyamorphs. Thisremarkable 2D polyamorphism of CO2 and the diverse array ofstructures is not seen in other molecular systems with weakintermolecular van der Waals (vdW) interactions. Our findingsmay promote a new research direction for vdW molecularsystems, i.e., 2D polymorphism. The rich 2D polymorphic andpolyamorphic solid CO2 structures not only enrich our knowl-edge of the phase behavior of CO2 in slit nanopores, but alsohave implications to the sequestration of CO2 in microporousmaterials under high pressure.

Author contributions: J.B., J.S.F., and X.C.Z. designed research; J.B. and X.C.Z. performedresearch; J.S.F. and X.C.Z. contributed new reagents/analytic tools; J.B., J.S.F., and X.C.Z.analyzed data; and J.B., J.S.F., and X.C.Z. wrote the paper.

Reviewers: L.D., Pacific Northwest National Laboratory; and R.Y., Kyoto University.

The authors declare no conflict of interest.

Published under the PNAS license.1To whom correspondence may be addressed. Email: [email protected] or [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1809198115/-/DCSupplemental.

Published online September 24, 2018.

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with P21/C symmetry is formed after 20 ns of MD simulation (SIAppendix, Fig. S3). For h = 6.5 Å (the smallest slit width con-sidered), a flat ML dry ice (named ML-DI II) is formed at 120 Kand 100 MPa with crystalline symmetry akin to PB4M (D2H-9)(SI Appendix, Fig. S4). Further compression of ML-DI II to 1GPa results in the ML-DI I phase through direct solid-to-solidtransition. For h = 7.1 Å, the ML CO2 liquid is stable at 1 GPaand 250 K. Again, cooling of the ML CO2 liquid to 120 K leadsto the formation of the ML-DI I phase (SI Appendix, Fig. S3).However, when the ML CO2 liquid at 1.5 GPa and 250 K is iso-thermally compressed to 2 GPa, the liquid is actually transformedto a BL dry ice (named BL-DI II) (Fig. 1B and Movies S1 and S2).The density of the BL-DI II phase is 10.78 nm−2, while the MLCO2 liquid density is 7.6 nm−2. BL-DI II is composed of two MLsstacked in a staggered fashion (Fig. 1B). The same structure canalso be achieved via cooling the ML CO2 liquid from 250 to 200 Kat 1.5 GPa. Both results suggest that a phase boundary betweenML-DI I and BL-DI II is located between 1- and 1.5-GPa pres-sure. The symmetry of BL-DI II is P-421M. Interestingly, the bulkcounterpart of BL-DI II is the CO2-II phase (with P42/mnmsymmetry) (32). Note that the solid-to-solid transition betweenBL-DI I and II has not been observed upon direct compression,likely due to a high free-energy barrier between BL-DI I and II.Hence, the slit width h is the only physical parameter that caninduce the solid-to-solid transition between the two BL dry ices.On the other hand, when h is increased from 8 to 9.6 Å, the BL

CO2 liquid remains stable at 500 MPa and 250 K. When the BL

CO2 liquid is cooled isobarically in 10-K steps, another BL CO2solid is formed at 160 K (SI Appendix, Fig. S5 A–E). Comparedwith the radial distribution function (RDF) of BL-DI I (SI Ap-pendix, Fig. S1A), the RDF of the BL CO2 solid (SI Appendix,Fig. S6A) exhibits broader peaks at both short and long ranges,suggesting that this BL CO2 solid is amorphous dry ice (namedBL-AD I). In this case, the angle distribution of the axes of theCO2 molecules exhibits two broad peaks at ∼38° and ∼77° (SIAppendix, Fig. S6B). Moreover, the density profile exhibits fourdistinctive peaks (SI Appendix, Fig. S6C). These results indicatethat in each ML, the CO2 molecules that give rise to the peak at38° are located ∼3.8 Å from one wall of the nanopore, while theother CO2 molecules are located ∼2.7 Å from the opposing wall.Note that bulk amorphous dry ice, called a-carbonia or a-CO2,exhibits a structure akin to that of a type of silica glass. Bulkamorphous dry ice can be formed only at a very high pressure of40–48 GPa (12). In contrast, the BL amorphous dry ice (BL-AD I)can be formed at a moderate pressure of 500 MPa (two orders ofmagnitude lower than 40 GPa) due to the nanoscale confinement.Can nanoscale slits accommodate low-density dry ice? To

address this question, we perform MD simulations with a dif-ferent thermodynamic path. Starting with a supercooled BL CO2liquid at 170 K and 500 MPa, the BL CO2 liquid is decompressedto 100 MPa and then isobarically cooled in 10-K steps, resultingin a transition to another BL amorphous CO2 solid at 130 K (SIAppendix, Fig. S5 F–H). This BL CO2 solid (named BL-AD II)exhibits a lower density than that of some other BL CO2 solidsbut higher than that of BL-DI I. The angle distribution of theCO2 molecular axes shows a peak at ∼59° (SI Appendix, Fig. S6B,black line). The RDF of the BL-AD II exhibits sharper peaksthan that of the higher-density BL-AD I. However, it still doesnot exhibit the distinctive long-range order seen in BL-DI I. Wethen performed additional MD simulations to seek a more or-dered structure with polymorphic features similar to those of BL-AD I (SI Appendix, Fig. S5C). By starting with the BL-AD I (SIAppendix, Fig. S5 A–E) and increasing the pressure and tem-perature to 5 GPa and 300 K, a trilayer (TL) dry ice named TL-DI I is obtained. The main geometric features of TL-DI I are asfollows: (i) CO2 molecules are arranged parallel to the wall, andthe two outer layers are in registry; (ii) the outer and middlelayers are out of registry. We use ABA to describe the stackingpattern of TL-DI I and AB for the two BL-DIs. SI Appendix, Fig.S6D shows a schematic pressure–temperature phase diagram forh = 9.67 Å.We also attempt to identify a crystalline structure with poly-

morphic features similar to those of the BL-AD phase in widerslits. For h = 11.2 Å, another TL CO2 solid (named TL-DI II)with an area density of 17.9 nm−2 is observed at 210 K when thestable TL CO2 liquid at 500 MPa and 250 K is cooled in 10-Ksteps (SI Appendix, Fig. S7 and Movies S3 and S4). The com-puted RDF suggests the presence of long-range ordering in TL-DI II. The axes of the CO2 molecules in TL-DI II mostly point toa direction tilted 78° with respect to the surface normal of thewalls. The diffusion coefficient CO2 in TL-DI II is ∼1 × 10−8 cm/s2

at 210 K, while the diffusion coefficient of the BL CO2 liquid is∼4 × 10−6 cm/s2 at 220 K.For h = 12.7 Å, a transition to another trilayer dry ice (TL-DI

III) is observed when the stable BL CO2 liquid at 500 MPa and250 K is isobarically cooled to 160 K (Fig. 1C and Movies S5 andS6). SI Appendix, Fig. S8 A and B show that the potential energydecreases sharply to 4.2 kJ/mol at 160 K. The diffusion co-efficient of CO2 in TL-DI III at 160 K and 500 MPa is ∼5 × 10−10

cm/s2, whereas that of the BL CO2 liquid at 170 K and 500 MPais ∼7 × 10−7 cm/s2. After TL-DI III is heated to 210 K, the po-tential energy exhibits a sharp rise. Similarly, the plot of areadensity versus temperature shows a marked hysteresis loop (SIAppendix, Fig. S8B). We note that the stacking pattern of TL-DI

Fig. 1. Two-dimensional dry ice structures: (A) BL-DI I formed at 260 K,1 GPa, h = 8.0 Å, and N = 400; (Upper) top view, (Middle) side view, and(Lower) zoomed top view of two stacked layers. Red and grey colors rep-resent oxygen and carbon atom of CO2. CO2 molecules highlighted withyellow belong to a different layer, as shown in zoom-in view. (B) BL-DI IIformed at 250 K, 2 GPa, h =7.1 Å, and N = 400; (Lower) zoom-in top and sideview of two cross-stacked layers. (C) Top and side views of TL-DI III formed at160 K, 500 MPa, and h = 12.75 Å (system size N = 800). (D) Top and side viewsof TL-DI IV formed at 50 MPa, 130 K, and h = 12.75 Å.

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III resembles that of bulk CO2-I with the [111] surface exposed(SI Appendix, Figs. S9–S12).We also investigate the possible formation of lower-density dry

ice in the slit with h = 12.7 Å. The CO2 liquid at 170 K and 500MPa is decompressed in four steps to 300, 200, 100, and 50 MPaand then cooled to 130 K. The liquid is transformed into a TLCO2 solid (named TL-DI IV) with an area density of 19.26 nm−2

(Fig. 1D). The potential energy (per molecule) of the TL CO2solid exhibits a sharp decrease to 2.7 kJ/mol upon phase transition.The diffusion coefficient of the TL CO2 solid is ∼1 × 10−9 cm/s2,whereas the diffusion coefficient of the CO2 liquid is ∼1 ×10−6 cm/s2 at 140 K. Fig. 1D displays the intrinsic structure of theTL CO2 solid with all three layers being out of registry (we callthis the ABC-stacking pattern). Fig. 2 A and B shows the pro-jected C-C RDFs and density profiles in the surface-normal di-rection of the intrinsic structures of TL-DI III, TL-DI IV, TLamorphous dry ice (TL-AD) (see below), and BL CO2 liquid ath = 12.7 Å. TL-DI II exhibits long-range order, while TL-DI IVexhibits broader RDF peaks due to the presence of a disordereddomain (Fig. 1D).For h = 12.7 Å, we also investigate the possible formation of

high-density dry ice. Upon cooling from 250 to 160 K at 1 GPa,the CO2 liquid becomes a TL-AD (SI Appendix, Fig. S13 A andB). The green line in Fig. 2C shows the angle distribution of TL-AD. The local CO2 arrangements and orientations in TL-ADresemble those of BL-AD (SI Appendix, Fig. S5A). When thetemperature and pressure are raised instantaneously to 300 Kand 2 GPa, TL-AD transforms into a four-layer dry ice (namedFL-DI I) with the ABAB-stacking pattern (SI Appendix, Fig. S13C and D). FL-DI I exhibits PCCA symmetry. The angle distri-bution of the axes of the CO2 molecules exhibits a peak at ∼90°(Fig. 2C, pink line). Thus, the surface of FL-DI I is very flat,similar to that of BL-DI I. FL-DI I is a very high-density dry icethat resembles bulk CO2-III with Cmca symmetry. Interestingly,bulk CO2-III can be obtained by compressing the bulk CO2liquid to 3 GPa at 300 K. SI Appendix, Fig. S13E shows thepolycrystalline phase of FL-DI I from our independent MDsimulation upon compressing a 2D CO2 liquid from 1 to 4 GPa(in 1-GPa steps) at 350 K. Similar to bulk CO2-III, FL-DI I isalso formed at high pressure and elevated temperature. Notethat the compression of the 2D CO2 liquid by high lateralpressure (e.g., 3 GPa) and at low temperature (e.g., 250 K) doesnot lead to FL-DI I. Bulk CO2-III can be obtained experimen-tally by compressing CO2-I at high pressure and temperature.Unlike bulk CO2-III, FL-DI I exhibits the same polymorphicstructure as bulk CO2-III but without forming an intermediatesolid similar to bulk CO2-I. A semiquantitative phase diagramthat illustrates the rich phase behavior of 2D CO2 for h = 12.7 Åis presented in Fig. 2D.Lastly, for wider slits, h = 14.3, 15.9, 17.4, and 20.5 Å, many

more 2D dry ice phases are observed (Fig. 3). Their structuraland transition behaviors are described in SI Appendix, Figs. S14–S20. In general, relatively slow cooling of the CO2 liquid (e.g., 2K per nanosecond) tends to result in either monomorphic orpolymorphic transitions at pressure <1 GPa, manifesting thethermodynamics of the polymorphic transition. Typically, 2D dryices are composed of multilayers in either ABC- or AB-stackingpatterns. Fast quenching of the confined CO2 liquid, however,tends to yield 2D solids with different stacking patterns, as therelevant polymorphic transitions are driven by kinetic factors [e.g.,an FL-AD with the ABAC-stacking pattern is seen at h = 14.3 Å(SI Appendix, Fig. S16)]. Starting from h = 12.7 Å, multilayers witha surface similar to the (111) surface of bulk CO2-I are formed atboth high and low pressure (e.g., TL-DI III at h = 12.7 Å and 500MPa; FL-DI III at h = 15.9 Å and 300 MPa; and 5L-DI II at h = 20.5 Å and 5 MPa). These results indicate that forh > 12.7 Å, the liquid-to-solid transition of 2D CO2 tends tofollow the trend of bulk CO2. At the critical width h = 20.5 Å, a

surface structure like that of the (111) surface of bulk CO2-I canarise even at 5 MPa, regardless of the confinement conditions. In-deed, at h = 20.5 Å, we observe the formation of a 7-layer flatstructure (named 7L-DI) with the ABABABA-stacking pattern that

Fig. 2. (A) Projected C-C RDFs of 2D dry ices and liquid (inherent structures)at h = 12.75 Å; (B) density profiles of CO2 in surface-normal direction;(C) angle distribution of CO2 molecular axis with respect to the surface normalof the slit, where red, black, green, and pink lines refer to the TL dry icesformed at 50 MPa (TL-DI IV), 500 MPa (TL-DI III), 1 GPa (TL-DA), and 2 GPa(FL-DI I), respectively, and blue line refers to the BL liquid at 500 MPa. Pink linein C indicates the four-layer flat structure with ABAB-stacking pattern, obtainedby heating and compressing TL-DA to 300 K and 2 GPa. This structure exhibitsthe same polymorphic feature as bulk CO2-II (Cmca). (D) A semiquantitativetemperature–pressure phase diagram of CO2 system at h = 12.75 Å.

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Fig. 3. Two-dimensional dry ices in silt nanopores. Blue arrow denotes increasing silt width h. (A) ML-DI II formed at 120 K and 200 MPa, (B) ML-DI I formedby compressing ML-DI II to 1 GPa at 120 K, (C) ML-DI I formed at 120 K and 1 GPa via direct quench, (D) BL-DI II formed by compressing a liquid to 2 GPa, (E) BL-DI I with herringbone structure, (F) BL-DA II formed at 100 MPa and 130 K upon cooling, (G) BL-DA I formed at 500 MPa and 160 K, (H) TL-DI I formed bycompressing and heating BL-DA to 5 GPa and 300 K, (I) TL-DI II formed at 210 K and 500 MPa, (J) TL-DI IV formed at 130 K and 100 MPa, (K) TL-DI III, whosestructure is similar to bulk CO2 I with [111] surface exposed, formed at 160 K and 500 MPa, (L) TL-DA formed at 160 K and 1 GPa, (M) FL-DI I formed bycompressing and heating TL-DI II to 2 GPa and 300 K, (N) FL-DI II with ABAB-stacking pattern, formed at 500 MPa and 150 K, (O) FL-DA with ABAC-stackingpattern, formed by direct quench of a liquid from 250 to 150 K at 500 MPa, (P) FL-DI IV formed at 130 K and 50 MPa with ABAB-stacking pattern, (Q) FL-DI IIIformed at 150 K and 300 MPa with ABCA-stacking pattern, (R) FL-DI V obtained by compressing FL-DI III to 5 GPa at 130 K with ABM2 symmetry, (S) 5L-DI Iformed at 150 K and 500 MPa with ABABA-stacking pattern, (T) 5L-DI II obtained by compressing 5L-DI I to 2 GPa and 40 K with ABCDE-stacking pattern, (U)5L-DI III obtained by compressing (T) to 5 GPa with ABCDA′-stacking pattern, (V) 5L-DI IV, obtained by compressing 5L-DA to 10 GPa, converted to ABACA-stacking pattern with flat layers, (W) 5L-DA, obtained by compressing 5L-DI I to 2.5 GPa and 140 K, with wave-like molecular distribution and A′BA′CA′-stacking pattern, (X) 5L-DI V formed at 130 K and 5 MPa, (Y) 6L-DI I formed at 150 K and 300 MPa, (Z) 6L-DA formed at 150 K and 700 MPa, (α) mixed six- toseven-layer amorphous formed at 160 K and 1 GPa, and (β) seven-layer dry ice obtained by compressing (α) to 2 GPa at 300 K.

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resembles the structure of bulk CO2-III (Fig. 3β and SI Appendix,Fig. S18E).We also explore possible solid-to-solid polymorphic transitions

upon lateral compression to produce intermediate or stablepolymorphs that cannot be easily derived via cooling or viacompressing the 2D CO2 liquid due to either high barriers orstrong path dependencies. First, we start with FL-DI III and IVstructures at h = 15.9 Å (SI Appendix, Fig. S17 A and B). Uponcompression of both solids initially at 130 K and at 500 MPa inthe 500-MPa step, the CO2 molecules in low-density FL-DI IIgradually become aligned in one direction (Fig. 4 A and B). Thefinal structure at 5 GPa exhibits Abm2 symmetry. In contrast, thehigh-density FL-DI III does not exhibit any structural changeunder increasing compression until 7.5 GPa, where FL-DI IIIbecomes a disordered structure without any distinctive poly-morphic features. However, if FL-DI II is compressed to 6 GPaat 310 K and h = 15.9 Å, a domain of aligned CO2 moleculesappears to arise (SI Appendix, Fig. S21). The transformation tothe high-pressure phase is very sluggish, similar to that betweenbulk CO2-I and CO2-III at higher pressures.For h = 17.4 Å, we start with a monomorphic phase—5L-DI I—

with the ABABA-stacking pattern at P < 1 GPa (SI Appendix,

Fig. S22 A and B). Upon compression at 40 K to 2 GPa with a500-MPa step, 5L-DI I transforms into a 5L structure (named5L-DI II) with the ABCDE-stacking pattern (SI Appendix, Fig.S22 C and D). As a lateral pressure of 5 GPa is applied to 5L-DIII, another 5L solid (named 5L-DI III) arises with the ABCDA′-stacking pattern (Fig. 4 G–I) and can maintain its structure upto 10 GPa. In contrast, when 5L-DI I is compressed at 140 K andat 2.5 GPa, it transforms into a 5L amorphous dry ice (named5L-AD) (Fig. 4 J–M). 5L-AD exhibits an intricate wave-like ar-rangement of CO2 molecules. Each layer of this structure isplotted in different colors in Fig. 4M to show that three layers areoverlaid on top of each other with a slight mismatch, while theother two layers are out of registry with respect to the first threelayers. Hence, 5L-AD exhibits the ABA′CA″-stacking pattern,following a transformation from the ABABA-stacking pattern.Movies S7 and S8 show that 5L-AD continues to maintain itswave-like structure during an additional 50 ns of MD simulation.The wave-like 5L-AD structure resembles the 1D double-walledice helix formed inside isolated carbon nanotubes (33). Bothsolids show fascinating molecular networks under high-pressureconfinement. More structural and thermodynamic informationon 5L-DI III and 5L-AD is provided in SI Appendix, Figs. S23and S24. If 5L-AD is further compressed at 10 GPa and 140 K, ittransforms into a relatively ordered flat-layer structure (named5L-DI IV) with the ABACA-stacking pattern (SI Appendix, Fig.S25). Overall, the solid-to-solid transition can be inducedthrough an intermediate 5L-AD phase. These path-dependentsolid-to-solid transitions are illustrated by red arrows in Fig. 3 S–W.As shown in Fig. 3 A–W, with an increase of h, we observed

diverse 2D CO2 polymorphs from ML to multilayers. Moreover,at higher lateral pressure, either more layers of 2D DIs areformed or molecular axis of CO2 makes larger angles against thewall of slit nanopore at given h to allow more CO2 moleculespacked together. As an example, at h = 12.7 Å, TL-DI VI (Fig.3J) is formed at lower pressure where CO2 are tilted against slitpore surface. As increasing pressure, some CO2 molecules pointcloser to surface normal (Fig. 3K) to compensate the smallervolume (SI Appendix, Figs. S11 and S12). As pressure furtherincreases, more CO2 molecules make larger tilting against thewall (Fig. 3M). Eventually, at very high pressure, FL-DIs areformed whose CO2 molecules are aligned in parallel (Fig. 3N).These trends of polymorphs versus h and lateral pressure arefairly generic.To confirm the stabilities of several 2D CO2 polymorphs, we

perform structure optimization using quantum density-functionaltheory (DFT) methods, as implemented in CASTEP 7.0 software(SI Appendix, section F). The structures shown in SI Appendix,Fig. S26 are obtained from DFT optimization using smaller unitcells that represent inherent structures of 2D DI. After relaxingthe atomic positions of 2D DI within a fixed system volume, weperformed DFT optimization by relaxing the lateral pressure ofthe supercells. As shown in SI Appendix, Fig. S26, the initialstructures from the MD simulations are no longer distorted afterDFT optimization. In addition, we perform ab initio Born–Oppenheimer MD simulations (BOMD) (SI Appendix, sectionF) to confirm the stability of 2D DI at finite temperature. Forexample, consider BL-DI II confined between two graphenesheets during BOMD simulation in a constant-volume andconstant-temperature ensemble with carbon atoms being fixed.At 180 K, BL-DI II does not show any structural distortionwithin 20 ps (Movie S9). The computed potential energy versustime (SI Appendix, Fig. S27) also suggests that BL-DI II is arobust structure.Experimental evidence of 2D solid phases of CO2 has been

shown through adsorption of CO2 on surface (34–39). For ex-ample, CO2 adsorbed on NaCl (001) surface can form ML her-ringbone structure where all CO2 molecules are tilted against thesurface (35, 36, 38). Notably, this ML structure is the same as the

Fig. 4. Solid-to-solid transition induced by isothermal compression. At h =15.9 Å and N = 960, isothermal compression of FL-DI IV (SI Appendix, Fig.S17B) at 130 K from 500 MPa to 5 GPa in steps results in a structure (A–F): (A)top view, (B) side view, and (C) zoomed view slightly titled with respect tosurface normal; (D–F) zoomed views with each layer highlighted in differentcolor: (D) side view, (E) top view, and (F) titled view. At h = 17.4 Å and N =960, compression of 5L-DI I (SI Appendix, Fig. S22A and B) at 40 K from 500MPato 5 GPa in steps results in a structure (G–I): (G) top view, (H) zoomed sideview, and (I) top view with each layer in different color. Snapshots of 5L-DA(J–M) at 140 K and 5 GPa, a strenuous structure that consists of wave-likelayers: (J) top view, (K) side view, (L) side, and (M) zoomed top view of thewave-like structure of CO2 solid with each layer highlighted in differentcolor.

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ML-DI I structure (SI Appendix, Fig. S3 B and C) formed withina slit nanopore. Another ML structure experimentally detected issuch that adsorbed CO2 molecules are parallel aligned (36). Tosee if this ML structure can be obtained in slit nanopore, weperformed a series of MD simulations at h = 6.5 Å, starting withML-DI at 120 K and 500 MPa. When the ML-DI I is compressedto 5 GPa at 120 K, the ML-DI I is still intact without showingnotable structural change. Another series of MD simulation wasconducted with increasing the CO2–wall interaction parameters(ec-wl, eo-wl) by four times and the structure obtained is shown inSI Appendix, Fig. S28A. The structure consists of several domains,including herringbone and parallel-aligned structures. Further in-creasing the pressure and temperature to 10 GPa and 200 K,without modification of the CO2–wall parameter, the parallel-aligned structure was obtained (SI Appendix, Fig. S28B), wherethe herringbone domain can be viewed as defects. The parallel-aligned ML structure is also energetically favorable on a KCl sur-face, based on DFT computation (39).In summary, we show MD simulation evidence of a large

number of 2D CO2 polymorphs and polyamorphs in nanoscaleslits. Our simulation shows rich phase behavior in terms of 2Dpolymorphism and polyamorphism in any nonpolar molecularsystem. One possible physical reason for the rich phase behaviorof CO2 is its large quadrupole moment. When the quadrupolemoment of CO2 is artificially reduced to zero, the CO2 moleculebehaves as a diatomic dumb-bell-like molecule. In such a case,our test simulation shows that the BL-DI I structure will become

a 2D close-packed hexagonal structure, akin to a layer of bulksmectic-B liquid crystal (SI Appendix, Fig. S29 A–C). Even whenthe quadrupole moment CO2 is purposely reduced by half, theherringbone structure of BL-DI I will become a 2D smecticstructure (SI Appendix, Fig. S29D). Hence, the combination of alarge quadrupole moment with a dumbbell-like structure allowsCO2 molecules under nanoscale confinement and high pressureto adopt remarkable 2D polymorphism and polyamorphism.These results may have important implications for CO2 seques-tration in microporous media. Moreover, the physical insightobtained from this study may be generalized to other nonpolarmolecular systems, such as triatomic N2O and diatomic N2 andH2 (40). Indeed, similar to CO2, N2O is another green-housegas and exhibits disordered hcp structure at high temperatureand PA3-cubic structure at low temperature with a bulkpolymorphous transition.

MethodsThe MD simulations are performed using the constant lateral pressure andconstant temperature (NpxxpyyT) ensemble. More details of the model sys-tems, MD methodology, validation of the CO2 force field, structural analysis,and computation of diffusion constant are shown in SI Appendix, sections A–D. Details of two-phase coexistence molecular dynamics simulations to de-termine the melting temperature of a 2D solid CO2 are given in SI Appendix,section G.

ACKNOWLEDGMENTS. This work was supported by NSF Grant CHE-1665325and the University of Nebraska Holland Computing Center.

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