Driving Force of Molecular/Ionic Superfluid Formation

Abstract

Open AccessCCS ChemistryMINI REVIEW1 Aug 2021Driving Force of Molecular/Ionic Superfluid Formation Xiqi Zhang, Bo Song and Lei Jiang Xiqi Zhang Key Laboratory of Bio-Inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190 Google Scholar More articles by this author , Bo Song School of Optical-Electrical Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093 Google Scholar More articles by this author and Lei Jiang *Corresponding author: E-mail Address: [email protected] Key Laboratory of Bio-Inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190 School of Future Technology, University of Chinese Academy of Sciences, Beijing 101407 Google Scholar More articles by this author https://doi.org/10.31635/ccschem.021.202100961 SectionsAboutAbstractPDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareFacebookTwitterLinked InEmail Ordered- and high-flux flow of molecules and ions in biological channels is considered as a quantum-confined superfluid, which is highly important in chemical reactions and bioinformation transmission. However, the driving forces for these ordered arrangements of molecules and ions in confined spaces have not been discussed. Herein, we demonstrate that the driving force of molecular/ionic superfluid formation is the attraction-repulsion balance of particles under the effect of interfacial confinement, as well as the space-confinement effect enough to reduce the degrees of freedom of the particles and then greatly limit the disorder of their movement. The competition of attractive potential energy (E) with the disorder caused by thermal noise (kBT) results in the phase transition temperature. When |E| > kBT, an ordered structure of the particles can be formed. A superfluid of 4He atoms is formed below 2.17 K. Molecules or ions can achieve a superfluid at a higher phase transition temperature (near body temperature) under a certain confined distance, for example, about twice van der Waals equilibrium distance (2d0) for molecules and twice Debye length (2λD) for ions and ion-molecules. Owing to the unique characteristic of ultralow resistance for particle transport, molecular/ionic superfluids will have a significant impact in areas such as energy transfer, storage, and conversion. Download figure Download PowerPoint Introduction Biological channels show ultrafast transmission of ions and molecules in a single chain, which has been defined as quantum-confined superfluid (QSF).1 Because ultrafast transport has a high flux and consumes low energy, molecular/ionic superfluid is highly important in chemical reactions and the transmission of bioinformation.2,3 QSF reactions order the reactant molecules in a nanochannel to satisfy symmetry-matching principles, and hence, these reactions can afford high flux and 100% selectivity with low reaction activation energy.4,5 Biophoton-driven DNA replication can be carried out via yield oscillations modulated by gold nanoparticle distance.6 It has been proposed that the transmission of nerve signals can be explained by ionic QSF, which are enthalpy-driven confined fluids.7 It has been further proposed that the frequency of quantum states consisting of ions and molecules is in the terahertz (THz) range, and hence, THz light can be used for noncontact bioinformation detection.8 However, the driving force responsible for the ordered arrangement of molecules and ions in the confined space has not yet been discussed. Superfluid: From Atoms to Molecules and Ions Kapitza9 and Allen10 were the first to report superfluidity in 4He below 2.17 K in 1938. The characteristic properties of a superfluid are zero viscosity and no loss of kinetic energy. Superfluidity often occurs along with Bose–Einstein condensation. The movement of the 4He superfluid can be considered an atomic collective motion.11 In channels with inner diameters of <100 nm, the velocity of the 4He superfluid is completely independent of pressure at all temperatures (Figure 1a).12 For superfluids moving through tightly packed fine powder, the observed viscosity is close to zero, similar to that observed in smooth channels of 100-nm diameter.13 It has also been demonstrated that the superfluid onset temperature increases as the diameter of the channel decreases.14,15 Another peculiar phenomenon is observed when liquid 4He is added to a small bowl below 2.17 K: a thin invisible film creeps up the inside wall of the bowl and down on the outside. A drop forms from this film and falls off outside the bowl until it is empty, demonstrating that the film behaves like a superfluid confined in a nanochannel (Figure 1b). The thickness of the liquid 4He film was measured as ∼20 nm by an optical method developed 12 years after the discovery of 4He superfluid.16 The sufficient and necessary condition for the formation of an ordered structure of particles is the attraction-repulsion balance, that is, the lowest point of potential well (or potential energy).17,18 For 4He at room temperature, the particles are far away from the lowest potential energy. The competition of attractive potential (E) with the disorder caused by thermal noise (kBT) gives rise to the critical temperature (TC) of phase transition, namely, TC ∼ |E|/kB. Thus, to obtain a 4He superfluid, the temperature T should be below TC = 2.17 K, so that the atoms can enter the condensation region near the lowest potential, where |E| > kBT (Figure 1c). Figure 1 | Atomic superfluid. (a) Schematic representation of 4He superfluid transport through a channel with ordered atoms stacking at a temperature below 2.17 K. In a channel with an intrinsic diameter below 100 nm, the velocity of 4He superfluid is completely independent of the channel length and pressure, and is only dependent on the temperature. (b) When the 4He superfluid is added to a small bowl at a temperature below 2.17 K, a thin invisible film with a thickness of ∼20 nm creeps up the inside wall of the bowl and down on the outside, indicating the formation of an atomic superfluid. (c) The potential-distance curve indicates that the sufficient and necessary condition for the formation of an ordered structure of atoms is the attraction-repulsion balance, that is, the lowest point of the potential well or potential energy (E0). Download figure Download PowerPoint For molecules in biological molecular channels, that is, water channels, the van der Waals (vdW) equilibrium distance (2d0) is the main factor affecting the attraction-repulsion balance. Reducing the size of the channel is key to achieving a molecular superfluid.1,2 Although the inner diameter of the biological water channel is only ∼0.4 nm, it allows an ultrahigh water flux of ∼109 s−1 at body temperature.19,20 Thus, it is believed that an ordered water flow must exist in the channel, which allows ultrafast transport of water molecules in a superfluidic manner (Figure 2a). In artificial nanochannels, water flux in a hydrophobic carbon nanotube (CNT) channel with a diameter of 2 nm can increase to seven orders of magnitude as compared with that of bulk water.21 The molecular dynamics (MD) simulation for water transport in CNTs with 4.99–1.66 nm of diameters demonstrate that the proportion of ordered water molecules increased, along with a significant enhancement in the water flux (Figure 2b).22 MD simulations further showed that more than one layer of ordered water molecules can form on a solid surface.23 A graphene oxide membrane (GOm) with stable porous zeolitic imidazolate framework-8 (ZIF-8) has also been reported for ultrafast water transport with 30-fold higher water permeability than that of GOm.24 When the size of a confined molecular system is fourfold that of the vdW equilibrium distance (d0), the molecules in the middle of the channel would diffuse freely in a disordered manner. However, when the channel size is reduced to ∼4d0, the molecules under confinement begin to arrange in order.25 When the channel size is further decreased to ∼2d0, the confined molecules enter the lowest point of the vdW potential (i.e., attraction-repulsion balance) and form a molecular superfluid (Figure 2c). The potential-distance curve in Figure 2d shows that the potential energy of the molecule in the channel is lowest when the confined distance of the channel is ∼2d0.26 Figure 2 | Molecular superfluid. (a) The biological water channel shows that ultrafast transmission of molecules occurs in a superfluidic manner involving single molecular chains at body temperature. Reproduced with permission from ref 19. Copyright 2004 Wiley-VCH. (b) Flow rate of water molecules significantly increases with decreasing diameter of the CNT channel. When the diameter is reduced to 1.66 nm, the proportion of ordered water molecules increases, indicating the formation of a molecular superfluid. Reproduced with permission from ref 22. Copyright 2008 ACS. (c) For the molecules, the confined channel size should be controlled at a distance of ∼2d0, which allows the confined molecules to enter the lowest point of vdW potential energy, reach the attraction-repulsion balance, and form molecular superfluid. (d) The potential-distance curve indicates that the potential energy of the molecule in the channel is lowest when the confined distance of the channel is ∼2d0. Download figure Download PowerPoint Superfluid not only comprises atoms and molecules, but also contains ions. Electrocytes in an electric eel can instantaneously generate a high potential of ∼600 V and a high current density of 500 A m−2 within 20 ms, without killing the eel.27 This fact indicates that the resistance of electrocytes in the electric eel is close to vanishing, and thus, the ion transmission through Na+ and K+ channels occurs in the form of a superfluid with a high ionic flux of ∼108 s−1.28 The biological MthK K+ channel is strongly K+ selective, which shows an ordered K+ chain in the form of a superfluid at body temperature with no permeability for other particles such as Na+ and water molecules (Figure 3a).29 For homologous ions, when the confined size is fourfold of the Debye length (λD), the ions in the middle of the channel diffuse freely in a disordered manner. When the channel size decreases to ∼4λD, the confined ions begin to arrange in order.30 Further reducing the channel size to ∼2λD allows the confined ions to enter the lowest area of the potential well (i.e., attraction-repulsion balance) and form an ionic superfluid (Figure 3b).31 The potential-distance curve shown in Figure 3c indicates that the lowest potential energy of ions in the channel is achieved when the confined distance D ∼ 2λD of the channel. In an artificial system, ultrafast ion transport occurs in the metal–organic framework (MOF) channels, further proving that ionic superfluid occur in microporous channels with a confined size of ∼2λD.32 The porous ZIF-8 membrane with an average pore size of ∼0.34 nm demonstrates an ultrafast K+ ion transport rate of 106–108 ions s−1 (Figure 3d). UiO-66 MOF channels with pores of ∼0.6 nm also showed an ultrahigh F− transport rate (108–1010 ions s−1).33 Figure 3 | Ionic superfluid and ionic-molecular superfluids. (a) Biological MthK K+ channel shows that the transmission of ultrafast ions occurs in a superfluidic manner involving single ionic chains at body temperature with no permeability for other particles such as Na+ and water molecules. (b) For ions, the confined channel size should be controlled at a distance of ∼2λD, which would make the confined ions enter the lowest point of potential energy, reach the attraction-repulsion balance, and form an ionic superfluid. (c) The potential-distance curve indicates that the potential energy of the ion in the channel is lowest when its confined distance is ∼2λD. (d) Artificial MOF K+ channel with subnanometer pores shows ultrafast transport of K+ (106–108 ions s−1) at room temperature. (e) Biological KcsA K+ channel shows permeability for both K+ and water molecules for superfluid transmission at body temperature. (f) For heterogeneous particles such as molecule-ions, the confined size must be ∼2λD to realize the attraction-repulsion balance and form an ionic-molecular superfluid. (g) Potential-distance curves indicate that the potential energy of the ions and molecules in the channel are lowest when the confined distance of the channel is ∼2λD. (h) An artificial CNT K+ channel of 0.6 nm radius embedded in the vertical direction between two graphite sheets demonstrates that the confined environment plays a dominant role in the ionic transport. Reproduced with permission from ref 37. Copyright 2010 ACS. Download figure Download PowerPoint For a system containing both ions and molecules under confinement, an ionic-molecular superfluid could be achieved in biological KcsA K+ channels at body temperature (Figure 3e).28 A KcsA K+ channel from Streptomyces lividans can hold an ordered ion strand containing two K+ ions approximately 0.75 nm apart and a single-water molecule in between.34 At high K+ concentrations, the water–ion coupling ratio reaches 1.0, indicating that the turnover between the alternating ion and water arrays occurs as a single-file.35 To form a superfluid using heterogeneous particles such as molecule-ions, the confined size must be ∼2λD to realize the attraction-repulsion balance (Figure 3f).36 The potential-distance curve shown in Figure 3g indicates that the potential energy of both the ion and molecule in the channel is lowest when the confined distance of the channel is ∼2λD. In an artificial K+-water channel, a (9,9) single-walled CNT of length 1.34 nm in length and radius 0.6 nm further proved that a confined environment plays a dominant role in the fast ion transport process and provides a better understanding for the mechanism of ultrafast ion transport in the KcsA channel (Figure 3h).37 It should be noted that the interface dipoles together with the wall structure and polarizability will be very important for the ordered structure of confined particles, such as the filter structures of K+ channels where the weak difference between the structures of MthK and KcsA channels causes significant differences in properties. The confinement effects give a chance for superfluidity to leave the liquid helium temperature to reach the biological temperature. Previous discussions suggest that the charged interface of confinement space can cause an effective attraction of like-charged particles, meaning an enthalpy increase of them. Besides this, the space confinement also provides a force to reduce the degrees of freedom of the particles when d ∼ 2d0 for molecule, or d ∼ 2λD for ions and ion-molecules, especially in the nanochannels (Figure 3) within which the dimensionality of particles moving is reduced to one. This dimensionality reduction will greatly limit the disordered movement of confined particles, as is equivalent to an effect of entropy decrease. Since the ratio of enthalpy over entropy closely relates to the transition temperature, all these confinement effects provide a possibility to achieve superfluidity at body temperature. Thus, it can be concluded that the superfluid state of particles (e.g., atoms, molecules, and ions) can be formed when an attraction-repulsion balance is achieved under interfacial confinement. Such an ordered structure of particles is formed when |E| > kBT. Atomic superfluid is formed at a low-phase transition temperature, while molecules or ions can form a superfluid at a higher temperature (near body temperature) under certain confined distances, (∼2d0 for molecules and ∼2λD for ions and ion-molecules). Since molecular/ionic superfluid afford ultralow resistance to particle transport, they greatly affect the energy transfer, storage, and conversion. Molecular Superfluid for Energy Transfer The potential effects of molecular superfluid on the performance of porous materials in energy transfer have seldom been considered. Gas–liquid and liquid–solid transitions are first-order phase transitions and generate latent heat of phase changes, which are in accordance with the Clausius Clapeyron equation. 38 However, the superfluid phase is neither a liquid phase nor a solid phase; instead, it is a phase of ordered liquid.39,40 When molecules are confined in a microporous channel of size ∼2d0, the confined molecules change from a disordered phase to a superfluid phase and generate a latent heat of phase change (ΔTA) (Figure 4a).41 In contrast, the desorption of molecules involves a superfluid-gas phase transition and absorbs heat (ΔTD). The InfraSORP Technology by Fraunhofer/Rubotherm has been recently developed to obtain more information about the absorption kinetics and heat transfer properties of porous materials (Figure 4b).42 Kaskel et al.43 reported the adsorption/desorption kinetics of bulk BNC, YP-50F, and bipolar BNC-CNT and analyzed them based on the thermal response measurements using n-butane as a probe molecule. In one measured cycle, the first peak corresponded to the adsorption process, while the second peak represented the desorption process of the adsorbed n-butane. The result indicated that the exothermic peak was larger than the endothermic peak (ΔTA > ΔTD) for the bulk BNC and YP-50F channels, while the opposite (ΔTA < ΔTD) was true for the BNC-CNT channels (Figure 4c). This asymmetric exothermic and endothermic behavior of the peaks is important for the heat transfer technology.44 The adsorption/desorption cyclability of four flexible MOFs [MIL-53(Al), ELM-11, SNU-9, and DUT-8(Ni)] was studied at 298 K using n-butane as the test gas.45 For MIL-53(Al), ELM-11, and SNU-9, ΔTA > ΔTD in all cycles, while for DUT-8(Ni), ΔTA < ΔTD for the first 10 adsorption/desorption cycles, after which it is ΔTA > ΔTD. Kaskel et al.46 used six carbide and carbon materials as model substances and n-butane as the test gas to compare the thermal response of mesoporous and microporous channels. The temperature of microporous materials (TiC-CDC) significantly increases during the first adsorption process compared with that of the mesoporous samples (CMK-3 and OM-SiC) (Figures 4d and 4e). As the pore size decreased, it became thermodynamically favorable for the molecule to condense to an ordered phase.2 The magnitude of the thermal response signal reflects the total heat of adsorption.47 When the surface areas of mesoporous CMK-3 and microporous TiC-CDC-600 become comparable, more latent heat of phase change is released during the adsorption of n-butane in the microporous sample, indicating high binding enthalpy for small pores. More importantly, the adsorption and desorption signals of the microporous samples were highly asymmetric, and the temperature decrease during desorption was significantly lower than the temperature increase in adsorption, implying much higher heat transfer performance for smaller pores. Figure 4 | Molecular superfluid for energy transfer. (a) Absorption of molecules in a microporous channel of size ∼2d0 shows gas-superfluid phase transition and generates latent heat of phase change, while their desorption shows superfluid-gas phase transition and absorbs heat. (b) InfraSORP setup for the thermal response measurement. (c) Adsorption and desorption kinetics measurements using InfraSORP techniques and n-butane as a probe molecule indicate that the exothermic peak is larger than the endothermic peak (ΔTA > ΔTD) for bulk BNC channels; the opposite (ΔTA < ΔTD) is observed for the BNC-CNT channels. Reproduced with permission from ref 43. Copyright 2016 ACS. (d) Thermal response measurements of n-butane adsorption/desorption of the mesoporous samples. (e) Thermal response measurements of n-butane adsorption/desorption of the microporous samples indicate higher exothermic performance and lower endothermic performance than those of mesoporous samples. Reproduced with permission from ref 46. Copyright 2016 ACS. Download figure Download PowerPoint Two-Dimensional Ionic Superfluid for Energy Storage and Conversion Ionic superfluid also has profound significance in energy storage and conversion, both theoretically and practically.48–50 Owing to the exceptional electrical conductance, mechanical properties, and high surface area of graphene two-dimensional (2D) materials, they are attracting increasing scientific interest in the fields of electrochemical capacitors and batteries over the past decade.51 However, the arrangement and transfer of ions in the charge–discharge process of supercapacitors and batteries have not been comprehensively understood.52 Supercapacitors show an ultrafast charge–discharge process that ends within seconds, while battery discharge occurs at a steady, flat rate until it is almost exhausted, at which point the energy drop-off increases its pace.53 Supercapacitors store energy in an electric field, while batteries use chemical reactions to store and release energy. We propose that the charge–discharge process of a supercapacitor is a purely ionic superfluid process, while that of a battery involves both ionic superfluid and redox reaction processes (Figure 5a). To maximize the fast ion transport kinetics of supercapacitors, it is essential to fabricate graphene materials in a highly compact and orderly configuration with a layer spacing of ∼2λD.54 Thus, an artificial electrical eel could be fabricated with an ultrahigh ion flux.55,56 Li et al.57 fabricated a chemically converted graphene hydrogel films to enable the integration of graphene sheets with electrolytes at a subnanometer scale and for a continuous ion transport network (Figure 5b). The theoretical estimation indicated that the size of the 2D channel ranges from 5.36 to 0.34 nm with increasing packing density. The volumetric capacitances of the carbon electrodes with varied charge–discharge current densities demonstrated the highest charge–discharge rate at a layer spacing of 0.34 nm, which is close to 2λD. Furthermore, the superdense ordering of Li between two graphene sheets has been shown by in situ transmission electron microscopy (TEM) measurements, providing evidence for the occurrence of ionic superfluid in Li batteries (Figure 5c).58 In addition, some anode and cathode materials, including MoS2, TiO2, LiMn2O4, LiFePO4, and LiCoO2, have also been reported to show a fast charge–discharge rate, providing further evidence that the 2D confined channels of the anodes and cathodes have ionic superfluid transport and redox reactions.59–63 In contrast, Li foil cells show a charge–discharge rate of one order of magnitude lower than that of anodes containing 2D channels with a confined distance of ∼2λD for Li ions.64 Therefore, during the charge–discharge of a Li battery, ultrafast transport of Li ions occurs in a superfluidic manner in the 2D channel with a confined distance of ∼2λD for Li ions. Figure 5 | 2D ionic superfluid for energy storage and conversion. (a) Supercapacitors charge and discharge rapidly, while battery discharge occurs at a steady, flat rate until it is almost exhausted, at which point the energy drop-off increases its pace. The charge–discharge process of the supercapacitor represents a purely ionic superfluidic process, while that of battery represents ionic superfluidic and redox reaction processes. (b) Scanning electron microscopy (SEM) images of densely packed carbon electrodes with different layer spacings. The middle scheme represents the fabrication of liquid electrolyte-mediated chemically converted graphene films with a layer spacing of ∼2λD. The bottom left curve describes the theoretical estimation of the relationship between the layer spacing and the packing density of graphene, indicating that the size of the 2D channel ranges from 5.36 to 0.34 nm with increasing packing density. The bottom right plots show volumetric capacitances of carbon electrodes with varied charge–discharge current densities. The highest charge–discharge rate was achieved at a layer spacing of 0.34 nm. Reproduced with permission from ref 57. Copyright 2013 AAAS. (c) The left scheme represents a side view of a device containing bilayer graphene on a Si3N4-covered Si substrate and a Li-ion electrochemical cell. The middle TEM image of the Li crystal shows superdense ordering of Li in the channel between two graphene sheets. The left scheme illustrates the Li-ion redox reaction in the anode and cathode of Li ion battery when charged and discharged. Superfluidic Li-ion transport through 2D channels of distance ∼2λD results in a high charge–discharge rate. Download figure Download PowerPoint Summary The sufficient and necessary conditions for the formation of an ordered structure of particles is the attraction-repulsion balance under the effect of interfacial confinement, together with the space-confinement effect enough to reduce the degrees of freedom of the particles and then greatly limit the disorder of their movement. The competition of attractive potential E with the disorder caused by kBT results in the phase transition temperature. When |E| > kBT, an ordered structure of the particles can be formed. Atomic superfluid can be formed at a low-phase transition temperature, while homologous molecules or ions can form a superfluid at body temperature under a certain confined size, for example, ∼2d0 for molecules and ∼2λD for ions. For heterogeneous particles such as molecule-ions, the confined size must be ∼2λD to form a superfluid. The use of molecular superfluid for energy transfer provides a new mechanism to understand the latent heat of phase change and promote the development of energy transfer technology. For energy storage and conversion, the concept of superfluid could help to understand the mechanism of ultrafast charging–discharging processes of batteries and supercapacitors, and establish a new principle for the fabrication of high-performance energy materials. Conflict of Interest There is no conflict of interest to report. Funding Information This work was supported by the National Key R&D program of China (nos. 2016YFA0200803 and 2018YFA0208502), the National Natural Science Foundation of China (nos. 51973227 and 21988102), and the Youth Innovation Promotion Association CAS (no. 2020028). Acknowledgments The authors appreciated Zexu Han from Beihang University for his help in drawing Figure 1.