1
|
Becchi M, Fantolino F, Pavan GM. Layer-by-layer unsupervised clustering of statistically relevant fluctuations in noisy time-series data of complex dynamical systems. Proc Natl Acad Sci U S A 2024; 121:e2403771121. [PMID: 39110730 PMCID: PMC11331080 DOI: 10.1073/pnas.2403771121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 07/01/2024] [Indexed: 08/21/2024] Open
Abstract
Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe "Onion Clustering": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data.
Collapse
Affiliation(s)
- Matteo Becchi
- Department of Applied Science and Technology, Politecnico di Torino, Torino10129, Italy
| | - Federico Fantolino
- Department of Applied Science and Technology, Politecnico di Torino, Torino10129, Italy
| | - Giovanni M. Pavan
- Department of Applied Science and Technology, Politecnico di Torino, Torino10129, Italy
- Department of Innovative Technologies, University of Applied Sciences and Arts of Southern Switzerland, Lugano, Viganello6962, Switzerland
| |
Collapse
|
2
|
Tokmachev AM. Networks of Hydrogen Bond Networks in Water Clusters. J Phys Chem A 2024; 128:2763-2771. [PMID: 38536704 DOI: 10.1021/acs.jpca.4c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
Water clusters play a prominent role in atmospheric and solution chemistry. Numerous arrangements of protons, H-bond configurations or networks, shape the cluster properties. Studies of small water clusters by cryogenic scanning tunneling microscopy and high-resolution rovibrational spectroscopy have established proton rearrangement mechanisms forming pathways between H-bond networks. The mechanisms, concerted tunneling in particular, describe the local processes connecting pairs of configurations. Here, proton rearrangement networks mapping these transformations are defined and explored to provide a global view of the H-bond configurations in clusters. The networks are constructed for clusters of different sizes and structures. Their analysis reveals an odd-even effect with respect to the number of water molecules, exponential growth of the small-world character, bimodality of the degree distributions, and gapped assortativity of the networks. The last two properties signify the unexpected division of H-bond configurations into two classes according to their network connectivity. The results demonstrate qualitative differences between proton rearrangement mechanisms, suggest a strong influence of the cluster structure. The generated networks are of interest as real-world models for network rewiring; they establish an alternative platform for studies of proton rearrangements in H-bonded systems.
Collapse
Affiliation(s)
- Andrey M Tokmachev
- National Research Center "Kurchatov Institute", Kurchatov Sq. 1, Moscow 123182, Russia
| |
Collapse
|
3
|
Azizi K, Laio A, Hassanali A. Solvation thermodynamics from cavity shapes of amino acids. PNAS NEXUS 2023; 2:pgad239. [PMID: 37545648 PMCID: PMC10400782 DOI: 10.1093/pnasnexus/pgad239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Revised: 07/07/2023] [Accepted: 07/17/2023] [Indexed: 08/08/2023]
Abstract
According to common physical chemistry wisdom, the solvent cavities hosting a solute are tightly sewn around it, practically coinciding with its van der Waals surface. Solvation entropy is primarily determined by the surface and the volume of the cavity while enthalpy is determined by the solute-solvent interaction. In this work, we challenge this picture, demonstrating by molecular dynamics simulations that the cavities surrounding the 20 amino acids deviate significantly from the molecular surface. Strikingly, the shape of the cavity alone can be used to predict the solvation free energy, entropy, enthalpy, and hydrophobicity. Solute-solvent interactions involving the different chemical moieties of the amino acid, determine indirectly the cavity shape, and the properties of the branches but do not have to be taken explicitly into account in the prediction model.
Collapse
Affiliation(s)
- Khatereh Azizi
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Alessandro Laio
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, Via Bonomea 265, I-34136 Trieste, Italy
| | - Ali Hassanali
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| |
Collapse
|
4
|
Yun Y, Khaliullin RZ, Jung Y. Correlated Local Fluctuations in the Hydrogen Bond Network of Liquid Water. J Am Chem Soc 2022; 144:13127-13136. [PMID: 35820142 DOI: 10.1021/jacs.2c02362] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The hypothesis that liquid water can separate into two phases in the supercooled state has been supported by recent experimental and theoretical studies. However, whether such structural inhomogeneity extends to ambient conditions is under intense debate. Due to the dynamic nature of the hydrogen bond network of liquid water, exploring its structure requires detailed insight into the collective motion of neighboring water molecules, a missing link that has not been examined so far. Here, highly sensitive quantum mechanical calculations detect that the time evolution of nearby hydrogen bonds is strongly correlated, revealing a direct mechanism for the appearance of short-range structural fluctuations in the hydrogen bond network of liquid water for the first time. This correlated dynamics is found to be closely connected to the static structural picture. The distortions from the tetrahedral structure do not occur independently but are correlated due to the preference of nearby donors and acceptors to be in similar environments. The existence of such cooperative fluctuations is further supported by the temperature dependence of the local structural evolution and explained by conventional analysis of localized orbitals. It was found that such correlated structural fluctuations are only observed on a short length scale in simulations at ambient conditions. The correlations of the nearby hydrogen bond pairs of liquid water unveiled here are expected to offer a new insight into connecting the dynamics of individual water molecules and the local structure of the hydrogen bond network.
Collapse
Affiliation(s)
- Yonghwan Yun
- Department of Chemical and Biomolecular Engineering (BK21 four), Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Daejeon 34141, South Korea
| | - Rustam Z Khaliullin
- Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec H3A 0B8, Canada
| | - Yousung Jung
- Department of Chemical and Biomolecular Engineering (BK21 four), Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Daejeon 34141, South Korea
| |
Collapse
|
5
|
Capelli R, Muniz-Miranda F, Pavan GM. Ephemeral ice-like local environments in classical rigid models of liquid water. J Chem Phys 2022; 156:214503. [DOI: 10.1063/5.0088599] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Despite great efforts over the past 50 years, the simulation of water still presents significant challenges and open questions. At room temperature and pressure, the collective molecular interactions and dynamics of water molecules may form local structural arrangements that are non-trivial to classify. Here, we employ a data-driven approach built on Smooth Overlap of Atomic Position (SOAP) that allows us to compare and classify how widely used classical models represent liquid water. Macroscopically, the obtained results are rationalized based on water thermodynamic observables. Microscopically, we directly observe how transient ice-like ordered environments may dynamically/statistically form in liquid water, even above freezing temperature, by comparing the SOAP spectra for different ice structures with those of the simulated liquid systems. This confirms recent ab initio-based calculations but also reveals how the emergence of ephemeral local ice-like environments in liquid water at room conditions can be captured by classical water models.
Collapse
Affiliation(s)
- Riccardo Capelli
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
| | - Francesco Muniz-Miranda
- Department of Chemical and Geological Sciences, University of Modena and Reggio-Emilia, Via Campi 103, I-41125 Modena, Italy
| | - Giovanni M. Pavan
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
- Department of Innovative Technologies, University of Applied Sciences and Arts of Southern Switzerland, Polo Universitario Lugano, Campus Est, Via la Santa 1, CH-6962 Lugano-Viganello, Switzerland
| |
Collapse
|
6
|
Gao Y, Fang H, Ni K, Feng Y. Water clusters and density fluctuations in liquid water based on extended hierarchical clustering methods. Sci Rep 2022; 12:8036. [PMID: 35577839 PMCID: PMC9110331 DOI: 10.1038/s41598-022-11947-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2022] [Accepted: 04/25/2022] [Indexed: 11/29/2022] Open
Abstract
The microscopic structures of liquid water at ambient temperatures remain a hot debate, which relates with structural and density fluctuations in the hydrogen bond network. Here, we use molecular dynamics simulations of liquid water to study the properties of three-dimensional cage-like water clusters, which we investigate using extended graph-based hierarchical clustering methods. The water clusters can cover over 95% of hydrogen bond network, among which some clusters maximally encompass thousands of molecules extending beyond 3.0 nm. The clusters imply fractal behaviors forming percolating networks and the morphologies of small and large clusters show different scaling rules. The local favored clusters and the preferred connections between adjacent clusters correspond to lower energy and conformational entropy depending on cluster topologies. Temperature can destroy large clusters into small ones. We show further that the interior of clusters favors high-density patches. The water molecules in the small clusters, inside which are the void regarded as hydrophobic objects, have a preference for being more tetrahedral. Our results highlight the properties and changes of water clusters as the fundamental building blocks of hydrogen bond networks. In addition, the water clusters can elucidate structural and density fluctuations on different length scales in liquid water.
Collapse
|
7
|
Offei-Danso A, Hassanali A, Rodriguez A. High-Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning. J Chem Theory Comput 2022; 18:3136-3150. [PMID: 35472272 DOI: 10.1021/acs.jctc.1c01292] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model. A battery of state-of-the-art unsupervised data-science techniques are used to characterize the free-energy landscape of water starting from encoding the water environment using local atomic descriptors, through dimensionality reduction and finally the use of advanced clustering techniques. Analysis of the free energy under ambient conditions was found to be consistent with a rough single basin and independent of the choice of the water model. We find that the fluctuations of the water network occur in a high-dimensional space, which we characterize using a combination of both atomic descriptors and chemical-intuition-based coordinates. We demonstrate that a combination of both types of variables is needed in order to adequately capture the complexity of the fluctuations in the hydrogen bond network at different length scales both at room temperature and also close to the critical point of water. Our results provide a general framework for examining fluctuations in water under different conditions.
Collapse
Affiliation(s)
- Adu Offei-Danso
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.,SISSA─International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
| | - Ali Hassanali
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Alex Rodriguez
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| |
Collapse
|
8
|
Eltareb A, Lopez GE, Giovambattista N. Evidence of a liquid-liquid phase transition in H[Formula: see text]O and D[Formula: see text]O from path-integral molecular dynamics simulations. Sci Rep 2022; 12:6004. [PMID: 35397618 PMCID: PMC8994788 DOI: 10.1038/s41598-022-09525-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 02/23/2022] [Indexed: 01/22/2023] Open
Abstract
We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H[Formula: see text]O and D[Formula: see text]O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density [Formula: see text], isothermal compressibility [Formula: see text], and self-diffusion coefficients D(T) of H[Formula: see text]O and D[Formula: see text]O are in excellent agreement with available experimental data; the isobaric heat capacity [Formula: see text] obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H[Formula: see text]O and D[Formula: see text]O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H[Formula: see text]O and D[Formula: see text]O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H[Formula: see text]O, from PIMD simulations, is located at [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D[Formula: see text]O is estimated to be [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of [Formula: see text] for D[Formula: see text]O and, particularly, H[Formula: see text]O suggest that improved water models are needed for the study of supercooled water.
Collapse
Affiliation(s)
- Ali Eltareb
- Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210 USA
- Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, NY 10016 USA
| | - Gustavo E. Lopez
- Department of Chemistry, Lehman College of the City University of New York, Bronx, NY 10468 USA
- Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, NY 10016 USA
| | - Nicolas Giovambattista
- Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210 USA
- Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, NY 10016 USA
- Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, NY 10016 USA
| |
Collapse
|
9
|
Azizi K, Laio A, Hassanali A. Model Folded Hydrophobic Polymers Reside in Highly Branched Voids. J Phys Chem Lett 2022; 13:183-189. [PMID: 34965118 DOI: 10.1021/acs.jpclett.1c03333] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
By using advanced data analysis techniques, we characterize the shape of the voids surrounding model polymers of different sizes in water, observed in molecular dynamics simulations. We find that even when the model polymer is folded, the voids are extremely rough, with branches that can extend to over 1 nm away from the polymer. Water molecules in contact with the void retain close-to-bulk properties in terms of local structure. The branches disappear, and the voids start resembling the quasispherical shape predicted by dewetting theory only when they surround particles with a radius ∼1 nm, well above the size occupied by a folded hydrophobic polymer. Our results provide fresh insights into the microscopic origins of the vapor-like interfaces underlying dewetting and drying transitions.
Collapse
Affiliation(s)
- Khatereh Azizi
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Alessandro Laio
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, Via Bonomea 265, I-34136 Trieste, Italy
| | - Ali Hassanali
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| |
Collapse
|
10
|
Zakhvataev VE, Kompaniets LA. On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover. Sci Rep 2021; 11:5417. [PMID: 33686146 PMCID: PMC7940660 DOI: 10.1038/s41598-021-84277-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Accepted: 02/04/2021] [Indexed: 11/11/2022] Open
Abstract
The problem of large-density variations in supercooled and ambient water has been widely discussed in the past years. Recent studies have indicated the possibility of nanometer-sized density variations on the subpicosecond and picosecond time scales. The nature of fluctuating density heterogeneities remains a highly debated issue. In the present work, we address the problem of possible association of such density variations with the dynamics of terahertz longitudinal acoustic-like modes in liquid water. Our study is based on the fact that the subpicosecond dynamics of liquid water are essentially governed by the structural relaxation. Using a mode coupling theory approach, we found that for typical values of parameters of liquid water, the dynamic mechanism coming from the combination of the structural relaxation process and the finiteness of the amplitude of terahertz longitudinal acoustic-like mode gives rise to a soliton-like collective mode on a temperature-dependent nanometer length scale. The characteristics of this mode are consistent with the estimates of the amplitudes and temperature-dependent correlation lengths of density fluctuations in liquid water obtained in experiments and simulations. Thus, the fully dynamic mechanism could contribute to the formation and dynamics of fluctuating density heterogeneities. The soliton-like collective excitations suggested by our analysis may be relevant to different phenomena connected with supercooled water and can be expected to be associated with some ultrafast biological processes.
Collapse
Affiliation(s)
- V E Zakhvataev
- Federal Research Center "Krasnoyarsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences", 660036, Krasnoyarsk, Russia.
- Siberian Federal University, 660041, Krasnoyarsk, Russia.
| | - L A Kompaniets
- Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences, 660036, Krasnoyarsk, Russia
| |
Collapse
|
11
|
Ansari N, Karmakar T, Parrinello M. Molecular Mechanism of Gas Solubility in Liquid: Constant Chemical Potential Molecular Dynamics Simulations. J Chem Theory Comput 2020; 16:5279-5286. [PMID: 32551636 DOI: 10.1021/acs.jctc.0c00450] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Accurate prediction of gas solubility in a liquid is crucial in many areas of chemistry, and a detailed understanding of the molecular mechanism of the gas solvation continues to be an active area of research. Here, we extend the idea of the constant chemical potential molecular dynamics (CμMD) approach to the calculation of the gas solubility in the liquid under constant gas chemical potential conditions. As a representative example, we utilize this method to calculate the isothermal solubility of carbon dioxide in water. Additionally, we provide microscopic insight into the mechanism of solvation that preferentially occurs in areas of the surface where the hydrogen network is broken.
Collapse
Affiliation(s)
- Narjes Ansari
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland.,Facoltà di informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, CH-6900 Lugano, Switzerland
| | - Tarak Karmakar
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland.,Facoltà di informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, CH-6900 Lugano, Switzerland
| | - Michele Parrinello
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland.,Facoltà di informatica, Istituto di Scienze Computazionali, Università della Svizzera Italiana, CH-6900 Lugano, Switzerland.,Italian Institute of Technology, Via Morego 30, 16163 Genova, Italy
| |
Collapse
|
12
|
Martelli F, Crain J, Franzese G. Network Topology in Water Nanoconfined between Phospholipid Membranes. ACS NANO 2020; 14:8616-8623. [PMID: 32578978 DOI: 10.1021/acsnano.0c02984] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Water provides the driving force for the assembly and stability of many cellular components. Despite its impact on biological functions, a nanoscale understanding of the relationship between its structure and dynamics under soft confinement has remained elusive. As expected, water in contact with biological membranes recovers its bulk density and dynamics at ∼1 nm from phospholipid headgroups but surprisingly enhances its intermediate range order (IRO) over a distance, at least, twice as large. Here, we explore how the IRO is related to the water's hydrogen-bond network (HBN) and its coordination defects. We characterize the increased IRO by an alteration of the HBN up to more than eight coordination shells of hydration water. The HBN analysis emphasizes the existence of a bound-unbound water interface at ∼0.8 nm from the membrane. The unbound water has a distribution of defects intermediate between bound and bulk water, but with density and dynamics similar to bulk, while bound water has reduced thermal energy and many more HBN defects than low-temperature water. This observation could be fundamental for developing nanoscale models of biological interactions and for understanding how alteration of the water structure and topology, for example, due to changes in extracellular ions concentration, could affect diseases and signaling. More generally, it gives us a different perspective to study nanoconfined water.
Collapse
Affiliation(s)
- Fausto Martelli
- Hartree Centre, IBM Research Europe, Daresbury WA4 4AD, United Kingdom
| | - Jason Crain
- Hartree Centre, IBM Research Europe, Daresbury WA4 4AD, United Kingdom
- Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, United Kingdom
| | - Giancarlo Franzese
- Secció de Física Estadística i Interdisciplinària, Departament de Física de la Matèria Condensada, and Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, C. Martí i Franquès 1, 08028 Barcelona, Spain
| |
Collapse
|