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Hydrophilic and Hydrophobic Effects on the Structure and Themodynamic Properties of Confined Water: Water in Solutions. Int J Mol Sci 2021; 22:ijms22147547. [PMID: 34299171 PMCID: PMC8304151 DOI: 10.3390/ijms22147547] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 06/26/2021] [Accepted: 07/07/2021] [Indexed: 11/17/2022] Open
Abstract
NMR spectroscopy is used in the temperature range 180–350 K to study the local order and transport properties of pure liquid water (bulk and confined) and its solutions with glycerol and methanol at different molar fractions. We focused our interest on the hydrophobic effects (HE), i.e., the competition between hydrophilic and hydrophobic interactions. Nowadays, compared to hydrophilicity, little is known about hydrophobicity. Therefore, the main purpose of this study is to gain new information about hydrophobicity. As the liquid water properties are dominated by polymorphism (two coexisting liquid phases of high and low density) due to hydrogen bond interactions (HB), creating (especially in the supercooled regime) the tetrahedral networking, we focused our interest to the HE of these structures. We measured the relaxation times (T1 and T2) and the self-diffusion (DS). From these times, we took advantage of the NMR property to follow the behaviors of each molecular component (the hydrophilic and hydrophobic groups) separately. In contrast, DS is studied in terms of the Adam–Gibbs model by obtaining the configurational entropy (Sconf) and the specific heat contributions (CP,conf). We find that, for the HE, all of the studied quantities behave differently. For water–glycerol, the HB interaction is dominant for all conditions; water–methanol, two different T-regions above and below 265 K are observable, dominated by hydrophobicity and hydrophilicity, respectively. Below this temperature, where the LDL phase and the HB network develops and grows, with the times and CP,conf change behaviors leading to maxima and minima. Above it, the HB becomes weak and less stable, the HDL dominates, and hydrophobicity determines the solution.
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Some Aspects of the Liquid Water Thermodynamic Behavior: From The Stable to the Deep Supercooled Regime. Int J Mol Sci 2020; 21:ijms21197269. [PMID: 33019640 PMCID: PMC7582456 DOI: 10.3390/ijms21197269] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Revised: 09/25/2020] [Accepted: 09/26/2020] [Indexed: 12/02/2022] Open
Abstract
Liquid water is considered to be a peculiar example of glass forming materials because of the possibility of giving rise to amorphous phases with different densities and of the thermodynamic anomalies that characterize its supercooled liquid phase. In the present work, literature data on the density of bulk liquid water are analyzed in a wide temperature-pressure range, also including the glass phases. A careful data analysis, which was performed on different density isobars, made in terms of thermodynamic response functions, like the thermal expansion αP and the specific heat differences CP−CV, proves, exclusively from the experimental data, the thermodynamic consistence of the liquid-liquid transition hypothesis. The study confirms that supercooled bulk water is a mixture of two liquid “phases”, namely the high density (HDL) and the low density (LDL) liquids that characterize different regions of the water phase diagram. Furthermore, the CP−CV isobars behaviors clearly support the existence of both a liquid–liquid transition and of a liquid–liquid critical point.
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Specific Heat and Transport Functions ofWater. Int J Mol Sci 2020; 21:ijms21020622. [PMID: 31963571 PMCID: PMC7014045 DOI: 10.3390/ijms21020622] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 01/13/2020] [Accepted: 01/14/2020] [Indexed: 11/21/2022] Open
Abstract
Numerous water characteristics are essentially ascribed to its peculiarity to form strong hydrogen bonds that become progressively more stable on decreasing the temperature. However, the structural and dynamical implications of the molecular rearrangement are still subject of debate and intense studies. In this work, we observe that the thermodynamic characteristics of liquid water are strictly connected to its dynamic characteristics. In particular, we compare the thermal behaviour of the isobaric specific heat of water, measured in different confinement conditions at atmospheric pressure (and evaluated by means of theoretical studies) with its configurational contribution obtained from the values of the measured self-diffusion coefficient through the use of the Adam–Gibbs approach. Our results confirm the existence of a maximum in the specific heat of water at about 225 K and indicate that especially at low temperature the configurational contributions to the entropy are dominant.
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The Proton Density of States in Confined Water (H 2O). Int J Mol Sci 2019; 20:ijms20215373. [PMID: 31671726 PMCID: PMC6861890 DOI: 10.3390/ijms20215373] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Revised: 10/17/2019] [Accepted: 10/24/2019] [Indexed: 12/05/2022] Open
Abstract
The hydrogen density of states (DOS) in confined water has been probed by inelastic neutron scattering spectra in a wide range of its P–T phase diagram. The liquid–liquid transition and the dynamical crossover from the fragile (super-Arrhenius) to strong (Arrhenius) glass forming behavior have been studied, by taking into account the system polymorphism in both the liquid and amorphous solid phases. The interest is focused in the low energy region of the DOS (E<10 meV) and the data are discussed in terms of the energy landscape (local minima of the potential energy) approach. In this latest research, we consider a unit scale energy (EC) linked to the water local order governed by the hydrogen bonding (HB). All the measured spectra, scaled according to such energy, evidence a universal power law behavior with different exponents (γ) in the strong and fragile glass forming regions, respectively. In the first case, the DOS data obey the Debye squared-frequency law, whereas, in the second one, we obtain a value predicted in terms of the mode-coupling theory (MCT) (γ≃1.6).
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Mallamace F, Corsaro C, Mallamace D, Fazio E, Chen SH. Some considerations on the water polymorphism and the liquid-liquid transition by the density behavior in the liquid phase. J Chem Phys 2019; 151:044504. [PMID: 31370513 DOI: 10.1063/1.5095687] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The bulk liquid water density data (ρ) are studied in a very large temperature pressure range including also the glass phases. A thorough analysis of their isobars, together with the suggestions of recent thermodynamical studies, gives evidence of two crossovers at T* and P* above which the hydrogen bond interaction is unable to arrange the tetrahedral network that is at the basis of the liquid polymorphism giving rise to the low density liquid (LDL). The curvatures of these isobars, as a function of T, are completely different: concave below P* (where maxima are) and convex above. In both the cases, a continuity between liquid and glass is observed with P* as the border of the density evolution toward the two different polymorphic glasses (low and high density amorphous). The experimental data of the densities of these two glasses also show a markedly different pressure dependence. Here, on the basis of these observations in bulk water and by considering a recent study on the growth of the LDL phase, by decreasing temperature, we discuss the water liquid-liquid transition and evaluate the isothermal compressibility inside the deep supercooled regime. Such a quantity shows an additional maximum that is pressure dependent that under ambient conditions agrees with a recent X-ray experiment. In particular, the present analysis suggests the presence of a liquid-liquid critical point located at about 180 MPa and 197 K.
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Affiliation(s)
- Francesco Mallamace
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Carmelo Corsaro
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra (MIFT), Università di Messina I-98166, Messina, Italy
| | - Domenico Mallamace
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra (MIFT), Università di Messina I-98166, Messina, Italy
| | - Enza Fazio
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra (MIFT), Università di Messina I-98166, Messina, Italy
| | - Sow-Hsin Chen
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Petkov V, Ren Y, Suchomel M. Molecular arrangement in water: random but not quite. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:155102. [PMID: 22418283 DOI: 10.1088/0953-8984/24/15/155102] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Water defines life on Earth from the cellular to the terrestrial level. Yet the molecular level arrangement in water is not well understood, posing problems in comprehending its very special chemical, physical and biological properties. Here we present high-resolution x-ray diffraction data for water clearly showing that its molecular arrangement exhibits specific correlations that are consistent with the presence of rings of H(2)O molecules linked together by hydrogen bonds into tetrahedral-like units from a continuous network. This level of molecular arrangement complexity is beyond what a simple 'two-state' model of water (Bernal and Fowler 1933 J. Chem. Phys.1 515-48) could explain. It may not be explained by the recently put forward 'chains-clusters of completely uncorrelated molecules' model (Wernet et al 2004 Science 304 995-9) either. Rather it indicates that water is homogeneous down to the molecular level where different water molecules form tetrahedral units of different perfection and/or participate in rings of different sizes, thus experiencing different local environments. The local diversity of this tetrahedral network coupled to the flexibility of the hydrogen bonds that hold it together may explain well the rich phase diagram of water and why it responds non-uniformly to external stimuli such as, for example, temperature and pressure.
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Affiliation(s)
- V Petkov
- Department of Physics, Central Michigan University, Mt. Pleasant, MI 48858, USA.
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Schellman JA. In memoriam: Walter Kauzmann (1916-2009). Protein Sci 2010; 19:363-71. [PMID: 20054833 PMCID: PMC2866263 DOI: 10.1002/pro.328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2009] [Accepted: 12/22/2009] [Indexed: 11/09/2022]
Affiliation(s)
- John A Schellman
- Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403-1229, USA
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Abstract
Hydrophobic interactions of xenon atoms dissolved in liquid water were studied by NpT Monte Carlo simulations in the temperature range 298.15 to 333K and at ambient pressure. Structural properties of dilute xenon solutions were calculated and compared to those of bulk water in order to show the influence of the hydrophobic solute. It was found that the xenon atoms tend to aggregate with increasing temperature. At low temperatures the aggregates are predominantly solvent-separated pairs; at higher temperatures the quota of contact pairs increases. Furthermore, the residual chemical potentials of xenon and water were calculated with different methods; it was found that the Widom insertion methods works best for this system. For the thermodynamic conditions of this work, the residual chemical potential of water in the presence of xenon was found to be a linear function of temperature.
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Malenkov G. Liquid water and ices: understanding the structure and physical properties. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:283101. [PMID: 21828506 DOI: 10.1088/0953-8984/21/28/283101] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
A review of the structure and some properties of condensed phases of water is given. Since the discovery of the polymorphism of crystalline ice (beginning of the twentieth century), 15 ice modifications have been found and their structures have been determined. If we do not take into consideration proton ordering or disordering, nine distinct crystalline ice modifications in which water molecules retain their individuality are known. In the tenth, ice X, there are no H(2)O molecules. It contains ions (or atoms) of oxygen and hydrogen. The structure of all these modifications is described and information about their fields of stability and about the transition between them is given. It is emphasized that there are ice modifications which are metastable at any temperature and pressure (ices Ic, IV and XII), and many modifications can exist as metastable phases beyond their fields of stability. The ability of water to exist in metastable states is one of its remarkable properties. Several amorphous ice modifications (all of them are metastable) are known. Brief information about their properties and transitions between them is given. At the end of the 1960s the conception of the water structure as a three-dimensional hydrogen-bonded network was conclusively formed. Discovery of the polymorphism of amorphous ices awakened interest in the heterogeneity of the water network. Structural and dynamical heterogeneity of liquid water is discussed in detail. Computer simulation showed that the diffusion coefficient of water molecules in dense regions of the network is lower than in the loose regions, while an increase of density of the entire network gives rise to an increase of diffusion coefficient. This finding contradicts the conceptions associated with the primitive two-state models and can be explained from pressure dependences of melting temperature and of homogeneous nucleation temperature. A brief discussion of the picture of molecular motions in liquid water based on experiment and on computer simulation is given. This picture is still very incomplete. The most fascinating idea that was put forward during the last 20 years was the second critical point conjecture. It is still not clear whether this conjecture corresponds to reality.
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Affiliation(s)
- George Malenkov
- AN Frumkin Institute of Physical Chemistry and Electrochemistry, Leninskii Prospect, 31 119991, Moscow, Russia
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Vafaie-Sefti M, Modarress H, Meibodi ME, Mousavi-Dehghani SA. Association Equation of State for Hydrogen-Bonded Substances. CAN J CHEM ENG 2008. [DOI: 10.1002/cjce.5450850106] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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11
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Henchman RH. Free energy of liquid water from a computer simulation via cell theory. J Chem Phys 2007; 126:064504. [PMID: 17313226 DOI: 10.1063/1.2434964] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A method to calculate the free energy of water from computer simulation is presented. Based on cell theory, it approximates the potential energy surface sampled in the simulation by an anisotropic six-dimensional harmonic potential to model the three hindered translations and three hindered rotations of a single rigid water molecule. The potential is parametrized from the magnitude of the forces and torques measured in the simulation. The entropy of these six harmonic oscillators is calculated and summed with a conformational term to give the total entropy. Combining this with the simulation enthalpy yields the free energy. The six water models examined are TIP3P, SPC, TIP4P, SPC/E, TIP5P, and TIP4P-Ew. The results reproduce experiment well: free energies for all models are within 1.6 kJ mol(-1) and entropies are within 3.6 J K(-1) mol(-1). Approximately two-thirds of the entropy comes from translation, a third from rotation, and 5% from conformation. Vibrational frequencies match those in the experimental infrared spectrum and assist in their assignment. Intermolecular quantum effects are found to be small, with free energies for the classical oscillator lying 0.5-0.7 kJ mol(-1) higher than in the quantum case. Molecular displacements and vibrational and zero point energies are also calculated. Altogether, these results validate the harmonic oscillator as a quantitative model for the liquid state.
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Affiliation(s)
- Richard H Henchman
- Manchester Interdisciplinary Biocentre, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK.
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Venktaramana G, Rajagopal E, Manohara Murthy N. Studies on the effect of chlorides of magnesium, calcium, strontium and barium on the temperature of the sound velocity maximum of water. J Mol Liq 2006. [DOI: 10.1016/j.molliq.2005.02.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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16
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Griffith J, Scheraga H. Statistical thermodynamics of aqueous solutions. I. Water structure, solutions with non-polar solutes, and hydrophobic interactions. ACTA ACUST UNITED AC 2004. [DOI: 10.1016/j.theochem.2004.06.003] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Jhon YI, Kim HG, Jhon MS. Equilibrium between two liquid structures in water: explicit representation via significant liquid structure theory. J Mol Liq 2004. [DOI: 10.1016/j.molliq.2003.12.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Malenkov G, Tytik D, Zheligovskaya E. Structural and dynamic heterogeneity of computer simulated water: ordinary, supercooled, stretched and compressed. J Mol Liq 2003. [DOI: 10.1016/s0167-7322(03)00106-5] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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19
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Cluster composition of liquid water derived from laser-Raman spectra and molecular simulation data. Food Chem 2003. [DOI: 10.1016/s0308-8146(02)00584-8] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Robinson GW, Cho CH, Urquidi J. Isosbestic points in liquid water: Further strong evidence for the two-state mixture model. J Chem Phys 1999. [DOI: 10.1063/1.479349] [Citation(s) in RCA: 88] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Weinhold F. Quantum cluster equilibrium theory of liquids: Illustrative application to water. J Chem Phys 1998. [DOI: 10.1063/1.476574] [Citation(s) in RCA: 91] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Aqueous molecular clusters isolated as liquid fragments by adiabatic expansion of liquid jets. ACTA ACUST UNITED AC 1990. [DOI: 10.1007/bf01437186] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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24
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Determination of critical micelle concentration of several nonionic surfactants by azo-hydrazone tautomerism of anionic dye. J Colloid Interface Sci 1985. [DOI: 10.1016/0021-9797(85)90122-5] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Kisel'nikov VN, Slivchenko ES, Markichev NA, Evseeva EM. Solubility of vitamin B1 in aqueous solutions of monohydric alcohols. Pharm Chem J 1981. [DOI: 10.1007/bf00760672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Effect of isomeric butanols on the temperature corresponding to the adiabatic compressibility minimum of water. J SOLUTION CHEM 1975. [DOI: 10.1007/bf00650392] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Hagler AT, Scheraga HA, Némethy G. Current status of the water-structure problem; application to proteins. Ann N Y Acad Sci 1973; 204:51-78. [PMID: 4574539 DOI: 10.1111/j.1749-6632.1973.tb30771.x] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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33
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The Structure and Molecular Dynamics of Water. ACTA ACUST UNITED AC 1973. [DOI: 10.1016/b978-0-12-571807-3.50011-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Anionenaustausch ? Selektivit�tssequenzen in homologen Reihen hydrophober Ionen. MONATSHEFTE FUR CHEMIE 1972. [DOI: 10.1007/bf00904964] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Gurikov YV. The basis of the bistructural model for water. J STRUCT CHEM+ 1971. [DOI: 10.1007/bf00739098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Arakawa K, Sasaki K. The Structure Theory of Water. III. The Order-Disorder Theory. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1970. [DOI: 10.1246/bcsj.43.3048] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Lumry R, Rajender S. Enthalpy-entropy compensation phenomena in water solutions of proteins and small molecules: a ubiquitous property of water. Biopolymers 1970; 9:1125-227. [PMID: 4918636 DOI: 10.1002/bip.1970.360091002] [Citation(s) in RCA: 869] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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42
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Arakawa K, Sasaki K. The Structure Theory of Water. I. Two State Theory. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1969. [DOI: 10.1246/bcsj.42.303] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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43
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Braunstein J. Some aspects of solution chemistry in liquid mixtures of inorganic salts with water. ACTA ACUST UNITED AC 1968. [DOI: 10.1016/0073-8085(68)80012-9] [Citation(s) in RCA: 32] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Jhon MS, Van Artsdalen ER, Grosh J, Eyring H. Further Applications of the Domain Theory of Liquid Water: I. Surface Tension of Light and Heavy Water; II. Dielectric Constant of Lower Aliphatic Alcohols. J Chem Phys 1967. [DOI: 10.1063/1.1703297] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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Austin G, Sato M, Yai H. Osmolality effects in neurons: I. permeability coefficient and a model of water flux. Math Biosci 1967. [DOI: 10.1016/0025-5564(67)90015-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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