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Höfling F, Dietrich S. Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction. J Chem Phys 2024; 160:104107. [PMID: 38469908 DOI: 10.1063/5.0186955] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 02/15/2024] [Indexed: 03/13/2024] Open
Abstract
Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.
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Affiliation(s)
- F Höfling
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
- Zuse Institut Berlin, Takustr. 7, 14195 Berlin, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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2
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Junio J, Cohen JA, Ou-Yang HD. Osmotic Bulk Modulus of Charged Colloids Measured by Ensemble Optical Trapping. J Phys Chem B 2016; 120:9187-94. [PMID: 27348273 DOI: 10.1021/acs.jpcb.6b05608] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The optical-bottle technique is used to measure osmotic bulk moduli of colloid suspensions. The bulk modulus is determined by optically trapping an ensemble of nanoparticles and invoking a steady-state force balance between confining optical-gradient forces and repulsive osmotic-pressure forces. Osmotic bulk moduli are reported for aqueous suspensions of charged polystyrene particles in NaCl solutions as a function of particle concentration and ionic strength, and are compared to those determined by turbidity measurements under the same conditions. Effective particle charges are calculated from the bulk moduli and are found to increase as a function of ionic strength, consistent with previously reported results.
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Affiliation(s)
- Joseph Junio
- Department of Physics, Lehigh University , Bethlehem, Pennsylvania 18015, United States
| | - Joel A Cohen
- Department of Physics, University of Massachusetts , Amherst, Massachusetts 01003, United States
| | - H Daniel Ou-Yang
- Department of Physics, Lehigh University , Bethlehem, Pennsylvania 18015, United States
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3
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Wu B, Iwashita T, Egami T. Anisotropy of stress correlation in two-dimensional liquids and a pseudospin model. Phys Rev E 2015; 92:052303. [PMID: 26651691 DOI: 10.1103/physreve.92.052303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Indexed: 11/07/2022]
Abstract
Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. In this paper, we examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions.
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Affiliation(s)
- Bin Wu
- Department of Physics and Astronomy, Joint Institute of Neutron Science, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Takuya Iwashita
- Department of Materials Science and Engineering, University of Tennessee, Knoxville,Tennessee 37996, USA
| | - Takeshi Egami
- Department of Physics and Astronomy, Joint Institute of Neutron Science, University of Tennessee, Knoxville, Tennessee 37996, USA.,Department of Materials Science and Engineering, University of Tennessee, Knoxville,Tennessee 37996, USA.,Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Nikoofard H, Esmaili BA. Determination of the structure factor for the rare gas fluids based on the ORPA theory and LIR equation of state. Mol Phys 2013. [DOI: 10.1080/00268976.2012.760056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Taffs J, Malins A, Williams SR, Royall CP. The effect of attractions on the local structure of liquids and colloidal fluids. J Chem Phys 2010; 133:244901. [DOI: 10.1063/1.3516210] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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Guarini E, Sampoli M, Venturi G, Bafile U, Barocchi F. Inelastic neutron scattering and molecular dynamics determination of the interaction potential in liquid CD4. PHYSICAL REVIEW LETTERS 2007; 99:167801. [PMID: 17995296 DOI: 10.1103/physrevlett.99.167801] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2007] [Indexed: 05/25/2023]
Abstract
Anisotropic interactions of liquid CD4 are studied in detail by comparison of inelastic neutron Brillouin scattering data with molecular dynamics simulations using up to four different models of the methane site-site potential. We demonstrate that the experimental dynamic structure factor S(Q,omega) acts as a highly discriminating quantity for possible interaction schemes. In particular, the Q evolution of the spectra enables a selective probing of the short- and medium-range features of the anisotropic potentials. We show that the preferential configuration of methane dimers at liquid densities can thus be discerned by analyzing the orientation-dependent model potential curves, in light of the experimental and simulation results.
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Affiliation(s)
- E Guarini
- Dipartimento di Fisica, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
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7
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Evans R, Tarazona P, Marconi UMB. On the failure of certain integral equation theories to account for complete wetting at solid-fluid interfaces. Mol Phys 2006. [DOI: 10.1080/00268978300102811] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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8
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Tarazona P, Evans R. Long ranged correlations at a solid-fluid interface A signature of the approach to complete wetting. Mol Phys 2006. [DOI: 10.1080/00268978200100772] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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9
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Bafile U, Guarini E, Barocchi F. Collective acoustic modes as renormalized damped oscillators: unified description of neutron and x-ray scattering data from classical fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061203. [PMID: 16906814 DOI: 10.1103/physreve.73.061203] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2006] [Indexed: 05/11/2023]
Abstract
In the Q range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor S(Q, omega) generalize in different ways the results obtained from linearized-hydrodynamics theory in the Q-->0 limit. Here we show that the models most commonly fitted to experimental S(Q, omega) spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation Q range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the Q dependence of the mode frequencies. The emerging picture describes the acoustic modes as Q-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.
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Affiliation(s)
- Ubaldo Bafile
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano, I-50019 Sesto Fiorentino, Italy
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Morita T, Takahashi Y, Tanaka Y, Arai AA, Nishikawa K. Density dependences of long-range fluctuations and short-range correlation lengths of CHF3 and CH2F2 in supercritical states. J Chem Phys 2006; 124:124519. [PMID: 16599709 DOI: 10.1063/1.2178807] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Small-angle x-ray scattering (SAXS) measurements are carried out for supercritical polar fluorocarbons, CHF3 and CH2F2, along the isotherm of 1.04 in reduced temperatures with the density range from 0.3 to 1.5 in reduced units. A novel apparatus for determination of absorption factors of the sample fluids is used in the present measurements. The apparatus enables us to detect simultaneously the accurate factors during the observation of the SAXS signals. Long-range fluctuations such as density fluctuations and correlation lengths are evaluated from the obtained SAXS data. The reduced correlation lengths are obtained by normalization by each molecular size, in order to discuss the fluctuations independent of the difference of the individual molecular size. The density fluctuations and the reduced correlation lengths of CHF3 and CH2F2 are compared with those of CO2 and H2O. The results are as follows: H2O>CH2F2>CHF3 approximately CO2 in the order of magnitude. The fluctuations of CH2F2 are significantly distinguishable from those of CHF3 and show intermediate aspect between H2O and a group of CO2 and CHF3. In addition, the short-range correlation lengths, i.e., the Ornstein-Zernike direct correlation lengths, are firstly discussed from both viewpoints of density and substance dependences. The reduced short-range correlation lengths normalized by individual molecular size are found to trace a universal curve as a function of the reduced density.
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Affiliation(s)
- Takeshi Morita
- Division of Diversity Science, Graduate School of Science and Technology, Chiba University, Yayoi, Inage-ku, Chiba 263-8522, Japan
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von Solms N, Anderson CO, Blanch HW, Prausnitz JM. Molecular thermodynamics for fluid-phase equilibria in aqueous two-protein systems. AIChE J 2006. [DOI: 10.1002/aic.690480615] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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12
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Keshavarzi E, Kamalvand M. Prediction of the Small- k Behavior of the Structure Factor ( S( k)) for Rubidium and Cesium via a New Model for the Direct Correlation Function and Evaluation of Some Reported Effective Pair Potentials. J Phys Chem B 2004. [DOI: 10.1021/jp0369802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ezat Keshavarzi
- Department of Chemistry, Isfahan University of Technology, Isfahan, Iran
| | - Mohammad Kamalvand
- Department of Chemistry, Isfahan University of Technology, Isfahan, Iran
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Abstract
Molecular dynamics simulations of a model bilayer in a solvent are used to determine the structure factors S(q) and other correlations at vanishing lateral tension of the system and at positive and negative tensions as well. The role played by curvature in the absence of surface tension, metastability, and phase transitions, and the dependence on the specific area, are discussed. Possible height-height correlation functions S(q) are examined and tested.
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Affiliation(s)
- J Stecki
- Department III, Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warszawa, Poland.
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14
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SOPER AK. Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water. Mol Phys 2001. [DOI: 10.1080/00268970110056889] [Citation(s) in RCA: 203] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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15
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Evans R, Sluckin TJ. The long-wavelength behaviour of the structure factor of liquid alkali metals. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/14/22/009] [Citation(s) in RCA: 76] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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16
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Copestake AP, Evans R. Charge ordering and the structure of ionic liquids: screened Coulomb versus Coulomb interionic potentials. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/15/24/009] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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17
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Nixon JH, Silbert M. On the long-wavelength behaviour of the structure factor of classical fluids and its derivatives: a few general results. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/15/7/001] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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18
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McLaughlin IL, Young WH. Low-angle structure factor calculations for some monatomic liquids away from their triple points. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/15/6/008] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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19
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Bowles RJ, Silbert M. Low-angle structure factor calculations for a model classical fluid. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/17/2/008] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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20
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Jiang J, Prausnitz JM. Molecular Thermodynamics for Protein Precipitation with a Polyelectrolyte. J Phys Chem B 1999. [DOI: 10.1021/jp990455e] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jianwen Jiang
- Chemical Engineering Department, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
| | - John M. Prausnitz
- Chemical Engineering Department, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
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Magli R, Barocchi F, Chieux P, Fontana R. Experimental Determination of the Long-Range Potential of Argon Pairs by Means of Small-Angle Neutron Diffraction. PHYSICAL REVIEW LETTERS 1996; 77:846-848. [PMID: 10062921 DOI: 10.1103/physrevlett.77.846] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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22
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23
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Structure and associated properties of concentrated SiO2 sols in dilute salt solutions. Colloid Polym Sci 1991. [DOI: 10.1007/bf00652537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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25
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Density fluctuations in liquid neon studied by neutron scattering. PHYSICAL REVIEW. A, GENERAL PHYSICS 1985; 32:2396-2412. [PMID: 9896355 DOI: 10.1103/physreva.32.2396] [Citation(s) in RCA: 59] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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26
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Foiles SM, Ashcroft NW, Reatto L. A crossover integral equation for the structure of simple liquids. J Chem Phys 1984. [DOI: 10.1063/1.447225] [Citation(s) in RCA: 90] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Barker JA, Henderson JR. Generalized van der Waals theories and the asymptotic form of the density profile of a liquid–vapor interface. J Chem Phys 1982. [DOI: 10.1063/1.443033] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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