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Okita K, Kasahara K, Matubayasi N. Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics. J Chem Phys 2022; 157:244505. [PMID: 36586971 DOI: 10.1063/5.0125432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.
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Affiliation(s)
- Kazuya Okita
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kento Kasahara
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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Körber T, Pötzschner B, Krohn F, Rössler EA. Reorientational dynamics in highly asymmetric binary low-molecular mixtures-A quantitative comparison of dielectric and NMR spectroscopy results. J Chem Phys 2021; 155:024504. [PMID: 34266265 DOI: 10.1063/5.0056838] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Previously, we scrutinized the dielectric spectra of a binary glass former made by a low-molecular high-Tg component 2-(m-tertbutylphenyl)-2'-tertbutyl-9,9'-spirobi[9H]fluorene (m-TPTS; Tg = 350 K) and low-Tg tripropyl phosphate (TPP; Tg = 134 K) [Körber et al., Phys. Chem. Chem. Phys. 23, 7200 (2021)]. Here, we analyze nuclear magnetic resonance (NMR) spectra and stimulated echo decays of deuterated m-TPTS-d4 (2H) and TPP (31P) and attempt to understand the dielectric spectra in terms of component specific dynamics. The high-Tg component (α1) shows relaxation similar to that of neat systems, yet with some broadening upon mixing. This correlates with high-frequency broadening of the dielectric spectra. The low-Tg component (α2) exhibits highly stretched relaxations and strong dynamic heterogeneities indicated by "two-phase" spectra, reflecting varying fractions of fast and slow liquid-like reorienting molecules. Missing for the high-Tg component, such two-phase spectra are identified down to wTPP = 0.04, indicating that isotropic reorientation prevails in the rigid high-Tg matrix stretching from close to Tg TPP to Tg1 wTPP. This correlates with low-frequency broadening of the dielectric spectra. Two Tg values are defined: Tg1 (wTPP) displays a plasticizer effect, whereas Tg2 (wTPP) passes through a maximum, signaling extreme separation of the component dynamics at low wTPP. We suggest understanding the latter counter-intuitive feature by referring to a crossover from "single glass" to "double glass" scenario revealed by recent MD simulations. Analyses reveal that a second population of TPP molecules exists, which is associated with the dynamics of the high-Tg component. However, the fractions are lower than suggested by the dielectric spectra. We discuss this discrepancy considering the role of collective dynamics probed by dielectric but not by NMR spectroscopy.
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Affiliation(s)
- Thomas Körber
- Department of Inorganic Chemistry III and Northern Bavarian NMR Centre, University of Bayreuth, 95440 Bayreuth, Germany
| | - Björn Pötzschner
- Department of Inorganic Chemistry III and Northern Bavarian NMR Centre, University of Bayreuth, 95440 Bayreuth, Germany
| | - Felix Krohn
- Department of Macromolecular Chemistry and Bavarian Polymer Institute, University of Bayreuth, 95440 Bayreuth, Germany
| | - Ernst A Rössler
- Department of Inorganic Chemistry III and Northern Bavarian NMR Centre, University of Bayreuth, 95440 Bayreuth, Germany
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Kasahara K, Sato H. Dynamics theory for molecular liquids based on an interaction site model. Phys Chem Chem Phys 2017; 19:27917-27929. [DOI: 10.1039/c7cp05423h] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.
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Affiliation(s)
- Kento Kasahara
- Department of Molecular Engineering
- Kyoto University
- Japan
| | - Hirofumi Sato
- Department of Molecular Engineering and Elements Strategy for Catalysts and Batteries (ESICB)
- Kyoto University
- Japan
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Elizondo-Aguilera LF, Zubieta Rico PF, Ruiz-Estrada H, Alarcón-Waess O. Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052301. [PMID: 25493790 DOI: 10.1103/physreve.90.052301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2013] [Indexed: 06/04/2023]
Abstract
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
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Affiliation(s)
- L F Elizondo-Aguilera
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, PUE, México
| | - P F Zubieta Rico
- Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | - H Ruiz-Estrada
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, PUE, México
| | - O Alarcón-Waess
- Departamento de Actuaría, Física y Matemáticas, Universidad de las Américas Puebla, Sta Catarina Mártir, C.P. 72810, Puebla, México
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Rovigatti L, Kob W, Sciortino F. The vibrational density of states of a disordered gel model. J Chem Phys 2011; 135:104502. [DOI: 10.1063/1.3626869] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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De Gaetani L, Prampolini G, Tani A. Subdiffusive dynamics of a liquid crystal in the isotropic phase. J Chem Phys 2008; 128:194501. [DOI: 10.1063/1.2916681] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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Rex M, Wensink HH, Löwen H. Dynamical density functional theory for anisotropic colloidal particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021403. [PMID: 17930035 DOI: 10.1103/physreve.76.021403] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2007] [Indexed: 05/25/2023]
Abstract
We generalize the formalism of dynamical density functional theory for translational Brownian dynamics toward that of anisotropic colloidal particles which perform both translational and rotational Brownian motion. Using a mean-field approximation for the density functional and a Gaussian-segment model for the rod interaction, the dynamical density functional theory is then applied to a concentrated rod suspension in a confined slab geometry made by two parallel soft walls. The walls are either expanded or compressed and the relaxation behavior is investigated for an equilibrated starting configuration. We find distinctly different orientational ordering during expansion and compression. During expansion we observe preferential parallel ordering of the rods relative to the wall while during compression there is homeotropic ordering perpendicular to the wall. We find a nonexponential relaxation behavior in time. Furthermore, an external field which aligns the rods perpendicular to the walls is turned on or switched off and similar differences in the relaxational dynamics are found. Comparing the theoretical predictions to Brownian dynamics computer simulation data, we find good agreement.
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Affiliation(s)
- M Rex
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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Moreno AJ, Chong SH, Kob W, Sciortino F. Dynamic arrest in a liquid of symmetric dumbbells: Reorientational hopping for small molecular elongations. J Chem Phys 2005; 123:204505. [PMID: 16351279 DOI: 10.1063/1.2085030] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.
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Affiliation(s)
- Angel J Moreno
- Dipartimento di Fisica and Istituto Nazionale per la Fisica della Materia (INFM)-Centri di Ricerca e Sviluppo (CRS)-Statistical Mechanics and Complexity (SMC), Universitá di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy.
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Veglio N, Bermejo FJ, Pardo LC, Tamarit JL, Cuello GJ. Direct experimental assessment of the strength of orientational correlations in polar liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:031502. [PMID: 16241439 DOI: 10.1103/physreve.72.031502] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2004] [Revised: 01/26/2005] [Indexed: 05/05/2023]
Abstract
The strength of molecular orientational correlations in polar liquids is assessed by means of comparison of the diffuse scattering patterns of a liquid composed by molecules devoid of permanent electric dipole but having a weak quadrupole moment and those for a liquid composed by permanent molecular dipoles. The extent of orientational correlations within the liquid phases is in both cases assessed by comparison of the liquid radial distributions to those present in the rotator-phase (plastic) crystal phases of both compounds. For such disordered-crystal phases, information concerning orientational correlations is directly derived from the experimental scattering patterns by means of analysis of the diffuse scattering background present beneath the Bragg peaks. The results show that rather than long-ranged, orientational correlations in polar or polarizable liquids are confined within distances comprising the second coordination sphere.
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Affiliation(s)
- N Veglio
- CSIC-Department of Electricity and Electronics, University of the Basque Country, P.O. Box 664, 48080 Bilbao, Spain
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Chong SH, Sciortino F. Structural relaxation in supercooled orthoterphenyl. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:051202. [PMID: 15244813 DOI: 10.1103/physreve.69.051202] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2003] [Indexed: 05/24/2023]
Abstract
We report molecular-dynamics simulation results performed for a model of molecular liquid orthoterphenyl in supercooled states, which we then compare with both experimental data and mode-coupling-theory (MCT) predictions, aiming at a better understanding of structural relaxation in orthoterphenyl. We pay special attention to the wave number dependence of the collective dynamics. It is shown that the simulation results for the model share many features with experimental data for real system, and that MCT captures the simulation results at the semiquantitative level except for intermediate wave numbers connected to the overall size of the molecule. Theoretical results at the intermediate wave number region are found to be improved by taking into account the spatial correlation of the molecule's geometrical center. This supports the idea that unusual dynamical properties at the intermediate wave numbers, reported previously in simulation studies for the model and discernible in coherent neutron-scattering experimental data, are basically due to the coupling of the rotational motion to the geometrical-center dynamics. However, there still remain qualitative as well as quantitative discrepancies between theoretical prediction and corresponding simulation results at the intermediate wave numbers, which call for further theoretical investigation.
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Affiliation(s)
- S-H Chong
- Dipartimento di Fisica and Istituto Nazionale per la Fisica della Materia, Center for Statistical Mechanics and Complexity, Università di Roma "La Sapienza," Piazzale Aldo Moro 2, I-00185, Roma, Italy
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Yamaguchi T, Chong SH, Hirata F. Theoretical study of the molecular motion of liquid water under high pressure. J Chem Phys 2003. [DOI: 10.1063/1.1578624] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yamaguchi T, Hirata F. Interaction-site model description of the reorientational relaxation of molecular liquids: Incorporation of the interaxial coupling into the site–site generalized Langevin/mode-coupling theory. J Chem Phys 2002. [DOI: 10.1063/1.1488586] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chong SH, Götze W. Structural relaxation in a system of dumbbell molecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:051201. [PMID: 12059539 DOI: 10.1103/physreve.65.051201] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2001] [Indexed: 05/23/2023]
Abstract
The interaction-site-density-fluctuation correlators, the dipole-relaxation functions, and the mean-squared displacements of a system of symmetric dumbbells of fused hard spheres are calculated for two representative elongations of the molecules within the mode-coupling theory for the evolution of glassy dynamics. For large elongations, universal relaxation laws for states near the glass transition are valid for parameters and time intervals similar to the ones found for the hard-sphere system. Rotation-translation coupling leads to an enlarged crossover interval for the mean-squared displacement of the constituent atoms between the end of the von Schweidler regime and the beginning of the diffusion process. For small elongations, the superposition principle for the reorientational alpha process is violated for parameters and time intervals of interest for data analysis, and there is a strong breaking of the coupling of the alpha-relaxation scale for the diffusion process with that for representative density fluctuations and for dipole reorientations.
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Affiliation(s)
- S-H Chong
- Physik-Department, Technische Universität München, 85747 Garching, Germany
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Chong SH, Götze W. Idealized glass transitions for a system of dumbbell molecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:041503. [PMID: 12005825 DOI: 10.1103/physreve.65.041503] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2001] [Indexed: 05/23/2023]
Abstract
The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule's constituent atoms as the basic structure variables. The theory is applied to calculate the liquid-glass phase diagram and the form factors for the arrested structure of a system of symmetric dumbbells of fused hard spheres. The static structure factors, which enter the equations of motion as input, are calculated as function of the packing fraction phi and the molecule's elongation zeta within the reference-interaction-site-model and Percus-Yevick theories. The critical packing fraction phi(c) for the glass transition is obtained as nonmonotone function of zeta with a maximum near zeta=0.43. A transition line is calculated separating a small-zeta-glass phase with ergodic dipole motion from a large-zeta-glass phase where also the reorientational motion is arrested. The Debye-Waller factors at the transition are found to be somewhat larger for sufficiently elongated systems than those for the simple hard-sphere system, but the wave-number dependence of the glass-form factors is quite similar. The dipole reorientations for zeta> or =0.6 are arrested as strongly as density fluctuations with wave vectors at the position of the first sharp diffraction peak.
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Affiliation(s)
- S-H Chong
- Physik Department, Technische Universität München, 85747 Garching, Germany
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