1
|
Xu H, Baggioli M, Keyes T. A fresh look at the vibrational and thermodynamic properties of liquids within the soft potential model. J Chem Phys 2023; 159:154501. [PMID: 37846955 DOI: 10.1063/5.0158089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 10/02/2023] [Indexed: 10/18/2023] Open
Abstract
Contrary to the case of solids and gases, where Debye theory and kinetic theory offer a good description for most of the physical properties, a complete theoretical understanding of the vibrational and thermodynamic properties of liquids is still missing. Liquids exhibit a vibrational density of states (VDOS) which does not obey Debye law, and a heat capacity which decreases monotonically with temperature, rather than growing as in solids. Despite many attempts, a simple, complete and widely accepted theoretical framework able to formally derive the aforementioned properties has not been found yet. Here, we revisit one of the theoretical proposals, and in particular we re-analyze the properties of liquids within the soft-potential model, originally formulated for glasses. We confirm that, at least at a qualitative level, many characteristic properties of liquids can be rationalized within this model. We discuss the validity of several phenomenological expressions proposed in the literature for the density of unstable modes, and in particular for its temperature and frequency dependence. We discuss the role of negative curvature regions and unstable modes as fundamental ingredients to have a linear in frequency VDOS. Finally, we compute the heat capacity within the soft potential model for liquids and we show that it decreases with temperature, in agreement with experimental and simulation data.
Collapse
Affiliation(s)
- Haichen Xu
- University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Matteo Baggioli
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tom Keyes
- Chemistry Department, Boston University, Boston, Massachusetts 02215, USA
| |
Collapse
|
2
|
Trachenko K. Viscosity and diffusion in life processes and tuning of fundamental constants. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:112601. [PMID: 37811635 DOI: 10.1088/1361-6633/acfd3e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 09/26/2023] [Indexed: 10/10/2023]
Abstract
Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics gives new insights into fundamental constants and their tuning. This is based on two observations: first, cellular life and the existence of observers depend on viscosity and diffusion. Second, the lower bound on viscosity and upper bound on diffusion are set by fundamental constants, and I briefly review this result and related recent developments in liquid physics. I will subsequently show that bounds on viscosity, diffusion and the newly introduced fundamental velocity gradient in a biochemical machine can all be varied while keeping the fine-structure constant and the proton-to-electron mass ratio intact. This implies that it is possible to produce heavy elements in stars but have a viscous planet where all liquids have very high viscosity (for example that of tar or higher) and where life may not exist. Knowing the range of bio-friendly viscosity and diffusion, we will be able to calculate the range of fundamental constants which favour cellular life and observers and compare this tuning with that discussed in high-energy physics previously. This invites an inter-disciplinary research between condensed matter physics and life sciences, and I formulate several questions that life science can address. I finish with a conjecture of multiple tuning and an evolutionary mechanism.
Collapse
Affiliation(s)
- K Trachenko
- School of Physical and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| |
Collapse
|
3
|
Zhang W, Douglas JF, Starr FW. What does the instantaneous normal mode spectrum tell us about dynamical heterogeneity in glass-forming fluids? J Chem Phys 2019; 151:184904. [PMID: 31731864 DOI: 10.1063/1.5127821] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum [unstable localized (UL) modes] and find that the particles making the dominant contribution to the participation ratio form clusters that grow upon cooling in a fashion similar to the dynamical heterogeneity in glass-forming fluids, i.e., highly mobile (or immobile) particles form clusters that grow upon cooling; however, a comparison of the UL mode clusters to the mobile and immobile particle clusters indicates that they are distinct entities. We also show that the cluster size provides an alternate method to distinguish localized and delocalized modes, offering a significant practical advantage over the finite-size scaling approach. We examine the trajectories of particles contributing most to the UL modes and find that they have a slightly enhanced mobility compared to the average, and we determine a characteristic time quantifying the persistence time of this excess mobility. This time scale is proportional to the structural relaxation time τα of the fluid, consistent with a prediction by Zwanzig [Phys. Rev. 156, 190 (1967)] for the lifetime of collective excitations in cooled liquids. Evidently, these collective excitations serve to facilitate relaxation but do not actually participate in the motion associated with barrier crossing events governing activated transport. They also serve as a possible concrete realization of the "facilitation" clusters postulated in previous modeling of glass-forming liquids.
Collapse
Affiliation(s)
- Wengang Zhang
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Francis W Starr
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| |
Collapse
|
4
|
Clapa VI, Kottos T, Starr FW. Localization transition of instantaneous normal modes and liquid diffusion. J Chem Phys 2012; 136:144504. [DOI: 10.1063/1.3701564] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
5
|
Zhao Z, Huang W, Richert R, Angell CA. Glass transition and fragility in the simple molecular glassformer CS(2) from CS(2)-S(2)Cl(2) solution studies. J Chem Phys 2010; 132:154505. [PMID: 20423187 DOI: 10.1063/1.3380833] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
With an interest in finding the fragility for a simple, single component, molecular glassformer, we have determined the dielectric relaxation and glass transition behavior for a series of glasses in the CS(2)-S(2)Cl(2) and CS(2)-toluene systems. Crystallization of CS(2) can be completely avoided down to the composition 20 mol% second component, and the fragility proves almost independent of CS(2) content in each system. Since the glass temperature T(g) obtained from both thermal studies and from dielectric relaxation (using T(g,diel)=T(tau=100 s)) is quite linear over the whole composition range in each system, and since relaxation time data for pure CS(2) fall on the same master plot when scaled by the linearly extrapolated T(g) value, we deduce that pure CS(2) has the same high fragility as the binary solutions. The value is m=86, as for ortho-terphenyl (OTP). Based on observations of independent studies for the vibrational density of states (VDoS) (of inherent structures for OTP and instantaneous, at-temperature structures for CS(2)), we attribute the high fragility to an excess vibrational heat capacity (defined by C(p) (vib, excess)=dS(vib, excess)/d ln T) originating in the behavior of the low frequency modes of the VDoS (the boson peak modes). Both low frequency DoS and anharmonicity increase with increasing temperature, augmenting the configurational entropy drive to the top of the system energy landscape. The surprising implication is that fragility is determined in the vibrational, not configurational, manifold of microstates.
Collapse
Affiliation(s)
- Zuofeng Zhao
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287, USA
| | | | | | | |
Collapse
|
6
|
Schulz R, Krishnan M, Daidone I, Smith JC. Instantaneous normal modes and the protein glass transition. Biophys J 2009; 96:476-84. [PMID: 19167298 DOI: 10.1016/j.bpj.2008.10.007] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2008] [Accepted: 10/15/2008] [Indexed: 11/29/2022] Open
Abstract
In the instantaneous normal mode method, normal mode analysis is performed at instantaneous configurations of a condensed-phase system, leading to modes with negative eigenvalues. These negative modes provide a means of characterizing local anharmonicities of the potential energy surface. Here, we apply instantaneous normal mode to analyze temperature-dependent diffusive dynamics in molecular dynamics simulations of a small protein (a scorpion toxin). Those characteristics of the negative modes are determined that correlate with the dynamical (or glass) transition behavior of the protein, as manifested as an increase in the gradient with T of the average atomic mean-square displacement at approximately 220 K. The number of negative eigenvalues shows no transition with temperature. Further, although filtering the negative modes to retain only those with eigenvectors corresponding to double-well potentials does reveal a transition in the hydration water, again, no transition in the protein is seen. However, additional filtering of the protein double-well modes, so as to retain only those that, on energy minimization, escape to different regions of configurational space, finally leads to clear protein dynamical transition behavior. Partial minimization of instantaneous configurations is also found to remove nondiffusive imaginary modes. In summary, examination of the form of negative instantaneous normal modes is shown to furnish a physical picture of local diffusive dynamics accompanying the protein glass transition.
Collapse
Affiliation(s)
- Roland Schulz
- University of Tennessee/ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
| | | | | | | |
Collapse
|
7
|
|
8
|
Chowdhary J, Keyes T. Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:026125. [PMID: 11863605 DOI: 10.1103/physreve.65.026125] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2001] [Revised: 07/12/2001] [Indexed: 05/23/2023]
Abstract
Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.
Collapse
Affiliation(s)
- J Chowdhary
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
| | | |
Collapse
|
9
|
Chisolm ED, Clements BE, Wallace DC. Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:031204. [PMID: 11308639 DOI: 10.1103/physreve.63.031204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2000] [Revised: 10/04/2000] [Indexed: 05/23/2023]
Abstract
We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function Z(t) and diffusion coefficient D. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for Z(t) and D agree remarkably well with molecular dynamics simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.
Collapse
Affiliation(s)
- E D Chisolm
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | |
Collapse
|
10
|
Keyes T. Entropy, dynamics, and instantaneous normal modes in a random energy model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:7905-8. [PMID: 11138073 DOI: 10.1103/physreve.62.7905] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2000] [Indexed: 11/07/2022]
Abstract
It is shown that the fraction f(u) of imaginary-frequency instantaneous normal modes (INM) may be defined and calculated in a random energy model (REM) of liquids. The configurational entropy S(c) and the averaged hopping rate among the states, R, are also obtained and related to f(u) with the results R approximately f(u) and S(c)=a+b ln(f(u)). The proportionality between R and f(u) is the basis of existing INM theories of diffusion, so the REM further confirms their validity. A link to S(c) opens new avenues for introducing INM into dynamical theories. Liquid states are usually defined by assigning a configuration to the minimum to which it will drain, but the REM naturally treats saddle barriers on the same footing as minima, which may be a better mapping of the continuum of configurations to discrete states. Requirements for a detailed REM description of liquids are discussed.
Collapse
Affiliation(s)
- T Keyes
- Chemistry Department, Boston University, Boston, Massachusetts 02215, USA
| |
Collapse
|
11
|
Li WX, Keyes T. Instantaneous normal mode theory of diffusion and the potential energy landscape: Application to supercooled liquid CS2. J Chem Phys 1999. [DOI: 10.1063/1.479810] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
12
|
Li WX, Keyes T. Temperature and density dependence of self-diffusion in supercooled liquid CS2. J Chem Phys 1999. [DOI: 10.1063/1.479274] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
13
|
Gezelter JD, Rabani E, Berne BJ. Calculating the hopping rate for diffusion in molecular liquids: CS2. J Chem Phys 1999. [DOI: 10.1063/1.478211] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
14
|
Keyes T, Li WX, Zurcher U. Comment on a critique of the instantaneous normal mode (INM) approach to diffusion [J. Chem. Phys. 107, 4618 (1997)]. J Chem Phys 1998. [DOI: 10.1063/1.477080] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
15
|
Gezelter JD, Rabani E, Berne BJ. Response to “Comment on a critique of the instantaneous normal mode (INM) approach to diffusion” [J. Chem. Phys. 109, 4693 (1998)]. J Chem Phys 1998. [DOI: 10.1063/1.477081] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
David EF, Stratt RM. The anharmonic features of the short-time dynamics of fluids: The time evolution and mixing of instantaneous normal modes. J Chem Phys 1998. [DOI: 10.1063/1.476690] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|