Thermodynamic Properties of a Rigid-Sphere Fluid

Carnahan, Norman F.; Starling, K.E.

doi:10.1063/1.1674033

Cited by 218 publications

(104 citation statements)

References 9 publications

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“…The fluidicity problems, including the singularity in entropy at zero frequency due to diffusion and the anharmonicities at lowfrequency regime, are resolved by decomposing the liquid S(υ) into a solid S s (υ) and a gas S g (υ) component, and treating each component with appropriate statistics. Lin et al have shown 40 The details of how to decompose S(υ) into S s (υ) and S g (υ) can be found in ref 35. Also note that the entropic contribution from molecular rotations is assumed to be a constant value of 44.58 J/(mol K) (3.2 kcal/mol in terms of TS at 300 K) as previous studies have shown that the rotational entropy in solution can be well estimated from the value in the ideal gas condition.…”

Section: Change Of Water Translation and Rotation Dynamics Under Diffmentioning

confidence: 99%

Dynamics and Thermodynamics of Water in PAMAM Dendrimers at Subnanosecond Time Scales

2005

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Atomistic molecular dynamics simulations are used to study generation 5 polyamidoamine (PAMAM) dendrimers immersed in a bath of water. We interpret the results in terms of three classes of water: buried water well inside of the dendrimer surface, surface water associated with the dendrimer-water interface, and bulk water well outside of the dendrimer. We studied the dynamic and thermodynamic properties of the water at three pH values: high pH with none of the primary or tertiary amines protonated, intermediate pH with only the primary amines protonated, and low pH with all amines protonated. For all pH values we find that both buried and surface water exhibit two relaxation times: a fast relaxation (∼1 ps) corresponding to the libration motion of the water and a slow (∼20 ps) diffusional component related to the escaping of water from one domain to another. In contrast for bulk water the fast relaxation is ∼0.4 ps while the slow relaxation is ∼14 ps. These results are similar to those found in biological systems, where the fast relaxation is found to be ∼1 ps while the slow relaxation ranges from 20 to 1000 ps. We used the 2PT MD method to extract the vibrational (power) spectrum and found substantial differences for the three classes of water. The translational diffusion coefficient for buried water is 11-33% (depending on pH) of the bulk value while the surface water is about 80%. The change in rotational diffusion is quite similar: 21-45% of the bulk value for buried water and 80% for surface water. This shows that translational and rotational dynamics of water are affected by the PAMAM-water interactions as well as due to the confinement in the interior of the dendrimer. We find that the reduction of translational or rotational diffusion is accompanied by a blue shift of the corresponding libration motions (∼10 cm -1 for translation, ∼35 cm -1 for rotation), indicating higher local force constants for these motions. These effects are most pronounced for the lowest pH, probably because of the increased rigidity caused by the internal charges. From the vibrational density of states we also calculate the enthalpies and entropies of the various waters. We find that water molecules are enthalpically favored near the PAMAM dendrimer: energy for surface water is ∼0.1 kcal/mol lower to that in the bulk, and ∼0.5-0.9 kcal/mol lower for buried water. In contrast, we find that both the buried and surface water are entropically unfavored: buried water is 0.9-2.2 kcal/mol lower than the bulk while the surface water is 0.1-0.2 kcal/mol lower. The net result is a thermodynamically unfavored state of the water surrounding the PAMAM dendrimer: 0.4-1.3 kcal/mol higher for buried water and 0.1-0.2 kcal/mol for surface water. This excess free energy of the surface and buried waters is released when the PAMAM dendrimer binds to DNA or metal ions, providing an extra driving force.

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Section: Change Of Water Translation and Rotation Dynamics Under Diffmentioning

confidence: 99%

Dynamics and Thermodynamics of Water in PAMAM Dendrimers at Subnanosecond Time Scales

2005

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“…where z is the compressibility, which can be obtained from the accurate Carnahan-Starling equation of state 9 for hard spheres z͑ y ͒ϭ 1ϩyϩy 2 Ϫy 3 ͑ 1Ϫy ͒ 3 ͑30͒…”

Section: ͑24͒mentioning

confidence: 99%

The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids

Lin¹,

Blanco²,

Goddard³

2003

The Journal of Chemical Physics

472

683

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We propose a general approach for determining the entropy and free energy of complex systems as a function of temperature and pressure. In this method the Fourier transform of the velocity autocorrelation function, obtained from a short ͑20 ps͒ molecular dynamics trajectory is used to obtain the vibrational density of states ͑DoS͒ which is then used to calculate the thermodynamic properties by applying quantum statistics assuming each mode is a harmonic oscillator. This approach is quite accurate for solids, but leads to significant errors for liquids where the DoS at zero frequency, S(0), remains finite. We show that this problem can be resolved for liquids by using a two phase model consisting of a solid phase for which the DoS goes to zero smoothly at zero frequency, as in a Debye solid; and a gas phase ͑highly fluidic͒, described as a gas of hard spheres. The gas phase component has a DoS that decreases monotonically from S(0) and can be characterized with two parameters: S(0) and 3N g , the total number of gas phase modes ͓3N g →0 for a solid and 3N g →3(NϪ1) for temperatures and pressures for which the system is a gas͔. To validate this two phase model for the thermodynamics of liquids, we applied it to pure Lennard-Jones systems for a range of reduced temperatures from 0.9 to 1.8 and reduced densities from 0.05 to 1.10. These conditions cover the gas, liquid, crystal, metastable, and unstable states in the phase diagram. Our results compare quite well with accurate Monte Carlo calculations of the phase diagram for classical Lennard-Jones particles throughout the entire phase diagram. Thus the two-phase thermodynamics approach provides an efficient means for extracting thermodynamic properties of liquids ͑and gases and solids͒.

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“…To approximate the excess free energy density f exc ͑n͑r͒͒ per unit volume of the reference system of density n, CarnahanStarling's formula 19 …”

Section: ͑13͒mentioning

confidence: 99%

Ion-induced nucleation: A density functional approach

Kusaka

Wang

Seinfeld

1995

The Journal of Chemical Physics

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Density functional theory is applied to ion-induced nucleation of dipolar molecules. The predicted reversible work shows a sign preference, resulting in a difference in the nucleation rate by a factor of 10-10 2 , for realistic values of model parameters. The sign effect is found to decrease systematically as the supersaturation is increased. The asymmetry of a molecule is shown to be directly responsible for the sign preference in ion-induced nucleation.

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Thermodynamic Properties of a Rigid-Sphere Fluid

Abstract: The excess thermodynamic properties for a rigid-sphere fluid have been calculated with an accurate equation of state. Values of (PV / NkT), and (H − H°) / RT, (S − S°) / R, (G − G°) / RT, and (f / P) are reported for a wide range of fluid density.

Cited by 218 publications

References 9 publications

Dynamics and Thermodynamics of Water in PAMAM Dendrimers at Subnanosecond Time Scales

Dynamics and Thermodynamics of Water in PAMAM Dendrimers at Subnanosecond Time Scales

The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids

Ion-induced nucleation: A density functional approach

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