Atomic test of the Stokes-Einstein law. II. Diffusion of Xe through liquid hydrocarbons

Pollack, Gerald L.; Enyeart, John J.

doi:10.1103/physreva.31.980

Cited by 111 publications

(59 citation statements)

References 22 publications

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“…Such relations or close variants were originally introduced for tracer diffusion in various stable liquids (55,56) and for diffusion in supercooled ortho-terphenyl (23,24). In the latter case, the FSE exponent exhibits a crossover from ζ = −1 at high temperature to ζ = −0.79 at low temperature.…”

Section: Resultsmentioning

confidence: 99%

Viscosity of deeply supercooled water and its coupling to molecular diffusion

Dehaoui

Issenmann

Caupin

2015

Proc. Natl. Acad. Sci. U.S.A.

196

213

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The viscosity of a liquid measures its resistance to flow, with consequences for hydraulic machinery, locomotion of microorganisms, and flow of blood in vessels and sap in trees. Viscosity increases dramatically upon cooling, until dynamical arrest when a glassy state is reached. Water is a notoriously poor glassformer, and the supercooled liquid crystallizes easily, making the measurement of its viscosity a challenging task. Here we report viscosity of water supercooled close to the limit of homogeneous crystallization. Our values contradict earlier data. A single power law reproduces the 50-fold variation of viscosity up to the boiling point. Our results allow us to test the Stokes-Einstein and Stokes-Einstein-Debye relations that link viscosity, a macroscopic property, to the molecular translational and rotational diffusion, respectively. In molecular glassformers or liquid metals, the violation of the Stokes-Einstein relation signals the onset of spatially heterogeneous dynamics and collective motions. Although the viscosity of water strongly decouples from translational motion, a scaling with rotational motion remains, similar to canonical glassformers.supercooled water | viscosity | Stokes-Einstein relations W ater, considered as a potential glassformer, has been a longlasting topic of intense activity. Its possible liquid-glass transition was reported 50 years ago to be in the vicinity of 140 K (1, 2). However, ice nucleation hinders the access to this transition from the liquid side. Bypassing crystallization requires hyperquenching the liquid at tremendous cooling rates, ca. 10 7 K · s −1 (3). As a consequence, many questions about supercooled and glassy water and its glass-liquid transition remain open (4-7).As an example, crystallization of water is accompanied by one of the largest known relative changes in sound velocity, which has been attributed to the relaxation effects of the hydrogen bond network (8, 9). Indeed, whereas the sound velocity is around 1,400 m · s −1 in liquid water at 273 K, it reaches around 3,300 m · s −1 in ice at 273 K and a similar value in the known amorphous phases of ice at 80 K (10). Such a large jump is usually the signature of a strong glass, i.e., one in which relaxation times or viscosity follow an Arrhenius law upon cooling. However, pioneering measurements on bulk supercooled water by NMR (11) and quasi-elastic neutron scattering (12), as well as recent ones by optical Kerr effect (8, 9), reveal a large super-Arrhenius behavior between 340 and 240 K, similar to what is observed in fragile glassformers (13,14). The temperature dependence of the relaxation time is well described by a power law (8, 9), as expected from mode-coupling theory (15, 16), which usually applies well to liquids with a small change of sound velocity upon vitrification. Based on these and other observations, it has been hypothesized that supercooled water experiences a fragile-tostrong transition (17). This idea has motivated experimental efforts to measure dynamic properties of supercooled wate...

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Section: Resultsmentioning

confidence: 99%

Viscosity of deeply supercooled water and its coupling to molecular diffusion

Dehaoui

Issenmann

Caupin

2015

Proc. Natl. Acad. Sci. U.S.A.

196

213

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“…Except for macromolecules, however, numerous experimental studies 3,[57][58][59][60][61][62][63][64][65][66] have shown that tracer diffusivity is inversely proportional to a fractional power of the viscosity of the solvent instead. This fractional power dependence of viscosity on diffusion is often referred to in the literature as the fractional Stokes-Einstein (FSE) relation, (D 12 /T) ∝ η −t , where t is known to be normally less than unity and generally around 2/3.…”

Section: B Solvent Dependencementioning

confidence: 99%

Diffusion of aromatic compounds in nonaqueous solvents: A study of solute, solvent, and temperature dependences

Chan

Tang

2013

The Journal of Chemical Physics

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Tracer diffusivities (limiting mutual diffusion coefficients) of nonassociated aromatic compounds in n-hexane and cyclohexane have been measured at 298.2 K by Taylor's dispersion method. These new data, together with other diffusivities of nonassociated pseudoplanar solutes reported in the literature, are used to determine the separate effects of solute and solvent on tracer diffusion. The data show that for a given pseudoplanar solute diffusing in different solvents at 298.2 K, the tracer diffusivity is dependent not only on the fractional viscosity of the solvent but also on a function of the solvent's molar density, molecular mass, and free volume fraction. For different pseudoplanar aromatic solutes diffusing in a particular solvent at a constant temperature, there is a linear relationship between the reciprocal of the tracer diffusivity and the molecular volume of the solutes. The results are discussed in respect to relevant theories and experimental studies in the literature. An idealized relation, developed on the basis of the Einstein equation by incorporating the newly found solute and solvent dependences, is capable of describing a total of 176 diffusivities of nonassociated pseudoplanar solutes in various solvents at different temperatures to within an average error of ±2.8%. © 2013 AIP Publishing LLC. [http://dx

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“…They examined the data of Pollack and Enyeart 14 for Xe ͑131 g/mol͒ diffusion in alkanes ͑72.15-226.44 g/mol͒ and argued that while the data for a small solute diffusing in a solvent of larger molecules fit an equation of the form of viscosity to some power very well, the viscosity itself is also related to other physical parameters, which might affect diffusion.…”

Section: Diffusion Of Small Solutesmentioning

confidence: 99%

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

Duncan²,

Momaya³

et al. 2010

The Journal of Chemical Physics

111

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While the Stokes-Einstein ͑SE͒ equation predicts that the diffusion coefficient of a solute will be inversely proportional to the viscosity of the solvent, this relation is commonly known to fail for solutes, which are the same size or smaller than the solvent. Multiple researchers have reported that for small solutes, the diffusion coefficient is inversely proportional to the viscosity to a fractional power, and that solutes actually diffuse faster than SE predicts. For other solvent systems, attractive solute-solvent interactions, such as hydrogen bonding, are known to retard the diffusion of a solute. Some researchers have interpreted the slower diffusion due to hydrogen bonding as resulting from the effective diffusion of a larger complex of a solute and solvent molecules. We have developed and used a novel micropipette technique, which can form and hold a single microdroplet of water while it dissolves in a diffusion controlled environment into the solvent. This method has been used to examine the diffusion of water in both n-alkanes and n-alcohols. It was found that the polar solute water, diffusing in a solvent with which it cannot hydrogen bond, closely resembles small nonpolar solutes such as xenon and krypton diffusing in n-alkanes, with diffusion coefficients ranging from 12.5ϫ 10 −5 cm 2 / s for water in n-pentane to 1.15ϫ 10 −5 cm 2 / s for water in hexadecane. Diffusion coefficients were found to be inversely proportional to viscosity to a fractional power, and diffusion coefficients were faster than SE predicts. For water diffusing in a solvent ͑n-alcohols͒ with which it can hydrogen bond, diffusion coefficient values ranged from 1.75ϫ 10 −5 cm 2 / s in n-methanol to 0.364ϫ 10 −5 cm 2 / s in n-octanol, and diffusion was slower than an alkane of corresponding viscosity. We find no evidence for solute-solvent complex diffusion. Rather, it is possible that the small solute water may be retarded by relatively longer residence times ͑compared to non-H-bonding solvents͒ as it moves through the liquid.

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Atomic test of the Stokes-Einstein law. II. Diffusion of Xe through liquid hydrocarbons

Cited by 111 publications

References 22 publications

Viscosity of deeply supercooled water and its coupling to molecular diffusion

Viscosity of deeply supercooled water and its coupling to molecular diffusion

Diffusion of aromatic compounds in nonaqueous solvents: A study of solute, solvent, and temperature dependences

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

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