Imaginary Part of the Surface Tension of Water

Xiong, Xiaohui; Chen, Lan; Zuo, Wenlong; Li, Longfei; Yang, Yukun; Pang, Zhiyong; Zhang, Jinxiu

doi:10.1088/0256-307x/31/7/076801

Cited by 7 publications

(18 citation statements)

References 11 publications

(10 reference statements)

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“…1The term

{normalσ}_{L V}^{*}

denotes the complex surface tension,

{normalσ}_{L V}

the real part and

{σ^{″}}_{L V} i

the imaginary part. The complex surface tension of water was determined at 26° C to σ* = 73 + 17i mN/m . Der Term

{normalσ}_{L V}^{*}

bezeichnet die komplexe Oberflächenspanung,

{normalσ}_{L V}

den reellen und

{σ^{″}}_{L V} i

den imaginären Teil. Die komplexe Oberflächenspannung des Wassers wurde bei 26 °C auf σ* = 73 + 17i mN/m bestimmt .…”

Section: Resultsunclassified

“…Since higher values of

{σ^{″}}_{L {normalV}_{normalℂ}}

have not yet been described, only the range of

{σ^{″}}_{L {normalV}_{normalℂ}}

= 0 to 17 mN/m is treated, Fig. (= imaginary surface tension restriction) . If the limitation of a maximal imaginary surface tension part of 17 mN/m is lifted, then all imaginary contact angles could theoretically be calculated.…”

Section: Resultsmentioning

confidence: 99%

“…Recently Xiong et al reported that the surface tension of water is also a complex quantity (

{normalσ}_{L V}^{*}

) consisting of a real and an imaginary part :

{normalσ}_{L V}^{*} = {normalσ}_{L V} + {σ^{″}}_{L V} i

where

{normalσ}_{L V}^{*}

denotes the complex surface tension

{normalσ}_{L V}

the real part (assumed as ideal) and

{normalσ}_{L V}^{''}

the imaginary part (assumed as non‐ideal) together with the imaginary unit i. The complex surface tension was reported to have the value

{normalσ}_{L V}^{*}

= 73 + 17i mN/m at 26 °C . It is however unclear, if the imaginary component of the surface tension of water is also a constant or possibly a variable.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…Recent evidence indicates that this assumption is false. Xiong et al 2014 have reported that the surface tension of water is a complex quantity consisting of a real and an imaginary part. In this paper it is demonstrated that imaginary contact angles can also originate after incorporation of a complex surface tension of water into the Young and Wilhelmy equations, thus confirming the concept of complex contact angles also from the side of the non-ideality of the fluid.…”

mentioning

confidence: 99%

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On the origin of the imaginary part of complex contact angles

Jennissen

2015

Materialwissenschaft Werkst

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Complex contact angles of water on rough surfaces have been described to consist of a real part for ideal wetting and of an imaginary part for non‐ideal wetting (Jennissen, 2011, 2014). The concept of imaginary contact angles has accordingly been successfully applied to the analysis of hyperhydrophilic rough surfaces. The origin of the imaginary part of complex contact angles has hitherto been attributed to the non‐ideality of surfaces (e.g. surface roughness) but is otherwise unclear. It is generally accepted that the Young equation is valid, if the criteria ideal surface and thermodynamic equilibrium are fulfilled. What has been overlooked is a third criterion, namely, if an ideal fluid also exists. This criterion, has never been seriously questioned, but is assumed to be fulfilled. Recent evidence indicates that this assumption is false. Xiong et al. 2014 have reported that the surface tension of water is a complex quantity consisting of a real and an imaginary part. In this paper it is demonstrated that imaginary contact angles can also originate after incorporation of a complex surface tension of water into the Young and Wilhelmy equations, thus confirming the concept of complex contact angles also from the side of the non‐ideality of the fluid.

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“…1The term

{normalσ}_{L V}^{*}

denotes the complex surface tension,

{normalσ}_{L V}

the real part and

{σ^{″}}_{L V} i

the imaginary part. The complex surface tension of water was determined at 26° C to σ* = 73 + 17i mN/m . Der Term

{normalσ}_{L V}^{*}

bezeichnet die komplexe Oberflächenspanung,

{normalσ}_{L V}

den reellen und

{σ^{″}}_{L V} i

den imaginären Teil. Die komplexe Oberflächenspannung des Wassers wurde bei 26 °C auf σ* = 73 + 17i mN/m bestimmt .…”

Section: Resultsunclassified

“…Since higher values of

{σ^{″}}_{L {normalV}_{normalℂ}}

have not yet been described, only the range of

{σ^{″}}_{L {normalV}_{normalℂ}}

Section: Resultsmentioning

confidence: 99%

“…Recently Xiong et al reported that the surface tension of water is also a complex quantity (

{normalσ}_{L V}^{*}

) consisting of a real and an imaginary part :

{normalσ}_{L V}^{*} = {normalσ}_{L V} + {σ^{″}}_{L V} i

where

{normalσ}_{L V}^{*}

denotes the complex surface tension

{normalσ}_{L V}

the real part (assumed as ideal) and

{normalσ}_{L V}^{''}

the imaginary part (assumed as non‐ideal) together with the imaginary unit i. The complex surface tension was reported to have the value

{normalσ}_{L V}^{*}

= 73 + 17i mN/m at 26 °C . It is however unclear, if the imaginary component of the surface tension of water is also a constant or possibly a variable.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

mentioning

confidence: 99%

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On the origin of the imaginary part of complex contact angles

Jennissen

2015

Materialwissenschaft Werkst

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“…9,10,19,20 Our previous work notes that the surface tension should be represented by a complex number, 16 i.e., σ* = σ + iσ′, instead of a real number, making it necessary to reexamine the attenuation of a capillary wave. Following a procedure similar to the one above, we assume that the propagating capillary wave is described by…”

Section: Theorymentioning

confidence: 99%

Role of Complex Surface Tension in the Dispersion Relation of a Capillary Wave

Chen

Zuo

et al. 2014

J. Phys. Chem. C

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We discuss theoretically the effect of complex surface tension on the dispersion relation of a capillary wave, and we deduce an analytical expression for the attenuation of a capillary wave due to the imaginary part of the complex surface tension. We make use of our recently developed apparent energy dissipation spectroscopy to measure the attenuation of a propagating capillary wave at an air− water interface via a microrheometer based on an atomic force microscope. We show that the revised theoretical expression for the attenuation of a capillary wave can satisfactorily explain the abnormal attenuation of such a wave, which stems from both the apparent energy dissipation spectrum and optical scattering, and we obtain the same value for the imaginary part of the surface tension of water. ■ INTRODUCTIONThe term "capillary wave" usually refers to the mechanical wave at an air−liquid or a liquid−liquid interface 1−3 and is an important way to reveal the properties of the interface, such as the viscoelasticity of a Langmuir−Blodgett film 4,5 or another absorbed molecular layer. 6,7 The attenuation of a capillary wave is described by the expression 2,8where ν is the dynamic viscosity of the liquid and q is the surface wave vector. The attenuation of a capillary wave comes entirely from the viscosity of the fluid. The viscosity of the air− liquid interface is unclear. Goodrich 9 suggested that the anisotropic momentum transport, which is involved in the molecularly diffuse interfacial region, will lead to surface viscosity effects. Earnshaw 10 developed this theory and showed that the surface viscosity causes the imaginary part of surface tension, i.e., the energy dissipation. However, careful experiments by optical techniques show that the surface viscosity is zero or very small for the surfaces of many air−liquid interfaces. 11−13 We noticed that in physics, the surface viscosity and the imaginary part of the surface tension are two different concepts. Both of these concepts can cause damping of the capillary wave. The difference is that whereas the surface viscosity is related to the velocity, the surface tension is related to the displacement. In other words, the surface viscosity is frequency-dependent, and the surface tension is frequency-independent. To date, finding experimental evidence of the imaginary part of the surface tension is still an open problem.The atomic force microscope (AFM) was invented for detection on the submicrometer to subnanometer scale and is an appropriate instrument for probing capillary waves. Recently, a microrheometer developed by us, which is based on the atomic force microscope, has been proven to be an instrument useful for exploring air−liquid interfaces. 14 By using this microrheometer and its corresponding analysis method of apparent dissipation factor frequency spectroscopy (ADFFS), 15 we can obtain those vibrational modes of a complex system that are difficult to detect by means such as X-ray scattering 7 and optical techniques. 2 Compared to these techniques, the advantage...

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Wonders of Water

Sun

2016

Springer Series in Chemical Physics

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Imaginary Part of the Surface Tension of Water

Cited by 7 publications

References 11 publications

On the origin of the imaginary part of complex contact angles

On the origin of the imaginary part of complex contact angles

Role of Complex Surface Tension in the Dispersion Relation of a Capillary Wave

Wonders of Water

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