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Dynamic Anomalies in Confined Supercooled Water and Bulk Fluids

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Book cover Modern Problems of Molecular Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 197))

Abstract

This review paper is aimed at studying the problems as follows: (1) the Widom line and its analogues in supercooled and supercritical regions; (2) effects of dimensional crossover (DC) on the critical exponents, effective spatial d eff and fractal d fr dimensionalities; (3) anomalous behavior of the diffusion coefficient D and the shear viscosity coefficient \( \eta \) in bulk fluids and confined supercooled water (CSW) near the critical points; (4) spectra of the light molecular scattering (LMS) and quasi-elastic neutron scattering (QENS) and its possible medical applications. The effective critical exponents as well as the effective spatial d eff and fractal d fr dimensionalities were calculated for confined fluids like CSW. A 3d \( { \leftrightarrow } \) 2d DC between the critical exponents \( \alpha = 0,\beta = 1/8,\delta = 15,\gamma = 7/4,\nu = 1 \) and \( \alpha = 0.110,\beta = 0.3265,\delta = 4.789,\gamma = 1.237,\nu = 0.630 \) for 2d and 3d systems belonging to the Ising-model universality class were taken into account. Anomalies of the diffusion coefficient were examined in bulk water and CSW in wide intervals of the size and thermodynamic variables corresponding to crossover phenomena between the dynamic fluctuation, crossover and regular regions. The transition between dynamic crossover and regular regions in bulk fluids, including bulk water, is illustrated by changes in the diffusion-coefficient dependences on: (a) the size variable—from D ~ L −1.963 to D ~ L −2, (b) the temperature variable—from D ~ (T − T c)1.237 to D ~ (T – T c), (c) the concentration variable—from D ~ (x – x c)3.789 to D ~ (x – x c)2, (d) the pressure variable D ~ (p – p c)0.791 to D ~ (p – p c)0.667. In confined 2d fluids like CSW such a transition between crossover and regular behaviors should be treated as 2d \( { \leftrightarrow } \) 4d crossover phenomena because results of the Landau mean-field theory are valid for d = 4 (with a logarithmic accuracy). A 2d \( \leftrightarrow \) 4d crossover leads to the following changes in dependence of the diffusion coefficient D on: (a) the size variable from D ~ L −1.75 to D ~ L −2, (b) the temperature variable from D ~ (T − T c)1.75 to D ~ (T – T c), (c) the concentration variable from D ~ (x – x c)14 to D ~ (x – x c)2, (d) the pressure variable from D ~ (p – p c)0.933 to D ~ (p – p c)0.667. Near the glass-transition critical point of CSW the shear viscosity has much stronger power-law singularity: \( \eta \sim (T - T_{c} )^{ - 1.81} \sim (x - x_{c} )^{ - 14.48} \sim (p - p_{c} )^{ - 0.965} \) than in the vicinity of the 3d high-temperature critical point: \( \eta \sim (T - T_{c} )^{ - 0.065} \sim (x - x_{c} )^{ - 0.199} \sim (p - p_{c} )^{ - 0.042}. \) An important problem of the violation of the Stokes-Einstein relation (SER) in CSW is discussed. Specific properties of LMS and QENS spectra in confined liquids were studied. It was shown that with increasing the characteristic system’s size L: (1) the widths \( \varGamma_{c} \) of the central Rayleigh line and \( \Delta E(q^{2} ) \) of the QENS peak, being proportional \( L^{ - 2} \), are rapidly decreasing; (2) the width Г MB of Mandelstam-Brillouin components is strongly shortening (broadening) according to Г MB ~ L 3; (3) the frequency shift ΔΩMB of the Mandelstam-Brillouin components is weakly increasing (decreasing) in accordance with ΔΩMB ~ L −0.087; (4) the Landau-Placzek relation is essentially decreasing (increasing) as is seen from I c/2I MB ~ L −1.79. These results create a reliable background to introduce a new additional diagnostic method of early detecting the tumor formation in practical medicine.

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Abbreviations

CSW:

Confined supercooled water

LLCP:

Liquid-liquid critical point

LDW:

Low density water

HDW:

High density water

CF:

Correlation function

OZ:

Ornstein-Zernike

DCF:

Direct correlation functions

DC:

Dimensional crossover

D:

Diffusion coefficient

d:

Spatial dimensionality

3d \( \Leftrightarrow \) 2d:

Crossover between 3-dimensional and 2-dimensional systems

\( d_{eff} \) :

Effective spatial dimensionality

\( d_{fr} \) :

Fractal dimensionality

SER:

Stokes-Einstein relation

LMS:

Light molecular scattering

MBC:

Mandelstam-Brillouin components

LPR:

Landau-Placzek relation

HB:

Hydrogen bond

NMR:

Nuclear magnetic resonance

QENS:

Quasi-elastic neutron scattering

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Acknowledgements

The author would like to thank Prof. M. A. Anisimov, Prof. T. M. Bryk, Prof. L. A. Bulavin, Prof. K. A. Chalyy, Prof. M. F. Holovko, Prof. M. P. Kozlovskii, Prof. H.-J. Moegel, Prof. W. Schroer, Prof. V. M. Sysoev, Prof. A. N. Vasilev, Dr. L. M. Chernenko, Dr. G. V. Hrapijchuk, Dr. A. V. Oleinikova, and Dr. E. V. Zaitseva for helpful remarks and collaboration.

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  1. Department of Medical and Biological Physics, Bogomolets National Medical University, 13, Shevchenko Blvd, Kiev, 01601, Ukraine

    Alexander V. Chalyi

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  1. Department of Molecular Physics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Leonid A. Bulavin

  2. Department of Medical and Biological Physics, Bogomolets National Medical University, Kyiv, Ukraine

    Alexander V. Chalyi

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Chalyi, A.V. (2018). Dynamic Anomalies in Confined Supercooled Water and Bulk Fluids. In: Bulavin, L., Chalyi, A. (eds) Modern Problems of Molecular Physics. Springer Proceedings in Physics, vol 197. Springer, Cham. https://doi.org/10.1007/978-3-319-61109-9_12

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