The anomaly appeared in the viscous force that was derived from a relationship between the shape of the HPLC peak and the velocity profile for the capillary flow. The observations were highly reproducible, and we conclude that the SAT is related to the quantum mechanical behaviour of water, in agreement of the characteristic acceptance of thermal displacement according to the Franck-Condon principle.
We performed the same experiments using heavy water and water mixed with a small amount of methanol, and the results support the quantum phenomenological origin. Water is common on earth and essential for life. However, the structure and properties of liquid water are still not well understood, and water remains a mysterious subject 1 , 2 , 3 and continued issues 4. To describe the structure of liquid water, quantum mechanical studies have been performed in various aspects, usually at a single temperature. The quantum mechanical treatments improved the classical results 5 , 6 , 7 , and quantum phenomena were obvious in confined water 8 , 9 , Recent issues are also to investigate the nuclear quantum effects 11 , 12 , However, the improvements have a certain distance from solving the mysteries of water for life.
However, no clear experimental evidences have been provided 18 , 19 , 20 , 21 , and the anomalous behaviour has been questioned The VWA has been explained as a quantum mechanical phenomenon by modelling the relationship between the thermal wavelength and the small molecular free volume space of water Obtaining apparent VWA has been difficult in previous experiments by measuring the heat capacity of water in silica pores 20 , 21 , probably because VWA is a quantum phenomenon that appears at a very short range of solid-water interface and is hard to be observed in a macroscopic variable such as the heat capacity.
In this study, we observed the anomalous temperature spectrum, probably related to VWA, by examining the laminar flow of water with a silica colloid sample flowing through a capillary using a high-performance liquid chromatography HPLC system Supplementary I and accurately varying the temperature. This new application of the HPLC system is different from the general purpose of chromatography of detecting only the peak positions.
The shape of an HPLC peak reflects the flow of an injected sample with differently developed speeds layer-by-layer through the capillary.
The characteristics of the flow was analysed from the peak shape see Methods. The sample contains a minute amount of thiourea so that it can be monitored by a UV detector and exhibits its own distinguished peak shape depending on the temperature and the pump speed. We used a silica colloid sample for examining the interfacial water. The silica colloids are easily dispersed in water and hydrogen bonding sites are on the surface of silica. The structure of interfacial water near silica colloid represents a wide distribution of strong hydrogen bonds Quantum phenomena are observed through coupling of hybrid systems 25 , 26 and at room temperature In Fig.
Interfacial Phenomena In Chromatography
Observation of the quantum behaviour and velocity profiles. An asymmetric HPLC peak shape is represented in c. The dashed vertical line in c is at the peak maximum. The negative sign was applied, since the velocity decreases from the capillary centreline to the wall.
Anomalies upon temperature appear in the up-peaks. The overlapping three data points at the same temperature in e,f signifies the high reproducibility of the experiment and analysis. We derived a relationship between the shape of the HPLC peak and the velocity as a function of the capillary radius see Methods. The calculated velocity profiles were different from a parabolic form that is commonly considered in a pipe flow for which the velocity derivative at the centre is zero Supplementary II.
The slope of the flow velocity along the capillary radius was generally flattened with increasing temperature or with decreasing viscosity, and the overall pump speed was the same for all temperatures. Therefore, the coloured lines were twisted in Fig. Hence, a substantial turbulence was not expected in our experiments. From the calculated velocity profile, we obtained the velocity derivatives with respect to the radius.
The velocity derivatives at the same radius around the twisted position in Fig.
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S2a , were plotted against the accurately controlled temperature for the samples with and without silica colloid in Fig. The temperatures were changed by 1. Anomalous temperatures ATs were present in the up-peaks that are far off the line of without silica. The measured velocity profiles with respect to the capillary radius and temperature also enable other various data analyses for the capillary flow. We formulated an equation for describing the velocity profile by separating the flow into a draw force term and a drag force term Supplementary II ; the anomalous behaviour reappeared clearly in the draw force term even in the first derivative Supplementary Fig.
In the velocity analyses, no anomaly occurred without silica colloid in the sample, either. Not only the velocity analysis, but we also examined the peak shapes in detail. The HPLC peaks were all asymmetric 29 when the shapes of the front and back from the top were compared see Fig. The peak widths and asymmetries depend on flow characteristics in liquid chromatography This ratio is little affected by the retention time in chromatography 30 , 31 or by the constitution of the capillary in this experiment.
The results showed a pattern of a temperature spectrum that appeared in the distinct down-peaks at consecutive temperatures.
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The differences between the widths of the front and the back were considerably small, but the reproducibility was high, as indicated by the small scattering of the data points in the figure. Disregarding the positions of the HPLC peak heights, the down-peaks appeared at the same ATs when the sample contained colloidal silica.
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Anomalous temperature spectra. The red arrows indicate ATs. The blue arrows in a,b,e indicate shoulder peaks to be discussed. However, the depths of the down-peaks increased with increasing silica concentration. When no silica was present, no peaks appeared and thus no anomalous behaviour was observed as in the velocity analysis. Therefore, we believe that the phenomena are due to the vicinal water near the silica solid surface, and a result of the combined and cumulative effects of the numerous thin layers of the flow through a long capillary as an ensemble coupling illustrated in Fig.
The effect of capillary-surface layer is not significant. The ATs showing the aforementioned down-peaks occurred when the pump speed was at 0. The series of ATs of the down-peaks altered when the pump speed was changed. At a high pump speed, the AT decreased and the intervals between the ATs became narrower. Although the peaks were unclear in the experiments at low pump speeds below 0.
Extrapolated anomalous temperatures. Experiments were performed at various pump speeds, and the results were extrapolated to a zero pump speed for a H 2 O and for b D 2 O. The open symbols were extrapolated with quadratic functions along the anomalous temperatures obtained in the experiments at the same pump speed, whereas the extrapolations along the pump speed were performed using linear functions. The factors for describing the slopes are formulated in the text.
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The down-peak indicates that the interaction between the layers of the flow is stronger Supplementary II at the ATs. The viscosity of water with silica colloid is higher than that of pure water. The previous suggestion 23 for VWA that the anomaly is due to the resonance matching of several multiples of thermal half-wavelength to the small free volume space is interesting.
We performed the same experiment with D 2 O an example is in Fig. Therefore, the model is less appropriate for describing the observations.
When the previous resonance matching model was adoptable, the thermal energy distribution may differ from the Boltzmann distribution. Regarding the ATs, we propose a similar quantum mechanical concept that also assumes the thermal displacement of water molecules in small free volume space. The accepted movements are stepwise along the parabolic-like potential curve. This displacement is assumed in a larger scale than the molecular vibration and is large enough to move the molecular position.
At this stage, we avoid exact peak assignments for energy level changes. This properly accepted condition maintains a localized stable structure when the impact is transferred without disturbing the structure.