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A Study of the Shift in the Temperature of Maximum Density of Water And

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A Study of the Shift in the Temperature of Maximum Density of Water And A Study of the Change in the Temperature of Maximum Density of Water and Aqueous Solutions as a function of Pressure A thesis presented for the degree of Doctor of Philosophy Presented by Gerard Cotter B.Sc. Department of Experimental Physics National University of Ireland, Maynooth Maynooth County Kildare 23rd September 2010 Research Supervisor Michael F. Cawley M.Sc., Ph.D. Head of Department J. Anthony Murphy M.Sc., M.S., Ph.D. Contents Abstract................................................................................................................. v Acknowledgements............................................................................................. vii 1 Introduction.......................................................................................................... 1 1.1 Introduction................................................................................................... 2 1.2 Review of the density maximum of pure water at atmospheric pressure ..... 4 1.3 Review of the density maximum of aqueous solutions at atmospheric pressure ......................................................................................................... 7 1.4 Recent studies of the temperature of maximum density of aqueous solutions at atmospheric pressure................................................................................. 8 1.5 Review of the density maximum under pressure .......................................... 9 1.5.1 The seawater equation.................................................................. 10 1.5.2 Adiabatic temperature gradient method....................................... 15 1.5.3 The temperature of maximum density at negative pressures....... 20 1.6 Aims of current work .................................................................................. 21 1.7 Thesis chapter outline ................................................................................. 21 1.7.1 Author’s direct contribution in this thesis.................................... 22 2 Experiment apparatus and procedures............................................................ 25 2.1 Introduction................................................................................................. 26 2.2 Heat exchange system................................................................................. 26 2.3 Pressure system ........................................................................................... 29 2.3.1 Hydraulic system.......................................................................... 29 2.3.2 Motion control of pressure........................................................... 31 2.3.2.1 Control electronics for stepper motor ................................. 33 2.4 Pressure chamber ........................................................................................ 35 2.4.1 The governing equations.............................................................. 35 2.4.2 Final pressure chamber design..................................................... 37 2.5 Thermometry............................................................................................... 39 ii 2.6 Data acquisition and control software......................................................... 44 3 Data analysis procedures and results ............................................................... 51 3.1 Determination of the temperature of maximum density from ramp runs ... 52 3.2 Pressure scanning........................................................................................ 59 3.3 Heat transfer in the vicinity of the density maximum................................. 62 3.4 Pure water results ........................................................................................ 64 3.5 Solution results............................................................................................ 66 3.5.1 Ionic salt results ........................................................................... 67 3.5.2 Monohydric alcohol results.......................................................... 72 3.5.3 Sugar results................................................................................. 79 3.5.4 Acetone results............................................................................. 83 3.6 Overview of results ..................................................................................... 84 3.7 Error analysis .............................................................................................. 91 4 Macroscopic modelling ..................................................................................... 94 4.1 Introduction................................................................................................. 95 4.2 Density of pure water and solutes under applied pressure.......................... 95 4.3 Macroscopic modelling of the behaviour of the density maximum of mixtures....................................................................................................... 98 4.4 The phase change of pure water and solutes as a function of pressure..... 103 4.5 Macroscopic modelling of the phase change of mixtures......................... 106 5 Microscopic modelling..................................................................................... 111 5.1 Introduction............................................................................................... 112 5.2 Review of molecular modelling................................................................ 113 5.3 Metropolis importance sampling............................................................... 115 5.3.1 Lattice models and Metropolis importance sampling ................ 115 5.4 Wang-Landau approach ............................................................................ 119 5.4.1 A simple example of the Wang-Landau approach..................... 120 5.4.2 Metropolis importance sampling versus the Wang-Landau approach ..................................................................................... 122 5.5 Mercedes-Benz 2-D model ....................................................................... 123 5.5.1 Off-lattice Monte Carlo simulations .......................................... 125 iii 5.5.2 Off-lattice results........................................................................ 127 5.6 Buzano gas lattice model .......................................................................... 130 5.6.1 Modifications to the Buzano gas lattice model.......................... 133 5.7 Monte Carlo simulation results ................................................................. 135 5.7.1 Metropolis importance sampling results .................................... 136 5.7.2 Wang-Landau method results .................................................... 139 5.7.3 Simulating experimental results................................................. 142 5.7.3.1 Addition of hydrophilic molecules to the lattice............... 145 5.7.3.2 Addition of non-bonding molecules to the lattice............. 147 5.7.3.3 Increased hydrogen bond strength .................................... 149 5.8 Strong and weak water.............................................................................. 151 5.8.1 Strong and weak water results.................................................... 153 6 Conclusions ....................................................................................................... 159 6.1 Conclusions............................................................................................... 160 6.2 Future work ............................................................................................... 164 Appendix A. Experimental data acquisition and control software code ......... 168 Appendix B. Area integration code for the extraction of the temperature of maximum density from ramp runs............................................... 182 Appendix C. Modified Buzano code using Wang-Landau method.................. 187 Appendix D. Post-processing code for the Wang-Landau method.................. 197 Bibliography ........................................................................................................... 201 iv Abstract The aim of this research is to study the shift in the temperature of maximum density of water and aqueous solutions as a function of pressure. One of the many anomalous properties of water is that it passes through a maximum in density in the liquid state. In order to accurately measure the temperature of maximum density (Tmd), convective flow is monitored in a rectangular container containing the fluid. A temperature gradient is held across the chamber and it is cooled and heated in a quasi-steady state manner. A double cell convection pattern forms in the vicinity of the density maximum. This double cell is tracked by monitoring the temperature at selected points in the fluid. The change in temperature of maximum density due to concentration and applied pressure can be investigated using this technique. At a pressure of one atmosphere, this density maximum occurs in pure water at a temperature of 3.98 C. It is known that the temperature of maximum density decreases as the pressure increases; for pure water this occurs at a rate of 1 C per 50 bar. Experimentally the shift in the temperature of maximum density of aqueous solutions is tracked over the pressure range 1 to 100 bar. It is found that the temperature of maximum density drops as the pressure rises for all solutes studied, but that the rate of decrease changes depending on the nature
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