Velacity auto corretetion functions for water and methanoJ

Velocity auto correlation functions for centre of mass motion relative to alaboratory frame of reference appear in Figures 5.35 - 5.36 below, and in Figures C.34 - C.37.

The negative region at intermediate times found for all mixtures is typical for liquids where density is so high that the average molecule change direction upon interaction with another moleeule. The oscillations of both methanol and water, particularly clear in Figure C.38, is a fingerprint of the hydrogen-bond, which makes the molecule os-cillate back and forth before an eventual escape from its neighbourhood [167]. These oscillations are seen to diminish with increasing temperature [98]. They are more pro-nounced with water than with methanol, perhaps not unexpected since water has more hydrogen bonds than methanol. Pure water also decorrelates more quickly initially, a decrease to l/e within -O.05ps, as compared to methanol which reaches Ile within -O.lps. A complete decorrelation seem to occur within approximately the same time, -1 ps for both Iiquids,

Chapter5Mixtures ofwater and methanol - results and analysis 137

Figure 5.35 Normalized velocity auto correlation function \fx(t)for water in mixtures with methanol from NVT-simulations. xmis methanol mole fraetion.

0.7

Figure 5.36 Normalized velocity auto correlation function\fx(t)for methanol in mixtures with water from NVT-simulations. xmis methanol mole fraetion.

138 Chapter5Mixtures o/water and methanol - results and analysis Pure water is characterized by a correlation peak at 0.15·10-3ns, which does not disap-pear with redueed mole fraetion water, but instead is systematieally lowered. In the negative region we find on the other hand no systematie variation with eomposition.

We have not been able to find any eentre of mass veloeity auto correlation funetions for pure TIP4P-water in literature, despite its wide and frequent applieation in model simulations, Stillinger and Rahman [98] calculated velocity auto eorrelation function for ST2-water at different temperatures. Our ealculated veloeity auto correlation func-tion is remarkably similar to their, exeept for being less oseillatory and having a loeal minimum with positive ordinate-value. We might however be misled by the lack of intermediate points.

Pure methanol has a small plateau at 0.2 - O.25·10-³ns, whieh disappears gradually for the mixtures. The negative region gets more negative with decreasing methanol con-tent. Our pure methanol velocity auto correlation function is in good agreement with the the result of Guardia et al., 1994 [168] ror OPLS-methanol and the results or Haughney et al., 1987 [147] and Alonso et al., 1991 [150] for the HI-modeI.

The curves for the pure liquids are probably approaehing zero faster than for the components in the mixtures.

Comparison between X-, y-, and z-components show only minor differenees at long delay times, whieh are probably due to statistical noise.

Also a eomparison between NVT and NVE results (Figures C.36 and C.37) reveal only small differenees. The veloeity auto correlations get less negative with the NVT-simulation. The difference with method in the backscattering region is only slightly larger than the differenee with direction (not shown for this mixture) for water. For methanol the differenees in direction is approximately equal to the differ-ence with method.

Veloeity auto correlation funetions provide an alternative route to the self-diffusion coefficients [15, 169]. The use ofthis procedure in addition to the Einstein relation might have provided insight to whether differences in self-diffusion coefficients with the NVE and NVT simulations arise from method or are due to statistical uncertain-ties.

Chapter5Mixtures ofwater and methanol - results and analysis

5.6 Summary

139

From the equilibrium molecular dynamics simulation of water and methanol, we summarize same of aur results presented and diseussed in the previous sections.

• The results for thermodynamic properties and structure are in good agreement with experiments and with simulations for the same models.

• There seem to be no difference between the NVE and the NVT results for thermo-dynamics and structure, except for differences caused by the NVE-temperatures being slightly higher than the NVT-temperatures.

• This disagreement of temperatures is largest for the pure liquids, and for the mix-tures the NVE temperamix-tures agree well with the predefined temperamix-tures.

• The calculated pressures are very high, but it seem to be an effect of the simulational procedure/model potentials, since all other quantities correspond to values at 1 atmosphere. The pressures in the pure water simulations are a factor 3-4 higher than the pressures found for the mixtures. The pair correlation functions show no sign of a compressed liquid.

• Energy conservation is good, and improves with decreasing water content. Total linear momentum is also conserved.

• All teststhat are performed and all variables that are investigated for both the NVE and the NVT methods, are consistent with systems in thermal and mechani-calliquid equilibrium.

• The NVT method fails however to reproduce the canonical ensemble for the par-ticular coupling parameters used. The possibility that the simulation would have become canonical if the simulation was continued, can however not be excluded.

• The Nase-Hoover dynamics is proved to generate canonical distributions provided the trajectories are ergodie, and that the total linear momentum is conserved at zero. The failure of aur simulations to generate canonical distributions, is then be-lieved to be caused by slightly toa large heat bath masses.

• The relaxation parameters used for mixtures were weighted averages of the sepa-rate water and methanol relaxation parameters. There seem to be no differences with the mixtures regarding the approach to the canonical ensemble, so a simple combination scheme is sufficient for mixtures.

• The radial positions of 1st maxima of the pair correlation function are not affected by varying concentrations, particularly we find no signs of increased cavities around the methyl site.

140 Chapter5Mixtures o/water and methanol - results and analysis

• The methyl-methyl coordination number decreases less than the other self eoordi-nation numbers with inereasing water content, and less than the redueed number density. There is thus a relative inerease in methyl-coordinated-methyL The 11Y-droxyl self coordination numbers deerease more than number density.

• The self correlations of water in the mixtures yield eoordination numbers that de-crease linearly with number density. Thus we tind no drastie reduetion or incre-ment of the water structure.

• The pair correlation functions for methanol are consistent with a simple V-chain, but we have not considered rings or branehed ehains. These possibilities are then not exeluded by aur results.

• Upon addition of water to methanol, we find that the nearest neighbour interac-tions of methanol-methanol deerease, while second nearest interaeinterac-tions are less af-feeted. This can be explained with water replaeing methanol.

• The results for self-diffusion earry some uneertainty. The general trends known from experiments are reproduced. Also the tendency of the TIP4P-model to over-estimate self-diffusion is confrrmed. Except for the self-diffusion of methanol in the 0.25 mixture, the NVT and NVE results are equal within estimated uneertain-ties.

Though the simulations are not strictly mierocanonical, the total of all results make us eonfident that we can proceed with simulations of the water-ethanol mixtures. The re-quirement of eanonieal distributions is partieularly important for calculations of de-rivative properties. We do not caleulate such properties.

Chapter6

Mixtures of water and ethanol