Properties of Methanol-Water Mixtures in a Coarse-Grained Model

Methanol and water rank among the most important liquids in modern world due to their versatile use. As water, methanol and their mixtures exhibit numerous anomalous properties, their description is challenging. The amphiphilic nature of methanol causes its aqueous solutions to have negative excess volume and enthalpy across the entire composition range. A simple isotropic water model and its coarse-grained extension were used to study the properties of methanol and water-methanol mixtures. Using Monte Carlo simulations, we showed that the model correctly describes the thermodynamic properties of methanol, density dependence of water-methanol mixtures upon temperature and composition, and excess properties of mixtures. Although no conscious effort was made to fine-tune the potential, the results are remarkably close to experimental data.


Introduction
Water, methanol and especially their solutions find abundant use in everyday life.2][3] Methanol can also be used as fuel. 4It is therefore important to understand their behaviour on the molecular scale.
Methanol and water share many properties due to their similarity on the molecular scale.Both are of comparable size, have comparable dipole moment and participate in hydrogen bonding.Consequently, they are fully miscible.Water, however, displays more anomalous properties due to stronger hydrogen bonding.The methyl group in methanol is weakly polar and diminishes the polar nature of the compound.
Water exhibits the temperature of maximum density at 4 °C at normal pressure, while methanol does not.Ice floats on water due to lesser density, while solid methanol sinks.Both, methanol and water, have higher boiling points than anticipated for the molecules of their size.
Methanol melting point, however, is much more depressed than that of water.][7] Water is usually described with models that deal with atoms and electronic pairs explicitly.Among the most popular models are SPC or TIP5P that perform remarkably well near ambient conditions.Analogously, methanol can be modelled explicitly with models, such as optimized potential for liquid simulations (OPLS), 8 L1 model, 9 H1 10,11 model or L2 model. 12,13These models are particularly useful when water or methanol is a medium and not the investigated substance, per se.In the latter case, simpler models are sometimes needed.These models may not reproduce experimentally measured properties verbatim, but on the other hand offer a chance to systematically study those properties, as there are fewer parameters that can be adjusted. 14,15oarse-grained models have been shown to describe the thermodynamic and structural properties of water surprisingly well.Although transferability 16 and reproducibility issues 17 hinder the determination of a complete panel of properties, it is still possible to extract a myriad of useful information.Examples of such isotropic potentials are repul-sive shoulder potential, 18 honeycomb potential, 19 Lennard-Jones-Gaussian potential, 20,21 Jagla potential 22,23,24 and the continuous shouldered well (CSW) potential. 25][28][29] In our work, we studied the properties of water-methanol mixtures with the Monte Carlo simulation method.A simple coarse-grained isotropic potential was used for water, while methanol was modelled with two-bead particles.After comparing calculated thermodynamic properties of pure methanol with the experimental data, density, excess volume and excess enthalpy of mixtures were systematically studied at various compositions and temperatures.
This paper consists of five sections.In Section II, the model is outlined.Section III deals with the theoretical background and simulation details, with results and discussion following in the Section IV.A short conclusion in Section V completes the paper.

The Model
To model methanol the two groups that form the molecule were treated separately.Atoms of the hydroxyl group (OH) were absorbed into a pseudoatom with CSW pair interaction (1)   This function can be viewed as the sum of a soft repulsive shoulder of height U R , an attractive Gaussian well of depth U A and width and a steep repulsive wall.R R and R A are the repulsive average radius and the distance of the attractive minimum, respectively.The repulsive shoulder steepness is determined by the parameter Δ and the represents Gaussian variance.In our work, we used the following parameters: Atoms of the methyl group (CH 3 ) form the other pseudoatom.The hydrophobic character of this groups is taken into account with the modified Lennard-Jones pair potential (2)   We have set σ 22 /a = 1.0 and ε 22 /U A = 0.1, effectively making the hydroxyl and methyl groups of the same size and methy-methyl interactions 90% weaker than the hydrogen bonding in water.
Mixed interaction (U 12 ) was calculated from the same equation with altered parameters.Parameters descri-bing the interaction strength (ε) and bond length (σ) are derived from Berthelot-Lorentz rules: and Water was modelled as a lone hydroxyl group.Methyl group and hydroxyl group were fixed in a tangential position (see Figure 1).See Figure 2 for details on potential functions.

Simulation Details
Monte Carlo simulations were performed in the isothermal-isobaric (NPT) ensemble in a cubic box with periodic boundary conditions and minimum image convention.Each time, a total of 500 particles were introduced in a box.The relative proportion of methanol and water particles was adjusted according to their respective molar masses (M methanol = 32, M water = 18).
Simulations were performed at a constant pressure p* = 0.018, which is below the critical point for both pure water and pure methanol.We limited our study to the li-Hu{ et al.: Properties of Methanol-Water Mixtures ... quid portion of the phase diagram, i.e. 0.5 < T* < 1.0.Equilibration part of the simulation consisted of 100 000 cycles and was followed by five sampling runs of 100 000 cycles.One cycle corresponded to an attempted displacement of every particle, one attempted rotation of each methanol molecule around a randomly chosen axis and one attempted change of the box size.Maximum displacement, rotation and resize factor were dynamically adjusted during the equilibration to reach 50% acceptance ratio.
Numerical density was calculated as inverse average volume per particle, N/V.Coefficients of thermal expansion, isothermal compressibility and heat capacity were calculated from fluctuations as (3)   Results are reported in dimensionless reduced units, relative to the diameter of hydroxyl group and the depth of its attractive well: and .
For the analysis of the mixture data, methanol weight fraction was used as a controlled variable.

1. Parameterisation Considerations
Parameterisation of the water particles, interacting with CSW potential, was kept unchanged from Franzese 25 and our previous work. 26,27As it has been previously proved that is in qualitative and semi-quantitative agreement with experimental data for real water, this is a reasonable assumption.To describe methanol in the extended CSW model, three additional parameters are needed: Lennard-Jones attraction well depth and location, and the distance between hydroxyl and methyl group.Their values (see Section III) were are the same as in our previous work to make comparisons possible.

2. Methanol Thermodynamics
In Figure 3, we compare real methanol thermodynamics from experimental data 30,31 (panels a-d) with model predictions (panels e-h).Model data were collected at subcritical pressure (p* = 0.018) in the temperature range 0.45 < T* < 1.0, where the model methanol is liquid.Specific volume (inverse of density) increases linearly with temperature, showing no density anomaly.Model data reproduce this behaviour rather well, although the slope gets larger at higher temperatures.The thermal expansion coefficient in methanol has a shallow minimum around T = -40 °C, which our model fails to predict.Isothermal compressibility increases monotonically with temperature in both the experiment and the model.Heat capacity also increases with temperature, again evidenced by real data and displayed in our model.

3. Water/methanol Mixtures
First, we investigate how the molecular structure of the mixture changes as the methanol fraction is increased.Figures 4a and Figure 4b show hydroxyl-water and methyl-water pair distribution functions (PDF), respectively, at T* = 0.60 and p* = 0.018.Although weight fraction of methanol changes from 20% to 80%, no major change in PDF is encountered.There is a very slight increase of the peaks and decrease of the troughs, suggesting greater order, as the methanol fraction is increased.Effect is consistent across the whole composition range, but is very small in magnitude.In Figure 4c, all possible combinations of PDFs are shown, all for wt(MeOH) = 0.4.
As expected due to similar potential functions used, the hydroxyl group and water molecule behave similarly and have almost coinciding PDFs (hydroxyl-hydroxyl, hydroxyl-water, water-water).Methyl-methyl PDF has the fewest and the smallest peaks, as methyl groups are not particularly organised due to weak interactions.
Density of methanol is lower than that of water and shows no temperature maximum.Consequently, densities of mixtures must decrease as the fraction of methanol increases.Additionally, there must exist a composition, where the density maximum vanishes.Experimental data have shown it is located slightly below 10% wt methanol.Figures 5a and 5b show the temperature and composition dependence of mixture densities, while Figures 5d and 5e show model predictions.Trends are in overall agreement, although there are some discrepancies.Most pronouncedly, the model predicts the density to increase with increasing methanol fraction at low temperatures and low methanol fraction.In reality, this effect is very small and confined to very low temperatures and is not nearly as strong.In the model (Figure 5f), the density maximum shifts to lower temperature as methanol fraction is increased and disappears altogether around 40% wt, while the experimental results show the same trend (Figure 5e).
Nonideality of mixtures of water and methanol can be described by excess volume and excess enthalpy of mixing.Attractive forces between molecules dominate and cause the solution to shrink, compared to the volume of the ideal mixture.The excess volume was calculated as , where V m and V w are molar volu- As this value is dimensionless, model data can be directly compared with experimental values, 32 as shown in Figure 6.The model correctly predicts negative excess volume, but the magnitude of the effect is too small.This agreement could be improved with a reparameterisation.Excess enthalpy was calculated as where H(x) is the enthalpy of the system when the molar fraction of methanol equals x, H m is the enthalpy of pure methanol and H w enthalpy of pure water.Enthalpy of the system is calculated as the sum of pair interactions and the P*V term.Figure 7 shows the model results juxtaposed with the experimental data 33 on secondary axis.For higher temperatures, the trend is quantitatively correct, showing negative excess enthalpy of mixing with a pronounced minimum near x = 0.4.At low temperatures, the trend reverses.

Conclusion
We have extended the CSW model, originally designed to describe water, to methanol particles.Tangentially joining two beads, one having the CSW pair potential and the other one having a modified Lennard-Jones potential, the model was deemed to correspond to methanol.
To get a basic overview of the model abilities, we calculated the thermodynamic properties of pure methanol and compared them with experimental data, where good agreement was found.Additionally, we compared the structure and ordering of particles at various compositions and found the effect to be negligible.Density, excess volume and excess enthalpy were studied as functions of temperature and composition, showing surprisingly good qualitative agreement with experimental data.Excess enthalpy was reproduced somewhat worse, probably owing to the fact that the hydroxyl group and water potential should have been modelled differently.Had we tried to tweak the potential parameters any further, we believe we could have quantitatively improved the agreement with the experimental data.Temperature of the maximum density was shown to decrease with increasing fraction of methanol.It disappears at around 40% of methanol, which is somewhat greater than in experimental data.

Acknowledgements
Financial support from Slovenian Research Agency through grant P1 0103-0201 and the Young Researcher programme is appreciated.

Figure 1 :
Figure 1: Methanol is modelled as two tangential spheres, representing the hydroxyl (black) and methyl (white) groups.Water is modelled as a sphere (black).Interactions between black particles is described by the CSW potential, other interactions are Lennard-Jonesian.

Figure 3 :
Figure 3: Thermodynamic properties of pure methanol at 1 atm (panels a-d) and results from the model (e-h) at subcritical pressure p* = 0.018 follow matching trends.a)

Figure 4 :Figure 5 :
Figure 4: Pair distribution functions in water/methanol mixtures at T* = 0.6 for different mass fractions of methanol -20% (pink), 40% (red), 60 (yellow) %, 80% (green) -as predicted by our model.Hydroxyl-water (panel a) and methyl-water (panel b) functions are weakly dependent on the methanol fraction.Panel c shows comparison with intraspecies methanol and water distribution function.

Figure 6 :
Figure 6: Excess volume as a function of mass fraction of methanol.Symbols represent simulation results at T* = 0.5 (blue), 0.6, 0.7 and 0.8 (red) and p* = 0.018 with connecting lines as guides-for-eye.Solid continuous line represents experimental data at 20 °C and 1 atm.

Figure 7 :
Figure 7: Excess enthalpy of mixing as a function of mass fraction of methanol.Legend as in Figure 6.