acetone mixtures

Journal of Molecular Liquids 159 (2011) 60–69

Contents lists available at ScienceDirect

Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m o l l i q

Molecular dynamics simulations and femtosecond optical Kerr effect spectroscopy of methanol/acetone mixtures K. Polok a,⁎, W. Gadomski a, F. Sokolić b, L. Zoranić b a b

Laboratory of Physicochemistry of Dielectrics and Magnetics, Department of Chemistry, University of Warsaw, ul. Żwirki i Wigury 101, 02-089 Warsaw, Poland Department of Physics, Faculty of Sciences, University of Split, Nikole Tesle 12, 21000 Split, Croatia

a r t i c l e

i n f o

Available online 21 October 2010 Keywords: Optical Kerr effect Molecular dynamics Methanol Acetone

a b s t r a c t Herewith we present the results of our studies on the dynamics of acetone/methanol binary mixtures by means of molecular dynamics simulations and femtosecond optical Kerr effect (OKE) spectroscopy. The OKE response exhibits the apparent dependence on a mole fraction of the mixture components, and thus carries the information about the influence of its composition on the intermolecular interactions and momentary local structures. The molecular dynamics simulations, which take into account the reorientational dynamics of the molecules, have been performed in order to explain the concentration dependence of the long time part of the experimental OKE response. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Liquid substances exhibit complicated short distance ordering. This ordering and its evolution reflect the physical properties of individual molecules. Liquids containing hydrogen bonded species are of great importance from the biological point of view. Examining properties of such systems can give us better understanding of biological processes. For our study we chose the methanol–acetone mixture, as it is one of the simplest hydrogen bonded systems. It consists of 2 types of molecules. Both of them can participate in up to 2 hydrogen bonds by accepting a proton, however only methanol can donate a proton to such a bond. In our study we considered 9 mixtures differing in methanol and acetone mole fraction, ranging from pure acetone to pure methanol. We analyzed our systems by means of molecular dynamics simulations and Optical Kerr effect measurements.

2. Materials and methods 2.1. Optical Kerr effect Optical Kerr effect is a technique used to analyze the ultrafast dynamics on femtosecond timescale [1,2,4,9]. In the experiment a strong laser pulse, called pump, affects the system, which gives rise to induced anisotropy. This anisotropy influences the propagation of a weak laser pulse called probe. The time delay between the pump and probe pulses is changed, which gives information about the time evolution of the induced birefringence. The signal contains information about diffusive ⁎ Corresponding author. E-mail address: [email protected] (K. Polok). 0167-7322/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2010.10.005

molecular reorientation, lifetime of ultrafast molecular structures and Raman intra- and intermolecular modes excited by the pump pulse. Our setup (Fig. 1) contains a femtosecond sapphire laser, pumped by a 7 W CW Ar laser. The sapphire laser generates 30 fs pulses at 80 MHz repetition rate and 500 mW power. The pulses from the laser are directed to the prism dispersion line, which was built in order to get the shortest possible pulse inside the sample. After the dispersion line the beam is split into a strong pump and a weak probe. The time delay between the pulses is swept in range of approximately 5 ps by a fast oscillating delay line. The pump and probe beams are polarized at 45∘ with respect to each other and then focused at the sample by a 100 mm focal length lens. The λ pump is blocked after the sample, whereas the probe passes a plate and 4 λ a polarizer at 90∘ with respect to the initial probe polarization. The 4 plate is used for heterodyne signal detection, which makes the detected signal linear instead of quadratic in probe intensity. The plate fast axis is slightly tilted from the probe polarization. The measurement is made for opposite signs of this tilt and the final signal is obtained by subtracting the resulting signals. The setup makes use of a fast oscillating delay line. The signal from the photodiode is gathered with a 16 bit, 1 MHz ADC converter. The resolution of the measurement is 2 fs.

2.2. Molecular dynamics In this part of work molecular dynamics simulations were performed using DL_POLY package for methanol, acetone and 7 mixtures of them. Potentials for the simulation were taken from [6]. In this article authors have analyzed for acetone the OPLS-UA (optimized potentials for liquid simulations-united atom) [7], TraPPE-UA (Transferable potential for phase equilibria-united atom) [8] potentials and their own new

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

61

Fig. 1. Scheme of the setup, where Ar — argon laser, Sapph — sapphire laser, S — spectrometer, BS — beamsplitter, P1, P2 — first and second probe polarizers, P3 — pump polarizer, DELAY — delay line, SMP — sample, QWP — waveplate, BB — beam blocker, PD1, PD2 — probe and reference photodiodes respectively.

potential, which is an extension of the previous two. The potential used for methanol was TraPPE-UA. The authors performed Grand-Canonical Monte Carlo simulation for calculating phase diagrams and showed that the results were closer to the experimental values when the new potential was used. The phase diagrams were done for vapor–liquid equilibrium for pure acetone and pressure-composition diagram for acetone–methanol mixture. For methanol there was no new potential established, as it behaved well with the old one. We therefore used the new potential for acetone and TraPPE-UA for methanol. The potential parameters are given in Tables 1–3. Briefly, the CH3 groups of acetone and methanol were treated in terms of united atom approximation. Bond lengths were set to constant values and only harmonic angular oscillations were allowed.

Table 1 Potential parameters for Lennard–Jones and Coulomb potentials. ε/kB(K)

Site–site interaction was set to Lennard–Jones potential and atoms carried fixed partial charges. All the mixtures were equilibrated in NPT ensemble, Berendsen thermostat and barostat were used in order to keep 300 K, 1 bar conditions. Two sets of simulations containing 512 and 2197 molecules were performed. The integration time step was 2 fs and Ewald summation was employed to treat the long range Coulomb interactions. After an equilibration period a 10 ps run for 2197 molecules and a 998 ps run for 512 molecules were performed, which generated radial distribution functions (RDFs) and history files for further analysis. The simulation for 2197 molecules was mainly used for calculating the RDFs, whereas the 512 molecules case was used for calculating the hydrogen bond data and reorientation of the molecules.

Table 3 Intramolecular potential parameters.

σ (A)

q(e)

Acetone CH3 C O=

98.0 27.0 79.0

3.75 3.82 3.05

−0.049 0.662 −0.564

Methanol CH3 O H

98.0 93.0 0.0

3.75 3.02 0.0

0.265 −0.7 0.435

Bonds

Bonds angle (deg)

kθ/kB (K)

Acetone CH3 − C = O CH3 − C − CH3

121.4 117.2

62,500 62,500

Methanol CH3 − O − H

108.5

55,400

Table 4 Investigated mixtures compositions. Table 2 Bond lengths. Bond

Bond length(A)

Acetone C=O CH3 − C

1.229 1.520

Methanol CH3–O O–H

1.43 0.945

Mixture label

Mole percent of methanol

Mole percent of acetone

0meth 12meth 25meth 37meth 50meth 63meth 75meth 88meth 100meth

0 12 25 37 50 63 75 88 100

100 88 75 63 50 37 25 12 0

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K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

For calculating the reorientation we assumed that the perturbation in local structure due to the pump pulse is very small. Based on this assumption the reorientational decay from the experiment can be approximated by assigning each molecule a unit vector. This vector rotates with the molecule and we observe the sum of dot products of the molecules vector in the first and current time point. The reorientational response can be then written as:
Rυec ðt Þ =

 d ð0Þ⋅ d ðt Þ ≊

→

→

D

E → → di ð0Þ⋅ di ðt Þ

N

∑i

= 1

N

;

ð1Þ

averaging the duration time of individual hydrogen bonds in the simulation. The duration of a hydrogen bond was calculated as the time interval between its creation and breaking moments. The criterion for hydrogen bond was taken from [5] and modified to have a more strict angle criterion. According to this definition a hydrogen bond between the OH group and oxygen atom exists if the distance between the oxygen atoms is lower than 0.35 nm and the angle between the OH bond and line connecting oxygen atoms is below 45∘. 3. Results and discussion 3.1. OKE results

where Rυec(t) — function describing the correlation between our vectors, → di ðt Þ — vector of i-th molecule at time t, N — number of molecules in the simulation cell. The hydrogen bond lifetimes were calculated by

The composition of the analyzed mixtures is given in Table 4. In Figs. 2 and 3 some of the gathered OKE signals after normalization are

1

0meth 25meth 50meth 75meth 100meth

0.9 0.8 0.7

Signal

0.6 0.5 0.4 0.3 0.2 0.1 0 -500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Delay [fs] Fig. 2. Normalized Kerr signal for 5 of the data sets in linear signal scale.

1 0meth 25meth 50meth 75meth 100meth

Signal

0.1

0.01

0.001

0.0001 -500

0

500

1000

1500

2000

2500

3000

3500

Delay [fs] Fig. 3. Normalized Kerr signal for 5 of the data sets in log signal scale.

4000

4500

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69 Table 5 Monoexponential fit results for pure methanol and pure acetone.

Acetone Methanol

τ[fs]

A

982±16 1570±360

0.0593±0.0011 0.00697±0.00081

presented. As methanol gives much weaker signal than acetone, its normalization causes a higher noise with respect to pure acetone signal. All the measured signals start with a high peak, which corresponds to the instantaneous response of the system, due to electron cloud displacement. Its shape reflects the autocorrelation of the laser pulses used in the experiment. It can be seen that acetone signal contains a second maximum on the curve, which gradually disappears with the decrease of acetone concentration. In Kerr Spectroscopy such part of the signal usually corresponds to low frequency intermolecular or intramolecular oscillations. In this paper we are interested in the long time decay of the Kerr signal. The analysis of the fast part of the signal will be the subject of our other study. The pure methanol and pure acetone data were fitted with a monoexponential decay: −τt

f ðt Þ = Ae

ð2Þ

with decay time τ and amplitude A, starting at 1000 fs. The results are given in Table 5 and sample fits are shown in Fig. 4. This part of the signal corresponds to a diffusive reorientation of the molecules, which is in range of picoseconds. As the methanol signal is weaker than that of acetone and its decay amplitude is one order of magnitude smaller, we have assumed that the mixtures signal is dominated by the acetone response. In order to see if the methanol contribution to the signal can be retrieved, we made a double exponent fit for the 88 mol% methanol data, however it converged to a sum of the same exponents (fit result in Fig. 4). Therefore we assume that the single exponent fitting procedure is valid for all the concentrations. The result of single exponent fitting of the experimental data is given in Fig. 5. It does not include fit results for pure methanol, as it differs much from the other results and has high error bar. Including it would make the shape of the curve for other concentrations less visible. The high increase in τ when going from the 88 mol% methanol to pure methanol is because

the pure methanol signal contains only methanol response, whereas the 88 mol% mixture has a high acetone contribution. We can see also that the amplitude of the decay drops with the decrease of acetone concentration almost linearly. It appears that the decay time for concentrations up to 25 mol% methanol is slightly dropping and above 25 mol% it is getting longer with methanol concentration. The behavior for the higher concentrations is probably caused by the increasing number of hydrogen bonds, which slows down the reorientation of molecules. We discuss this further in the simulation part of the article.

3.2. Simulation results The reorientation of the molecules was calculated using Eq. (1) and the resulting data were fitted with the same exponential decay as the experimental data (Eq. (2)). The decay times are given in Fig. 6 and example fit is given in Fig. 7. The literature decay time for pure methanol [10] is 1960 fs, which is in between the simulation result 2937 fs and the experimental data fit 1570 fs. The situation is similar for acetone, where the value reported in the literature and value from our experiment and simulations are 1210 fs, 982 fs and 1910 fs respectively [11]. The difference between the experimental value reported in literature and that obtained in the present work for methanol, may be due to the very weak Kerr signal of this substance, which contains a lot of noise and the fit is not very precise (indicated by high error range of ±360 fs). For the case of acetone the difference might be due to different fitting ranges that were used. The difference might be also partially caused by the temperature difference between the two experiments (about 3 K) [12]. The simulation gave us reorientational response separately for methanol and acetone molecules. Both calculated reorientation times exhibit a tendency to increase with increasing methanol concentration. As the experimental data (Fig. 5) for mixtures are dominated by the acetone response, we compare the experimental data obtained for acetone/methanol mixtures with those simulated for acetone in the same mixtures. The computed values of the decay times are about 2 times higher than those from the experiment, which is probably due to the use of nonpolarizable model. Also the fact, that we are not calculating exactly the Kerr signal, but just the orientational correlation function, might be the source of difference. The

1

0meth fit

0.1

Signal

63

0.01 0.001 0.0001 88meth fit

Signal

0.1 0.01 0.001 0.0001

100meth fit

Signal

0.1 0.01 0.001 0.0001 -500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Delay [fs] Fig. 4. Fit of long time decay of experimental signal for pure acetone (top), 88 mol% methanol mixture (middle), pure methanol (bottom).

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K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

Decay time [fs]

1200

1100

1000

Amplitude

0.06

0.04

0.02

0

0

20

40

60

80

100

Mole percent of methanol Fig. 5. Monoexponential fit results for the methanol–acetone mixtures and pure acetone.

concentration dependence of the simulated decay times reflects the behavior of the experimental data for concentrations above about 30 mol% quite well. Even though with some fluctuation around 60 mol %, both curves have a tendency to increase with methanol concentration. For concentrations below 30 mol% the experimental values are dropping with the increase of methanol concentration, whereas the theoretical ones are rising. kWe can also see that the change in slope around 30 mol% visible in the experimental data is barely visible on the theoretical curve for acetone, whereas theoretical curve for methanol exhibits a slope change. We expect that the differences in the experimental data and the theoretical ones are due to use of a nonpolarizable model in simulations and the uncertainty of the experimental data, given by the error bars. The structural properties of our mixtures strongly depend on hydrogen bonding. As methanol is here the only hydrogen donor for the bonding, its interactions with the surrounding are tightly connected with the behavior of our mixtures. The slope change of methanol theoretical decay curve at about 30 mol% suggests two

Acetone Methanol

Decay time [fs]

3000

2500

2000

1500

0

20

40

60

Mole percent of methanol Fig. 6. Theoretical decays.

80

100

organization regimes and we observe a change between them around 30 mol%. There is also some bump at about 90 mol%. In previous works it was shown that pure methanol tends to form chainlike clusters, with the most probable structure size of about 5 to 6 molecules [14–18]. In contrary to methanol, pure acetone forms just dimers in which molecules tend to orient their dipole moments antiparallel to each other [19–21]. In Fig. 8 we have reported the average number of hydrogen bonds calculated for all considered acetone/methanol mixtures. We can clearly see a linear increase of the total number of hydrogen bonds with methanol concentration. The plot of the number of hydrogen bonds between methanol and acetone exhibits a maximum as besides the increasing number of hydrogen donors with methanol concentration, we observe a decrease in the acetone concentration. The curve for hydrogen bonds number between methanol molecules exhibits a nonlinear increase with increasing methanol concentration. This is because some of the methanol molecules form hydrogen bonds with acetone molecules. As the methanol concentration increases, the concentration of acetone molecules drops. The sum of methanol– methanol and methanol–acetone hydrogen bonds gives the total amount of hydrogen bonds. Another graph (Fig. 9) presents some statistics about the number of bonds formed per molecule (do not confuse it with the number of bonds, that molecule takes part in). We can see here that for each mixture almost every methanol molecule is used as a donor (diamonds). This corresponds to the linear increase of hydrogen bonds count with methanol concentration (Fig. 8). The number of bonds accepted per methanol (circles) and per acetone molecule (triangles) is rising, which can be easily explained by an increasing probability of having a hydrogen donating neighbor molecule with increase of methanol concentration. The graph shows also a drop in the probability of finding acetone molecule for hydrogen bonding near the methanol molecule as amount of acetone molecules is decreased (squares). If we look at the curves representing the methanol–acetone hydrogen bonds per methanol molecule and methanol–methanol hydrogen bonds per methanol molecule, we can see that they show a slope change (more visible for methanol– methanol case) at about 30 mol% of methanol. In Fig. 10 we present the calculated expected value of cluster size, that molecule belongs to. The cluster is here defined as a connected graph, where the molecules and hydrogen bonds represent vertices

Signal

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

Signal

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

65 acetone fit

methanol fit

0

500

1000

1500

2000

2500

3000

3500

4000

Delay [fs] Fig. 7. Example fit of the theoretical decays for 50 mol% methanol.

Me->Me per Me Me->Ac per Me Me->Me + Me->Ac per Me Me->Ac per Ac

1

Bonds per molecule

and edges respectively. A nonlinear increase of the expected value of the cluster size with increasing methanol concentration is clearly visible. As the number of hydrogen bonds grows linearly with increasing methanol concentration (Fig. 8), we conclude that at higher methanol concentrations molecules tend to form less clusters, but of larger size. The expected value of methanol cluster size (178) is much higher than the most probable structure size reported in other articles (5–6). This is because our calculation is not based on the amount of clusters of a given size, but on the amount of molecules belonging to a cluster of a given size. In order to get more information about the structure of our mixtures, we have calculated statistics describing the probability of different hydrogen bonding configurations the molecule can take part in (Figs. 11–14). The symbols of the configurations are written as Xabcd, where X is the molecule that is considered, a and b are the numbers of protons accepted from the same or different type of molecule respectively, c and d are the number of protons donated to the same or different type of molecule respectively. We can see on those figures that the fraction of methanol molecules that are inside a linear chain (Me1001 + Me1010) is

0.5

0

0

20

40

60

80

100

Mole percent of methanol Fig. 9. Number of methanol–methanol hydrogen bonds per methanol molecule (circles), methanol–acetone hydrogen bonds per methanol molecule (squares), methanol–acetone hydrogen bonds per acetone molecule (triangles), any hydrogen bonds per methanol molecule (diamonds).

600 30

500

Cluster size expected value

Number of hydrogen bonds

Me->Me Me->Ac Me->Me + Me->Ac

400

300

200

100

0 0

20

40

60

80

100

Mole percent of methanol

20

10

0

0

20

40

60

Mole percent of methanol Fig. 8. Number of hydrogen bonds between methanol molecules (circles), between methanol and acetone molecules (squares), total (diamonds).

Fig. 10. Expected value of cluster size.

80

100

66

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

1

1

0.8

Configuration probability

Configuration probability

Ac0000 Ac0100 Ac0200

0.6

0.4

0.2

Me1000 Me1001 Me1010 Me1001+Me1010

0.8

0.6

0.4

0.2

0 0

20

40

60

80

0

100

0

20

Fig. 11. Probabilities of acetone molecules configurations.

60

80

100

Fig. 13. Probabilities of methanol molecules configurations with 1 acceptor hydrogen bonds.

growing, which confirms, that the clusters are getting bigger with methanol concentration. As every chain of molecules starts with methanol in Me0001 or Me0010 configuration, we can see that less chains are formed with increasing methanol concentration. A chain may connect to another chain and thus belong to the same cluster. The sum of Me2001 and Me2010 configurations shows that the fraction of branching methanol molecules is increasing with methanol concentration. We thus suggest that for low methanol concentrations methanol forms small structures of 1–3 molecules, surrounded by acetone molecules. Similar behavior has been reported for water in the water– methanol mixtures [3]. At about 30 mol% we get a transition, where the structure of our mixtures gets more uniform for higher concentrations. We suggest that at higher concentrations methanol structures are not separated by acetone, but rather spread all around the system and get penetrated by acetone molecules. The transition at about 30 mol% corresponds to the concentration of methanol, where the small hydrogen bonded clusters start to be close enough to each other to connect into larger structures. This theory is in agreement with the data presented above. At about 30 mol% the fraction of branching methanol molecules starts to grow rapidly (Me2010 + Me2010, Fig. 14), the fraction of methanol molecules starting a chain of methanol molecules stops rising (Me0010, Fig. 12), the fraction of linear chain methanol molecules

donating hydrogen to acetone molecule starts to drop (Me1001, Fig. 13). This transition was also reflected by the change in the reorientation time of the molecules measured experimentally (Fig. 5) and calculated based on the simulation results (Fig. 6). It could be also seen in the number of methanol–methanol hydrogen bonds per methanol molecule and methanol–acetone hydrogen bonds per methanol molecule. In Fig. 9, for lower concentrations the plots for methanol–methanol bonds per methanol molecule (circles) and methanol–acetone bonds per methanol molecule (squares) are steeper than for higher concentrations, which reflects the fact that when methanol is highly dispersed in acetone it is much easier to find acetone molecule to form a hydrogen bond. An important factor in our analysis is also the lifetime of the hydrogen bonds (Fig. 15). As it can be seen, both acetone–methanol and methanol–methanol hydrogen bond lifetimes decrease with the concentration of methanol. Additionally this change is small for bonds between methanol and acetone molecules, while being high for methanol–methanol bonds. Hydrogen bonds between methanol molecules are stronger than those between methanol and acetone, which is reflected in the simulation by longer lifetime of methanol– methanol bonds. For the methanol–methanol curve there is a slope change at about 30 mol%. At low methanol concentration methanol– methanol hydrogen bond lifetime corresponds mainly to molecules at

0.1

0.8

Configuration probability

Me0000 Me0001 Me0010 Me0001+Me0010

Configuration probability

40

Mole percent of methanol

Mole percent of methanol

0.6

0.4

0.2

Me2000 Me2001 Me2010 Me2010+Me2001

0.08

0.06

0.04

0.02

0

0

20

40

60

80

100

Mole percent of methanol Fig. 12. Probabilities of methanol molecules configurations with 0 acceptor hydrogen bonds.

0

0

20

40

60

80

100

Mole percent of methanol Fig. 14. Probabilities of methanol molecules configurations with 2 acceptor hydrogen bonds.

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

2500 Me->Me Me->Ac

1500

1000

500

20

40

60

80

Mole percent of methanol Fig. 15. Calculated lifetime of hydrogen bonds.

100

end of a chain, however as the terminal methanol molecules fraction starts to drop, the lifetime is being dominated by bonds inside a chain. Although the hydrogen bonds for molecule with one donor and one acceptor bond should be stronger than for molecule with just one hydrogen bond, the lifetime is decreasing. We expect that the cause for hydrogen bond lifetime decrease is twofold. First, the hydrogen donor that has broken its bond has a higher probability of finding another methanol molecule nearby for higher methanol concentrations, thus it can form a bond with methanol molecule that already had one acceptor bond. If a molecule has two acceptor bonds then they are weaker and more prone to breaking. Second, the growth of hydrogen bonded structures with increasing methanol concentration may cause a higher strain to affect the hydrogen bonds, which would lead to a decrease in the hydrogen bond lifetime. The methanol– acetone hydrogen bond lifetime does not change much. If we look at the fractions of acetone configurations (Fig. 11), we can clearly see that the hydrogen bond lifetime is dominated by singly bonded acetone (Ac0100). Even for 90 mol% methanol there is about 50% of unbonded acetone molecules (Ac0000) and just about 1% of doubly

CH3M-CH3M OM-OM OM-HM

g(r)

4 3 2 1

CH3A-CH3A CA-CA OA-OA

g(r)

1.5

1

0.5

0

5

10

15

20

r[A] Fig. 16. RDFs for methanol (top) and acetone (bottom).

25meth 50meth 75meth 100meth

2.5

g(r)

0

2 1.5 1

g(r)

0

g(r)

Bond lifetime [fs]

2000

67

10 8 6 4 2

25meth 50meth 75meth 100meth

12

25meth 50meth 75meth 100meth

8 4 0

5

10

15

20

r[A] Fig. 17. Change in methanol CH3 groups (top) RDF, oxygen RDF (middle) and oxygen–hydrogen RDF (bottom) with concentration.

68

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69 0meth 25meth 50meth 75meth

1.3

g(r)

1.2 1.1 1 0.9

0meth 25meth 50meth 75meth

g(r)

1.4 1.2 1 0.8

0meth 25meth 50meth 75meth

g(r)

1.2 1.1 1 0

5

10

15

20

r[A] Fig. 18. Change in acetone CH3 groups RDF (top), central carbon RDF (middle) and oxygen RDF (bottom) with concentration.

bonded ones (Ac0200). The doubly bonded acetone molecules have weaker hydrogen bonds. We suggest that the hydrogen bonds between methanol and acetone are also weakened because of elongation of methanol chains and the resulting increase of strain. The lifetime and number of hydrogen bonds influence the system viscosity. We suggest that the drop in the acetone hydrogen bond lifetime in the real system might be higher for low methanol concentrations. This could give rise to a decrease in viscosity as the effect of decreasing bond lifetime would overcome the effect due to increase of the hydrogen bonds number. As the reorientation time of the molecules is proportional to the system viscosity, the initial decrease in the reorientation time from the experiment can be explained (Fig. 5). The viscosity of the investigated system was presented in [13] and confirms our results. The viscosity concentration dependence curve exhibits a minimum at about 30 mol% of methanol. We have also analyzed radial distribution functions, which also seem to be in agreement with the structure concentration dependence described above. The RDFs presented on graphs contain an A or M letter at the end of site names, indicating their belonging to acetone or methanol respectively.

The calculated radial distribution functions for pure methanol and pure acetone are shown on Fig. 16. For methanol it can be seen that the RDF of CH3 group has the first peak of shape indicating a sum of at least 2 peaks, which suggests that there is not only one preferred orientation of methanol molecules with respect to each other. The oxygen first maximum corresponds to a shorter distance of about 0.27 nm, which fulfills one of the previously discussed criterions for hydrogen bonding. The peak at 0.18 nm indicates that the distance from an oxygen atom to its first neighbor hydrogen from another molecule is shorter than the distance to the first neighbor oxygen atom, which should be due to hydrogen bonding. As the first peaks for OM–OM and OM–HM RDFs are quite high, with a very deep minimum after, the local structure of the methanol molecules appears to be very well defined all around the system. For the acetone case RDF for central carbon atoms seems to correspond to uniform angular distribution. This in turn gives the explanation for the doubled first peak in the other two RDFs. The double oxygen peak informs us that orientation of different first neighbor pairs differs, giving at least 2 different orientation possibilities. Also should be noted that acetone molecule contains 2 12meth 37meth 63meth 88meth

g(r)

1.8 1.4 1 0.6

12meth 37meth 63meth 88meth

1.6

g(r)

1.4 1.2 1

0

5

10

15

20

r[A] Fig. 19. Change in methanol CH3 group–acetone central carbon RDF (top) and methanol oxygen–acetone central carbon RDF (bottom) with concentration.

K. Polok et al. / Journal of Molecular Liquids 159 (2011) 60–69

69 12meth 37meth 63meth 88meth

2

g(r)

1.5 1 0.5

12meth 37meth 63meth 88meth

4

g(r)

3 2 1

0

5

10

15

20

r[A] Fig. 20. Change in methanol oxygen–acetone oxygen RDF (top) and methanol hydrogen–acetone oxygen (bottom) with concentration.

CH3 groups and so they can lead to the doubling of the first peak in CH3A–CH3A RDF. The rest of the figures present the RDF dependence on system composition. On Figs. 17 and 18 the change with concentration in the methanol RDFs and acetone RDFs is given respectively. Figs. 19 and 20 present the concentration dependence of the RDFs describing pairs of atoms, where one of the peers is a part of acetone molecule and the other is a part of methanol molecule. On all the figures containing only methanol species the first peak drops drastically with increasing methanol concentration. The change in size can be seen also for the second peak for methanol hydrogen– oxygen RDF. The cause is simple. If two molecules of methanol contain a hydrogen of one of the molecules in between their oxygens, then the distance between the hydrogen from the second molecule and the oxygen from the first one is larger than the distance between the hydrogen atom from the first one and oxygen from the second one. This means that the second peak corresponds to the same molecule as the first one. It is smaller than the first one as the integration sphere is larger for longer distance in RDF calculation. This drop indicates that at lower concentrations methanol molecules tend to form groups in the system instead of spreading all around it. We do not observe such change in the acetone RDFs as at lower concentrations methanol groups are spread quite uniformly in the acetone solution, whereas for higher concentrations acetone tends to be almost uniformly distributed among the methanol molecules. Also RDFs joining species from methanol and acetone exhibit the drop in the first peak with methanol concentration. However here the interpretation is not so straightforward, as the curves depend on both species and the concentration dependence is more complicated. The RDFs containing as one of the species CH3 group from methanol or acetone exhibit a shift of the second and further peaks to shorter distances with increasing methanol concentration. We suggest that this is due to the increased stiffness of the structure of our liquid due to hydrogen bonding. This causes the steric repulsion to be less effective in separating molecules, which leads to shorter distances. In [14] authors suggest that the methyl groups rotate freely around the chain structures and do not feel each other. This suggestion seems to be reasonable, as the first peak position for methyl groups does not change. Also the second and third RDF peaks for acetone central carbons show shorter distances (Fig. 18). Some structural change at about 80 mol% methanol concentration can be seen. It is visible for the first

peak of acetone oxygen RDF (Fig. 18) and in the second and third neighbor distribution on acetone methanol oxygen–acetone central carbon RDF (Fig. 19) and methanol oxygen–acetone oxygen, methanol hydrogen–acetone oxygen RDFs (Fig. 20). This might suggest that at high methanol concentrations if two molecules of acetone happen to be close to each other, they will orient with oxygen atoms towards each other more frequently due to high amount of hydrogen donors nearby, therefore we get higher first peak in acetone oxygen RDF.

Acknowledgements Project is operated within the Foundation for Polish Science MPD Programme co-financed by the EU European Regional Development Fund.

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