Local Structural Effects and Related Dynamics in ... - ACS Publications

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J. Phys. Chem. B 2009, 113, 8898–8910

Local Structural Effects and Related Dynamics in Supercritical Ethanol. 2. Hydrogen-Bonding Network and Its Effect on Single Reorientational Dynamics Ioannis Skarmoutsos and Elvira Guardia* Departament de Fı´sica i Enginyeria Nuclear, UniVersitat Polite`cnica de Catalunya, B4-B5 Campus Nord UPC, 08034 Barcelona, Catalonia, Spain ReceiVed: February 18, 2009; ReVised Manuscript ReceiVed: March 27, 2009

The local hydrogen-bonding (HB) network and its possible interconnection with the single reorientational dynamics in pure supercritical (sc) ethanol have been systematically investigated by employing molecular dynamics simulation techniques. The results obtained reveal a nonlinear density dependence of the calculated average number of hydrogen bonds 〈nHB〉, similar to that of the calculated coordination numbers Nc, signifying also the interrelation between the local HB network and the local density augmentation in sc ethanol. Additionally, the HB dynamics were investigated in terms of several appropriate time correlation functions. The results obtained reveal that the density dependence of HB dynamics has some similarities with local density and residence dynamics, corresponding to very short length scales. Moreover, the effect of mutual reorientation on HB dynamics seems to be more important than that of mutual diffusion. Finally, the reorientational dynamics of several intramolecular vectors of ethanol have been systematically studied. From the results obtained, we may observe that the dynamics of several reorientational modes in the molecule exhibit significant differences between them. Furthermore, the effect of the HB state of each molecule on these dynamics has also been studied, revealing significant differences, especially in the case of the dynamics of HB free molecules. I. Introduction Supercritical fluids (scf’s) represent a class of solvents with very important applications in chemistry, material science, and engineering. Several aspects of the peculiar characteristics of scf’s, which have classified them as very powerful solvents in a wide range of applications, have been reviewed.1-10 During the previous decade, most of the efforts in developing new supercritical (sc) fluid technologies had been mainly focused on the applications of sc CO210 and water.5,8,9 One of the main reasons for this attention to these specific scf’s is their environmentally friendly “character”, enhancing, thus, the applicability of these fluids in many “green” chemical and industrial processes. Furthermore, in the case of sc CO2, its low critical point values are also a crucial factor for this attention, since many applications could take place at mild and, hence, more cost-efficient conditions. However, the applicability of CO2 becomes restricted in some cases due to its limited capability in dissolving polar compounds.11,12 On the other hand, the significantly high critical parameters of water constitute also a limiting factor in the applicability of this fluid in several processes. Therefore, the necessity in finding scf’s exhibiting similar properties to those of sc water, but at milder conditions, becomes apparent. In this sense, sc alcohols are often used as solvents in scf applications as an alternative for sc water13-16 because they provide similar characteristics and exhibit lower critical parameters. Moreover, their dielectric constant could be appropriately tuned with small density and pressure changes,15,17 allowing, thus, the eclectic dissolution of polar or nonpolar compounds over a wide density range. One other very important application of this class of solvents is that the lower alcohols (methanol, * Corresponding author: [email protected].

ethanol, 2-propanol, etc.) can be used as cosolvents with sc CO2 to increase the solubility of polar and high molecular weight compounds in pure sc CO2.11,12,18-20 Several experimental studies reported up to now have revealed that a local HB network, which is one of the most basic characteristics of liquid alcohols, still exists in the supercritical state.13,14,16,21-35 Moreover, a few reported simulation studies36-42 have also confirmed this behavior by investigating the pressure and temperature effect on the creation of hydrogen bonds between the lower alcohol molecules (methanol, ethanol, etc.). However, none of these investigations were performed in the range of thermodynamic conditions where the local density inhomogeneities (LDIs)43 are present, and no attempt to relate the HB properties of sc alcohols with LDIs has ever been published. Therefore, a systematic investigation of the possible interconnection between the HB structure and dynamics, local environment reorganization processes, and related single and collective dynamic properties could provide a deeper insight about fundamental issues on the behavior of these HB sc solvents. In this sense, the present study has been devoted to the thorough investigation of all the aforementioned issues by performing a series of molecular dynamics simulations for one of the most commonly used sc alcohols, namely sc ethanol. Such a treatment could shed some light on many open questions regarding these issues and is the main aim of this work. This work is the second part of our studies on sc ethanol, following our systematic investigations on the LDIs and corresponding dynamics in this system.43b This paper is organized as follows: the computational details of the performed simulations are presented in section II. The results obtained are presented and discussed in section III. Finally, the general conclusions and remarks drawn from the present study are in section IV.

10.1021/jp901489c CCC: $40.75  2009 American Chemical Society Published on Web 06/05/2009

Reorientational Dynamics in Supercritical Ethanol

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8899

TABLE 1: Summary of the Simulated Thermodynamic State Points of Supercritical Ethanol at T ) 533 Ka simulated state points

F (g/cm3)

A B C D E F G H I

0.053 0.097 0.168 0.237 0.316 0.348 0.395 0.432 0.552

a The critical parameters for ethanol are Tc ) 516.2 K and Fc ) 0.276 g/cm3 (ref 15).

II. Simulation Details The sc ethanol simulation runs were performed in the NVT ensemble along the sc isotherm of 533 K and for a series of densities in the range 0.2-2.0 Fc. The simulated state points of sc ethanol are presented in Table 1. The simulations were carried out using 500 molecules. Each simulation was extended to 1.0 ns to achieve equilibrium, starting from an initial face-centered cubic (fcc) configuration, and the properties of the system were evaluated in subsequent simulations with duration 500 ps. In all simulations, the equations of motion were integrated using a leapfrog-type Verlet algorithm, and the integration time step was set to 1 fs. The Berendsen thermostat44 with a temperature relaxation time of 0.5 ps was also used to constrain the temperature during the simulations. The intramolecular geometry of the species was also constrained by using the SHAKE method.45 The flexible OPLS-UA46 potential model was employed to describe the site-site interactions between the ethanol molecules. This four-site potential model has been successfully used in previous studies of liquid and sc ethanol,38,47-49 as well as in the case of sc CO2-ethanol mixtures.11 The intermolecular interactions are represented as pair-wise additive with site-site Lennard-Jones (LJ) plus coulomb interactions due to the dipole moment of ethanol molecules. Moreover, the intramolecular torsion around the central C2-O bond has been expressed by using the following dihedral angle potential function:46

1 1 V(θ) ) V0 + V1(1 + cos θ) + V2(1 - cos 2θ) + 2 2 1 V (1 + cos 3θ) (1) 2 3 In our simulations, a cutoff radius of 12.5 Å has been applied for all LJ interactions, and long-range corrections have been also taken into account. For the cross interactions, the geometric combining rules, instead of the common Lorentz-Berthelot, were used. Moreover, to account for the long-range electrostatic interactions, the Ewald summation technique was used, based on the more exact approximation of the Newton-Gregory forward difference interpolation scheme. III. Results and Discussion A. Static Local Structure: HB Network. In order to reveal some information relative to the local intermolecular structure in sc ethanol, we have calculated the site-site pair radial distribution functions (prdf’s), and herein, we present those mainly related with HB interactions, namely O-H, O-O, and H-H. The density dependence of the shape of these prdf’s is

Figure 1. Calculated atom-atom pair radial distribution functions g(r) of sc ethanol for some representative thermodynamic state points: (a) O-H, (b) O-O, and (c) H-H.

presented in Figure 1. By inspecting these functions, we may observe that the existence of HB interactions is clearly indicated, even at these extreme thermodynamic conditions. Concerning the O-H prdf’s, we may observe that they start to exhibit nonzero values at very short interatomic distances, close to 1.4 Å, and the first peak of these functions is located at about 1.9 Å. We have to mention that the location of this peak does not change with density; however, its amplitude decreases significantly at higher densities. The first minimum of the O-H prdf’s is located at about 2.7 Å, followed by a second peak located at 3.4 Å and a second minimum at 4.2 Å. The amplitude of this second peak decreases also at higher densities, whereas the location remains more or less constant. In the case of the O-O

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prdf’s, they start exhibiting non-zero values at larger interatomic distances than in the case of the O-H ones, close to 2.3 Å and their first peak is located at about 2.8 Å. The amplitude of this peak is higher than the corresponding one for the O-H prdf and exhibits more or less the same density dependence. The first minimum is located at 3.8 Å, whereas we did not observe a second peak in this case. Finally, concerning the behavior of the H-H prdf’s, their first non-zero values are located at more or less the same distance as in the case of the O-H prdf’s, and their first peak is located at 2.5 Å with amplitude similar to that of the O-O function. Their first minimum is located at about 3.9 Å at the higher density, whereas at lower densities we may observe a very small shift toward higher distances. This behavior is also observed in the case of the O-O functions. Finally, as in the case of the O-O prdf’s, we do not observe a second peak for the H-H functions. In general, we may say that the shape of these site-site prdf’s indicates a possible existence of HB interactions in the fluid. However, in order to have a more quantitative representation of the extent of the degree of HB in ethanol at sc conditions and its density dependence, we have performed a HB analysis based on previously used simple geometric criteria.47,48 According to the criterion used in our study, a hydrogen bond between two ethanol molecules exists if the intermolecular distances are RO · · · O e 3.5 and RH · · · O e 2.6 Å and the angle φ ≡∠H-O · · · H e 30° ( · · · denotes an intermolecular vector, whereas - denotes an intramolecular one). We have to mention that this criterion has been successfully used in the past to predict the HB properties of ethanol and methanol,36,39,47,48 and therefore, we decided to employ it in our investigation. In view of the above, the calculated average number of hydrogen bonds per ethanol molecule 〈nHB〉 corresponding to each simulated state point is presented in Figure 2. Moreover, our calculations have been extended to incorporate hydrogen-bond statistics by estimating the percentage distribution fn of molecules with n (n ) 0, 1, 2,...) bonds per molecule, where f0 denotes the percentage of no bonded molecules or monomer, f1 the percentage of the molecules with one H-bond, etc. The calculated values of f0, f1, and f2 are presented in Figure 2. The percentages f3 have been also calculated, but their values are very small even at the highest density and, therefore, are not displayed in Figure 2. From the results obtained, we may conclude that the HB network in ethanol still exists at sc conditions, though it is significantly weaker. This conclusion is totally consistent with previous experimental13,14 and simulation38,39 studies. Even at the lowest density investigated, about 12% of the molecules remain hydrogen bonded, whereas at the highest simulated density the corresponding percentage is close to 60%. By inspecting also the density dependence of the mean number of hydrogen bonds per ethanol molecule 〈nHB〉, we may observe that it is clearly nonlinear. This nonlinear behavior has been also observed in the case of the calculated local coordination number Nc for the first solvation shell of ethanol.43b In general, according to the literature, the existence of local density augmentation effects in scf’s has been directly related to this nonlinear behavior.43,50,51 The same nonlinear density dependence has been also observed in the case of the fraction of molecules forming one hydrogen bond f1, whereas in the case of molecules forming two hydrogen bonds the density dependence of f2 is clearly linear. On the other hand, the decrease of the percentage of free molecules f0 with density also exhibits a nonlinear behavior. These observations signify that the nonlinear increase of the number of molecules forming one hydrogen bond is the most important factor which determines the nonlinear

Skarmoutsos and Guardia

Figure 2. Density dependence of: (a) the calculated average number of hydrogen bonds per ethanol molecule 〈nHB〉 and (b) the percentage distribution fi of molecules with i (i ) 0, 1, 2) bonds per molecule.

density dependence of 〈nHB〉. Moreover, the nonlinear decrease of the number of molecules which remain non-hydrogen bonded (free) is also presumably related to this nonlinear increase of f1. Therefore, it seems that all these nonlinear behaviors are possibly more closely related with the existence of local density augmentation effects in sc ethanol. In order to have also a picture of the geometrical characteristics of the hydrogen bonds formed among the ethanol molecules, we have calculated the hydrogen-bond length RH · · · O and bond angle φ distributions between pairs of molecules. The selected angle φ is the angle H-O · · · H, which has been also used in the HB criterion. In the framework of the present study, we initially calculated the distribution of angles φij for pairs of molecules having only RO · · · O e 3.5 and RH · · · O e 2.6 Å, in order to see also the effect of the cutoff angle used in the geometric criterion (φc ) 30°). Additionally, we calculated the distribution of bond lengths and angles only for the hydrogen-bonded pairs of molecules (for pairs having RO · · · O e 3.5 and RH · · · O e 2.6 Å, φij e φc) to obtain the actual geometrical characteristics of the hydrogen bonds. The results obtained for some representative state points are presented in Figure 3. The first significant observation from Figure 3 is that the results obtained are almost density independent. Concerning the first type of angle distribution, we have to mention that the obtained distributions are somewhat wider compared to the one corresponding to liquid ethanol. However, the majority of molecule pairs having RO · · · O


J. Phys. Chem. B, Vol. 113, No. 26, 2009 8901 B. HB Dynamics. Besides the static properties of the HB network in sc ethanol, we investigated, in the framework of the present study, the dynamics of the hydrogen bonds formed between the ethanol molecules. To do so, we have calculated some specific time correlation functions (tcf’s) related with the dynamic behavior of these hydrogen bonds. According to the literature, the average HB tcf for the pairs i, j of hydrogenbonded molecules could be defined as52,53

CHB(t) )

〈hij(0)hij(t)〉t* 〈hij(0) 〉 2

)

〈hij(0)hij(t)〉t* 〈h〉

(2)

In this definition 〈h〉 ≡ 〈hij(0)2〉 and is a dimensionless parameter, which can be directly related with the static average number of hydrogen bonds in the system.54,55 The corresponding HB lifetime is defined as ∞

τHB )

∫ CHB(t) dt

(3)

0

The variable hij has been defined in the following way:

hij(t) ) 1, if molecule j is hydrogen bonded with molecule i at times 0, and t and the bond has not been broken in the meantime for a period longer than t*. hij(t) ) 0, otherwise

Figure 3. (a) Distribution of angles φ ≡ H-O · · · H for pairs of molecules having only RO · · · O e 3.5 and RH · · · O e 2.6 Å. (b) Distribution of angles φ ≡ H-O · · · H for pairs of molecules satisfying the HB criteria. (c) Distribution of lengths RH · · · O for pairs of molecules satisfying the HB criteria.

e 3.5 and RH · · · O e 2.6 Å make angles with values less than the specified HB cutoff value φc ) 30°. In the case where only HB pairs have been considered from the obtained distributions, we calculated the mean values for the HB length RH · · · O and angle φ. The calculated average HB length values for the state points investigated are close to 2.0 Å, and the average HB angles are in the range 15-16°, in other words, close to values where the obtained distributions exhibit their maxima. As a general conclusion, we may see that as the density of the system increases, although as the values of 〈nHB〉 increase, the geometrical characteristics of the bonds formed among the molecules remain more or less the same.

(4)

Of course, using this definition, the calculation of CHB(t) depends upon the selection of the parameter t*. The two limiting cases arise from this definition: (a) If t* ) 0, which represents the so-called continuous definition. In this case, the calculated tcf is the continuous one CHBC(t), and the corresponding lifetime is the continuous lifetime τHBC. (b) If t* ) ∞, which represents the so-called intermittent definition. In this case, the calculated tcf is the intermittent one CHBI(t), and the corresponding lifetime is the intermittent lifetime (or HB relaxation time) τHBI. We have to mention that these two definitions describe very different aspects of HB dynamics. According to the continuous definition, the breaking of a hydrogen bond during the time interval [0, t] is not allowed, and the continuous lifetime is the time required for the first breaking of a bond created at time t ) 0. On the other hand, in the intermittent case, the persistence probability at time t of a hydrogen bond created at t ) 0 is investigated, regardless of multiple breakings and re-formations of this bond during the time interval [0, t]. In order to investigate the effects of the mutual diffusion between the molecules i, j which form a hydrogen bond, we have also calculated another HB tcf defined as follows:

d CHB (t)

〈hij(0)hijd (t)〉t* ) ) 〈h〉 〈hij(0)hijd (0)〉 〈hij(0)hijd (t)〉t*

The corresponding HB lifetime is defined as

(5)

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∞

d τHB

)

∫

d CHB (t)

dt

(6)

φ-I CHB (t)

)

〈hij(0)(hijφ(t) - p∼ φ)〉t*)∞

)

〈hij(0)hijφ(t)〉t*)∞ - 〈h〉p∼ φ

0

The variable hij has been defined previously, whereas the variable hijd is defined in the following way:

hijd(t) ) 1, if the intermolecular distance RO · · · O for the pair of molecules i, j which are hydrogen bonded at time t ) 0 is RO · · · O 〈3.5 Å and has not been larger in the meantime for a period longer than t*. hijd(t) ) 0, otherwise (7) As mentioned previously, in the two limiting cases t* ) 0 and t* ) ∞, we obtain the continuous CHBd-C(t) and intermittent CHBd-I(t) tcf’s and their corresponding lifetimes τHBd-C and τHBd-I, respectively. This definition is very similar to the definition used by Chandra54 to investigate the effects of mutual diffusion on the HB dynamics in water. However, in the present study, in order to present a more complete description of the processes contributing to the dynamics of hydrogen bonds, we defined a new function describing the effect of mutual reorientation of a pair of hydrogen-bonded molecules on the HB dynamics. Therefore, we initially defined this new function in the following way:

φ CHB (t) )

〈hij(0)hijφ(t)〉t* 〈hij(0)hijφ(0)〉

)

〈hij(0)hijφ(t)〉t* 〈h〉

(8)

In this new definition, the variable hij is again the same one that has been defined previously, concerning the overall HB state between a pair of molecules, whereas the variable hijφ is defined in the following way:

hijφ(t) ) 1, if the HB angle φ ≡ H-O · · · H (the same used in the HB criterion) for a pair of molecules i, j which are hydrogen bonded at time t ) 0 is φ e 30◦ and has not been larger in the meantime for a period longer than t*. hijφ(t) ) 0, otherwise (9) Our calculations have shown that, in the case of the continuous function CHBφ-C(t) (t* ) 0), the function after some time converges to zero. However, in the case of the intermittent one CHBφ-I(t) (t* ) ∞) due to the fact that there is always a probability that a pair of molecules which were initially hydrogen bonded will have the previously specified orientation even at tf∞, the function converges to a non-zero value. In order to eliminate this effect, we defined the intermittent function in the following way. If this average probability for a molecule j around i to have the specified orientation is defined as p˜˜ φ ) 〈Nijφ〉/(N - 1), where 〈Nijφ〉 is the average number of molecules j around i having the specified orientation, and N is the overall number of molecules in the simulation; then the intermittent function couned as follows:

〈hij(0)(hijφ(0) - p∼ φ)〉 〈h〉 - 〈h〉p∼ φ

(10)

So the definition of the continuous function is described in eq 6, whereas the intermittent one is described by eq 8. Of course, this procedure was performed in order to obtain a convergent value for the numerical integral of this tcf, which will represent the relaxation time corresponding to this dynamic process. Note that in the case of intermittent HB functions, similar approaches have also been applied in recently published works to correct finite size effects.55 The corresponding HB lifetimes τHBφ-C and τHBφ-I have also been defined as the time integrals of these functions, as in the previous cases (see eqs 3, 6). The density dependence of all the calculated HB lifetimes is presented in Figure 4. From this figure we may see that the density dependence of these HB lifetimes is similar to that obtained for residence times corresponding to local regions with a very short radius around the central particle.43b This behavior indicates that the behavior of pair dynamic properties at short intermolecular distances, like the residence and HB dynamics, is similar. At low densities, the values of the HB lifetimes are higher, especially in the intermittent case, and then we may observe a decrease of these lifetimes, which exhibit a plateau at intermediate and higher densities. This finding comes in agreement with the previous assumptions,43a according to which at low densities, the molecules form small metastable clusters which are longer lived and cause a corresponding retardation on the local density reorganization at short length scales. This finding, together with our previous findings43b that the local reorganization times and residence times corresponding to shortlength scale regions around a central particle are increased at the low-density region, supports further these assumptions. One other important conclusion arising from the observation of Figure 4 is that the contribution of mutual reorientation seems to affect more strongly the HB dynamics than the mutual diffusion between the hydrogen-bonded ethanol molecules. This effect is significantly more pronounced in the case of continuous dynamics, meaning that the mutual reorientation between two hydrogen-bonded molecules is the main mechanism responsible for the first breaking of a bond. In the case of intermittent HB dynamics, which correspond to an overall relaxation mechanism describing multiple breakings and reformations of a hydrogen bond until the survival probability of the initial bond is finally lost, the contribution of mutual diffusion starts to become more significant. This may be easily observed for Figure 4, where we may clearly see that whereas the continuous HB lifetimes τHBC and τHBφ-C are almost the same and significantly lower than τHBd-C, in the case of the corresponding intermittent lifetimes, the calculated values of τHBφ-I are somewhat different than the τHBI ones but closer to τHBI than the τHBd-I ones. C. Reorientational Dynamics. One of the main purposes of the present study was to investigate in more detail the effect of the local environment of the reorientational motions of sc ethanol. The main motivation for this was a previous observation by one of the present authors that the reorientational motions of specific intramolecular vectors in sc methanol are affected differently by the density of the fluid.43 In that previous study, it had been revealed that the density dependence of the calculated second-order Legendre reorientational times τ2R,


J. Phys. Chem. B, Vol. 113, No. 26, 2009 8903 it has been revealed that the density dependence of the firstand second-order Legendre reorientational times τ1R and τ2R, respectively, are in general different.58 This fact indicates that these two different ways of depicting and analyzing molecular reorientation in fluids are differently influenced by the local environment. Therefore, in the framework of the present study, we investigated all these issues in a more detailed way, trying to reveal some new information related with all the previously mentioned, very important information. In general, the reorientational dynamics for specified intramolecular vectors are investigated by means of the Legendre reorientational tcf’s:

ClR(t) ) 〈Pl(u b(0)u b(t))〉,

l ) 1, 2

(11)

In this equation b u is a unit vector along a specified direction inside a molecule and Pll is a Legendre polynomial P1(x) ) x, P2(x) ) 1/2(3x2 - 1). The corresponding reorientational times τlR (l ) 1, 2) are defined as follows: ∞

τlR )

∫ ClR(t) dt

(12)

0

Figure 4. Density dependence of all the calculated (a) continuous and (b) intermittent HB lifetimes.

corresponding to the O-H and C-O vectors of methanol, is substantially different in each case. The fact that the O-H reorientational motion is more affected by the formation of hydrogen bonds and the local HB network than the C-O one signifies that possibly this different density dependence is due to the effect of the intermolecular interactions on single molecule reorientation. In other words, the special characteristics of the intermolecular forces and the local environment around the molecules in a sc fluid are differently reflected on the several reorientational “modes” of the molecules. Previous studies on the reorientational dynamics of relatively weakly interacting fluids56-58 have shown that the obtained τ2R values exhibit a plateau behavior in a wide range of densities, signifying thus, that the τ2R reorientational times in these systems are not significantly affected by LDIs and the corresponding augmentation effects. The same plateau has been observed in the case of the C-O reorientational dynamics in sc methanol.43 However, in the case of the O-H reorientational dynamics, it seems that τ2R is affected by the local environment around the molecules,43 indicating thus, that even in the same molecule the local environment affects differently several aspects of molecular reorientation. In this sense, sc ethanol provides an excellent example to investigate all these features in more detail, in order to shed some light on the issues concerning the interconnection of the local environment and the special characteristics of the intermolecular interactions with molecular reorientation in a sc fluid. Moreover, from previous calculations

In the present study, we have investigated the reorientational dynamics of six different intramolecular vectors of ethanol. We have to note here that the (CH3-) and (CH2-) groups (sites) of the OPLS-UA model used in our simulations are named as C1 and C2, respectively. The ground-state intramolecular geometry and the site names of OPLS-UA ethanol are also depicted in the Supporting Information (Figure S1). The vectors taken into account in our study are the intramolecular bond vectors C1-C2, µ and the vectors C2-O, and O-H, the molecular dipole vector b f f f f b u1p ) (C2C1)(C2O) and b u2p ) (OC2)(OH), which are perpendicular to the planes defined by the sites C1, C2, O and C2, O, H, respectively. The density dependence of the calculated Legendre reorientational times τ1R and τ2R for all the aforementioned intramolecular vectors is presented in Figures 5 and 6, whereas the density dependence of the calculated reorientational tcf’s may also be found in the section of the Supporting Information (Figures S2-S5). By inspecting carefully Figures 5 and 6, some very interesting remarks may be drawn. First of all, we may observe that there are three different groups of vectors where the reorientational times exhibit more or less the same density dependence. So, we may clearly see that the reorientational times τ1R for the vectors C1-C2 and u1p exhibit similar density dependence, and this happens also for the vectors µ and O-H, as well as for the third group of vectors, consisting of the vectors C2-O and u2p. The same behavior has been also observed for τ2R. However, we have to say that the density dependence of τ2R is not the same with the one observed for τ1R, especially in the case of the C1-C2 and u1p vectors, where we may observe a plateau for the τ2R values, as in the case of CO2 or for the C-O vector of sc methanol. So, we may say that in general the first-order Legendre reorientational dynamics seem to be more strongly related with the local environment than the corresponding second-order ones, since we may observe a clear density effect for all the vectors in the case of the τ1R values. Moreover, we may see that reorientational modes related to weaker intermolecular interactions (e.g., C1-C2 and u1p reorientation) are less affected by the local environment, and this behavior is mainly reflected on the behavior of the τ2R values.

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Figure 5. Density dependence of the calculated average first-order Legendre reorientational times τ1R of the investigated intramolecular vectors of ethanol.

On the other hand, we may see that for the group consisting of the O-H and molecular dipole vectors, which are, of course, more closely related to stronger interactions and to the local HB network, the τ1R and τ2R values seem to be strongly affected by the local environment and increase as the bulk density of the system increases. This behavior has been also observed for sc methanol.43a At this point, we have to also mention that the obtained average τ2R values for the O-H vector of sc ethanol are in good agreement with reported experimental values obtained by NMR measurements, corresponding to similar thermodynamic state points (543 K).59 Therefore, in order to depict more clearly the significance of the strength of the intermolecular interactions and of the local


Figure 6. Density dependence of the calculated average second-order Legendre reorientational times τ2R of the investigated intramolecular vectors of ethanol.

structural network on the reorientational dynamics in sc ethanol, we performed an additional analysis of reorientational dynamics, where we calculated the Legendre reorientational tcf’s as a function of the hydrogen bonds per molecule. These functions can be defined as follows:

Cn,lR(t) )

〈Pl(u b(0)u b(t))Θn(0)〉 〈Θn(0)〉

n ) 0, 1, 2

and

l ) 1, 2

(13)



As previously, the index l defines the order of the Legendre polynomial, whereas the index n defines the instantaneous number of hydrogen bonds which forms a molecule at each time t. The function Θn(t) is defined as follows:

Θn(t) ) 1, if a molecule forms n hydrogen bonds at time t. Θn(t) ) 0, otherwise (14) The corresponding reorientational times are defined as ∞

τn,lR )

∫ Cn,lR(t) dt

n ) 0, 1, 2

and

l ) 1, 2

0

(15) Therefore, we investigated the reorientational dynamics of molecules forming n ) 0 (free molecules), n ) 1 and n ) 2 hydrogen bonds, in order to see the effect of the local HB network on these properties. This analysis was performed for three representative vectors of each of the aforementioned vector groups, namely the three intramolecular bond vectors C1-C2, C2-O, and O-H. These calculated first- and second-order Legendre tcf’s for some representative state points are depicted in Figures 7-12, and the density dependence of the corresponding reorientational times is presented in Figures 13 and 14. From the results obtained, we may clearly see that the local HB network around the molecules affects strongly their reorientational dynamics. In all the figures, we may observe that especially the reorientational dynamics of HB free molecules (n ) 0) are substantially different, and their corresponding correlation times are lower in comparison with those obtained for hydrogen-bonded molecules. In general, we may observe a slower decay in the reorientational tcf’s Cn,lR(t) as the values of n increase, and this retardation is reflected on the calculated reorientational correlation times τn,lR. Moreover, in the case of the C1-C2 and C2-O vectors, we may observe that at low densities the first-order Legendre tcf’s, corresponding to HB free molecules (see Figures 8 and 9) C0,1R(t), exhibit negative parts, and this specific shape of these tcf’s is somewhat similar with the free rotor behavior. However, this behavior is not present for higher n values (n ) 1, 2), signifying the strong effect of the local HB network on these dynamics. On the other hand, we may also see that the behavior of the O-H dynamics at very short time scales (∼0.1 ps) exhibits characteristics typical for HB fluids (see Figures 7 and 10), and the characteristic local minima observed at short time scales are much more pronounced for higher n values. One other very interesting finding is that the density dependence of the second-order Legendre reorientational times for the vectors C1-C2 and C2-O, corresponding to the HB free molecules (n ) 0), is different than in the case of hydrogenbonded ones, and we may see that the relaxation times τ0,2R for these vectors exhibit plateau. On the other hand, in the case of hydrogen-bonded molecules, the times τ1,2R and τ2,2R increase with the density. Even in the case of the O-H dynamics, the times τ0,2R do not change significantly with the density, and a very slight increase with density has been observed. This result verifies our previous hypotheses, that in the cases where the interactions among the molecules are relatively weak,43a the second-order Legendre reorientational dynamics are not significantly affected by the bulk density of the system. On the other hand, when these interactions become stronger, the local

Figure 7. Representative calculated first-order Legendre reorientational tcf’s Cn,1R(t) (eq 13) for the O-H vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

structural network (HB and local density augmentation) affects the reorientational dynamics of the molecules, and this effect is clearly reflected on the density dependence of the obtained reorientational times. This finding could be very useful for experimentalists working on the investigation of the local density augmentation effects in scf’s. According to the literature, the experimentally determined reorientational times could be used in order to calculate the average local density around a molecule in a scf.60 Our findings indicate that one should be very careful when selecting the appropriate reorientational mode to be used as a probe of the local structure around a molecule. Taking, hence, into

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Figure 8. Representative calculated first-order Legendre reorientational tcf’s Cn,1R(t) (eq 13) for the C2-O vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

Figure 9. Representative calculated first-order Legendre reorientational tcf’s Cn,1R(t) (eq 13) for the C1-C2 vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

account the facts that the reorientational times τ1R and τ2R are in general different probes of the interconnection between local intermolecular structure and reorientational dynamics in scf’s and, on the other hand, that the effect of intermolecular interactions on the density dependence of reorientational times is significantly “mode-dependent”, the experimentalists should be very careful when selecting the appropriate mode for their analyses. A similar point has been also discussed in previous works,43a focusing mainly on the experimental determination of local density augmentation effects using vibrational line shifts as probes of the local structure. In these cases, the results have also shown that the results obtained are dependent on the

vibrational mode used in the analysis of spectral shifts. Therefore, the behavior of the reorientational times could be in general very helpful on the selection of the appropriate modes which could be used as probes by the experimentalists for the determination of local density inhomogeneities in scf’s. IV. General Conclusions The present work has focused mainly on the investigation of the static and dynamic behavior of the local HB network in sc ethanol and its effect on the single reorientational dynamics of the molecules in the fluid. The results obtained have revealed



Figure 10. Representative calculated second-order Legendre reorientational tcf’s Cn,2R(t) (eq 13) for the O-H vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

Figure 11. Representative calculated second-order Legendre reorientational tcf’s Cn,2R(t) (eq 13) for the C2-O vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

that the behavior of the average number of hydrogen bonds per molecule 〈nHB〉 with density is clearly nonlinear. This nonlinearity, in general, which is also observed in the density dependence of the local coordination number in scf’s, indicates clearly that the local HB network determines significantly the existence of local density augmentation effects, which have been also observed for sc ethanol and have been presented elsewhere.43b The HB statistics performed in the framework of the present study also reveal that the nonlinear increase with density of the fraction of molecules forming one hydrogen bond f1 is the most important factor in determining the overall nonlinear behavior of 〈nHB〉. Moreover, it seems that there is probably some relation between the nonlinear increase of f1 with

the nonlinear decrease of the fraction of HB free molecules f0. We have to note also that, although the HB local network becomes more cohesive at higher densities, the geometrical characteristics of the bonds formed among the molecules remain more or less the same. Moreover, the density effects on the HB dynamics in sc ethanol exhibit similarities with those observed for the residence dynamics at short intermolecular distances.43b This observation signifies that the dynamic properties related to the persistence of pairs of molecules at relatively short intermolecular distances are not significantly affected by the local structural network, especially in the range of intermediate and liquid-like densities.

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Figure 12. Representative calculated second-order Legendre reorientational tcf’s Cn,2R(t) (eq 13) for the C-C2 vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

In general, we might say that, although there is a strong interconnection between the static HB network and local density inhomogeneity effects in sc ethanol, the dynamic behavior of this local HB network seems to be not so strongly affected by the local structure of the system, and such an interrelation is observed only at very low bulk densities. The higher HB lifetimes observed at low densities have been related with the formation of small longer-lived clusters, which have been related in previous publications with the slowing down effects in the local density reorganization of the first solvation shell around the molecules in scf’s.


Figure 13. Density dependence of the calculated first-order Legendre reorientational times τn,1R (eq 15) for the O-H, C2-O, and C1-C2 vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

The microscopic mechanisms related to the dynamic behavior of hydrogen bonds have been also investigated in order to reveal the contributions of mutual diffusion and reorientation to the HB relaxation dynamics. The results obtained have revealed that, especially in the case of continuous HB dynamics, the microscopic processes related to the mutual reorientation of the ethanol molecules have a more significant contribution on HB dynamics. However, in the case intermittent HB dynamics, the contribution of mutual diffusion starts also to affect the intermittent structural relaxation of the hydrogen bonds.


J. Phys. Chem. B, Vol. 113, No. 26, 2009 8909 intermolecular interactions on reorientational dynamics. In the cases where the interactions among the molecules are relatively weak, the τ2R values are not significantly affected by the bulk density of the system. When these interactions become stronger, the local structural network affects the reorientational dynamics of the modes related with these interactions, and this effect is clearly reflected on the density dependence of the obtained τ2R reorientational times. On the other hand, the first-order Legendre reorientational dynamics seem to be more sensitive to the local environment around the molecules. This behavior is very clearly reflected on the significant density dependence, which is observed in the calculated τ1R values for all the intramolecular vectors taken into account in our calculations. Acknowledgment. I.S. acknowledges the postdoctoral financial support of the Department of Physics and Nuclear Engineering (DFEN, http://www.fen.upc.edu) of the Technical University of Catalonia (UPC), Barcelona-Spain. The CPU time allocation on the facilities of the Computer Simulation in Condensed Matter Research Group in DFEN is also gratefully acknowledged. E.G. gratefully acknowledges financial support from the Direccio´ General de Recerca de la Generalitat de Catalunya (Grant 2005SGR-00779) and from the Ministerio de Educacio´n y Ciencia of Spain (Grant FIS2006-12436-CO2-01). Supporting Information Available: Equilibrium geometry of the OPLS-UA ethanol molecules, as well as the density dependence of the Legendre reorientational tcf’s for several intramolecular vectors of ethanol. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 14. Density dependence of the calculated second-order Legendre reorientational times τn,2R (eq 15) for the O-H, C2-O, and C1-C2 vector of ethanol molecules forming n ) 0, 1, and 2 hydrogen bonds.

Finally, in the present work it has been revealed that the reorientational dynamic behavior of the ethanol molecules is significantly affected by the local HB network, especially in the case of the reorientation of intramolecular vectors more strongly related with the formation of hydrogen bonds. Furthermore, it has been revealed that the density dependence of the second-order Legendre reorientational times τ2R depends strongly on the “reorientational mode” taken into account in our calculations. The results obtained in this study reveal that the plateau behavior of τ2R observed for some intramolecular vectors is possibly related to the effect of the strength of

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