View Article Online View Journal
PCCP Accepted Manuscript
This article can be cited before page numbers have been issued, to do this please use: I. Skarmoutsos, T. Welton and P. Hunt, Phys. Chem. Chem. Phys., 2013, DOI: 10.1039/C3CP54551B.
This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains.
www.rsc.org/pccp
Page 1 of 11
Physical Chemistry Chemical Physics
Journal Name
RSCPublishing View Article Online
DOI: 10.1039/C3CP54551B
Cite this: DOI: 10.1039/x0xx00000x
The Importance of Timescale for Hydrogen Bonding in Imidazolium Chloride Ionic Liquids Ioannis Skarmoutsosa* Tom Weltonb and Patricia A. Huntc*
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
Received 00th January 2012, Accepted 00th January 2012 DOI: 10.1039/x0xx00000x www.rsc.org/
Hydrogen bond (H-bond) dynamics have been investigated for "hot" 1-ethyl-3-methylimidazolium chloride and "cold" 1-butyl-3-methylimidazolium chloride ionic liquids (IL). While the average number of H-bonds remains constant for a ≈100ºC temperature change we show that the underlying dynamics of the H-bonding changes dramatically. H-bond dynamics are investigated based on distance and angle criteria, and on the H-bond state (zero, single or bifurcated H-bonds). Temperature effects on the cation ring reorintational dynamics are also examined. Angle deformations are found to be more important than bond stretching in determining the lifetime of individual H-bonds, and decay occurs on two time scales related to the magnitude of the deviation from linearity. Rapid angular oscillation of the anion breaks the H-bond (for the first time) and minimal temperature effects indicate that H-bonds are readily reformed even near the melting point. Intermittent H-bonds repeatedly break and reform over a longer timescale, and exhibit very strong temperature effects. In the hot IL H-bonding with ring and alkyl chain H-atoms occurs, ring reorientational dynamics is anisotropic and the corresponding lifetimes are similar to the intermittent H-bond lifetimes. In the cold IL ring H-atoms dominate the Hbonding and intermittent H-bonds last for ≈5ns, ring reorientation occurs on a much slower timescale. The hot IL favours single H-bonds, but the individual ions often change, while the cold IL favours bifurcated H-bonds with the same co-located ions.
1. Introduction The properties of many liquid solvents are significantly 1,2 affected by the presence of hydrogen bonds (H-bonds). However, even for water, the precise nature of the H-bond is 3-7 still under debate and for more complex systems such as ionic liquids (ILs) H-bonds are still far from being well8,9 understood. Thus, the investigation of H-bond structure and dynamics at a microscopic level is important for achieving a deeper understanding of these liquids. Ionic liquids have attracted significant attention in both the 10-14 scientific and technological communities. They have a range of interesting physical and chemical properties including; a very low vapour pressure, high thermal conductivity, high thermal stability and a wide electrochemical window. The ability to tune the dissolving capability and solvation characteristics of ILs with the appropriate selection of the cations or anions has identified ILs as an important class of solvents, with a wide range of potential applications. However, the use of ILs as reaction media and electrolytes has been seriously limited by poor transport properties. For example, ILs can be as viscous as oils, the high viscosity 15 leading to a lower electrical conductivity. Recent studies have identified the importance and impact of H-bonding 16-19 interactions on the transport properties of ILs. A deeper
This journal is © The Royal Society of Chemistry 2013
understanding of the nature of H-bonding interactions in ILs may therefore act as a springboard for better rational design of ILs with improved transport properties. The relationship between H-bonding and molecular behavior for the imidazolium based ILs has been studied both 20-35 experimentally and theoretically.8,9,36-48 These studies have provided detailed insight into the nature of H-bonds within ILs. Traditionally diffusion and reorientation dynamics have been examined, however very few studies have explicitly considered 41,49,50 the H-bond dynamics. Herein we investigate, using MD simulation techniques, the H-bond dynamics of 1-butyl-3methylimidazolium chloride [C4C1im]Cl and 1-ethyl-3methylimidazolium chloride [C2C1im]Cl ILs. One issue for describing H-bonding in these ILs, is that there is evidence that the geometric conditions used to define 51 the H-bond can qualitatively affect the results. Previously we have determined that the average number of H-bonds per hydrogen atom in [C4C1im]Cl at 353 K, just 13 ºC above its melting point, is very similar to that obtained for [C2C1im]Cl, 51 90ºC above its melting point. This result was counterintuitive; the viscosities of [C4C1im]Cl and [C2C1im]Cl are sensitive to temperature changes, and decrease upon heating. Thus, we expected the higher temperature and more fluid liquid to be associated with a reduced H-bonding network, and a reduced average number of H-bonds. However, no significant
J. Name., 2013, 00, 1-3 | 1
Physical Chemistry Chemical Physics Accepted Manuscript
ARTICLE
Physical Chemistry Chemical Physics
Page 2 of 11
ARTICLE
Figure 1 Representation of the continuous and intermittent H-bond dynamics.
Continuous and intermittent H-bond dynamics have been examined for a limited number of ILs. In [C4C1im][PF6] the continuous lifetime has been related to rotation of the anion leading to rapid breaking and forming of the H-bonds, and the intermittent lifetime has been associated with caging and 49 librational motion. For [C2C1im][SCN] the intermittent 50 lifetime was associated with the H-bonding network. Studies on [C2C1im]Cl, 90ºC above the melting point, have shown ballistic behaviour for about 0.1ps, a sub-diffuse regime and 52,41 then gaussian diffusive behaviour after about 1.5ns. Similarly [C4C1im][PF4], at 10ºC and 90ºC above the melting point has shown sub-diffusive behaviour in the range ≈2-40ps and ≈3-10ps respectively. Sub-diffuse dynamics are related to breaking out of the local caging environment and can encompass a distribution of processes with different rates. Cation dynamics (ring orientational dynamics) has been related to local cage librations followed by complete relaxation as 53,54 aggregates break-up and diffuse. Thus, an understanding of the H-bonding dynamics can also offer insight into the more general dynamics within an IL. In the following section computational details are outlined. In the results and discussion section residence dynamics, Hbonding dynamics, dynamics of the individual H-bonding states (0,1 or 2 H-bonds) and ring orientational dynamics are presented and discussed. The final section includes a rationalisation of the dynamics observed.
2 | J. Name., 2012, 00, 1-3
2. Computational
View Article Online
DOI: 10.1039/C3CP54551B
Molecular dynamics (MD) simulation runs were performed for [C4C1im]Cl and [C2C1im]Cl, at constant temperature and 55 volume (NVT) using the DL_POLY simulation code. To the best of our knowledge, reliable experimental data of liquid densities for these systems are relatively scarce. Two previously reported experimental state points have been simulated, [C4C1im]Cl at a thermodynamic state (1052.8 kg m3, 353.15 K) close to its melting point (Tm = 340.1 K) and [C4C1im]Cl at a thermodynamic state (1040.0 kg m-3, 450.0 K) 56-59 well above its melting point ( Tm = 360.0 K ). The simulations were carried out using 128 pairs of anions and cations. Equilibration simulations of 5 ns were initially performed for each liquid, starting from a structure produced after performing an energy minimization from a crystal structure. Three sequential 5 ns simulations were then performed producing 15ns of trajectory from which data was collected. In all simulations the equations of motion were 60 integrated using a leapfrog-type Verlet algorithm with the time step set to 1 fs. A Nose-Hoover thermostat (relaxation 61 time of 0.2 ps) was used to constrain the temperature, possibly affecting sub ps timescales. Intermolecular interactions are represented as pair wise additive with site-site Lennard-Jones (LJ) plus Coulomb interactions. The intramolecular interactions have been represented in terms of harmonic bond stretching and angle bending, as well as of a cosine series for the dihedral angle internal rotations. The potential model proposed by Lopes and Padua has been employed to describe the site-site interactions between species in the system, taking into account corrections made by the authors in the supporting information of a later 20,22 publication. The intramolecular geometry was constrained 62,63 using a modified version of the SHAKE algorithm. A cutoff radius of 12.0 Å has been applied for all LJ interactions and long-range corrections have been also taken into account. Moreover, the standard Ewald summation technique has been used to account for the long-range electrostatic interactions. Dynamics have been examined using pair residence time autocorrelation functions (TCFs) defined in equation (1), where aij is the value of a specified parameter for a pair of atoms i and j at a time origin determined as t=0, and at t=t. Specifically aij(t)=1 if an atom j and a second atom i, at times 0 and t, satisfy a set of criteria (are coupled) for a period shorter than t*, otherwise aij(t)=0. Criteria can, for example, be distance based for residence dynamics or more complex combinations of distances and angles for H-bonding. The equation used for Hbond state is similar (see the ESI for more details) and criteria 64,65 are applied for the formation 0, 1 or 2 H-bonds.
C (t ) =
aij ( 0 ) aij (t ) aij ( 0 )
2
t
*
(1)
This journal is © The Royal Society of Chemistry 2012
Physical Chemistry Chemical Physics Accepted Manuscript
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
change in the average number of H-bonds was obtained on changing the temperature. This has lead us to examine how the H-bonding dynamics changes with temperature. In an IL a H-bond can form, but some time later it breaks; due to the local motion of the ions or new interactions formed with other ions, Figure 1. In one case a strong initial H-bond can be maintained continuously over a long period of time, but at some point the H-bond breaks and the ions diffuse away from each other, the H-bond is not re-established. In another case, a weaker H-bond can rapidly break, but because of "caging" effects constraining the local movement of the ions, the H-bond can reform again a short time later. This type of Hbond can form intermittently multiple times before finally breaking permanently.
Journal Name
Page 3 of 11
Physical Chemistry Chemical Physics
Journal Name
ARTICLE
=
∫ C (t ) dt
(2)
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
0
The corresponding time constants are defined as in equation (2). The TCFs are dependent on the selection of the parameter t*, and two limiting cases arise; t*=0 and t*=∞. t*=0 corresponds to atom i and j remaining coupled continuously for the whole time interval [0, t]. t*=∞, corresponds to the localised but intermittent coupling of atom i and j at time t, regardless of the number of times this coupling is turned off or on during the time interval [0, t]. This type of analysis has previously been applied to molecular H-bonding liquids such as 66-68 water and ethanol, and to the ILs [C4C1im][PF6], 41,49,51,50 [C4C1im]Cl, [C2C1im]Cl and [C2C1im][SCN]. Local residence lifetimes have been determined by numerically integrating the calculated TCFs up to 400 ps. Where the TCF has not decayed to zero within this timescale the computed TCFs have been fit to analytical functions and a tail correction determined by integrating the fitting function over the relevant range. Several forms of function were fitted (stretched exponential, sums of 3-5 exponential functions) and the best fit across the data range has been obtained for a sum of three exponential decay functions of the form given in equation (3) where c3=1-c2-c1. Orientational TCFs for the cations have been obtained using Legendre polynomials. Exponential fits to the TCFs of rank 1 and 2 have been obtained and integrated to determine life-times, additional details are provided in the ESI.
C(t ) = c1 exp(−t τ 1 ) + c2 exp(−t τ 2 ) + c3 exp(−t τ 3 ) (3) MD carried out for viscous ILs near the melting point are difficult due to problems of reaching equilibration and the presence of glassy amorphous states. A larger system size and longer equilibration period will provide more accurate results especially for decays with long timescales, however in comparing two systems of essentially the same size (at different temperatures) the impact of size effects can be reduced. Previous studies on [C2C1im]Cl, 90ºC above the melting point, have shown ballistic ( 4.5ps -> 0.1ps and the intermittent lifetime change is 5.5ns -> 4.7ns -> 0.5 ns. Thus, the dynamics of the H-bonds is very sensitive to angular motion, and a deeper understanding of the H-bonding can be obtained by examining more than one angular cut-off. Temperature effects are also evident in the H-bond dynamics. The continuous lifetime for the C2-H…Cl– H-bond of hot [C2C1im]Cl is ≈1ps, is only slightly shorter than that for the cold [C4C1im]Cl IL ≈4ps. In contrast, the intermittent Hbond lifetime changes from ≈103ps to 4700ps (≈45 times longer for the cold IL). Similar trends are also observed for the other H…Cl– pairs. The continuous lifetime of the first H-bonds is much less than that of the ring H-bonds at both temperatures, consistent with weaker H-bonds being formed by the first H-atoms. However, in the cold [C4C1im]Cl, the intermittent lifetime of
6 | J. Name., 2012, 00, 1-3
Journal Name the first H-bonds has decreased significantly relative to the ring H-bonds. For example, the time constants for the first H-bonds View Article Online I are now significantly shorter ( τ HB ≈1.3ns) than the C4/5-H HDOI: 10.1039/C3CP54551B I I 7 2 bonds ( τ HB ≈3.4ns). The ratio of τ HB for C -H/C -H in the cold IL is 0.27, compared to 0.47 for the hot IL. Thus, in the cold IL, the first H-bonds are playing a proportionally much smaller role in the H-bonding network. The exponents fitted to the intermittent TCF for the ring C2H…Cl– H-bond are presented in Table 5. It is important to distinguish the integrated life-time of C(t), from these exponents used to fit the C(t) decay function. There are three decay components, the two slower components exhibit similar timescales at both temperatures, one sub-picosecond timescale and one ≈50ps component. However, the third and slowest component shows significant differences at the different temperatures, ≈300ps (hot IL) and ≈6000ps (cold IL). Our first study revealed that the average number of H-bonds in [C2C1im]Cl at 450 K is almost the same as that in [C4C1im]Cl at 353 K, and thus is not significantly affected by the temperature change of ≈100ºC. However, we have found that while there is little change in the static H-bonding on reducing the temperature there is a substantial change in the underlying dynamics over this temperature range. There is a very slight slowing down for the continuous (first) decay of the H-bond, but there is also a substantially more dramatic (≈40 times) slow down in the intermittent residence and H-bonding dynamics. 3.3 Numbers of Hydrogen Bonds Employing radial cut-offs (both RH…Cl and RC…Cl) and an angular cut-off (φ=60º) the average number of H-bonds for each H-atom can be determined. Previously we have established that within the liquid, on average 5% of the primary ring H-atoms 51 form 0 bonds, 85% form 1 H-bond and 10% form 2 H-bonds. Here we further investigate the dynamics with respect to the number of H-bonds formed by the ring H-atoms (C2, C4 and C5).68 Table 6 Calculated continuous and intermittent lifetimes (ps) for H-atoms in [C4C1im]Cl, 353.15 K, to form n=0,1 or 2 H-bonds. C
–
C2-H…Cl – C4-H…Cl – 5 … C -H Cl
I
τ HB ( n ) (ps)
Specific H n=0 0.10 0.67 0.60
n=1 4.84 2.89 3.53
τ HB ( n ) (ps) n=2 0.09 0.06 0.06
n=0 26.9 38.5 37.7
n=1 129.3 47.6 46.1
n=2 225.5 91.8 123.4
Table 7 Calculated continuous and intermittent lifetimes (ps) for H-atoms in [C2C1im]Cl, 450.0 K, to form n=0,1 or 2 H-bonds. τ HB ( n ) (ps)
Specific H – C2-H…Cl – 4 … C -H Cl – C5-H…Cl
τ HB ( n ) (ps) I
C
n=0 0.09 0.17 0.19
n=1 1.03 0.92 0.92
n=2 0.05 0.04 0.04
n=0 1.02 1.02 1.13
n=1 1.62 1.02 1.05
n=2 2.73 1.76 1.56
This journal is © The Royal Society of Chemistry 2012
Physical Chemistry Chemical Physics Accepted Manuscript
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
ARTICLE
Physical Chemistry Chemical Physics
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
Journal Name
For the continuous TCF, a H-atom forms n H-bonds continuously over a time period t. Within this time period, an anion can be exchanged, the H-atom however remains in a state with n-H-bonds. For the intermittent TCF a H-atom that had n H-bonds at time t=0, has at a later time t, n H-bonds again independent of whether or not the H-bond state has changed in C I the intervening time. The associated lifetimes τ HB(n ) and τ HB(n) are presented in Tables 6 and 7, respectively. The n=1 continuous and intermittent H-bond state TCFs for the ring C2H…Cl– H-bonds of [C4C1im]Cl and [C2C1im]Cl are compared in Figure 10. The corresponding TCFs for other selected Hatoms in [C4C1im]Cl and [C2C1im]Cl are presented in the SM, Figures F6 - F7. The lifetime to the first disruption of a single (n=1) H-bond C state is only slightly longer in the cold ( τ HB (1) ≈4ps), compared to the hot IL (≈1ps). Moreover, the lifetime for the recurring single (n=1) H-bond state is also not much longer in the hot IL, I but it is substantially longer in the cold IL going from τ HB ≈2ps (1) to ≈130ps. Thus, again it is the intermittent dynamics that shows the largest temperature effects. The lifetime to the first breaking of the bifurcated H-bond state is very short (
PCCP Accepted Manuscript
This article can be cited before page numbers have been issued, to do this please use: I. Skarmoutsos, T. Welton and P. Hunt, Phys. Chem. Chem. Phys., 2013, DOI: 10.1039/C3CP54551B.
This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains.
www.rsc.org/pccp
Page 1 of 11
Physical Chemistry Chemical Physics
Journal Name
RSCPublishing View Article Online
DOI: 10.1039/C3CP54551B
Cite this: DOI: 10.1039/x0xx00000x
The Importance of Timescale for Hydrogen Bonding in Imidazolium Chloride Ionic Liquids Ioannis Skarmoutsosa* Tom Weltonb and Patricia A. Huntc*
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
Received 00th January 2012, Accepted 00th January 2012 DOI: 10.1039/x0xx00000x www.rsc.org/
Hydrogen bond (H-bond) dynamics have been investigated for "hot" 1-ethyl-3-methylimidazolium chloride and "cold" 1-butyl-3-methylimidazolium chloride ionic liquids (IL). While the average number of H-bonds remains constant for a ≈100ºC temperature change we show that the underlying dynamics of the H-bonding changes dramatically. H-bond dynamics are investigated based on distance and angle criteria, and on the H-bond state (zero, single or bifurcated H-bonds). Temperature effects on the cation ring reorintational dynamics are also examined. Angle deformations are found to be more important than bond stretching in determining the lifetime of individual H-bonds, and decay occurs on two time scales related to the magnitude of the deviation from linearity. Rapid angular oscillation of the anion breaks the H-bond (for the first time) and minimal temperature effects indicate that H-bonds are readily reformed even near the melting point. Intermittent H-bonds repeatedly break and reform over a longer timescale, and exhibit very strong temperature effects. In the hot IL H-bonding with ring and alkyl chain H-atoms occurs, ring reorientational dynamics is anisotropic and the corresponding lifetimes are similar to the intermittent H-bond lifetimes. In the cold IL ring H-atoms dominate the Hbonding and intermittent H-bonds last for ≈5ns, ring reorientation occurs on a much slower timescale. The hot IL favours single H-bonds, but the individual ions often change, while the cold IL favours bifurcated H-bonds with the same co-located ions.
1. Introduction The properties of many liquid solvents are significantly 1,2 affected by the presence of hydrogen bonds (H-bonds). However, even for water, the precise nature of the H-bond is 3-7 still under debate and for more complex systems such as ionic liquids (ILs) H-bonds are still far from being well8,9 understood. Thus, the investigation of H-bond structure and dynamics at a microscopic level is important for achieving a deeper understanding of these liquids. Ionic liquids have attracted significant attention in both the 10-14 scientific and technological communities. They have a range of interesting physical and chemical properties including; a very low vapour pressure, high thermal conductivity, high thermal stability and a wide electrochemical window. The ability to tune the dissolving capability and solvation characteristics of ILs with the appropriate selection of the cations or anions has identified ILs as an important class of solvents, with a wide range of potential applications. However, the use of ILs as reaction media and electrolytes has been seriously limited by poor transport properties. For example, ILs can be as viscous as oils, the high viscosity 15 leading to a lower electrical conductivity. Recent studies have identified the importance and impact of H-bonding 16-19 interactions on the transport properties of ILs. A deeper
This journal is © The Royal Society of Chemistry 2013
understanding of the nature of H-bonding interactions in ILs may therefore act as a springboard for better rational design of ILs with improved transport properties. The relationship between H-bonding and molecular behavior for the imidazolium based ILs has been studied both 20-35 experimentally and theoretically.8,9,36-48 These studies have provided detailed insight into the nature of H-bonds within ILs. Traditionally diffusion and reorientation dynamics have been examined, however very few studies have explicitly considered 41,49,50 the H-bond dynamics. Herein we investigate, using MD simulation techniques, the H-bond dynamics of 1-butyl-3methylimidazolium chloride [C4C1im]Cl and 1-ethyl-3methylimidazolium chloride [C2C1im]Cl ILs. One issue for describing H-bonding in these ILs, is that there is evidence that the geometric conditions used to define 51 the H-bond can qualitatively affect the results. Previously we have determined that the average number of H-bonds per hydrogen atom in [C4C1im]Cl at 353 K, just 13 ºC above its melting point, is very similar to that obtained for [C2C1im]Cl, 51 90ºC above its melting point. This result was counterintuitive; the viscosities of [C4C1im]Cl and [C2C1im]Cl are sensitive to temperature changes, and decrease upon heating. Thus, we expected the higher temperature and more fluid liquid to be associated with a reduced H-bonding network, and a reduced average number of H-bonds. However, no significant
J. Name., 2013, 00, 1-3 | 1
Physical Chemistry Chemical Physics Accepted Manuscript
ARTICLE
Physical Chemistry Chemical Physics
Page 2 of 11
ARTICLE
Figure 1 Representation of the continuous and intermittent H-bond dynamics.
Continuous and intermittent H-bond dynamics have been examined for a limited number of ILs. In [C4C1im][PF6] the continuous lifetime has been related to rotation of the anion leading to rapid breaking and forming of the H-bonds, and the intermittent lifetime has been associated with caging and 49 librational motion. For [C2C1im][SCN] the intermittent 50 lifetime was associated with the H-bonding network. Studies on [C2C1im]Cl, 90ºC above the melting point, have shown ballistic behaviour for about 0.1ps, a sub-diffuse regime and 52,41 then gaussian diffusive behaviour after about 1.5ns. Similarly [C4C1im][PF4], at 10ºC and 90ºC above the melting point has shown sub-diffusive behaviour in the range ≈2-40ps and ≈3-10ps respectively. Sub-diffuse dynamics are related to breaking out of the local caging environment and can encompass a distribution of processes with different rates. Cation dynamics (ring orientational dynamics) has been related to local cage librations followed by complete relaxation as 53,54 aggregates break-up and diffuse. Thus, an understanding of the H-bonding dynamics can also offer insight into the more general dynamics within an IL. In the following section computational details are outlined. In the results and discussion section residence dynamics, Hbonding dynamics, dynamics of the individual H-bonding states (0,1 or 2 H-bonds) and ring orientational dynamics are presented and discussed. The final section includes a rationalisation of the dynamics observed.
2 | J. Name., 2012, 00, 1-3
2. Computational
View Article Online
DOI: 10.1039/C3CP54551B
Molecular dynamics (MD) simulation runs were performed for [C4C1im]Cl and [C2C1im]Cl, at constant temperature and 55 volume (NVT) using the DL_POLY simulation code. To the best of our knowledge, reliable experimental data of liquid densities for these systems are relatively scarce. Two previously reported experimental state points have been simulated, [C4C1im]Cl at a thermodynamic state (1052.8 kg m3, 353.15 K) close to its melting point (Tm = 340.1 K) and [C4C1im]Cl at a thermodynamic state (1040.0 kg m-3, 450.0 K) 56-59 well above its melting point ( Tm = 360.0 K ). The simulations were carried out using 128 pairs of anions and cations. Equilibration simulations of 5 ns were initially performed for each liquid, starting from a structure produced after performing an energy minimization from a crystal structure. Three sequential 5 ns simulations were then performed producing 15ns of trajectory from which data was collected. In all simulations the equations of motion were 60 integrated using a leapfrog-type Verlet algorithm with the time step set to 1 fs. A Nose-Hoover thermostat (relaxation 61 time of 0.2 ps) was used to constrain the temperature, possibly affecting sub ps timescales. Intermolecular interactions are represented as pair wise additive with site-site Lennard-Jones (LJ) plus Coulomb interactions. The intramolecular interactions have been represented in terms of harmonic bond stretching and angle bending, as well as of a cosine series for the dihedral angle internal rotations. The potential model proposed by Lopes and Padua has been employed to describe the site-site interactions between species in the system, taking into account corrections made by the authors in the supporting information of a later 20,22 publication. The intramolecular geometry was constrained 62,63 using a modified version of the SHAKE algorithm. A cutoff radius of 12.0 Å has been applied for all LJ interactions and long-range corrections have been also taken into account. Moreover, the standard Ewald summation technique has been used to account for the long-range electrostatic interactions. Dynamics have been examined using pair residence time autocorrelation functions (TCFs) defined in equation (1), where aij is the value of a specified parameter for a pair of atoms i and j at a time origin determined as t=0, and at t=t. Specifically aij(t)=1 if an atom j and a second atom i, at times 0 and t, satisfy a set of criteria (are coupled) for a period shorter than t*, otherwise aij(t)=0. Criteria can, for example, be distance based for residence dynamics or more complex combinations of distances and angles for H-bonding. The equation used for Hbond state is similar (see the ESI for more details) and criteria 64,65 are applied for the formation 0, 1 or 2 H-bonds.
C (t ) =
aij ( 0 ) aij (t ) aij ( 0 )
2
t
*
(1)
This journal is © The Royal Society of Chemistry 2012
Physical Chemistry Chemical Physics Accepted Manuscript
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
change in the average number of H-bonds was obtained on changing the temperature. This has lead us to examine how the H-bonding dynamics changes with temperature. In an IL a H-bond can form, but some time later it breaks; due to the local motion of the ions or new interactions formed with other ions, Figure 1. In one case a strong initial H-bond can be maintained continuously over a long period of time, but at some point the H-bond breaks and the ions diffuse away from each other, the H-bond is not re-established. In another case, a weaker H-bond can rapidly break, but because of "caging" effects constraining the local movement of the ions, the H-bond can reform again a short time later. This type of Hbond can form intermittently multiple times before finally breaking permanently.
Journal Name
Page 3 of 11
Physical Chemistry Chemical Physics
Journal Name
ARTICLE
=
∫ C (t ) dt
(2)
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
0
The corresponding time constants are defined as in equation (2). The TCFs are dependent on the selection of the parameter t*, and two limiting cases arise; t*=0 and t*=∞. t*=0 corresponds to atom i and j remaining coupled continuously for the whole time interval [0, t]. t*=∞, corresponds to the localised but intermittent coupling of atom i and j at time t, regardless of the number of times this coupling is turned off or on during the time interval [0, t]. This type of analysis has previously been applied to molecular H-bonding liquids such as 66-68 water and ethanol, and to the ILs [C4C1im][PF6], 41,49,51,50 [C4C1im]Cl, [C2C1im]Cl and [C2C1im][SCN]. Local residence lifetimes have been determined by numerically integrating the calculated TCFs up to 400 ps. Where the TCF has not decayed to zero within this timescale the computed TCFs have been fit to analytical functions and a tail correction determined by integrating the fitting function over the relevant range. Several forms of function were fitted (stretched exponential, sums of 3-5 exponential functions) and the best fit across the data range has been obtained for a sum of three exponential decay functions of the form given in equation (3) where c3=1-c2-c1. Orientational TCFs for the cations have been obtained using Legendre polynomials. Exponential fits to the TCFs of rank 1 and 2 have been obtained and integrated to determine life-times, additional details are provided in the ESI.
C(t ) = c1 exp(−t τ 1 ) + c2 exp(−t τ 2 ) + c3 exp(−t τ 3 ) (3) MD carried out for viscous ILs near the melting point are difficult due to problems of reaching equilibration and the presence of glassy amorphous states. A larger system size and longer equilibration period will provide more accurate results especially for decays with long timescales, however in comparing two systems of essentially the same size (at different temperatures) the impact of size effects can be reduced. Previous studies on [C2C1im]Cl, 90ºC above the melting point, have shown ballistic ( 4.5ps -> 0.1ps and the intermittent lifetime change is 5.5ns -> 4.7ns -> 0.5 ns. Thus, the dynamics of the H-bonds is very sensitive to angular motion, and a deeper understanding of the H-bonding can be obtained by examining more than one angular cut-off. Temperature effects are also evident in the H-bond dynamics. The continuous lifetime for the C2-H…Cl– H-bond of hot [C2C1im]Cl is ≈1ps, is only slightly shorter than that for the cold [C4C1im]Cl IL ≈4ps. In contrast, the intermittent Hbond lifetime changes from ≈103ps to 4700ps (≈45 times longer for the cold IL). Similar trends are also observed for the other H…Cl– pairs. The continuous lifetime of the first H-bonds is much less than that of the ring H-bonds at both temperatures, consistent with weaker H-bonds being formed by the first H-atoms. However, in the cold [C4C1im]Cl, the intermittent lifetime of
6 | J. Name., 2012, 00, 1-3
Journal Name the first H-bonds has decreased significantly relative to the ring H-bonds. For example, the time constants for the first H-bonds View Article Online I are now significantly shorter ( τ HB ≈1.3ns) than the C4/5-H HDOI: 10.1039/C3CP54551B I I 7 2 bonds ( τ HB ≈3.4ns). The ratio of τ HB for C -H/C -H in the cold IL is 0.27, compared to 0.47 for the hot IL. Thus, in the cold IL, the first H-bonds are playing a proportionally much smaller role in the H-bonding network. The exponents fitted to the intermittent TCF for the ring C2H…Cl– H-bond are presented in Table 5. It is important to distinguish the integrated life-time of C(t), from these exponents used to fit the C(t) decay function. There are three decay components, the two slower components exhibit similar timescales at both temperatures, one sub-picosecond timescale and one ≈50ps component. However, the third and slowest component shows significant differences at the different temperatures, ≈300ps (hot IL) and ≈6000ps (cold IL). Our first study revealed that the average number of H-bonds in [C2C1im]Cl at 450 K is almost the same as that in [C4C1im]Cl at 353 K, and thus is not significantly affected by the temperature change of ≈100ºC. However, we have found that while there is little change in the static H-bonding on reducing the temperature there is a substantial change in the underlying dynamics over this temperature range. There is a very slight slowing down for the continuous (first) decay of the H-bond, but there is also a substantially more dramatic (≈40 times) slow down in the intermittent residence and H-bonding dynamics. 3.3 Numbers of Hydrogen Bonds Employing radial cut-offs (both RH…Cl and RC…Cl) and an angular cut-off (φ=60º) the average number of H-bonds for each H-atom can be determined. Previously we have established that within the liquid, on average 5% of the primary ring H-atoms 51 form 0 bonds, 85% form 1 H-bond and 10% form 2 H-bonds. Here we further investigate the dynamics with respect to the number of H-bonds formed by the ring H-atoms (C2, C4 and C5).68 Table 6 Calculated continuous and intermittent lifetimes (ps) for H-atoms in [C4C1im]Cl, 353.15 K, to form n=0,1 or 2 H-bonds. C
–
C2-H…Cl – C4-H…Cl – 5 … C -H Cl
I
τ HB ( n ) (ps)
Specific H n=0 0.10 0.67 0.60
n=1 4.84 2.89 3.53
τ HB ( n ) (ps) n=2 0.09 0.06 0.06
n=0 26.9 38.5 37.7
n=1 129.3 47.6 46.1
n=2 225.5 91.8 123.4
Table 7 Calculated continuous and intermittent lifetimes (ps) for H-atoms in [C2C1im]Cl, 450.0 K, to form n=0,1 or 2 H-bonds. τ HB ( n ) (ps)
Specific H – C2-H…Cl – 4 … C -H Cl – C5-H…Cl
τ HB ( n ) (ps) I
C
n=0 0.09 0.17 0.19
n=1 1.03 0.92 0.92
n=2 0.05 0.04 0.04
n=0 1.02 1.02 1.13
n=1 1.62 1.02 1.05
n=2 2.73 1.76 1.56
This journal is © The Royal Society of Chemistry 2012
Physical Chemistry Chemical Physics Accepted Manuscript
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
ARTICLE
Physical Chemistry Chemical Physics
Published on 13 January 2014. Downloaded by Aston University on 13/01/2014 13:28:13.
Journal Name
For the continuous TCF, a H-atom forms n H-bonds continuously over a time period t. Within this time period, an anion can be exchanged, the H-atom however remains in a state with n-H-bonds. For the intermittent TCF a H-atom that had n H-bonds at time t=0, has at a later time t, n H-bonds again independent of whether or not the H-bond state has changed in C I the intervening time. The associated lifetimes τ HB(n ) and τ HB(n) are presented in Tables 6 and 7, respectively. The n=1 continuous and intermittent H-bond state TCFs for the ring C2H…Cl– H-bonds of [C4C1im]Cl and [C2C1im]Cl are compared in Figure 10. The corresponding TCFs for other selected Hatoms in [C4C1im]Cl and [C2C1im]Cl are presented in the SM, Figures F6 - F7. The lifetime to the first disruption of a single (n=1) H-bond C state is only slightly longer in the cold ( τ HB (1) ≈4ps), compared to the hot IL (≈1ps). Moreover, the lifetime for the recurring single (n=1) H-bond state is also not much longer in the hot IL, I but it is substantially longer in the cold IL going from τ HB ≈2ps (1) to ≈130ps. Thus, again it is the intermittent dynamics that shows the largest temperature effects. The lifetime to the first breaking of the bifurcated H-bond state is very short (
