- Email: [email protected]
Dynamics in Acetamide+LiNO3 Deep Eutectic Solvents
Physica B: Condensed Matter 562 (2019) 13–16
Contents lists available at ScienceDirect
Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
Dynamics in Acetamide+LiNO3 Deep Eutectic Solvents a
a,∗
H. Srinivasan , V.K. Sharma , S. Mitra a b c
a,b
c
, R. Biswas , R. Mukhopadhyay
T a,b
Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai-400085, India Homi Bhabha National Institute, Anushakti Nagar, Mumbai-400094, India S.N. Bose National Centre for Basic Sciences, Sector III, Salt Lake, Kolkata 700106, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Deep eutectic solvents QENS MD simulation Dynamics
Deep eutectic solvents (DES) are composite mixtures which have freezing point lesser than that of their individual components. A mixture of acetamide and lithium nitrate in the molar ratio of 78:22 is observed to form a DES with freezing point below room temperature. Here we report nanoscale dynamics in acetamide + LiNO3 DES as studied using quasielastic neutron scattering (QENS) and molecular dynamics (MD) simulation techniques. The results of MD simulation show a transient subdiffusive motion for acetamide molecules. The acetamide molecules form a hydrogen-bond network with its neighbouring set of molecules resulting in a transient cage. The motion of the acetamide molecules is described by considering a power law memory kernel for the relaxation of the cage. The intermediate scattering function obtained from the QENS experiments of DES are described using stretched exponential relaxation function. The power law exponent describing the results of MD simulation is found to match well with the stretching exponent obtained from QENS experiments.
1. Introduction Deep eutectic solvents (DES) have emerged as a novel variety of solvents useful in various applications like electrodeposition [1], nanoparticle synthesis [2], catalysis [3], etc. The high solubility of metal salts and better conductivity compared to non aqueous solvents make DES an extremely good solvent in the metal deposition industry [4]. Some mixtures of DES have been shown to replace traditional precursors in shape-controlled synthesis of gold and silver nanoparticles [5]. Some DES possessing biocompatibility and poor toxicity have also been shown to be useful in vectorisation of drugs. Due to its biodegradability and cheaper preparation methods they are industrially more viable solvents compared to ionic liquids. In order to prepare DES with tailor-made physiochemical properties, it is of interest to study the structure and dynamics of these solvents on a molecular scale. DESs are generally prepared by mixing a metal salt and hydrogen bond donor in a particular molar ratio [4]. It is observed that the charge delocalization due to hydrogen-bonding in the mixture is responsible for depression in their freezing points [4]. Mixture of amides and electrolytic salts in a given molar ratio has been observed to form deep eutectic (DE) mixtures with freezing points below room temperature [6]. Recently, a mixture of acetamide (CH3CONH2) and lithium nitrate (LiNO3) in the molar ratio (78:22) has been shown to form DES and is found to remain in liquid at room
∗
temperature [6]. Fluorescence spectroscopy on these mixtures reveals that the dynamics of acetamide is strongly affected by the nature of the anion in the salt [6]. Further, it's found that the presence of these anions disrupt the inter-amide hydrogen bonding network leading to depression of the freezing point of the liquid. The disruption of hydrogenbonding alters the dynamical features of acetamide molecules in the mixture. The viscosity and conductivity of DES which play a major role in various applications like electrodeposition, catalysis etc. is deeply related to the dynamics of molecules in the mixture. Therefore studying the molecular dynamics of acetamide in the DES can shed light into the network of hydrogen-bonds and help in designing solvents with variable viscosity. Quasielastic neutron scattering is a suitable technique to study dynamics of atom/molecules in the nanoseconds to picoseconds time scale and length scale of angstroms to nanometer [7]. Molecular dynamics (MD) simulation covers the same length and time scales and can be used in synergy to get microscopic insight of the relaxation process. Here, we report dynamics in acetamide + LiNO3 DES as studied using QENS and MD simulation techniques. 2. Materials and methods Acetamide and lithium nitrate powders were obtained from SigmaAldrich. Acetamide was mixed with lithium nitrate with a mole fraction
Corresponding author. E-mail addresses: [email protected], [email protected] (V.K. Sharma).
https://doi.org/10.1016/j.physb.2019.01.003 Received 2 October 2018; Received in revised form 6 December 2018; Accepted 4 January 2019 Available online 09 March 2019 0921-4526/ © 2019 Elsevier B.V. All rights reserved.
Physica B: Condensed Matter 562 (2019) 13–16
H. Srinivasan, et al.
acetamide molecules at very short times (t < 10−2 ps) is governed by ballistic motion (α ∼ 2), which is followed by a sub-diffusive regime and at t > 102ps it follows Fickian diffusion. The behavior of MSD can be described by considering the following process for diffusion of acetamide. At very short times, the acetamide molecules don't undergo any collisions giving rise to ballistic regime. Subsequently, the given acetamide molecule interacts with its neighbouring molecules which have formed a transient cage due to hydrogen-bonding. During this process, once the cage relaxes the acetamide molecule dissociates its hydrogen bond with its existing neighbours and starts diffusing. In this time regime, the motion of acetamide molecule shows Fickian diffusion. This description of the motion of acetamide COM can be verified in more detail using velocity autocorrelation function (VACF) of the acetamide COM.
of 78:22 respectively. The mixture was then heated to a temperature of ∼65 °C for 30 min. After a clear solution was obtained from heating, the solution was left to cool down naturally to the room temperature. QENS spectrometer at Dhruva reactor in Bhabha Atomic Research Centre was used to carry out QENS experiments on DES mixture formed by acetamide and lithium nitrate at 300 K. The spectrometer operates in multi-angle reflecting crystal (MARX) mode with a large single crystal for energy dispersion [8]. In the current configuration, the spectrometer has an energy resolution of 200 μeV and energy range of ± 1 meV. QENS data were recorded in the momentum transfer (Q) range of 0.67 Å−1–1.8 Å−1 at room temperature (300 K). The resolution of the instrument was measured using standard vanadium sample. A system of 400 acetamide molecules and 56 lithium and nitrate ions were arranged in a cubic box of length 36 Å. The number of atoms was chosen to replicate the molar ratio (78:22) of the DE mixture. While, the potential parameters for acetamide were obtained from CHARMM force field [9], the parameters for lithium and nitrate ions were obtained from Joung and Cheatham [10] and Cadenna and Maginn [11] respectively. The system was equilibrated at atmospheric pressure (1 atm) and a temperature of 300 K using the Nose-Hoover NPT ensemble for 10 ns. The MD simulations were carried out using DLPoly 4 [12]. Subsequent to equilibration, the simulation was continued for another 5 ns to record atomistic trajectories for analysis at an interval of 1 ps.
3.2. MD simulation – cage relaxation The VACF of the acetamide COM is calculated from MD simulation trajectories. The motion of acetamide molecules can be described as hopping of acetamide molecules from one transient cage to the other. The transient cage around a given acetamide molecule can be formed by its hydrogen bonding with the neighbouring set of anions and acetamide. Therefore, the motion of the acetamide molecules will consist of both the relaxation of the transient cage and subsequently the motion of acetamide molecules to neighbouring site. The relaxation of cage formed by the neighbours of a given acetamide molecule will be ingrained in the motion of the acetamide COM. In order to account for the cage relaxation, the VACF (Cv(t))is described based on the equation,
3. Results and discussion 3.1. MD simulation – motion of acetamide centre of mass
dCv =− dt
MD simulation of the DES mixture of acetamide and lithium nitrate is carried out at 300 K. The nature of acetamide dynamics is studied extensively to understand the effect of hydrogen bonding in the solvent. As a primer, the mean squared displacement (MSD) of acetamide centre of mass (COM) is calculated to characterise the nature of its diffusion. It shows a transient subdiffusive regime until ∼100 ps, beyond which the motion of the molecules is found to be diffusive. This is explicitly indicated by calculating the (sub)diffusive exponent, α(t), as a function of time,
MSDACM (t ) = At α ⇒ α (t ) =
d (ln MSDACM (t )) d (ln t )
∫0
t
Cv (t − t ′) M (t ′) dt ′
(2)
where, memory function M(t) takes into consideration cage relaxation in the system. This equation can be transformed to an algebraic equation by Laplace transform and can be written as,
−Cv (0) ~ Cv (s ) = s + M (s )
(3)
Two simplest models of memory function were used, (i) exponential decay and (ii) power law decay to model the cage relaxation. Laplace transform of the VACF of the acetamide COM, Cv(s) is shown along with the fits using the two model functions in Fig. 2. It is clearly seen that the power law memory kernel is a much better fit compared to exponential memory kernel. The power law memory kernel is explicitly given by,
(1)
The MSD of acetamide COM and the variation of sub-diffusive parameter is shown in Fig. 1 and its inset respectively. The motion of
t −β −Cv (0) ~ M (t ) = p⎛ ⎞ ⇒ Cv (s ) = s + pτ βΓ (β − 1) s1 − β ⎝τ ⎠
(4)
where, τ is the cage relaxation time, p is the magnitude of memory
Fig. 2. Laplace transform of VACF of acetamide COM, Cv(s) is indicated by circles. The fits based on exponential (green line) and power law (blue) memory kernels are also shown.
Fig. 1. Mean squared displacement of acetamide COM. The inset shows the variation of the (sub)diffusive exponent α(t) with time. 14
Physica B: Condensed Matter 562 (2019) 13–16
H. Srinivasan, et al.
function, β is the power law exponent of cage relaxation and Г(x) is the gamma function. The cage relaxation time, τ, from the fit of equation (4) was found to be ∼10.2 ps and the exponent, β, was found to be ∼0.55. The transient sub-diffusive part of MSD of acetamide COM can be associated to power law behavior of the memory kernel. The diffusion mechanism of acetamide is analogous to the dynamics of supercooled water that is strongly hydrogen bonded, which is described considering an intra-basin fluctuation in a cage followed by inter-basin motion [13]. Diffusivity of the acetamide COM can be obtained directly by integrating the velocity autocorrelation function obtained from MD simulation,
DMD =
1 3
∫0
∞
Cv (t ) dt =
C˜ v (0) 3
(5) −6
Diffusivity, DMD, thus obtained is found to be ∼0.9 × 10 for acetamide COM in the mixture.
cm2/s
3.3. Comparison with quasielastic neutron scattering The total scattering law, S (Q,ω), measured in neutron scattering experiments, contains information about both coherent and incoherent scattering. However, for the hydrogenous system, the main contribution to S (Q,ω) is from incoherent scattering since the incoherent scattering cross section of hydrogen is very high compared to the total scattering cross section of any other element [7]. The incoherent part of neutron scattering spectra can be related to self-correlation function of the particle. Hence, for hydrogenous systems, quasielastic neutron scattering (QENS) experiments provide information about the mechanism of self diffusion of hydrogenous molecules in the system. In present case, QENS experiments have been carried out on DE mixture made of acetamide + LiNO3 to investigate dynamics of acetamide in it. QENS experiments on DES mixture of acetamide and lithium nitrate was carried out at 300 K. Significant quasielastic broadening is observed over the instrument resolution indicating presence of stochastic molecular motion of acetamide. In the previous section, MD simulation showed that the motion of acetamide COM shows a subdiffusive behavior up to 100 ps. In this context, the incoherent intermediate scattering function (IISF) should decay as stretched exponential function. Experimental IISF have been calculated from inverse Fourier transform of neutron scattering law, S (Q,ω). The obtained IISF is fitted using Kohlrausch-Williams-Watts (KWW) stretched exponential function,
I (Q, t ) = exp(−[
t ]β ′ ) R (t , σ ) τQENS (Q)
Fig. 3. Typical experimental IISF calculated from inverse Fourier transform of the QENS spectra at two different Q-values. The solids lines shown are the fits for the experimental IISF based on stretched exponential (eq. (5)).
(5)
where β′ is stretching exponent and τQENS is the characteristic timescale of relaxation. R (t,σ) is the resolution function of the instrument and σ is the full-width half maximum of the resolution which is found to be ∼200 μeV. It is found Eq. (5) described the experimental IISF well at all Q-values. Typical fitted experimental IISF's at two different Q-values are shown in Fig. 3. It was found that β′ obtained from the fit of experimental IISF using eq. (5) is ∼0.56 and remains fairly constant over the observed Q-range. It is observed that the stretching exponent obtained from QENS experiments matches really well with the power law exponent obtained from the results of MD simulation. Considering the stretched exponential to be sum of single exponential relaxation functions distributed over a time regime, an average relaxation time, < τ > , can be calculated using the obtained parameters τQENS and β with the following equation,
τQENS 1 〈τ 〉 = Γ( ) β β
Fig. 4. Variation of inverse of average relaxation timescale obtained from experimental IISF (eq. (6)) with respect to Q. The solid line indicates the fit corresponding to Fickian law, DavgQ2.
QENS spectra compares quite well with diffusivity obtained from the VACF in the MD simulations. This indicates the robustness of the model describing the dynamics of acetamide molecule in the mixture.
4. Conclusions Deep Eutectic Solvents (DES) are an emerging class of solvents that have a lot of applications in the industrial processes. The understanding of molecular dynamics in these systems plays a key role in unraveling the schemes of tuning macroscopic properties like viscosity, surface tension, etc. Here we have presented our results on the dynamics of acetamide in the DES mixture made of acetamide and lithium nitrate. The diffusion mechanism of acetamide molecules is comprised of a
(6)
The variation of inverse average relaxation time with respect to Q is shown in Fig. 4. It is found that inverse average relaxation time follow DavgQ2 as shown by the solid line in Fig. 4. The average diffusivity, Davg, of the acetamide is obtained by fitting 1/ < τ > = DavgQ2 is found to be ∼1.9 × 10−6 cm2/s. The average diffusivity obtained from the 15
Physica B: Condensed Matter 562 (2019) 13–16
H. Srinivasan, et al.
rattling motion of acetamide molecule in a cage followed by the diffusion of the molecule to the next transient cage. A power law memory kernel was able to describe the relaxation of cage. The experimental incoherent intermediate scattering function (IISF) obtained from QENS experiments were well described with a stretched exponential relaxation function. The power law exponent describing the cage relaxation was found to match with the stretching exponent obtained from the results of QENS experiments. Our study suggest that the motion of acetamide molecules is strongly dictated by the cage formation due to the strong hydrogen bonding network with it's neighbouring acetamide molecules and ions. In view of this, it may be possible to tune the viscosity of the DES by altering the chemical nature of the constituents of the mixture to adjust the hydrogen bond strength.
[2] Wei Lu, You-Jun Fan, Na Tian, Zhi-You Zhou, Xue-Qin Zhao, Bing-Wei Mao, ShiGang Sun, J. Phys. Chem. C 116 (2012) 2040–2044. [3] P.M. Pawar, K.J. Jarag, G.S. Shankarling, Green Chem. 13 (2011) 2130–2134. [4] E.L. Smith, A.P. Abbott, K.S. Ryder, Chem. Rev. 114 (2014) 11060–11082. [5] H.G. Liao, Y.X. Jiang, Z.Y. Zhou, S.P. Chen, S.G. Sun, Angew. Chem. Int. Ed. 47 (2008) 9100–9103. [6] B. Guchhait, S. Das, S. Daschakraborty, R. Biswas, J. Chem. Phys. 140 (2014) 104514. [7] M. Bée, Quasielastic Neutron Scattering : Principles and Applications in Solid State Chemistry, Biology and Materials Science, A. Hilger, Bristol; Philadelphia, 1988. [8] R. Mukhopadhyay, S. Mitra, S.K. Paranjpe, B.A. Dasannacharya, Nucl. Inst. Meth. A 474 (2001) 45. [9] R.B. Best, X. Zhu, J. Shim, P.E.M. Lopes, J. Mittal, M. Feig, A.D. MacKerell, J. Chem. Theory Comput. 8 (2012) 3257–3273. [10] I.S. Joung, T.E. Cheatham III, J. Phys. Chem. B 112 (2008) 9020–9041. [11] C. Cadena, E.J. Maginn, J. Phys. Chem. B 110 (2006) 18026–18039. [12] W. Smith, C.W. Yong, P.M. Rodger, Mol. Simulat. 28 (2002) 385–471. [13] Johan Qvist, Helmut Schober, Bertil Halle, J. Chem. Phys. 134 (2011) 144508.
References [1] A.P. Abbott, G. Frisch, K.S. Ryder, Annu. Rev. Mater. Res. 43 (2013) 335–358.
16
Contents lists available at ScienceDirect
Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
Dynamics in Acetamide+LiNO3 Deep Eutectic Solvents a
a,∗
H. Srinivasan , V.K. Sharma , S. Mitra a b c
a,b
c
, R. Biswas , R. Mukhopadhyay
T a,b
Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai-400085, India Homi Bhabha National Institute, Anushakti Nagar, Mumbai-400094, India S.N. Bose National Centre for Basic Sciences, Sector III, Salt Lake, Kolkata 700106, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Deep eutectic solvents QENS MD simulation Dynamics
Deep eutectic solvents (DES) are composite mixtures which have freezing point lesser than that of their individual components. A mixture of acetamide and lithium nitrate in the molar ratio of 78:22 is observed to form a DES with freezing point below room temperature. Here we report nanoscale dynamics in acetamide + LiNO3 DES as studied using quasielastic neutron scattering (QENS) and molecular dynamics (MD) simulation techniques. The results of MD simulation show a transient subdiffusive motion for acetamide molecules. The acetamide molecules form a hydrogen-bond network with its neighbouring set of molecules resulting in a transient cage. The motion of the acetamide molecules is described by considering a power law memory kernel for the relaxation of the cage. The intermediate scattering function obtained from the QENS experiments of DES are described using stretched exponential relaxation function. The power law exponent describing the results of MD simulation is found to match well with the stretching exponent obtained from QENS experiments.
1. Introduction Deep eutectic solvents (DES) have emerged as a novel variety of solvents useful in various applications like electrodeposition [1], nanoparticle synthesis [2], catalysis [3], etc. The high solubility of metal salts and better conductivity compared to non aqueous solvents make DES an extremely good solvent in the metal deposition industry [4]. Some mixtures of DES have been shown to replace traditional precursors in shape-controlled synthesis of gold and silver nanoparticles [5]. Some DES possessing biocompatibility and poor toxicity have also been shown to be useful in vectorisation of drugs. Due to its biodegradability and cheaper preparation methods they are industrially more viable solvents compared to ionic liquids. In order to prepare DES with tailor-made physiochemical properties, it is of interest to study the structure and dynamics of these solvents on a molecular scale. DESs are generally prepared by mixing a metal salt and hydrogen bond donor in a particular molar ratio [4]. It is observed that the charge delocalization due to hydrogen-bonding in the mixture is responsible for depression in their freezing points [4]. Mixture of amides and electrolytic salts in a given molar ratio has been observed to form deep eutectic (DE) mixtures with freezing points below room temperature [6]. Recently, a mixture of acetamide (CH3CONH2) and lithium nitrate (LiNO3) in the molar ratio (78:22) has been shown to form DES and is found to remain in liquid at room
∗
temperature [6]. Fluorescence spectroscopy on these mixtures reveals that the dynamics of acetamide is strongly affected by the nature of the anion in the salt [6]. Further, it's found that the presence of these anions disrupt the inter-amide hydrogen bonding network leading to depression of the freezing point of the liquid. The disruption of hydrogenbonding alters the dynamical features of acetamide molecules in the mixture. The viscosity and conductivity of DES which play a major role in various applications like electrodeposition, catalysis etc. is deeply related to the dynamics of molecules in the mixture. Therefore studying the molecular dynamics of acetamide in the DES can shed light into the network of hydrogen-bonds and help in designing solvents with variable viscosity. Quasielastic neutron scattering is a suitable technique to study dynamics of atom/molecules in the nanoseconds to picoseconds time scale and length scale of angstroms to nanometer [7]. Molecular dynamics (MD) simulation covers the same length and time scales and can be used in synergy to get microscopic insight of the relaxation process. Here, we report dynamics in acetamide + LiNO3 DES as studied using QENS and MD simulation techniques. 2. Materials and methods Acetamide and lithium nitrate powders were obtained from SigmaAldrich. Acetamide was mixed with lithium nitrate with a mole fraction
Corresponding author. E-mail addresses: [email protected], [email protected] (V.K. Sharma).
https://doi.org/10.1016/j.physb.2019.01.003 Received 2 October 2018; Received in revised form 6 December 2018; Accepted 4 January 2019 Available online 09 March 2019 0921-4526/ © 2019 Elsevier B.V. All rights reserved.
Physica B: Condensed Matter 562 (2019) 13–16
H. Srinivasan, et al.
acetamide molecules at very short times (t < 10−2 ps) is governed by ballistic motion (α ∼ 2), which is followed by a sub-diffusive regime and at t > 102ps it follows Fickian diffusion. The behavior of MSD can be described by considering the following process for diffusion of acetamide. At very short times, the acetamide molecules don't undergo any collisions giving rise to ballistic regime. Subsequently, the given acetamide molecule interacts with its neighbouring molecules which have formed a transient cage due to hydrogen-bonding. During this process, once the cage relaxes the acetamide molecule dissociates its hydrogen bond with its existing neighbours and starts diffusing. In this time regime, the motion of acetamide molecule shows Fickian diffusion. This description of the motion of acetamide COM can be verified in more detail using velocity autocorrelation function (VACF) of the acetamide COM.
of 78:22 respectively. The mixture was then heated to a temperature of ∼65 °C for 30 min. After a clear solution was obtained from heating, the solution was left to cool down naturally to the room temperature. QENS spectrometer at Dhruva reactor in Bhabha Atomic Research Centre was used to carry out QENS experiments on DES mixture formed by acetamide and lithium nitrate at 300 K. The spectrometer operates in multi-angle reflecting crystal (MARX) mode with a large single crystal for energy dispersion [8]. In the current configuration, the spectrometer has an energy resolution of 200 μeV and energy range of ± 1 meV. QENS data were recorded in the momentum transfer (Q) range of 0.67 Å−1–1.8 Å−1 at room temperature (300 K). The resolution of the instrument was measured using standard vanadium sample. A system of 400 acetamide molecules and 56 lithium and nitrate ions were arranged in a cubic box of length 36 Å. The number of atoms was chosen to replicate the molar ratio (78:22) of the DE mixture. While, the potential parameters for acetamide were obtained from CHARMM force field [9], the parameters for lithium and nitrate ions were obtained from Joung and Cheatham [10] and Cadenna and Maginn [11] respectively. The system was equilibrated at atmospheric pressure (1 atm) and a temperature of 300 K using the Nose-Hoover NPT ensemble for 10 ns. The MD simulations were carried out using DLPoly 4 [12]. Subsequent to equilibration, the simulation was continued for another 5 ns to record atomistic trajectories for analysis at an interval of 1 ps.
3.2. MD simulation – cage relaxation The VACF of the acetamide COM is calculated from MD simulation trajectories. The motion of acetamide molecules can be described as hopping of acetamide molecules from one transient cage to the other. The transient cage around a given acetamide molecule can be formed by its hydrogen bonding with the neighbouring set of anions and acetamide. Therefore, the motion of the acetamide molecules will consist of both the relaxation of the transient cage and subsequently the motion of acetamide molecules to neighbouring site. The relaxation of cage formed by the neighbours of a given acetamide molecule will be ingrained in the motion of the acetamide COM. In order to account for the cage relaxation, the VACF (Cv(t))is described based on the equation,
3. Results and discussion 3.1. MD simulation – motion of acetamide centre of mass
dCv =− dt
MD simulation of the DES mixture of acetamide and lithium nitrate is carried out at 300 K. The nature of acetamide dynamics is studied extensively to understand the effect of hydrogen bonding in the solvent. As a primer, the mean squared displacement (MSD) of acetamide centre of mass (COM) is calculated to characterise the nature of its diffusion. It shows a transient subdiffusive regime until ∼100 ps, beyond which the motion of the molecules is found to be diffusive. This is explicitly indicated by calculating the (sub)diffusive exponent, α(t), as a function of time,
MSDACM (t ) = At α ⇒ α (t ) =
d (ln MSDACM (t )) d (ln t )
∫0
t
Cv (t − t ′) M (t ′) dt ′
(2)
where, memory function M(t) takes into consideration cage relaxation in the system. This equation can be transformed to an algebraic equation by Laplace transform and can be written as,
−Cv (0) ~ Cv (s ) = s + M (s )
(3)
Two simplest models of memory function were used, (i) exponential decay and (ii) power law decay to model the cage relaxation. Laplace transform of the VACF of the acetamide COM, Cv(s) is shown along with the fits using the two model functions in Fig. 2. It is clearly seen that the power law memory kernel is a much better fit compared to exponential memory kernel. The power law memory kernel is explicitly given by,
(1)
The MSD of acetamide COM and the variation of sub-diffusive parameter is shown in Fig. 1 and its inset respectively. The motion of
t −β −Cv (0) ~ M (t ) = p⎛ ⎞ ⇒ Cv (s ) = s + pτ βΓ (β − 1) s1 − β ⎝τ ⎠
(4)
where, τ is the cage relaxation time, p is the magnitude of memory
Fig. 2. Laplace transform of VACF of acetamide COM, Cv(s) is indicated by circles. The fits based on exponential (green line) and power law (blue) memory kernels are also shown.
Fig. 1. Mean squared displacement of acetamide COM. The inset shows the variation of the (sub)diffusive exponent α(t) with time. 14
Physica B: Condensed Matter 562 (2019) 13–16
H. Srinivasan, et al.
function, β is the power law exponent of cage relaxation and Г(x) is the gamma function. The cage relaxation time, τ, from the fit of equation (4) was found to be ∼10.2 ps and the exponent, β, was found to be ∼0.55. The transient sub-diffusive part of MSD of acetamide COM can be associated to power law behavior of the memory kernel. The diffusion mechanism of acetamide is analogous to the dynamics of supercooled water that is strongly hydrogen bonded, which is described considering an intra-basin fluctuation in a cage followed by inter-basin motion [13]. Diffusivity of the acetamide COM can be obtained directly by integrating the velocity autocorrelation function obtained from MD simulation,
DMD =
1 3
∫0
∞
Cv (t ) dt =
C˜ v (0) 3
(5) −6
Diffusivity, DMD, thus obtained is found to be ∼0.9 × 10 for acetamide COM in the mixture.
cm2/s
3.3. Comparison with quasielastic neutron scattering The total scattering law, S (Q,ω), measured in neutron scattering experiments, contains information about both coherent and incoherent scattering. However, for the hydrogenous system, the main contribution to S (Q,ω) is from incoherent scattering since the incoherent scattering cross section of hydrogen is very high compared to the total scattering cross section of any other element [7]. The incoherent part of neutron scattering spectra can be related to self-correlation function of the particle. Hence, for hydrogenous systems, quasielastic neutron scattering (QENS) experiments provide information about the mechanism of self diffusion of hydrogenous molecules in the system. In present case, QENS experiments have been carried out on DE mixture made of acetamide + LiNO3 to investigate dynamics of acetamide in it. QENS experiments on DES mixture of acetamide and lithium nitrate was carried out at 300 K. Significant quasielastic broadening is observed over the instrument resolution indicating presence of stochastic molecular motion of acetamide. In the previous section, MD simulation showed that the motion of acetamide COM shows a subdiffusive behavior up to 100 ps. In this context, the incoherent intermediate scattering function (IISF) should decay as stretched exponential function. Experimental IISF have been calculated from inverse Fourier transform of neutron scattering law, S (Q,ω). The obtained IISF is fitted using Kohlrausch-Williams-Watts (KWW) stretched exponential function,
I (Q, t ) = exp(−[
t ]β ′ ) R (t , σ ) τQENS (Q)
Fig. 3. Typical experimental IISF calculated from inverse Fourier transform of the QENS spectra at two different Q-values. The solids lines shown are the fits for the experimental IISF based on stretched exponential (eq. (5)).
(5)
where β′ is stretching exponent and τQENS is the characteristic timescale of relaxation. R (t,σ) is the resolution function of the instrument and σ is the full-width half maximum of the resolution which is found to be ∼200 μeV. It is found Eq. (5) described the experimental IISF well at all Q-values. Typical fitted experimental IISF's at two different Q-values are shown in Fig. 3. It was found that β′ obtained from the fit of experimental IISF using eq. (5) is ∼0.56 and remains fairly constant over the observed Q-range. It is observed that the stretching exponent obtained from QENS experiments matches really well with the power law exponent obtained from the results of MD simulation. Considering the stretched exponential to be sum of single exponential relaxation functions distributed over a time regime, an average relaxation time, < τ > , can be calculated using the obtained parameters τQENS and β with the following equation,
τQENS 1 〈τ 〉 = Γ( ) β β
Fig. 4. Variation of inverse of average relaxation timescale obtained from experimental IISF (eq. (6)) with respect to Q. The solid line indicates the fit corresponding to Fickian law, DavgQ2.
QENS spectra compares quite well with diffusivity obtained from the VACF in the MD simulations. This indicates the robustness of the model describing the dynamics of acetamide molecule in the mixture.
4. Conclusions Deep Eutectic Solvents (DES) are an emerging class of solvents that have a lot of applications in the industrial processes. The understanding of molecular dynamics in these systems plays a key role in unraveling the schemes of tuning macroscopic properties like viscosity, surface tension, etc. Here we have presented our results on the dynamics of acetamide in the DES mixture made of acetamide and lithium nitrate. The diffusion mechanism of acetamide molecules is comprised of a
(6)
The variation of inverse average relaxation time with respect to Q is shown in Fig. 4. It is found that inverse average relaxation time follow DavgQ2 as shown by the solid line in Fig. 4. The average diffusivity, Davg, of the acetamide is obtained by fitting 1/ < τ > = DavgQ2 is found to be ∼1.9 × 10−6 cm2/s. The average diffusivity obtained from the 15
Physica B: Condensed Matter 562 (2019) 13–16
H. Srinivasan, et al.
rattling motion of acetamide molecule in a cage followed by the diffusion of the molecule to the next transient cage. A power law memory kernel was able to describe the relaxation of cage. The experimental incoherent intermediate scattering function (IISF) obtained from QENS experiments were well described with a stretched exponential relaxation function. The power law exponent describing the cage relaxation was found to match with the stretching exponent obtained from the results of QENS experiments. Our study suggest that the motion of acetamide molecules is strongly dictated by the cage formation due to the strong hydrogen bonding network with it's neighbouring acetamide molecules and ions. In view of this, it may be possible to tune the viscosity of the DES by altering the chemical nature of the constituents of the mixture to adjust the hydrogen bond strength.
[2] Wei Lu, You-Jun Fan, Na Tian, Zhi-You Zhou, Xue-Qin Zhao, Bing-Wei Mao, ShiGang Sun, J. Phys. Chem. C 116 (2012) 2040–2044. [3] P.M. Pawar, K.J. Jarag, G.S. Shankarling, Green Chem. 13 (2011) 2130–2134. [4] E.L. Smith, A.P. Abbott, K.S. Ryder, Chem. Rev. 114 (2014) 11060–11082. [5] H.G. Liao, Y.X. Jiang, Z.Y. Zhou, S.P. Chen, S.G. Sun, Angew. Chem. Int. Ed. 47 (2008) 9100–9103. [6] B. Guchhait, S. Das, S. Daschakraborty, R. Biswas, J. Chem. Phys. 140 (2014) 104514. [7] M. Bée, Quasielastic Neutron Scattering : Principles and Applications in Solid State Chemistry, Biology and Materials Science, A. Hilger, Bristol; Philadelphia, 1988. [8] R. Mukhopadhyay, S. Mitra, S.K. Paranjpe, B.A. Dasannacharya, Nucl. Inst. Meth. A 474 (2001) 45. [9] R.B. Best, X. Zhu, J. Shim, P.E.M. Lopes, J. Mittal, M. Feig, A.D. MacKerell, J. Chem. Theory Comput. 8 (2012) 3257–3273. [10] I.S. Joung, T.E. Cheatham III, J. Phys. Chem. B 112 (2008) 9020–9041. [11] C. Cadena, E.J. Maginn, J. Phys. Chem. B 110 (2006) 18026–18039. [12] W. Smith, C.W. Yong, P.M. Rodger, Mol. Simulat. 28 (2002) 385–471. [13] Johan Qvist, Helmut Schober, Bertil Halle, J. Chem. Phys. 134 (2011) 144508.
References [1] A.P. Abbott, G. Frisch, K.S. Ryder, Annu. Rev. Mater. Res. 43 (2013) 335–358.
16