Temperature Dependence of Volumetric and Dynamic Properties of

Subscriber access provided by UNIVERSITY OF TOLEDO LIBRARIES

Article

Temperature Dependence of Volumetric and Dynamic Properties of Imidazolium-Based Ionic Liquids Fardin Khabaz, Yong Zhang, Lianjie Xue, Edward L Quitevis, Edward J. Maginn, and Rajesh Khare J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b12236 • Publication Date (Web): 05 Feb 2018 Downloaded from http://pubs.acs.org on February 10, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Temperature Dependence of Volumetric and Dynamic Properties of Imidazolium-Based Ionic Liquids

Fardin Khabaz1*, Yong Zhang2*, Lianjie Xue3*, Edward L. Quitevis3, Edward J. Maginn2, and Rajesh Khare1 1

2

Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556 3

Department of Chemistry, Texas Tech University, Lubbock, TX 79409

*

FK ([email protected]), YZ ([email protected]) and LX ([email protected]) are the co-corresponding authors of this manuscript. Corresponding authors phone number: 512-466-3332 (FK), 574-631-3937(YZ), and 806-787-8579(LX)

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Atomistically detailed molecular dynamics (MD) simulations were used to investigate the temperature dependence of the specific volume, dynamic properties, and the viscosity of linear alkyl chain ([CnC1Im][NTf2], n = 3-7) and branched alkyl chain ([(n-2)mCn-1C1Im][NTf2]) ionic liquids (ILs). The trend of glass transition temperature (Tg) values obtained in the simulations as a function of the alkyl chain length of cations was similar to the trend seen in experiments. In addition, the system relaxation behavior as determined from the temperature dependence of the diffusion coefficient, rotational relaxation time, and viscosity close to the Tg was observed to follow the Vogel-Fulcher-Tammann (VFT) expression.

Furthermore, the reciprocal of the

diffusion coefficient of the anion and cation in both linear and branched IL systems showed a linear correlation with viscosity, thus confirming the validity of the Stokes-Einstein (SE) relationship for these systems. Similarly, the average rotational relaxation time of the ions also found to correlate linearly with the viscosity of the ILs over a wide range of temperature, thereby validating the Debye-Stokes-Einstein (DSE) relationship for the ILs. These simulation findings suggest that the temperature dependence of the relaxation time of ILs is very similar to that of other glass-forming liquids.


Page 2 of 35

Page 3 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Introduction Ionic liquids (ILs) have unique properties such as a tunable structure, a low vapor pressure and slow dynamics at room temperature.1

These properties make ILs attractive for many

applications such as mass spectrometry,2 chemical separation,3 pharmaceuticals,4-5 solar thermal energy,6-8 carbon capture,9 and contact angle characterization.10 The imidazolium-based cations similar to those studied here were utilized in anion exchange membranes,11 and have also been found to be effective for dispersing fullerenes in water.12

Understanding the fundamental

structure-dynamics relationship of ILs is the key to optimizing their use in various applications. Experimentally, structural differences in anions have been observed to lead to different dynamics in ILs. In some situations, ILs with smaller cations and anions yielded a higher conductivity than those with large ions, due to higher diffusivities of the ions. Noda et al.13 determined the density, diffusion coefficient, and viscosity of several ILs, and found that the temperature dependence of the dynamics and viscosity of ILs can be quantified by means of the Vogel-Fulcher-Tammann (VFT) equation.14 Sippel et al.15 also demonstrated that the conductivity of various ILs follows the VFT equation. While

experimental measurements

present

a

quantitative

description

of

the

physicochemical properties of ILs, molecular dynamics (MD) simulations are capable of providing a molecular-level characterization of the underlying interactions that give rise to these observable properties.16 Prior simulation studies of ILs have focused on determining a reliable force field for the systems and characterizing the structure and transport properties (e.g. diffusion coefficient and zero shear viscosity) of ILs.17-24 Zhu et al.19 used MD simulations to investigate the structure and dynamics of ILs over a narrow range of temperatures (293 K < T < 373 K), and found that the rotational mobility of the ions increases with an increase in the temperature. The effect of anion 3 ACS Paragon Plus Environment


chemical structure on the diffusivity of ions was characterized at different temperatures and it was found that ILs containing Cl- and Br- ions exhibit a lower mobility compared with the ILs containing large anions such as OTf- and NTf2-.25 Chaban and Prezhdo26 calculated the diffusion coefficients of anions and cations of ILs in the high temperature range (600 K < T < 800 K) and found an Arrhenius behavior for the temperature dependence of the diffusion coefficient of anion and cation. The authors also suggested that this relationship could be used to determine the diffusivities of ions at lower temperatures. Recently, some of us27 synthesized a series of linear and branched imidazolium-based ILs and characterized their physiochemical behavior by measuring a number of properties, namely density, the glass transition temperature (Tg), zero shear viscosity, and the diffusion coefficients of anions and cations in the ILs. It was found that the zero shear viscosity of branched ILs increases in a non-monotonic fashion with the alkyl chain length of the cation. Similar observations were also made for the diffusion coefficients of the anion and cation in the branched ILs. Subsequently, we studied the viscosity of these ILs using MD simulations,28 and found that the ion-pair (IP) lifetimes20 are correlated with the minima of the potential of mean force (PMF) surface. We also discovered that the non-monotonic behavior of the zero shear viscosity is governed by the shape of the branched ILs. In this study, we utilize the same model structures that were prepared in our previous work28 to investigate the temperature dependence of a number of volumetric and dynamic properties of these ILs. We show that atomistically detailed MD simulations are capable of reproducing the exact experimental trends in volumetric properties such as glass transition temperatures of the ILs. Simulation results for the dynamic properties indicate that the temperature dependence of the diffusivity and rotational relaxation time of the ions can be quantified by the


Page 4 of 35

Page 5 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


VFT equation at temperatures close to the Tg. Furthermore, we show that the average rotational relaxation time of the ions and IL viscosity show a linear relationship over a range of temperatures. We begin with describing the molecular model and the simulation methods used in the current study, and then present the Results and Discussion section. We close the paper with a summary of our findings and conclusions.

2. Simulation Details and Methods 2.1. Simulation Details A series of linear ILs (1-(n-alkyl)-3-methylimidazolium bistriflimide, [CnC1Im][NTf2]) and branched ILs (1-(iso-alkyl)-3-methylimidazolium bistriflimide, [(n-2)mCn−1C1Im][NTf2]) were studied in this work. For brevity, we will use the abbreviation as CnC1 for the linear ILs and (n-2)mCn-1C1 for the branched ILs. Details of the model structures and the simulation force field were given in our previous paper.28 Here, we briefly describe the important points of the model structures and the methods used in the simulations. Initially, a cation-anion pair was placed in the simulation box and the cell was replicated twelve times in each dimension. The interactions between atoms in the systems were modeled by the GAFF force field.29-30 The Gaussian 09 package31 was used to optimize an isolated ion structure at the B3LYP/6-311++g (d,p) level, and the RESP method32 was employed to calculate the partial charges on each atom. The partial charges were then scaled uniformly by a factor of 0.8 in order to take into account the effect of charge transfer and polarizability.33 A cut-off distance of 12 Å was used to determine van der Waals and Coulombic interactions. The long range pair and electrostatic interactions were treated by employing the tail approximation and the Particle-Particle Particle-Mesh (PPPM) method34 , 5 ACS Paragon Plus Environment


respectively. The Nosé-Hoover thermostat35 and the extended Lagrangian approach36 were applied to maintain the temperature and pressure of the system constant. A time step of 1 fs was used to integrate the equations of motion and all simulations were performed using the LAMMPS37 package.

Averages were obtained from simulations of five independent replicas, with

uncertainties estimated as the standard deviations in quantities. 2.2. Volumetric Properties Quenching simulations were performed to determine the volume-temperature behavior of the ILs. These simulations were started at a high temperature and a quench rate of 10 K/ns (steps of 20 K with 2 ns long simulation per temperature) was used to cool down all ILs in a step-wise fashion. A temperature range of T = 80 K to 560 K was used to determine the specific volume of the ILs. At each temperature, the volumetric data (density or specific volume) were only averaged over the second half of the simulation trajectory at that temperature. 2. 3. Transport Properties Transport properties were characterized for only two ILs, i.e., a linear IL and its branched counterpart with n = 3. The translational and rotational dynamics of the anion and the cation were characterized by determining the diffusion coefficient and the rotational relaxation time of the ions. The temperature range T = 280 K to 560 K was utilized for calculating the dynamic properties. Simulations were performed for a duration of 80 ns at low temperatures to ensure that the diffusive regime is observed in simulations (this run time was 12 ns at high temperatures). Ion trajectories were recorded at regular intervals during these simulations. The time-decomposition method38-39 was used to determine the zero shear viscosity of this ILs in the canonical (NVT) ensemble. A temperature range of 300 K to 560 K was used to determine the zero shear viscosity


Page 6 of 35

Page 7 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of the selected branched and linear ILs. The nonlinear least-squares method was used to fit different data to various equations. We refer the reader to our prior article for additional details of the viscosity calculation.38 Specific details of the calculations for individual properties are given in the Results and Discussion section. 3. Results and Discussion 3.1. Simulated Volumetric Properties Are Consistent with Those Obtained in Experiments The relaxed model structures of all ILs at a high temperature (T = 560 K) were cooled in a step-wise fashion with a quench rate of 10 K/ns, using the same protocol as in the prior simulation studies.40-42 The specific volume as a function of temperature for both linear and branched ILs is shown in Figure 1a and Figure 1b. The figure shows that increasing the carbon number of the cation leads to a higher specific volume (or lower density) of the ILs in both branched and linear systems. As seen in Figure 2, the simulation density results are in excellent agreement (overall agreement is within 0.1%) with those obtained in the experiments by Xue et al.27 The volume-temperature plot for all ILs shows two regions of different slopes, which is indicative of the glass transition. The glass transition region can be located more accurately by monitoring the change in the coefficient of volume thermal expansion (CVTE), which is defined as  

1  V    (where V and T are the specific volume and temperature of the system, V  T P

respectively). As seen in Figure 3a Figure 3b, α is constant at high temperatures ( T > 300 K) for all the ILs (corresponding to the rubbery state), and it then reduces over a range of temperature (100 < T < 300) to a constant value at lower temperatures. The temperature range over which the

 value drops corresponds to the glass transition process. We note that the glass transition region



observed in simulations is much broader than that observed in experiments.43 The plateau region in α values at low temperatures corresponds to the glassy state. The value of  in the liquid regime obtained from simulations is approximately 6.9 × 10-4 K-1. As expected, due to the agreement between the simulation and experiment volume-temperature behavior, over the experimental temperature range, the values of  are in agreement with the experimental values for these systems (see Table 1).27 The glass transition temperature (Tg) of each of the ILs was obtained by determining the point of intersection of the linear fits to the volume-temperature data in the rubbery and glassy states as identified using the CVTE values. The dependence of simulation Tg on the cation chain length (N) is shown in Figure 4a. The observed abnormal trend i.e. non-monotonic increase in the Tg of the branched systems with N seen in simulation results was also observed in the experimental data by Xue et al.27, and is consistent with our previous observation of non-monotonic behavior of viscosity38 with n for these ILs. We note that the simulation value of the Tg is ~77 K higher than the experimental value27 due to the utilization of the very high cooling rate in simulations. Thus, to compare the simulation and experimentally observed trends in the Tg with the chain length of the ILs, we have normalized the Tg values in each case by using the Tg of the branched IL with n = 3 (1mC2C1). As seen in Figure 4b, such normalized Tg values of the ILs as obtained from the experiments and simulations are in a good agreement, with simulations almost quantitatively predicting the experimentally observed non-monotonic behavior of the Tg of the branched ILs as a function of chain length.


Page 8 of 35

Page 9 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLE 1. Comparison of the coefficient of volume-thermal expansion (CVTE) values obtained from the simulations and experiments. Values of CVTE are reported at T = 300 K. The experimental values of CVTE were obtained from Xue et al.27 The uncertainty on the simulation data is less than 2.0% of the reported values. Ionic liquid

 sim. ×10-4 (K-1)

 exp. ×10-4 (K-1)

C3C1 C4C1 C5C1 C6C1 C7C1 1mC2C1 2mC3C1 3mC4C1 4mC5C1 5mC6C1

6.98 6.96 6.91 6.97 6.91 6.80 6.82 6.76 6.77 6.84

6.65 6.67 6.70 6.57 6.59 6.64 6.61 6.81 6.63 6.65



Figure 1. Simulated values of the specific volumes of the (a) linear and (b) branched ILs as a function of the temperature.


Page 10 of 35

Page 11 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Comparison of density values determined by experiments27 and MD simulations at different temperatures. The differences in the simulated and the experimental density values for linear and branched are within 0.1%.



Figure 3. Coefficient of volume-thermal expansion (CVTE) as a function of the temperature determined in simulations of (a) linear and (b) branched ILs.


Page 12 of 35

Page 13 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Tg values as a function of carbon number (N) for linear and branched ILs. Figure shows (a) values obtained from simulations, and (b) normalized values (relative to the Tg of 1mC2C1) obtained from both simulations and experiments.27



3.2. Temperature Dependence of Dynamics of Ions Is Quantified by the Vogel-FulcherTammann (VFT) Equation. The relaxation behavior of ILs in the vicinity of the Tg was studied by focusing on the translational and rotational dynamics of the anion and the cation. In particular, the temperature dependence of the dynamics and zero shear viscosity of the branched and linear ILs with n = 3 (which correspond to 1mC2C1 and C3C1) was studied. These ILs were selected for the study because they have the smallest size and hence the smallest relaxation time, which makes the calculation of transport properties more convenient. Translational dynamics: The translational mobility was characterized by determining the meansquared displacement (MSD) of the center of mass of the anion and cation in both linear and branched systems as a function of time at different temperatures in the range 280 K  T  560 K . The results at the two extreme temperatures i.e. 280 and 560 K, respectively, are shown in Figure 5a and Figure 5b. The mobility of both of the ions increases and consequently the time required to attain the diffusive regime (i.e. slope = 1.0 in Figure 5a and Figure 5b) decreases with an increase in temperature. The cation has a larger translational mobility than the anion at all temperatures; this behavior is consistent with previous work showing that imidazolium cations have higher mobility than [NTf2]- size.21, 44 The diffusion coefficient (D) was determined using the Einstein relation in the diffusive regime of the MSD vs. time plot. As seen in the Figure 6a and Figure 6b, the diffusion coefficients of the anion and the cation in the C3C1 and 1mC2C1 systems increase with an increase in the temperature. The temperature dependence of the dynamic properties of glass forming liquids can be modeled by the VFT equation (

 B  1 1  exp   , where D0, B, and T0 are the VFT equation D D0  T  T0  14 ACS Paragon Plus Environment

Page 14 of 35

Page 15 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


parameters).14, 40 This equation is widely used for quantifying the temperature dependence of viscosity and dynamics (diffusion coefficient) of glass-forming liquids.40, 45 In particular, the VFT relationship was successfully utilized to describe the temperature dependence of dynamics of polymers,14 and has also been used to represent the simulation results for the dynamics of supercooled water46 and asphalt.40 Unlike the Arrhenius model,45 which does not account for the rapid increase in the relaxation time of a glass-forming material as it approaches its glass transition temperature, the VFT equation captures such rapid increase near Tg and predicts divergence of the relaxation time of a finite temperature T0 below the Tg. The diffusivity results were fitted to the VFT equation, with results shown in Figure 6a and Figure 6b. The diffusion coefficients of the anion and cation follow the VFT equation at temperatures above the Tg of the ILs in the simulations. This result is in contrast with the prior claim by Chaban and Prezhdo17 that the diffusion coefficient of ionic liquids at low temperatures can be represented by an Arrhenius fit obtained at very high temperatures. The values of the fit parameters are listed in Table 2. As shown in the Table, T0 is lower than the Tg of these ILs (which are 261 K and 269 K for linear and branched ILs, respectively). This result is consistent with the expectation of the VFT model.40 TABLE 2. Fit parameters of VFT equation for the diffusion coefficient of anion and cation in the branched and linear ILs. The Tg of the linear and branched ILs are 261 K and 269 K, respectively. The uncertainties in the D0, B, and T0 values are 10%, 8%, and 6% of their values, respectively. D0 ×10-15 (m2/s)

B

T0 (K)

Anion (linear)

5.7164

1084.28

157.7

Cation (linear)

6.0009

990.60

158.8

Anion (branched)

4.33768

1224.75

148.4

Cation (branched)

3.47064

1221.65

145.4



Figure 5. Mean-squared displacement (MSD) of the center of mass of anion and cation of 1mC2C1 at (a) 280K and (b) 560 K as a function of time.


Page 16 of 35

Page 17 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. Diffusion coefficient of anion and cation in (a) C3C1 and (b) 1mC2C1 as a function of the reciprocal of temperature.

Rotational dynamics: The rotational relaxation time of the anion and cation in the systems with linear and branched cation side chains was quantified by determining the second-order Legendre polynomial ( P2  t  

3cos 2    1 2

) for the reorientation of C-C and N-N vectors of anion and

cation, respectively, where  is the angle between the vector at t  0 and at time t . The vectors are shown schematically for the anion and cations in Figure 7a, Figure b, and Figure 7c. Figure 8a and Figure 8b show a plot of the order parameter P2  t  as a function of time for anion and cation in 1mC2C1 at T = 300 K and T = 560 K, respectively. P2 (t) exhibits a significantly faster decay at the higher temperature, thus indicating that the rotational relaxation times of the anion and cation decrease with an increase in the temperature. The Kohlrausch-Williams-Watts (KWW)

  t   equation ( P2  t   exp      ), where τ and β are the relaxation time and stretching exponent       14



Page 18 of 35

of KWW equation) can be used to quantify the dynamics of the reorientation of the ILs. Using the KWW equation parameters, the average relaxation time of the system (  av. )47 can be determined as 

 av.   P2  t  dt  0

 1  ,    

(1)

where Γ is the Gamma function. Simulation results of P2  t  at different temperatures for the anion and cation were initially fitted to the KWW equation. The resulting values of the relaxation time (  ) and stretching exponent (  ) for anion and cation in C3C1 and 1mC2C1 are shown in Figure 9a, Figure 9b, Figure 9c, and Figure 9d. For the branched system, the relaxation time  av. of the cation is slightly larger than that of the anion. As expected, an increase in the temperature reduces the rotational relaxation time of the ions. The value of  is indicative of the width of the distribution of the relaxation times of a glass-forming material such that   1 corresponds to a liquid-like relaxation, while   1 shows that the distribution of the relaxation times is broader and the system becomes glassy. The values of β so obtained for 1mC2C1 show a larger scatter compared to the values for C3C1 over the temperature range studied. For all systems studied, β increases with an increase in the temperature. This behavior of the stretching exponent indicates that the relaxation spectrum of these ILs shows liquid-like single exponential behavior at high temperatures. The β values for the cation and the anion are close to each other for 1mC2C1, while β is consistently larger for the anion in the C3C1 system. In addition, the relaxation time of the ions in the linear systems are much longer for the anion compared with cation. Similar to translational dynamics, we have applied the VFT equation to quantify the temperature dependence of the rotational dynamics of the ILs. The average rotational relaxation 18 ACS Paragon Plus Environment

Page 19 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


time as a function of the temperature and the corresponding fits are shown in Figure 10a and Figure 10b for the linear IL and Figure 10c and Figure10d for the branched IL, respectively. As seen in the figure, τav. shows a clear VFT behavior in the systems, and the values of the VFT parameters are listed in Table 3. Not only that the functional form of these VFT relationships can describe the temperature dependence of the translational and rotational dynamics, but also the numerical values of the fit parameters are in good agreement within statistical uncertainties.

Figure 7. Schematic representation of the vectors used for the rotational mobility calculations for the cations ((a) and (b) in the linear and branched ILs, respectively) and anion (c).

TABLE 3. Fit parameters of VFT equation for the average rotational relaxation time of anion and cation in the branched and linear ILs. The uncertainties in the τ0, B, and T0 values are 9%, 13%, and 5.0% of their values, respectively. τ0 ×10-4 (ns)

B

T0 (K)

Anion (linear)

7.70092

930.3

162.1

Cation (linear)

7.67018

881.1

165.0

Anion (branched)

5.45395

1025.0

159.2

Cation (branched)

4.66618

1176.0

148.0



Figure 8. P2 (t) function of anion and cation in [1mC2C1] [NTf2] system at (a) T = 300 K and (b) T = 560 K as a function of time.


Page 20 of 35

Page 21 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9. Rotational relaxation time of anion and cation in (a) [C3C1][NTf2] and (b) [1mC2C1][NTf2] as a function of temperature. Stretching exponent for (c) [C3C1][NTf2] and (d) [1mC2C1][NTf2] as a function of temperature.



Figure 10. Average rotational relaxation time (τav.) of (a) anion and (b) cation in [C3C1][NTf2] and (c) anion and (d) cation in [1mC2C1][NTf2] as a function of temperature. Inset: Arrhenius plot of the average rotational relaxation time.

3.3. Transport Properties of Ionic Liquids Follow Stokes-Einstein (SE) and Debye-StokesEinstein (DSE) Relationships Viscosity and its dependence on temperature: The zero shear viscosity of C3C1 and 1mC2C1 was determined using equilibrium molecular dynamics (EMD) at different temperatures above the Tg of the ILs. The branched IL has a larger viscosity compared to the linear systems at a given temperature. This trend is consistent with prior experiments48 and MD simulation work on the effect of branching of alkanes,49 in which branching increased the shear viscosity by almost a 22 ACS Paragon Plus Environment

Page 22 of 35

Page 23 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


factor of two. This is also consistent with the results for the dynamics of these ILs that were described in the previous section. As expected, the viscosities of the ILs increase with a decrease in temperature. The viscosity increase becomes very rapid as the temperature approaches the Tg of the systems. Similar to the case for the translational and rotational dynamics, we applied the VFT equation to represent

 B  the temperature dependence of the viscosity:   0 exp   , where η0 is the viscosity  T  T0  prefactor. The VFT equation provides an excellent fit to the simulation data as seen in Figure 11. The values of T0 are 181.3 K and 143.6 K for the branched and the linear IL, respectively.

Figure 11. Zero shear viscosity of C3C1 and 1mC2C1 as a function of temperature. Inset: Plot of the zero shear viscosity versus inverse temperature.



Page 24 of 35

The VFT fit to the viscosity provides an opportunity to quantify the shift in the Tg that is observed in simulations.40 Given that the glass transition temperature is a temperature at which the relaxation time of the system is equal to the time scale of measurement, the Williams-LandelFerry (WLF) equation, which is equivalent to the VFT equation, can be used to estimate the shift in the Tg. The WLF equation, which relates the temperature and the rescaled relaxation time of the system, is as follows:

log at  log

 C1 (T  T0 ) ,   0 C2  T  T0

(2)

where  and  0 are the relaxation time values at temperatures T and T0, respectively, while C1 and C2 are the constants of the WLF equation. In particular, the very high cooling rates that are used in molecular simulations compared to the experiments lead to a much higher Tg in simulations compared to the experiments. In previous work on polymeric systems,50-51 we showed that this shift in the Tg due to the utilization of a large cooling rate in the simulations can be calculated based on the WLF equation (Eq.2) as

log10

 g,exp C1 (Tg ,shifted  Tg ,sim ) texp qsim  log10  log10  qexp tsim  g, sim C2  Tg , shifted  Tg ,sim

(3)

where q and t are the cooling rate and timescale, respectively. Tg , shifted is the shifted value of the

Tg (this shift in this case is to a lower value. Since the VFT and WLF equations are mathematically equivalent, we obtained the values of the constants in the WLF equation from the values of the VFT equation parameters. Using Eq. (3) and the values of the experimental Tg, values of Tg , shifted for these pair of the linear and branched IL are 145.43 K and 181.4 K, respectively. The Tg values


Page 25 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


which are calculated from the VFT equation parameter values for viscosity, are within ~ 40 K and ~ 10 K of the experimentally measured values for the linear and branched ILs, respectively. Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) relationships: The SE relationship connects the viscosity to the diffusion coefficient of spherical particles via the expression

D

kT 6 R

, where kT is the thermal energy of the particle,  is the viscosity of the liquid, and

R is the hydrodynamic radius of the particle. For more complicated systems, the pre-factor of

this relationship, i.e. 1/6, can change, but there is always an inverse relationship between the diffusivity and viscosity (i.e. 1 D  ). The validity of the SE relationships for the ILs under consideration can be tested using the calculated values of diffusivity and viscosity. Since these values are at different temperatures, we have plotted 1 D vs.  T ,52 which provides an even more stringent test of the SE equation for the ILs (Figure 12a and Figure 12b). The data in these figures were successfully fitted to a power-law relationship ( 1 D

 T 

a

, where a is the fit parameter).

For the anion these exponents are 1.015 ± 0.002 and 0.955 ± 0.010 in the linear and branched ILs respectively. Similarly for the cations, a values are 0.972± 0.003 and 0.920 ± 0.007 in the linear and branched ILs, respectively, thus confirming the validity of the SE relationships for these ILs over the temperature range of interest. The DSE relationship Dr 

kT , where Dr is the rotational diffusion coefficient, 8 R 3

connects the rotational dynamics of immersed bodies to the liquid viscosity. For this purpose, the average rotational relaxation time ( av. ) of the ions, which is proportional to the reciprocal of their rotational diffusion coefficient, was used to quantify the rotational mobility. Similar to the case



for the translational dynamics, to test the validity of the DSE relationship,  av. of anion and cation was plotted against the  T in Figure 13a and Figure 13b. The data show a power-law behavior i.e.  av.

 T 

a

. For the anion these exponents are 0.891 ± 0.002 and 0.884 ± 0.005 in the linear

and branched ILs respectively. Similarly for the cations, a values are 0.870 ± 0.003 and 0.921 ± 0.010 in the linear and branched ILs, respectively. The values are slightly less than unity, indicating that the DSE relationship is only approximately applicable to these ILs over the temperature range of interest. This deviation from unity can be attributed to the non-spherical shape of these ions.38


Page 26 of 35

Page 27 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 12. Reciprocal of diffusion coefficient of anion and cation as a function of the zero shear viscosity in (a) C3C1 and (b) 1mC2C1. The dashed and dotted lines show the power-law fits to data.



Figure 13. Average rotational relaxation time as a function of the zero shear viscosity in (a) C3C1 and (b) 1mC2C1. The dashed and dotted lines show the power-law fits to data.

Summary and Conclusions We have used atomistically detailed MD simulations to characterize the temperature dependence of volumetric and dynamic properties of several imidazolium-based ILs. The density values obtained from simulations for a series of ILs are in an excellent agreement with experiments. The volume-temperature behavior shows a distinct change in temperature indicating that similar to molecular glasses,53 ILs exhibit a glass transition on lowering the temperature.


Page 28 of 35

Page 29 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Importantly, the MD simulations were able to predict the non-monotonic change in the Tg of the system with increasing the chain length of the IL that is observed in the experiments. The translational and rotational dynamics of the selected linear and branched ILs were quantified at temperatures above the Tg of the systems. Diffusion coefficients of the anion and cation showed a VFT behavior. Similarly, a VFT-temperature dependence was found for the rotational dynamics of these ions. Within statistical uncertainties, the VFT fit parameters for temperature dependence of the translational and rotational dynamics agree with each other. The diffusivity and viscosity values obtained from simulations indicated that the ILs follow the StokesEinstein relationship. On the other hand, the correlation between viscosity and the rotational relaxation time values is only in approximate agreement with the Debye-Stokes-Einstein relationship. We expect that the same functional forms as for the temperature dependence of diffusion coefficient and average rotational relaxation time of the ILs in this study will be applicable to other imidazolium-based ILs. Atomistically detailed simulations have primarily been used in the literature to predict the volumetric properties or individual dynamic properties of the ILs. We have shown that the simulations can not only predict a wide range of volumetric and dynamic properties but also more subtle effects such as glass transition, the exact temperature dependence of the viscosity and diffusivity, and the interrelationships between these dynamic properties. These results suggest that simulation tools can be utilized to guide experiments for the development of new ionic materials with target property values at the specified temperature.



Page 30 of 35

Acknowledgements YZ and EJM are supported by the U.S. Department of Energy, Basic Energy Science, Joint Center for Energy Storage Research under Contract No. DE-AC02-06CH11357.

Computational

resources were provided by the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231, and the Center for Research Computing (CRC) at the University of Notre Dame. LX and ELQ were supported on National Science Foundation (CHE 1153077).

Supporting Information (SI): Table S1. Simulated values of the glass transition temperature (Tg) of the linear and branched ILs. Table S2. Simulated values of the diffusion coefficient of ions in the C3C1. Table S3. Simulated values of the diffusion coefficient of ions in 1mC2C1. Table S4. Simulated values of the average rotational relaxation time of ions in C3C1. Table S5. Simulated values of the average rotational relaxation time of ions in 1mC2C1.

Present Addresses FK: McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, TX. LX: James R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS, 66506-2601.


Page 31 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


REFERENCES 1. 2. 3.

4.

5. 6. 7.

8.

9.

10. 11.

12. 13.

14. 15. 16.

17.

Hayes, R.; Warr, G. G.; Atkin, R. Structure and Nanostructure in Ionic Liquids. Chem. Rev. 2015, 115 (13), 6357-6426. Abdelhamid, H. N. Ionic Liquids for Mass Spectrometry: Matrices, Separation and Microextraction. TrAC, Trends Anal. Chem. 2016, 77, 122-138. Tian, K.; Qi, S.; Cheng, Y.; Chen, X.; Hu, Z. Separation and Determination of Lignans from Seeds of Schisandra Species by Micellar Electrokinetic Capillary Chromatography Using Ionic Liquid as Modifier. J. Chromatogr. A 2005, 1078 (1–2), 181-187. Weaver, K. D.; Kim, H. J.; Sun, J.; MacFarlane, D. R.; Elliott, G. D. Cyto-Toxicity and Biocompatibility of a Family of Choline Phosphate Ionic Liquids Designed for Pharmaceutical Applications. Green Chem. 2010, 12 (3), 507-513. Hough, W. L.; Rogers, R. D. Ionic Liquids Then and Now: From Solvents to Materials to Active Pharmaceutical Ingredients. Bull. Chem. Soc. Jpn. 2007, 80 (12), 2262-2269. Wishart, J. F. Energy Applications of Ionic Liquids. Energy Environ. Sci. 2009, 2 (9), 956961. MacFarlane, D. R.; Tachikawa, N.; Forsyth, M.; Pringle, J. M.; Howlett, P. C.; Elliott, G. D.; Davis, J. H.; Watanabe, M.; Simon, P.; Angell, C. A. Energy Applications of Ionic Liquids. Energy Environ. Sci. 2014, 7 (1), 232-250. Wang, P.; Wenger, B.; Humphry-Baker, R.; Moser, J.-E.; Teuscher, J.; Kantlehner, W.; Mezger, J.; Stoyanov, E. V.; Zakeeruddin, S. M.; Grätzel, M. Charge Separation and Efficient Light Energy Conversion in Sensitized Mesoscopic Solar Cells Based on Binary Ionic Liquids. J. Am. Chem. Soc. 2005, 127 (18), 6850-6856. Cadena, C.; Anthony, J. L.; Shah, J. K.; Morrow, T. I.; Brennecke, J. F.; Maginn, E. J. Why Is Co2 So Soluble in Imidazolium-Based Ionic Liquids? J. Am. Chem. Soc. 2004, 126 (16), 5300-5308. Gao, L.; McCarthy, T. J. Ionic Liquids Are Useful Contact Angle Probe Fluids. J. Am. Chem. Soc. 2007, 129 (13), 3804-3805. Guo, M.; Fang, J.; Xu, H.; Li, W.; Lu, X.; Lan, C.; Li, K. Synthesis and Characterization of Novel Anion Exchange Membranes Based on Imidazolium-Type Ionic Liquid for Alkaline Fuel Cells. J. Membr. Sci. 2010, 362 (1–2), 97-104. Fileti, E. E.; Chaban, V. V. Imidazolium Ionic Liquid Helps to Disperse Fullerenes in Water. J. Phys. Chem. Lett. 2014, 5 (11), 1795-1800. Noda, A.; Hayamizu, K.; Watanabe, M. Pulsed-Gradient Spin−Echo 1h and 19f Nmr Ionic Diffusion Coefficient, Viscosity, and Ionic Conductivity of Non-Chloroaluminate RoomTemperature Ionic Liquids. J. Phys. Chem. B 2001, 105 (20), 4603-4610. Larson, R. G. The Structure and Rheology of Complex Fluids (Topics in Chemical Engineering) 1st Edition. 1 ed.; Oxford University Press: New York, 1998. Sippel, P.; Lunkenheimer, P.; Krohns, S.; Thoms, E.; Loidl, A. Importance of Liquid Fragility for Energy Applications of Ionic Liquids. Sci. Rep. 2015, 5, 13922. Liu, H.; Maginn, E. A Molecular Dynamics Investigation of the Structural and Dynamic Properties of the Ionic Liquid 1-N-Butyl-3-Methylimidazolium Bis(Brifluoromethanesultonyl)Imide. J. Chem. Phys. 2011, 135 (12), 124507. Chaban, V. V.; Prezhdo, O. V. Computationally Efficient Prediction of Ionic Liquid Properties. J. Phys. Chem. Lett. 2014, 5 (11), 1973-1977.



18.

19.

20.

21. 22.

23. 24.

25.

26. 27.

28.

29. 30.

31.

32.

33.

34.

Chaban, V. V.; Voroshylova, I. V.; Kalugin, O. N. A New Force Field Model for the Simulation of Transport Properties of Imidazolium-Based Ionic Liquids. Phys. Chem. Chem. Phys. 2011, 13 (17), 7910-7920. Zhu, G.; Kang, X.; Zhou, S.; Tang, X.; Sha, M.; Cui, Z.; Xu, X. Molecular Insight into the Microstructure and Microscopic Dynamics of Pyridinium Ionic Liquids with Different Alkyl Chains Based on Temperature Response. RSC Adv. 2017, 7 (9), 4896-4903. Zhang, Y.; Maginn, E. J. Direct Correlation between Ionic Liquid Transport Properties and Ion Pair Lifetimes: A Molecular Dynamics Study. J. Phys. Chem. Lett. 2015, 6 (4), 700705. Morrow, T. I.; Maginn, E. J. Molecular Dynamics Study of the Ionic Liquid 1-N-Butyl-3Methylimidazolium Hexafluorophosphate. J. Phys. Chem. B 2002, 106 (49), 12807-12813. Konieczny, J. K.; Szefczyk, B. Structure of Alkylimidazolium-Based Ionic Liquids at the Interface with Vacuum and Water—a Molecular Dynamics Study. J. Phys. Chem. B 2015, 119 (9), 3795-3807. Wang, Y.; Voth, G. A. Unique Spatial Heterogeneity in Ionic Liquids. J. Am. Chem. Soc. 2005, 127 (35), 12192-12193. Bedrov, D.; Borodin, O. Thermodynamic, Dynamic, and Structural Properties of Ionic Liquids Comprised of 1-Butyl-3-Methylimidazolium Cation and Nitrate, Azide, or Dicyanamide Anions. J. Phys. Chem. B 2010, 114 (40), 12802-12810. Ramya, K. R.; Kumar, P.; Venkatnathan, A. Molecular Simulations of Anion and Temperature Dependence on Structure and Dynamics of 1-Hexyl-3-Methylimidazolium Ionic Liquids. J. Phys. Chem. B 2015, 119 (46), 14800-14806. Chaban, V. V.; Prezhdo, O. V. Ionic and Molecular Liquids: Working Together for Robust Engineering. J. Phys. Chem. Lett. 2013, 4 (9), 1423-1431. Xue, L.; Gurung, E.; Tamas, G.; Koh, Y. P.; Shadeck, M.; Simon, S. L.; Maroncelli, M.; Quitevis, E. L. Effect of Alkyl Chain Branching on Physicochemical Properties of Imidazolium-Based Ionic Liquids. J. Chem. Eng. Data 2016, 61 (3), 1078-1091. Zhang, Y.; Xue, L.; Khabaz, F.; Doerfler, R.; Quitevis, E. L.; Khare, R.; Maginn, E. J. Molecular Topology and Local Dynamics Govern the Viscosity of Imidazolium-Based Ionic Liquids. J. Phys. Chem. B 2015, 119 (47), 14934-14944. Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25 (9), 1157-1174. Wang, J.; Wang, W.; Kollman, P. A.; Case, D. A. Automatic Atom Type and Bond Type Perception in Molecular Mechanical Calculations. J. Mol. Graphics Modell. 2006, 25 (2), 247-260. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. Gaussian 09, Revision A.1; Gaussian, Inc.: Wallingford, CT. 2009. Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The Resp Model. J. Phys. Chem. 1993, 97 (40), 10269-10280. Zhang, Y.; Maginn, E. J. A Simple Aimd Approach to Derive Atomic Charges for Condensed Phase Simulation of Ionic Liquids. J. Phys. Chem. B 2012, 116 (33), 1003610048. Hockney. R . W ; W, E. J. Particle-Particle-Particle-Mesh (P3m) Algorithms. In Computer Simulation Using Particles, Taylor & Francis 1988: 1988; pp 267–304. 32 ACS Paragon Plus Environment

Page 32 of 35

Page 33 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


35. 36. 37. 38.

39.

40. 41.

42.

43. 44.

45. 46.

47. 48.

49. 50.

51.

52.

Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31 (3), 1695-1697. Shinoda, W.; Shiga, M.; Mikami, M. Rapid Estimation of Elastic Constants by Molecular Dynamics Simulation under Constant Stress. Phys. Rev. B 2004, 69 (13), 134103. Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117 (1), 1-19. Zhang, Y.; Otani, A.; Maginn, E. J. Reliable Viscosity Calculation from Equilibrium Molecular Dynamics Simulations: A Time Decomposition Method. J. Chem. Theory Comput. 2015, 11 (8), 3537-3546. Otani, A.; Zhang, Y.; Matsuki, T.; Kamio, E.; Matsuyama, H.; Maginn, E. J. Molecular Design of High Co2 Reactivity and Low Viscosity Ionic Liquids for Co2 Separative Facilitated Transport Membranes. Ind. Eng. Chem. Res. 2016, 55 (10), 2821-2830. Khabaz, F.; Khare, R. Glass Transition and Molecular Mobility in Styrene–Butadiene Rubber Modified Asphalt. J. Phys. Chem. B 2015, 119 (44), 14261-14269. Khare, K. S.; Khabaz, F.; Khare, R. Effect of Carbon Nanotube Functionalization on Mechanical and Thermal Properties of Cross-Linked Epoxy–Carbon Nanotube Nanocomposites: Role of Strengthening the Interfacial Interactions. ACS Appl. Mater. Interfaces 2014, 6 (9), 6098-6110. Mani, S.; Khabaz, F.; Godbole, R. V.; Hedden, R. C.; Khare, R. Structure and Hydrogen Bonding of Water in Polyacrylate Gels: Effects of Polymer Hydrophilicity and Water Concentration. J. Phys. Chem. B 2015, 119 (49), 15381-15393. Schmelzer, J. W. P.; Tropin, T. V. Dependence of the Width of the Glass Transition Interval on Cooling and Heating Rates. J. Chem. Phys. 2013, 138 (3), 034507. Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. Physicochemical Properties and Structures of Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in Imidazolium Cation. J. Phys. Chem. B 2005, 109 (13), 6103-6110. Ferry, J. D. Viscoelastic Properties of Polymers. 3 ed.; Wiley: New York, 1980. Chen, S.-H.; Mallamace, F.; Mou, C.-Y.; Broccio, M.; Corsaro, C.; Faraone, A.; Liu, L. The Violation of the Stokes–Einstein Relation in Supercooled Water. Proc. Natl. Acad. Sci. 2006, 103 (35), 12974-12978. Khabaz, F.; Mani, S.; Khare, R. Molecular Origins of Dynamic Coupling between Water and Hydrated Polyacrylate Gels. Macromolecules 2016, 49 (19), 7551-7562. Dixon, J.; Webb, W.; Steele, W. Properties of Hydrocarbons of High-Molecular Weight Synthesized by Research Project 42 of the American Petroleum Institute. Pennsylvania State University 1962. Khare, R.; Pablo, J. d.; Yethiraj, A. Rheological, Thermodynamic, and Structural Studies of Linear and Branched Alkanes under Shear. J. Chem. Phys. 1997, 107 (17), 6956-6964. Soni, N. J.; Lin, P.-H.; Khare, R. Effect of Cross-Linker Length on the Thermal and Volumetric Properties of Cross-Linked Epoxy Networks: A Molecular Simulation Study. Polymer 2012, 53 (4), 1015-1019. Khare, K. S.; Khare, R. Directed Diffusion Approach for Preparing Atomistic Models of Crosslinked Epoxy for Use in Molecular Simulations. Macromol. Theory Simul. 2012, 21 (5), 322-327. Thakurathi, M.; Gurung, E.; Cetin, M. M.; Thalangamaarachchige, V. D.; Mayer, M. F.; Korzeniewski, C.; Quitevis, E. L. The Stokes-Einstein Equation and the Diffusion of Ferrocene in Imidazolium-Based Ionic Liquids Studied by Cyclic Voltammetry: Effects of 33 ACS Paragon Plus Environment


53.

Cation Ion Symmetry and Alkyl Chain Length. Electrochimica Acta 2018, 259 (Supplement C), 245-252. Swallen, S. F.; Kearns, K. L.; Mapes, M. K.; Kim, Y. S.; McMahon, R. J.; Ediger, M. D.; Wu, T.; Yu, L.; Satija, S. Organic Glasses with Exceptional Thermodynamic and Kinetic Stability. Science 2007, 315 (5810), 353-356.


Page 34 of 35

Page 35 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


Temperature Dependence of Volumetric and Dynamic Properties of

Recommend Documents