Investigation of Nonlinear Output-Input Microwave Power of DMSO-Ethanol Mixture by Molecular Dynamics Simulation

The nonlinear response of output-input microwave power for DMSO-ethanol mixture, which was exhibited as the direct evidence of non-thermal effect in experiment, was investigated by molecular dynamics simulation. Effects of microwave field on the mixture were evaluated from the alteration in structure, transport, hydrogen bonding dynamics and intermolecular interaction energy. Increasing the strength of the microwave field did not lead to any markedly conformational change, but decrease the diffusion coefficient. Prolonged hydrogen bonding lifetimes, which caused by the redistribution of microwave energy, was also detected. Distinct threshold effect was observed, which was consistent with the behavior in the experiment.

Microwave irradiation as non-conventional energy source plays a leveraged role in chemical transformations (e.g., organic synthesis [1][2][3][4][5] , polymer chemistry 6,7 , materials science 8,9 , nanotechnology 10 and biochemical processes [11][12][13][14]. It offers considerable advantages for accelerating chemical reaction, including shortening reaction time, enhancing product yield and purity [15][16][17] , comparing with conventional heating methods. However, there is an ongoing controversy over the nature of microwave-assisted acceleration [18][19][20][21][22] . Most chemists today will agree that the observed enhancements in microwave heated reactions are the consequence of pure thermal/kinetic effects 15,19,23 . Because they believe that the absorption of microwave photons is far too low to cause any chemical bond breaking, and that therefore microwaves could not "induce" molecules to undergo chemical reactions 24,25 . Nevertheless, there are reports which also demonstrate the existence of "specific" on "non-thermal" microwave effects 22,26,27 . Microwave non-thermal effects have been postulated to result from a direct, often stabilizing interaction of the electromagnetic field with specific molecules, intermediates, or even transition states in the reaction medium that is not related to a macroscopic temperature effect 21 . It has been suggested that understanding the non-thermal effect of microwave field with the systems under consideration is of great importance to the development of novel separation technologies 28,29 , selective heating, heterogeneous catalysis 30,31 , and in solid phase organic synthesis (SPOS) [32][33][34][35] . Over the past decades, a number of experiential techniques 21,[36][37][38][39][40][41] and theoretical methods [42][43][44][45] have been carried out to illustrate the non-thermal microwave effects. Investigating the variation of dielectric property caused by external electric fields (and therefore of the microwave power) is an effective way to understand the microwave non-thermal mechanism 46 . Based on our previously experimental system (see Fig. 1a), dielectric property changes of Dimethyl sulfoxide (DMSO) -ethanol (EOH) mixtures under microwave field are investigated, the non-thermal effects are demonstrated owing to the non-linearity ratio between output and input microwave power 46 . Interestingly, we found that only the combination of DMSO-primary alcohol mixtures remarkably presences this effect among the numerous binary mixtures.
DMSO is extensively used in organic chemistry, industry, cryoprotection and biology [47][48][49][50] . It consists of a highly polar S=O group, which interacts easily with water forming strong hydrogen bond, and two hydrophobic -CH3 groups 51,52 . Ethanol is widely applied as a chemical reagent, solvent, paint stripper, fuel, and a component in alcoholic beverages 53 . The hydroxyl group (-OH) is tending to attract partially positive hydrogen atoms of another ethanol molecules to form winding hydrogen chain structure in liquid ethanol 54 . Both of them are commonly used in microwave heating as polar solvents. Several works have demonstrated that DMSO-ethanol mixture exhibits properties deviating from ideal due to the intrinsical variation of hydrogen bonding interaction [55][56][57][58] . In the case of experiment, we have deduced that the nonlinear behaviors of the DMSO-ethanol mixture are related to the alteration of hydrogen bonds, which caused by the application of microwave. However, for the restrictions in experimental conditions, we only measure the ratio of output-input power. There is not any direct experimental method to observe the concomitant effect of the microwave field at the molecular level.
Molecular dynamics (MD) simulation proves an viable and potentially valuable way in studying the effects of external electric field in molecular systems, it has been utilized to provide an significant insight for understanding the microwave non-thermal effects on water 59-61 , hydrates 62 , metal oxides 63 , zeolites 64,65 and polystyrene solutions 28 . Thus, in order to further interpret the microwave non-thermal effect in our experiment, a series of molecular dynamics simulations were performed to investigate the structure, transport property, hydrogen bond dynamics and intermolecular interaction energy of DMSO-ethanol mixture under the microwave field. What's more, mixture with ethanol mole fraction = . X 0 41 EOH is chosen as the subjects of the MD simulation due to its excellent performances in experiment 46 . The results and discussion of previous experiment are briefly explained in the part of experimental results.

Experimental Results
Figure 1 depicts the experimental system and the ratio of output versus input microwave power with different mole fraction DMSO-ethanol mixtures and pure DMSO. The interaction between microwave and substances mainly embodies in microwave absorption and reflection, which strongly correlate with the medium's dielectric property 58 . Nonlinear output-input microwave power appears after a threshold ("critical point") input power suggests the redistribution of microwave energy and dielectric property changes in DMSO-ethanol mixtures, which Noting that the first peaks for O D -H E and O E -H E pairs are exactly the same in height and position, this distribution is conducive to creating mutually reinforce hydrogen bonds and enhance the stability or the structure. Indeed, liquid ethanol tends to form winding chain-like hydrogen bonds 54 , when DMSO solvent is dissolved, they are having a tendency to form dimers or timers in mixtures owing to the hydrogen bond interaction (Fig. 3) 57 . Thus, these results indicate that the fluid structuring remains unchanged with applying a sufficient e/m field. Transport property. Molecular transport has been estimated via the self-diffusion coefficients, which are calculated by Einstein's equation (Eq. 1) with the appropriate slope of MSDs 66 . = . × V/m. Moreover, the self-diffusion coefficients at = . × E 9 0 10 max 9 are even lower than in the case of = E z ero max , it seems that the strong field even hinders molecular diffusion. Figure 4 indicates that the application of microwave can reduce the diffusion coefficient, which is the direct evidence of the presence of microwave non-thermal effects. It is known that microwave fields can lead to molecular dipole moments continuous rotate to align the external electric field. Combining with the almost constancy of the first peak position shown in Fig. 2, thus, the reduction of self-diffusion coefficient was attributed to the molecular rearrangement in fluid structuring. Assume that the hydrogen bond is intact at time zero with the bonding state, the probability that it was intact at time t can be described by the autocorrelation function C HB (t) 68 . The dynamics of C HB (t) evaluating the hydrogen-bond structural relaxation and the associated relaxation time can be interpreted as the time-scale reorganization of hydrogen bonds [69][70][71][72][73] . The time-dependence C HB (t) under different strengths of microwave field are shown in Fig. 5. There is a threshold effect at about 2 5 10 8 . × V/m, when the field strength is bigger than this threshold value, the decay rate of C HB (t) decreases as strengthening the e/m field. The hydrogen bonding lifetimes is obtained from the long time decay of the autocorrelation function takes the values 0 or 1 depending on the hydrogen-bond state of a given pair of oxygen i and hydrogen j at time t 74 . The single-exponential relation between C HB (t) and τ is utilized to get the changing trend of the hydrogen bonding lifetimes with the microwave field rather than the accurate value. The corresponding hydrogen bonding lifetimes are listed in Table 1.
As shown in Table 1, hydrogen bonding lifetimes are apparently prolonged at field intensities larger than 2.5 × 10 8 V/m, which is coincident with the threshold effect mentioned previous paragraph, indicating that the hydrogen bonds between ethanol and DMSO are significantly strengthened with increasing the field strength. What's more, hydrogen bonding lifetimes of DMSO-ethanol mixture are about three times longer than that of the pure water 75 , which also demonstrates the stronger hydrogen bond interaction in the mixture. It is well known that the faster diffusion will result in faster hydrogen bond relaxation and vice versa 69 . The mechanism by which the mobility distinctly decrease in Fig. 4 can ascribe the longer lifetimes of hydrogen bonds.
The molecular rotation following the external electric field should affects hydrogen bonding, which is strongly dependent on molecular orientation between interacting pairs 76 ; thus, the variation in the average number of hydrogen bonds with the implementation of the microwave was calculated (Fig. 6). The results in Fig. 6, the average hydrogen bonding numbers of ethanol-ethanol show minor changes, but a slightly increase for  DMSO-ethanol in large field intensity, it is therefore logical that microwave fields boost molecular rotation and provides more opportunities for creating hydrogen bonds between DMSO and ethanol.

Intermolecular interaction energy.
In order to further interpret the properties changes mentioned above, intermolecular energy of DMSO-ethanol compound, split in their Lennard-Jones and Coulombic contributions, as a function of field intensity is reported in Fig. 7. As can be seen from the diagram, increasing field intensities lead to increase average interaction energy, in absolute value. This behavior of intermolecular energy would justify the lower diffusivities and longer hydrogen bonding lifetimes displayed in Figs 4 and 6. Moreover, from the two quartiles and median lines in boxplot, both instantaneous Lennard-Jones and Coulombic potential energy show strong vibration when the applied field intensities are larger than 2.5 × 10 8 V/m. Nevertheless, the intermolecular energy is almost no change at all for the weak fields, intensities lower than 2.5 × 10 8 V/m, which is accordance with the "critical point" in experiment. Moreover, Fig. 7 also illustrates that microwave energy was redistributed   Table 1. The hydrogen bonding lifetimes of DMSO-ethanol and ethanol-ethanol. a The unit of hydrogen bonding lifetime is ps, and the error is ±5%. b The unit of the intensity of microwave field is V/m. and partially stored as the intermolecular interaction potential energy, leading to significantly strengthen of the hydrogen bonding network.

Conclusions
In this paper, molecular dynamics simulation of DMSO-ethanol mixture were performed under microwave fields ranging from 0 to 9.0 × 10 9 V/m to investigate the nonlinear characteristic of output-input microwave power emerged in experiment. The effects of microwave field on the structure, transport property, hydrogen bonding dynamics and intermolecular interaction energy were analyzed. These properties show a pronounced threshold effect (about E 2 5 10 max 8 = . × ), which is consistent with the experiment. Stronger fields have little effect on the conformation of the mixture but lead to a remarked decrease in molecular diffusion. The increased intermolecular interaction energy, arising from redistribution of microwave energy, alters the hydrogen bonding arrangement dynamics, and prolongs lifetimes of hydrogen bond as a result. The tangible effects of microwave on DMSO-ethanol mixture were estimated in MD simulation via the sufficiently intense e/m field, which is expected to further interpret the mechanism of non-thermal effect. where E ab is the interaction energy between molecules a and b. The Lennard-Jones interaction parameters (ε ij and σ ij ) between sites i and j on distinct molecules are set by combining rules, ε ε ε = ( ) . q i is the partial charge on site i and r is the separation between these sites. In this equation, f ij is the correction factor for the Lennard-Jones 1-4 interaction, equal to 2. The potential parameters q i , ε ij , and σ ij for DMSO and ethanol, and corresponding molecular structures were displayed in Supplementary Materials. (Table 1 and Scheme 1). Application of an External Electric Field. The homogeneous microwave is applied along the x-axis direction, and it is represented by spatially uniform, time-alternating electric field of the form

Methods
where E max and ω stands for the field amplitude and frequency, respectively. The applied external electric fields were of frequency 2 45 ω = . GHz and of intensity = . × E 1 0 10 max 5 , 2 5 10 6 . × , 2 5 10 7 . × , 2 5 10 8 . × , 2 5 10 9 . × , and 9 0 10 9 . × V/m, respectively (Fig. 8). Note that although the field's intensities applied in the simulation are several order of magnitude larger than that in experiment ( . × 1 0 10 5 V/m), in fact, due to the microwave attenuate in the dielectric medium, the microwave field surrounding vacuum space should be considerably lager compared with the actual microwave field within the experimental sample 81 . Furthermore, it has been proposed that applying e/m field intensity of the order of 0.1 V/Å is necessary to observe tangible effects within limited nanosecond time scales 82 . Thus, strengths of e/m field applied in this simulation are reasonable.
Simulation Details. All simulations were carried out using the GROMACS 4.6.3 83 simulation package.
Initial simulation systems were built using the Packmol program, including 420 ethanol molecules and 604 DMSO molecules in a cubic box with a length of 4.5 nm. Periodic boundary conditions were imposed in all three dimensions. Real-space Ewald interactions and van der Waals interactions were truncated at 10 Å. Particle Mesh-Ewald method 77,78 was applied to handle long-range electrostatics to within a relative tolerance of 1 0 10 6 . × − . And the LINCS algorithm 79 was applied to constrain bond lengths of hydrogen atoms. Prior to system relaxation MD, the energy of the initial configurations was performed with a protocol of steepest descent, using termination gradients of 5000 kJ/mol·nm. And it is prior to production simulations, the systems were simulated on the canonical (N, V, T) ensemble for 1 ns at 300 K, using velocity-rescaling thermostat 84 to maintain the system temperature in order to study the non-thermal effects of the electromagnetic field on the DMSO-ethanol mixtures, and isotropic (N, P, T) ensemble for 1 ns at 1 bar, using Parrinello-Rahman barostat 85,86 . The external fields were applied in conjunction with NPT coupling, which are referred as nonequilibrium NNPT simulation, in order to isolate athermal effects as much as possible from thermal effects. A series of NNPT simulation was carried out for 5 ns, as well as equilibrium, zero-fields simulations. A leapfrog algorithm 87 was accompanied by a time step of 2 fs.