Anomalous diffusion and diffusion anomaly in confined Janus dumbbellsLeandro B. Krott, Cristina Gavazzoni, and José Rafael Bordin

Citation: J. Chem. Phys. 145, 244906 (2016); doi: 10.1063/1.4972578View online: http://dx.doi.org/10.1063/1.4972578View Table of Contents: http://aip.scitation.org/toc/jcp/145/24Published by the American Institute of Physics

THE JOURNAL OF CHEMICAL PHYSICS 145, 244906 (2016)

Anomalous diffusion and diffusion anomaly in confinedJanus dumbbells

Leandro B. Krott,1,a) Cristina Gavazzoni,2 and Jose Rafael Bordin3,b)1Centro Ararangua, Universidade Federal de Santa Catarina, Rua Pedro Joao Pereira, 150,CEP 88905-120 Ararangua, SC, Brazil2Instituto de Fısica, Univeridade Federal do Rio Grande do Sul, Caixa Postal 15051,CEP 91501-570 Porto Alegre, RS, Brazil3Campus Cacapava do Sul, Universidade Federal do Pampa, Av. Pedro Anunciacao, 111,CEP 96570-000 Cacapava do Sul, RS, Brazil

(Received 14 October 2016; accepted 3 December 2016; published online 30 December 2016)

Self-assembly and dynamical properties of Janus nanoparticles have been studied by moleculardynamic simulations. The nanoparticles are modeled as dimers and they are confined between twoflat parallel plates to simulate a thin film. One monomer from the dumbbells interacts by a standardLennard-Jones potential and the other by a two-length scales shoulder potential, typically used foranomalous fluids. Here, we study the effects of removing the Brownian effects, typical from col-loidal systems immersed in aqueous solution, and consider a molecular system, without the dragforce and the random collisions from the Brownian motion. Self-assembly and diffusion anomalyare preserved in relation to the Brownian system. Additionally, a superdiffusive regime associ-ated to a collective reorientation in a highly structured phase is observed. Diffusion anomaly andanomalous diffusion are explained in the two length scale framework. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4972578]

I. INTRODUCTION

Janus nanoparticles are characterized as particles with twoor more surfaces with distinct chemical or physical properties.They have distinct shapes, as spheres, rods, disks, and dumb-bells, and can assemble in a variety of nanoscale morphologieslike spheres, cylinders, lamellae phases, and micelles with dis-tinct shapes and functionality.1–10 Due to it versatility, Janusnanoparticles have promising application to medicine, self-driven molecules, catalysis, photonic crystals, stable emulsion,and self-healing materials.11–19 Particularly, Janus dimers20–23

are nanoparticles formed by two monomers linked together.Each monomer has distinct functionality and characteristic, aswell as can have different size.

Regarding to diffusion, we can raise two interesting phe-nomena. The first is the anomalous diffusion. The diffusioncoefficient is obtained from the scaling factor between themean square displacement, 〈r(0)r(t)〉, and the exponent oftime, tα. For regular, or Fick, diffusive process α = 1.0. Ifα > 1.0 we say that the system is superdiffusive, and if α < 1.0the regime is subdiffusive. For Brownian systems, the colli-sions between solute and solvent and the solvent viscosity,considered using a white noise and a drag force,24 usuallylead the system to a Fick diffusion. On the other hand, formolecular systems, where there are no solvent effects, the Fickdiffusion is achieved due to the collisions between the parti-cles of the system. If the collision is rare, as in a infinitivelydiluted gas, the diffusion tends to be ballistic. Anomalousdiffusion was observed in several systems, as proteins and

a)E-mail: leandro.krott@ufsc.brb)E-mail: josebordin@unipampa.edu.br. Tel.: +55 55 3281-1711.

colloids in crowded environments,25,26 self-propelled parti-cles,27 and confined nanoparticles.28

The second interesting phenomenon is the diffusionanomaly. For most materials, the diffusion coefficientdecreases when the pressure (or density) increases. However,materials as water,29 silicon,30 and silica31 show diffusionanomaly, characterized by a maximum in the diffusion coeffi-cient at constant temperature. Besides diffusion (or dynamical)anomaly, water, silicon, silica, and others fluids, the so-calledanomalous fluids, also have other classes of anomalies, asstructure and thermodynamic anomalies.

Experimental studies have reported the production ofsilver-silicon (Ag–Si)21 and silica-polystyrene (SiO2–PS)32

dimeric nanoparticles. Therefore, we have a Janus dumb-bell with one anomalous monomer and another regular, ornon-anomalous, monomer. Inspired in this specific shapeand composition, we have proposed a model to study thisclass of nanoparticles9,10 based on an effective two lengthscales potential33 to model the anomalous monomer, whilethe regular monomer is modeled with a standard Lennard-Jones (LJ) potential. We have shown that despite the presenceof the non-anomalous monomer, the diffusion anomaly waspreserved.

Usually, colloidal solutions are dissolved in a solvent—aswater. In these cases, Langevin dynamics has been employedto mimic the solvent effects in the colloids.9,10,34 On theother hand, molecular systems, without solvent effects, arerelevant as well. For instance, Munao and Urbic recently pro-posed a model for alcohols combining anomalous and regularmonomers35 and Urbic proposed a model for methanol.36 Aswell, anomalies in dimeric anomalous systems have been theobject of computational studies.37–39

0021-9606/2016/145(24)/244906/6/$30.00 145, 244906-1 Published by AIP Publishing.

244906-2 B. Krott, Gavazzoni, and Bordin J. Chem. Phys. 145, 244906 (2016)

Therefore, a natural question that rises is how the Janusdimer will behave when the Brownian dynamics effects areremoved. In this way, we perform intensive Molecular Dynam-ics (MD) simulations using the Berendsen thermostat. Com-parisons are made with the system behavior in our previouswork,34 where we have used the Langevin thermostat. Thedimers are confined between two parallel walls, in order tosimulate a thin film. We show how the thermostat affects theaggregation, the dynamic, and the thermodynamic propertiesof this Janus nanoparticle. Specially, we show how the absenceof solvent effects leads the system to have not only diffusionanomaly but also a superdiffusive regime related to a highlyordered structure.

The paper is organized as follows: first we introduce themodel and describe the methods and simulation details; nextthe results and discussion are given; and then we present ourconclusions.

II. THE MODEL AND THE SIMULATION DETAILS

The system consists in Janus dumbbells confined betweentwo flat and parallel plates separated by a fixed distance inz-direction. The Janus particles are formed by N = 288 dimers,totalizing N = 576 monomers, linked rigidly at a distanceλ = 0.8σ. The monomers can be of type A and type B. Par-ticles of type A interact through a two length scales shoulderpotential, defined as33,40

UAA(rij)

ε= 4

(σ

rij

)12

−

(σ

rij

)6+ u0 exp

−

1

c20

( rij − r0

σ

)2,

(1)

where rij = |~ri − ~rj | is the distance between two A particlesi and j. The first term is a standard 12-6 Lennard-Jones (LJ)potential24 and the second one is a Gaussian shoulder centeredat r0, with depth u0 and width c0. The parameters used areu0 = 5.0, c0 = 1.0, and r0/σ = 0.7. In Figure 1, this potential isrepresented by potential AA. Monomeric and dimeric bulksystems modeled by this potential present thermodynamic,dynamic, and structural anomalies like observed in water,silica, and other anomalous fluids.33,39–42 Under confinement,

FIG. 1. Interaction potentials between particles of type A (potential AA indotted blue line), between particles of type B (potential BB in dot-dashed redline) and between particles of type A and B (potential AB in solid green line).Potential AB in the z-direction gives the interaction between dimers and walls.The inset shows a picture of a Janus dumbbells formed by particles A and B,with monomers separated by a distance λ.

the monomeric system also presents water-like anomalies andinteresting structural phase transitions.43–52

Particles of type B interact through a standard 12-6 LJpotential, whose equation is the same as the first term ofEq. (1). This potential is represented in Figure 1 by potentialBB. We use a cutoff radius of rc = 2.5. Finally, the interac-tion between particles of type A and type B is given by aWeeks-Chandler-Andersen (WCA) potential, defined as24

UCSLJ(rij) =

{ULJ(rij) − ULJ(rc), rij ≤ rc,0, rij > rc.

(2)

The WCA potential considers just the repulsive part of thestandard 12-6 LJ potential, as shown in Figure 1 by potentialAB. Dimers and walls also interact by a WCA potential butprojected in the z-direction,

Uwall(zij) =

{ULJ(zij) − ULJ(zc), zij ≤ zc,0, zij > zc,

(3)

where zc = rc = 21/6σ.The walls are fixed in the z-direction separated by a dis-

tance of Lz = 4σ. We choose this separation to observe theeffects of strong confinement, like in quasi-2D thin films.Standard periodic boundary conditions are applied in x andy directions.

The simulations are done in NVT-ensemble using a homemade program. The temperature was fixed with the Berendsenthermostat and the equation motions were integrated by veloc-ity Verlet algorithm with a time step δt = 0.01 in reduced unit.The number density is calculated as ρ = N/V , where N is thenumber of monomers particles and V = L2Lz is the volume ofthe simulation box. We simulate systems varying the values ofL from 19.0σ to 60.0σ to obtain different densities. We use theSHAKE algorithm53 to link rigidly each dimer at a distance ofλ = 0.8σ.

We performed 5× 105 steps to equilibrate the system fol-lowed by 5×106 steps run for the results production stage. Theequilibrium state was checked by the analysis of potential andkinetic energies as well as the snapshots of distinct simulationtimes. Simulations with up to N = 5000 particles were carriedout, and essentially the same results were obtained.

The dynamic of the system was analyzed by the lat-eral mean square displacement and the velocity autocorrela-tion function vacf . The lateral mean square displacement wascalculated by

〈[~r‖cm(t) −~r‖cm(t0)]2〉 = 〈∆~r‖cm(t)2〉 , (4)

where ~r‖cm(t0) = (xcm(t0)2 + ycm(t0)2) and ~r‖cm(t) = (xcm(t)2

+ ycm(t)2) denote the parallel coordinate of the nanoparticlecenter of mass (cm) at a time t0 and at a later time t, respec-tively. The Fick diffusion has a diffusion coefficient that canbe calculated by Einstein relation,

D‖ = limt→∞

〈∆~r‖cm(t)2〉

4t. (5)

The velocity autocorrelation function vacf was evaluatedtaking the average for all nanoparticles center of mass andinitial times,

vacf = 〈~vi(t0) · ~vi(t + t0)〉, (6)

244906-3 B. Krott, Gavazzoni, and Bordin J. Chem. Phys. 145, 244906 (2016)

where~vi(t0) is the initial velocity for the ith nanoparticle centerof mass and ~vi(t + t0) is the velocity at an advanced time t + t0

for the same particle center of mass.The system structure was analyzed with the lateral radial

distribution function g||(r ||), evaluated in the xy plane in allphases and defined as54

g | |(r) ≡1

ρ2V

∑i,j

δ(r − rij)

[θ

(|zi − zj | +

δz2

)

− θ

(|zi − zj | −

δz2

)], (7)

where δ(x) is the Dirac δ function and the Heaviside func-tion θ(x) restricts the sum of particle pair in the same slab ofthickness δz = σ.

Directly related to g||(r ||), we also use the translationalorder parameter τ, defined as55

τ ≡

∫ ξc

0|g‖(ξ) − 1| dξ, (8)

where ξ = r‖(ρl)1/2

is the interparticle distance in the direc-tion parallel to the plates scaled by the density of the layer,ρl = N l/L2. N l is the average of particles for each layer. We

use ξc = (ρl)1/2

L/2 as cutoff distance.The snapshots of the systems also were used to

analyze the self-assembled structures at different densi-ties and temperatures. The pressure-temperature phase dia-gram was constructed using the parallel pressure (P‖), cal-culated by Virial expression in x and y directions. Allthe system properties were evaluated for all simulatedpoints.

All physical quantities are computed in the standard LJunits.24 Distance, density of particles, time, parallel pressure,

and temperature are given, respectively, by

r∗ ≡rσ

, ρ∗ ≡ ρσ3, and t∗ ≡ t(ε

mσ2

)1/2,

P∗‖≡

pσ3

ε, and T ∗ ≡

kBTε

,

(9)

where σ, ε , and m are the distance, energy, and mass parame-ters, respectively. Considering that we will omit the symbol ∗

to simplify the discussion.

III. RESULTS AND DISCUSSION

Controlling the self-assembly of chemical building blocksin distinct structures is the goal in the studies of con-fined molecules and nanoparticles with this characteristic,56–58

as Janus nanoparticles. Therefore, we first report the self-assembled structures observed in our simulations. The aggre-gates were classified using snapshots, the lateral mean squaredisplacement, the vacf and the g||(r ||).

The small separation Lz = 4.0 between the plates used inour simulations induces the system to form two layers, onenear each plate, regardless of the system density, as we shownin Figure 2(h). To map the particle arrangement, we analyze thefrontal vision of the system, summarized in Figure 2. At hightemperatures, the system is in a fluid phase, without a definedarrangement. For instance, we can see the snapshot at densityρ = 0.25 and temperature T = 0.400, shown in Figure 2(g).At lower temperatures, the nanoparticles aggregate. The shapeand structure of these aggregates depend on the system density.Let us take the isotherm T = 0.100. At the smallest densities,ρ < 0.16, the system remains in a fluid phase. The aggregationstarts at ρ = 0.16, with the nanoparticles assembled in trihedralaggregate (TA3), tetrahedrical aggregate (TA4), or hexagonal

FIG. 2. Frontal vision snapshots of confined Janus parti-cles at λ = 0.8. We show (a) structured elongated micelles(SEM) at ρ = 0.48 and T = 0.200, (b) elongated micelles I(EMI) at ρ = 0.50 and T = 0.100, (c) elongated micelles II(EMII) at ρ = 0.40 and T = 0.100, (d) spherical micelles(SM) at ρ = 0.28 and T = 0.100, (e) hexagonal aggregates(HA) at ρ = 0.25 and T = 0.100, (f) coexistence betweenhexagonal and trihedral aggregates (TA) at ρ = 0.15 andT = 0.100, and (g) fluid phase at ρ = 0.25 and T = 0.400.(h) Lateral view of the simulation box showing the bilayerstructure for smaller (bottom) and higher (up) densities.For simplicity, the plates are not shown.

244906-4 B. Krott, Gavazzoni, and Bordin J. Chem. Phys. 145, 244906 (2016)

aggregate (HA). As the name indicates, the first one is com-posed of three dimers, the second one by four, and the thirdby six dimers. The snapshot in Figure 2(f) shows the coexis-tence of these aggregates. Increasing the density, the TA3/4binds and more HA aggregates are observed, as shown inFigure 2(e) for ρ = 0.25.

Spherical micelles (SM) were also obtained, as we show inFigure 2(d) for ρ= 0.28, as well elongated micelles II (EMII),shown in Figure 2(c). HA, SM, and EMII structures wereobserved in the bulk system.10 The confinement leaded tothe assembly in TA3/4 at lower densities and longer elon-gated micelles I (EMI) at higher densities. The EMI canshow no preferential orientation, as the one shown in Fig-ure 2(b) for ρ = 0.50 and T = 0.100, or have a well definedorientation, as in Figure 2(a) for ρ = 0.48 and T = 0.200.We will refer to this last case of oriented elongated micellesas structured elongated micelles (SEM). The main differ-ence in the aggregation compared to the Brownian system34

is in the SEM phase. Here, this lamellar phase is straight,while in our previous work we have observed a rippledlamellae structure. Nevertheless, this small structural dif-ference leads to a new dynamical feature, as we discussbelow.

The structural and dynamical behavior of two lengthscale fluids is strongly connected.33,40,50 Therefore, in order tounderstand the difference between the EMI and SEM aggre-gates we investigated the dynamical characteristics of thesemicelles. For instance, we take the isochore ρ = 0.53, wherethe Janus dimers are assembled in both EMI and SEM. The lat-eral mean square displacement for temperature T = 0.275, reddashed line in Figure 3(a), shows an initial ballistic behaviorand a Fick regime as t → ∞. On the other hand, for T = 0.175,black dashed line in Figure 3(a), the initial ballistic evolves toa superdiffusive regime, with α ≈ 1.75. This superdiffusive

regime was observed in all SEM structures, with α rangingfrom ∼1.30 to ∼1.80. For simplicity, we will not show all lat-eral mean square displacement curves. Basically, in the fluidregions and for all aggregates, except the SEM, the nanopar-ticle collisions lead the system to the Fick regime. However,in the SEM lamellae phase, the liquid-crystal structure pre-vents the collisions. As consequence, the dimers move freelyin the line defined by the structure, leading to the superdif-fusive regime. For the Brownian system,34 since the lamellaephase is not straight, but rippled, the superdiffusive regimewas not observed. This shows how the white noise and dragforce from the Brownian Dynamics effects on the dynamicwill reflect in the structure. Particularly, the SEM region cor-responds to a region where the translational order parameter τhas a maximum. This result, shown in Figure 3(b), highlightsthe relation between structure and dynamics. Therefore, theSEM micelles are highly diffused and highly structured aggre-gates. This relation between structure and dynamics is wellknown in the literature of anomalous fluids.33,40,50 However,it was never related to anomalous diffusion, only to diffusionanomaly.

The velocity autocorrelation function vacf is a powerfultool to understand the dynamics of the systems. In Figure 3(c)we show vacf as a function of time for ρ = 0.53 and tempera-tures ranging from T = 0.175 to T = 0.275. The superdiffusiveregime and SEM micelles were observed for T = 0.175, 0.200,and 0.225. As we can see in Figure 3(c), at these tempera-tures the curves cross the zero axis at shorter times than inthe Fick regime with EMI micelles, T = 0.250 and 0.275.This shows that in the superdiffusive regime, the nanoparti-cles are strongly caged by the neighbor dimers. Thereat, weknow that the system has a superdiffusion regime related to acollective behavior and assembly in a specific well structuredmicelle.

FIG. 3. (a) Lateral mean square dis-placement as function of time fornanoparticles center of mass in the Fick(red dashed line) and superdiffusive(black dashed line) regime. Straight linesin green and magenta are guide to theeyes to show the curve slope. (b) Trans-lational order parameter τ as function oftemperature for distinct isochores show-ing the relation between the maximumin τ and the superdiffusivity. (c) Veloc-ity autocorrelation function for ρ = 0.53and distinct velocities. (d) Lateral radialdistribution function showing the behav-ior of the first two peaks, related to thetwo length scales.

244906-5 B. Krott, Gavazzoni, and Bordin J. Chem. Phys. 145, 244906 (2016)

FIG. 4. Results for Janus confined par-ticles with λ= 0.8. In (a) we showthe parallel pressure versus temperaturephase diagram for isochores between0.05 and 0.50 in solid gray lines. In (b)we show the lateral diffusion coefficientas a function of time for fixed tempera-tures of T = 0.150, 0.200, 0.250, 0.300,and 0.350.

It is well reported in the literature that the competitionbetween the two scales in Eq. (1) is the main ingredient to afluid present water-like anomalies.59 To see the influence ofthis competition, we analyzed the g||(r ||) for the A monomerswhen the system enters and leaves the SEM phase. As weshow in Figure 3(d), when we walk through the isochoreρ = 0.53, from T = 0.150—before the superdiffusion region—to T = 0.225—the limit of the superdiffusion region—the firstpeak in the g||(r ||) decays, while the second peak rises. This isthe competition between the scales, where the particles movefrom one of the preferential distances to the other. As weheat the system, both peaks decay, as when we walk fromT = 0.225 to T = 0.275—outside the superdiffusive regime.Therefore, the competition between the two length scales leadsthe nanoparticles from a non-oriented Fick diffusion elon-gated micellae phase to an oriented superdiffusive elongatedmicellae phase.

With this informations, we can draw the P‖ −T phase dia-gram for this system, shown in Figure 4(a). We should addressthat the phase diagram is qualitative, based on direct observa-tion of the various assembled structures, the vacf , the g||(r ||),and lateral mean square displacement. The regions where thedistinct self-assembled structures were observed are indicatedin the phase-diagram. In addition to the anomalous diffusion,the system also shows diffusion anomaly. This anomaly ischaracterized by the maximum and minimum in the curveof the lateral diffusion coefficient D|| as a function of den-sity at constant temperature. Figure 4(b) shows these curves,with the diffusion extrema indicated. These extrema are alsoshown in the phase diagram. Notice that the anomaly regionoccurs in the fluid and in the SM phase, indicating that theanomaly can be observed in spherical micelles. In this way,it is possible to construct spherical self-assembled structurethat will diffuse faster when compressed. As usual, the dif-fusion anomaly is explained using the competition betweenthe two scales. The graphic showing this was omitted for sim-plicity, since this result is well known and discussed in theliterature.9,10,33

Another interesting difference between the Brownian andthe molecular system P‖ − T phase diagram is the absenceof a melting induced by the density increase in the SEMphase.34 This suggests that the melting scenario for theseJanus nanoparticles is strongly affected by the solvent. Aswell, the fluid phase structure is also affected. This is evi-dent once for the molecular system we have not observedthe density anomaly, only the diffusion anomaly. For the

Brownian system, the density anomalous region ended in themelting induced by density increase region. Therefore, thiscomparison between the Brownian and molecular system hasshown that not only the dynamical behavior is distinct, whatwas expected due the thermostats characteristics, but also thestructural, assembly, and thermodynamic properties of thesenanoparticles are strongly affected.

IV. CONCLUSION

We reported the study of Janus nanoparticles confined in athin film. Here, the effects of Brownian motion were removed,and we studied the molecular system without solvent. Thissystem has special interest in the design of new material usingthe confinement to control the self-assembled structures. Wehave found a rich variety of aggregates and micelles, includingstructures not observed in the bulk system or in the Browniansystem. More than that, our results show that the more struc-tured micelle has an anomalous diffusion, with a superdiffusiveregime related to a maximum in the translational order param-eter. We have shown that this anomalous diffusion is relatedto the competition between the two length scales. As well, thesystem has diffusion anomaly, where the diffusion constantincreases with the density increases. These results show thatmaterials which can be modeled by two length scale potentialshave an interesting and peculiar behavior. New studies on thissystem are in progress, as anisotropy effects.

ACKNOWLEDGMENTS

We thank the Brazilian agency CNPq for the financialsupport.

1K.-H. Roh, D. C. Martin, and J. Lahann, Nat. Mater. 4, 759 (2005).2S. H. L. Klapp, Curr. Opin. Colloid Interface Sci. 21, 76–85 (2016).3Y. Liu, W. Li, T. Perez, J. D. Gunton, and G. Brett, Langmuir 28, 3–9 (2012).4S. Whitelam and S. A. F. Bon, J. Chem. Phys. 132, 074901 (2010).5G. Munao, D. Costa, A. Giacometti, C. Caccamo, and F. Sciortino, Phys.Chem. Chem. Phys. 15, 20590 (2013).

6G. Munao, P. O’Toole, T. S. Hudson, and F. Sciortino, Soft Matter 10, 5269(2014).

7G. Munao, P. O’Toole, T. S. Hudson, D. Costa, C. Caccamo, F. Sciortino,and A. Giacometti, J. Phys.: Condens. Matter 27, 234101 (2015).

8G. Avvisati, T. Visers, and M. Dijkstra, J. Chem. Phys. 142, 084905 (2015).9J. R. Bordin, Physica A 459, 1–8 (2016).

10J. R. Bordin, L. B. Krott, and M. C. Barbosa, Langmuir 31, 8577–8582(2015).

11C. Casagrande, P. Fabre, E. Raphael, and M. Veyssie, Europhys. Lett. 9,251–255 (1989).

244906-6 B. Krott, Gavazzoni, and Bordin J. Chem. Phys. 145, 244906 (2016)

12D. M. Talapin, J.-S. Lee, M. V. Kovalenko, and E. V. Shevchenko, Chem.Rev. 110, 389–458 (2010).

13A. Elsukova, Z.-A. Li, C. Moller, M. Spasova, M. Acet, M. Farle,M. Kawasaki, P. Ercius, and T. Duden, Phys. Status Solidi A 208, 2437–2442(2011).

14F. Tu, B. J. Park, and D. Lee, Langmuir 29, 12679–12687 (2013).15A. Walther and A. H. E. Muller, Soft Matter 4, 663–668 (2008).16A. Walther and A. H. E. Muller, Chem. Rev. 113, 5194–5261 (2013).17J. Zhang, E. Luijten, and S. Granick, Annu. Rev. Phys. Chem. 66, 581–600

(2015).18T. Bickel, G. Zecua, and A. Wurger, Phys. Rev. E 89, 050303 (2014).19X. Ao, P. K. Ghosh, Y. Li, G. Schmid, P. Hanggi, and F. Marchesoni,

Europhys. Lett. 109, 10003 (2015).20Y. Yin, Y. Lu, and X. Xia, J. Am. Chem. Soc. 132, 771–772 (2001).21V. Singh, C. Cassidy, P. Grammatikopoulos, F. Djurabekova, K. Nordlund,

and M. Sowwan, J. Phys. Chem. C 118, 13869–13875 (2014).22Y. Lu, Y. Yin, Z.-Y. Li, and Y. Xia, Nano Lett. 2, 785–788 (2002).23K. Yoon, D. Lee, J. W. Kim, and D. A. Weitz, Chem. Commun. 48,

9056–9058 (2012).24P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford

University Press, Oxford, 1987).25D. S. Banks and C. Fradin, Biophys. J. 89, 2960–2971 (2005).26P. Illien, O. Benichou, G. Oshanin, and R. Voituriez, Phys. Rev. Lett. 113,

030603 (2014).27B. ten Hagen, S. van Teeffelen, and H. Lowen, J. Phys.: Condens. Matter

23, 194119 (2011).28C. Xue, X. Zheng, K. Chen, Y. Tian, and G. Hu, J. Phys. Chem. Lett. 7,

514–519 (2016).29P. A. Netz, F. W. Starr, M. C. Barbosa, and H. E. Stanley, Physica A 314,

470 (2002).30T. Morishita, Phys. Rev. E 72, 021201 (2005).31S. Sastry and C. A. Angell, Nat. Mater. 2, 739–743 (2003).32B. Liu, C. Zhang, J. Liu, X. Qu, and Z. Yang, Chem. Commun. 26,

3871–3873 (2009).33A. B. de Oliveira, P. A. Netz, T. Colla, and M. C. Barbosa, J. Chem. Phys.

124, 084505 (2006).34J. R. Bordin and L. B. Krott, Phys. Chem. Chem. Phys. 18, 28740–28746

(2016).35G. Munao and T. Urbic, J. Chem. Phys. 142, 214508 (2015).

36M. Hus, G. Zakelj, and T. Urbic, Acta Chim. Slov. 62, 524–530 (2015).37G. Munao and F. Saija, Phys. Chem. Chem. Phys. 18, 9484–9489

(2016).38C. Gavazzoni, G. K. Gonzatti, L. F. Pereira, L. H. C. Ramos, P. A. Netz, and

M. C. Barbosa, J. Chem. Phys. 140, 154502 (2014).39A. B. de Oliveira, E. Nevez, C. Gavazzoni, J. Z. Paukowski, P. A. Netz, and

M. C. Barbosa, J. Chem. Phys. 132, 164505 (2010).40A. B. de Oliveira, P. A. Netz, T. Colla, and M. C. Barbosa, J. Chem. Phys.

125, 124503 (2006).41G. S. Kell, J. Chem. Eng. Data 12, 66 (1967).42C. A. Angell, E. D. Finch, and P. Bach, J. Chem. Phys. 65, 3063–3066

(1976).43L. B. Krott and M. C. Barbosa, J. Chem. Phys. 138, 084505 (2013).44L. B. Krott and M. C. Barbosa, Phys. Rev. E 89, 012110 (2014).45J. R. Bordin, L. B. Krott, and M. C. Barbosa, J. Chem. Phys. 141, 144502

(2014).46L. Krott and J. R. Bordin, J. Chem. Phys. 139, 154502 (2013).47J. R. Bordin, L. Krott, and M. C. Barbosa, J. Phys. Chem. C 118, 9497–9506

(2014).48L. B. Krott, J. R. Bordin, and M. C. Barbosa, J. Phys. Chem. B 119, 291–300

(2015).49J. R. Bordin, A. B. de Oliveira, A. Diehl, and M. C. Barbosa, J. Chem. Phys.

137, 084504 (2012).50J. R. Bordin, A. Diehl, and M. C. Barbosa, J. Phys. Chem. B 117, 7047–7056

(2013).51J. R. Bordin, J. S. Soares, A. Diehl, and M. C. Barbosa, J. Chem. Phys. 140,

194504 (2014).52L. B. Krott, J. R. Bordin, N. Barraz, Jr., and M. C. Barbosa, J. Chem. Phys.

142, 134502 (2015).53J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comput. Phys. 23,

327 (1977).54P. Kumar, S. V. Buldyrev, F. W. Starr, N. Giovambattista, and H. E. Stanley,

Phys. Rev. E 72, 051503 (2005).55J. R. Errington and P. D. Debenedetti, Nature 409, 318 (2001).56M. P. Kim and G.-R. Yi, Front. Mater. 2, 45 (2015).57G. Rosenthal and S. H. L. Klapp, Int. J. Mol. Sci. 13, 9431 (2005).58G. Rosenthal and S. H. L. Klapp, J. Chem. Phys. 134, 154707 (2011).59A. B. de Oliveira, P. A. Netz, and M. C. Barbosa, Physica A 386, 744–747

(2007).