Core-softened water-alcohol mixtures: the solute-size effects
Murilo S. Marques, Vinicius F. Hernandes, Jose Rafael Bordin
CCore-softened water-alcohol mixtures: the solute-size effects
Murilo Sodr´e Marques ∗ Centro das Ciˆencias Exatas e das Tecnologias, Universidade Federal do Oeste da BahiaRua Bertioga, 892, Morada Nobre, CEP 47810-059, Barreiras-BA, Brazil andInstituto de F´ısica, Universidade Federal do Rio Grande do Sul,Av. Bento Gon¸calves 9500, Caixa Postal 15051, CEP 91501-970, Porto Alegre - RS, Brazil
Vin´ıcius Fonseca Hernandes and Jos´e Rafael Bordin
Departamento de F´ısica, Instituto de F´ısica e Matem´atica,Universidade Federal de Pelotas. Caixa Postal 354, 96001-970, Pelotas-RS, Brazil. (Dated: February 19, 2021)Water is the most anomalous material on Earth, with a long list of thermodynamic, dynamic andstructural behavior that deviate from the expected. Recent studies indicate that the anomalies canbe related to a competition between two liquids, which means that water has a potential liquid-liquid phase transition (LLPT) that ends in a liquid-liquid critical point (LLCP). In a recent work [J.Mol. Liq. 320 (2020) 114420], using molecular dynamics simulations and a core-softened potentialapproach, we have shown that adding a simple solute as methanol can ”kill” the anomalous behavioras the LLCP is suppressed by the spontaneous crystallization in a hexagonal closed packing (HCP)crystal near the LLPT. Now, we extend this work to see how alcohols with longer chains will affectthe complex behavior of water mixtures in the supercooled regime. Besides CS methanol, ethanoland 1-propanol were added to CS water. We observed that the anomaly vanishes as the alcoholchain increases. Curiously, the LLCP did not vanishes together with the anomalous behavior. Thereason is that the mechanism for ethanol and 1-propanol is distinct to the one observed previouslyfor methanol: here, the longer chains affect the competition between the scales in the CS potential.Also, the chain size affects the solid phases, favoring the HCP solid and the amorphous solid phaseover the body-centered cubic (BCC) crystal. This findings helps to elucidate the behavior of watersolutions in the supercooled regime, and indicates that the LLCP can be observed in systems withoutanomalous behavior.
I. INTRODUCTION
Life, as we known, started and evolved in water solu-tions. Then, we can say that elucidate the demeanor ofcomplex molecules in water, at both micro- and macro-levels, is of paramount importance in modern science[1, 2]. Although the behavior of complex biological pro-teins in water is a huge and complex problem, with manyhydrophobic and hydrophilic sites, we can draw someinformation from simpler systems. In this way, a spe-cial class of aqueous solutions are those containing short-chain alcohols (i.e., alcohols with a small number of car-bon atoms in the chain, like methanol, ethanol, or 1-propanol), most of which are miscible in water over thefull range of concentrations [3, 4]. They have attracteda great attention of scientific community for decades fora number of reasons: (i) they are ubiquitous in the med-ical [5], food industries [6], transportation [7] and per-sonal care [8], among others, and thus have attractedmuch theoretical and experimental attention; (ii) com-paratively to water, the molecular structure of alcoholsshows the presence of an organic radical in place of oneof the hydrogen atoms; as a consequence, alcohols donot form a completely developed hydrogen-bonded net-work, as in the case of water; (iii) On the other hand, ∗ [email protected] the presence of both the hydroxyl group and the organicradical, usually non-polar (amphiphilic character), allowsfor the interaction with a huge number of organic and in-organic compounds, making alcohols good solvents, sincethe solute-solvent interaction can have the same order ofmagnitude as the solute-solute and solvent-solvent inter-actions [9]. In addition, (iv) although the interactionswith molecules of a dual nature, such as alcohols, involvenot only the hydrophobic hydration of the non-polar moi-ety of the molecule but also the hydrophilic interactionsbetween the polar groups and the water molecules, stillthey constitute a model for the investigation of the hy-drophobic effect [10, 11].With water as a solvent, both the complexity of analy-sis and the richness of phenomena observed for such solu-tions are highlighted. Water is the most anomalous mate-rial, with more than 70 known anomalies [12]. Probably,the most well known is the density anomaly. While mostof the materials increases the density upon cooling, liq-uid water density decreases when cooled from 4 o C to 0 o Cat atmospheric pressure [13]. Recent findings indicated arelation between the anomalies and another unique fea-ture of water: the liquid polymorphism and the phasetransition between two distinct liquids [14]. In additionto the usual liquid-gas critical point (whose near-criticalproperties are so drastically different from those of liquidwater [15]), since the 1990s [16] the existence of a secondcritical point - the liquid-liquid critical point (LLCP) hasbeen hypothesized by simulations and subject of exten- a r X i v : . [ c ond - m a t . s o f t ] F e b sive debate [17–21]. It has not yet been reported from ex-periments once is located in the so-called no-man’s land:due the spontaneous crystallization it is (almost) impos-sible to reach this region by experiments - however, somerecent experiments show strong evidence of the existenceof the LLCP [22–24]. The LLCP locates at the end of afirst order liquid-liquid phase transition (LLPT) line be-tween low-density liquid (LDL) and high-density liquid(HDL) at low temperatures [14, 16, 25–32]. Unlike theliquid–gas phase transition (LGPT), which always hasa positive slope of the first-order phase transition linebecause ∆ S >
V > CH − CH − OH ) and 1-propanol( CH − CH − CH − OH ), by modeling such alcoholsas linear chains constituted by three (trimers) and four(tetramers) partially fused spheres, respectively, and theprimary objective is to complement our previous studyby exploring the influence of the size of the solute on thethermodynamic properties of mixtures of core-softenedwater and alcohols: methanol, ethanol and 1-propanol.The remaining of the paper is organized as follows.In Section II we present our interaction models for wa-ter and alcohols molecules, and summarize the details ofthe simulations. Next, in section III our most significantresults for our CS mixture model are introduced. In par- ticular, we will focus on the concentration dependence ofthe LLCP and influence on the excess entropy of mix-ture in comparison with pure CS water. The paper isclosed with a brief summary of our main conclusions andperspectives. II. MODEL AND SIMULATION DETAILS
Our water-like solvent here will be modeled by a 1-sitecore-softened fluid in which particles interact with thepotential model proposed by Franzese [57]. Water-likeparticles W CS are represented by spheres with a hard-core of diameter a and a soft-shell with radius 2 a , whoseinteraction potential is given by U CS ( r ) = U R exp [∆( r − R R )] − U A exp (cid:18) − ( r − R A ) δ A (cid:19) + U A (cid:16) ar (cid:17) . (1)With the parameters U R /U A = 2, R R /a = 1 . R A /a =2, ( δ A /a ) = 0 .
1, and ∆ = 15 this potential displaysan attractive well for r ∼ a and a repulsive shoulder at r ∼ a , as can be seen in figure 1(a) (red curve). The com-petition between these two length scales leads to water-like anomalies, as the density, diffusion anomalies, andto the existence of a liquid liquid critical point [57–60].As a direct extension and building on our previouswork on mixtures of water and methanol, where a sin-gle methanol molecule was constituted by two tangentspheres, in this work we have followed the extension madeby Urbic et al towards ethanol ( CH − CH − OH ) and1-propanol ( CH − CH − CH − OH ) being modeledas linear trimers and tetramers, respectively (Fig. 1).Trimers are constructed as linear rigid molecules consist-ing of three partially fused spheres, where two adjacentspheres are placed at fixed distance L ij = 0 . a , with a as the unit length. Analogously, tetramers are modeledas linear rigid molecules consisting of four partially fusedspheres, where two adjacent spheres are placed at fixeddistance L ij = 0 . a . In all models, hydroxyl groups in-teract through a soft-core potential (eq 1), while CH and CH groups are nonpolar and interact through LJ-like potential, U LJ = 43 2 / (cid:15) (cid:20)(cid:16) σr (cid:17) − (cid:16) σr (cid:17) (cid:21) , (2) OH − CH and OH – CH interactions are of LJ type aswell. LJ parameters are reported in Table I. As in lastwork, quantities are reported in reduced dimensionlessunits relative to the hydroxyl group diameter and thedepth of its attractive well.The simulations were performed in the N P T ensem-ble with a fixed number of molecules ( N tot = 1000). N alc = x alc N tot is the number of alcohol (methanol,ethanol or propanol) molecules and N w = N tot − N alc L ij (cid:15) n (cid:15) nn σ n σ nn Dimers 1.000 0 .
316 0 .
100 1 .
000 1 . .
400 0 .
400 1 .
115 1 . .
500 0 .
500 1 .
115 1 . n = 2), trimers( n = 2 , n = 2 , , OH group islabeled with 1. As for the bond length, j = i + 1 [56]. (a) (b)(c) . . . . . . . r ∗ = r/a − U ∗ = U / U A CSW potentialLJ potentialCrossLJ potential (d)
FIG. 1. In (a), (b) and (c), our model for methanol, ethanoland 1-propanol is outlined, while in (d) we see the interactionbetween water and hydroxyl’s is described by the CSW poten-tial, while other interactions behave like a 24-6 Lennard-Jonespotential. that of water molecules, where x alc is the alcohol molefraction, which has been varied from 0.0 (pure water),0.01, 0.05 and 0.1 (we’ve focused in low-concentrationrange). The temperature and pressure were controlledusing the optimized constant pressure stochastic dynam-ics proposed by Kolb and D¨unweg [61] as implemented inthe ESPResSo package [62, 63]. This barostat implemen-tation allows for the use of a large time step. This wasset to δt ∗ = 0 .
01, and the equations of motion were inte-grated using the velocity Verlet algorithm. The Langevinthermostat [64], that keeps the temperature fixed, has acoupling parameter γ = 1 .
0. The piston parameters forthe barostat are γ p = 0 . m p = 0 . × time steps in the N V T ensemble to thermalize the system. This was followed by1 × time steps in the N P T ensemble to equilibratethe system’s pressure and 1 × time steps further forthe production of the results, with averages and snap-shots being taken at every 1 × steps. To ensure thatthe system temperature and pressure were well controlledwe averaged this quantities during the simulations. Aswell, to monitor the equilibration the evolution of the po-tential energy along the simulation was followed. Here,the molecule density ρ is defined as N m / < V m > with < V m > being the mean volume at a given pressure and temperature. Isotherms were evaluated from T ∗ = 0 . T ∗ = 0 .
70 with changing intervals - a finer gridwas used in the vicinity of the critical points. In thesame sense, the pressure was varied from P = 0 .
005 upto P = 0 .
30 with distinct intervals.Also in a similar way to the previous work, we evalu-ated the temperature of maximum density (TMD) andthe locus of the maximum of response functions close tothe critical point at the fluid phase (the isothermal com-pressibility κ T , the isobaric expansion coefficient α P andthe specific heat at constant pressure C P ): κ T = 1 ρ (cid:18) ∂ρ∂P (cid:19) T , α P = − ρ (cid:18) ∂ρ∂T (cid:19) P , C P = 1 N tot (cid:18) ∂H∂T (cid:19) P , (3)where H = U + P V is the system enthalpy, with V themean volume obtained from the N P T simulations. Thequantities shown in the Electronic Supplementary Mate-rial (ESI) † were obtained by numerical differentiation. Asconsistency check, we have obtained the same maxima lo-cations when using statistical fluctuations: the compress-ibility is a measure of volume fluctuations, the isobaricheat capacity is proportional to the entropy fluctuationsexperienced by N molecules at fixed pressure, and thethermal expansion coefficient reflects the correlations be-tween entropy and volume fluctuations [64, 65].In order to describe the connection between structureand thermodynamics, we have analyzed the radial dis-tribution function (RDF) g ( r ∗ ), which was subsequentlyused to compute the excess entropy. s ex can be obtainedby counting all accessible configurations for a real fluidand comparing with the ideal gas entropy [66]. Conse-quently, the excess entropy is a negative quantity sincethe liquid is more ordered than the ideal gas. Note that s ex increases with temperature just like the full entropy S does; in fact s ex → s ex exists in terms of two-particle,three-particle contributions, etc., s ex = s + s + s + ... (4)The two-particle contribution is calculated from theradial distribution function g ( r ) as follows: s = − πρ (cid:90) ∞ [ g ( r ) lng ( r ) − g ( r ) + 1)] r dr, (5)since s is the dominant contribution to excess entropy[70, 71] and it is proved to be between 85% and 95% ofthe total excess entropy in Lennard-Jones systems [72].Also, the translational order parameter τ was evaluates.It is defined as [73] τ ≡ (cid:90) ξ c | g ( ξ ) − | dξ, (6)where ξ = rρ / is the interparticle distance r scaled withthe average separation between pairs of particles ρ / . ξ c is a cutoff distance, defined as ξ c = Lρ / /
2, where L is the simulation box size. For an ideal gas (completelyuncorrelated fluid), g ( ξ ) = 1 and τ vanishes. For crystalor fluids with long range correlations g ( ξ ) (cid:54) = 1 over longdistances, which leads to τ >
0. The excess entropy andthe translational order parameter τ are linked once bothare dependent on the deviation of g ( r ) from unity.Another structural quantity evaluated was the orien-tational order parameter (OOP), that gives insight onthe local order [73–76]. The OOP for a specific particle i with N b neighbors, is given by q l ( i ) = (cid:118)(cid:117)(cid:117)(cid:116) π l + 1 l (cid:88) m = − l | q lm | , (7)with q lm ( i ) = (cid:118)(cid:117)(cid:117)(cid:116) N b N b (cid:88) j =1 Y lm ( θ ( (cid:126)r ij ) , φ ( (cid:126)r ij )) . (8)where Y lm are the spherical harmonics of order l and (cid:126)r ij is the vector from particle i to its neighbour j . The OOPfor a whole system is obtained taking the average overthe parameter value for each particle i , q l = (cid:104) q l ( i ) (cid:105) i . Inthis work we evaluated the OOP for l = 6, using thefreud python library [77], and the number of neighborsfor each particle was found computing Voronoi diagramsusing voro++ [78].The dynamic behaviour was analyzed by the meansquare displacement (MSD), given by (cid:104) [ (cid:126)r ( t ) − (cid:126)r ( t )] (cid:105) = (cid:104) ∆ (cid:126)r ( t ) (cid:105) , (9)where (cid:126)r ( t ) = and (cid:126)r ( t ) denote the particle position at atime t and at a later time t , respectively. The MSD isthen related to the diffusion coefficient D by the Einsteinrelation, D = lim t →∞ (cid:104) ∆ (cid:126)r ( t ) (cid:105) t . (10)For alcohol molecules we have considered the center ofmass displacement. The onset of crystallization wasmonitored analyzing the local structural environment ofparticles by means of the Polyhedral Template Match-ing (PTM) method implemented in the Ovito soft-ware [79, 80]. Ovito was also employed to visualize thephases and take the system snapshots. III. RESULTS AND DISCUSSIONA. Pure CS Water phase diagram
Water is fascinating and unique. From its numerousanomalous behaviors the most well known is, probably, . . . . . . T ∗ . . . . P ∗ I L D L II III H D L Cp maxCp desc.α P maxα P desc.TMD LLCL k T desc.WL (a) T *-1 D * τ P = 0.13P = 0.15 (b) s P = 0.05P = 0.11P = 0.14P = 0.20P = 0.28 T * -4 -3 -2 -1 D * (c) FIG. 2. (a)
P T phase diagrams for pure CS water showing thesolid phases I (BCC solid), II (HCP solid) and III (amorphoussolid) and the low and high density liquid phases. The pointsin the phase separations indicate distinct discontinuities ormaxima in the evaluated response functions. The Widom Linecorresponds to maxima in κ T . The solid-liquid coexistencelines were draw based in the discontinuities in the pair excessentropy, the structure factor (not shown here for simplicity)and in the diffusion constant, as indicated in the figure (b).Also, the pair excess entropy (not shown here for simplicity),the structure factor and D ∗ have discontinuities in the LDL-HDL transition, as we show in the figure (c) for the subcriticalisobar P ∗ = 0 .
13, and a fragile to strong transition for thesupercritical isobar P = .
15 as it crosses the Widom Line. the density anomaly. It be characterized by the Tem-perature of Maximum Density (TMD) line, that corre-sponds to the maxima in the ρ × T isobar. Recent find-ings indicates that the water anomalies are related tothe Liquid-Liquid Critical Point (LLCP) [16, 81]. Al-though hypothetical and not observed (yet) in experi-ments, there is strong and many evidences that the waterliquid polymorphism in the supercooled regime ends inthe LLCP [14, 82]. We can estimate the critical pointlocation using the isothermal density derivatives of thepressure [83] (cid:18) ∂P∂ρ (cid:19) T = (cid:18) ∂ P∂ρ (cid:19) T = 0 . (11)Coming from the supercritical region, the LLCP laysat the end of the Widom Line (WL) - a line in the P × T phase diagram that can be obtained by the maxima inthe response function κ T and corresponds to the sepa-ration between LDL-like and HDL-like behavior in thesupercritical regime. In the figure 2 (a) we show the CSwater phase diagram obtained from our simulations. TheWL, indicated by the dotted purple line and the purplesquares, ends at the LLCP. Below the LLCP we have thetransition between the liquid phases, indicated by the dis-continuity in the thermodynamic property κ T – shown inthe ESI † for all isotherms – and in the structural and dy-namic properties. For instance, the upper panel in thefigure 2(b) shows the structure factor τ for the subcriti-cal pressure P ∗ = 0 .
13 and for the supercritical pressure P ∗ = 0 .
15 as function of the inverse of temperature. As T decreases we can see a discontinuity in the subcriticalisobar, indicating an abrupt change in the fluid struc-ture. On the other hand, the supercritical isobar has amonotonic increase in τ as T decreases, indicating an in-crease in the particles order. Similarly, the dependenceof the diffusion coefficient D with T ∗− is discontinuousin the supercritical isobar. For the supercritical pressure P ∗ = 0 .
15 we see a change in the diffusion inclinationwith temperature when it crosses the Widom Line, in-dicating the HDL-dominated to LDL-dominated regime.These results are in agreement with our recent work ob-tained by the heating of the system [55] and previousworks employing this potential [57–60]. r* g ww ( r ) BCCHCPAmorphous (a)(b) (c) (d) (e)
FIG. 3. (a) CS water-water radial distribution function(RDF) along the isotherm T ∗ = 0 .
26. Black lines are thepressures in the BCC phase, red lines in the HCP phase andcyan in the amorphous phase. System snapshots in the (b)BCC phase, HCP phase with (c)straight or (d) rippled planesand in (e) the amorphous solid phase.
However, the solid phases weren’t explored for thissystem. In fact, the HCP phase was observed in ourwork [55] and in the study by Hus and Urbic using themethanol model [84, 85]. Here, exploring a larger re-gion in the phase diagram, we characterized three distinctsolid phases. The solid phase I corresponds to a body- centered cubic (BCC) crystal at lower pressures. Increas-ing P it changes to the solid phase II, with a hexagonalclosed packed (HCP) structure, and at even higher com-pression we observe the amorphous solid, named phaseIII. The transition between the solid phases, and fromLDL to HCP, are well defined by the discontinuous be-havior in κ T , shown in the SI. The transition from solidphase I to LDL and from solid phase II to HDL have dis-continuities in the response functions α p and C p , shownin the SI. Also, the structure (here characterized by thepair excess entropy) and the dynamic behavior (given bythe diffusion coefficient) are discontinuous for these solid-fluid transition. This can be observed in the figure 2(c).Here, the pressure P ∗ = 0 .
05 is a isobar that cross theBCC-LDL transition, P ∗ = 0 .
11, 0.14 and 0.20 the HCP-HDL transition and P ∗ = 0 .
28 the amorphous-HDL tran-sition. As we can see, the structure and dynamics changesmoothly for this last transition, as the magenta line for P ∗ = 0 .
28 indicates in the figure 2 (c). Also, the responsefunctions C p and α p are not discontinuous in this tran-sition, but have a maximum – indicating that this is asecond order, smooth transition. The distinct phases canalso be observed when we analyze the water-water radialdistribution function (RDF) g ww ( r ) along one isotherm.For instance, we show in the figure 3(a) the g ww ( r ) forpressures ranging from P ∗ = 0 .
01 to P ∗ = 0 .
30 alongthe isotherm T ∗ = 0 .
26. We can see clear changes in thestructure as P varies. At lower pressures the particlesare separated mainly at the second length scale, charac-terizing the BCC phase – a snapshot at P ∗ = 0 .
01 and T = 0 .
26 is shown in the figure 3(b). Increasing the pres-sure the system changes for the HCP phase, where theoccupation in the first length scale dominates the struc-ture. In fact, the HCP planes are separated by a distanceequal to the second length scale, while the distance be-tween particles in the same plane is the first length scale.It becomes clear when we use the Ovito [80] feature ”cre-ate bonds” if the distance is equal to the first scale. Whilefor the BCC snapshot we did not see any bond, for theHCP snapshot at P ∗ = 0 .
14 in the figure 3(c) we cansee the bonds between particles in the same plane. As P grows, the HCP planes get rippled, as we can see infigure 3(d) for P ∗ = 0 .
24 and in the behavior of the RDFred lines. Finally, it changes to an amorphous structureat high pressure, as we show for P ∗ = 0 .
30 in figure 3(e).Now, with the phase behavior of the CS water modeldepicted, we can see how the presence of short alcoholaffects the observed phases and the density anomaly.
B. Water-short alcohol mixtures
Small concentrations of short chain alcohols such asmethanol, ethanol and 1-propanol create a very interest-ing effect in the TMD line [86, 87]. They act as ”structuremaker”, promoting the low density ice-like water struc-ture and increasing the TMD. This is usually observed foralcohol concentrations χ alc smaller than 0.01 - and is not .
50 0 .
55 0 . . . . . . . . χ = . χ = . χ = . pure watermethanolethanolpropanol .
50 0 .
55 0 . χ = . χ = . pure watermethanolethanol .
50 0 .
55 0 . χ = . pure watermethanol T ∗ ρ ∗ T M D (a) r* g ww ( r ) (b) r* g ww ( r ) (c) r* g ww ( r ) (d) FIG. 4. (a) TMD behaviour of all CS alcohols used in thiswork: for χ alc = 0 .
05, 1-propanol didn’t show TMD and for χ alc = 0 .
10, only methanol shows TMD. (b) CSW-CSW ra-dial distribution function g ww ( r ) along the isobar P ∗ = 0 . χ alc = 0 .
10 case with temperatures rang-ing from T = 0 .
50 (black solid line) to T = 0 .
68 (magentasolid line). The intermediate temperatures are shown withred dashed lines. The arrows indicate the competition be-tween the scales as T increases. (c) is for the case with ethanolconcentration at χ alc = 0 .
05, were the competition betweenthe scales and the TMD are still observable, while for (d) χ alc = 0 .
10 both competition and TMD vanish. our goal here. We want to analyze the TMD vanishingand what happens in the phase diagram as it vanishes.This can be observed as x increases and methanol actsas ”structure breaker”. Using the CS model for water-methanol mixtures [55] we found that the TMD persistsup to high methanol concentrations, as χ <
70% – muchhigher than in experiments. This is a consequence ofthe model: the same potential is employed for water-water, water-OH and OH-OH. On the other hand, theenergy for the water-water h-bonds is equal to the water-OH h-bonds. Nevertheless, we can increase the structurebreaker effect by increasing the solute size. In fact, forethanol the TMD line vanishes at χ alc = 0 .
10, while for1-propanol the TMD is only observed at χ alc = 0 .
01 -the TMD lines are shown in the figure 4(a).The water anomalous behavior is related to the compe-tition between two liquids that coexist [14, 88, 89]. Thiscompetition can be observed using the g ww ( r ). Here weshow the RDFs the isobar P ∗ = 0 .
080 between the tem-peratures T ∗ = 0 .
50 and T ∗ = 0 .
68 for a fraction ofethanol of χ alc = 0 .
01 in the figure 4(b), for χ alc = 0 . xxxx . . . . xxxx L D L IIIII H D L I χ = . Methanol L D L IIIII H D L I χ = . Ethanol I L D L IIIII H D L χ = . Propanol . . . L D L IIIII H D L I χ = . L D L IIIII H D L I χ = .
05 I L D L IIIII H D L χ = . . . . . . . L D L IIIII H D L I χ = . . . . L D L IIIII H D L I χ = . . . . I L D L IIIII H D L χ = . T ∗ P ∗ FIG. 5.
P T phase diagrams for aqueous solutions of (a)methanol, (b) ethanol and (c) propanol for all concentrationsanalyzed in this work. in the figure 4(c) and for χ alc = 0 .
10 in figure 4(d). Aswe can see, for the fractions χ alc = 0 .
01 and χ alc = 0 . T increases, as indicated by thearrows. On the other hand, for χ alc = 0 .
10 there is prac-tically no increase in the occupation of the first lengthscale as the occupation in the second length scale de-creases. Once there is no competition, we do not ob-serve the density anomaly. This indicates that addinghigher concentration of alcohol changes the competitionbetween the scales in the CSW water model and that theCS alcohol chain length also affects the competition - inour previous work for methanol, we only observe this at χ alc = 0 .
70 [55].Curiously, even without the density anomaly, all thewater-alcohol mixtures have liquid-liquid phase transi-tion. In the figure 5 we show the
P T phase diagrams forall the fractions and types of alcohols. After the liquid-liquid critical point, The Widom Line (WL) separateswater with more HDL-like local structures at high tem-peratures from water with more LDL-like local structuresat low temperatures [90]. Looking at the diffusion coef-ficient D ∗ isotherms we can see the distinct transitions.At lower temperatures, as T ∗ = 0 .
34 it melts from thesolid phase to the HDL phase at high pressures, as weshow in the figure 6. Increasing T ∗ , we can see the sys-tem going from the LDL phase (with D ∗ >
0) to theHCP phase, with diffusion near zero, to the HDL phase,were D ∗ increases again. In the isotherms that cross theLDL-HDL transition we can see the discontinuity in thecurve, indicating the phase transition. Above the LLCPwe can see a change in the D ∗ × P ∗ curve behavior as it FIG. 6. Diffusion coefficient versus pressure for all solutionsanalyzed in this work. From bottom to top in each diagram,we have the isotherms T ∗ = 0 . , . , . , ... .
66. Each rowrepresents a concentration of solute: x alc = 0 . , . and . crosses the WL. (a) (b)(c) FIG. 7. Local bond orientation order parameter q as functionof pressure for the isotherms (a) T ∗ = 0 .
46, (b) T ∗ = 0 .
56 and(c) T ∗ = 0 . The same discontinuity can be observed in the struc-tural behavior. Besides τ and s , we also evaluated the q to analyze the structure. For simplicity, we show hereonly the case of pure water and water-ethanol mixtures.Along the isotherm T ∗ = 0 .
46, that crosses the phasesLDL, HCP and HDL, we can see in the figure 7(a) clearlythe discontinuities correspondents to this transitions forall fractions of ethanol. Also, it is noticeable how the ethanol is structure breaker: the value of q in the LDLand HCP phases are smaller as χ alc increases. Along theisotherm T ∗ = 0 .
56, shown in the figure 7(b), we can seethe same structure breaker effect in the LDL regime, anda discontinuous transition to the HDL phase. In contrast,above the LLCP there is no discontinuity. The isotherm T ∗ = 0 .
66, shown in the figure 7(c), have a smooth de-cay in q as it crosses the WL and goes from LDL-liketo HDL-like. This is interesting, once it indicates that asystem can have a LLCP without have density anomaly. r* g ww ( r ) BCCHCPAmorphous
Methanol χ alc = 0.10 (a) r* g ww ( r ) BCCHCPAmourphous
Ethanol χ alc = 0.10 (b) r* g ww ( r ) BCCHCPAmourphous
Propanol χ alc = 0.10 (c)(d) (e) (f)(g) FIG. 8. CSW-CSW radial distribution function g ww ( r ) alongthe isotherm T ∗ = 0 .
26 for water-alcohol mixtures with χ alc = 0 .
10 for (a) methanol, (b) ethanol and (c) propanol.Snapshots for the correspondents mixtures: χ alc = 0 .
10 of(d) methanol, (e) ethanol and (f) propanol. (g) Local bondorientation order parameter q as function of pressure for theisotherm T ∗ = 0 . As in the pure CSW water case, three solid phases wereobserved. However, an interesting finding is how the car-bon chain length affects the solid phases. It is clear thatlonger apolar chains affects the extension of the regionoccupied by each solid phase: the BCC crystal (regionI) loses space, moving to lowers pressures. Likewise, theHCP crystal (region II) moves to lower pressures as thealcohol chain increase. However, the area occupied in the
P T phase diagram remains - it just shifts to lower pres-sures as the size and fraction of alcohol increases. For thistwo solid phases, the temperature range in the
P T phasediagram seems to be independent of the fraction χ alc . Onthe other hand, the amorphous solid phase (region III)is favored as the it expands its extension to lower pres-sures and higher temperatures as the apolar chain grows.To understand why the HCP phase remains occupyinga large area in the phase diagram while the BCC areashrinks we show in the figure 8 the g ww ( r ) for the threealcohols with fraction χ alc = 0 .
10 along the isotherm T ∗ = 0 .
26 from P ∗ = 0 .
01 to P ∗ = 0 .
30. Comparingthe three cases with the pure CSW case, figure 3(a), isclear that increasing the size of the apolar tail in thealcohol favor the occupation in the second length scale.While for methanol and ethanol we see a low occupa-tion in the first length scale at the lower pressures, forpropanol this occupancy is high even for P ∗ = 0 .
01. Thisis consequence of a alcohol bubble formation: for the CSmethanol, once the molecule size is comparable to thesecond length scale and the OH is modeled as a CSWparticle, the molecules merge in the BCC structure, aswe show in the figure 8(d). However, the longer alco-hols creates bubbles, as we can see in figure 8(e) and (f)for ethanol and propanol, respectively. It alters the waterstructure near the bubbles, favoring the first length scale.It reflects in the local orientation. In the figure 8(g) weshow the q for this isotherm for the case of pure CS wa-ter ( χ alc = 0 .
00) and the three fractions of ethanol. Wecan see that for both crystal phases, BCC and HCP, thelocal order is affected by the alcohol once q is small forhigher fractions. IV. CONCLUSIONS
In this paper we have explored the supercooled regimeof pure water and mixtures of water and short chainalcohols: methanol, ethanol and propanol using a two-length scale core-softened potential approach. Our aimhas been to understand the influence of chain size on den- sity anomaly, the liquid-liquid phase transition and onthe polymorphism which are generally observed in thesemodels. There’s a pronounced influence of the apolarchain size on solid polymorphism. The BCC phase losesspace in the phase diagram once longer alcohols favor theoccupancy in the first length scale. Once the HCP phasehas a higher occupancy in this length scale it is shifted tosmaller pressures, while the amorphous solid phase growsfavored by the disorder induced by alcohol.The density anomaly vanishes as the competition be-tween the scales is suppressed in the LDL phase. How-ever, the LDL-HDL phase transition persists for all cases.This indicates that the competition between two liquidsis connected with waterlike anomalies, but the systemwill no necessarily have the anomalies if it has a liquid-liquid phase transition and liquid-liquid critical point.This results helps to understand the complex behaviorof water and mixtures with amphiphilic solutes in thesupercooled regime.
ACKNOWLEDGMENTS
MSM thanks the Brazilian Agencies Conselho Nacionalde Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq)for the PhD Scholarship and Coordena¸c˜ao de Aper-fei¸coamento de Pessoal de N´ıvel Superior (CAPES) forthe support to the collaborative period in the Institutode Qu´ımica Fisica Rocasolano. VFH thanks the CAPES,Finance Code 001, for the MSc Scholarship. JRB ac-knowledge the Brazilian agencies CNPq and Funda¸c˜aode Apoio a Pesquisa do Rio Grande do Sul (FAPERGS)for financial support. All simulations were performed inthe SATOLEP Cluster from the Group of Theory andSimulation in Complex Systems from UFPel.
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