How attractive and repulsive interactions affect structure ordering and dynamics of glass-forming liquids?
aa r X i v : . [ c ond - m a t . s o f t ] F e b How attractive and repulsive interactions affect structure ordering and dynamics ofglass-forming liquids?
Ankit Singh and Yashwant Singh
Department of Physics, Banaras Hindu University, Varanasi-221 005, India. (Dated: February 24, 2021)The theory developed in our previous papers is applied in this paper to investigate the depen-dence of slowing down of dynamics of glass-forming liquids on the attractive and repulsive parts ofintermolecular interactions. Through an extensive comparison of the behavior of a Lennard-Jonesglass-forming liquid and that of its WCA reduction to a model with truncated pair potential withoutattractive tail, we demonstrate why the two systems exhibit very different dynamics despite havingnearly identical pair correlation functions. In particular, we show that local structures characterizedby number of mobile and immobile particles around a central particle markedly differ in the twosystems at densities and temperatures where their dynamics show large difference and nearly iden-tical where dynamics nearly overlap. We also show how the parameter ψ ( T ) that measures the roleof fluctuations embedded in the system on size of the cooperatively reorganizing cluster (CRC) andthe crossover temperature T a depend on the intermolecular interactions. These parameters stem-ming from the intermolecular interactions characterize the temperature and density dependence ofstructural relaxation time τ α . The quantitative and qualitative agreements found with simulationresults for the two systems suggest that our theory brings out the underlying features that determinedynamics of glass-forming liquids. I. INTRODUCTION
In previous papers [1–3] of this series we introduceda new theory for slowing down of dynamics of fragileliquids on cooling. The theory identifies the local struc-tural order that defines the cooperativity of relaxationand brings forth a temperature T a and a temperature de-pendent parameter ψ ( T ) that characterize temperatureand density dependence of structural relaxation time. InRef. [3], hereafter referred to as I , we reported resultsfor the Kob-Anderson 80 : 20 binary Lennard-Jones (LJ)mixture [4] and compared them with simulation results[5, 6]. In this paper we investigate how different branchesof intermolecular interaction potentials affect the localstructural order and dynamics of supercooled liquids. Inparticular, we consider a model system in which parti-cles interact via a purely repulsive pair potential formedby truncating the LJ potential at its minimum [7]; a po-tential known as the Weeks-Chandler-Anderson (WCA)binary mixture potential. The two potentials, the LJ andWCA, have same repulsive core but different attractivepart; the LJ has an attractive tail while the WCA has noattraction. These models therefore offer an ideal bench-mark for evaluating the role of repulsive and attractiveinteractions on the local structural order and on slowingdown of dynamics of glass-forming liquids, and have beenstudied extensively over last several years [5, 6, 8–21]. Wecompare results of the two systems and identify causesthat give rise a large difference in their local structuralorder and dynamics at lower liquid-like densities but al-most identical results at sufficiently large densities.It is almost universally accepted that the structure andthermodynamics of nonassociated liquids are primarilygoverned by the short range repulsive branch of pair po-tential while the attractive part of the potential provides,in the first approximation, a homogeneous cohesive back- ground [7, 22, 23]. This led to formulation of theories inwhich properties of liquids are related to those of the re-pulsive core reference system, the attractive part of thepotential being treated as a perturbation. The success ofthese perturbation theories [23] in predicting equilibriumproperties of normal liquids led to expectation that thestructure and dynamics of supercooled liquids should alsobe governed primarily by the local packing and the stericeffects produced by the repulsive forces [24, 25]. Thisexpectation was, however challenged by results found viamolecular dynamics simulations by Bertheir and Tarjus[5, 6] for the LJ and WCA mixtures. They found thatwhile these systems exhibit nearly identical equilibriumstructure, but at lower liquid-like densities and temper-atures, very different dynamics: The value of structuralrelaxation time τ α is much smaller in the WCA systemthan in the LJ ones at the same supercooled temperatureindicating that the attractive forces have a nonperturba-tive effect on the relaxation dynamics. However, thislarge difference in values of τ α decreases and ultimatelyvanishes as the density is significantly increased. Recentsimulation studies [19, 20] done in the two and in threedimensions show similar effect of attractive interactionsin slowing down of dynamics in the supercooled region.The above findings bring forth the limitations [8, 9]of “microscopic” theories based on pair correlation func-tion g ( r ) [26–28]. For example, mode coupling theory wasfound to largely underestimate the difference in dynam-ics of the WCA and LJ systems [9]. This negative resultled some authors to believe that g ( r ) does not containthe physical information required to capture subtletiesinvolved in dynamical slowdown and therefore any the-ory based on g ( r ) is bound to fail [8]. It was suggestedthat the origin of this failure might be their neglect ofhigher order than pair correlations. Subsequent simu-lations of triplet correlation functions indicate that thelocal ordering is more pronounced in the LJ system, anobservation consistent with its slower dynamics [12]. Thispronounced structure was, however, shown to arise due,to a good extent, to an amplification of the small dis-crepancies observed at the pair level [13]. Recently, Lan-des et al. [21] have used a standard machine learningalgorithm to show that a properly weighted integral of g ( r ) which amplifies the subtle differences between thetwo systems, correctly captures their dynamical differ-ences. Local structure analysis using topological clus-ter classification [29] and Voronoi face analysis [12] alsopoint to subtle structural difference. Using the config-urational entropy as the thermodynamic maker via theAdam-Gibbs relation [30], Banerjee et al. [16–18] showedthat the difference in dynamics of the WCA and LJ sys-tems is due to difference in their configurational entropy.These results prompt one to ask whether a unified phys-ical framework exists to understand the structure anddynamics and their relationship for systems such as theLJ and WCA glass forming liquids. Our goal here is tofind answer to this question.In Sec. II we give a brief account of our theory rele-vant to the present work. In Sec. III we calculate and re-port results for the WCA system and compare them withthose found for the LJ system reported in I . Sec. IV isdevoted to conclusion that emerged from similarity andcontrast of results of the two systems and comparisonwith simulation findings. II. THEORY:
Our theory provides a method to distinguish and cal-culate number of dynamically free, metastable and sta-ble neighbors of a tagged (central) particle in a liquidat different temperatures and densities. This is achievedby including momentum distribution in the definition of g ( r ) and using information of the configurational entropy S c . The g ( r ) of a binary mixture written in the center-of-mass coordinates is [1–3], g αγ ( r ) = (cid:18) β πµ (cid:19) Z d p e − β ( p µ + w αγ ( r )) . (1)Here β = ( k B T ) − is the inverse temperature measuredin units of the Boltzmann constant k B , p is the relativemomentum of a particle of mass µ = m/ m being themass of a particle of the liquid). The potential of meanforce w αγ ( r ) = − k B T ln g αγ ( r ) is a sum of the (bare) po-tential energy u αγ and the system induced potential en-ergy of interaction between a pair of particles of species α and γ separated by distance r [23]. The peaks andtroughs of g αγ ( r ) create, respectively, minima and max-ima in βw αγ ( r ) as shown in Fig. 1 of I . A region betweentwo maxima, leveled as i − i ( i ≥
1) is denoted as i th shell and minimum of the shell as βw ( id ) αγ . The valueof i th maximum (barrier) is denoted as βw ( iu ) αγ and itslocation by r ih . All those particles in region of i th shell whose energiesare less or equal to the barrier, w ( iu ) αγ would be trappedas they do not have enough energy to escape the barrier.These particles are considered as bonded (nonchemical)with the central particle. On the other hand, all thoseparticles whose energies are higher than βw ( iu ) αγ are freeto move around and collide with other particles. Thenumber of bonded particles is found form a part of g αγ ( r )defined as [1, 3] g ( ib ) αγ ( r ) = 4 π ( β πµ ) / e − βw ( i ) αγ ( r ) Z q µ [ w ( iu ) αγ − w ( i ) αγ ( r )]0 × e − βp / µ p d p, (2)where w ( i ) αγ ( r ) is the effective potential in the range of r il ≤ r ≤ r ih of i th shell. Here r il is value of r where w ( i ) αγ ( r ) = w ( iu ) αγ on the left hand side of the shell (seeFig. 1 of I ). The total number of particles that formbonds with the central particle of species α is n ( b ) α = 4 π X i X γ ρ γ Z r ih r il g ( ib ) αγ ( r ) r d r, (3)where summations are over all shells and over all speciesand ρ γ is number density of γ component. The partof g αγ ( r ) that corresponds to free particles is g ( f ) αγ ( r ) = g αγ ( r ) − g ( b ) αγ ( r ).Fluctuations embedded in the system (bath) activatesome of these bonded particles, particularly those whoseenergies are close to the barrier height, to escape theshell. These particles are referred to as metastable (or m -) particles. The remaining bonded particles stay trappedin shells and form stable (long lived) bonds with the cen-tral particle. They are referred to as s -particles. Thisseparation between the m - and s -particles is achieved viaa parameter ψ ( T ) which measures effect of the bath in ac-tivating bonded particles to escape the potential barrier.All those particles of i th shell whose energies lie between βw ( iu ) αγ − ψ and βw ( iu ) αγ escape the shell are m -particles.On the other hand, all those particles whose energies arelower than [ βw ( iu ) αγ − ψ ] remain trapped in the shell, are s -particles. The value of ψ ( T ) in a normal (high tem-perature) liquid is one but decreases on cooling belowa certain temperature denoted as T a which depends ondensity ρ and on microscopic interactions between parti-cles.The number of s -particles at a given temperature anddensity is found from a part of g αγ ( r ) defined as g ( is ) αγ ( r ) = 4 π ( β πµ ) / e − βw ( i ) αγ ( r ) Z q µ [ w ( iu ) αγ − ψk B T − w ( i ) αγ ( r )]0 × e − βp / µ p d p, (4)where w ( i ) αγ ( r ) is in the range r ′′ il ≤ r ≤ r ′′ ih . Here r ′′ il and r ′′ ih are, respectively, value of r on the left and the right K ρ =1.2 ρ =1.4 ρ =1.6(a) (b) (c)WCALJ FIG. 1: Comparison of values of K for the LJ and WCA systems. These values were found when value of ψ wasfixed to 1 at all temperatures. In both cases, K is constant above a density dependent temperature, T a , anddecreases from its constant value on cooling below T a . Values of T a of the two systems at different densities aregiven in Table I. Symbols represent calculated values and curves are least square fit.hand side of the shell where βw ( i ) αγ ( r ) = βw ( iu ) αγ − ψ . Thenumber of s -particles around a α particle is n ( s ) α = 4 π X i X γ ρ γ Z r ′′ ih r ′′ il g ( is ) αγ ( r ) r d r. (5)The averaged number of s -particle bonded with a cen-tral particle in a binary mixture is n ( s ) = x a n ( s ) a + x b n ( s ) b , (6)where x α is the concentration of species α .The n ( s ) , s -particles bonded with a central particleform a cooperatively reorganizing cluster (CRC). Thenumber of particles in the cluster is related to the config-urational entropy S c through the Adam and Gibbs [30]relation, n ( s ) ( T ) + 1 = KS c ( T ) , (7)where K is a temperature independent constant. For anevent of structural relaxation to take place the CRC hasto reorganize irreversibly; The energy involved in thisprocess is the effective activation energy βE ( s ) of relax-ation. It is equal to the energy with which the centralparticle is bonded with n ( s ) , s -particles and is given as βE ( s ) ( T, ρ ) = 4 π X i X γ x γ ρ γ Z r ′′ ih r ′′ il [ βw ( iu ) αγ − ψ ( T ) − βw ( i ) αγ ( r )] × g ( is ) αγ ( r ) r d r, (8)where energy is measured from the effective barrier βw ( iu ) αγ − ψ ( T ). The structural relaxation time τ α is ob-tained from the Arrhenius law, τ α ( T, ρ ) = τ exp [ βE ( s ) ( T, ρ )] , (9)where τ is a microscopic time scale.The data of g αγ ( r ) and S c found from simulations andreported in Ref. [18] are used in the calculation. III. RESULTS AND DISCUSSIONS
In this section we report results found for the WCAsystem and compare them with those reported in I forthe LJ system at densities ρ = 1 .
2, 1 . . K calculated from Eqs. (4) − (7)with value of parameter ψ ( T ) fixed at one at all temper-atures T , are plotted as a function of T . In the figure wealso plot values of K found in a similar way (see Fig. 2 of I ) for the LJ system. We note that, in general, the tem-perature dependence of K of the WCA system is similarto the one found for the LJ system; K is constant abovea temperature denoted as T a and decreases from its con-stant value on cooling below T a . As explained in I , thedecrease in value of K below T a is due to the unphysicalcondition that has been imposed on ψ ( T ) by fixing itsvalue equal to one for T < T a . It is the temperature in-dependent value of K , i.e. value of K found for T > T a ,that should be, as argued in I , used in Eq. (7). Values of K and T a of both systems for three densities are listed inTable I. We note that value of K for the WCA system ishigher at the same density than that for the LJ system.The difference, however, is found to decrease on increas-ing the density; while at ρ = 1 . . ρ = 1 .
6. This density dependentdifference is a measure of the density dependent role ofattractive interaction on configurations that is assessedTABLE I: Value of constant K and the crossovertemperature T a of the LJ and WCA systems at differentdensities. LJ WCA ρ K T a K T a . .
10 0 .
68 4 .
80 0 . . .
80 1 .
43 3 .
55 1 . . .
75 2 .
68 3 .
00 2 . ψ ρ =1.2 ρ =1.4 ρ =1.6 WCA LJ
FIG. 2: Comparison of values of ψ ( T, ρ ) of the two systems at different temperatures and densities. Symbols arecalculated values and curves are least square fit. A large difference in values of ψ ( T, ρ ) of the two systems for ρ = 1 . T = 0 .
68 is seen whereas for ρ = 1 . ψ ( T ) almost overlap at all temperatures.by a CRC.Values of K listed in Table I and of the configurationalentropy S c found from simulations [18] are used in Eq.(7) to calculate values of n ( s ) ( T, ρ ). From known values of n ( s ) ( T, ρ ) we determine ψ ( T, ρ ) from Eqs. (4) − (6) for dif-ferent values of T and ρ . We plot ψ ( T ) vs T in Fig. 2. Wenote that for both systems, the high temperature value of ψ ( T ) is equal to one and decreases rather sharply on cool-ing below T a . The transition from the high temperatureregion to the low temperature region begins at T a witha crossover region spreading over a narrow temperaturewidth. Since the crossover region separates the high tem-perature region where slowing down of dynamics is slowerfrom the low temperature region where slowing down ofdynamics is faster, T a can be taken as the crossover tem-perature. From Fig. 2 one finds that for ρ = 1 . T ≤ .
68 whereas the slowing down of the WCA sys-tem would remain at slower rate till T a = 0 .
47 on cooling.This results into a large difference in values of τ α below T = 0 .
68 of the two systems. However, as ρ increasestemperature dependence of dynamics of the two systemscome closer as the difference in values of T a decreases.In Figs. (3 −
5) we compare radial distribution function g αγ ( r ) and its different parts, g ( f ) αγ ( r ) = g αγ ( r ) − g ( b ) αγ ( r ), g ( m ) αγ ( r ) = g ( b ) αγ ( r ) − g ( s ) αγ ( r ) and g ( s ) αγ ( r ), where α, γ = a, a and a, b (notations are of I ) for the two systems at( ρ, T ) = (1 . , . , (1 . , .
0) and (1 . , . g ( f ) αγ ( r ), g ( m ) αγ ( r ) and g ( s ) αγ ( r ) describe,respectively, distributions of free, m and s -particlesaround a central particle in a liquid. A look at thesefigures shows that while g αγ ( r ) of the two systems inall cases nearly overlap, differences are seen in values of g ( f ) αγ ( r ), g ( m ) αγ ( r ) and g ( s ) αγ ( r ). In particular, first peaksof g ( m ) αγ ( r ) and g ( s ) αγ ( r ) in Fig. 3 show large differenceat ρ = 1 .
2. The difference becomes less pronouncedat ρ = 1 . ρ = 1 . g ( m ) αγ ( r ) is higher and g ( s ) αγ ( r ) is lower for the WCA system compared to those for the LJ system. Since free and m particles are mo-bile whereas s particles are immobile, a particle in theWCA system is surrounded by a relatively larger popula-tion of mobile particles and a less population of immobileneighbors compared to those of the LJ system, leading todifference in their dynamical behavior. The subtle localstructural order that defines the cooperativity of relax-ation and remains hidden to experiments that measurepair correlation functions is defined in terms of g ( s ) αγ ( r ).A useful information that shed light on the underlyingfeatures related to the local structural order and dynam-ics can be derived from the dynamical states of particlesof the first shell surrounding the central particle as afunction of temperature and density. In Fig. 6 we com-pare values of n ( f )1 , n ( m )1 and n ( s )1 as a function of 1 /T for the two systems at different densities. Here the sub-script 1 indicates the first coordination shell. In the figuresolid lines indicate values for the LJ system and dashedlines for the WCA system. Letters f , m and s stand, re-spectively, for free, metastable and stable. We note thattemperature dependence of number of particles of differ-ent dynamical states that surround the central particlein the two systems is, in general, similar. In both caseswe find that at high temperatures most particles are freewhile a few are m -particles and a very few are s -particles.On cooling the systems, n ( m )1 ( T ) remains nearly constantbut n ( s )1 ( T ) increases though slowly till T = T a , but for T < T a , n ( m )1 ( T ) decreases and n ( s )1 ( T ) increases withincreasing rate at the cost of both free and m -particles.The rate is expected to increase rapidly on further low-ering of temperatures, resulting into a rapid increase innumber of s -particles and therefore in the cooperativityof relaxation. There is, however, a large difference par-ticularly at low temperatures, in the number of particlesof a given category of the two systems at ρ = 1 .
2; thedifference decreases on increasing the density and almostdisappears at ρ = 1 . m -particles) and immobile (localized) first neighbors de- r g aa (r) ρ =1.2 T=0.5 LJWCA r g aa ( m ) (r) r g aa (f) (r) r g aa ( s ) (r) (a) r g b a (r) ρ =1.20 T=0.50 LJWCA r g b a ( m ) (r) r g b a (f) (r) r g b a ( s ) (r) (b) FIG. 3: Comparison of values of g αγ ( r ) and its different parts g ( f ) αγ ( r ), g ( m ) αγ ( r ) and g ( s ) αγ ( r ) of the LJ (full lines) andWCA (dashed lines) for ρ = 1 . T = 0 .
5. In figure ( a ), α, γ = a, a and in ( b ), α, γ = a, b . A large difference canbe seen between values of g ( s ) αγ ( r ) and of g ( m ) αγ ( r ) of the two systems, while values of g αγ ( r ) are nearly identical. r g aa (r) ρ =1.4 T=1.0 LJWCA r g aa ( m ) (r) r g aa (f) (r) r g aa ( s ) (r) (a) r g b a (r) ρ =1.4 T=1.0 LJWCA r g b a ( m ) (r) r g b a (f) (r) r g b a ( s ) (r) (b) FIG. 4: Same as in Fig. 3 but for ρ = 1 . T = 1 .
0. A relatively small difference is seen between values of g ( s ) αγ ( r )and of g ( m ) αγ ( r ) of the two systems compared to ρ = 1 . r g aa (r) ρ =1.6 T=2.0 LJWCA r g aa ( m ) (r) r g aa (f) (r) r g aa ( s ) (r) (a) r g b a (r) ρ =1.6 T=2.0 LJWCA r g b a ( m ) (r) r g b a (f) (r) r g b a ( s ) (r) (b) FIG. 5: Same as in Fig. 3 but for ρ = 1 . T = 2 .
0. Values of g αγ ( r ) and of its components, g ( f ) αγ ( r ), g ( m ) αγ ( r ) and g ( s ) αγ ( r ) of the two systems are nearly identical. ρ =1.4 ρ =1.6(a) (b) (c)mf msf msf ρ =1.2 FIG. 6: Comparison of values of n ( f )1 , n ( m )1 and n ( s )1 as a function of 1 /T for the two systems. Letters f , m and s stand, respectively, for free, metastable and stable and the subscript 1 stands for the first shell. Full lines representvalues of the LJ system and dashed lines of the WCA system. p l , p m ρ =1.2 ρ =1.4 ρ =1.6(a) (b) (c)p m p m p m p l p l p l FIG. 7: Comparison of values of fraction of mobile, p m , and immobile, p l , (defined in the text) particles in the firstshell around the central particle of the two systems. Line symbols are same as in Fig. 6. The dotted part of each linerepresents extrapolated values. The two curves of p m and p l meet at T = T mc where half of particles of the firstneighbor become immobile.fined, respectively, as p m ( T ) = n ( f )1 ( T )+ n ( m )1 ( T ) n ( t )1 ( T ) and p l ( T ) = n ( s )1 ( T ) n ( t )1 ( T ) to compare the local ordering relevantto dynamics. In Fig. 7 we plot and compare values of p m ( T ) and p l ( T ) of the two systems as a function of1 /T . In the figure, lines (full for the LJ and dashed forthe WCA) represent calculated values and dotted part ofeach line represents extrapolated values. A glance at thisfigure reveals how the local ordering defined in terms ofthe fraction of mobile and immobile particles around thecentral particle in the two systems compare with eachother at different densities. The extrapolated parts oflines representing p m ( T ) and p l ( T ) meet at a tempera-ture (denoted as T mc ) where half of the neighbors becomeimmobile. The values of T mc found for densities ρ = 1 . . . .
41, 0 . .
64 whereas the corresponding values for the WCAsystem are 0 .
26, 0 .
77 and 1 .
62. The large difference in the temperature dependence of p m ( T ) and p l ( T ) and val-ues of T mc found at ρ = 1 . ρ = 1 . ρ = 1 . βE ( s ) ( T, ρ ) and therelaxation time τ α ( T, ρ ) calculated, respectively, fromEqs. (8) and (9) are plotted in Fig. 8. In Fig. 8( a ) valuesof βE ( s ) of the two systems are compared as a functionof 1 /T . In Fig. 8( b ) we compare values of τ α /τ of thetwo systems with each other and with values found fromsimulations [5, 6]. An excellent agreement is found withsimulation values for all densities for both systems.The density dependence of T a is shown in Fig. 9. Inthe figure, circles - full for the LJ and open for the WCA-denote calculated values and the curves- full line for theLJ and dashed line for the WCA- represent fit with apower law form T a = a ρ γ . In case of the LJ system, a = 0 .
287 and γ = 4 .
757 while in case of the WCA, τ α β E ( s ) (a) (b) ρ =1.4 ρ =1.2 ρ =1.2 ρ =1.6 ρ =1.4 ρ =1.6 FIG. 8: Comparison of values of activation energy βE ( s ) for the relaxation in column ( a ) and therelaxation time in column ( b ) as a function of 1 /T atthree densities of the two systems. Curves (full for theLJ and dashed for the WCA) represent calculatedvalues and circles (full for the LJ and open for theWCA) in column ( b ) represent simulation values. ρ T a with a =0.175 γ =5.821 LJWCA[T a = a ρ γ ] with a =0.287 γ =4.757 FIG. 9: Comparison of density dependence of thetemperature T a of the two systems. Circles (full for theLJ and open for the WCA systems) represent calculatedvalues (given in Table I) and curves (full for the LJ anddashed for the WCA) represent fit T a = a ρ γ with γ = 4 .
757 and 5 . a = 0 .
175 and γ = 5 . I that when ψ ( T ), τ α , βE ( s ) , etc., are plotted as a function of T a /T (or T /T a )the data collapse on master curves. However, incase of the WCA such a collapse fails in agreement withresult found from simulations [5, 6]. We plot calculatedvalues (shown by lines) and simulation values by symbols a /T10 τ α ρ =1.2 ρ =1.4 ρ =1.6 a /T10 τ α ρ =1.2 ρ =1.4 ρ =1.6 (a)(b) WCALJ FIG. 10: Comparison of collapse of calculated (lines)and simulation (symbols) data of τ α of the two systemsas a function of T a /T . While in the case of LJ system( b ) good collapse takes place, in case of the WCA ( a ),both the calculated as well as simulation values fail tocollapse on one curve.of τ α /τ as a function of T a /T for densities ρ = 1 .
2, 1 . . a ) for the WCA system and in 10( b )for the LJ system. While in case of the LJ system agood collapse of data happens, in case of the WCA boththe calculated as well as simulation values fail to collapseon one curve and therefore violates the density scalingrelation; a feature attributed to the fact that the WCAliquid follows an “isomorph” different from that of theLJ liquid [10, 11]. IV. CONCLUSION
Through an extensive comparison of the behavior ofa LJ glass forming liquid and its WCA reduction to amodel with truncated potential without attractive tail,we have shown that our theory brings out several under-lying features that characterize slowing down of dynamicsof these systems. It is shown that though the equilib-rium static structures measured by the pair correlationfunctions, g αγ ( r ) of the two systems are nearly identical,0there is a marked difference, particularly at low densitiesand low temperatures, in their components representingfree, metastable and stable particles distributed in coor-dination shells around a central particle. In particular,the parameters p m ( T ) and p l ( T ) which define, respec-tively, the fraction of mobile and immobile first neighborsand plotted in Fig. 7 provide information about the localstructure relevant to dynamics.The other intrinsic parameters stemming from the in-termolecular interactions and which explain why slowingdown of dynamics of the two systems are qualitativelyand quantitatively different at lower densities and lowertemperatures but nearly identical at higher densities andhigher temperatures are ψ ( T ) and the crossover temper-ature T a . The value of parameter ψ ( T ) which measuresthe effect of fluctuations embedded in the system on sta-bilizing the shape and size of CRC, takes a turn fromits high temperatures value of 1 at T = T a and startsdecreasing rather sharply as T is lowered. There is aone-to-one correspondence between the crossover regionof ψ ( T ) and τ α (for more details see I ) indicating the sig-nificance of embedded fluctuations on temperature anddensity dependence of local structure and dynamics. Thetemperature T a separates the high temperature behaviorregion where slowing down of dynamics is slower from a low temperatures region where slowing down of dynamicsis faster. Both ψ and T a depend on details of intermolec-ular interactions. Whenever the attractive part of inter-molecular interaction is effective in suppressing entropydriven escapes of particles out of shells, the crossovertemperature T a shifts to higher temperatures resultinginto slowing down of dynamics at faster rate than in ab-sence of the attractive part. The reason why value of τ α for ρ = 1 . T = 0 .
5, than the LJ ones, lies in the difference in theirvalues of T a (see Table I). The quantitative and quali-tative agreements found with simulation results for thetwo systems suggest that our theory accurately describesthe intricate nature of the connection between the localstructural order and dynamics arising due to attractiveand repulsive interactions in glass-forming liquids. ACKNOWLEDGMENTS
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