Use of Parsons-Lee and Onsager theories to - APS Link Manager ...

USE OF PARSONS-LEE AND ONSAGER THEORIES TO…ing fractions in the range =0.45–0.50, which overlaps withthe demixing regime found in the present study for the I-Ncoexistence of that particular mixture. In fact, in the snapshotfor the demixed state shown in Fig. 2 it can be appreciatedthat the segregated HSC particles are more tightly packedthan a typical nematic phase and display an arrangementmore related to a smectic or solidlike phase. Hence, the applicationof the present theory, in which the demixing transitionsare treated within the context of nematic ordering islimited to HSC elongations greater than L * =5. Fortunately,as L * is increased the transition to the lamellar phase is alsodelayed to greater packing fractions and, in addition, the demixednematic regime takes place at smaller packing fractionssee Fig. 1. In this way, for the particular case of L *=20, the smectic A phase becomes stable at 0.5 58, avalue well above the range where the I-N demixing occurssee Fig. 1. It follows that the conclusions related to thedemixing behavior of the HSC-HS fluid drawn from thepresent theoretical treatment are expected to be robust,within the framework of the Parsons-Lee and Onsager approximations,for mixtures of HSC particles with elongationsof L * 10–20 or greater.We will now focus the discussion in more detail on thetheoretical predictions for the dependence of the I-N coexista)b)PHYSICAL REVIEW E 75, 061701 2007FIG. 2. Snapshots from Monte Carlo simulations of theHSC-HS fluid with L * =5, D * =1 in a a mixed nematic state withx v =0.065 and =0.442 and b a demixed nematic state with x v=0.536 and =0.412. The computations were performed as describedin Ref. 43.state of coexistence becomes progressively smaller and tendsto vanish.In the demixed regime, the relative magnitude of thepacking fractions of the coexisting states depends on therelative sizes of the HSC and HS particles. This is noteworthysince in the mixed regime the I-N coexistence impliessystematically a greater packing fraction in the nematicphase. Figure 1 shows that for L * =300, D * =10 the sphererichisotropic branch eventually becomes more compact thanits nematic counterpart. For the other two cases L * =20, D *=2 and L * =5, D * =1, the demixed nematic states are alwaysdenser than the isotropic ones. Furthermore, the coexistencediagram for L * =5, D * =1 displays a nonmonotonous behaviorof the packing fraction in the isotropic branch. It will beshown below that this feature is associated to the demixingregime mixtures with small D/L ratios, where the isotropicbranch becomes less dense as it expels HSC particles.The appearance of highly partitioned isotropic and nematicphases in rod-sphere mixtures was originally predictedtheoretically by Flory 53. In fact, coexistence diagrams inqualitative agreement with the ones shown in Fig. 1 havebeen observed experimentally for different systems19,32,33,35–41. Lekkerkerker and Stroobants 54 describedin detail this qualitative behavior for mixtures of colloidalrods and flexible polymers, guided by scaled particletheory. It is therefore gratifying to confirm that Parsons-Leetheory and also Onsager theory as shown below captures, atleast on qualitative grounds, the behavior observed in realsystems on the basis of depletion interaction effects.Figure 1 also shows that at low values of x v within themixed regime, the nematic phase is perturbed by the introductionof spherical particles on the dominant bulk of rodlikeparticles. Any increment in the fraction of spheres results ina systematic displacement of the I-N transition toward higherpacking fractions of both coexisting states. This type of retardationof the nematic phase has been found in a recentsimulation study of the HSC-HS mixture with L * =5 andD * =1 43, and appears to be a general effect for small andmoderate values of x v . Figure 1 bottom panel illustrates thefair agreement existing between the Parsons-Lee coexistencediagram and the NPT-MC simulation data of Ref. 43 in thesmall x v regime x v 0.07 for the particular case of the L *=5, D * =1 mixture. A similar level of quantitative agreementis found for the coexistence pressures not shown. Figure 2shows snapshots corresponding to NPT-MC simulations ofnematic states for the L * =5, D * =1 HSC-HS fluid with x vvalues in the mixed and demixed regimes. The simulationscorroborate the theoretical predictions by showing that themixed case maintains the bulk structure of the nematic phaseof the pure HSC fluid, whereas a clear segregation of therodlike and spherical molecules takes place at high x v .A question that emerges at this point is whether the demixingtransitions predicted in the present theoretical treatmentare stable with respect to liquid crystalline transitionsother than the nematic one. The most plausible situation tothis respect would be the entrance of the fluid into a lamellarphase in which the HSC and HS particles arrange in alternatelayers. Phases of this kind have been investigated previously23–25,43,44. For the L * =5, D * =1 HSC-HS fluid it hasbeen shown that the lamellar phase becomes stable at pack-061701-5