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

USE OF PARSONS-LEE AND ONSAGER THEORIES TO…which no converged results could be obtained was eventuallyreached. It will be discussed below that the observed lack ofconvergence in the demixing region of the I-N curves may beattributed to the entrance of the system into a N-N coexistenceregion.One of the main conclusions that can be drawn from theresults of Fig. 4 is that the stability of the mixed I-N coexistenceis reduced with the increase in size of the sphericalcomponent in the binary mixture. According to the PL calculation,for L * =300 and increasing D * =1, 3, 5, and 15, I-Nstates coexist under mixed conditions up to progressivelysmaller HS volume fractions, of x v =0.71, 0.66, 0.60, and0.28, respectively. For L * =20, a similar trend is found, althoughin this case the transitions to the demixing regimetakes place at roughly the same x v 0.165 within D *=0.7–1.5, with a shallow maximum of x v 0.167 for D *=1.25. This same behavior was found for L * =5 not shownwhere the turning point into the demixing regime is delayedto x v 0.83 for D * =1.5, in comparison to x v 0.72 for bothD * =1 and 2. Such weak dependence of the demixing transitionon the size of the spherical articles in the region of smallD * values, even featuring a non-monotonous character, appearsto be reminiscent of the excluded volume contributionscontained in the second order virial terms of the free energy.In fact, Onsager theory predicts a much more pronouncednonmonotonous dependence on D * of the stability of themixed regime. Within the Onsager approximation, for theL * =300 fluid the demixing regime enters, for instance, atx v =0.49, 0.64, 0.60, and 0.27 for D * =1, 2, 3, and 15, with adetailed computation showing that the range of stability ofthe mixed I-N coexistence becomes indeed maximum forD * 3. This is the reason for the strong discrepancy betweenthe Onsager and Parsons-Lee coexistence curves for the L *=300, D * =1 fluid that can be appreciated in Fig. 4.A further remarkable aspect illustrated in Fig. 4 is theappreciable maximum in displayed by the isotropic branchof the L * =20 fluid in the small D * limit. Such trend is observedfor D * 1 and indicates that the expel of HSC particlesfrom the isotropic phase as the system enters the demixingregime leads to a less efficient packing of the fluid inthat phase. A similar behavior of the isotropic branch forsmall D * was observed for L * 20, as illustrated in Fig. 1 forL * =5. As the volume of the HS particles becomes comparableor greater than that of the HSC particles, this effectvanishes and the packing fraction isotropic branch increasesmonotonously over the whole x v range. In fact, for the mixtureswith L * =20 and D * 2, the packing fraction of theisotropic branch for x v close to unity reaches values typicalof the solid phase of the bulk HS system. Hence, these lattercases correspond to a situation in which the HS particlesfreeze upon segregation from the HSC particles. The pertinenceof this remark is related to the experimental observationof a similar type of behavior reported by Fraden andco-workers for mixtures of rodlike viruses and spherical colloids33. In these experiments the colloids were found toform arrangements of solidlike filaments segregated from thebulk of nematic viruses. This phenomenology, still without aclear explanation, presents similarities with the nematicHSC-solid-HS phase separation described here.Figure 5 illustrates the stability of the isotropic and nematicphases against I-I and N-N demixing transitions. This is0.80.6η0.4D * =1D * =100.2L * =3000 0.2 0.4 0.6 0.8 10.4ηη0.20.1D * =4D * =1D * =0.7D * =4D * =1D * =4D * =1, 0.7L * =200 0.1 0.2D * =1D * =10PHYSICAL REVIEW E 75, 061701 2007D * =10L * =20D * =100 0.2 0.4 0.6x vL * =300FIG. 5. Top panel: isotropic-isotropic spinodal demixing curvesfor HSC-HS fluids with L * =300, D * =1 and 10 solid curves andL * =20, D * =1 and 4 dashed curves. Middle panel: Nematicnematicspinodal demixing curves dashed lines for HSC-HS fluidswith L * =20, D * =0.7, 1, and 4. The corresponding nematic branchesof the I-N coexistence are also included for direct comparison. Notethe discontinuity in the I-N curve for D * =0.7 symbols not presentin the closely overlapping curve for D * =1 solid line. Bottompanel: Same as middle panel but for L * =300, D * =1 and 10. The I-Ior N-N demixing transitions can take place at packing fractionsabove the corresponding spinodals.done by means of the Parsons-Lee spinodal curves resultingfrom the mapping on the x v - plane of the conditions definedin Eq. 16. Demixing could take place if the packing fractionsassociated to the corresponding spinodal becomesmaller than the packing fractions obtained for I-N coexistence.Spinodals for I-I demixing were computed for HSCaspect ratios ranging L * =5–1000 and HS diameters up toD * =1000. Figure 5 shows only some illustrative examples.The detailed analysis of these spinodals indicates that I-Icoexistence becomes feasible for sufficiently large D * values,namely, e.g., D * 4, 6, 10, 20, 30, and 90 for L * =5, 10, 20,100, 300, and 1000, respectively. It can be noted that theseHS diameters are significantly greater than the ones consideredabove for the I-N coexistence and therefore do not interferewith the diagrams of Figs. 2–4. This conclusion issupported by the fact that our algorithm never converged to aI-N coexistence configuration of low orientational order inthe a priori nematic phase. This type of convergence wouldhave been plausible, since the h distribution was free toadjust through its Legendre coefficients to the configurationof minimum free energy. This result is also consistent withthe prediction outlined in Ref. 54 that for sufficiently long061701-7