Figure 1

(Color online) A sequence of images illustrating the preparation of a sample which was used in determining the phase diagram. (a) A nematic liquid crystal of $fd$ virus in buffer between crossed polarizers showing disordered birefringent domains. (b) A highly concentrated solution of Dextran labeled with yellow fluorescein is added to the transparent $fd$ nematic liquid crystal. (c) After the sample in (b) is vigorously shaken its phase separates into the coexisting nematic and isotropic phases. The macroscopic phase separation takes from few hours to couple of days depending on the location in the phase diagram. (d) Same sample as image (c) but taken between crossed polarizers. Image shows dense birefringent nematic phase on the bottom and Dextran rich isotropic phase on the top which is yellow in appearance. Images (a)–(d) are taken on the same sample.Reuse & Permissions

Figure 2

Depletion potentials $U$ between two walls, two perpendicular cylinders, and two spheres obtained from computer simulation are shown by open spheres, squares and triangles, respectively. In the two-wall simulation the wall size was $313\times 313{\mathrm{\AA }}^2$ and periodic boundary conditions were used. The diameter of the spheres and cylinders is $66\mathrm{\AA }$ while $R_g$ of the polymer is $111\mathrm{\AA }$. The lines indicate depletion potentials as predicted by the penetrable sphere (AO) model. The separation $x$ is the closest distance between two surfaces. The number concentration of the polymer $\rho$ is equal to the overlap concentration $\rho =3∕\left(4\pi R_g^3\right)$, while the radius of the penetrable spheres is $R^{\text{AO}}=2R_g∕\sqrt{\pi }=125\mathrm{\AA }$. The AO theory overestimates the potential between spheres and between cylinders because polymer deforms around colloidal particles.Reuse & Permissions

Figure 3

Total interaction potential $U$ as a function of separation $x$ between two viruses $(D=66\mathrm{\AA })$ oriented at $90°$ with respect to each other and immersed in a suspension of polymers of concentration $\rho =3∕\left(4\pi R_g^3\right)$ and radius $R_g=111\mathrm{\AA }$ at three different ionic strengths. The interaction potential is a sum of electrostatic repulsion and depletion interaction. The effect of electrostatic repulsion for $fd$ with net linear charge density $1e^{-}∕\text{Å}$ is accounted for by treating the $fd$ as a hard particle with a larger effective diameter $D_{\text{eff}}$ [11, 33]. Filled circles indicate the depletion potential obtained from Monte Carlo simulation of polymers without excluded volume interactions. Since the polymer diameter is larger than the rod diameter, the polymer and rodlike viruses can easily interpenetrate. This results in an effective depletion attraction which is smaller than what is predicted by the AO model (indicated by the full line). The phase diagrams corresponding to these interaction potentials are shown in Fig. 6. Inset: In theoretical calculations we approximate the intermolecular potential between rods with an effective hard core diameter $D_{\text{eff}}$ [11] and attractive potential. The attractive part of the potential is modeled by AO penetrable spheres whose effective radius and concentration best fits the potential obtained through computer simulation. This effective intermolecular potential is compared to the potential obtained through the computer simulation in the inset. In the inset ${\rho }_{\text{eff}}∕\rho =0.39$ and $R_{\text{eff}}^{\text{AO}}∕R^{\text{AO}}=0.99$.Reuse & Permissions

Figure 4

Phase diagram for rigid and semiflexible rods calculated using the SPTA theory. The boundary between the isotropic- (I) nematic (N) two-phase region and the region where a single phase is stable is indicated by the thick dashed line for semiflexible rods and thick full lines for rigid rods. Tie lines between the coexisting phases are shown by thin lines. For the flexible particle the ratio of the contour length to persistence length is $L∕P=0.4$. The phase diagram was calculated using $\delta =84$ and $q=2.2$. The polymer concentration is defined as follows: ${\varphi }_{\text{polymer}}=\rho (4\pi R_g^3∕3)$.Reuse & Permissions

Figure 5

Phase diagram for a mixture of $fd$ virus and Dextran ($\text{MW}\mathrm{500\hspace{0.17em}000}$, $R_g=176\mathrm{\AA }$ or $R^{\text{AO}}=199\mathrm{\AA }$) at $100\text{mM}$ ionic strength. The measured points indicate the rod and polymer concentrations of the coexisting isotropic and nematic phases. The full line is a guide to the eye indicating the two-phase region. Tie lines are indicated by thin full lines. The SPTA and SVTA predictions are indicated by the dotted lines and dashed lines, respectively.Reuse & Permissions

Figure 6

Phase diagrams of a mixture of $fd$ virus and Dextran polymer ($\text{MW}\mathrm{150\hspace{0.17em}000}$, $R_g=111\mathrm{\AA }$ or $R^{\text{AO}}=125\mathrm{\AA }$) at $50\text{mM}$, $100\text{mM}$, and $200\text{mM}$ ionic strength. Coexisting phases are indicated by open circles while the full line is an eye guide separating two-phase region from isotropic and nematic phases. The predictions of the SPTA and SVTA theories are indicated with dashed and dotted lines, respectively. The polymer concentration is defined as follows: ${\varphi }_{\text{polymer}}=\rho (4\pi R_g^3∕3)$.Reuse & Permissions

Figure 7

Measurements of the order parameter of the nematic phase in coexistence with the isotropic phase for a mixture of $fd$ (rod) and Dextran ($\text{MW}\mathrm{500\hspace{0.17em}000}$, polymer) at $100\text{mM}$ ionic strength. Order parameter $\left(S\right)$ is graphed as a function of $fd$ concentration (a) and Dextran concentration (b) for the coexisting nematic concentrations shown in (c). The order parameter is double valued in (b) because along the nematic branch of the coexistence curve there are two different rod concentrations with the same polymer concentration as shown in (c). Data in (c) are the same as those shown in Fig. 5. Dashed line in (a) indicates the theoretical dependence of the order parameter on the concentration of rods as obtained using scaled particle theory. This relationship agrees well with experimental data for $fd$ at high ionic strength using x-ray scattering [28]. Arrows in (b) and (c) indicate the direction of increasing $fd$ concentration. Below ${\varphi }_{\text{polymer}}\sim 0.2$ the nematic $fd$ concentration is essentially constant.Reuse & Permissions

Figure 8

The order parameter of the nematic phase of the $fd∕\text{Dextran}$ ($\text{MW}\mathrm{500\hspace{0.17em}000}$) mixture at $33\text{mg}∕\text{ml}$ $fd$ and $100\text{mM}$ ionic strength as a function of increasing polymer concentration. The horizontal line drawn is a guide to the eye showing the independence of the nematic order parameter with polymer concentration. The vertical line indicates the location of the nematic-isotropic transition.Reuse & Permissions