Figure 1

Isotropic-cholesteric phase boundary as a function of ionic strength for a bare virus ($fd$) and for virus coated with neutral polymer ($fd$-PEG-5k and $fd$-PEG-20k). The lines represent the highest concentration for which the isotropic phase, $I$, is stable (below line), whereas the range of the cholesteric phase, N*, is above each line. Squares and circles indicate the I-N* transition in $fd$ and in $fd$ coated with PEG-5k respectively [8], while triangles refer to the $fd$ virus coated with PEG-20k. The concentration of the I-N* transition for bare $fd$ increases as a function of ionic strength as $1/D_{\mathrm{e}\mathrm{f}\mathrm{f}}$ (solid line), where $D_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective diameter taking into account the electrostatic repulsion between rods at the I-N* transition [11]. $fd$ with grafted PEG shows identical behavior to nongrafted, up to an ionic strength corresponding to a $D_{\mathrm{e}\mathrm{f}\mathrm{f}}$ that matches the size of the stabilizing polymer layer. For a higher amount of added salt, the phase diagram becomes independent of ionic strength, and the $fd$-PEG system behaves as a sterically stabilized suspension. This is schematically represented by the cartoon of a virus with polymers grafted on its surface where $D_{\mathrm{e}\mathrm{f}\mathrm{f}}^{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}}<D_{\mathrm{e}\mathrm{f}\mathrm{f}}^{\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{m}\mathrm{e}\mathrm{r}}$.Reuse & Permissions

Figure 2

Ionic strength dependence of the nematic order parameter of $fd$ virus coated with PEG-20k measured close to the I-N* transition (sample concentrations around $c\sim 9\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{l}$). The order parameter is obtained from birefringence measurements after unwinding the cholesteric phase with a magnetic field. The dashed line is a guide for the eye.Reuse & Permissions

Figure 3

Evolution of the cholesteric pitch ($P$) with the concentration ($c$) of $fd$ virus grafted with PEG-20k, for three different ionic strengths ($I=15$, 60, and 110 mM). Cholesteric pitch was measured from the “fingerprint” texture, as shown in the inset. The sample is contained in a cylindrical glass capillary of diameter 0.7 mm and several cm long. Error bars have been obtained by repeating the same measurement along the full length of the sample. The scaling exponent of the fit to $P\propto c^b$ is indicated for each ionic strength.Reuse & Permissions

Figure 4

Schematic representation of the “corkscrew” model: the chirality is transmitted between viruses by the helical shape (accentuated for illustration) of the whole virus at the micron length scale and not by the helical structure of the protein coat.Reuse & Permissions

Figure 5

Graph of the cholesteric pitch ($P$) versus the concentration ($c$) for mutant viruses of different contour lengths ($L$). The ionic strength is 60 mM. The result of the fit $P=a_{\mathrm{f}\mathrm{i}\mathrm{t}}{c}^b$ indicates the same scaling exponent $b=-1.45$ for all mutants. The inset indicates the dependence of the pitch with the length of the virus at a given concentration: $P\propto a_{\mathrm{f}\mathrm{i}\mathrm{t}}\propto 1/L^{0.25}$. This result contradicts the main existing theories of chirality in liquid crystals which predict $P\propto L^2$ [21, 22].Reuse & Permissions