Figure 1

(a) A tactoid is defined by the following related parameters: ($r_1$, $r_2$) or ($R$, $\alpha$). The tactoid is considered to be the volume created by rotating the region of two overlapping circles. The major and minor axes of the overlapping region are defined as $r_1$ and $r_2$, respectively. The radius of the overlapping circles is given as $R$, while $\alpha$ represents the angle corresponding to half the arclength of the overlapping region. The relations between these parameters are given in Eqs. (1, 2). (b) A group of tactoids are shown with their defining circles. The overlapping regions are seen to clearly bound the tactoids, suggesting that this characterization accurately captures the defining features of the tactoid.Reuse & Permissions

Figure 2

The specific retardance of F-actin is plotted as a function of concentration with varying average filament lengths. F-actin solutions with average filament lengths of $10.7\mathrm{\mu }\mathrm{m}$ $(◻)$, $3.9\mathrm{\mu }\mathrm{m}$ $(엯)$, $2.5\mathrm{\mu }\mathrm{m}$ $(▵)$, and $1.0\mathrm{\mu }\mathrm{m}$ $(◇)$ are shown. The dashed lines are guides for the eye. Tactoids are only seen for solutions along the curve farthest to the right. Shown below the plot are two representative images of tactoid formation: nematic tactoids in an isotropic background (bottom left) and isotropic tactoids in a nematic background, sometimes referred to as atactoids [29] (bottom right). Scale bars are $50\mathrm{\mu }\mathrm{m}$.Reuse & Permissions

Figure 3

Different orientations of the director field under crossed polarizers leads to an optical effect that makes the tactoids appear asymmetric. Scale bars are $25\mathrm{\mu }\mathrm{m}$. (a) A tactoid is shown rotated through various angles. The inset in each frame shows the tactoid in relation to the polarizers. The brightest regions correspond to an average alignment $45°$ from the polarizers. Dark regions represent an average alignment along either polarizer or regions with no average alignment. The dark regions in the tactoid are shown to migrate as the tactoid is rotated with respect to the polarizers, corresponding always with the regions where the director field is aligned along one of the polarizers. This also confirms that the director field is bipolar. (b) The tactoid at $15°$ is enlarged and overlaid with a bipolar director field. (c) A diagram representing the filaments inside of a nematic tactoid. Individual filaments are not perfectly aligned, but the average direction corresponds to a field as shown in (b). The diagram is not drawn to scale. The actual filaments are shorter and thinner, in addition to being many times more numerous than depicted.Reuse & Permissions

Figure 4

Tactoids are shown to grow through a process of nucleation, growth, and coalescence in a $10.8\mathrm{mg}∕\mathrm{ml}$ solution with an average filament length of $1.3\mathrm{\mu }\mathrm{m}$. The scale bars are $25\mathrm{\mu }\mathrm{m}$ and the time format is given in h:min. (a) A nematic tactoid grows in isolation over a period of $9\mathrm{h}$. (b) During the growth process neighboring tactoids can be seen to coalesce into a single tactoid. The resulting product retains the familiar shape and characteristics of a tactoid. It is interesting to note that the process of coalescence does not seem to impact either the rate of growth or the final size of the tactoid.Reuse & Permissions

Figure 5

The length (a) and width (b) of three nucleating tactoids were measured using time-lapse microscopy. All three tactoids reached approximately the same final size despite nucleating at different times. The tactoids that nucleated later grew much faster, until they caught up with those that nucleated earlier in the same sample. No further growth was seen after $\sim 1200\min$. The inset shows a plot of the aspect ratio with respect to time for one of the tactoids.Reuse & Permissions

Figure 6

A capillary seen under $4\times$ magnification using crossed polarizers. (a) Nucleation has occurred in the capillary. There are only a few tactoids present, and all are approximately the same size. (b) The same capillary in (a) has been sonicated and allowed to relax for $\sim 100\mathrm{h}$. The solution is again in a steady state but now exhibits a large range of sizes, in addition to having a much greater density of tactoids.Reuse & Permissions

Figure 7

Nematic tactoids in an isotropic background were measured in a capillary that was shaken and allowed to settle. The sample contained a $10.8\mathrm{mg}∕\mathrm{ml}$ actin solution with $\ell =1.2\mathrm{\mu }\mathrm{m}$. (a) Following the convention of [35, 36] the graph shows the tactoid aspect ratio plotted against the length of their long axis. The solid line is identical to the fit discussed in (b), but plotted in terms of aspect ratio against long axis. (b) The same data from above is converted to the convention of [38, 39] using Eqs. (1, 2) and plotted along with a solid line fitted using Eq. (A6), which is explained in the Appendix. The fitting parameters are $K_1∕\sigma =1.92\pm 0.57\mathrm{\mu }\mathrm{m}$ and $K_3∕\sigma =103.4\pm 8.6\mathrm{\mu }\mathrm{m}$, where $K_1$ and $K_3$ are the splay and bending elastic constants and $\sigma$ is the surface tension. The general trend of the data is consistent with the numerical work of both treatments, though an appreciable scatter in the data suggests that the tactoid’s size and shape are not tightly controlled.Reuse & Permissions

Figure 8

A solution of $10.8\mathrm{mg}∕\mathrm{ml}$ F-actin with an average filament length of $1.4\mathrm{\mu }\mathrm{m}$ underwent the process of spinodal decomposition. The images were captured using crossed polarizers oriented horizontally and vertically under $4\times$ magnification, and the time format is given as h:min. (a) The initial state of the solution showed almost uniform alignment within the capillary. This alignment was a residual effect of injecting the solution into the capillary directly after polymerization. (b) Almost immediately (within minutes) the solution began to show a breakdown in the initial alignment. What looked like small pockets of isotropic and nematic domains appeared. (c) After $7\mathrm{h}$ the solution showed larger isotropic and nematic regions, though none showed the distinctive tactoid shape. The kinetics at this point slowed down considerably, showing very little change over a few hours. (d) Finally after almost a full day, the solution settled into a metastable state with both isotropic and nematic tactoids present in a weakly aligned nematic background.Reuse & Permissions

Figure 9

The characteristic length and width of the spinodal regions were determined by taking an image (a) and performing a two-dimensional fast Fourier transform (b). The transform is clearly elongated at an angle of roughly $50°$ from the horizontal. The average intensity was calculated as a function of distance from the center of the transform within a $30°$ wedge directed along the two major directions. Fits to plots of these average radial intensities show a peak that gradually shifts towards the center of the transform for the length (c) and width (d). The length $(◻)$ and width $(▵)$ wave vectors were determined by the position of this peak. The peak is seen to steadily progress towards the origin, indicating an increasing domain size (e).Reuse & Permissions

Figure 10

Tactoids were prepared in a thin $\left(100\text{−}\mathrm{\mu }\mathrm{m}\right)$ capillary and allowed to grow until they were flattened by the capillary walls. Intensity measurements were recorded for the regions completely filling the capillary space between both walls. Regions well beyond the domain of the tactoid were averaged to calculate the intensity value outside of the tactoid. Each data point represents an average of a number of tactoids. For a true first-order transition we would expect the average intensity to remain constant in both regions. The roughly linear increase shows that the actin concentration of both coexisting domains increase with the average concentration of the initially uniform solution of actin. This result strongly suggests that the system is only in a metastable state.Reuse & Permissions