Characterization of orientation correlation kinetics: chiral-mesophase domains in suspensions charged DNA-rods

Bacteriophage DNA fd-rods are long and stiff rod-like particles which are known to exhibit a rich equilibrium phase behavior. Due to their helical molecular structure, they form the stable chiral nematic (N*) mesophases. Very little is known about the kinetics of forming various phases with orientations. The present study addresses the kinetics of chiral-mesophases and N*-phase, by using a novel image-time correlation technique. Instead of correlating time-lapsed real-space microscopy images, the corresponding Fourier images are shown for time-correlated averaged orientations. This allows to unambiguously distinguish to detect the temporal evolution of orientations on different length scales, such as domain sizes (depending on their relative orientations), and the chiral pitch within the domains. Kinetic features are qualitatively interpreted in terms of replica symmetry breaking of elastic deformations in the orthogonal directional axes of chiral-mesophase domains, as well by the average twist angle and the order parameter. This work can be interesting for characterizing other types of charged rods, mimicking super-cooled liquids and orientation glasses.


Introduction
Among many biological systems exhibiting enzymatic cleavages, the DNA replication is well played by an initiative role with gene protein functions in the change of shapes and forms The relations between structural and functional filamentous bacteriophages (so called Ff coliphages) are extensively reviewed by Rasched and Oberer in 1986 [1], where the genetic and physical maps of DNA bacteriophage fd are depicted in great detail with 10 featuring gene proteins. In particular, the regulation of bacteriophage DNA fd is initiated by a gene 2 protein 2 (g2p), a male-specific infection androphage for enzymatic activity and the duplex DNA replication with polymerase (holoenzyme) that converts the single-stranded super-coiled DNA to unwind fd-replicated forms [2]. This is mainly done by extracellular complex gene-5 protein (g5p) dimers forming helicase conformation [3], a key function allowing a weak interaction for the specific reversible binding affinity of the enzyme to its cleavage site. Nevertheless, there are few unclear functions and roles of gene proteins (for instance, gXp and the g4p-g1p morphogenesis towards the intergenetic region (IR) form). This ambiguity can be then interesting for a thermodynamic system with degrees of freedom in bulk motions of polar solvents. However, the gap of understanding single bacteriophage DNA strands towards collective behaviors of forming stable phases is still far challenging task to be exploited.
Up to now, most fibrous structures that may exist in the domains, consisting aligned fibers or irregular anisotropic particles, for para-crystals or amorphous morphologies [4], are probed by diffraction and scattering methods (introduced by A. Guinier). Protein mixtures are examples of natural systems that mimic rich phase behavior similar to colloids [5], as well fluctuations of orientational glass (found for a small protein levoglucose), which could be distinguished from the structural glass [6]: Typically, when the small domains are formed by can be made between the growth kinetics on several length scales, thus distinguishing, for example, the growth of domain size and the temporal development of the chiral pitch.

Concentration-dependent orientations of twisted chiral-nematic N * -domains
The optical morphologies of collective orientations for aligned charged DNA rods are collected from the birefringence under crossed polarizers, resulting in the degree of optical anisotropy. The order parameter is then estimated (or calculated) by the average orientations in long waiting times (typically as 135-240 h). In practice, acquiring the whole data of 'randomly' slow dynamics leading to the equilibrium is quite demanding in both real-and the corresponding spectral intensity in Fourier-space. For the characterization, polarized optical morphologies are obtained, for varying the concentration of DNA-rods, shown in figure 1, at a long waiting time of 135 hours and more. In an increase of the concentration, the isotropic-nematic coexistent N-phase, a chiralnematic N * , and an X-pattern, and the helical domain (HD) phase are formed. The corresponding FTs of polarized optical morphologies are then obtained (by a program) from converting systematically fast Fourier transform (FFT) images in time, which is shown in figure 2, at a given low buffer solution (0.032 mM Tris/HCl). By varying the concentration of DNA rods, the center zone of the FT represents orientational distributions of N * -domains that are distinguished by the parallel and perpendicular component, q D,∥ and perpendicular q D,⊥ , slightly tilted in the horizontal and vertical axes in FTs, respectively (see figures 2 and 3). As it can be seen in overall FTs, the slight tilt of two orthogonal axes in the FT peaks is originated by existing local orientations of N *domains, and collectively averaged for the concentration-dependent orientations (see the supplementary movie data in figure 2 available online at stacks.iop.org/JPCO/6/015001/mmedia): Below the N-N * transition concentration (1.8 mg/ml), only the center peak is shown in FT, without chiral-nematic N * -domains. However, at higher concentrations, more profound changes of orientations occur in FT spectral distributions in time: figure 3(a) shows the example of intensity distribution profiles in FTs: for the concentration of DNA rods (10.5 mg/ml) as the X-HD transition at a waiting time of t W ∼ 30 h, while the comparison of FTs for two high concentrations (10.5 mg/ml and 14 mg/ml) is shown in figure 3(b) at a longer waiting time (t W ∼ 100 h). Here, three distinguishable FT spacings are obtained in length scales corresponding to the spectral distances of chiralnematic N * -domains; two orthogonal axes in the center zone of FTs are decomposed as the parallel q D,∥ and perpendicular q D,⊥ components, as well as the optical pitch inside the N * -domains as q P . Moreover, visible differences of intensity distributions in FT lobes appearing between the q D,∥ and q D,⊥ for all the concentrations, above the N-N * transition (figures 2 and 4), towards the equilibrium.
The most drastic changes in FTs are captured in the middle concentrations of the X-pattern (see figure 4(c) at 5.4 mg/ml in times), occurred as a critical concentration at low ionic strengths [22]. Also, the local orientational intensity distribution profiles show that both axes contribute to unique behaviors between these two orthogonal directions of N * -domains, q D,∥ and q D,⊥ , by varying the concentration of DNA rods (see the supplementary data movies, Movies F-I in figure 2). Temporal changes of the orientation distributions of the N * -domains in the FTs of figure 4, show that the N * -domains with optical pitch vary slowly over time (135-240h). By further increasing the concentration of DNA rods in the X-pattern approaching the X-HD transition (in the comparison of 10.5 mg/ml (Movie K) and 14 mg/ml (Movie L)), half-sized reduced domains appear, resulting in an FT spacing that becomes twice as large (figure 4). Further different orientation distributions of the critical concentrations (near the X-pattern) are provided for longer waiting times, t W = 200-220 h, between the N * -X transition (at 4.7 mg/ml) and the X-pattern (5.4 mg/ml) (see figure 7).

Kinetics of orientation distribution of N * -domain, image-time correlation in FT
The particular interest is focused to demonstrate the long-time equilibriated orientation distributions via imagetime correlation (ITC) in FTs, performed in-house automated program that is rigorously employed for the conversion of real images in morphology to FTs, followed by the calculations of ITCs for spectral intensity distributions. Image-time correlation (ITC) spectroscopy is then used to extract characteristics in the FT images: Compared to the ITC in real space [22], the ITC in FT turns out to be a rather direct way of visualizing the average orientational motions of N * -domains from the temporal changes of spectral intensity distributions. As previously found at a low ionic strength, the equilibrium phases below the critical value (at 1.2mM Tris/HCl buffer) [21] carry out the following features: (i) N * -phase is stabilized by oriented chiral-nematic N * -domains that appear orthogonally together with the N * optical pitch (stripes in the N * domains) inside domains. The corresponding FT of the N * phase (2.6 mg/ml) is shown in figure 4(a) for the averages distributions in orientations of overall N * -domains, in the center FTs, compared to a more pronounced stable N * phase at a higher concentration (3.8 mg/ml) in figure 4(b). (ii) However, above the N * phase (5.4 mg/ml), in an increase of the concentration, a unique phase of X-pattern occurs such that the N * -X pattern transition has notably different intensity distribution; the reflection symmetry is broken in the axes of N * -domain perpendicular, q D,⊥ , shown independently as the diverging intensity profiles in FTs (see figure 4(c)). On the contrary, the parallel component q D,∥ appears to be localized as the spherical distribution. (iii) The average size of the spectral domains, 〈q D 〉, increases with an increase of the concentration of DNA rods due to the smaller sizes of domains seen in real space. Also, the X-pattern (in figure 4(d)) at a higher concentration, has shown twice larger spacing in FTs, compared to a chiral-neamtic N * -phase (in figure 4(a)) with visible differences between q D,∥ and q D,⊥ . (iv) Furthermore, a clear decomposition of Fourier component is carried out in the orientations, corresponding to the N * -domain as parallel and perpendicular in the center zone of intensity lobes. Such features are illustrated in figure 3(b) (see the Movie K and Movie L in figure 2), for a comparison of two high concentrations of the X-pattern (10.5 mg/ml) and X-HD transition (14 mg/ml), respectively. The intriguing observation is then well interplayed between the N * -domains and the chiral pitch within the domains (see the right panel of in figure 3(a)) via the intensity distributions in FTs. This indicates the orientations of N * -domains are indeed affected by the elastic deformations, leading to rather sharp transitions near the N * -X pattern and X-HD concentration, found as the RSB concentration for a symmetry breaking in orientations [22]. A more detailed description of the elastic properties of N * -domains near the X pattern is provided in the following section.
The quantification of morphological changes in time-lapsed images are done as follows: the twodimensional image matrix is converted to the numbers of all 2D array intensity values for each pixel [27]. The image-time correlation function is then defined by the instantaneous transmitted intensity, I(t) detected by a given pixel of the CCD camera. For the time traces recorded for all these pixels, the image-time correlation function CV (t) is defined as, where V indicates the 'video', or time-lapsed images, and the brackets 〈 L 〉 denote the averaging of whole field of views in the CCD camera pixels at 2D (i, j) matrix indices. Each individual image at a time trace is used to construct an image correlation function, depending on the application, such that the region of interest in the square (e.g, 512 × 512) pixels, performed for various other systems [27][28][29]. Here, the application of ITCs in FTs is particularly aimed to obtain the collective orientation degrees of freedom for charged DNA rods observed in slow times and the effective concentrationdependent order parameter in bulk.   kinetic fractions of orientational distribution of N * -domains are extracted by the fits. The fitting function of the ITC in FTs is chosen here as a single mode decay function, as C θ ∼ A e −Γ t + B, in terms of the three characteristic parameters, defined as the amplitude A ∼ S, the background B ∼ q D , and the decay rate Γ ∼ θ tw , interpreted as the order parameter, N * -domain size, and twist angle, respectively. Here, q D , θ tw , and τ indicate the N * -domain size (q D ), twist angle (θ tw ), and the lag (or delay) time (τ) of waiting, respectively. The results of physical observation for overall changes are then shown in figure 5, with the average coherence for orientations analyzed by an image-time correlation (ITC) function, C θ (q D , θ tw , τ), obtained for a long measuring time: The performance of ITC function in FTs is shown by varying the concentrations of DNA rods (1.8 mg/ml, 2.6 mg/ ml, 3.5 mg/ml, 3.8 mg/ml, 5.3 mg/ml, 5.4 mg/ml, 10.5 mg/ml, and 14 mg/ml), and the delay time (τ ∼ 120 h, 60 h, 40 h and 20 h). The image-time correlation functions of Fourier transformed images are related to the elastic motions of N * -domains. ITCs in FTs perform a single exponential decay function, except for the local oscillatory behaviors and low concentrations with large intensity fluctuations. Figure 6 shows C θ (q D , θ tw , τ) with different waiting times of t W ∼ 0 h, 62 h, 80 h and 100 h, as well a delay time (or a lag time), τ = t − t W for the comparable equilibrium time, t eq ∼ 86 h in previous observations [8,9].
Below the lower N * -domains in the concentrations of 1.8 mg/ml and 2.6 mg/ml, slightly increased correlation is obtained, due to the presence of nematic N-domains compared to the chiral-nematic N * -domains. This can be partly understood by the instability, existing thermal fluctuations near the N-N * transitions. In contrast, ITCs in FTs decrease at higher concentrations, shown with 'perturbing' oscillation peaks in longer time window, which is originated by the slow process of varying intensity for the elastic motions of fluctuating N *domains in the collective orientation distributions. The ITCs in FTs are then fitted by a single exponential decay function except for the oscillatory behaviors at longer times and low concentrations (at large intensity fluctuations). Based on the elastic orientations of N * -domains, there are no visible changes in orientations at longer times, above the equilibrium time (t > t eq ), however larger variations of correlations exist in the earlier time (t < t eq ). Thus, this implies that reaching an equilibrium time is indeed important to determine the thermodynamics for a lyotropic system.

Elastic kink of N * -domains near the X-pattern (a chiral glass)
When the (network) glasses consisting rigidity of the molecules in variations of the soft phonon mode and discrete glassy percolation [30], the optical contrast can be revealed by the anisotropy of crystallinity and molecular orientations. In particular, the optical birefringence and elastic moduli are exhibited by the rod-like molecules of the rigid core, embedded in an elastic medium [31,32]. However, when the core of particle is less rigid than the outer structure, its thermal fluctuations vary by some extent and deviate from the scaling laws. In addition, a computational algorithm of generic rigidity is limited to predict the order parameter, only in 2D percolation, mapping to the heat capacity, for the free energy distributions of bond and site percolation in the glassy system. There are no yet reliable theories in 3D bulk properties [31,32]. Thus, it is worthwhile to evaluate the RSB that experimentally observed in X-pattern, as a chiral glass resembling 3D orientation glass [22]. The direct evidence of physical observation for the replica symmetry breaking (RSB) is shown by the mechanical kinks randomly occurred in the fast time scale, in the middle concentrations (of the X-pattern) [21]. The rigorous measurements of orientations in FTs are necessary to provide a long continuation of time, without loss of information, to observe the whole processes. The sharp kinetic changes of critical concentrations (see the figure 7(a)) are captured for the comparison of concentrations, in 4.7mg/ml (N * phase) and 5.4 mg/ml (N * -X pattern) at longer waiting times (up to t W = 220 h): Sensitive changes of correlation functions are provided in figure 7(b) for different longer waiting times in both concentrations of DNA rods, where the N * -domains become unstable towards the X-pattern, as well at the N * -X pattern transition concentration (5.4 mg/ml).
As a novel finding from the results of ITC in FTs, the decoupling of orientation axes in N * -domains is obtained such that the two orthogonal axes of N * -domains are captured not only in the direction ofq D and  q D , but also a divergence of length scale, in the component ofq D and the relevant optical pitch q P in the X-pattern. This result is well-agreed with the fact that replica symmetry breaking (RSB) occurred in the middleconcentration of DNA rods (in 4-6 mg/ml), shown in figure 8, as the consequence of an effective decoupling betweenq D and  q D , for varying the concentrations and different waiting times. The more vivid realization of RSB is found at a middle concentration of DNA rods, 5.4 mg/ml, which is also the concentration where the mechanical kink appeared randomly in the real space, for a short period of time, before reaching to an equilibrium [9,21,22]. This is originated by the density being compensated by the orientations of chiral-nematic N * -domains, at the N * -X transition concentration, and balanced by two orthogonal orientation axes of chiralmesophase domains. However, further increase of the density (at a higher rod-concentration), the replicas of smaller helical domains (formed in the X-HD transition) occur, similar to the optical morphology of larger scale N * -domains for lower concentration in an equilibrium phase [22], in which now the density of charged DNA rods overcomes against their orientations. According to above observations, the driving mechanisms of RSB are suggested as follows: A sudden reverse of cluster (or domains) may occur in the development of orientation orders, similarly forming a microscopic lattice at the (thermotropic) glass-like transitions ( figure 13 of [16]). The intensity fluctuations of orientations are then a precursor to such transitions steady until the actual development of cluster occurs in a finite space (e.g. a sudden jump or mechanical kink), followed by a weak time dependence for a long period of time (likewise the behavior of effective temperature-time diagram in figure 14 of [16]). In addition, the reason for replica symmetry breaking (RSB) occurring in the middle concentration (between above the N * -X-pattern and below the X-HD transition), is resulted by a diminishing of N * -domains in an increase of DNA rod concentration. Whether this can be relevant with an unusual isotope effect, observed in a hightemperature superconductor [33] would be an open concern; for instance, whether the X-pattern is a coexistent state between the partially molten state of N * -domains against disordered (in isotropic) and the ordered as out of the plane (homeotropic-nematic) state or not. More details of the equilibrium phase diagram formed in stable phases of charged DNA rods are shown different at the higher concentration (14 mg/ml) for higher ionic Note that there are sharp differences in the middle concentrations of DNA rods (in 4.7-6 mg/ml), depending on the characteristic time for t < t eq , t ∼ t eq , and t > t eq , respectively. strengths, which is discussed compared to below and near the critical ionic strength (of 1.2 mM) for the longtime kinetic arrests [21,22].

Characteristics of N * -domains: Twist angle, domain size and order parameter in concentrations
As shown before, the kinetics of orientation distribution in the suspensions of charged DNA rods are shown by the effective parameters as long waiting times and varied concentration in the lyotropic system. The characteristic crossover in orientations occurs at a concentration of DNA rods for 4-6 mg/ml (see figure 8), by the amplitude of order parameter, S and the averaged background value that obtained from the inverse of N *domain size, 〈q D 〉. Also, the findings are in good agreement with the result in a real space, where the kinetics of orientation distribution of N * -domains are taken at a typical equilibrium time of t W ∼ 80 h [22]. Therefore, when the duration time is similar or larger than the equilibrium time (see t ∼ t eq or t > t eq in figure 8), rather significant changes are seen in the critical concentration regimes. However, for the shorter duration time, at t < t eq , the critical concentrations are mostly hindered by the apparent changes, at high concentrations. The resulting characteristics of featured parameters for ITC in FTs are plotted in figure 9 as a function of concentration: The simple illustrations of systematic increase in the concentration of charged DNA rods are shown in figure 9(a), at the lowest ionic strength (of 0.032 mM) exhibiting the characteristic changes of orientation distribution in FTs, for the N-N * transition, N * phase, N * -X pattern, X-pattern, and X-HD transition phase. For the low concentration of N-N * transition, the N * -domains show dominant peaks in an increase of the concentration, while at a high concentration of X-HD transition, above the RSB, chiralmesophase domains are being half-sized smaller in real-size, carrying out twice larger outer intensity lobes of pitches (see the left illustrations of figure 9(a)).
The decays of ITC function in FTs, C θ (q D , θ tw , τ), are presented by the twist angles in time correlations, θ tw , in figure 9(b). The inverse of chiral-mesophase domains, 〈q D 〉, and the order parameter, S, are presented in Fig. 9(c), and figures 9(d), (e), respectively obtained from the fittings. Due to the finite Fourier component analysis, the background value is seen for the stationary value corresponding to the N * -domains as 〈q D 〉. In addition, the average twist angle, 〈θ tw 〉 is converted from the decay constant of ITC in FTs, as the multiplication of a complete 2 π turn (see figure 9(b)) for the sum of possible spherical intensities. The values of concentrationdependent averaged order parameter, 〈S〉, in figures 9(d) and (e), a.e. estimated separately from the effective Debye screening length and dissociation constants for the release of condensed ions at a given ionic strength. Thus, in the results of figure 9, clearly visible gaps are obtained from the above characteristic parameters, where the middle-concentration is identified as the RSB (notified as the pink region in figure 9). A special note is that the monotonically decreased reduced order parameter is found before the occurrence of RSB concentration, while above in the concentration of 10 mg/ml, relatively large spread of order parameters are observed, depending on both concentration and lag-times in figures 9(d) and (e). This hints that still local orientations of smaller helical domains may possibly to progress microscopically in a hierarchical chiral-mesophases.

Discussion and conclusion
We have shown here the collective changes of orientations approaching to the equilibrium phase diagram of charged DNA rods at low ionic strengths by the average orientational distribution of N * -domains over a long time shown in FTs, for various stable chiral-mesophases and glasses. One of the most unique observations is the X-pattern in FTs as the diverging domains near the RSB. The overall orientations of charged DNA rods are responded as an increase of DNA-rod concentration, by following reasons: (i) There is an asymmetric transition of a non-monotonic N-N * line, in the phase diagram above the upper binodal line (I-N transition) and below the X-pattern. This asymmetry becomes symmetric, in the N * -X transition phase boundary line with a variation of ionic strength for two chiral-mesophases (in the X-pattern and helical domains, HDs). This is now explained and clarified by the decoupling mechanism of two independent degrees of freedom in the orientational axes of q D and  q D in FTs. (ii) Below the critical ionic strength, pronounced chirality expands as the concentration increases, such that the most pronounced stable chiral-nematic N * phase at the N * -X transition. This is relevant with the intrinsic microscopic relaxations in the lower binodal that as far slower than the reorientation of an aligned planar nematic phase at higher ionic strengths [21,22]. (iii) The increase of FT spectral spacing corresponds rigorously to a decrease of the N * -domain size as the replica of half-sized twisted helical domains at higher concentrations (at the HD-phase) near the X-pattern, above the N * -phase boundary. Also near the critical ionic strength (confirmed independently as 1.2mM), found in [21,22], the long-time kinetic arrests (LTKA1 and LTKA2) in the equilibrium phase behaviors at low ionic strengths, have been observed smaller center peaks, due to the fact that larger scales of domains are accompanied by scattered intensity fluctuations of chiral-mesophases [21]. (iv) On the contrary, above the critical ionic strength, the coexistence of I-N is located at a narrow gap for different long-time kinetic arrest (LTKA3) of N-N * phase, which shows bright peaks in the center zone in FTs for two emerging phases of N-N * and I-N transitions in the equilibrium. Therefore, the current system demonstrates the macroscopic behavior of orientation dynamics resembling the slow dynamics of orientation glasses found in metallic alloys (see figure 5 in [18]) of rigid rod-shape molecules. Furthermore, there are two effective parameters for a lyotropic system: The first parameter of collective motions for thees charged DNA rods is the concentration-dependent orientation distribution revealing the intermediate concentration of the X-pattern between N * -X and X-HD phase boundaries at a low ionic strength, as a unique replica symmetry breaking (RSB) as a chiral glass [22]. This has been evidently highlighted here by the Fourier transformed images, with the effective decoupling of orientation axes inq D and  q D . This is fundamentally responsible to the RSB of chiral-mesophase domains, for varying both concentrations and waiting times, by means of the image-time correlation in FTs. As the result, the characterization of domain formation are determined by the twist angles; overall orientations of N * -domains that enable to predict order parameter. Moreover, the decoupling and divergence of orientations for N * -domains inq D , distinct from the  q D , are all carried out in featured parameters for the orientation distribution. More intriguingly, the replica of smaller helical domains (HDs) forms again, by upon increasing the concentration (after the RSB concentration), and continuous changes in orientation evolving to a local symmetry breaking within the direction of  q D , in the concentration (14 mg/ml) of X-HD transition (see the Movie L in figures 2 and 9(a)).
The second effective parameter in realization of the current system is the time to reach an equilibrium state, for depicting the unique concentration of RSB, in a similar way to define the 'critical isotherm' (see figure 30 in [7]), discussed in thermodynamics for both the order parameter and the microscopic stress of elastic deformation. The microscopic orders are essential for orientational anomalies in the vicinity of transitions, occasionally accompanied by the elastic waves (resembling cavity loops observed slowly over time as a chiral glass in [22]). This suggests then the X-pattern (at given low ionic strengths) is formed possibly by a rotational diffusion and affected by the annihilation of twisted chiral-nematic N * -domains, which are reoriented at long waiting times in equilibrium, effectively by pronounced perpendicular motions of thick electric double layers, for low ionic strengths. This may be understood as the sufficiently slower cooling in the case of supercooled liquids, where most charged particles and ions exhibit often no crystallization by long-ranged repulsive interactions in the equilibrium thermodynamic system. On the contrary, at a higher ionic strength, above the critical value (1.2 mM), relatively fast diffusion along the spatial extent of the DNA rod direction for the overall kinetics. Thus, the ionic strength-dependent electric double layers for charged DNA rods are underlying mechanism for given waiting times, characteristic reduced time, promoting enhanced contrast in such rich phase behaviors, including the RSB. Therefore, in conclusion, the results of image-time correlation (ITC) of Fourier transformed images, evidently facilitate the investigation of orientation kinetics of N * -domains, driven by the ambient dissociation/association from the condensed ions, cooperated by mobile diffusive ions surrounding interacting charged DNA rods in the equilibrium. Finally, the work provides not only the useful application of ITCs in FTs, but also a possible driving mechanism of RSB in the orientation of charged DNA rods, for the lyotropic system. The fundamental physics for the long time it takes for crystallization to occur, underlies most probably the same principles as for other systems before phase separation occurs, like other types of charged systems, supercooled liquids, and glasses. 7. Experimental details 7.1. Sample preparation and optical measurements of birefringent charged DNA rods Suspensions of charged DNA rods are prepared from the concentrated stock of DNA viruses (fd) at an ionic strength of 20 mM and dialyzed against the buffer solution of a lower ionic strength (0.032 mM Tris/HCl buffer) for 2 consecutive days using the Slide-A-Lyzer Dialysis Cassette (Extra Strength, 10,000 MWCO, 0.5-3 ml capacity) membrane cassette purchased from Thermo scientific Inc. (Lot.No LL151432). The buffer is exchanged for a fresh new one after 24 hours for further purification of both the solvents and the sample. The concentrated suspension of DNA viruses (fd) is then prepared by a Donann equilibrium with a buffer solution. The concentrations of DNA viruses are measured by optical density (OD) at a wavelength of 269 nm to weigh the mass of W g for the very small amount (10 μl) using a UV/Vis spectrometer (Cary, 50 Bio, Win UV scan Application, Varian, Australia, Pty, Ltd). The fd concentration is then obtained by the relation , where the factor of 0.260 42 ∼ 1/3.84 is considered for the extinction (absorption) coefficient of a single fd virus as 3.84. For lower ionic strengths, the same procedures are followed to measure the concentration of DNA suspensions by repeating the sampling process in 5 times. The dissociation constant and an effective diameter for the ionic strength of 0.032 mM Tris/HCl buffer are considered as 643 e − , and ∼292 nm, respectively. The optical measurements are done by a commercially available Quartz transparent cylinder cuvette with a thickness of 1 mm and a diameter of 20 mm (120 QS 1 mm, Hellma Precision in Spectro-Optics) is used to contain an approximately 380 μl sample volume. The sample holder is placed between two crossed polarizer sheets to capture polarized images of the birefringent orientation texture. In addition, the large field of view is