Supramolecular Organization in Calf-Thymus DNA Solutions under

Article pubs.acs.org/Macromolecules

Supramolecular Organization in Calf-Thymus DNA Solutions under Flow in Dependence with DNA Concentration L. Mónica Bravo-Anaya,*,†,‡,§ E. Rebeca Macías,§ J. Humberto Pérez-López,§ Hélène Galliard,†,‡ Denis C. D. Roux,†,‡ Gabriel Landazuri,§ Francisco Carvajal Ramos,∥ Marguerite Rinaudo,⊥ Frédéric Pignon,†,‡ and J. F. Armando Soltero§ †

LRP, University Grenoble Alpes, F-38000 Grenoble, France LRP, CNRS, F-38000 Grenoble, France § Departamento de Ingeniería Química, Universidad de Guadalajara, Blvd. M. García Barragán #1451, C.P. 44430, Guadalajara, Jalisco, México ∥ CUTonalá, Departamento de Ingenierías, Universidad de Guadalajara, Nuevo Periférico #555 Ejido San José Tatepozco, C.P. 45425, Tonalá, Jalisco, México ⊥ Biomaterials Applications, 6 rue Lesdiguières, 38000 Grenoble, France ‡

S Supporting Information *

ABSTRACT: DNA dynamics and flow properties are of great importance for understanding its functions. DNA is a semiflexible polymer chain characterized by having a large persistence length of around 50 nm and high charge density; DNA chains are interacting efficiently at high concentrations, in dependence of the ionic concentration. In relation with DNA molecular characteristics, it is also known that DNA solutions are able to form liquid crystalline phases over a critical polymer concentration. In this work, the supramolecular organization in calf-thymus DNA solution, with low degree of entanglement, appearing under flow was studied in a wide DNA concentration range from 2 to 10 mg/mL, at a pH of 7.3 and 20 °C. The rheological behavior of the system was studied using steady state flow and oscillatory measurements. Transient regimes were also tested by imposing controlled shear rates on a short time up to steady state. Furthermore, a combination of visual observations and flow birefringence measurements was proposed to reach a better understanding of the obtained rheological behavior. The presence of a shear-induced texture is revealed under flow for the calf-thymus DNA solutions at CDNA> 5 mg/mL and attributed to organized domains of DNA molecules, named in the text as crystalline parts, which are progressively oriented under shear. Finally, at high shear rates (over 100 s−1), it is shown that for the DNA solutions the orientation of these organized DNA domains and connecting chains under flow goes to an anisotropic monodomain.

1. INTRODUCTION

It is worth to recall that from polymers theory there exists an important difference between dilute solutions when coils are isolated and more concentrated solutions when they overlap.13 This overlap onset corresponds to a transition zone between the dilute and the semidilute regimes and is known as the overlap concentration (C*).14,15 At higher concentrations, a second critical concentration, defined as the entanglement concentration, C**, has also been reported for the onset of the

Deoxyribonucleic acid (DNA) is a long linear polyelectrolyte containing nucleotides as their basic units and bearing the hereditary genetic information on living organisms.1−3 DNA dynamics and flow properties are of great importance for understanding its functions as well as cell division.4−6 At high DNA concentrations, molecules having large contour length are entangled, forming a dynamic network leading to an elastic behavior, which could prevent DNA partition after replication during cell division.7,8 Moreover, this biopolymer is considered as a model for the study of the dynamics and macroscopic properties of semirigid macromolecules in solution.9−12 © XXXX American Chemical Society

Received: June 4, 2017 Revised: August 31, 2017

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DOI: 10.1021/acs.macromol.7b01174 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules semidilute regime with entanglements.7,15−18 In a recent paper concerned with rheology on the same DNA sample as used in this work, three concentration domains have been reported for calf-thymus DNA solutions: the dilute domain, where C < C* with C* ≈ 0.23 mg/mL, the semidilute regime without entanglements, between C* and C** with C** ≈ 2.4 mg/mL, and the entangled regime, where C > C**.15 The degree of structural stiffness of polymeric chain can be estimated through its intrinsic persistence length Lp around 50 nm for DNA.14,19 Depending on the external salt content, the effective total persistence length LT = Lp + Le including an electrostatic contribution Le according to Odijk.20,21 Many authors have also extensively studied the effect of electrostatics on the rigidity of the double helix of DNA and its persistence length in dependence of the ionic strength.20−24 As well as other polyelectrolytes in solution and at charged surfaces, DNA properties depend on the intrinsic persistence length Lp, salt concentration, and electrostatic interactions, among others.15,25−27 Additionally, the electrostatic intrachain and interchain interactions are of great importance on chain extension and supramolecular organization.28,29 In polyelectrolyte solutions, due to electrostatic repulsions between charged chains, a local organization is observed in light and small-angle neutrons scattering through the presence of a correlation peak at a low external ionic concentration.30 Local organization of semirigid segments at a critical concentration was proposed by Odijk.14 In specific conditions, attractive electrostatic forces were also suggested by Manning and Odijk.14,20,21,31 Furthermore, semidiluted and concentrated double-stranded DNA solutions have been previously a subject of interest due to their multimolecular aggregational behavior.32 DNA semiflexible polymer chains, characterized by having a large persistence length, interact more efficiently at high concentrations, in dependence of the ionic concentration.33 Signs of long-range attractive forces, which are stronger at low ionic strength, have already been mentioned for mononucleosomal DNA semidilute solutions.32 The pretransitional behavior of mononucleosomal DNA aqueous solutions with concentrations of 50.0 mg/mL up to the onset of the isotropicto-cholesteric transition was studied by Wissenburg et al.,32,33 showing the appearance of DNA aggregation into globules before the onset of the cholesteric phase,34,35 which could apparently break up under shear. Hard et al.36 inferred that DNA sample (with 80−105 base pairs) should start to aggregate at a DNA concentration of 5 mg/mL in 1 M NaCl at room temperature. The formation of these aggregates was observed for a range of DNA sizes (26−118 base pairs). In agreement with the theoretical predictions of Onsager37 and Flory38 for rigid polymers, DNA solutions could separate into two macroscopic phases, i.e., the isotropic and anisotropic phases, at concentrations higher than a critical value. The entrance into the biphasic domain was observed in concentrated solutions (above 188 mg/mL in 0.01 M NaCl) of short DNA fragments, with a total length around 50 nm, corresponding to DNA persistence length.34 According to Strzelecka et al.,34,35 DNA solutions undergo an isotropic− anisotropic phase separation with textures reassembling to nematic or cholesteric mesophase. However, a precholesteric phase has also been proposed for lower DNA concentrations than the critical value, where the anisotropic phase is a weak and slightly twisted nematic phase. 34 Two kinds of structure were considered as precholesteric according to Livolant:39 (i) structures where

molecules align progressively from the isotropic phase to give a nematic structure and which have been described as relaxation processes that appear right after an applied shear and (ii) precholesteric stages, corresponding to the general way for long polymer chains to reach the cholesteric organization. At high concentration of long chains, complex liquid crystalline phases are obtained and are fully described in the literature.40−43 Up to now, several efforts have been undergone in order to investigate and explain the nature of nonlinear rheological behavior of entangled DNA solutions, particularly, the transformation from steady-state flow to the so-called bulk shear inhomogeneities.44 From a mechanical point of view, in the steady-state flow curve, the onset of a stress plateau above a critical shear has been associated with the existence of nonhomogeneous flow.44,45 Jary et al.46 studied the dependence of the steady-state shear stress with shear rate in semidilute T4 DNA solutions, showing the existence of a stress plateau in the most concentrated solutions. More recently, Boukany et al.47,48 reported that DNA solutions at high concentrations and high degrees of entanglement also displayed a nonhomogeneous flow after a certain lag of time when an abrupt shear rate is applied. Authors linked this event to what they call a “collapse” of the entangled network during shear.44,47,48 Finally, Hu et al.49 interpret the inhomogeneous flow as shear induced bands coming from the strong interchain electrostatic interactions present in 0.01 M NaCl solutions. In this paper, the supramolecular organization in entangled calf-thymus DNA solutions under flow is studied in a large DNA concentration range between 2 and 10 mg/mL at pH = 7.3 and at 20 °C. The rheometric parameters obtained from steady state flow measurements combined with oscillatory measurements were formulated in terms of the normalized quantities σ* = σ/Gc and γ̇* = γ̇τc,50 where τc corresponds to the reciprocal of the crossover frequency (ωc) at which G′ = G″ = Gc, allowing identifying the appearance of different flow regions. The conditions at which the onset of a stress plateau appears in flow experiments are revealed in terms of DNA concentration and applied shear rate. Then, the molecular nature of this behavior is reviewed in terms of a nonhomogeneous flow of organized domains. Rheometric measurements in combination with visual observations and flow birefringence measurements are proposed in this work to reach a better understanding of the mechanisms involved in this particular heterogeneous rheological behavior.

2. MATERIALS AND METHODS 2.1. Materials and Solutions Preparation. DNA/buffer solutions were prepared by using calf-thymus DNA samples with a high molecular weight (MW = 6 560 000 g/mol).15 A buffer solution was prepared in order to maintain a selected pH (7.3) using Trizma, C4H12ClNO3 (Tris-HCl at 100 mM), with a purity of 99% and ethylenediaminetetraacetic acid (EDTA at 10 mM), with a purity of 99%. A solution of sodium hydroxide (NaOH, 3 M) was added to obtain the desired pH of 7.3. This buffer was diluted in a 9:1 ratio with HPLC water to get the TE buffer (ionic concentration around 10 mM) used to prepare each DNA solution. The vials were closed and sealed with Parafilm to prevent water evaporation and changes in the concentration. All solutions were stored in a refrigerator at a temperature of 4 °C in order to prevent degradation. Sigma-Aldrich Company supplied all reagents. 2.2. Rheometric Measurements and Visualizations. The rheological behavior of DNA/TE buffer in the DNA concentration range from 2 to 10 mg/mL was studied at 20 °C using different rheometers: DHR-3, ARES-G2, and ARES-22 from TA Instruments Company and a MCR-501 from Anton-Paar Company. Different B


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Macromolecules geometries were used depending on the experiment carried out: (i) a steel cone−plate geometry with a 40 mm diameter and an angle of 0.035 rad was used in DHR3 rheometer; (ii) a steel cone−plate geometry with a 49 mm diameter and an angle of 0.076 rad was employed in the ARES-G2 rheometer to carry on visualizations with TiO2 filaments; (iii) quartz parallel plate−plate geometry with a 38 mm diameter was employed in the ARES-22 rheometer to perform birefringence measurements and birefringence visualizations between the plates along the diameter of the geometry; (iv) quartz plate−plate geometry with a 50 mm diameter was employed with the MCR501 rheometer to observe birefringence under crossed polarizers. Visualizations are integrated through the gap with a wave vector in the direction of the velocity gradient. In order to define the linear viscoelastic regime, oscillatory strain sweeps were carried out at different angular frequency of 0.1, 1, and 10 rad/s in a strain range from 0.01 to 100%. Frequency sweeps were performed at a selected strain within the linear viscoelastic regime of G′ and G″ in a frequency range between 0.01 and 100 rad/s with 5 points per decade. Simple steady state shear measurements were performed at shear rates from 10−3 to 1 000 s−1 with 5 points per decade. The appearance of an inhomogeneous flow during rheological measurements was studied with two visualization techniques. The first one consists on a visualization device of the strain field inside the sample.51,52 For this purpose, after loading the DNA solution between the cone and plate geometry (49 mm diameter and 0.076 rad angle) a small vertical filament made of TiO2 mixed with the DNA solution is introduced by the mean of a hole positioned at 3 mm of the cone edge (cf. Figure 1). The white filament is positioned vertically and touches

Figure 2. (a) Schematic diagram of the setup for performing flow birefringence observations through the middle of the plane. Plate− plate geometry (1), DNA sample (2), parallel white source light illumination (3), and crossed polarizers (4). The images were taken by a coupled device camera for various imposed shear rates (CDD) (5). (b) Schematic diagram of the setup for performing flow birefringence observations through the plane. (1) to (5) have been already described; (6) corresponds to the mirrors used to reflect the light. (c) Schematic diagram of the setup for flow birefringence measurements in a plate−plate geometry: (1) laser, (2) polarizer cube (linear), (3) rotating half-wave plate, (4) beam splitter, (5) circular polarizer, (6) sample detector, (7) linear polarizer, and (8) reference detector. having a diameter of 38 mm and a gap of 1 mm with the TA Instruments Rheometric Series Optical Analysis Module (OAM2). The optical analysis module was used with a laser diode class IIIb, which emits light at a maximum continuous output wave with a power of 8 mW at a wavelength of 670 nm. The laser light is polarized in a ratio 100 to 1 by the polarizer cube and is passed through a rotating half-wave plate. A brushless motor, coupled with a half-wave plate, accomplishes the rotation (400 Hz) and results in a plane-polarized light beam. The light passes through a beam splitter, where a portion of the beam is reflected and subsequently passed through a polarizer and detector, generating a 1600 Hz phase reference signal for the lock in amplifier electronics. The nonreflecting data beam is finally directed to the sample compartment. The laser beam passes vertically through the gap and positioned at a radius of 16 mm from the center of the geometry. The birefringence (Δn) was measured for different imposed shear rates in the steady state. All measurements were performed at 20 °C. 2.4. Crossed-Light Polarized Microscopy. DNA samples with concentrations from 40 to 100 mg/mL were observed with an Olympus BX51 polarizing microscope with an objective ×4 and a Q Imagine Camera or a Leica DMLM polarizing microscope with an objective ×4 and a 3.0 MP MoticaM, between crossed polarizers at room temperature. The samples were placed on a glass slide and covered with a coverslip, previously cleaned with ethanol and carefully washed in distilled water.

Figure 1. Sketch of the monitored mark placed in the gap between the upper cone and the lower plate utilized to detect nonhomogeneous shear flow. the upper cone and the lower plate of the geometrical tools (Figure 1a). When the lower plate starts to rotate, the filament follows the homogeneous shear, as sketched in Figure 1b, and eventually can show an inhomogeneous flow as sketched in Figure 1c. In this last representation, a bulk fracture of the sample is schematized. To avoid the evaporation of the sample during the test, a transparent cover was placed around the geometry in order to saturate the environmental humidity around the sample. 2.3. Flow Birefringence Visualizations and Measurements. Two birefringence visualization techniques were performed in this paper in order to detect the appearance of the birefringence phenomena. The first one (Figure 2a) consists of a rheometer equipped with a quartz plate−plate geometry with a 1 mm gap, placed between crossed polarizers and illuminated by a white light source in the radial direction of the geometry. In order to follow the evolution of the birefringence with the shear rate, several pictures were taken at different imposed shear rates with a coupled device camera (CDD) mounted with an adequate lens.53 The second one (Figure 2b) uses a quartz plate−plate configuration with a 0.4 mm gap, placed between crossed polarizers, one below and another just above the geometry containing the sample. The sample was illuminated vertically by a white source of light reflected by a mirror placed 45° below the first polarizer under the geometry. A second mirror, placed 45° above the upper polarizer, was used to collect the pictures at different imposed shear rates with a coupled device camera (Sony DSLR-A580) with an adapted commercial zoom (EX-Sigma Macro105). Birefringence measurements under shear (Figure 2c) were performed in a rheometer ARES-22 with a plate−plate geometry

3. RESULTS AND DISCUSSION 3.1. Viscoelastic Properties. First, it is worth mentioning that a detailed description of the linear rheology of calf-thymus DNA solutions has been already provided in a recent paper15 and also reported by several authors in different experimental conditions.7,49 The linear viscoelastic moduli of entangled calfthymus DNA solutions over C** (≈2.4 mg/mL) were C


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Macromolecules measured at a fixed deformation γ = 0.02, inside the linear viscoelastic region (LVR). Figure 3 shows the dependence of

Figure 4. Steady shear viscosity η(γ̇) and modulus of the complex viscosity |η*|(ω) obtained from Cox−Merz rule for a DNA solution with a concentration of 10 mg/mL (T = 20 °C). Figure 3. Variation of the storage (G′) and the loss modulus (G″) as a function of the angular frequency for DNA solutions in TE buffer with the following concentrations: 2, 3, 4, 5, 7, and 10 mg/mL (T = 20 °C).

viscosity no longer superimpose. According to the literature, this behavior corresponds to some modifications of the DNA sheared sample. It is known that the Cox−Merz empirical rule works on many experimental measurements, as shown in the paper of Kulicke et al.55 However, it deviates from the quasisuperimposed curves due to changes in the sample such as hydrogen bonds,55 the appearance of structural changes like in the shear banding phenomenon,56−58 or when a strong hydrodynamic change occurs like in wormlike micelles.59 3.2.1. Concentration Dependence. Figure 5 shows the behavior of the shear stress (σ) as a function of the shear rate

G′ and G″ for different DNA solutions in TE buffer in the semidilute regime with entanglements, from 2 to 10 mg/mL, obtained at 20 °C. The longest relaxation time of DNA molecules in solution, τc, corresponds to the reciprocal of the crossover frequency, ωc, at which G′ = G″ = Gc. This characteristic time τc increases with the increase of DNA concentration, as was previously discussed by Teixeira et al.9 For DNA solutions with concentrations higher than 4.0 mg/ mL, it is possible to obtain the value of the plateau modulus Gp, which can be estimated from the value of G′ at the frequency where G″ shows a minimum.44 In a previous paper, it was reported that the characteristic time constant and the crossover plateau modulus follow the subsequent power laws: τc ∼ CDNA2.32 and Gc ∼ CDNA1.5. These exponents were related to the Rouse relaxation time varying as C9/4 for an entanglement strand in the entangled semidilute concentration regime and to the variations imposed by polymer concentration and density of entanglements, respectively.15,54 Moreover, the entanglement molecular weight Me was estimated with Me = CDNART/Gp, with R, CDNA, and T being the ideal gas constant, DNA solution concentration, and temperature, respectively. The number of entanglements is given by Z(CDNA) = Mw/Me, and the Rouse time can be estimated with the relation τR = τc/3Z(CDNA).44,48 These numerical values are summarized in Table 1. In the studied conditions, the degree of entanglement Z remains low in the whole concentration range examined.

Figure 5. Shear stress (σ) as a function of shear rate (γ̇) for calfthymus DNA solutions in TE buffer in the concentration range between 2 and 10 mg/mL, measured at the temperature of 20 °C.

(γ̇) for DNA solutions with concentrations between 2 and 10 mg/mL in TE buffer. Each point was taken after the steady state regime was reached. All DNA solutions, at low shear rates, are in the Newtonian regime up to a critical shear rate γ̇c. At higher shear rates, solutions enter in the non-Newtonian regime,15,60−62 characterized by a shear thinning behavior. For DNA solutions with concentrations higher than 5.0 mg/mL, i.e., 7 and 10 mg/mL, flow curves σ(γ̇) show an apparent stress plateau often present in nonhomogeneous flow. In addition, on 7 and 10 mg/mL DNA solutions, a rapid curvature inversion is observed at ∼1 and 0.3 s−1, respectively. This apparent stress plateau region was also observed by Boukany et al.44 in a linear doublestranded DNA calf-thymus solution (with a molecular weight of 7.5 × 104 base pairs) with a concentration of 10 mg/mL using an aqueous buffer having a pH of 7.9 as solvent and by Jary et

Table 1. Viscoelastic Characteristics of Calf-Thymus DNA Entangled Solutions in TE Buffer CDNA (mg/mL)

ωc (rad/s)

Gc (Pa)

Gp (Pa)

Z

τR (s)

4 5 7 10

0.76 0.40 0.21 0.15

0.97 1.40 2.53 4.41

5.21 7.85 15.00 26.12

3 4 6 7

0.125 0.198 0.273 0.316

3.2. Shear Flow Properties. Figure 4 shows the steady shear viscosity η(γ̇) from flow measurements and the modulus of the complex viscosity |η*|(ω) from dynamic measurements, obtained by applying the Cox−Merz rule, for a 10 mg/mL DNA solution. It is possible to observe that over a critical shear rate of around 0.3 s−1 the dynamical viscosity and the shear D


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Macromolecules al.46 in a semidilute T4 DNA solution for a concentration of 1.05 mg/mL and a high molecular weight (MW = 1.1 × 108 g/ mol). These last authors discussed their results in terms of Doi and Edwards theory10,63 for polymer chains, reporting that the concentration dependence of the plateau elastic modulus is the expected one for entangled chains. In addition, Jary et al. claimed that the concentration dependence of the lower limit of the stress plateau region is in good agreement with the reciprocal of the disengagement time.46 In fact, in Figure 5, an original behavior is observed where the beginning of the smooth plateau is suddenly interrupted by a discontinuity around a shear rate of 0.3 s−1 at 10 mg/mL which, to our knowledge, was not noticed on DNA samples even if it is present in some publications (see Figure 4 of ref 9). Moreover, to our knowledge, the curvature inversion from concave to convex shape was never observed in polymer solution over the plateau onset. Finally, from Figure 5, we can extract the information on the plateau for DNA concentrations of 7 and 10 mg/mL. For a DNA concentration of 7 mg/mL it was found σ = 8.1 Pa for a shear rate between γ̇1 = 6 s−1 and γ̇2 = 114 s−1 and σ = 14 Pa between γ̇1 = 2.5 s−1 and γ̇2 = 270 s−1 for a DNA concentration of 10 mg/mL. Furthermore, using the relaxation time (τc) and the crossover modulus (Gc), it becomes possible to normalize the flow measurements using σ* = σ/Gc and γ̇* = γ̇τc in dimensionless units. Figure 6 shows the flow master curve obtained for σ* as a function of γ̇* for DNA concentrations between 2 and 10 mg/

for several applied shear rates. Figures 7a and 7b show the shear stress as a function of time for a DNA solution with a

Figure 7. Transient response of the shear stress for different applied shear rates for a 10.0 mg/mL DNA solution (T = 20 °C): (a) for shear rate from 0.05 to 10 s−1; (b) for shear rate from 10 to 500 s−1.

concentration of 10 mg/mL, obtained at different imposed shear rates. The shear rate was applied to the DNA sample at rest, and the evolution of the shear stress with time was monitored until the steady state was reached. The transient response from a shear rate of 0.05 s−1 is characterized by the presence of a slight overshoot, which becomes higher when the applied shear rate increases. It is followed by a fast relaxation toward a stationary state. This overshoot is related to the flow behavior observed in Figure 5 in the onset of the non-Newtonian regime. Like for polymer solutions, we interpret the stress versus time overshoot in shear flow as the stretching of the network formed by entangled DNA polymers.63 As predicted by Doi and Edwards, the overshoot increases with the applied shear rate and its time position decreases. Moreover, when γ̇τr is lower than 1, no overshot can be seen. On the other hand, when γ̇τr is greater than 1, the contribution of the molecular spring is stronger for higher shear rates. Many systems show the overshoot as semidilute micellar systems,65−67 polymer networks,68 and sidechain liquid-crystal polymers.68 Interestingly, if we plot the maximum values of the shear stress obtained for a 10 mg/mL DNA solution (Figure 8a obtained from the values given in Figure 7a) and for a 3 mg/ mL DNA solution against the strain, we can observe two regimes in Figure 8b. The first one is characterized by the increase of σmax around a nearly constant strain between 2 and 3 for the 3 mg/mL DNA concentration and between 1.5 and 2 for the 10 mg/mL DNA concentration. We interpret this behavior as the reversible stretching of the network, as predicted in the Doi and Edwards model.10 The secondary regime is more surprising as the maximum stress value is strain dependent. In fact, we expected

Figure 6. Flow master curve of calf-thymus DNA solutions in TE buffer. The normalized shear stress versus the normalized shear rate was obtained for DNA concentrations from 2 to 10 mg/mL at the temperature of 20 °C.

mL at a temperature of 20 °C. Below γ̇* = 1, all data points are superimposed in this master curve, independently of DNA concentration, as expected for the linear regime. At γ̇* > 1, all the curves dissociate in dependence with DNA concentration. Only for DNA concentrations of 7 and 10 mg/mL, a stress plateau (σ* = 3.3) is observed around γ̇* ∼ 20. The shear stress normalized by the crossover modulus and plotted against the reduced shear rate does not show any difference in the plateau value at different DNA concentrations as observed for the shear banding effect in micellar systems,64 which is an argument to exclude the shear banding effect to interpret our data. 3.2.2. Transient Response. The time-dependent mechanical response of DNA solutions subjected to a shear rate is presented in terms of the transient response of the shear stress E


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Figure 8. (a) Shear stress as a function of the strain γ for a DNA solution at 10 mg/mL and 20 °C for different shear rates applied. (b) Shear stress at maximum (σmax) as a function of the strain at 10 and 3 mg/mL DNA solutions at 20 °C for different shear rates applied.

Figure 9. Strain dependence of the storage and the loss modulus, G′ and G″, respectively, for a DNA concentration of 7 mg/mL at a temperature of 20 °C. Visualization of the strain field inside the bulk of the solution.

a maximum shear stress at a fixed or quasi-constant strain value when γ̇τr is higher than 1.69 In our case, the power law is a clue of an organizational change inside the sample. Hence, σmax follows a power law with the following exponent values: 1.4 and 0.95 for DNA concentrations of 3 and 10 mg/mL, respectively. In this second regime, DNA solutions are in disentanglement process combined with a strong organizational modification of the network.64 Logically, the fact that the abrupt increase of σmax is lower at 10 mg/mL (around 0.8 or 0.95) than at 3 mg/ mL (around 2.5) is related to a greater number of entangled polymers at a higher concentration. Second, the fact that σmax follows a power law with a higher exponent at lower concentration means that the organizational change is faster in strain at lower concentrations. Reassuringly, the maximum stress value is always higher at high DNA concentrations than at lower concentrations. 3.3. Visualizations with TiO2 Filaments inside the Bulk of the DNA Solutions. In order to explore in more detail the appearance of organizational changes during linear and nonlinear rheological measurements, a visualization device51,52 was set up, and the deformation of a fine filament of white DNA solution injected in the sample was monitored during the rotation of the plate. It is worth to mention that the injected solution has the same concentration that the one tested. Figure

9 shows the strain dependence of G′ and G″ for a DNA concentration of 7 mg/mL at a temperature of 20 °C. In oscillatory measurements, rheometric measurements show that the elastic moduli (G′) is 3 times higher than the viscous moduli (G″), which is in good agreement with the statement of a greater elastic behavior of DNA solutions at high concentrations due to entanglements. We identify a critical strain, γc, around 0.3, as the onset of structural modifications in the solution. Below this critical strain, a homogeneous strain field is preserved in the solution as it is observed in images on the left side of the Figure 9 (right and left oscillations images). Then, we can consider that the DNA molecules organization in the solution is preserved. Above this strain level, viscoelastic properties of DNA solutions change, G′ breaks down, and the deformation becomes a function of the apparent strain applied, so the response to stress is not linear anymore. In steady state flow measurements, visual evidence of the strain field inside the bulk of the solution obtained at equilibrium is presented in Figure 10. The curve presents the evolution of the shear stress as a function of shear rate for a DNA concentration of 10 mg/mL at the temperature of 20 °C. Pictures show selected profiles in the two different regions: (i) in the linear Newtonian region (image at 0.01 s−1) and (ii) in the shear-thinning region (images at 0.1 and 1 s−1) which includes the stress plateau region (image at 10 s−1). F


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flow measurements (Figure 2a). Figure 11 shows the evolution of birefringence with the shear rate in a DNA solution at a concentration of 10 mg/mL. For this DNA concentration, the gap remains dark during an applied shear rate of 0.01 s−1, followed by a slight birefringent effect at 0.1 s−1, corresponding to the onset of the nonNewtonian regime. At a shear rate of 0.5 s−1, a strong birefringence in the gap can be distinguished, suggesting the presence of DNA orientations. From 2.5 to 270 s−1, the birefringence observed in the direction of the velocity evolves with a very colored pattern. Those differences of colors are interpreted as the presence of DNA textures with different orientations inside the gap. Because of the fact that the birefringent signal has been integrated into a large thickness, it is difficult to go further in the interpretation of the images. To complete those experiments, birefringence visualizations of DNA solutions in a concentration range between 2 and 10 mg/mL were taken under shear between crossed polarizers by using the experimental setup described in Figure 2b and presented in Figure 12. Figure 12a shows several images of the evolution of a sheared DNA solution with a concentration of 10 mg/mL. The birefringence patterns of a polarized light interacting with the sample through the plate−plate gap are observed from the upper view (i.e., the beam light is parallel to the gradient velocity), as presented in Figure 2b. The appearance of birefringent textures detected from a shear rate of 2.5 s−1 corresponds to the entrance on the shear plateau in the flow curve (Figure 5). It reveals clearly that a shear-induced texture orientation is taking place in these conditions of DNA concentration and at a certain imposed shear rate. This behavior is in good agreement with previous data given in Figure 11. With the increase of the shear rate, it is observed an increase of the global birefringence marked by an increase of the global whiteness. This is consistent with the increase of DNA chains orientation as observed in numerous polymer systems.77,82,83 It is recalled that as for the polymers in

Figure 10. Shear stress as a function of shear rate for a DNA concentration of 10 mg/mL at the temperature of 20 °C. Each image corresponds to a visualization of the strain field inside the bulk of the solution obtained at the steady state.

It is worth to mention that the plateau regime has been previously observed in many different systems50,70−73 and explained by the presence of heterogeneities in the flowing sample. The presence of the stress plateau has also been attributed to different origins in the literature, such as orientation phenomena, water release in the specific shear band, or local concentration fluctuations in initially inhomogeneous structured organization of the molecules.74−81 The origin of this phenomenon in calf-thymus DNA solutions was previously presented by Boukany et al.47 as a localized “collapse” of the entangled network in response to the fast shear and by Hu et al.49 as a possible nematic ordering. However, a description of the molecular nature behavior is still missing. To discuss this point, complementary experiments of birefringence were performed. 3.4. Flow Birefringence. 3.4.1. Qualitative Observations of Flow Birefringence. Visualizations of DNA solutions in the gap (1 mm) of the plate−plate configuration with a source of white light were performed between crossed polarizers during

Figure 11. Visualizations of a sheared DNA solution with a concentration of 10 mg/mL at room temperature (20 °C) in the gap between crossed polarizers. Each image corresponds to a visualization obtained at the steady state for a specific imposed shear rate. The birefringence signal was integrated through the velocity direction. G


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Figure 12. (a) Visualizations of a 10 mg/mL DNA solution under shear between crossed polarizers radially oriented (i.e., respectively horizontally and vertically on the presented pictures). The light comes from the bottom part of the plate−plate geometry before being collected by the camera. The observed bow delimited by the iridescent lines contains the sample. The horizontal black line is due to the alignment of DNA molecules with the direction of one polarizer. Each image corresponds to a visualization obtained at the steady state for a specific imposed shear rate. (b) Visualizations of a series of DNA concentrations from 2 to 10 mg/mL at 50 and 500 s−1. Temperature of the measurements: 20 °C.

Such flow birefringence observed when the applied shear increases was interpreted in the literature as a shear-induced nonhomogeneous flow due to an orientational ordering.49 In our work, the critical polymer concentration for which the average distance between parallel chains is lower than DNA persistence length, Lp = 50 nm, can also be estimated and corresponds to the formation of possible orientated domains. Following our previous determinations of the interchain correlation, discussed from neutron scattering experiments,85 this concentration is found to be around 2 mg/mL. Over this estimated critical concentration, due to long-range electrostatic repulsions, local organization of DNA chains may exist, forming domains also named as crystalline phase, connected by isolated chains, also named amorphous part. To better connect rheology and birefringence, quantitative determination of the birefringence of DNA solutions at different concentrations was determined in the steady state as a function of the shear rate applied. 3.4.2. Quantitative Measurements of Flow Birefringence. Taking into account the steady state flow measurements presented previously (Figure 5) and the appearance of birefringence and textures under flow (Figures 10 and 11), it seems important to have rheology and birefringence measurements obtained in the same experimental conditions (Figures 13). First, considering the birefringence response to the applied shear rate using the experimental conditions described in Figure 2c, it follows a similar trend for all DNA concentrations in the semidilute regime with entanglements. It is observed that

a semidilute or concentrated regime the birefringence is due to the intrinsic birefringence and not to the form birefringence. This global birefringence is related to the orientation of the polymeric segments in flow and relaxes when the shear rate is stopped (see Supporting Information videos). The appearance of these textures occurs in the shear rate range at which the overshoot position shown in Figure 7a or 8a changes, i.e., over 1 s−1. This phenomenon has been previously discussed by several authors in thermotropic nematics,77,82 lyotropic nematics,83 and cholesterics such as hydroxypropyl cellulose (HPC).84 Gleeson et al.77 also reported similar textures for several liquid-crystalline solutions of poly(benzyl glutamate) obtained during and after shear. As discussed for lyotropic and thermotropic materials at high shear rates, here 500 s−1, an uniform monodomain is obtained, resulting in a fully oriented sample. What is remarkable in the texture evolution in these ADN solutions is the fact that the textured size domains increases with the shear rate instead of decreasing as for thermotropic liquid crystalline polymers.77,82 Figure 12b shows the evolution of birefringent textures at two selected shear rates (50 and 500 s−1) for a set of DNA concentrations from 2 to 10 mg/mL. For an applied shear rate of 50 s−1, the presence of the birefringent textures is detected from a DNA concentration of 6 mg/mL, which is consistent with the previously mentioned statement of the presence of an apparent stress plateau in the flow curves σ(γ̇) at DNA concentrations higher than 5 mg/mL. For an applied shear rate of 500 s−1, over a DNA concentration of 4 mg/mL, no more textured domains appear and DNA solution is fully orientated. H


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Scheme 1. Suggested Mechanism for Supramolecular Organization Changes as a Function of the Applied Shear Rate: (a) Initial Solution at Rest; (b) Formation and Orientation of Clusters Made of Organized Domains (in Green) under Flow, Involving Partial Disentanglement; (c) Homogeneous Orientation of the Crystalline and Amorphous Chains under a High Shear Ratea

Figure 13. Steady-state variations of the absolute value of the birefringence Δn (open symbols) as a function of the shear rate for 2, 6, 8, and 10 mg/mL DNA solution in TE buffer. Shear stress σ (filled squares) as a function of the shear rate for a 10 mg/mL DNA solution in TE buffer. The measurements were performed 20 °C.

birefringence increases progressively, suggesting a reorganization of DNA organized domains under flow in the shearthinning regime. Moreover, from a DNA concentration larger than 5 mg/mL, a deviation in the behavior of the increasing birefringence is detected in the curves at a specific shear rate (around 1 s−1), which can be related to the appearance of the birefringent textures. These data are consistent with the onset of the obtained shear stress discontinuity of the plateau for DNA concentrations of 7 and 10 mg/mL as mentioned previously. It is clear that these entangled DNA solutions undergo a shear-induced macroscopic transition, which is highly dependent on DNA concentration and on the applied shear rate. In Figure 13, considering a DNA concentration of 10 mg/mL, different rheological regimes which can be identified and discussed later are consistent with the described mechanism proposed in Scheme 1 for the supramolecular organization transitions depending on the applied shear rate and DNA concentration regimes. Scheme 1a shows the sketch of a DNA solution with a concentration C > C**, at rest or under a gentle shear rate, presenting an amorphous phase connecting crystalline parts with random orientation. In Scheme 1b, for γ̇τr > 1, the amorphous and crystalline parts are oriented and assembled in clusters, resulting in the appearance of the intrinsic birefringence. This process of orientation and crystalline organization is correlated to the discontinuity in the rheological plateau shown in Figure 5. At end, when the shear rate is sufficiently high, the behavior corresponds to the reincrease of the shear stress in the rheological curve (Figure 5) due to the transformation of textures having different orientations to an anisotropic monodomain texture, consisting of crystalline domains and amorphous chains oriented in the direction of the flow (Scheme 1c). Second, considering the rheological behavior, from the results obtained at 10 mg/mL, it is possible to propose a scenario that allows understanding the complex behavior of these DNA solutions. Regime I, for γ̇ ≤ 0.01 s−1, corresponds to the Newtonian region of this DNA solution (σ = ηγ̇), with no macroscopic apparent birefringence, where an amorphous phase and crystalline parts with random orientation are present

a

Green parts correspond to the orientated chain segments in organized domains, and black portions are chain segments connecting the organized domains forming a network.

in the solution (Scheme 1a for γ̇τr ≪ 1). As long as γ̇τr < 1, nonorganized chains or amorphous chains can relax during the flow, resulting in no global birefringence at low shear rates, as seen in Figure 12a,b. Regime II, delimited by the shear rate range between 0.01 and 1−2 s−1, corresponds to the transition from the Newtonian region to a shear-thinning region (γ̇τr ∼ 1). In this regime, the birefringence exhibits a progressive increase, presumably related to the progressive orientation of the amorphous and crystalline parts (up to clusters formation, Scheme 1b). The appearance of the apparent shear stress plateau (γ̇ = 1−2 s−1) defines the onset of regime III, where the system is characterized by the induction of textures based on clusters as shown in Figure 12 for shear rates from 3 to 500 s−1 for a DNA concentration of 10 mg/mL. In this regime, when γ̇τr > 1, it is possible to explain also Figure 8b where the bump in transient experiments or maximum stress is plotted against the strain. In the regime of entangled solutions, when the shear rate is sufficiently high, the transient network is stretched for a strain around 2.5, for CDNA∼ 3 mg/mL and 0.8 for CDNA ∼ 10 mg/ I


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Figure 14. Optical micrographs obtained between crossed polarizers of anisotropic calf-thymus DNA solutions in TE buffer with the following concentrations: (a) 40, (b) 50, (c) 60, (d) 80, (e) 90, and (f) 100 mg/mL.

textures appear at the discontinuity of the rheological plateau regime followed by monodomain formation at higher shear rate. 3.5. Polarized Light Microscopy. Morphologies of anisotropic phases of calf-thymus DNA samples with concentrations higher than 40 mg/mL were examined by polarized light microscopy (Figure 14) to show the progressive appearance of greater DNA crystalline parts at rest when the DNA concentration increases. It is worth to mention that for lower DNA concentrations the anisotropic phases were not possible to be observed at rest with the microscope. Figure 14a shows clear evidence of birefringent textures in a DNA solution with a concentration of 40 mg/mL, as previously reported by Merchant et al. for high molecular weight DNA samples (MW = 5 × 106 g/mol).41 The increase of DNA concentration results in the increase of the background birefringence, as observed from Figure 14a−f corresponding to DNA concentrations from 40 to 100 mg/mL. All these images present areas with textures similar to the ones reported by Merchant et al. for a high molecular weight DNA sample at 47 mg/mL41 but also to that obtained in this work under shear at lower concentrations (Figure 12a).

mL. As it can be seen in Figure 12a, rapidly some textures appear from the outside of the plate−plate geometry, where the shear rate is more important and will propagate toward the axis of rotation tool when the shear will be increased. The bump, defined as σmax, is a signature of the energy density necessary to orient the transient network and the crystalline parts. At this stage, crystalline parts form textures dispersed in the whole sample volume. In opposite to the behavior of the crystalline phases studied in the literature,11,81−83 where textures size decreases when shear rate increases, the size of the textures in DNA solution increases. This behavior is interpreted as a consequence of the existence of clusters made of crystalline parts. This regime in the flow curve also coincides with the results presented in Figure 11 for shear rates from 0.5 to 100 s−1, where the gap is mostly occupied by the strongly birefringent phase. Considering the influence of polymer concentration, at low polymer concentrations (over C*), the rheological curve (cf. Figure 5) shows a small inflection point corresponding to a very small shear thinning. The global birefringence seems to be null or nondetectable with our setting. At those lower DNA concentrations, birefringence is often quite small as mostly due to the form factor causing a small anisotropy in the material permittivity tensor. When polymer concentration increases, an inflection point in rheological curves is noticeable, giving a higher shear thinning behavior. In this range of concentration, global birefringence increases slowly with the DNA concentration as it can be seen on Figure 12b. When C is of the order of C** (C up to 4 mg/mL), under shear, sample undergoes directly to a monodomain. Over 4 mg/mL, crystalline clusters

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CONCLUSION In this work, it is revealed through local birefringence measurements and visualizations that shear-induced textures are produced by flow in connection with the organization of DNA pre-existing domains at rest. Supramolecular organization in calf-thymus DNA solutions in TE buffer is characterized in J


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ACKNOWLEDGMENTS Dr. J. F. A. Soltero acknowledges CONACYT for financial support through Project No. 223549. L. M. Bravo-Anaya acknowledges the scholarship granted by CONACYT, the Bourse Eiffel scholarship granted by French Government, and financial support granted by G. Bravo-Galván and M. Anaya. Laboratoire Rhéologie et Procédés is a part of the LabEx Tec 21 (Investissements d’Avenir - Grant agreement no. ANR-11LABX-0030), of PolyNat Carnot Institut (Investissements d’Avenir - Grant agreement no. ANR-11-CARN-030-01) and of the program ANR-15-IDEX-02. We acknowledge M. Karrouch, E. Faivre, and X. Garciá from Laboratoire Rhéologie et Procédés, Grenoble, for their valuable help and technical support.

detail in the semidilute regime with a low degree of entanglements (2 ≤ CDNA ≤ 10 mg/mL). DNA solutions flow response in steady and transient states were studied in combination with optical measurements. The flow rheological behavior is interpreted on the basis of the analysis proposed by Wang et al.69 The obtained results are in good agreement with the polyelectrolyte organization in solution predicted by Odijk.14 Observations of the strain field combined with mechanical measurements were used to demonstrate the appearance of shear inhomogeneities in DNA/TE buffer solutions with concentrations higher than 5 mg/mL. The flow behavior was formulated in terms of the normalized quantities σ* = σ/G0 and γ̇* = γ̇τc, from which a flow master curve was obtained. Below γ̇*=0.20, all data points are superimposed, as expected for the linear Newtonian region with no flow birefringence. Then, the presence of a shearthinning phenomena with progressive stretching of the disordered chains and orientation of preexisting anisotropic domains was observed when 0.20 ≤ γ̇* ≤ 20 with appearance of birefringence (Figure 10 over γ̇ = 0.1 s−1 at 10 mg/mL). In the case of DNA concentrations higher than 6.0 mg/mL, a clear onset of an apparent stress plateau was identified around γ̇* = 20, with a discontinuity around 1−2 s−1 for 10 mg/mL. The origin of the discontinuity in the stress plateau is related to appearance of textured DNA clusters produced by progressive stretching of the network connecting the organized (crystalline) part and assembly of the crystalline domains which orientate progressively in the flow. At the highest shear rates, a complete orientation of the anisotropic domains up to fully orientated anisotropic solutions is obtained, where the shear stress increases again as a function of the shear rate. The mechanism of supramolecular organization is schematized in Scheme 1. To summarize, under shear, the amorphous parts of polymeric chains are progressively stretched and orientated in the flow involving the orientation of the pre-existing organized domains (crystalline part) assembled in orientated clusters revealed by the presence of birefringent textures. At high shear rates, a complete orientation of the chains gives a uniform anisotropic monodomain. At rest, in a higher DNA concentration range, from 40 to 100 mg/mL, crystalline phases presenting areas with textures having similar patterns as the ones observed under flow where observed using crossed polarized microscopy.

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ABBREVIATIONS DNA, deoxyribonucleic acid; TE buffer, Tris-HCl/ethylenediaminetetraacetic acid buffer; LVR, linear viscoelastic region.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01174.

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Captions to videos (PDF) Video 7759 (MP4) Video 7623 (MP4)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.M.B.-A.). ORCID

L. Mónica Bravo-Anaya: 0000-0002-8121-6887 Notes

The authors declare no competing financial interest. K


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Supramolecular Organization in Calf-Thymus DNA Solutions under

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