Najmul
Arfin
a and
H. B.
Bohidar
*ab
aPolymer and Biophysics Laboratory, School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India. E-mail: bohi0700@mail.jnu.ac.in; Fax: +91 11 2674 1837; Tel: +91 11 2670 4699
bSpecial Centre for Nanosciences, Jawaharlal Nehru University, New Delhi-110067, India
First published on 22nd October 2013
We have observed DNA concentration and hydration dependent inversion from ergodic to non-ergodic phase followed by reentry into the ergodic phase in DNA–nanoclay (laponite) dispersions at room temperature (25 °C), using results obtained from dynamic light scattering (DLS) and rheology data. The interaction between the DNA strand and the anisotropically charged discotic platelets of laponite (L) was found to be strongly hierarchical in DNA concentration. For a fixed laponite concentration (CL = 1% (w/v)) and varying DNA concentration (CDNA) from 0.3–2.3% (w/v), we observed three distinct phase regions characterized by the following: region (i): CDNA < 1.0% (w/v), ergodic region with weak DNA–L attractive interaction, region (ii): 1.0% < CDNA < 1.6% (w/v), non-ergodic regime having strong DNA–L associative interaction and region (iii): CDNA > 1.6% (w/v), showing phase reentry into the ergodic regime due to repulsion between DNA strands. Hydration study in these three regions revealed that a loss in the abundance of amorphous water, signified by Raman frequency 3460 cm−1, caused the ergodic to nonergodic phase transition. In summary, it is shown that maximum stability and interaction between DNA and nanoclay platelets occurred at an intermediate concentration of DNA where the hydration was at its minimum. The present system is qualitatively different from the hard-sphere/polymer systems for which reentrant phase transition has been reported in the literature. However, some similarity between the two classes of systems is not ruled out.
On the other hand, reentrant phase transition has been observed in a large class of soft matter systems, prominent among them being the colloidal systems. Liu et al.11 have reported reentrant structural phase transition in amphiphilic self-assembly of the quillaja saponin–cholesterol system and here discuss the relevance of precursors for hierarchical structure formation. They have highlighted a three-stage dynamical process for reentrant phase transition caused by cholesterol. Reentrant glass transition in colloid–polymer mixtures with depletion attractions has been reported by Eckert and Bartsch.12 In this experiment, short-range interactions were introduced into a hard-sphere colloidal dispersion by the addition of a polymer that produced novel glass transitions. It was clearly shown that dramatic acceleration of density fluctuations resulted in melting of the colloidal gel. Evidence of reentrant phase behavior in the laponite–polyethylene oxide system was reported by Baghdadi et al.,13 where it was shown that depletion forces caused melting of colloidal glass. In high molecular weight PEO, this glassy phase was reformed. Grandjean and Mourchid14 observed the emergence of a reentrant liquid–glass transition with increasing attraction between soft spheres. They noticed that the particle dynamics exhibited extended logarithmic decay with increasing concentration of sticky soft spheres in the reentrant transition branch. The results were discussed within the framework of mode coupling theory, which stipulates coupling between pairs of density fluctuations. Thus, enhancing the said coupling induced structural arrest and a sharp ergodic-to-nonergodic phase transition. Such phase transitions are an interplay of short and long range forces, entropy effects, structural and charge anisotropy of interacting particles etc.
As far as the reentrant phase transitions of DNA–colloid systems are concerned, Nguyen and Shklovskii15 have reported a detailed study on the interaction profile of DNA and positively charged colloidal macroions and concluded the following: (i) at low colloid concentration, the DNA–colloid complexes are negatively charged, with DNA wrapping the colloids, while (ii) at high colloid concentration the complexes showed charge reversal and revealed a positive charge. The aforesaid two situations were separated by an intermediate phase where the DNA–colloid complexes were fully charge neutralized. Therefore, the concentration of colloidal macroions governed the condensation and reentrant condensation in this system.
A close examination of the literature established that the ergodic-to-nonergodic phase transition has largely been probed by experiments in two classes of systems: colloid–colloid or colloid–polymer. The polymers used were mostly neutral or had low charge density. Herein, we have reported a detail study on the DNA–laponite dispersion and have shown that a high charge density polymer like DNA can hierarchically interact with anisotropically charged laponite platelets to exhibit a ergodic-to-nonergodic phase transition followed by reentry into the ergodic phase. Thus, our system does not belong to any of the aforesaid classes, though some similarities can be invoked, which makes these results unique.
The zeta potential measurements of sample solutions were performed on an electrophoresis instrument (Zeecom – 2000, Microtek, Japan). The zeta potential ξ of a uniformly charged sphere is given by ξ = 4πσ/εκ, where σ is the surface charge density of the particle and ε and κ are the dielectric constant and the Debye–Hückel parameters of the solution, respectively. The surface charge can be determined from the measured zeta potential data if the geometrical shape is known.17 Rheology experiments were performed using an AR-500 model stress controlled rheometer (T. A. Instruments, UK). The elastic moduli of the samples was measured using cone–plate geometry (2 cm diameter, 2° cone angle and 50 mm truncation gap) with the oscillation stress value set at 0.1 Pa. These studies determined the frequency ω dependence of the storage G′(ω) and loss moduli G′′(ω). Rheological characterization of viscoelastic materials is discussed at length by Barnes.18
Dynamic light scattering (DLS) experiments were performed at a scattering angle of 90° and laser wavelength of 632.8 nm on a 256-channel Photocor-FC (Photocor Inc., USA), which was operated in the multi-tau mode (logarithmically spaced channels). The goniometer was placed on a Newport (USA) vibration isolation table. Correlation function for samples at different time intervals were recorded and analyzed for relaxation times. Further details on DLS can be found elsewhere.19 Raman spectroscopy was used to study the hydration behavior of the samples. Raman spectra were recorded on a FT-IR/Raman spectrometer with Microscope – Varian 7000 FTIR, Varian FT-Raman and Varian 600 UMA.
The aging behaviour and slow dynamics in soft matter systems is best probed by dynamic light scattering experiments through dynamic structure factor analysis. Usually, the intensity auto-correlation function g2(q, t) is directly correlated to the corresponding dynamic structure factor g1(q, t) through the Siegert relation g2(q, t) = A + B|g1(q, t)|2, where A defines the baseline of the correlation function and |g2(t)|t→∞ = A and B is the spatial coherence factor when the system is ergodic.18 In the arrested phase, scattering centers are localized near their fixed average positions and are only able to execute limited Brownian motion about these positions and non-ergodicity then ensues. A completely ergodic system is one where the scattering moiety is capable of exploring the entire phase space. Furthermore, when the time and the ensemble averages are identical, the system is stationary, implying that the process is independent of the origin of time, which is adequately satisfied only in the case of scattering from homogeneous dilute solutions. The issue of non-ergodicity in DLS experiments has been addressed in several ways, which include rotating the sample cell to scan the entire phase space, expanding the incident beam to collect data from many coherence areas and extracting the non-ergodic contribution from the measured data as a heterodyne contribution.20
Herein, we use the heterodyne approach. The normalized intensity correlation function, g2(q, t), obtained from the sample can be related to the dynamic structure factor, g1(q, t) as
g2(q, t) = 1 + β′[2X(1 − X)g1(q, t) + X2|g1(q, t)|2] | (1) |
Here, β′ is the coherence factor having a maximum value of 1. In a real experiment, it defines the signal modulation, which is a measure of the signal-to-noise ratio. The parameter X (0 ≤ X ≤ 1) defines the ergodicity through the amount of heterodyne contribution present in the g2(q, t) data. When the value of X = 1, the system is completely ergodic and the Siegert relation is established, whereas in the arrested state X < 1 and the term 2X(1 − X) makes a finite contribution to g2(q, t) and hence it must be accounted for. The intercept of the plot of [g2(q, t) − 1] vs. delay time t at t → 0 gives β′[2X − X2], from which the value of X, which is an instrumental factor, can be calculated if β′ is known. The measured intensity auto-correlation data was analyzed exactly, following the description given elsewhere.21 The pre-factor of the linear term in g1(q, t) in eqn (2) is in most cases much larger than the quadratic second term. Thus
g1(q, t) ≈ [g2(q, t) − 1]/[2β′(X(1 − X))] | (2) |
The exact evaluation of the dynamic structure factor, g1(q, t), from the measured intensity auto-correlation function g2(q, t) was achieved by substituting the values of β′ and X into eqn (2). A situation may arise where the signal modulation is so low that it is impossible to construct the dynamic structure factor from the measured g2(q, t) data. In such events, the baseline of the evaluated dynamic structure factor provides a quantitative estimation of non-ergodicity, say Y. For a fully ergodic system, the baseline would be located close to Y = 0, whereas for a fully non-ergodic system it will assume a value Y = 1. Thus, in terms of the already defined parameter X, Y = (1 − X).
Typically, the g1(q, t) curve was fitted to a two-exponential decay function defined by two characteristic relaxation times: the fast mode τf and a slow mode τs. This is given by
![]() | (3) |
Relative amplitudes of the modes are A and B.
Fig. 3a (CDNA = 0.3% (w/v)) depicts region (i) of DNA–L system. Here, single mode relaxation time τ was found to change into two relaxation modes i.e. fast mode relaxation time (τf) and slow mode relaxation time (τs), with sample aging indicating the evolving dynamics in the growth process. However, this region remained in the ergodic phase, as is clear from the indicative correlation curves shown in the inset of Fig. 3a. Fig. 3b (CDNA = 0.6% (w/v)) depicts a deviation in the behavior and the onset of non-ergodicity can be seen at a later stage (inset of Fig. 3b, observe the rising baseline). The relaxation times of both modes begin to slow down and give rise to a single mode relaxation time, with the raised baseline implying approaching dynamic arrest.
Increasing the concentration of DNA led to the system moving deeper into the non-ergodic phase, which is shown in Fig. 4a and b. Data in Fig. 4a (CDNA = 1.0% (w/v)) was fitted to a single exponential function, and it was clearly seen that the relaxation mode (τ) saturated after about 104 s of sample aging, with the system firmly located inside the non-ergodic phase. This non-ergodic behavior can be seen by looking at the indicative correlation functions given in the inset of Fig. 4a, where the baseline is seen to rise considerably.
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Fig. 4 Variation of (a) fast relaxation time (τf) at CDNA = 1.0% (w/v) and (b) non-ergodic parameter (Y) at CDNA = 1.3% (w/v), as a function of aging time. Insets show indicative correlation curves. |
At CDNA = 1.3% (w/v), the degree of non-ergodicity in the system was so high that we could only register the baselines of correlation curves, as shown in the inset of Fig. 4b, implying a complete dynamic arrest. The baseline analysis of these curves in the time region 105 to 106 μs of decay time yielded the non-ergodicity parameter Y, which increased with aging time, as shown in Fig. 4b. Here, the non-ergodicity parameter is determined from the upward shift of the baseline of correlation curves as discussed earlier.
One interesting observation was made here. The nascent dispersions were associated with non-ergodicity, which increases with aging of the samples. This clearly implies the reorganization of DNA and laponite in the dispersion medium.
Further increase of CDNA to 1.6% (w/v) raised abundance of DNA strands, where enhanced DNA–DNA repulsion caused reorganization of the intermolecular complexes. The mobility of the complexes started to increase, which led to the transition from the non-ergodic to the ergodic phase. Analyzing the baseline of the correlation curves (inset Fig. 5a), in the region 105 to 106 μs of decay time, we observed that non-ergodicity parameter Y decreased with time, as shown clearly in Fig. 5a. At CDNA = 2.3% (w/v), ergodicity was restored completely, which is clear from the indicative correlation curves shown in the inset of Fig. 5b. Fig. 5b depicts a slight decrease in the fast and slow relaxation mode relaxation times with aging, which is a signature of the transition from the non-ergodic to the ergodic phase. Thus, we have clearly observed reentrant ergodic transition in our system fully driven by DNA concentration.
Analysis of DLS data supported the rheology results to a large extent. DLS classified region (i) as the ergodic region, where a weak DNA–L attraction existed (Fig. 3a and b) and DNA–L complexes could explore the entire phase space. Region (ii) is classified as a non-ergodic region where the correlation function ceased to exist due to immobility of the DNA–L complex (Fig. 4a and b). In region (iii), reentrant ergodicity behavior owing to preferential DNA–DNA repulsion was noted (Fig. 5a and b). A simplistic model, which describes the interaction between DNA and laponite, has been formulated and discussed in some detail (see ESI†).
G′(ω) ∼ ωn | (4) |
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Fig. 6 Frequency sweep of elastic moduli for CDNA (a) 0.3%, (b) 0.6%, (c) 1.0%, (d) 1.3%, (e) 1.6%, (f) 2.0% and (g) 2.3% (w/v) at different time intervals. The data were fitted to eqn (4). |
The linear visco-elasticity model, for pre and post gel situations, proposed by Winter and Chambon,23 predicts that the stress-relaxation will follow the power-law frequency dependence behaviour given by eqn (4) with 0 < n < 1. Stoichiometrically balanced and imbalanced crosslinked networks showed n = 1/2 (excess crosslinker) and n > 1/2 (lack of crosslinker), respectively. However, this description strictly applies to chemically crosslinked gels. Here, the very low values obtained for n indicate the elasticity of the materials. The elastic strength increased with increasing CDNA and the maximum strength found was ≈80 Pa at 122 h in the system with CDNA = 1.3% (w/v). The elastic strength was reduced on addition of more DNA in the dispersion, due to intermolecular repulsion between the DNA strands.
Fitting to frequency sweep data for the time period 7–122 h was carried out as per eqn (4), as shown in Fig. 6. The values of n are plotted as a function of CDNA in Fig. 7, where these values were calculated for the samples concerned after allowing aging for 122 h. Fig. 7 illustrates clearly that after CDNA = 1.6% (w/v), the value of n increased. This increase denotes reorganization of the network structure, which owes its origin to DNA–DNA repulsion.
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Fig. 7 Variation of the exponent n determined from eqn (4) as a function of DNA concentration. Note the sharp rise in the value of the exponent in region (iii), signifying strong DNA–DNA repulsion. The line is a guide to the eye, and the arrows demarcate various viscoelastic regions. See text for details. |
It has been observed that the biological function of proteins and other intracellular biopolymers cannot be understood without taking into account their hydration behaviour.24 In addition, the ionic state of the aqueous solution has considerable influence on the biological function of biomolecules.25 Furthermore, the mobility of water on inter and intra molecular length scales, and the effect of differential hydration features, have been reported for different soft matter systems.26–28 In the current study, we have clearly observed the correlation between hydration and ergodicity of a given soft matter phase.
Footnote |
† Electronic supplementary information (ESI) available: A simplistic model depicting the interaction between DNA and laponite has been formulated and discussed. See DOI: 10.1039/c3sm52218k |
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