THE SHEAR RHEOLOGY OF SEMI-DILUTE DNA SOLUTIONS

Transcription

1 THE SHEAR RHEOLOGY OF SEMI-DILUTE DNA SOLUTIONS Sharadwata Pan 1,2,3, Duc At Nguyen 2, P. Sunthar 3,1, T. Sridhar 2,1 and J. Ravi Prakash 2,1,* 1 IIT-B Monash Research Academy, Indian Institute of Technology Bombay, Powai, Mumbai , India 2 Department of Chemical Engineering, Monash University, Melbourne, VIC 3800, Australia 3 Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai , India address: 1,2,3 sharadwata@iitb.ac.in, 2 duc.nguyen@monash.edu, 3,1 sunthar@che.iitb.ac.in, 2,1 tam.sridhar@monash.edu, 2,1,* ravi.jagadeeshan@monash.edu ABSTRACT Dilute polymer solutions and polymer melts in shear flow have been extensively studied experimentally and theoretically. However, a systematic experimental study to understand the influence of concentration, temperature and molecular weight on the rheology of semidilute polymer solutions is currently lacking. Such knowledge is of crucial importance in a number of industrial and biological contexts. In this work, the shear rheology of linear DNA molecules (which have near perfect monodispersity) has been investigated in a wide range of molecular weights ( kilobasepairs), temperatures and concentrations. Steady state shear viscosities in semi-dilute regime have been determined. The dependence of the zero shear rate viscosity on concentration is observed to display universal behaviour that can be understood in the framework of scaling theories for polymer solutions. Further, the shear rate dependence of viscosity, at various temperatures, can be collapsed onto a master curve when interpreted in terms of a concentration dependent Weissenberg number. The current work will provide benchmark data that can be used for the validation of theoretical studies. Keywords: Semi-dilute DNA solutions; blob theory, hydrodynamic interactions, zero shear rate viscosity, Weissenberg number.

2 INTRODUCTION Experimental characterization of polymer solutions has been carried out in great detail by rheologists for many years. The rheology of polymeric liquids is also well understood because of extensive theoretical predictions and simulation studies. The underlying curiosity to understand the rheological behavior of long chain polymers close to equilibrium and in flow stems from their fascinating chemical and physical properties and from their applicability. Polymer solutions are divided into many regimes when interpreting their behavior according to their concentration and molecular weight: dilute, semi-dilute unentangled, concentrated unentangled, semi-dilute entangled, and concentrated entangled (Graessley, 1980). The dynamical behavior of dilute solutions (where the chains are far apart so that they do not interact with each other) are well understood and can be effectively interpreted according to the Zimm model (Zimm, 1956) with a predominance of hydrodynamic interactions between the monomers of a single chain. On the other hand, the behaviour of entangled polymer melts (where there is no solvent and only polymer chains) can be represented by the tube model since any sidewise movement of a particular chain is denied due to the presence of surrounding chains, which is depicted as a tube surrounding the chain (de Gennes, 1979; Doi and Edwards, 1986). However, in between the dilute and entangled regimes, a comparatively newer and less explored semi-dilute unentangled regime arises in polymer solutions. This is due to the fact that single polymer chains can influence the presence of each other even though the monomer concentration is small (Doi and Edwards, 1986). The semi-dilute regime of polymer solutions is important because it involves many-body interactions, thereby giving rise to complexity and thus requires a thorough rheological characterization. The theoretical understanding of static and dynamic properties of polymer chains in a semidilute unentangled solution close to equilibrium is largely based on scaling theories using the blob picture (de Gennes, 1979). According to the blob theory, a polymer chain is envisioned as a chain of N/g blobs (where g is the number of monomers in a blob and N is the degree of polymerization). Within the volume of a single blob, the polymer perceives that it is in a dilute solution, and the polymer dynamics are well captured by the widely postulated Zimm model for dilute solutions (with a dominance of excluded volume and hydrodynamic interactions). But on a length scale larger than a blob, hydrodynamic interactions are screened (Rubinstein and Colby, 2003). If the polymer chains are short and do not fall into the entangled regime, the dynamics on scales greater than the size of a blob can be explained by the Rouse model (Heo and Larson, 2005; Rubinstein and Colby, 2003). Thus, if we assume that a blob is basically a rescaled monomer of the blob-chain, then on length scales larger than a blob, a semi-dilute unentangled solution can be thought of as a melt of blob chains (degennes 1979; Doi and Edwards, 1986; Heo and Larson, 2005; Rubinstein and Colby, 2003). Scaling theories based on the blob concept can provide appreciable physical insight into the equilibrium behavior of semi-dilute unentangled polymer solutions. Scaling theories have been postulated for both static (size) and dynamical equilibrium properties (diffusivity, viscosity) for linear polymer chains close to equilibrium (Rubinstein and Colby, 2003). The 2

3 relaxation time of a polymer chain in a semi-dilute unentangled solution is dependent on the polymer concentration and is shown to be a function of solvent viscosity and temperature (Rubinstein and Colby, 2003). Experimental observations so far have confirmed these predictions. Dependence of polymer contribution to viscosity on concentration in semi-dilute unentangled solutions have been shown to be in accordance with blob theory predictions (Rubinstein and Colby, 2003). The concentration dependence of the longest relaxation time of unentangled and entangled semi-dilute polymer solutions has also been investigated (Liu et al., 2009). The scaling exponents are consistent with those expected for semi-dilute polymer solutions in the unentangled and entangled regime. Recently significant progress has been achieved in our understanding of semi-dilute polymer solution dynamics through simulation studies close to and far from equilibrium. The most significant of these are a Brownian Dynamics (BD) simulation study of semidilute polymer solutions (Stolz et al., 2006) subjected to shear and extensional flow and a combined Molecular Dynamics (MD) and Multiparticle Collision Dynamics (MPCD) approach to simulate semi-dilute polymer solution properties under shear flow (Huang et al., 2010). Both of these simulations lead to predictions that agree with scaling predictions at equilibrium. However, there are very few comparisons with experimental data far from equilibrium (shear or extensional flow). As a matter of fact, the amount of experimental data in literature for semi-dilute unentangled polymer solutions is scarce. The far from equilibrium data till date is focused mainly on the dependence of steady state shear viscosity on the Weissenberg number and the determination of the slope of the shear thinning region (Hur et al., 2001; Doyle et al., 1997). In this work, we have investigated the shear rheology of linear DNA molecules in a wide range of molecular weights ( kilobasepairs), temperatures and concentrations. The monodispersity of DNA and its ability to be stained for visualization has made it a model polymer system for investigating polymeric liquids. The overall objective of the current work is to generate a set of benchmark data for semi-dilute solutions across a range of molecular weight, concentration and temperature; for close to equilibrium and non equilibrium properties. METHODOLOGY Sample procurement and preparation: Linear genomic DNA (#N3011L) of λ-phage (size 48.5 kilobasepairs, or kbp) was purchased from New England Biolabs (U.K.). Linear genomic DNA (# ) of T4 phage (size kbp) was purchased from Nippon Gene (Japan). 25 kbp DNA was originally procured from Prof. Douglas E. Smith s group (UC San Diego, USA) as agar stab cultures of Escherichia coli (E. coli) containing these as specialized double stranded DNA constructs. The details about preparation of the 25 kbp fosmid DNA is mentioned elsewhere (Laib et al., 2006). After procurement, the DNA was extracted, linearized and purified according to a protocol suggested elsewhere (Laib et al., 2006) and also the 3

4 standard molecular biology protocols (Sambrook and Russell, 2001). Briefly, E. coli cells containing the 25 kbp (double stranded, circular) DNA was grown for 16 to 18 hours at 37 C with vigorous shaking in standard LB medium (#L3022, Sigma-Aldrich) supplemented with mg/ml Chloramphenicol or CAM (#C0378, Sigma-Aldrich) and 0.01% L-arabinose (#A3256, Sigma-Aldrich). The arabinose acts as an inducer for the extra origin of replication inserted into the 25 kbp fragment, primarily to overcome the problem of extremely low copy number (~1 or 2 copies per cell) (Laib et al., 2006). This gives a higher yield of the 25 kbp DNA than usual. The cells were harvested and cell wall lysed through alkaline lysis method. The undesirable contaminants in the form of proteins, RNA and genomic DNA were removed using Phenol (#P4557, Sigma-Aldrich), RNaseA (#R6513, Sigma-Aldrich) etc. and the DNA was precipitated with ethanol. The purified double stranded DNA was linearized with ApaI (#R0114L, New England Biolabs) which contains its unique site in the 25 kbp DNA sequence (Laib et al., 2006). The linearized DNA was subjected to phenol-chloroform (# , Merck) extraction and ethanol precipitation and finally dissolved in a solvent containing 10 mm Tris (#T1503, Sigma- Aldrich), 1 mm EDTA (#E6758, Sigma-Aldrich) and 0.5 M NaCl (#S5150, Sigma- Aldrich). The same solvent was used for dissolving DNA pellets after precipitation (for λ, T4 and 25 kbp) and for preparing subsequent dilutions. This solvent has a viscosity of 1.01 mpa-s at 20 C ( water viscosity). Concentration and purity of DNA Samples: For λ-phage genomic DNA, a company specified value of 0.5 mg/ml was considered. For T4 genomic DNA, a company indicated value of 0.24 mg/ml was considered. It s expected that the purity of these DNA samples are of the highest order. For the 25 kbp linear DNA, the concentration of DNA was determined to be mg/ml by agarose gel electrophoresis by comparing with a standard DNA marker (#N0468L, New England Biolabs). Also, the purity of the 25 kbp DNA sample was assessed by UV-VIS spectrophotometry (#UV-2450, Shimadzu). The A 260 /A 280 ratio was 1.92 which indicates good purity for DNA samples, though it is largely an assumption (Laib et al., 2006). The A 260 /A 230 ratio was 2.1, which indicates absence of organic reagents like phenol, chloroform etc (Sambrook and Russell, 2001). Viscometer For all shear viscosity measurements, Contraves Low Shear 30 with cup and bob geometry (1T/1T) was used. This is efficient in measuring low viscosities and has very low zeroshear rate viscosity sensitivity at a shear rate of s -1 (Heo and Larson, 2005). The measuring principle of this device is detailed in an earlier study (Heo and Larson, 2005). The primary advantage of using this is a small sample requirement (minimum 0.8 ml), which is ideal for measuring DNA solutions. The zero error was adjusted prior to each measurement. The instrument was calibrated with appropriate Newtonian Standards with known viscosities (around 10, 100 and 1000 mpa-s at 20 C) before measuring actual DNA samples. Values obtained fall within 5% of the company specified values. 4

5 Rheometry: Steady state shear viscosities were measured at a temperature range of 10 to 35 C for all linear DNA samples and a continuous shear ramp was avoided. Prior to measurements, λ and T4 DNA were kept at 65 C for 10 minutes and immediately put in ice for 10 minutes for their maximum concentrations. This was done to prevent aggregation of long DNA chains (Heo and Larson, 2005). The shear rate range of the instrument under the applied geometry is from 0.01 to 100 s -1. At each shear rate, a delay of 30 seconds was employed so that the DNA chains get ample time to relax to their equilibrium state. At each temperature, a 30 minutes incubation time was employed for sample equilibration. The shear viscosities at each temperature and concentration in the plateau (very low shear rate) region were least-square fitted (along with the errors) with straight lines and extrapolated to zero shear rate. The zero shear rate viscosities were determined in this manner for the different molecular weight DNA samples and were analyzed in the context of the blob model. KEY RESULTS AND DISCUSSION Close to equilibrium: The zero shear rate viscosities, η o were determined at different concentrations for three different molecular weights of DNA (25 kbp, 48.5 kbp and kbp). The experimental data covers a high range of molecular weights ( to daltons) and concentrations (0.008 to 0.5 mg/ml), which is ideal for investigating scaling laws. As predicted by the blob model, the polymer contribution to the zero shear rate viscosity, η po (= η o η s ; here η s denotes solvent viscosity) is highly dependent on polymer concentration, c in the semi-dilute unentangled regime and grows as a power law with c (Rubinstein and Colby, 2003). Interestingly, this behavior is strongly influenced by solvent quality and thus differs under theta (θ) and good solvent conditions. For a given polymer-solvent pair, the θ condition is satisfied at a certain solvent temperature at which the polymer coil acts like an ideal chain. However, in good solvents (at temperatures higher than θ), the solvent quality comes into play resulting in a swollen state for the polymer (Rubinstein and Colby, 2003). The value of θ for DNA in the solvent used in this study is approximately 13 o C, which has been determined by static and dynamic light scattering measurements (Sharadwata et al., 2011). The concentration range of DNA samples used in this work is characterized in terms of overlap concentration, c* (the concentration at which the combined pervaded volume of the chains is equal to the volume of the system as a whole). At c*, the polymer chains start to just overlap each other which separates the dilute and semi-dilute unentangled regimes. The c* values were obtained according to the following equation (Doi and Edwards, 1986): c * 3M = 4π N R 3 A g (1) 5

6 Here M is molecular weight, N A is Avogadro s constant and R g is the equilibrium static radius of gyration of the polymer. We have measured R g values of the DNA fragments at different temperatures in the dilute regime (Sharadwata et al., 2011). According to the blobmodel, in unentangled semi-dilute θ-solutions, the specific viscosity, η po / η s is predicted to grow as the square of polymer concentration whereas in good solvents, it grows as a weaker power of concentration (Rubinstein and Colby, 2003): c 3ν 1 η η (2) s η s c * The exponent 1/(3ν -1) is 2 in θ solvents (since ν = 1/2) and 1.25 in very good solvents (since ν = 2/3). The concentration dependence of specific viscosity for different molecular weights at the θ temperature is shown in Fig.1. The substantial difference observed in the concentration dependence for the different molecular weights disappears when the data is reinterpreted in terms of the non-dimensional ratio (c/c*) (see Fig. 2). In this study, we have measured the shear viscosities in the range of c/c* from 1 to 10, which defines the semi-dilute regime of concentrations (Graessley, 1980). 1 η η po s Fig 1: Concentration dependence of specific viscosity at θ for linear DNA fragments. The specific viscosity plotted in this way shows a universal increase (irrespective of molecular weight) with c/c* in the semi-dilute unentangled regime; with different slopes for θ and good solvent conditions. In these plots, the slopes agree with the predictions of scaling theories. 6

7 Fig. 2: The normalized polymer contribution to viscosity, η po / η s for different DNA fragments as a function of normalized concentration, c/c* in (a) θ solvent (b) good solvent limit. The green line in (a) and the purple line in (b) is the least square fit in accordance with the blob model. Shear Flow: Along with a close to equilibrium property, we have also investigated the properties of linear λ DNA solutions in shear flow. At very high shear rates, linear DNA chains undergo conformational changes due to the flow-driven alignment (Huang et al., 2010). We have defined a characteristic concentration dependent Weissenberg number, Wi: Wi = λ η M ( η η o s) & γ = & γ cn AkBT (3) where λ η is a concentration dependent relaxation time in the semi-dilute unentangled regime. When the normalized polymer contribution to shear viscosity is plotted as a function of Wi (see Fig. 3), we see an expected shear thinning behavior with a universal temperature superposition across different concentrations. With increasing concentration, the shear thinning region enters as a broad power law region before reaching a slope of -0.5, which is the asymptotic slope observed previously in an earlier study (Hur et al., 2001). 7

8 Fig 3: Shear rate dependence of polymer contribution to shear viscosity for linear λ DNA at different temperatures and concentrations in the semi-dilute regime. CONCLUSIONS In this paper we have investigated the shear rheology of semi-dilute unentangled DNA solutions close to and far from equilibrium for a wide range of temperatures, concentrations and molecular weights. Close to equilibrium, the zero shear rate viscosities for different molecular weights scale universally with concentration in accordance with blob theory in both θ and good solvents. Under shear flow, the properties of semi-dilute solutions can be interpreted in terms of a characteristic concentration dependent relaxation time. The experiments presented here will act as benchmark data for validation of theoretical simulations. REFERENCES de Gennes, P. G., Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca, NY. Doi, M. and Edwards, S. F., The Theory of Polymer Dynamics. Oxford Science, Oxford, U K. Doyle, P. S., Shaqfeh, E. S. G. and Gast, A. P., Dynamic simulation of freely draining, flexible polymers in steady linear flows. J. Fluid Mech. 334,

9 Graessley, W. W., Polymer chain dimensions and the dependence of viscoelastic properties on concentration, molecular-weight and solvent power. Polymer. 21, Heo, Y. and Larson, R. G., The scaling of zero-shear viscosities of semidilute polymer solutions with concentration. J. Rheol. 49 (5), Huang, C. C., Winkler, R. G., Sutmann, G. and Gompper, G., Semidilute polymer solutions at equilibrium and under shear flow. Macromolecules. 43 (23), Hur, J. S., Shaqfeh, E. S. G., Babcock, H. P., Smith, D. E. and Chu, S, Dynamics of dilute and semidilute DNA solutions in the start-up of shear flow. J. Rheol. 45 (2), Laib, S., Robertson, R. M. and Smith, D. E., Preparation and characterization of a set of linear DNA molecules for polymer physics and rheology studies. Macromolecules. 39 (12), Liu, Y., Jun, Y. and Steinberg, V., Concentration dependence of the longest relaxation times of dilute and semi-dilute polymer solutions. J. Rheol. 53 (5), Pan, S., Sunthar, P., Sridhar, T. and Prakash, J. R., Polymeric Behaviour of DNA: Theta temperature and Good Solvent Crossover of Gyration and Hydrodynamic Radii. Macromolecules (under review). Rubinstein, M. and Colby, R. H., Polymer Physics. Oxford University Press, NY. Sambrook, J. and Russell, D. W., Molecular Cloning: A Laboratory Manual (3rd edition). Cold Spring Harbor Laboratory Press, NY. Stoltz, C., de Pablo, J. J. and Graham, M. D., Concentration dependence of shear and extensional rheology of polymer simulations: Brownian dynamics simulations. J. Rheol. 502, 137. Zimm, B. H., Dynamics of polymer molecules in dilute solutions: Viscoelasticity, flow birefringence and dielectric loss. J. Chem. Phys. 24, BRIEF BIOGRAPHY Dr. Ravi Prakash Jagadeeshan is a Reader in the Department of Chemical Engineering at Monash University. 9