Dynamic Properties of an Extended Polymer in Solution

Abstract

Extended polymers are relevant in a variety of situations ranging from the classic coil-stretch problem to recent single molecule polymer experiments with DNA. We present theoretical calculations and computer simulations of the dynamic properties of extended single polymers. We discuss the effects of tension and hydrodynamics on t, the fundamental relaxation time of the polymer, and find that tension dominates the behavior of t. Furthermore, the symmetry breaking caused by extending the polymer "splits" t, leading to distinct longitudinal and transverse relaxation times. Our results are in agreement with recent experiments, and we discuss implications for the coil-stretch transition.[ S0031-9007(99) PACS numbers: 83.10. Nn, Extended polymers play an important role in many rheological problems: Under shear or strain forces, polymers will extend. A classic example is the coilstretch transition, in which polymers in a strain flow will undergo a phase transition from a coiled state to a highly stretched state when the strain rate exceeds a critical value [1]. The physics of this transition depend crucially on the relationship between hydrodynamic and entropic forces as a polymer is extended. Recent experiments with single molecules of DNA [2,3] have revealed its importance in a context outside biology-as a model system for studying polymer dynamics. When DNA is partially extended, one can use optical microscopy to image the internal modes of the polymer and study the normal mode structure. However, to analyze the results completely requires a detailed theory of the effects of extension.Here we calculate the fundamental relaxation time of a polymer as a function of its extension. The effects of nonlinear force curves and changing hydrodynamic interactions are incorporated in the theory. We have performed computer simulations of an extended polymer, the results of which are in agreement with the theory. The theoretical predictions are compared with the single molecule DNA data of Ref.[2], and their implications for the coil-stretch transition are discussed.Earlier theoretical studies of the dynamics of extended polymers [4,5] have made use of the blob model [6]. However, the blob model gives an incorrect prediction of polymer forces, which limits its applicability. For example, experiments with the synthetic polymer dextran have demonstrated that the force is best described by a modified freely jointed chain model [7]. We show below that a proper understanding of the forces of an extended polymer is crucial in predicting the dynamics. In the case of DNA, its stiffness precludes the application of blobs since the assumption fb͞k B T ø 1 is not generally met, where f is the force extending the polymer, b is the Kuhn length, k B is the Boltzmann constant, and T is the temperature. Other authors have considered the subtleties of extending polyelectrolyte polymers with flows and electric fields, but their primary results do not concern the dynamics of the polymer [8,9].Polymer dynamics are usually considered within the co...

Turbulence of polymer solutions

“…Recent experiments with DNA molecules indicate that the relaxation is linear in the wide region of scales R 0 ≪ R ≪ R max , where R max is the maximum extension [5]. In the case of polymer molecules, theoretical arguments and numerics presented in [6] support the linear relaxation. These results can be understood if we assume that at R ≫ R 0 the role of excluded volume and hydrodynamic interactions between the monomers becomes negligible.…”

Stretching tethered DNA chains in shear flow

“…Calculations by Larson et al [15] and by Hatfield and Quake [9] have shown that for DNA in free solution (far from surfaces) the inclusion of hydrodynamic interactions between chain segments for these lengths of DNA molecules only slightly modifies the drag coefficient (by ≈ 20% for λ DNA [9]). Furthermore, the work of Hatfield and Quake [9] has demonstrated that the relaxation times of highly extended chains is dominated by the tension in the chain, i.e. the nonlinear force law of the molecule, and not by hydrodynamic interactions.…”

Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

“…This is consistent with previous findings. 30 A first order semi-implicit scheme described in an earlier paper 16 The decomposition of the diffusion tensor ͓Eq. ͑2͔͒ was performed using Fixman's method 31 as described in earlier work.…”