Brownian dynamics simulations are used to predict the evolution of DNA conformations in elongational flow. The DNA molecule is represented by a bead-spring chain model, and excluded-volume and hydrodynamic interactions between the beads are taken into account. Two distinct types of behavior are examined, corresponding to infinite and finite chains. In the former case, Hookean springs are used, and simulations data accumulated for chains with increasing numbers of beads, N, are extrapolated to the limit N f ∞. In this nondraining limit, universal DNA stretch vs strain curves are obtained as a function of the solvent quality parameter z. In the case of finite chains with N k Kuhn steps, finitely extensible springs are used, and the extrapolation of finite chain data is restricted to the limit (N -1) f Nk. It is shown that in the presence of finitely extensible springs both the excluded-volume and hydrodynamic interaction parameters need to be redefined appropriately. The role of finite size effects and sensitivity to the choice of parameter values is examined by comparing the finite chain stretch vs strain curves with the universal curves. Theoretical predictions are also shown to compare favorably with experimental observations of DNA stretch.

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The scaling behaviour of the zero shear rate viscosity of semidilute unentangled DNA solutions, in the double crossover regime driven by temperature and concentration, is mapped out by systematic experiments. The viscosity is shown to have a power law dependence on the scaled concentration c/c * , with an effective exponent that depends on the solvent quality parameter z. The determination of the form of this universal crossover scaling function requires the estimation of the θ temperature of dilute DNA solutions in the presence of excess salt, and the determination of the solvent quality parameter at any given molecular weight and temperature. The θ temperature is determined to be T θ ≈ 15 • C using static light scattering, and the solvent quality parameter has been determined by dynamic light scattering. Typeset by REVT E Xand AIP 15 • C 20 • C 25 • C 30 • C 35 • C z 0 0.11 0.22 0.32 0.43 2.9 kbp c * 0.371 0.313 0.278 0.253 0.234 z 0 0.16 0.31 0.46 0.60 5.9 kbp c * 0.251 0.201 0.173 0.155 0.142 z 0 0.19 0.37 0.54 0.71 8.3 kbp c * 0.214 0.165 0.141 0.125 0.114 z 0 0.22 0.43 0.63 0.83 11.1 kbp c * 0.184 0.139 0.117 0.103 0.093 z 0 0.33 0.64 0.95 1.24 25 kbp c * 0.123 0.084 0.068 0.059 0.052 z 0 0.44 0.86 1.27 1.66 45 kbp c * 0.092 0.058 0.045 0.039 0.034 z 0 0.69 1.37 2.03 2.66 114.8 kbp c * 0.057 0.031 0.023 0.019 0.017 z 0 1.11 2.18 3.22 4.22 289 kbp c * 0.036 0.016 0.012 0.010 0.008 minutes at 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 have sufficient time to relax to their equilibrium state. Some typical relaxation times observed in dilute and semidilute solutions are given in Table I. At each temperature, a 30 minutes incubation time was employed for sample equilibration. III. SOLVENT QUALITY CROSSOVER OF THE ZERO SHEAR RATE VISCOSITY A. Zero shear rate viscosity of semidilute solutionsThe scaling behaviour of the zero shear rate viscosity of semidilute polymer solutions can be determined by measuring the viscosity as a function of concentration and temperature for a range of molecular weights, and then representing this behaviour in terms of the crossover variables z and c/c * . In order to do so, however, as discussed earlier in section I, it is first necessary to

The swelling αH of the hydrodynamic radius of a polymer, obtained using Brownian dynamics simulations of the continuum Edwards model, is found to obey a crossover in the excluded-volume parameter z, which is significantly different from that observed for the swelling αg of the radius of gyration. It is shown that this difference arises due to contributions from dynamic correlations to the diffusivity, which are ignored in the commonly used definition of hydrodynamic radius based on the Kirkwood expression. Simulated values of αH are found to be in remarkable agreement with experimental measurements

Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic interactions. In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique. By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we develop a BD algorithm in which the computational cost scales as O(N 1.8 ), where N is the number of monomers in the simulation box. We show that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that θ-solutions can be simulated by switching off excluded-volume interactions. A comparison of the predictions of the radius of gyration, the end-to-end vector, and the self-diffusion coefficient by BD, at a range of concentrations, with the hybrid Lattice Boltzmann/Molecular Dynamics (LB/MD) method shows excellent agreement between the two methods. In contrast to the situation for dilute solutions, the LB/MD method is shown to be significantly more computationally efficient than the current implementation of BD for simulating semidilute solutions. We argue however that further optimisations should be possible.