J.G. Hernández Cifre

Steady-state behavior of dilute polymers in elongational flow. Dependence of the critical elongational rate on chain length, hydrodynamic interaction, and excluded volume

The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, e exceeds a certain critical value ec. In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of ec is the same in theta conditions as in good solvent conditions. Combining ec with other solution properties such as the longest relaxation time, the intrinsic viscosity, and the radius of gyration, dimensionless compound quantities can be formulated. From our simulation results, we obtain numerical values for such quantities, which include the HI effect, and which are therefore useful for analyzing experimental data.The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, e exceeds a certain critical value ec. In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of ec is the same in theta conditions as in good solvent conditions. Combining ec with other solution properties such as the longest relaxation time...

Kinetic aspects of the coil-stretch transition of polymer chains in dilute solution under extensional flow

When linear polymer chains in dilute solution are subject to extensional flow, each chain in the sample experiences the coil-stretch transition at a different time. Using Brownian dynamics simulation, we have studied the distribution of transition times in terms of the extensional rate and the length of the chains. If instead of time one characterizes the effect of the flow by the accumulated strain, then the distribution and its moments seem to take general forms, independent of molecular weight and flow rate, containing some numerical, universal constants that have been evaluated from the dynamical simulation. The kinetics of the transition, expressed by the time-dependence of the fraction of remaining coils, has also been simulated, and the results for the kinetic rate constant has been rationalized in a manner similar to that used for the transition time. The molecular individualism, characterized in this work by the distribution of transition times, is related to the excess of the applied extensional...

Translational diffusion coefficients of macromolecules

The calculation of the translational diffusion coefficient of a single flexible polymer chain in dilute solution can be basically addressed either a) within the Einstein theory (calculating the time autocorrelation function of the macromolecule center of mass), or b) within the Kirkwood and Riseman theory for irreversible processes of macromolecules in solution. The equations of the latter theory can be solved employing different approximations that give rise to different values of the diffusion coefficient. In general, the value of the diffusion coefficient obtained through the different theories and approaches varies slightly depending on polymer features like flexibility. In this paper, we evaluate the most common procedures to compute the diffusion coefficient of flexible macromolecules via computer simulation and the difference between the values obtained.Graphical abstract

Simulation of polymers in dilute solution under elongational flow

Abstract The behavior of polymer chains, modeled as chains of finitely extensible non-linear elastic springs, in solutions undergoing elongational flow, has been studied by Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, ϵ , exceeds some critical ϵ c that is determined, in steady-state condition, as a function of chain length. We have simulated the time dependence of polymer dimensions when ϵ is increased from below to above ϵ c , and then decreased to the initial value. In the coil-to-stretch transition there is an induction time, required to observe the onset of the transition, which varies among the chains in a sample. However, the stretch-to-coil transition follows the same path for all the molecules. The observable properties (sample averages) show a hysteresis cycle that is intensified by the effect of hydrodynamic interaction (HI).

Conformation and dynamics of star-branched flexible polymer chains in a flowing solution

Abstract When linear or star-branched polymer chains in dilute solution are subjected to extensional flow of adequate intensity, each chain in the sample experiences a coil-stretch transition. Using Brownian dynamics simulation, we have studied both static and dynamic aspects of this phenomenon. We have determined the power law that relates the critical extensional rate, ϵ c , to the molecular weight of the chain. In the case of linear chains we have studied the distribution of transition times. If the accumulated strain is used to characterize the flow effect a seemingly universal behavior, independent of molecular weight is found. The molecular individualism is related to the excess of the applied extensional rate over its critical value, which will determine the transition time and other features of the coil-stretch transition.

Prediction and analysis of analytical ultracentrifugation experiments for heterogeneous macromolecules and nanoparticles based on Brownian dynamics simulation

In the prediction of sedimentation profiles in analytical ultracentrifugation, the counterflow due to diffusion must be taken into account for a proper analysis of experimental data in the determination of molecular properties. This is usually achieved by numerical solution of the Lamm equation. This paper presents an alternative approach, in which the displacement of the solute in the cell, resulting from the opposite effects of ultracentrifugal force and diffusional drift, is described by Brownian dynamics simulation of the solute particles. The formalism is developed for heterogeneous solutes, composed of several species, and implemented in computational schemes and tools. The accuracy of the procedure is verified by comparison with other methods based on the Lamm equation, and its efficiency is illustrated. The possibilities offered by the Brownian dynamics methods in the determination of solute properties and sample composition are demonstrated.

Simulation of Polymer Solutions in Steady Elongational Flow

In this work, we employ Brownian dynamics simulation to calculate steady-state properties of polymer chains in dilute solution when they are subjected to an elongational flow. The well-known coil-stretch transition, (De Gennes, 1974) is studied in terms of the variation of polymer properties on elongational rate, e. Prom this variation we evaluate the critical elongational rate e c , whose dependende on polymer features, such as hydrodynamic interacion and excluded volume is determined. Also, e c is combined with other solution properties to form dimensionless, length-independent compound quantities.