Effect of molecular topology on the transport properties of dendrimers in dilute solution at Theta temperature: a Brownian dynamics study

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Theta conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Modeling of the molar mass distribution of six-arm star-branched poly-epsilon-caprolactam using size-exclusion chromatography

This paper presents a modeling-based approach to the prediction of the molar mass distribution of the various species in a star-branched polycondensation mixture. The interpretation of experimental SEC data of the mixture of linear, cyclic and star-branched molecules is not straightforward, because of the different sizes of those molecules (having the same molecular mass). Therefore we have opted to use SEC analysis with only a concentration detector and fit the experimental data to the theoretical mass distribution, corrected for the volume of the various molecules. This allows the relative fraction and the distribution of the various species in the mixture (linear, cyclic and star-branched) to be determined. To demonstrate this, the six-arm star-branched poly-epsilon-caprolactam based on the six-functional coupling molecule, hexa(6-caproic acid) melamine has been analyzed. Five polymer mixtures with different initial concentration of coupling molecule have been synthesized. As the initial concentration of coupling molecule increased, we found that the weight fraction of star-branched molecules increased, while the weight fraction of linear and cyclic molecules decreased. We also found that the weight-average molar mass and the arm length decrease as the initial fraction of the coupling molecule increases.     

Observation of entropic effect on conformation changes of complex systems under well-controlled temperature conditions

We report direct observation of an entropic effect in determining the folding of a linear dicarboxylate dianion with a flexible aliphatic chain [(-)O(2)C-(CH(2))(6)-CO(2)(-)] by photoelectron spectroscopy as a function of temperature (18-300 K) and degree of solvation from 1 to 18 water molecules. A folding transition is observed to occur at 16 solvent water molecules at room temperature and at 14 solvent molecules below 120 K due to the entropic effect. The (-)O(2)C-(CH(2))(6)-CO(2)(-)(H(2)O)(14) hydrated cluster exhibits interesting temperature-dependent behaviors, and its ratio of folded over linear conformations can be precisely controlled as a function of temperature, yielding the enthalpy and entropy differences between the two conformations. A folding barrier is observed at very low temperatures, resulting in kinetic trapping of the linear conformation. The current work provides a simple model system to study the dynamics and entropic effect in complex systems and may be important for understanding the hydration and conformation changes of biological molecules.     

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.     

DNA electrophoresis in confined, periodic geometries: a new lakes-straits model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimm's approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.     

Computer simulations of diffusion and dynamics of short-chain polyelectrolytes

Brownian dynamics simulations are conducted to investigate the diffusional and dynamic properties of polyelectrolytes in dilute salt-free solutions. The polyelectrolyte molecule is represented by a bead-spring chain in a primitive model. The long-range hydrodynamic and Coulomb interactions are both taken into consideration through the Ewald summations for the first time. The major finding of our simulations is that the dependence of the long-time chain diffusivity on the Coulomb interaction strength is very different from that of the Kirkwood short-time diffusivity, which simply shows a trend nearly opposite to the chain size. When ignoring the hydrodynamic interaction (HI), the coupling effect between the chain and its counterions gives rise to a noticeable increase in the long-time diffusivity at intermediate electrostatic interaction strengths. However, the incorporation of HI suppresses this effect to a degree that one can no longer discern it. Moreover, the rotational relaxation is found to show a dependence opposite to that of the gyration radius relaxation.     

The molecular kink paradigm for rubber elasticity: numerical simulations of explicit polyisoprene networks at low to moderate tensile strains

Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.     

Statics of polymer droplets on deformable surfaces

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different surface/drop compatibility and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness, and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupre? wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.     

Directed self-assembly of surfactants in carbon nanotube materials

The self-assembly of surfactant molecules on crossing carbon nanotubes has been investigated using a bead-spring model and implicit solvent dissipative particle dynamics simulations. Adsorption is directed to the nanotube crossing by its higher hydrophobic potential which is due to the presence of two surfaces. As a consequence of the tendency of surfactant molecules to self-assemble into micelles, the adsorbed molecules form a "central aggregate" at the crossing, thus, confining the molecules to the immediate vicinity of the crossing. Adsorption on the remaining nanotube surface becomes significant only at higher surfactant concentrations, where the molecules self-assemble to hemimicelles which grow continuously to full micelles upon increase of the (bulk) surfactant concentration. Our results allow two conclusions for the rational design of nanostructured materials: (i) the size of the central aggregate can not be much larger than that of a bulk micelle and (ii) control of the adsorbed structures is conveniently possible via the (bulk) surfactant concentration.     

Simulation of the gyroid phase in off-lattice models of pure diblock copolymer melts

Particle-based molecular simulations of pure diblock copolymer (DBC) systems were performed in continuum space via dissipative particle dynamics and Monte Carlo methods for a bead-spring chain model. This model consisted of chains of soft repulsive particles often used with dissipative particle dynamics. The gyroid phase was successfully simulated in DBC melts at selected conditions provided that the simulation box size was commensurate with the gyroid lattice spacing. Simulations were concentrated at conditions where the gyroid phase is expected to be stable which allowed us to outline approximate phase boundaries. When more than one phase was observed by varying simulation box size, thermodynamic stability was discerned by comparing the Helmholtz free energy of the competing phases. For this purpose, chemical potentials were efficiently simulated via an expanded ensemble that gradually inserts/deletes a target chain to/from the system. These simulations employed a novel combination of Bennett's [J. Comput. Phys. 22, 245 (1976)] acceptance-ratio method to estimate free-energy differences and a recently proposed method to get biasing weights that maximize the number of times that the target chain is regrown. The analysis of the gyroid nodes revealed clear evidence of packing frustration in the form of an (entropically) unfavorably overstretching of chains, a phenomenon that has been suggested to provide the structural basis for the limited region of stability of the gyroid phase in the DBC phase diagram. Finally, the G phase and nodal chain stretching were also found in simulations with a completely different DBC particle-based model.     

Properties of star-branched and linear chains in confined space: a computer simulation study

We studied the properties of simple models of linear and star-branched polymer chains confined in a slit. The polymer chains were built of united atoms and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain linear and star-branched with three branches (of equal length) were studied. The excluded volume was the only potential introduced into the model and thus, the system was athermal. The chains were put between two parallel and impenetrable surfaces. Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation were carried out. The differences and similarities in the global size and the structure and of linear and star-branched chains were shown and discussed.     

Effect of molecular weight on the capillary absorption of polymer droplets

We study capillary absorption of small polymer droplets into nonwettable capillaries using coarse-grained molecular dynamics simulations and a simple analytical model. Studies of droplets of simple fluids have revealed that the capillary process depends on the ratio of tube-to-droplet radii [Willmott Faraday Discuss., 2010, 146, 233; Marmur J. Colloid Interface Sci. 1988, 122, 209]. Here we consider the absorption of droplets of polymers and study the effect of polymer chain length on the capillary absorption process. Our simulations reveal that for droplets of the same size (radius), the critical tube radius, below which there is no absorption, increases with the length of the polymer chains that constitute the droplets. We propose a model to explain this effect, which incorporates an entropic penalty for polymer confinement and find that this model agrees quantitatively with the simulations. We also find that the absorption dynamics is sensitive to the polymer chain length. In some cases during the capillary uptake transient partial absorption states, where the droplet is partially in and partially out of the tube, were observed. Such dynamics cannot be explained by a generalized Lucas-Washburn approach.     

The effect of hydrodynamic interactions on the dynamics of DNA translocation through pores

In this work, we investigate the effect of hydrodynamic interactions on the dynamics of DNA translocation through micropores. We simulate DNA as a bead-spring chain and use a lattice Boltzmann method to simulate the flow field that arises from the motion of the molecule. We investigate the free-draining entrance of DNA to the pore by diffusion and find that, consistent with experiments, molecules have a higher probability of entering the pore from one end. We then consider the electric-field driven translocation of 21-210 microm DNA with and without hydrodynamic interactions. Consistent with experiments, we study translocation events that are much shorter than the relaxation time of DNA. We find that the effect of hydrodynamic interactions on this process is to cause different regions of a molecule, other than the ones pulled by voltage or chain connectivity into the pore, to move toward the pore. We quantify this effect and show that it is smaller than the difference in the translocation dynamics of chains that arises from different initial configurations of the molecules. A power-law scaling of translocation time with chain length is observed, with exponents of 1.28+/-0.03 and 1.31+/-0.03 in simulations with and without hydrodynamic interactions, respectively. Our results are in good agreement with recent translocation experiments conducted in small pores and show that, for the regime considered in this work, hydrodynamic interactions play a minor role in the relation of the translocation time to chain length. For fast translocation processes, the effect of hydrodynamic interactions is local and the main factor determining the dynamics of DNA is the initial configuration of the molecules.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.     

Continuum transport model of Ogston sieving in patterned nanofilter arrays for separation of rod-like biomolecules

This article proposes a simple computational transport model of rod-like short dsDNA molecules through a microfabricated nanofilter array. Using a nanochannel consisting of alternate deep wells and shallow slits, it is demonstrated that the complex partitioning of rod-like DNA molecules of different sizes over the nanofilter array can be well described by continuum transport theory with the orientational entropy and anisotropic transport parameters properly quantified. In this model, orientational entropy of the rod-like DNA is calculated from the equilibrium distribution of rigid cylindrical rod near the solid wall. The flux caused by entropic differences is derived from the interaction between the DNA rods and the solid channel wall during rotational diffusion. In addition to its role as an entropic barrier, the confinement of the DNA in the shallow channels also induces large changes in the effective electrophoretic mobility for longer molecules in the presence of EOF. In addition to the partitioning/selectivity of DNA molecules by the nanofilter, this model can also be used to estimate the dispersion of separated peaks. It allows for fast optimization of nanofilter separation devices, without the need of stochastic modeling techniques that are usually required.     

Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow

The role of solvent quality in determining the universal material properties of dilute polymer solutions undergoing steady simple shear flow is examined. A bead-spring chain representation of the polymer molecule is used, and the influence of solvent molecules on polymer conformations is modelled by a narrow Gaussian excluded volume potential that acts pairwise between the beads of the chain. Brownian dynamics simulations data, acquired for chains of finite length, and extrapolated to the limit of infinite chain length, are shown to be model independent. This feature of the narrow Gaussian potential, which leads to results identical to a delta-function repulsive potential, enables the prediction of both universal crossover scaling functions and asymptotic behavior in the excluded volume limit. Universal viscometric functions, obtained by this procedure, are found to exhibit increased shear thinning with increasing solvent quality. In the excluded volume limit, they are found to obey power law scaling with the characteristic shear rate beta, in close agreement with previously obtained renormalization group results. The presence of excluded volume interactions is also shown to lead to a weakening of the alignment of the polymer chain with the flow direction.     

Electrophoretic mobility of linear and star-branched DNA in semidilute polymer solutions

Electrophoresis of large linear T2 (162 kbp) and 3-arm star-branched (N(Arm) = 48.5 kbp) DNA in linear polyacrylamide (LPA) solutions above the overlap concentration c* has been investigated using a fluorescence visualization technique that allows both the conformation and mobility mu of the DNA to be determined. LPA solutions of moderate polydispersity index (PI approximately 1.7-2.1) and variable polymer molecular weight Mw (0.59-2.05 MDa) are used as the sieving media. In unentangled semidilute solutions (c* < c < c(e)), we find that the conformational dynamics of linear and star-branched DNA in electric fields are strikingly different; the former migrating in predominantly U- or I-shaped conformations, depending on electric field strength E, and the latter migrating in a squid-like profile with the star-arms outstretched in the direction opposite to E and dragging the branch point through the sieving medium. Despite these visual differences, mu for linear and star-branched DNA of comparable size are found to be nearly identical in semidilute, unentangled LPA solutions. For LPA concentrations above the entanglement threshold (c > c(e)), the conformation of migrating linear and star-shaped DNA manifest only subtle changes from their unentangled solution features, but mu for the stars decreases strongly with increasing LPA concentration and molecular weight, while mu for linear DNA becomes nearly independent of c and Mw. These findings are discussed in the context of current theories for electrophoresis of large polyelectrolytes.     

Coarse grained model of diffusion in entangled bidisperse polymer melts

Chain diffusion is studied in mixtures of bidisperse linear polymers of same chemical identity by means of simulations. The two subpopulations are moderately to highly entangled, with the shorter chain length N(S), fulfilling N(S)N(e)> or =5. To this end, a coarse grained model calibrated to reproduce both the structure and dynamics of chains in monodisperse entangled melts is used [A. Rakshit and R. C. Picu, J. Chem. Phys. 125, 164907 (2006)]. Its performance in reproducing chain dynamics in a polydisperse melt is tested by extensively comparing the results with those obtained from an equivalent fine scale representation of the same system (a bead-spring model). The coarse grained model is used further to investigate the scaling of the diffusion coefficient with the length of the two types of chains and its dependence on the respective fractions. The model reproduces many features observed experimentally. For example, the diffusion coefficient of one of the chain types decreases with increasing the length of the other type chains. It is shown that, in this model, this effect is not linked to constraint release. When the matrix chains become sufficiently long, their length does not influence the diffusion coefficient of the short chains anymore. The diffusion coefficient of the short chains scales with their weight fraction in a manner consistent with experimental observations. In mixtures, the dynamics of the short chains is slower and that of the long chains is marginally faster than in their respective monodisperse melts.