Juan J. Freire

Conformational Properties of Branched Polymers: Theory and Simulations

The prediction and interpretation of conformational properties of branched polymers is difficult, due to the complexity and variety of these structures. Numerical simulations are, consequently, very useful in the investigation of these systems. This review describes the application of numerical simulation techniques to relevant theoretical problems concerning branched polymer systems, taking also into account the related experimental data. Monte Carlo, Molecular Dynamics and Brownian Dynamics methods are employed to simulate the equilibrium and dynamic behavior, and also to reproduce hydrodynamic properties. The simulations are performed on several polymer models. Thus, different Monte Carlo algorithms have been devised for lattice and off-lattice models. Moreover, Molecular Dynamics and Brownian Dynamics can be carried out for detailed atomic or coarse-grained chains. A great amount of investigation has been engaged in the understanding of uniform homopolymer stars as single chains, or in non-diluted solutions and melts, employing this variety of techniques, models and properties. However, other important structures, such as stars with different types of monomer units, combs, brushes, dendrimers and absorbed branched polymers have also been the subject of specific simulation studies.

A Multiscale Scheme for the Simulation of Conformational and Solution Properties of Different Dendrimer Molecules

We propose a multiscale protocol for the simulation of conformation and dynamics of dendrimer molecules in dilute solution. Conformational properties (radius of gyration, mass distribution, and scattering intensities) and overall hydrodynamic properties (translational diffusion and intrinsic viscosity) are predicted by means of a very simple coarse-grained bead-and-spring model, whose parameters are not adjusted against experimental properties, but rather they are obtained from previous, atomic-level simulations which are also quite simple, performed with small fragments and Langevin dynamics simulation. The scheme is described and applied systematically to four different dendrimer molecules with up to seven generations. The predictive capability of this scheme is tested by comparison with experimental data. It is found that the predicted geometric and hydrodynamic radii of the dendrimer molecules are in agreement (typical error is about 4%) with a large set experimental values of the four dendrimers with various numbers of generations. Agreement with some X-ray scattering experimental intensities also confirms the good prediction of the internal structure. This scheme is easily extendable to study more complex molecules (e.g., functionalized dendrimers) and to simulate internal dynamics.

Hydrodynamic interaction effects in the rheological properties of Hookean dumbbells in steady shear flow: a Brownian dynamics simulation study

Abstract In this paper we present a Brownian dynamics simulation study where we employ the algorithm of Ermak and McCammon including solvent flow in the calculation of the rheological properties of Hookean dumbbells in steady shear flow. We have also included the possibility of the excluded volume and we have studied several possibilities with and without hydrodynamic interactions (HI). When hydrodynamic interaction is rigorously treated, the intrinsic viscosity is found to increase. If the Rotne-Prager-Yamakawa HI tensor is used instead of the Oseen tensor, the changes in the material functions are quite small. On the other hand, excluded-volume interactions produce, as expected, an increase in the viscosity. This is so both with and without HI. Our results are compared with those of other works in which the HI tensor is pre-averaged or consistently averaged.

Potential parameters of methyl and methylene obtained from second virial coefficients of n-alkanes

The second virial coefficients of a number of n-alkanes (from butane to hexadecane) have been evaluated by using the Rotational Isomeric State model. Methyl and methylene groups have been modelled as Lennard-Jones (12 – 6) interaction sites centered on the position of the carbon atoms. Equal size has been assigned to the methyl and methylene groups but differences in the well-depth of the potential were considered. We have chosen the values of the potential well-depths of methyl and methylene group to fit the second virial coefficient of several n-alkanes in a range of about 300 K. The agreement with experimental results is good. Then, it is shown that a simple site-site potential model is able to reproduce the second virial coefficient of several n-alkanes in a wide range of temperatures.

The shape of linear and star polymers with and without excluded volume

The shape of isolated linear and star polymers, with and without excluded volume, has been determined by Monte Carlo simulations using a pivot algorithm. Stars with 3, 4, 5, and 6 arms are studied. The high efficiency of the pivot algorithm has allowed us to obtain accurate data for long chains. Good agreement is found with existing analytical expressions for nonexcluded volume chains and with other computer simulations for excluded volume chains.

Investigation of the end-to-end vector distribution function for linear polymers in different regimes

Monte Carlo simulations employing the pivot algorithm are used to generate off‐lattice three‐dimensional linear polymers in three regimes: nonexcluded volume, theta, and excluded volume. The end‐to‐end vector distribution function is calculated from the resulting configurations. It is found that the shape of the distribution function is Gaussian for nonexcluded volume chains, nearly Gaussian for theta chains, and that the scaling form derived by des Cloizeaux fits the data for excluded volume chains well.

Application of the rotational isomeric model to the calculation of binary interactions between flexible chains

Orientational and conformational averages of the Mayer function corresponding to binary interactions of flexible n-alkane molecules have been computed by means of a Monte Carlo sampling of pairs of conformations generated with randomly chosen rotational angles and relative orientations. The conformations are generated according to conditional probabilities and molecular parameters corresponding to the rotational isomeric state model. The intermolecular interactions between -CH2 or -CH3 groups are described through a Lennard-Jones potential, with a fixed value of the length parameter d and a value of the energy parameter ϵ fitted to reproduce experimental results or justified theoretical predictions for second virial coefficients over a wide temperature range. We find a good agreement with these data employing values of ϵ which has a modest variation with chain length (about 30 per cent with respect to the highest value within the range n = 4–16). The averaged results for the interactions are discussed and...

Mean reciprocal distances of short polymethylene chains. Calculation of the translational diffusion coefficient of n‐alkanes

The reciprocal distance averages of chain molecules 〈R−1ij〉 are calculated by a nonlattice Monte Carlo method. These 〈R−1ij〉’s are needed in the theory of hydrodynamic properties. The calculation is carried out for polymethylene chains of up to 50 C–C bonds. Interactions of short range and of long range are taken into account by means of the relative stability of rotational isomers and of a hard sphere excluded volume. The results obtained are used to interpret literature data on the translational diffusion coefficient of n‐alkanes, in benzene, and in carbon tetrachloride.

Monte Carlo calculations for the intrinsic viscosity of several dendrimer molecules

We have performed Monte Carlo simulations to reproduce the intrinsic viscosity corresponding to different generation of several types of dendrite molecules: polyamidoamine dendrimers with an ethylendiamine core, polypropylene-imine with a diaminobutane core, and monodendrons and tridendrons of polybenzylether. With this end, we have employed coarse-grained idealizations of the molecules constituted by only two beads in each repeat unit (one in a branching or end unit and one intermediate along the repeat unit) and a simple hard-sphere potential between non-neighboring beads. Our goal is to investigate if this simple model is able to provide a reasonable description of some differences between these systems that have been observed experimentally, in particular, the location of the maximum in the intrinsic viscosity as a function of the generation number. Experimental radii of gyration in a given solvent are reproduced by a fit of the hard-sphere potential diameter. Subsequently, intrinsic viscosities are calculated by the variational approach of Fixman, which yields an accurate lower-bound value with an additional hydrodynamic interaction parameter (the friction radius of the beads). The results show a pronounced variation of the maximum location with the value of the friction radius and the structural details that cannot be mimicked with simpler models. The initial conformations for the Monte Carlo procedure are taken from atomistic configurations thermalized by means of a molecular dynamics.

Brownian dynamics simulation of flexible polymer chains with excluded volume and hydrodynamic interactions. A comparison with Monte Carlo and theoretical results

Abstract The generation of Brownian dynamics trajectories for a flexible polymer constituted of statistical Gaussian units with intramolecular long-range (excluded volume) interactions is accomplished. The intramolecular interactions are described by relatively soft repulsive forces derived from an exponentially decaying potential with a cut-off distance. The validity of this method is satisfactorily tested through the comparison of a wide set of numerical results for equilibrium properties (different averaged dimensions and internal distances, and the end-to-end distance distribution factor) with Monte Carlo results from a model that includes the customary hard-spheres representation of excluded volume forces. Furthermore, the numerical values obtained in this study for the different properties are shown to agree with the scaling theories or Renormalization Group predictions. A transport property, the translational diffusion coefficient, is also obtained and included in the numerical analysis.