Hydrodynamic properties of A8B8 type miktoarm (Vergina) stars

The dilute solution properties of three (PS)₈(PI)₈ miktoarm (Vergina) stars were investigated by viscometry and dynamic light scattering in toluene and tetrahydrofuran (THF) (common good solvents), cyclohexane at 34.5°C (theta solvent for PS and good for PI) and dioxane at 34°C (theta solvent for PI and good for PS). Experimental intrinsic viscosity [η] and hydrodynamic radii, R_h, values in all solvents were larger for the miktoarm stars in comparison to the calculated ones using a simple model which describes the size of the copolymers as a weighted average of the sizes of the homopolymer stars with the same total molecular weight and number of arms as the copolymer. This expansion is discussed on the basis of the increased number of heterocontacts, the topological constrains imposed by the common junction point in this highly branched miktoarm architecture and the asymmetry in molecular weights of the different kinds of arms. The conformation adopted in dilute solutions can explain, to some extent, the morphological results obtained on the same materials. The ratios of viscometric to hydrodynamic radii are consistent with previous investigations on linear and star polymers and in accord with the hard sphere model. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1329–1335, 1999     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

Concentration dependence of the global and anisotropic dimensions of confined macromolecules

The chain dimensions 〈R²〉 of nondilute polymer solutions confined to a slit of the width D were studied using lattice simulations. It was found that the chain compression induced in good solvents by the concentration ϕ is enhanced in a slit relative to the bulk. The global dimensions of chains also change with ϕ in confined and unconfined theta solutions. At intermediate slit widths, a region was noted where coils are squeezed along all three axes. This region is manifested as a channel on the three‐dimensional surface 〈R²〉(D,ϕ) in both good and theta solvents. The coil anisotropy, given by the ratio of the parallel and perpendicular components of the chain dimensions 〈R_y²〉/〈R_x²〉, reaches high values at strong confinements, where coils form quasi‐two‐dimensional pancakes. The concentration‐induced reduction of the global chain dimensions in good solvents is almost fully transmitted to the parallel component 〈R_y²〉. The computed effects of concentration and confinement were compared with the predictions of mean‐field and scaling theories, and implications of the results to ultrathin films and layered nanocomposites were discussed. In addition, the distribution functions of the components of the end‐to‐end distance R perpendicular and parallel to the plates, W (R_x) and W (R_y), were calculated. The function W (R_x) combined with the concentration profile ϕ (x) along the pore provided details of the chain structure close to walls. A marked difference in the pace of the filling up of the depletion layer was noticed between chains in theta and good solvents. From the distribution functions W (R_x) and W (R_y), the highly anisotropic force‐elongation relations imply the deformation of chains in confined solutions and ultrathin bulk films.     

Hydrodynamic studies on model branched polystyrenes

The measurement of the sedimentation velocity coefficient of narrow distribution linear, four-arm and six-arm star and comb polystyrenes in a theta solvent permits the experimental determination of h, i.e., the ratio of the translational friction coefficients of the branched polymer to that of its linear homolog. A comparison of experimental h/g^1/2 values with theoretical predictions can then be made. It was observed that the equivalent hydrodynamic radii derived from sedimentation and intrinsic viscosity measurements are identical within experimental error.     

Segment densities in star and comb random-flight chains

Segment densities of comb and star branched random-flight chains have been computed. It is found that the commonly used gaussian differs more significantly for branched chains than for linear chains. The asymptotic results are also found to depend on the branching parameter g.     

Monte carlo study of the dynamics of star-branched polymers

A uniform star-branched polymer model with f = 3 arms based on a simple cubic lattice was studied by means of the dynamic Monte Carlo method. The model chain is athermal with excluded-volume interactions and it is flexible. A new type of local micromodification was introduced to make the branching point movable. Static properties of the star polymer are in accordance with other theoretical predictions and experimental evidence. Scaling of the self diffusion constant and the terminal relaxation times is close to those of the Rouse theory and to simulation results of linear chains.     

Monte Carlo simulation studies of the size and shape of linear and star‐branched polymers embedded in the tetrahedral lattice

In recent years the author investigated the size and shape of linear and star‐branched model chains as a function of functionality (number of arms) F and chain length (total number of beads) N for several lattice and off‐lattice random walk models as well as for self‐avoiding random walks (embedded in the tetrahedral lattice) subjected to various thermodynamic conditions. Not only mean values – characteristic quantities averaged over a large number of configurations of given length, functionality and thermodynamic conditions – have been computed, but also distributions of shape parameters, and the correlation operative between size and shape has been explored. The present feature article in principle summarizes these results, however, the data given in part are recomputed for still larger sample sizes and chain‐lengths as in the underlying papers. In addition to stars with F = 4, 8 and 12 arms, so far unpublished investigations on stars with F = 3, F = 6 and F = 10 arms are presented and discussed.     

Monte Carlo simulation of tetrahedral chains, 7 the shape of linear and star-branched polymers near to theta-conditions

By use of the pivot algorithm, star-branched chains with F = 4, 8 and 12 arms of length n and linear chains (F = 2) are generated on a tetrahedral lattice (120 ≤ nF ≤ 3 840). By taking into account nearest neighbour interactions (each contact contributes an energy ϕ kT to the total energy of the configuration) a variation of the thermodynamic quality of the solvent is simulated by a variation of the energy parameter ϕ near the value of ϕ_θ = -0,475, characteristic of theta-conditions. For theta-conditions various quantities characteristic of the instantaneous shape of polymers exhibit similar values as found for nonreversal random walks; furthermore, while linear theta-chains are slightly less asymmetric than athermal ones, the opposite behaviour is found for star-branched polymers. Clearly, for all thermodynamic conditions the asymmetry of configurations decreases with increasing number of arms but remains appreciable even for F = 12.     

Monte Carlo investigations of dense copolymer systems, 1. Pivot algorithm and pair distribution function

ABA triblock copolymers (the solvent being a θ-solvent for B and an athermal one for A) as well as their constituent homopolymers were investigated by means of Monte Carlo simulations in a 5-choice cubic lattice. The polymer concentration (represented by the fraction ϕ of sites occupied by the polymer) varied from 0 (isolated chain) to 0.80. An investigation of the usefulness of the pivot algorithm in dense systems resulted in reasonable acceptance fractions up to a volume fraction of 0.12 (athermal chain and ABA copolymer) and 0.05 (θ-chain). For larger volume fractions only the chain-ends remain mobile. The overlap concentration of the polymers defined by several quantities was approximately 0.07 (athermal chain), 0.12 (θ-chain) and 0.09 (ABA copolymer). At a polymer fraction of 0.32, the chains had the same number of inter- and intramolecular contacts on average. At higher concentrations, the behaviour of the chains was primarily determined by intermolecular interactions. Contrary to isolated pairs, the pair distribution function g(r) of two athermal chains in a (cubic) box exceeded unity at intermediate distances because of the influence of the finite size of the box. The larger the size of the box, the smaller the (positive) deviation was. In the limit of r → 0 the pair distribution function g(r) – being smaller than unity – increased with increasing concentration while the maximum at intermediate distances simultaneously decreased. Ultimately, at the highest concentration, the pair distribution function resembled that of isolated θ-chains. The concentration dependence of the θ-pair distribution function itself, however, is negligible. At low concentrations the pair distribution function of the ABA triblock copolymer behaved like that of an athermal chain (up to ϕ ≈ 0.40) where characteristic oscillations around 1 developed. This might be taken as indicative of the formation of a lamellar phase.     

Combination of nitroxide‐mediated polymerization and SET‐LRP for the synthesis of high molar mass branched and star‐branched poly(n‐butyl acrylate) characterized by size exclusion chromatography and rheology

Branched and star‐branched polymers were successfully synthesized by the combination of two successive controlled radical polymerization methods. A series of linear and star poly(n‐butyl acrylate)‐co‐poly(2‐(2‐bromoisobutyryloxy) ethyl acrylate) statistical copolymers, P(nBA‐co‐BIEA)_x, were first synthesized by nitroxide‐mediated polymerization (NMP at T > 100 °C). The subsequent polymerization of n‐butyl acrylate by single electron transfer‐living radical polymerization (SET‐LRP at T = 25 °C), initiated from the brominated sites of the P(nBA‐co‐BIEA)_x copolymer, produced branched or star‐branched poly(n‐butyl acrylate) (PnBA). Both types of polymerizations (NMP and SET‐LRP) exhibited features of a controlled polymerization with linear evolutions of logarithmic conversion versus time and number‐average molar masses versus conversion for final M_n superior to 80,000 g mol^?1. The branched and star‐branched architectures with high molar mass and low number of branches were fully characterized by size exclusion chromatography. The Mark–Houwink Sakurada relationship and the analysis of the contraction factor (g′ = ([η]_branched/[η]_linear)_M) confirmed the elaboration of complex PnBA. The zero‐shear viscosities of the linear, star‐shaped, branched, and star‐branched polymers were compared. The modeling of the rheological properties confirmed the synthesis of the branched architectures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Monte carlo calculations of second virial coefficients of chain molecules

Monte Carlo calculations have been performed for different types of chain molecules whose units interact through Lennard-Jones potentials. From the averaged Mayer function, we have evaluated the intermolecular two-body cluster integral, obtaining results for second virial coefficients. We have investigated the following points: a) the site modelization of alkanes by comparison of our results with gas phase data of different linear and branched alkanes and their mixtures. b) the prediction of interpenetration factors for flexible linear and star polymer chains in a good solvent (or excluded volume conditions). c) the determination of the theta point for a model of flexible polymer chains and the comparison of data for finite chains with theoretical predictions.     

Elastic behavior of uniform star polymer chains

Elastic behaviors of uniform star polymer chains with two to seven branches (namely, functionality f = 2-7) are investigated using Monte Carlo simulation and the bond fluctuation model. Here chain dimensions and thermodynamic properties of uniform star polymer chains during the process of tensile elongation are studied, and comparisons with linear chain are also made. Static properties of chains such as chain sizes and asphericities of chains are calculated, and g-value of g = 〈S²〉_star/〈S²〉_linear decreases with elongation ratio increasing for different functionality f. Thermodynamic properties such as average energy 〈U〉, free energy per bond 〈A′〉 and elastic force F are also investigated during the process of tensile elongation. In the meantime, scatting functions P(q) are calculated for star polymer chains with different functionality f. Additionally, we also discuss the influence of elongation ratio on scattering form factor. The impenetrability of the star cores is known to cause a discontinuity in the osmotic pressure showed through a peak in the scattering functions, and some different behaviors in the tensile process for uniform star chain are obtained.     

Electron-pair radial density functions

We introduce and discuss a generalized electron-pair radial density function G(q; a) that represents the probability density for the electron-pair radius |r ₁+ar ₂| to be q, where a is a real-valued parameter. The density function G(q; a) is a projection of the two-electron radial density D ₂(r ₁, r ₂) along lines r ₁ + ar ₂ ± q = 0 in the r ₁ r ₂ plane onto a point in the qa plane, and connects three densities S(s), D(r), and T(t), defined independently in the literature, as a smooth function of a: For an N-electron (N ≥ 2) system, S(s) = G(s; + 1), D(r) = 2G(r; 0)/(N − 1), and T(t) = G(|t|;−1)/2, where S(s) and T(t) are the electron-pair radial sum and difference densities, respectively, and D(r) is the single-electron radial density. Simple illustrations are given for the helium atom in the ground 1s² and the first excited 1s2s ³S states.     

Conformational properties of <Emphasis Type="Italic">ortho</Emphasis>-nitrobenzenesulfonamide in gas and crystalline phases. Intra- and intermolecular hydrogen bond

A combined gas-phase electron diffraction and quantum chemical (B3LYP/6-311+G**, B3LYP/cc-pvtz, MP2/cc-pvtz) study of molecular structure of 2-nitrobenzenesulfonamide (2-NBSA) was carried out. Quantum chemical calculations showed that 2-NBSA has four conformers, two of which are stabilized by intramolecular hydrogen bond. The latter (with the S–N bond in a close to orthogonal position around the phenyl ring and differing from each other by staggered or eclipsed positions of the N–H and S=O bonds in the SO₂NH₂ group) presented in a saturated vapor over 2-NBSA at T = 433 (3) K in commensurable amounts. Experimental internuclear distances (Ǻ) for the staggered conformer are (?): r _h1(C–H)_av. = 1.071(9), r _h1(C–C)_av. = 1.390(4), r _h1(C–S) = 1.789(8), r _h1(S=O)_av. = 1.427(6), r _h1(S–N) = 1.644(6), r _h1(N–O)_av. = 1.221(4), r _h1(C′–N) = 1.487(8), r _h1(N–H)_av. = 1.014. Calculations at B3LYP/cc-pvtz level were performed to determine the structure and the energies of the transition states between conformers. It was shown that the conformer structures of free molecule differ from those of a molecule stabilized by intermolecular hydrogen bonds in a crystal. Influence of a substituent X (X = –CH₃, –NO₂) on conformational features of the ortho-substituted benzenesulfonamide was established.     

Force-length relations in deformed coils above and below the theta state. Possible bimodality in the chain distribution function

Stretching of flexible macromolecules by an external force, acting on the chain ends, in solvents of variable quality was simulated by the Monte Carlo method on a tetrahedral lattice. The forcelength relations and the stress-induced changes in the population of the gauche conformers were calculated for coils in theta and athermal solvents. In poor solvents, the stretching of a collapsed coil involves a rather abrupt upturn of the force-length curve explained as a transition of a globular coil into an extended coil. In conformity with this interpretation, a bimodal shape of the chain vector distribution function P(R) was found in the intermediate range of deformation of collapsed coils. The significance of the results to the stress-strain behavior of networks with pronounced interaction (such as collapsed gels) are discussed.     

Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Effect of MoO<Subscript>3</Subscript> additions on the thermal stability and crystallization kinetics of PbO–Sb<Subscript>2</Subscript>O<Subscript>3</Subscript>–As<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

The present paper reports on the effect of MoO₃ on the glass transition, thermal stability and crystallization kinetics for (40PbO–20Sb₂O₃–40As₂O₃)_100−x –(MoO₃) _x (x = 0, 0.25, 0.5, 0.75 and 1 mol%) glasses. Differential scanning calorimetry (DSC) results under non-isothermal conditions for the studied glasses were reported and discussed. The values of the glass transition temperature (T _g) and the peak temperature of crystallization (T _p) are found to be dependent on heating rate and MoO₃ content. From the compositional dependence and the heating rate dependence of T _g and T _p, the values of the activation energy for glass transition (E _g) and the activation energy for crystallization (E _c) were evaluated and discussed. Thermal stability for (40PbO–20Sb₂O₃–40As₂O₃)_100−x –(MoO₃) _x glasses has been evaluated using various thermal stability criteria such as ΔT, H _r , H _g and S. Moreover, in the present work, the K _r(T) criterion has been considered for the evaluation of glass stability from DSC data. The stability criteria increases with increasing MoO₃ content up to x = 0.5 mol%, and decreases beyond this limit.