Gerhard Zifferer

Is the rate constant of chain propagation kp in radical polymerization really chain-length independent ?

A careful investigation of the k p data obtained from pulsed-laser polymerization at different pulse separations to in a lot of systems has revealed that k p exhibits a slight but significant decrease when t 0 is increased, corresponding to an about 20% decrease of k p extending over several hundreds in degree of polymerization. Transformation of this integral effect to individual chain-lengths reduces this range, of course, but still shows more than one hundred propagation steps to be concerned. This is interpreted in terms of a decrease of the monomer concentration at the site of propagation caused by the segments already added to the growing chain.

Molecular dynamics simulations of the adsorption of industrial relevant silane molecules at a zinc oxide surface

The physical behavior of different adsorbed silane molecules (octyltrihydroxysilane, aminopropyltrihydroxysilane, and thiolpropyltrihydroxysilane) at a ZnO surface (0001) dissolved in isopropanol are studied via constant temperature (298 K) molecular dynamics simulations. The adsorbed silane molecules exhibit a different behavior depending on the chemical nature of their tail. Octyltrihydroxysilane molecules with their rather unpolar tail show two distinct, energetic different orientations at the polar metal oxide surface. Mostly the three polar hydroxy groups of the head are in contact with ZnO the unpolar tail remaining in the isopropanol phase. Occasionally only two hydroxy groups interact with the surface the whole tail simultaneously being attached. On the contrary, due to their highly polar tail aminopropyltrihydroxysilane molecules have only one favorite orientation at the surface: Apart from some minor fluctuations two hydroxy groups as well as the amino group of the tail are in contact with the ...

Monte Carlo Simulation Studies of the Size and Shape of Ring Polymers

The present work gives a comparison between the properties of athermal ring polymers and those of linear chains. Based on bond fluctuation (BF) and pivot algorithm (PIV) for the construction of molecules, a new algorithm was developed, which proved most efficient due to large acceptance fractions and small (integral) auto-correlation times of global properties, in addition having the advantage of a large set of different bond vectors. While the topological state of ring polymers remains unchanged by exclusive use of BF, knotted structures (which were identified with the help of Alexander polynomials) can by formed and removed by the use of PIV. In accordance with previous work, it turned out that the probability of unknotted rings (in principle) exponentially decreases with an increasing number of segments, however, so slowly that the appearance of knotted structures (ca. 0.1 % for N)512) is a rare event in the range of chain-lenths evaluated (N=132-8192). The chain-length dependence of global quantities of ring polymers are described by the use of scaling relations with proper short chain corrections, in analogy to linear chains. The instantaneous shape of ring polymers is more symmetric than that of linear chains. Local quantities, i.e., mean squared bond lengths and mean bond angles are the same for both systems, at least in the limit of an infinite number of segments

Shape distribution and correlation between size and shape of tetrahedral lattice chains in athermal and theta systems

By means of Monte Carlo simulation, linear (F=2) and star-branched tetrahedral lattice chains with F=3–12 arms of length n=480 connected to a hard core consisting of MIN(5,F+1) segments (the total number of segments thus ranging from 963 to 5765) were produced for athermal and theta conditions. Nonreversal random walks (random walks without backfolding bonds) were generated as a reference. Several quantities (asphericity factor δ*, prolateness factor S*, and shape factors sfi*) characteristic of the instantaneous shape of molecules—being based on the orthogonal components of the squared radius of gyration taken along the principal axes of inertia—were computed. The probability distributions of these quantities were calculated and their interdependence as well as their correlation with quantities characteristic of the size of configurations was analyzed. Shape and size of star-branched chains for athermal as well as for theta conditions are highly correlated as earlier found for linear chains and random wa...

Shielding effects in polymer-polymer reactions. II. Reactions between linear and star-branched chains with up to six arms.

The shielding effect of surrounding arms and chains on the encounter probability of reactive sites located both at the end of a linear chain and at several positions along the arms of star-branched chains with up to six arms is calculated by means of exact enumeration of samples prepared by Monte Carlo simulation. The changes of parameters that characterize the size and the shape of chain configurations during the approach of reactive centers located at the end of the linear chain and at the center of the star are evaluated. In addition to this specific case, which represents the central reaction step in reversible addition-fragmentation chain transfer star polymerization following the Z-group approach, a general discussion is given on the chain-length dependence of shielding factors associated with distinct segment positions.

Simulation of dilute solutions of linear and star-branched polymers by dissipative particle dynamics.

A most promising off-lattice technique in order to simulate not only static but in addition dynamic behavior of linear and star-branched chains is the dissipative particle dynamics (DPD) method. In this model the atomistic representation of polymer molecules is replaced by a (coarse-grained) equivalent chain consisting of beads which are repulsive for each other in order to mimic the excluded volume effect (successive beads in addition are linked by springs). Likewise solvent molecules are combined to beads which in turn are repulsive for each other as well as for the polymer segments. The system is relaxed by molecular dynamics solving Newtons laws under the influence of short ranged conservative forces (i.e., repulsion between nonbonded beads and a proper balance of repulsion and attraction between bonded segments) and dissipative forces due to friction between particles, the latter representing the thermostat in conjunction with proper random forces. A variation of the strength of the repulsion between different types of beads allows the simulation of any desired thermodynamic situation. Static and dynamic properties of isolated linear and star-branched chains embedded in athermal, exothermal, and endothermal solvent are presented and theta conditions are examined. The generally accepted scaling concept for athermal systems is fairly well reproduced by linear and star-branched DPD chains and theta conditions appear for a unique parameter independent of functionality as in the case of Monte Carlo simulations. Furthermore, the correspondence between DPD and Monte Carlo data referring to the shape of chains and stars is fairly well, too. For dilute solutions the Zimm behavior is expected for dynamic properties which is indeed realized in DPD systems.

Chain‐length dependent termination in pulsed‐laser polymerization, 7. The evaluation of the power‐law exponent b from the chain‐length distribution in the low frequency (single‐pulse) limit for the reference systems styrene and methyl methacrylate in bulk at 25°C

The chain-length distribution (CLD) was examined for polymers prepared by low frequency pulsed laser polymerization (LF-PLP), i.e. for very long pulse separations in the so-called low frequency or single pulse limit. The data were fitted to the theoretical CLD which could be derived in a closed form for a chain-length dependent rate coefficient k t and the parameter b that characterizes this chain-length dependence was determined by this fitting procedure, b values close to 0.2 were obtained for styrene as well as for MMA, indicating a moderate chain-length dependence of k t at low conversions. This result, which is in good agreement with data evaluated by other methods in our laboratory, points to the fact that under these conditions end-segment diffusion is the rate-determining step in bimolecular termination. Factors like moderate chain transfer to monomer and uncertainties with respect to the mechanism of termination (combination or disproportionation) appear to have very little influence on this result.

SHAPE ASYMMETRY OF RANDOM WALKS AND NONREVERSAL RANDOM WALKS

Random walks (RWs) and nonreversal random walks (NRRWs) embedded in various lattices and freely jointed (off‐lattice) chains—consisting of up to N≊1000 segments—have been produced and analyzed with respect to their instantaneous shape. While the results of different RWs (as expected) coincide for all chain‐lengths examined, the short‐chain behavior of NRRWs is strongly dependent on the lattice type. In the limit of infinitely long chains, however, quantities characteristic of the shape converge to common values for all types of RWs and NRRWs examined.

Shape asymmetry of star‐branched random walks with many arms

Star‐branched (off‐lattice) random walks with up to F=96 arms and a total chain‐length of up to 15 361 segments have been produced by means of Monte Carlo simulation. Several quantities that characterize the shape asymmetry of molecules have been calculated. By suitable regression long‐chain limits of these quantities were obtained and analyzed with respect to the number of arms. Shape factors as well as asphericities are described very well by polynomials in F−1 or F−1/2, respectively.

Molecular dynamics simulations for drug dosage form development: thermal and solubility characteristics for hot-melt extrusion

Properties of pharmaceutical drug polymer mixtures like miscibility, stability and drug release are determined by the interactions of active pharmaceutical ingredients (APIs) and excipients (e.g. plasticisers) with functional polymers. Molecular dynamics (MD) simulations (Materials Studio®, COMPASS force field) are used to predict the principal behaviour of such drug products, especially miscibility and glass transition temperature (T g). Different mixtures containing APIs (theophylline or ibuprofen (IBU)) and water-soluble (triethyl citrate, (TEC)) or water-insoluble plasticiser (acetyl tributyl citrate (ATBC) or dibutyl sebacate (DBS)) dissolved/dispersed in a cationic polymethacrylate (EUDRAGIT® RS) were studied. Force field-based calculations of the cohesive energy densities of single constituents led to a qualitative approach according to Hanson describing the solid state of the mixture, while further calculations on the basis of the theory of free energy of mixing facilitated a semi-quantitative prediction. In the case of miscibility also calculation of T g was possible via modelling specific volumes of amorphous cells at various temperatures. The simulated data correlated well with the experimental data obtained from differential scanning calorimetry (DSC) of drug products processed via hot-melt extrusion. Accordingly, the described method facilitates a good estimate of pharmaceutical polymer drug mixtures, thus decreasing product development time, as well as the consumption of active ingredients.