bluuebunny/crossref_metadata_2025 huggingface dataset:
Simulations of excluded volume effects due to chain thickness and solvent quality on the chain vector distributions and mean coil dimensions
Authors: Cifra Peter , Bleha Tomáš
Published: April 2003

Lattice simulations of chains in good, theta and poor solvents were performed with an explicit incorporation of the excluded volume (chain thickness) into the model. The scaling power law for chain dimensions was found to apply in the theta and athermal states and to fail in the region below the theta state where collapsed chains with voids inside a globule occur. The solvent‐induced globule‐to‐coil transition is transparently manifested by changes in the chain vector distribution functions. In the region of small and medium chain elongations, the simulation data can be fitted in the theta solvent by a Gaussian distribution function and in the athermal solvent by a function due to Oono et al. The stored elastic energy of the chains with fixed ends was calculated as a function of the chain‐end displacement for fully flexible molecules in all three types of solvent and for poly(methylene).
Characteristic ratio of the mean‐square end‐to‐end distance of poly(vinylidene fluoride) with microstructural defects
Authors: Zhou Zhiping , Yan Deyue , Alfonso Giovanni C.
Published: April 2003

The segment length distribution of isoregic head‐to‐head and tail‐to‐tail sequences in poly‐(vinylidene fluoride) (PVF2)

System. name: poly(1,1‐difluoroethylene).

chains is calculated from 19F NMR literature data. It is found that the average length of inverse segments is very close to one unit; therefore almost all head‐to‐head defects are immediately repaired by an adjacent tail‐to‐tail addition. The role of microstructure on the characteristic ratio of the end‐to‐end distance is then investigated. Results obtained by two different methods indicate that, in agreement with previous Monte Carlo calculations, defects play a minor role for the conformational characteristics of PVF2. However, a slight contraction of about 4% is expected for very defective chains.
The kinetics of free radical polymerizing systems at low conversion, 3. On the variation of the termination rate coefficient with monomer and with temperature
Authors: Russell Gregory T.
Published: April 2003

This paper shows that variations with temperature and with monomer of overall termination rate coefficients, denoted 〈kt〉, are not what they seem. This is important because such variations, as determined experimentally, are usually taken as making direct statements about the actual termination reaction. For example, it has always been assumed that the activation energy of 〈kt〉, signified Ea (〈kt〉), reflects the activation energy of the rate determining step behind the termination reaction. However it is shown that purely as a consequence of termination rate coefficients being chain length dependent, this is not so. In fact, simply given chain length dependent termination, Ea (〈kt〉) will be a function of the means of initiation, of the initiator itself, of the initiator concentration [I], and of whether [I] is held constant or varied with temperature. These results not only suggest interesting experiments for microscopic probing of the termination process, but they also help explain the wide variety of experimental Ea(〈kt〉) found in the literature. Much literature data concerning 〈kt〉 is also made sense of in the second half of this paper. Here variations of 〈kt〉 with monomer are examined, and it is shown that in order to explain these, it is likely that variations of rates of propagation and of transfer are often of major importance. Also considered are the effects on 〈kt〉 of diffusion coefficient variations, these of course being directly related to the rate coefficients of the actual termination process. Interesting results, ones relevant to experimental data interpretation, again emerge. For all these calculations a termination model appropriate for very low conversion bulk and solution polymerizations is used, and steady state 〈kt〉 computed. However the principles that emerge are general, and their relevance is contingent only upon termination being chain length dependent. It is therefore to be envisaged that these principles will assist in explaining far more actual polymerization data than has been looked at here.
The extension of the “restricted” penultimate scheme of binary copolymerization to ternary systems
Authors: Olaj Oskar Friedrich , Schnöll‐Bitai Irene
Published: April 2003

The so‐called “restricted” penultimate scheme of binary copolymerization — first presented by Fukuda et al. — is extended to ternary systems without introducing extra parameters not inherent in the three binary systems which form the ternary systems. The crucial assumption is that the restricted penultimate effect is only dependent (1) on the type of monomer forming the terminal radical and (2) the monomer replacing this type of monomer in the penultimate unit, but is independent of the monomer to be added. Accordingly, the scheme is fully described by quantities taken from the binary copolymerizations forming the ternary system. This general principle is still valid when the number of different monomers in the copolymerization system is even increased beyond three. Comparison between predicted values of the phenomenological propagation constant k̄p with the few experimental data available for terpolymerization systems indicates a satisfactory agreement.
Fourier‐transformation of model chain pair configurations and their analysis in fourier‐space
Authors: Zifferer Gerhard , Olaj Oskar Friedrich
Published: April 2003

Light scattering experiments may be used to determine a lot of quantities characteristic of a polymer. Numeric analysis of calculated scattering intensities of ensembles of polymer model chains in dilute solution (taking into account intramolecular as well as intermolecular interferences) according to the familiar methods and comparison of the results to the respective quantities evaluated directly in real space allows a check of the liability of data extracted from light scattering experiments. It turned out that the mean‐square radius of gyration as well as the excluded volume (which may be regarded as the second moment of the pair distribution function) are nearly perfectly reproduced. Higher moments, however, are subject to some error which is due to the characteristic changes in size, shape and orientation of polymers caused by intermolecular interaction which are not accounted for in the theories forming the basis of the analysis of light scattering data.
Theory of the orientational ordering for dimers with conformational flexibility
Authors: Mercurieva Anna , Birshtein Tatiana
Published: April 2003

In the self‐consistent field approximation a theory of the orientational ordering is developed for the melt of dimers containing two mesogenic fragments capable of conformational reorganization. Discrete conformations of the dimers (rotational isomers) are characterized by the values of valence angles. Both three‐dimensional and two‐dimensional melts are considered. It is shown that the presence of bent isomers in the melt reduces the temperature of the phase transition to the anisotropic phase. For a three‐dimensional system with first‐order phase transition to the ordered state, the jump of the order parameter at the transition point for dimers with conformational flexibility appears to be greater than for rigid dimers. For dimers with two isomers (a linear and a bent one) the order parameter and the statistical weight of the linear isomer at the transition point depend nonmonotonously on the statistical weight of this isomer in the isotropic phase. The effect of “supercooling” of the isotropic phase for linear conformations of flexible dimers is discussed.
Distributions of the unperturbed dimensions of Markov‐chain copolymers
Authors: Jung Bernd
Published: April 2003

This investigation shows that Markov‐chain copolymers can be regarded as random copolymers the segment lengths of which depend on the copolymerization parameters. It was possible to derive simple analytical formulae for the mean‐square end‐to‐end distance (〈r2〉), the Kuhn length, and the distribution of r2 under theta‐conditions. The results of these equations are in excellent agreement with data from simulations. It is shown that 〈r2〉 as well as the non‐uniformity of r2 increase strongly with increasing probabilities of homopropagation, i.e., with increasing mean homosequence lengths. Furthermore it is demonstrated by simulation that even chains of identical length and composition show a distribution of r2 because of different arrangements of the sequences inside the chains. For chains or chain segments shorter than the average homosequences, a double‐peak distribution of r2 is found. The equations derived in this paper can be applied to real copolymers as well as to chains the curvature of which is altered locally by the association of ligands.
Monte Carlo simulation of freely jointed chains with variable bond lengths
Authors: Reiter Johannes , Duering Edgardo R.
Published: April 2003

Monte Carlo simulation of freely jointed off‐lattice chains with variable bond length is usually done with local random displacements of beads and with reptation moves (displacements of a bead along a chain). In dense systems, the acceptance ratio of reptations decreases strongly with density. We discuss versions of reptation moves, which are effective in dense systems. The idea, which comes from lattice systems, is to use a pseudovacancy (walker), which has the same size as a bead of a chain. The walker is attached to a neighbor chain and then another bead of that chain is cleaved. This is equivalent to a reptation move and a nonlocal displacement of the walker and since no free volume is needed, the move can be used with advantage in dense systems. A related technique are cooperative motions, which were introduced by T. Pakula for lattice models, where several chains change their conformation concomitantly. Such cooperative loops are implemented in the Monte Carlo algorithm by creating a temporary walker by cleaving a bead from a chain, moving it with reptations and finally annihilating the walker by attaching it to the same chain it was cleaved from. These moves and the condition of detailed balance are discussed in detail. As an example, we study the integrated autocorrelation time τint for the radius of gyration for a two‐dimensional system. For reduced densities larger than 0,4, we find that with standard reptations and local bead displacements τint increases strongly with density. If reptations with either a permanent or a temporary walker are used in addition to local moves, the integrated autocorrelation time changes only very little with density and very dense systems can still be simulated efficiently.
Modelling the free‐radical polymerization of methyl methacrylate over the complete range of conversion
Authors: Panke Dietrich
Published: April 2003

A model is proposed for the radical‐induced polymerization of methyl methacrylate which combines concepts given in the literature. Consecutive steps for diffusion and reaction are used for both the propagation and the termination process, and the termination at higher degrees of conversion is dominated by reaction diffusion as described by Buback. The diffusional contributions to the processes are semi‐empirically based on the free‐volume theory, following a suggestion made by Marten and Hamielec, and the diffusion of the macroradicals is assumed to depend on the instantaneous molar mass (as representative for their chain length) and on the cumulative molar mass (representing the matrix of the dead polymer). With one fixed and four adjustable parameters, the model successfully not only describes the bulk polymerization but also takes account of the presence of solvent, chain transfer agent and pre‐polymer.
A new kinetic model for the accumulation of poly(3‐hydroxybutyrate) in alcaligenes eutrophus, 1. Granule growth
Authors: Kurja Jenci , Zirkzee Hennie F. , De Koning Gertjan M. , Maxwell Ian A.
Published: April 2003

A new kinetic model is proposed for the accumulation of poly(3‐hydroxybutyrate) (PHB) in Alcaligenes eutrophus. The model developed is closely related to the descriptive model of Harkins for the emulsion polymerization process. The PHB accumulation is discussed in terms of polymerization events such as initiation, propagation and termination, taking into account the heterogeneous nature of the system. Experimental results on the PHB accumulation in Alcaligenes eutrophus can be described in both a quantitative and qualitative manner by the model. Further, it is shown that the decrease in the rate of polymerization during the PHB accumulation can be explained by coalescence of the granules. The decrease of the molecular weight of the polymer formed during the accumulation process can be fully explained in terms of the kinetic mechanisms of progapation and chain transfer, and the effect of granule size on these.
Bifurcational analysis of the isotropic‐nematic phase transition of rigid rod polymers subjected to biaxial stretching flow
Authors: Rey Alejandro D.
Published: April 2003

A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non‐equlibrium isotropic‐nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic‐biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non‐equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules15, 1272 (1982)], which are based on a version of the Onsager theory of isotropic‐nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.
Strain effects on the microphase separation in interpenetrating polymer networks and cross‐linked polymer mixtures
Authors: Stepanow Semjon , Frisch Harry L.
Published: April 2003

We study the microphase separation in cross‐linked polymer mixtures and interpenetrating polymer networks by taking into account the coupling between the fluctuations of the order parameter and the strain tensor. We predict that thermal fluctuations of the order parameter decrease the compression and shear moduli and that compression of the sample decreases the critical temperature of microphase separation. We also compute the scattering function in the case of shear and uniaxial deformations.
Molecular dynamics treatment of torsional interactions accompanied by dissociation
Authors: Tuzun Robert E. , Noid Donald W. , Sumpter Bobby G.
Published: April 2003

When three atoms in a bend sequence move into a linear configuration, any torsional angle involving those three atoms becomes undefined and its Cartesian derivatives singular. In molecular dynamics simulations, this is most likely to occur during and after a bond‐breaking process, leading to spuriously large torsional forces and energies which invalidate the simulation. By including appropriate bend angle switching functions in torsional interaction terms, one may approach the linear bend limit in a well‐defined manner and make torsional forces vanish around this limit, as expected on physical grounds. Although this expense can be greatly reduced by observing that any internal force must not move the center of mass of the particles involved. Several approximations explored in this paper can reduce this effort even further.
On the contribution of covalent and ionic species to the chain growth. Monte Carlo simulations and theoretical considerations
Authors: Szymanski Ryszard
Published: April 2003

Contributions of the covalent and ionic species to the chain building in cationic reversible polymerizations are analyzed by means of Monte Carlo simulations and by solving the formulated set of equations. The validity of the equation for the contribution of covalent propagation, derived for reversible polymerization with simplifying assumptions, is discussed. It is shown that repeating units incorporated into the chain by covalent propagations are distributed uniformly only when direct monomer insertion into covalent bonds is not possible, or when intramolecular interconversion of covalent and ionic species is very fast in comparison with propagation.
Theory of time‐dependent log‐normal molecular weight distribution of polylefins in heterogeneous Ziegler polymerization
Authors: Keii Tominaga
Published: April 2003

An explanation of the time‐dependent log‐normal molecular weight distribution of polyolefins in heterogeneous Ziegler polymerization is proposed on the basis of the non‐uniformity of surface sites concerning the activation energy of the propagation reaction. It is a theoretical derivation of the Wesslau equation from the usual kinetic model. The theory explains the behavior of the molecular weight distribution, i.e., time and temperature dependences of polydispersity as well as large values of polydispersity in the early stages of polymerization, which have been observed experimentally.
Critical properties for gelation in free‐radical crosslinking copolymerization
Authors: Okay Oğuz , Naghash Hamid J. , Pekcan Önder
Published: April 2003

A kinetic model was used to predict the molecular weight developments and the critical properties in free‐radical crosslinking copolymerization. The predictions of the model were compared to the experimental data reported previously. Agreement of the kinetic model with experiments is satisfactory for both low and high crosslinker contents. The model parameters indicate increasing extent of shielding of pendant vinyl groups as the reaction proceeds due to the increasing number of multiple crosslinkages. The calculation results indicate that the real critical exponents can only be observed in the region ε < 10−2–10−3 where experimental studies are very difficult. Outside of this region, the apparent critical exponent γ describing the divergence of the weight‐average molecular weight was found to deviate from the classical value due to the conversion dependent kinetics of free‐radical crosslinking copolymerization.
Molecular modelling of polymers, 1. Prediction of critical values of oligomethylenes
Authors: Tan Ton That Minh , Rode Bernd Michael
Published: April 2003

Most procedures for the estimation of critical values of oligomethylenes assume these critical values to depend only on the chain length n and/or the molecular weight M. In this work, we introduce new equations for estimating the critical values by inclusion of quantum chemical data calculated by a semiempirical SCF‐MO

SCF‐MO: Self‐consistent field, molecular orbital.

method (AM1). These models give a much superior prediction for the critical values such as the normal boiling point Tb, critical temperature Tc, critical pressure Pc, critical valume Vc, surface tension yb and enthalpy of vaporization ΔHvp of 18 oligomethylenes. The predictions for polyethylene (with infinite chain length) for the values of Tb, Tc, Pc, Vc, ΔHvp and yb are 1029.3 K, 1029.3 K, 1.013 bar, 15723.3 m3/mol, 0 KJ/mol and 0 mN/m, respectively.
The sol fraction and conversions in AaBb type polymerisation
Authors: Xiao Xing‐cai , Huang Xu‐ri , Li Ze‐sheng , Sun Chia‐chung , Tang Au‐chin
Published: April 2003

The sol fraction for the post‐gel regime in AaBb‐type polymerisations is investigated in a way which allows to study the total, the sol, the gel, the tree‐gel and the loop‐gel fractional conversions. Associated with these conversions, corresponding gel points are discussed as the threshold of sol‐gel transition. (AaBb is a monomer with a functional groups of type A and b functional groups of type B.)
On the relation between conformational changes and electronic structure defects in polypyrrole
Authors: Breza Martin , Laurinc Viliam
Published: April 2003

Using the semiempirical quantum‐chemical AM1 method, the dependence of geometry and electronic structure on the torsion angle δ between neighbouring pyrrole rings of quaterpyrrole in various charge and spin states is investigated. The magnitudes of changes in the electronic structure of polypyrrole caused by geometrical changes of the chain may be comparable with those caused by charge and spin fluctuations. A limited amount of negative charge may be spontaneously stabilized on the polypyrrole chain due to chain deformations caused by solid state influences without any charged dopants. Charge fluctuations are most probably concentrated at nitrogen atoms. N—C bonds are less dependent on δ variations as well as on charge and spin perturbations than C—C bonds.
Phenomenological transient shear behavior of liquid crystalline polymers after the start‐up of shear flow
Authors: Kim Kwang Man , Chung In Jae
Published: April 2003

Transient stresses of liquid crystalline polymers appear as damped oscillatory patterns after the start‐up of shear flow. They are examined by using the constitutive equations which were modified to include the idea of an initial domain state in the Larson‐Doi polydomain equation set. In order to be consistent with the phenomenological transient shear stress after the start‐up in the region of low shear rates, the Hinch‐Leal closure approximations were adopted for the domain‐averaged (mesoscopic) fourth‐order tensors of the director field. It is predicted as an important result that the amplitude of the first overshoot in the transient stress increases with an increase in the shear rate imposed at the start‐up, which was found to be largely in agreement with phenomenology. In addition, the effects of parameters such as molecular concentration, initial domain size, and intensities of viscous and elastic contributions on the transient stress under the start‐up process were also evaluated.
Thermodynamic treatment of ligand‐receptor interactions
Authors: Di Noto Vito , Via Lisa Dalla , Toninello Antonio , Vidali Maurizio
Published: April 2003

This work reports the development of a physico‐chemical model for ligand‐receptor interactions. It considers receptors having groups of different binding sites in equilibrium and far from equilibrium where each of these may have multiple occupancies. The obtained results under appropriate simplifications give the well known Scatchard, Hill and Adair relations and provide a very interesting tool for studying receptor‐ligand phenomena and for determining the related parameters and interaction energies.
Molecular simulation of the comparative flexibility of bridging linkages in poly(aryl ether sulfone)s and poly(aryl ether ketone)s from a study of isolated oligomers
Authors: Hamerton Ian , Heald C. Richard , Howlin Brendan J.
Published: April 2003

Atomistic molecular modelling of the bridging linkages in poly(aryl ether sulfone)s and poly(aryl ether ketone)s have been studied in vacuo. The results of these simulations indicate that models that have bond lengths and angles that agree with X‐ray data are produced from the energy minimised structures and additionally that conformational analysis of these linkages produces low energy conformers that are also accessible in the X‐ray data. The results of these simulations provide confidence in the modelling techniques used and indicate the potential for these models in further simulation of the bulk amorphous state.
Quantum‐Monte‐Carlo simulations on linear chains
Authors: Kreitmeier Stefan N. , Noid Donald W. , Sumpter Bobby G.
Published: April 2003

The diffusion Quantum‐Monte‐Carlo method is applied to a set of coupled oscillators as a first approach to a polyethylene chain. The obtained energy eigenvalues are in good agreement with normal mode analysis. For chains shorter than 50 atoms a distinction between center oscillators and end oscillators is possible. For longer chains non‐negligible deviations are discussed.
Molecular reinforcement: A force field evaluation
Authors: Wendling Jürgen , Wendorff Joachim H.
Published: April 2003

Computer simulations on the basis of a force field approach are used to test the concept of molecular reinforcement and to get an insight into the parameters controlling the reinforcement effect. The finding is that molecular reinforcement may be as effective as fiber reinforcement. The molecular interactions between the matrix and the rigid molecules replace the adhesion between fiber and matrix and the axial ratio of the molecules plays the same role as the axial ratio of the fiber in the case of fiber reinforcement.
Molecular modelling of polymers, 3. Prediction of glass transition temperatures of poly(acrylic acid), poly(methacrylic acid) and polyacrylamide derivatives
Authors: Tan Ton That Minh , Rode Bernd Michael
Published: April 2003

The establishment of the relations between the glass transition temperatures of polymers, such as poly(acrylic acid), poly(methacrylic acid), polyacrylamide and their derivatives, and the electronic structure of their monomers calculated by various methods such as the quantum chemical methods AM1 and PM3, and the Gasteiger‐Hückel method has been investigated. Partial charges of some important atoms in the monomer together with the degree of substitution and chain length of the hydrocarbon group of ester or amide functions of the monomer were used as descriptors. The results indicate that the quantum chemical methods PM3 and especially AM1 lead to models of superior predictability compared to the one obtained by the Gasteiger‐Hückel method.
Bivariate chain length and long chain branching distribution for copolymerization of olefins and polyolefin chains containing terminal double‐bonds
Authors: Soares João B. P. , Hamielec Archie E.
Published: April 2003

Polyolefins containing long chain branches can be synthesized using certain metallocene catalysts such as Dow Chemical's constrained geometry catalyst. These polyolefins combine the excellent mechanical properties of polymers with narrow molecular weight distribution with the easy processability of polymers containing long chain branches. A mathematical model for the chain length distribution for these novel polyolefins was derived from basic principles and an analytical solution for the chain length distributions of the populations containing different number of long chain branches per polymer molecule was obtained. The analytical solution agrees with the direct solution of the population balances and with a Monte‐Carlo simulation model. It is also shown that this solution applies for copolymers using pseudo‐kinetic rate constants and Stockmayer's bivariate distribution.
Physically meaningful discrete relaxation spectrum: Rheological behaviour of monodisperse polymer melts
Authors: Smail Rachid , Carrot Christian , Guillet Jacques
Published: April 2003

A discrete relaxation spectrum using a small number of modes is derived to describe the relaxation behaviour of monodisperse polystyrene melts. Attention is focused on keeping the physical meaning of the relaxation times. Therefore, molecular dynamics theories are used in the terminal, plateau and transition zones and in the case of entangled melts. The spectrum is divided into three parts corresponding to three assumed different relaxation mechanisms: Rouse mechanism at short times, modified Rouse for tube equilibration and reptation with tube fluctuation in the long time range. This description only requires the knowledge of a limited number of parameters, namely the molecular weight of the polymer under investigation, the scaling law for Newtonian viscosity, the plateau modulus and the molecular weight between entanglements. The method is sucessfully applied to entangled monodisperse polystyrene melts and enables the recovery of final spectra containing only a few relaxation modes.
Computer simulation of DNA orientation and deformation in a shear flow field
Authors: Ødegaard‐Jensen Arvid , Elvingson Christer , Håkansson Christer
Published: April 2003

The structure and orientation of semiflexible chain molecules in a shear flow field were studied by Brownian dynamics simulation. Molecules in the size range 200 nm to 1 μm were modeled as chains of spherical subunits with parameters chosen to mimic the size and persistence length of B‐DNA. The analysis of the steady‐state orientation showed a rather broad and asymmetric distribution. The simulations also showed that the orientation of the largest main axis of the moment of inertia tensor is significantly higher compared to the orientation obtained from averaging over the individual bonds in the molecules, the latter procedure being the relevant case when comparing with, e.g., linear dichroism experiments.
On the equation of state for thermal polymer solutions and melts with attractive interaction
Authors: Wolfgardt Matthias , Binder Kurt
Published: April 2003

We perform Monte Carlo simulations of a lattice model for polymer melts, i. e., the bond fluctuation model in three dimensions. By using an energy parameter that prefers relatively long bonds, the model exhibits a glass transition at low temperatures, in close qualitative similarity to experiment. We modify this model by adding an attractive interaction of variable strength. We demonstrate that a small interaction strength has only a very small effect on the static properties of the melt. For a fixed strength of the potential, the chemical potential is measured by a modified particle‐insertion method over a large range of temperatures and densities. The osmotic pressure is obtained by thermodynamic integration. In contrast to the original version our extended model exhibits a positive thermal expansion.
Aggregation processes in self‐associating polymer systems: Computer simulation study of micelles in the superstrong segregation regime
Authors: Khalatur Pavel G. , Khokhlov Alexei R. , Nyrkova Irina A. , Semenov Alexander N.
Published: April 2003

We present the results of extensive molecular dynamics and Monte Carlo studies of the self‐organization in the solution of short polymer chains with strongly attracting head groups at their end. The formation of micelles (multiplets) is studied in detail. Both two dimensional (2d) and three‐dimensional (3d) systems are considered. The off‐lattice and lattice models under study incorporate physical factors which control micelle structure and growth in the so‐called superstrong segregation regime. These factors include (i) conformational effects associated with short‐range excluded‐volume interaction between the tails of flexible‐chain molecules and (ii) very strong attraction of head groups. Our computer simulations of 3d micelles, constructed a priori from chains with strong attraction of head groups (with the characteristic energy ≈ 10 kBT), show that size and shape of the micellar core depends crucially on the radius rc of the interaction of head‐groups. If the value of rc is comparable with chain length, then micelles of nearly spherical shape emerges. The decrease of rc can induce a sharp polymorphic transition from the micellar core which is spheric in shape to a disk‐like (bilayer‐shaped) aggregate. Such molecular organization differs from the commonly held notion of a radially symmetric micellar core. On the other hand, these findings fall into line with a recent theory of the super strong segregation regime. When the starting configuration is a random one (i.e., no micelles were a priori formed) the type of final microstructures, emerging as a result of micellization in the superstrong segregation regime, also depends essentially on the radius of head‐head attraction. In the case of three‐dimensional systems and/or short range attractive potentials we always obtain many small spherically shaped aggregates which, once formed at initial stages of micellization, remain stable for all time scales. Such a behavior is due to both the strong head‐head attraction and the screening (repulsive) action of micellar shells creating insurmountable potential barriers. As a result, we deal with kinetically “frozen‐in” microstructures which are not reversible and cannot exchange molecules with one another. In dense systems, we observe the formation of a (quasi) periodic pattern of alternating microdomains.
Mean square radius of gyration and hydrodynamic radius of jointed star (dumbbell) and H‐comb polymers
Authors: Radke Wolfgang , Müller Axel H. E.
Published: April 2003

Equations for the mean square radius of gyration and the hydrodynamic radius for jointed stars (dumbbells) and H‐combs are derived, based on random flight statistics for each subchain. Comparision with literature data on computer simulations and experimental data for H‐combs show good agreement for the g‐value of the mean square radius of gyration even in good solvents. This suggests that for the mean square radius of gyration the relative dimension of a H‐comb relative to the linear molecule of the same degree of polymerization is not altered significantly by long range interactions, as in the case of star polymers. For the hydrodynamic radius the situation is different. Fair agreement is found when comparing our results with viscosity measurements under θ conditions, while in good solvents the viscosity of the branched molecule is more reduced than predicted by our results.
Efficient computation of potential energy first and second derivatives for molecular dynamics, normal coordinate analysis, and molecular mechanics calculations
Authors: Tuzun Robert E. , Noid Donald W. , Sumpter Bobby G.
Published: April 2003

By using two‐ and three‐body internal coordinates and their derivatives as intermediates, it is possible to enormously simplify formulas for three‐ and four‐body internal coordinates and their derivatives. Using this approach, simple formulas are presented for stretch (two‐body), two types of bend (three‐body), and wag and two types of torsion (four‐body) internal coordinates and their first and second derivatives. The formulas are eminently suitable for economizing molecular dynamics and molecular mechanics calculations and normal coordinate analysis of complicated potential energy surfaces. Efficient methods for computing derivatives of entire potential energy terms, and in particular cross terms with switching functions, are presented.
Calculation of phase diagrams not requiring the derivatives of the Gibbs energy for multinary mixtures
Authors: Horst Roland
Published: April 2003

A method for the calculation of phase diagrams (tie lines and binodal, spinodal, critical points and their stability) based exclusively on the Gibbs energy of mixing with no need of its derivatives with respect to the composition variables is extended to multinary mixtures for any number of components. The mathematical description of the (K‐1)‐dimensional phase diagram of a K‐component mixture is presented. The method is demonstrated for a quinternary blend of five polymers exhibiting a closed miscibility gap; all binary, ternary and quaternary subsystems are completely miscible. The phase separation in the quinternary system is caused by very favorable interactions in the ternary subsytem 1/2/3 and the binary subsystem 4/5.
Phenomenological theory of textured mesophase polymers in weak flows
Authors: Rey Alejandro D.
Published: April 2003

A macroscopic viscoelastic model for incompressible, isothermal, homogeneous lyotropic mesophases exhibiting the nematic polydomain texture is presented. Under equilibrium static conditions the model describes a three dimensional tessellation, where each region or nematic domain has a characteristic size and orientation, and where the polydomain texture has a random orientation. Close form expressions that define the characteristic texture size and the number of randomly oriented domains are given. When subjecting the model lyotropic liquid crystalline polymer displaying the polydomain texture to a steady rectilinear shear flow, the predicted characteristic texture size decreases with increasing shear rates. The power law scaling relations of texture size with shear rate are in excellent agreement with the experimental measurements. The steady shear flow orientation predictions, characterized by a positive shear dependent alignment angle and a low orientation, are in agreement with experimental data.
Configurational‐conformational statistics of stereoirregular polystyrene
Authors: Zhou Zhiping , Yan Deyue
Published: April 2003

The dependence of the configurational‐conformational characteristics, such as the mean‐square end‐to‐end distance, the mean‐square radius of gyration, and the temperature coefficient of the stereoirregular polystyrene chains on the fraction of meso dyads, Pm was investigated, using the periodic condition method. The calculation shows that polystyrene has the most compact chain when Pm = 0.7, and the temperature coefficient of the characteristic ratio of the mean‐square end‐to‐end distance reaches the minimum, −0.89 × 10−3 K−1, at Pm = 0.5. The theoretical result of the mean‐square radius of gyration for atactic polystyrene, 〈S2〉1/2 = 0.2245 M0.5106 shows good agreement with the experimental measurement in both bulk amorphous state and θ‐solvent.
Comparison of two force fields in MD‐simulations of α‐helical structures in keratins
Authors: Knopp Birgitta , Jung Bernd , Wortmann Franz‐Josef
Published: April 2003

Molecular dynamic (MD) simulations based on two different force fields, CVFF and CFF91, were carried out in order to check their feasibility for the structural investigation of the wool intermediate filament (IF) monomeric unit. Selecting an ideal α‐helix as start conformation, all MD‐simulations with CVFF in vaccum show the α‐helix to be unstable. Independently of the amino acid sequence of the α‐helix, a new helical structure with a larger diameter arises during the MD‐simulation, due to a shift of the intrahelical hydrogen bonds. However in simulations with surrounding water the α‐helix remains stable throughout the simulations with the CVFF force field. In contrast to this, MD‐simulations in vaccume based on the CFF91 force field are able to determine different stabilities for the α‐helical start conformation of various IF‐segments, that agree well with secondary structure predictions. The simulation results obtained with CFF91 in vacuum can like wise be verified using an explicit water environment. We found that higher partial charges attributed to the atoms of the amide groups that form the intrahelical hydrogen bonds are the reason for the superiority of the CFF91 force field.
Computer simulation of DNA gel electrophoresis: influence of solid friction on linear and circular chains
Authors: Widgren Stefan , Elvingson Christer
Published: April 2003

The effect of solid friction between DNA molecules and gel fibres during gel electrophoresis has been studied using Brownian dynamics simulations. To investigate the effect of the topology of the polyelectrolyte chains, we have studied both linear and circular molecules. The results show that the migration properties of linear molecules seem to be almost uneffected by solid friction. There is, however, a significant effect on the mobility of circular molecules of the same size. Increasing the electric field strength increases the mobility of the linear molecules while for the circular chains, the mobility goes through a maximum when friction is included.
Reptation theory: geometrical and topological aspects
Authors: Kholodenko Arkady L.
Published: April 2003

This paper discusses topological and geometrical aspects of reptation theory which are common to all versions of reptation theory. These are: the postulated existence of the tube, the functional relationship between the tube diameteraand the polymer/monomer densityp, the crossover from the Rouse to reptation regime. Statistical mechanics of the geometrically confined polymer chain is reanalyzed by careful separation of the diffusive motion of the chain into the longitudinal and transversal parts. Connection between old results and the new formalism is established. It is shown that the longitudinal motion resembles that known for directed polymers. This provides a source of the effective rigidification of the reptating chain's backbone thus facilitating the viscosity exponent to be larger than 3. The transversal motion is also reanalyzed. It is shown that the diffusion on the Bethe lattice used before to describe the transversal (planar) motion (conformational statistics) of the trapped chain is actually the diffusion on the universal covering of the corresponding Riemannian surface. This fact allows to reanalyze the tube stability using topological arguments. Detailed numerical comparison of the obtained new theoretical results with available experimental and Monte Carlo data is provided. Very good agreement between theory and experiment is found. It is also shown that the emerging physical picture of the tube destruction is isomorphic to that which was developed earlier with the help of the quantum Hall effect analogy (J. Phys. I4, 843 (1994)). Remarkable connections between the reptation theory and the theory of quantum chaotic/mesoscopic systems are established thus making the reptation theory part of the more general theory of quantum chaotic systems.
Polymer coupling and theory of on‐random crosslinking: an analytical solution
Authors: Zhu Shiping , Ma Min
Published: April 2003

Gel formation is an important feature in free‐radical polymer coupling. Due to the different possible combination reactivities of each polymer backbone radical, polymer chains are crosslinked in a non‐random manner. Equations of the moments have been derived to predict the pregel molecular weight development and the crosslink density at gel point. This work provides an analytical solution for the differential equations. The model agrees with the Flory‐Stockmayer gelation theory under the condition of random crosslinking. The magnitude of deviations from the classical theory for non‐random crosslinking depends on the product of the radical termination reactivity ratios (r1r2), the ratio of the rate constants of backbone radical generation (k), the ratio of the weight‐average chain lengths of primary polymers (y), and the polymer weight fractions (w2).
Extended kinetic theory of polymeric fluids
Authors: Grmela Miroslav , Dlugogorski Bogdan Z. , Lebon Georgy
Published: April 2003

The setting of classical configuration space kinetic theory of polymeric fluids is extended by adopting the field of internal momentum into the set of independent state variables. The internal momentum predicated by the extended theory compares well with the internal momentum seen in molecular simulations. The extended theory is also shown to provide an intrinscially consistent formulation of the time evolution of macromolecules with internal friction.
Correction of scaling exponents for self‐avoiding walks in two dimensions
Authors: Dayantis Jean , Palierne Jean‐François
Published: April 2003

The first and second correction‐to‐scaling exponents for two‐dimensional self‐avoiding walks have been estimated using exact enumeration data up to twenty‐two steps, and Monte Carlo simulation data from twenty‐three up to two hundred steps. It was found that Δ1, the first correction‐to‐scaling exponent, is not the same when deduced from root‐mean‐square end‐to‐end distance and root‐mean‐square radius of gyration data. In the former case it was found that Δ1 = 0.84 ± 0.10, and in the latter case it was found that Δ1 = 1.13 ± 0.03. These results are discussed with reference to previous estimates. The reliability of our Monte Carlo data has been checked making two different tests, including the use of a different random number generator, and it is concluded that apparently no artefact can account for the above different values found for Δ1.
Polydisperse polymer liquid crystals near the anisotropic‐isotropic transition
Authors: Brostow Witold , Walasek Janusz
Published: April 2003

Polydisperse systems of polymer liquid crystal (PLC) macromolecules consisting of LC and flexible sequences are considered, particularly at the phase transition LC‐i from an anisotropic to the isotropic phase. The Flory and Matheson lattice model is used for formulation of the partition function; the orientation distribution function for LC orienting potential interactions introduced by Flory and Ronca is included. Using a Landau approach to calculating the Helmholtz function of the system as a function of the orientation parameter s, we obtain the formulae for parameters of the model in the vicinity of the LC‐i transition. The critical values at the transition of s, of the strength of orienting interactions, the system temperature, and the anisotropy of LC sequences are calculated and discussed as functions of the polydispersity parameter d. Regions of d are found where polydispersity has a weak influence on the LC‐i equilibrium parameters. There is also a region of d values in which the influence of polydispersity is quite pronounced.
Modeling of the transition temperature for the helical denaturation of α‐keratin intermediate filaments
Authors: Knopp Birgitta , Jung Bernd , Wortmann Franz‐Josef
Published: April 2003

Simulations of the stability of the secondary and tertiary structure of the α‐keratin intermediate filament (IF) monomeric unit of wool are reported. Based on the assumed secondary structure three segments of the primary structure were selected: 1A, L12, and a part of 2B. Starting with an ideal α‐helical conformation for each IF‐segment, molecular dynamics simulations were carried out on the atomistic level at various temperatures in vaccum using the CFF91 force field. In either simulation the expected destabilization of the helical structure with increasing simulation temperature was observed. By use of different procedures of analysis, transition temperatures for the α‐helical denaturation were determined that are significantly higher for the supposedly α‐helical segments 1A and 2B than for the linker segment L12. The different stabilities of segments 1A and L12 were further verified through simulations in water environment that show the linker segment to be non‐helical at room temperature. The lower transition temperature of segment L12 confirms the expectation that its amino acid sequence leads to increased conformational flexibility. The mobility of the water molecules surrounding the IF‐segment is found to be significantly decreased by protein/water interactions.
Semiflexible chain molecules with nonuniform curvature, 2. . Brownian dynamics simulations of electric dichroism orientation dynamics
Authors: Håkansson Christer , Elvingson Christer
Published: April 2003

The hydrodynamically induced orientation dynamics of charged polymer molecules during electric dichroism has been studied by Brownian dynamics simulations. The effect of a locally changed flexibility or bending angle has been of special interest. The results show that simultaneously changing the bending angles and the corresponding force constants so as to keep the persistence length constant does not produce any large changes in the orientation dynamics or molecular shape although, quantitatively, a larger number of kinks in the chain will give a smaller steady‐state orientation. Releasing the constraint of a fixed persistence length when randomly increasing or decreasing the flexibility at different positions in the molecule drastically changes the dynamics, and the corresponding results are discussed and also compared with the orientation obtained when introducing the inhomogeneities in a cooperative manner.
The swelling of nematic elastomers by nematogenic solvents
Authors: Wang Xin‐Jiu , Warner Mark
Published: April 2003

The swelling of a nematogenic elastomer by an isotropic solvent was earlier predicted (Macromolecules 25, 445 (1992)) to be more complex than that of a classical elastomer. We extend here to the swelling by solvents having a nematic‐isotropic transition in the pure phase in the region of that of the pure elastomer. The phase diagrams are qualitatively different from the first case, but still with the novel features of a triple point and a gel‐gel biphasic gap reported in the initial study. Where the cross‐coupling is stronger than the self‐couplings we have an azeotropic point.