bluuebunny/crossref_metadata_2025 huggingface dataset:
On a quantity describing the degree of chain entanglement in linear polymer systems
Authors: Kröger Martin , Voigt Harald
Published: April 2003

In the present paper we define a quantity which describes how strong a polymer system is entangled. In MD computer simulations we apply this definition to samples of polymer melts which were generated with a specific large‐scale structure, as characterized by their radius of gyration, end‐to‐end distance and the “degree” of mutual entanglement of the chains. The quantities mentioned above are monitored over the relaxation of the samples towards equilibrium.
A simple model for finitely extensible polymers
Authors: Carl Wilfried
Published: April 2003

A simple model for the calculation of configurational and rheological properties of finitely extensible polymers in flow is introduced. The finite extensibility of the chain is incorporated into the common Rouse model by varying the spring constant such that a constant contour length is maintained for every flow strength. For elongational flow, a comparison with Monte Carlo simulations of a bead‐rod chain with 100 links yields qualitative agreement. For shear flow, this model predicts non‐Newtonian flow behaviour.
Optimization of isothermal batchwise bulk free radical polymerization with and without chain transfer agent for minimum reaction time
Authors: Sajjadi Shahriar , Jahanzad Fatemeh
Published: April 2003

In this work the minimum reaction time was studied for a specific final monomer conversion and number‐average chain length by adjusting the amount of initial initiator concentration in the presence of a fixed amount of chain transfer agent at the best isothermal temperature. A new method for the determination of the best initial initiator concentration ([I]0) and isothermal temperature (T) in the presence of chain transfer agent was developed by the application of a simple optimization algorithm, based on the Lagrangian multiplier, to the basic free radical kinetics. Numerical examples for the polymerization of styrene are presented. It is shown that in the presence of a fixed amount of chain transfer agent the best isothermal policy for minimum time would deviate from dead‐end polymerization. As the concentration of chain transfer agent increases, a stronger deviation from dead‐end polymerization is observed. It was found that for a given pair of desired conversion and number‐average chain length the usage of a chain transfer agent would result in a longer reaction time. The results give insights into operation of batchwise bulk free radical polymerization for minimum reaction time under isothermal conditions.
Molecular weight distribution in random crosslinking of polymers: Modality of the molecular weight distribution
Authors: Tobita Hidetaka , Yamamoto Yoshiyasu , Ito Kenji
Published: April 2003

The molecular weight distribution (MWD), formed during random crosslinking of polymers whose initial molecular weight distribution is given by the Schulz‐Zimm distribution, is proposed. The obtained equation can be considered as a good approximation even for nonrandom crosslinking reactions such as free‐radical and living crosslinking copolymerizations. When the initial molecular weight distribution is very narrow, namely, the polydispersity index (Pw/Pn) is smaller than about 1,1, a multimodal distribution can be obtained. Quite often the MWD is represented solely by the average molecular weights such as number‐ and weight‐average molecular weights in conventional approaches; however, such types of measure can not give enough description for multimodal distributions. Multimodal distributions may be obtained for the primary polymer molecules formed via living polymerizations. On the other hand, for the primary polymer molecules formed by free‐radical polymerization whose polydispersity index must be larger than 1,5, it is impossible to form a bimodal distribution as long as nonideal kinetics such as the size and structure dependence of crosslinking reactions are neglected.
Perturbation expansion of polymers in shear flow
Authors: Carl Wilfried
Published: April 2003

The effect of shear flow on the excluded volume properties of bead spring chains is calculated via the perturbation expansion of the mean‐square end‐to‐end distance with respect to the excluded volume parameter z. The coefficient of the series 〈R2〉/〈R2〉0 = 1 + C1 · z − … vanishes for large flow rates but shows a strong dependence on the shear rate in the intermediate regime.
Tension and mobility of a DNA fragment in the lakes‐straits model
Authors: Loomans Dirk , Sokolov Igor M. , Blumen Alexander
Published: April 2003

We consider numerically, in the framework of the lakes‐straits model, the mobility of a DNA chain under field‐inversion gel‐electrophoresis (FIGE). Here we investigate the role of the gel's structure on the mobility. We consider two situations: (i) a DNA chain fragment is bounded by two straits (narrow gateways) at a fixed distance, but is otherwise free, and (ii) the fragment is, in addition, confined with in a closed volume (pore). We calculate the tension on the DNA fragment in the two cases. For Gaussian chains we evaluate the corresponding statistical weights exactly, using a cellular automation algorithm. We find that the resulting tension differs drastically in the two models considered. Nonetheless this difference influences only weakly the overall FIGE mobility.
Conformational analysis of highly extended poly(ethylene terephthalate) chains by Monte Carlo calculations
Authors: Auriemma Finizia , Corradini Paolo , Guerra Gaetano , Vacatello Michele
Published: April 2003

The conformational disorder compatible with the highly extended chains found in mesomorphic poly(ethylene terephthalate) has been studied by Monte Carlo calculations on model oligomers confined inside cylindrical tubes. The distribution of torsional angles for such extended chains is characterized by OCCO bonds being always in the trans domain, while the COCC bonds show an approximately similar probability of being found in trans and gauche states, the probability maxima being centered at 90° and −90° in the latter cases. At variance with the torsional angles of the OCCO and the ester bonds, always very close to 180°, the distributions for all other torsional angles show flat and broad probability maxima, indicating the possibility of substantial deviations from the average value inside each domain. This is also true for the fictitious OC˙˙˙CO bonds across the phenylene rings, for which a nearly trans geometry is preferred in extended conformations.
Simulation of free radical addition reactions modified by the presence of cobalt macrocycles
Authors: Davis Thomas P. , Kukulj Dax , Maxwell Ian A.
Published: April 2003

Free radical addition reactions in the presence of cobaloximes and related compounds have been modelled. Several mechanisms are presented and similarities with the “persistent radical effect” noted by Daikh and Finke are discussed. Cobaloximes and salophen

System. name: N‐acetyl‐p‐aminophenyl salicylate.

derivatives are widely used in organic synthesis to build carbon‐carbon bonds, whereas in polymer synthesis they are used as catalytic chain transfer agents in the production of oligomers. This work shows that these reactions are closely related and also demonstrates the influence that an external radical source has on the overall reaction kinetics.
Quantum chemical PM‐3 study of the thermal stability of heterocyclic fragments of heteropolymers, 3. Thermal stabilities of different components of heteropolymer repeating units
Authors: Zubkov Vladimir A. , Bogdanova Svetlana E. , Yakimansky Alexander V. , Kudryavtsev Vladislav V.
Published: April 2003

Dissociation energies (ED) of different components of repeating units of heteropolymers (HPs) have been calculated by the semiempirical PM‐3 method. Comparison of ED values of heterocycles (HCs) and of single bonds contained in phenyl‐substituted benzoheterocycles have shown that for polybenzazoles and HPs with carbonyl‐containing HCs the initial degradation in the absence of weak links (uncyclized units, structural defects, etc.) preferably starts with HC homolytic decomposition. For these two groups of HCs the relationship between the ED of HCs and the initial degradation temperature of corresponding HPs is, on the whole, similar to the one found upon calculation of benzoheterocycles. In HPs based on quinoline and quinoxaline the single bond between HC and phenyl (Ph) group is less stable than the HC, and the breaking of that single bond can accompany the initial HP degradation. An analysis of relative stabilities of X‐Ph bonds of Ph‐X‐Ph fragments of HPs with X = O, S, CH2, CO and of the relationship between their stabilities and those of other fragments of the HP repeating unit has been performed by using both calculated ED values and those obtained from thermochemical data. ED values for Ph‐X‐Ph decompositions turned out to be close to those for some HCs.
Persistence lengths of aromatic polyamides: a computer simulation approach
Authors: He Chaobin , Windle Alan H.
Published: April 2003

A range of polyamides has been modelled using Monte Carlo routines based on carefully determined bond‐rotation potentials, bond length and bond angle. For each polymer type, a large number of chains has been built for different simulated temperatures, and the persistence lengths determined as an average over all models for a given set of conditions. The simulations predict mesogenicity of aromatic polyamides to be smaller than that of equivalent aromatic polyesters, while the experimental values of persistence length obtained from polyamides in solution are large on account of the strong bonding between polymer and solvent.
Unusual finite size effects in the Monte Carlo simulation of microphase formation of block copolymer melts
Authors: Micka Uwe , Binder Kurt
Published: April 2003

Extensive Monte Carlo simulations are presented for the Fried‐Binder model of block copolymer melts, where polymer chains are represented as self and mutually avoiding walks on a simple cubic lattice, and monomer units of different kind (A, B) repel each other if they are nearest neighbors (εAB> 0). Choosing a chain lengthN= 20, vacancy concentration Φv= 0,2, composition ƒ = 3/4, and aL×L×Lgeometry with periodic boundary conditions and 8 ≤L≤ 32, finite size effects on the collective structure factorS(q) and the gyration radii are investigated. It is shown that already above the microphase separation transition, namely when the correlation length ξ(T) of concentration fluctuations becomes comparable withL, a nonmonotonic variation of bothS(q) and the radii withLsets in. This variation is due to the fact that the wavelength λ*(T) of the ordering (defined from the wavenumberq*whereS(q) is maximal at λ*= 2 π/q*) in general is incommensurable with the box. The competition of two nontrivial lengths ξ(T), λ*(T) withLmakes the straigthforward application of finite size scaling techniques impossible, unlike the case of polymer blends. Since also the specific heat is found to have a broad rounded peak near the transition only, locating the transition accurately from Monte Carlo simulations remains an unsolved problem.
Calculation of phase diagrams not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding copolymer
Authors: Horst Roland
Published: April 2003

A method is presented which allows the calculation of phase diagrams (spinodal, binodal and tie lines) on the basis of the Gibbs energy of mixing ΔG. No derivatives of ΔG with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of ΔG is very complex and no analytical representation of the derivatives can be given. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. The complex phase separation behavior resulting for a 1 : 1 copolymer becomes much simpler as one monomeric unit starts to predominate in the copolymer.
The kinetics of free radical polymerizing systems at low conversion, 1. On the rate determining step of the bimolecular termination reaction
Authors: Russell Gregory T.
Published: April 2003

Using a styrene bulk system as a model, this paper examines rates of termination at very low conversions in bulk and solution polymerizations. No definitive answer to the question of what determines such rates of termination is arrived at. Indeed, it is argued that on the basis of existing kinetic information, no such definitive answer is possible. However several things may be said with conviction. To begin with, it is rigorously shown that low conversion rates of termination cannot be explained by assuming that all radical chain end encounters result in termination, and then using center‐of‐mass diffusion coefficients of polymer in free solution to calculate rates of chain end encounter. However this does not mean that rates of center‐of‐mass diffusion do not determine rates of low conversion termination, as is shown; the idea that it may be the case that not all chain end encounters result in termination, this a manifestation of a spin multiplicity effect, is especially worthy of mention. It is also possible to explain low conversion rates of termination, as has traditionally been done, in terms of chain end motions being hindered by the presence of another polymer chain. However in concentrating on interactions between overlapping long chain macroradical coils, this traditional picture is certainly inaccurate, for it is shown that most termination interactions must involve at least one radical of shorter than expected degree of polymerization. This has the important consequence that an understanding of overall rates of dilute solution termination must be founded on an understanding of the diffusional behavior of the ends of short and intermediate length polymer chains.
The kinetics of free radical polymerizing systems at low conversion, 2. On the influence of the monomer and initiator concentrations
Authors: Russell Gregory T.
Published: April 2003

In this paper are calculated variations of steady state rates of polymerization Rpol with initiator concentration [I] and monomer concentration [M]. For these calculations a chain length dependent termination model which provides a microscopic description of zero conversion bulk and solution polymerization of styrene at 20°C is used. Despite the calculations being necessarily specific in this respect, the principles that are uncovered are general, and so are germane for polymerization of all monomers at all conversions. The central such principle is that any chain length dependence of termination rate coefficients may alone be expected, in the first instance, to induce non‐classical polymerization behavior; specifically, Rpol will scale with a weaker than square root dependence on [I] and a stronger than linear dependence on [M]. Further, while the extent of deviation from classical behavior does depend on the severity of the chain length dependence of termination rate coefficients, it does not depend on whether a Smoluchowski or geometric mean model of termination is operative, a finding which counsels reappraisal of some commonly held perceptions regarding low conversion termination. It is also shown that regardless of the chain length dependence of the termination rate coefficient, the occurrence of chain transfer to monomer will act to promote classical polymerization behavior, and it is argued that this has been a factor in many low conversion experimental investigations appearing to have found an at most rather weak chain length dependence of termination; it is further argued that existing experimental data for the variation of Rpol with [I] and [M] is not inconsistent with termination being center‐of‐mass diffusion controlled at low conversions. Close attention is paid to experimental data throughout this paper, which concludes by discussing aspects of experimental design, this in the hope that simple measurements of steady state Rpol might be more profitably used to elucidate the complexities of free radical polymerization kinetics.
Energy gap of alternant carbon nanotubes
Authors: Tyutyulkov Nikolai , Dietz Fritz , Baumgarten Martin , Müllen Klaus
Published: April 2003

The energy spectra of two types of non‐helical carbon nanotubes are investigated theoretically. It is shown that either the topological or the correlational contributions determine the width of the band gap. In some cases (for nanotubes with diameter < 1 nm) the electron correlation changes qualitatively the results for the width of the energy gap ΔE: if in the one‐electron approximation the band width ΔE = 0, the contribution of the electron correlation becomes dominant and increases the band gap ΔE > 0. At small diameter of the nanotubes (D > 1 nm) the ground state of the tubes corresponds to semiconductors with moderate or narrow energy gap, while at D > 1 nm ΔE decreases monotonously. The energy spectra of the planar ribbon polymers are compared with those of the iso‐electronic nanotubes.
Spinodal decomposition in asymmetric polymer mixtures
Authors: Zhang Hongdong , Zhang Jianwen , Yang Yuliang
Published: April 2003

We present a preliminary numerical study of spinodal decomposition in an asymmetric polymer mixture, i.e., of polymer with different chain lengths, in three dimensions with full Flory‐Huggins‐de Gennes free energy, numerically integrating the time evolution equations for the conserved order parameter. For the sake of comparison, we also present a numerical study of the symmetric polymer mixture. The results indicate that the scaled structure factor for the asymmetric polymer mixture is much broader than that of a symmetric polymer mixture. It is interesting that the growth exponents are not symmetric around the critical quench, i.e., growth exponents on the two sides of the critical composition are different. In addition to that, the magnitudes of the pair correlation functions of asymmetric mixtures are very small for x larger than the characteristic domain size rg and the oscillations seen in the symmetric mixture are almost absent. We have attributed this finding to the rough interfaces and broader domain size distribution in the phase separated asymmetric polymer mixtures. Therefore, the simulation reveals that the asymmetry plays an important role for the spinodal decomposition dynamics of polymer mixtures.
Some aspects of theory and simulations of polymers in steady flows
Authors: Carl Wilfried
Published: April 2003

We present a study of various properties of bead spring chains in steady flows. The Langevin equation of the normal modes of the chain is solved by Fourier transformation. From the resulting power spectrum, the autocorrelation functions of all configuration‐dependent quantities can be calculated. In equilibrium, the influence of the bead masses on the short‐time dynamics is discussed. The influence of different flow fields (shear, elongational and Kramers potential flow) on the mean‐square chain dimension is calculated. A comparison with results obtained from non‐equilibrium molecular dynamics and Monte Carlo calculations is made. Finally, the influence of shear flow on the configurational and rheological properties of cyclic polymers and on the excluded volume behavior of linear chains is examined.
On the contribution of different reaction routes to polymer formation in reversible polymerization. Oxepane and 1,3‐dioxolane polymerization cases
Authors: Szymanski Ryszard
Published: April 2003

The analysis of the contributions of different propagation routes in reversible polymerization was performed. It was shown by computer simulations that material and kinetic contributions of the given propagation route can differ. An especially large difference between these quantities was found in the simulated polymerization of 1,3‐dioxolane. This allowed to explain the unexpectedly large difference between the values of the apparent rate constant of propagation and the estimated rate constant of the corresponding elementary reaction of propagation in the polymerization of 1,3‐dioxolane.
Calculation of rotational barriers in amorphous polymers
Authors: Tiňo Jozef , Koreň Igor , Mach Pavol , Urban Ján
Published: April 2003

The Monte Carlo method was used for generation of amorphous polyethylene configurations on a diamond lattice. Chain building was performed on the tetrahedral lattice of edges 36, 62 and 43 Å with periodic boundary conditions imposed.32 chains were generated, each with a length of 100 CH2‐groups (resulting density = 0.81 g·cm−3). Small spherical volumes with a radius of 10 Å were chosen at random from the total volume for the calculation of rotational barriers. The rotating bond was chosen to be close to the center of this sphere. We employed the method of molecular mechanics in order to calculate the rotational barriers. The calculation was made for 578 rotating bonds and the obtained distribution of rotational barriers is approximated by the corresponding Γ‐distribution.
Molecular dynamics simulation of the crystal nucleation behavior of a single chain touching a substrate surface
Authors: Yang Xiaozhen , Qian Renyuan
Published: April 2003

Molecular dynamics simulation has been used in exploring the crystal nucleation behaviour of a single chain touching a substrate surface. It shows that a polyethylene chain (980 CH2) changed its overall shape from an isotropic coil to an oriented one in the case of touching a substrate surface of amorphous carbons at 300 K. Most repeats of the chain were aligned and ordered in a zigzag package. Surprisingly, the direction of the package is not parallel to the plane of the substrate, but almost perpendicular to it. This is in accordance with experimental observations.
On the chirality of paper
Authors: ten Bosch Alexandra
Published: April 2003

On a macroscopic level, a paper sheet has a fiber structure similar to the chains of a molecular chiral membrane. The continuum model of membranes based on chiral elasticity can be applied to calculate the spontaneous curl observed in paper sheets. Twist of the paper sheet is shown to occur in the presence of a tilt relative to the sheet geometry of the constituent cellulose fibers. The dependence of the twist angle on the width of the sheet, on external mechanical fields and on the elastic constants of the paper is given.
Apparent glassy dynamics of an adsorbed polymer chain in the bond‐fluctuation model
Authors: Lai Pik‐Yin
Published: April 2003

The dynamics of a single homopolymer chain strongly adsorbed on a flat surface is investigated by Monte Carlo simulation using the bond‐fluctuation model. Previously observed anomalous glassy dynamics at low temperatures [Phys. Rev. E 49, 5420 (1994)] is revisited in detail. We also study the dynamics of a polymer chain confined in a narrow slit of width of a monomer and a modified bond‐fluctuation model in three dimensions to include more relevant bond vectors. We show that the previously observed glassy dynamics is due to an artifact of the bond‐fluctuation model in three dimensions in that it does not cross‐over to the two dimensional bond‐fluctuation model with the correct Rouse dynamics. With the proper inclusion of the extra bond vectors P(2,2,0) and P(3,2,0), no glassy behavior appears for the strongly adsorbed chain.
A theoretical approach to the thermochemistry of radical and anionic polymerizations of various unsaturated monomers
Authors: Leroy Georges , Dewispelaere Jean‐Pierre , Benkadour Hanan , Wilante Claude
Published: April 2003

In this work, we have calculated the thermodynamic parameters of the first steps of the free radical and anionic polymerizations of various unsaturated monomers, using ab initio methods of quantum chemistry. The enthalpies and entropies of polymerization were estimated assuming that they correspond to those of the model reaction A  B(p) + HABAH(p′) → HABABAH(p′) where p and p′ stand for the physical state of the considered species. The enthalpies of polymerization were rationalized using the equation ΔH = −ΔΣ NABEAB + SE(A  B) + SE(HABAH) − SE(HABABAH) where NAB is the number of A  B bonds, EAB the corresponding bond energy, − ΔΣ NABEAB the variation of the sum of the bond energy terms, and SE(X) the thermodynamic stabilization energy of compound X. The preferential mode of polymerization of each monomer was derived from the enthalpies of the initiation and initial propagation steps of the two types of polymerization. Thus, we were able to make some comments concerning the feasibility of the polymerization of the monomers under consideration.
Theoretical considerations on the directionality in polymerization mechanism and polymer type
Authors: Weegels Peter Louis
Published: April 2003

The directionality (Dn) of a polymerization mechanism can be defined as the average orientation of the reaction or the degree of randomness of head‐to‐tail, head‐to‐head, tail‐to‐tail or tail‐to‐head reactions within the polymer at the n‐th monomer or reaction (n ≫ 2). Directionality of a polymer type can be defined as the average orientation inside a polymer. If the directionality is random, Dn = 0.5. For full directionality, Dn = 1. It is demonstrated that these situations correspond to step and chain polymerization, respectively. Directionality can be as important for the functional properties of polymers as length and composition distributions and the functionality of the original monomers.
The molecular structure and polarizabilities of poly(aryl ether ketone)s
Authors: Shibata Mitsuhiro , Yosomiya Ryutoku , Ke Yang‐Chuan , Zhen Yu‐Bin , Wu Zhong‐Wen
Published: April 2003

The molecular structure and polarizabilities of poly(aryl ether ketone)s were investigated with quantum chemical calculations, based on the fully optimized structures of model compounds (S5: ArCOArOArOArCOAr and BS6: ArOArCOArArCOArOAr) for their chain segments. The results showed that the average dihedral angle between their aromatic rings was in the range of 36°−37° relative to the molecular zig‐zag plane. Especially, when a biphenyl group was introduced into the molecular chain of this polymer, its two aromatic rings were distorted by 48.0° to each other. Also, the calculation results of refractive indices for pure crystals obtained by using the structural parameters were in good accordance with those reported in the literature.
Monte Carlo simulation studies of the interfaces between polymeric and other solids as models for fiber‐matrix interactions in advanced composite materials
Authors: Baschnagel Jörg , Binder Kurt
Published: April 2003

As a coarse‐grained model for dense amorphous polymer systems interacting with solid walls (i.e., the fiber surface in a composite), the bond fluctuation model of flexible polymer chains confined between two repulsive surfaces is studied by extensive Monte Carlo simulations. Choosing a potential for the length of an effective bond that favors rather long bonds, the full temperature region from ordinary polymer melts down to the glass transition is accessible. It is shown that in the supercooled state near the glass transition an “interphase” forms near the walls, where the structure of the melt is influenced by the surface. This “interphase” already shows up in static properties, but also has an effect on monomer mobilities and the corresponding relaxation behavior of the polymer matrix. The thickness of the interphase is extracted from monomer density oscillations near the walls and is found to be strongly temperature dependent. It is ultimately larger than the gyration radius of the polymer chains. Effects of shear deformation on this model are simulated by choosing asymmetric jump rates near the moving wall (large jump rate in the direction of motion, and a small rate against it). It is studied how this dynamic perturbation propagates into the bulk of the polymer matrix.
Orientational ordering of a polymer chain in a strong dipole field. Tetrahedral lattice model
Authors: Gotlib Yulii Ya. , Lyulin Sergey V.
Published: April 2003

Orientational and conformational properties have been investigated of a rotational isomeric model of a polar polymer chain on a tetrahedral lattice in a strong electric or mechanical field of dipole symmetry. Two types of dipole moment distribution along the chain are discussed: (A) constant signs of longitudinal components of the dipole moments, and (B) alternating signs of the longitudinal components of the dipole moments. The second case represents polymer chains such as \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} ({\rm CH}_{\rm 2} \hbox{---} {\rm CR}_{\rm 2} {\rm \rlap{--} )}_n $\end{document}>/UEQN> when the dipole moments are oriented along the bisector of the CR2‐angle, i.e., normal to the extended trans‐chain conformation. It is shown that only a discrete most probable orientation of the lattice relative to the field should be considered, namely that coinciding with one of the symmetry axes of the lattices. The average dipole order parameter and dichroic functions (quadrupole order parameter) are calculated in a strong external dipole field for unit vectors with different orientation relative to the chain backbone. The quadrupole order parameter for different unit vectors is obtained also as a function of chain elongation. The polarizability induced by an additional weak dipole field is calculated as a function of the magnitude of the strong external dipole field. For the model considered here the order parameters are more strongly influenced by the external field than those for the freely jointed chain (FJC) model having the same distribution of dipole moments along the chain. The orientational ordering of the chain in a dipole field is higher than in a quadrupole field of the same magnitude.
The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach
Authors: Hołyst Robert , Vilgis Thomas A.
Published: April 2003

The polymer systems are discussed in the framework of the Landau‐Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi‐block copolymer melts, random copolymer melts, ring polymers, rigid‐flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean‐field model, self consistent one‐loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid‐flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.
On phase equilibria, interfacial tension and phase growth in ternary polymer blends
Authors: He David Qiwei , Kwak Soonjong , Nauman E. Bruce
Published: April 2003

A gradient squared free energy functional of the Landau‐Ginzburg type is combined with Flory‐Huggins theory to calculate minimum domain sizes, concentration profiles and interfacial tensions in ternary polymer blends. The dynamic equations governing spinodal decomposition are linearized to show that the minimum size for growth is identical to the thermodynamic minimum on phase volume. It is shown that unseparated, third components are enriched at the interface, reduce interfacial tension, increase stability and increase the minimum domain sizes. Enrichment of the third component at the interface causes concentrations at the major components to lie outside their binodal limits at a distance from the interface. Although the effects are most pronounced when the third component is a compatibilizer, the general phenomena remain true even when the third component is relatively incompatible. Generalizations to blends of N components are presented, and a robust method for calculating multicomponent phase diagrams is described.
Influence of polymolecularity on the second virial coefficient of polymers, 2
Authors: Jung Bernd , Bareiss Rolf E.
Published: April 2003

It is shown that the recently developed scaling theory for the second virial coefficient, A2, of dilute solutions of polymers with non‐uniform molecular weight distributions in a good solvent is able to explain in principle all seemingly contradictory observations reported in the literature, in contrast to all other theories proposed so far.
Modeling of molecular weight distribution in pulsed laser free‐radical homopolymerizations
Authors: Buback Michael , Busch Markus , Lämmel Ralf A.
Published: April 2003

The use of pulsed lasers to induce radical polymerization with a subsequent analysis of the polymer molecular weight distribution (MWD) through size exclusion chromatography (PLP‐SEC method) revolutionized the determination of propagation rate coefficients kp. In this paper the program package PREDICI is applied to the simulation of PLP‐SEC orginated MWDs. The comparison with SPEEDUP‐simulations from Hutchinson et al. Shows that both programs are equally well suited for the calculation of the MWD of PLP samples. The emphasis is on the study of the effects that the experimental parameters, i.e. the primary radical concentration in a specific experiment, the gradients of this radical concentration, and above all the instrumental broadening of SEC analysis, have on the measured MWD, and therewith on the kp determination via PLP experiments. By detailed consideration of a styrene bulk polymerization experiment at 70°C and ambient pressure, it is shown that the PLP‐SEC technique at primary radical concentrations between those given by the limiting cases of the low and high termination rate limits and with simulatioenous high quality of the SEC (low broadening) is very well suited for the kp determination. As the MWD of samples from PLP is influenced in a rather complex fashion by the kinetics of the polymerizing system, by the choice of the experimental parameters determining laser‐induced primary free radical concentration, and by the performance of the SEC device, it appears highly recommendable to accompany PLP studies by simulation.
Computer simulation of solutions of telechelic polymers with associating end‐groups
Authors: Khalatur Pavel G. , Khokhlov Alexei R.
Published: April 2003

We present the results of numerical Monte Carlo simulations of solutions of telechelic chains with strongly attracting end‐groups. Formation of micelles (aggregates), their structure and structural characteristics of the system as a whole are studied in detail. The features revealed in computer experiments are qualitatively similar to the recent theoretical predictions. In particular, we show that micelles formed by telechelic chains attract each other even if the solvent is good for the soluble blocks forming micellar shells. As a result, A “micellar gel” structure with a number of chain “bridges” connecting micelles is formed. The bridging chains turn out to be significantly stretched. Furthermore, we observe a pronounced maximum in the wave‐vector dependence of the static structure factor for the associating end‐units which is a manifestation of a quasiperiodic pattern of alternating microdomains consisting of dense micellar cores and the swollen soluble chain blocks.
Dielectric relaxation of polymer networks built from macromolecules with dipole moment directed along the end‐to‐end chain vector
Authors: Gotlib Yuli Ya. , Gurtovenko Andrei A.
Published: April 2003

The dielectric relaxation properties are considered for polymer networks built from polar macromolecules with the dipole moment directed along the end‐to‐end chain vector. The viscoeleastic cubic model of a regular network is used. The fixed average volume of a polymer network is ensured by the effective internal pressure. The dynamic models of polymer networks with external and interchain friction are studied. Two cases are considered: (1) polar chains cross‐linked in a network at their ends, and (2) a densely cross‐linked network with many network junctions per polar chain. The expressions for the autocorrelation functions of the total dipole moment of a network, which determine the dielectric susceptibility, are calculated. The relaxation spectrum of the autocorrelation function consists of two regions: the high‐frequency relaxation spectrum of a chain fragment between two neighbouring junctions (intrachain relaxation spectrum) and the lowfrequency interchain relaxation spectrum. The interchain relaxation spectrum is determined by cooperative motions of chains which form a network. The characteristic time of this spectrum for networks of type (1) is the relaxation time of a chain between junctions τmin. For networks of type (2) a second time scale τ1 exists, which corresponds to motions inside the volume occupied by a single long polar chain included in a network. It leads to different time behaviour of the autocorrelation functions for both network models. The existence of only interchain friction in the network model leads to a cut‐off of the relaxation spectrum at the time τmax depending on the volume of viscous interchain interactions.
Ellipsoidal potential parameterization for bisphenol‐A polycarbonate
Authors: Zimmer Klaus M. , Linke Andreas , Heermann Dieter W. , Batoulis Jannis , Bürger Thorsten
Published: April 2003

We present a coarse‐grained parameterization for the intra‐ and intermolecular potential for bisphenol‐A polycarbonate (BPA‐PC). The parameterization is based on the ellipsoidal‐shaped monomer unit model applied to BPA‐PC. Because of the symmetries of the model a Lennard‐Jones type or even a mere repulsive potential with the usual parameters suffices to model the non‐bonded interactions. We determined the potential parameters from ab‐initio quantum calculations for the BPA‐PC monomer. Results of molecular dynamics simulations using our model compare favourably with experimental data.
Strain‐dependent dynamic properties of filled rubber network systems
Authors: Lin Chen‐Ron , Lee Yu‐Der
Published: April 2003

A model for strain‐dependent dynamic properties of filler loaded rubber systems has been derived based on the Links‐Nodes‐Blobs (L‐N‐B) model of percolation theory. It is the first time that a L‐N‐B model is applied in the study of dynamic properties of filled rubbers. The density distribution function of the number of singly connected bonds f1a(ϵ) and the apparent yield strain amplitude ϵapp that corresponds to the on‐set point of corruption of the filler network are introduced in the model. Simulation results indicate that both f1a(ϵ) and ϵapp control the break‐down and recombination of the filler network. Two recombination mechanism are adopted in this study. Results of simulations from the extreme ends recombination mechanism match the experimental data better than those from the zero strain recombination mechanism. Also, via the proposed model, the strain‐dependent storage modulus correlates well with the peak loss modulus at a low strain range of around 0.1% to 100%. Moreover, a universal plot of the normalized storage modulus (ZL‐N‐B) as a function of the normalized Log strain amplitude (ϵ0/ϵapp) for different rubber systems is obtained. The loss moduli of systems are also simulated by the L‐N‐B model.
Theory of dilute polyampholyte solutions in external electrical fields
Authors: Schiessel Helmut , Blumen Alexander
Published: April 2003

In this work we display recent findings on the conformations and dynamics of polyampholytes (PAs; polymers with positively and negatively charged monomers) in external electrical fields. We consider the case in which the interactions between the charges are less important (weak coupling limit) and also the case in which they are fundamental (strong coupling case). In the weak coupling limit we present analytical results for Gaussian and also for freely‐jointed chains. Through scaling arguments we discuss the influence of the excluded volume on the PA's configurations. Furthermore we evaluate the dynamics of PAs in the framework of the Rouse and of the Zimm models. In the strong‐coupling regime PAs with vanishing total charge form spherical globules. Using a droplet analogy we examine the response of PAs to external fields and show the onset of an instability reminiscent of a first‐order phase transition.
Computer simulation of network formation via crosslinking copolymerization
Authors: Schröder Uwe Paul , Oppermann Wilhelm
Published: April 2003

The topology of networks formed by radical crosslinking copolymerization is strongly dependent on the type of crosslinker chosen. By a series of computer simulations, the influence of the relative reactivities of crosslinker and monomer on the network properties was investigated. Basic condition of the simulation is the postulation of a diffusion process control of the polymerization reaction. The resulting networks are analyzed with respect to cycle rank, loop formation, dangling ends, sol fraction and crosslinker molecules reacted only by one double bond. The results of the computer simulations indicate that the reactivity of the crosslinker decisively affects the properties of the network. Particularly the cycle rank, which determines the elastic properties of the network, is influenced strongly by the reactivity of the crosslinker. A change of the cycle rank of approximately one decade was observed. The influence of the reactivity was found to be most important in the region where the reactivity of the crosslinker is less than the reactivity of the monomer.
Mean‐square radius of gyration of polysiloxanes
Authors: Zhou Zhiping , Yan Deyue
Published: April 2003

The mean‐square radius of gyration for polysiloxanes has been derived according to the exact definition. Taking account of the examples of symmetrically substituted poly(dimethylsiloxane) and unsymmetrically substituted poly(methylphenylsiloxane), we find that the dependence of 〈S2〉 on the molecular weight follows the general formula 〈S2〉 = aMb with b = 1 ± 0.016, which is analogous to the theoretical outcomes for vinyl or vinylidene polymers even though the skeletal bone of polysiloxanes consists of alternating heteroatoms. A numerical comparison of the rigorous expression of the mean‐square radius of gyration given in this paper with that reported by Flory shows that the difference is obvious for low‐molecular‐weight polymer and it gradually declines with increasing degree of polymerization.
On the use of the gaussian chain as a monte carlo simulation model for the equilibrium properties of polymer solutions
Authors: Jorge Sonia , Freire Juan J. , Rey Antonio
Published: April 2003

We have explored the performance of a simulation model for Gaussian chains at different concentrations in a good solvent. The Gaussian statistics for the distances between contiguous beads in the model is directly implemented in the individual moves of a Monte Carlo algorithm. When the results of conformational properties for the Gaussian model are compared with those provided by a freely jointed model in the same conditions, significant differences arise at finite concentrations. The modeled Gaussian chain yields incorrect results for the quadratic average dimensions 〈R2〉 and 〈S2〉 at high concentrations, but correctly reproduces the results for the scaled end‐to‐end distance distribution function at any concentration, showing the effects of the screening of excluded volume when concentration increases. The reason for the wrong behavior of the simulated Gaussian model comes from a strong distortion of the “bond distance” distribution as a result of the concentration increase. We conclude that this model can only be safely applied to infinitely dilute solutions.
Computer simulation of irreversible gelation of polymers with stickers
Authors: Khalatur Pavel G. , Men'shikova Larisa V. , Khokhlov Alexei R.
Published: April 2003

The “bond fluctuation model” is used for Monte Carlo simulations of irreversible aggregation in solutions of associating macromolecules with regularly spaced stickers. The irreversible aggregation process follows the kinetically‐limited‐aggregation model first proposed by Eden. The fractal structures produced in the course of the aggregation are analyzed depending on the number of chains involved in the final cluster, n, chain length, N, and the number of stickers per chain, ns. It is shown that the chains with ns ≥ 2 form aggregates crosslinking the chains in a network‐like structure. The mesh size of this network mainly depends on the chain length between two stickers; there is also a weaker dependence on the number of associating groups per chain, ns. The chains connecting two aggregates turn out to be strongly extended. It is shown that the aggregates have a rather broad size distribution and that there is always a significant fraction of free single stickers. The inter‐ and intrachain screening effects control the local morphology of the aggregates.
Shape asymmetry of star‐branched random walks and nonreversal random walks
Authors: Zifferer Gerhard
Published: April 2003

Star‐branched random walks with 3, 4, 6, 8 and 12 arms (the total chain‐length ranging from N = 49 to 1925) have been produced and analysed with respect to their instantaneous shape. The short‐chain behaviour of nonreversal random walk stars (NRRWs) embedded in various lattices is compared to that of star‐branched freely jointed (off‐lattice) chains (RWs). While for all types of NRRW‐stars examined as well as for RW‐stars with bonds of constant length shape‐asymmetry increases with increasing chain‐lengths, the opposite behaviour is found for RW‐stars with Gaussian‐distributed bond‐lengths. The amount of short‐chain effects is strongly dependent on the number of arms and on the lattice type used. In the limit of infinitely large molecules, however, quantities characteristic of the shape converge to common values for all types of RWs and NRRWs examined.