A new technique for generating statistical properties of chain-molecule conformations is presented. Conditional probability density functions (PDFs) describing the frequency of occurrence of the relative position and orientation of frames of reference affixed to selected backbone atoms serve as the inputs. Ensemble statistical properties of whole chains are generated by performing multiple generalized convolutions of these conditional PDFs. The formulation is shown to include classical theories such as the hindered and freely rotating chains, the Gaussian random walk, and the rotational isomeric state model. The convolution model is modified to include the long-range effects of excluded volume. An analytical example is used to illustrate the procedure. A general algorithm to calculate the ensemble properties of an arbitrary chain macromolecule is presented. In this algorithm, each of the N degrees of freedom (e.g. torsion angles) is assumed to have K discrete states. Using the convolution procedure, a chain is divided into P statistical units. The computational requirement is reduced from an O(KN) calculation (corresponding to direct enumeration) to one which is O(P(C+KN/P)) where C is the computational complexity of the convolution procedure. In the case of a homopolymer, computations are reduced further to O(Clog(P)+KN/P).
A kinetic model simulating the glass transition and enthalpic relaxation in poly(3-hydroxybutyrate) is introduced. The model is based on the concept that enthalpic relaxation or physical ageing is a continuation of the glass forming process and uses the KWW function to describe the glass formation process and the subsequent ageing of the glass. Non-linearity is introduced by incorporating a dependence of the relaxation time on the fictive temperature. The effects of non-linearity on the distribution of relaxation times and the physical ageing process are investigated together with the development of the endothermic ageing peak at the glass transition with increasing extents of ageing.
Simple models of the star-branched and linear polymers were studied by means of a Monte Carlo method. The chains were confined on a simple cubic lattice. Star-branched polymers consisted of f=3 arms of equal length. The total number of beads in both types of polymers was varied from N=49 to N=799. The simulations were performed in different solvent qualities—from a good solvent to a collapsed globule regime. The static properties of the chains under consideration were measured as functions of the temperature of the system. It appeared that the ratio of the radius of gyration to the mean end-to-end vector is very sensitive to solvent quality. It shows that the coil-to-globule transition is a complicated phenomenon. The possible explanation of the phenomenon is discussed.
A method described in the statistical literature for the numerical inversion of Laplace Transforms of real functions has been adapted for the derivation of molecular weight distributions from calculations of the generating function for a polymeric system. It has been shown that a third-order refinement is sufficiently accurate for molecular weight distributors broader than 4.0. This allows the calculations to be carried out with a precision of 16 decimal digits which is commonly used in Fortran. Where higher precision is available, the treatment is applicable to narrower MWDs.
Asymptotic methods based on the slenderness ratio are used to obtain the leading-order equations that govern the fluid dynamics of axisymmetric, isothermal, Newtonian, annular liquid jets such as those employed in the manufacture of textile fibres, annular membranes, composite fibres and optical fibres, at low Reynolds numbers. It is shown that the leading-order equations are one-dimensional, and analytical solutions are obtained for steady flows at zero Reynolds numbers, zero gravitational pull, and inertialess jets. A linear stability analysis of the viscous flow regime indicates that the stability of annular jets is governed by the same eigenvalue equation as that for the spinning of round fibres. Numerical studies of the time-dependent equations subject to axial velocity perturbations at the nozzle exit and/or the take-up point indicate that the annular jet dynamics evolves from periodic to chaotic motions as the extension or draw ratio is increased. The power spectrum of the annular jet's radius at the take-up point broadens and the phase diagrams exhibit holes at large draw ratios. The number of holes increases as the draw ratio is increased, thus indicating the presence of strange attractors and chaotic motions.
Molecular simulations of poly(vinyl phenol) were performed to study the effect of hydrogen bonds. Three conformations were constructed and their structure was validated in terms of the solubility parameter and gyration radius. Amorphousness was confirmed by calculating the X-ray pattern and pair correlation function. Isotropy of the structure was verified using the bond-orientational correlation function for backbone, phenyl rings, and O–H groups forming hydrogen bonds. Glass transition temperature was calculated using a stepwise change on temperature at constant pressure. The values were found to be comparable to experimental data and were consistent with poly(styrene) simulations published in the literature. The percentage of hydrogen bonds found in the model, 63%, was in good agreement with previous semi-quantitative evaluation by FTIR spectroscopy.
Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AK. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t(w), which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t(1/4) law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length I, a comparatively weak dependence, while t(w) is proportional to l(3), a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t(w) is surprisingly close, at least for the monodisperse polymers investigated here. (C) 2000 Elsevier Science Ltd. All rights reserved.
Polyamides have many desirable properties such as high melting temperatures, chemical resistance and superior mechanical properties. However, its crystalline morphology can limit its applications. It is the specific interaction, hydrogen bonding that gives rise to the crystalline structure of polyamides. This interaction is strong and important when blending on the final morphology and mechanical properties. Polyurethane contains polar functionality that can also interact with the polar component of polyamide. Hence, it is important to study the interaction between such a blend as polyurethane can enhance the toughness of polyamide due to its elastic properties. This study is an insight into the specific interaction between two polar polymers in a simulation whereby the interaction is maximised. Hydrogen bonding has been observed between molecules of either polyamide–polyurethane and polyamide–polyamide, and it is sufficiently strong to cause the polymer chains to distort rather than disrupt the hydrogen bonds. When groups of like polarity, such as carbonyl groups, come into proximity, the polymer chains again distort from their regular conformation because of mutual repulsion.
The semi-empirical ZINDO/1 method is used to calculate the electronic structure and thermodynamic properties of aniline trimers adsorbed onto cluster models of the Al(100) and Fe(100) surfaces. The effects of progressive oxidation and protonation of the trimers on corrosion inhibition are interpreted in terms of these calculations.
Molecular dynamics simulations for 4-n-pentyl-4′-cyanobiphenyl (5CB) with as many as 944 molecules are reported. The order-N fast multipole method (FMM) is used to treat the long-range interactions. For a droplet of 944 molecules, the simulation shows a correlation between the droplet shape and the nematic order and a strong surface effect; little nematic order is found in a 118 molecule droplet. Simulations of the bulk system result in similar order parameters for both the 118 and 944 molecular ensembles. Although the nematic–isotropic transition was not observed at temperatures as high as 400K using the CHARMM force field, a modification of the force field using ab initio determined partial atomic charges lowers the order parameters.
Dendrimers and hyperbranched polymers represent a novel class of structurally controlled macromolecules derived from a branches-upon-branches structural motif. The synthetic procedures developed for dendrimer preparation permit nearly complete control over the critical molecular design parameters, such as size, shape, surface/interior chemistry, flexibility, and topology. Dendrimers are well defined, highly branched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction sequence that guarantees complete shells for each generation, leading to polymers that are mono-disperse. This property of dendrimers makes it particularly natural to coarsen interactions in order to simulate dynamic processes occurring at larger length and longer time scales. In this paper, we describe methods to construct 3-dimensional molecular structures of dendrimers (Continuous Configuration Boltzmann Biased direct Monte Carlo, CCBB MC) and methods towards coarse graining dendrimer interactions (NEIMO and hierarchical NEIMO methods) and representation of solvent dendrimer interactions through continuum solvation theories, Poisson–Boltzmann (PB) and Surface Generalized Born (SGB) methods. We will describe applications to PAMAM, stimuli response hybrid star-dendrimer polymers, and supra molecular assemblies crystallizing to A15 colloidal structure or Pm6m liquid crystals.
The model of electrical degradation describes the observed growth of damage in polymers quantitatively. It is shown that the fractal approach can be used to explain the non-monotonic behaviour of voltage versus scale for electrical degradation.
The paper reports the development of a Monte Carlo lattice model (cubic F) of polymer chains which is able to access times where the diffusion of the centre-of-mass of the chains is the dominant process, even though the chain lengths are well above that for entanglement. The volume of the model is large when compared with the volume of gyration of the individual molecules. The model incorporates an algorithm, which allows for the possibility of co-operative motions over sections of the chains and increases the time efficiency of the simulation. Both the model and the modifying algorithm have been tested against the known scaling laws.The model, for shorter chains, is 'reverse mapped' into full atomic detail as polyethylene and the shorter time processes simulated using molecular dynamics (MD). The MD model is tested against experimental diffusion data for polyethylene, of the same molecular weight and at the same temperature, and then used to time-calibrate the lattice model.Both the fine grained MD model and the coarse grained MC model are thus interlocked to cover a time range from the individual atomic motions of MD up to the order of a microsecond, a range of six orders of magnitude. (C) 2000 Elsevier Science Ltd. All rights reserved.
Advances in theory and methods are making it practical to consider fully first principles (de novo) predictions of structures, properties and processes for organic materials. However, despite the progress there remains an enormous challenge in bridging the vast range of distances and time scales between de novo atomistic simulations and the quantitative continuum models for the macroscopic systems essential in industrial design and operations. Recent advances relevant to such developments include: quantum chemistry including continuum solvation and force field embedding, de novo force fields to describe phase transitions, molecular dynamics (MD) including continuum solvent, non equilibrium MD for rheology and thermal conductivity and mesoscale simulations. To provide some flavor for the opportunities we will illustrate some of the progress and challenges by summarizing some recent developments in methods and their applications to polymers and biopolymers. Four different topics will be covered: (1) hierarchical modeling approach applied to modeling olfactory receptors, (2) stabilization of leucine zipper coils by introduction of trifluoroleucine, (3) modeling response of polymers sensors for electronic nose, and (4) diffusion of gases in amorphous polymers.
Polymerization-induced phase separation (PIPS) via spinodal decomposition (SD) under a temperature gradient for the case of a monomer polymerizing in the presence of a non-reactive polymer is studied using high performance computational methods. An initial polymer (A)/monomer (B) one-phase mixture, which has an upper critical solution temperature (UCST) and is maintained under a temperature gradient, phase-separates and evolves to form spatially inhomogeneous microstructures. The space-dependence of the phase-separated structures under the temperature gradient field is determined and characterized using quantitative visualization methods. It is found that a droplet-type phase-separated structure is formed in the high-temperature region, corresponding to the intermediate stage of SD. On the other hand, lamella or interconnected cylinder type of phase-separated structure is observed in the low-temperature region, corresponding to the early stage of SD structure, in the large or small temperature gradient field, respectively. The kinetics of the morphological evolution depends on the magnitude of the temperature gradient field. The non-uniform morphology induced by the temperature gradient is characterized using novel morphological techniques, such as the intensity and scale of segregation. It is found that significant non-uniform structures are formed in a temperature gradient in contrast to the uniform morphology formed under constant temperature.
We performed molecular dynamics simulations to analyze the initial stage of the thermal degradation of polyethylene, which is dominated by the random scission reaction. The simulations were initiated from structures that were taken from previously equilibrated snapshots of the amorphous polymer and of a free-standing thin film. Isolated chains were also used for comparison. Our systems were coupled to a thermal heat bath, and the effect of different coupling constants was studied. Rate of random scission increases as the strength of the temperature coupling increases. Rates of reaction are almost similar in thin films and the bulk, whereas the rates are much faster in isolated chains. Expansion of the free-standing thin film accompanies degradation, producing fragments of various sizes. Chains of higher molecular weights than the initial chains can be produced due to recombination of fragments during the expansion of thin films. The polydispersity index of the resulting fragments is higher in thin films compared to the bulk. The bonds at the low density portion of the thin films have a higher probability of being broken.
Monte Carlo (MC) simulations of structure formation for short polyethylene chains at low temperature are performed based on a recent developed method that uses coarse-grained chains on a high coordination lattice. Local short-range interactions based on rotational isomeric state (RIS) model and long-range interactions obtained from Lennard–Jones (LJ) potential are introduced during the simulation. Properties evaluated from the simulations are the mean square dimensions, anisotropy of the radius of gyration tensor, local conformation determined by the occupancy of trans state and orientation correlation functions, energy of the system, and chain packing reflected by the pair correlation functions and structure factors. All of these parameters reveal an ordering process that produces an approximation to a hexagonal crystal phase. The hexagonal structure is imposed by the presence of a diamond lattice underlying the high coordination lattice on which the simulation is performed. Folding of the chains in the crystal is mandatory, because they have fully extended lengths in excess of the dimension of the simulated periodic box. Nevertheless, the simulations demonstrate that a high degree of crystallinity can be achieved in reasonable computer time. The simulation technique should be applicable to other choices of periodic boundary conditions that do not affect the results as strongly as in the present case.
This study concentrates on the important conducting polymer, polypyrrole. Detailed atomistic molecular models have been developed with the help of ab initio and semi-empirical quantum mechanical calculations.The vibrational spectra of isolated pyrrole monomers and oligomers from n = 1 and 2, where n is the number of structural repeat units used, have been computed using the ab initio 3-21G basis set. The results obtained are compared with data for the case of oligomers with n = 2-5 for both neutral benzenoid and quinonoid oligopyrroles, from semi-empirical predictions obtained by AM1 and PM3. The trends in the computed harmonic force fields, vibrational frequencies and intensities are monitored as a function of the chain length. The data are analysed in conjunction with the trends in computed equilibrium geometries.Also the examination of the heat of formation of these two degenerate forms (quinonoid and benzenoid) has been conducted with respect to increases in the number of rings and the change of methods from AM1 to PM3. (C) 2000 Elsevier Science Ltd. All rights reserved.
Two simple simulation methods, which will be useful for the prediction of the infrared (IR) spectral features of polymers, are reported. This paper focusses on simple aromatic models of the main aromatic backbones of structural polymeric resins. These methods were normal coordinate analysis (NCA) using the PM3 Hamiltonian implemented under MOPAC6 and a dipole autocorrelation function (DACF) calculated using coordinates and velocities from a series of molecular dynamics runs performed using the universal force-field (UFF) as implemented in the Cerius2 modelling package. The semi-empirical NCA approach yielded useful information about the fundamental modes of vibration of the molecules but, as expected, could not be used to predict combination modes for anything but the simplest of molecules. The DACF approach showed potential for the prediction of combination bands but thorough evaluation of the method was found to be extremely difficult, owing to problems with band assignment for all but the simplest of molecules. An estimate of the accuracy of prediction for the different types of vibrational mode is included for each method.
Prediction of swelling behaviour of hydrogels containing cationic and anionic moieties, sensitive to pH and ionic strength changes of the swelling medium was investigated. The equations derived for the prediction of the theoretical swelling curves are based on the phantom network theory and the approaches of Peppas et al. For all predictions, a number of polymer based parameters, solution property parameters and polymer–solvent combination type parameters were evaluated typical of amphiphilic copolymers. The advantages of the derived equations for the determinations of average molecular weight between the cross-links, and also polymer–solvent interaction parameter have been exemplified.
