Statistics of polymer chains in orienting fields

The theory of a freely jointed polymer chain is modified by introduction of interactions between dipole chain segments and an orienting field. Such a field results either from external forces (e.g. external electric or magnetic fields) or represents interactions between dipole segments of chains (molecular mean-field). The distribution of orientations of chain segments and the free energy of a chain in such orienting fields are calculated and discussed.     

Effects of chain flexibility on polymer conformation in dilute solution studied by lattice monte carlo simulation

Effects of chain flexibility on the conformation of homopolymers in good solvents have been investigated by Monte Carlo simulation. Bond angle constraint coupled with persistence length of polymer chains has been introduced in the modified eight-site bond fluctuation simulation model. The study about the effects of chain flexibility on polymer sizes reveals that the orientation of polymer chains under confinement is driven by the loss of conformation entropy.The conformation of polymer chains undergoing a gradual change from spherical iso-diametric ellipsoid to rodlike iso-diametric ellipsoid with the decrease of polymer chain flexibility in a wide region has been clearly illustrated from several aspects. Furthermore, a comparison of the freely jointed chain (FJC) model and the wormlike chain (WLC) model has also been made to describe the polymer sizes in terms of chain flexibility and quasi-quantitative boundary toward the suitability of the models.     

Density functional approach to the adsorption of spherical molecules on a surface modified with attached short chains

A density functional and Monte Carlo simulation study of end-grafted polymers immersed by simple fluids is presented. The polymer molecules are modeled as freely jointed tangent hard spheres with the end segments linked to the surface. The authors analyze an influence of the chain length, the grafting density, and a nature of solvent on the brush structure. Adsorption of hard-sphere mixtures on the modified surface is also discussed. The theory precisely approximates simulation data.     

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.     

Calculation of conformation-dependent biomolecular forces

We develop a numerical scheme that calculates forces under given conformational states of a biomolecule by using a harmonic sampling potential. It can also be used for calculating the potential of mean force, as tested by random walks on Gaussian enthalpy barriers. Further, Brownian dynamics simulations of a finite-length freely jointed chain confirm the analytic expressions for its entropic elasticity that we derive. Our method, while generally applicable to many systems, will be particularly useful for studying the elasticity of biopolymers where various types of ensembles differ due to the finite size effect.     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

The Estimation of Statistical Parameters Determining the Relaxation Times of Nematic Elastomers: A Three‐Chain Network Model

A simplified “three‐chain” network model formed from freely jointed polymer chains consisting of Gaussian elements with fixed mean‐square lengths is proposed for describing local dynamic properties of nematic elastomers. The boundaries of a polymer network are supposed to be fixed when sample volume and shape do not change with ordering. Relaxation times characterising intrachain motions in both isotropic and ordered states are determined by two factors. The first (“dynamic”) factor is related to the friction of chain elements and the second one (“statistical” factor) is determined by statistical mean–square fluctuations of segment projections on the three axes of rectangular frame of reference. The “statistical” factor of relaxation times is calculated here as a function of the order parameter and the parameter characterising the degree of network crosslinking. Statistical factor obtained in the framework of a network model consisting of Gaussian subchains is compared with that calculated here by using freely‐jointed‐rods chain model. Good agreement is shown between statistical factors obtained in the framework of the two chain models considered. This result confirms the validity of describing the dynamics of real rod‐like mesogenic groups in nematic elastomers in terms of a simplified chain model consisting of Gaussian segments with fixed average lengths which do not change with ordering. The influence of “dynamic” factor on the relaxation spectrum of a nematic elastomer is discussed qualitatively.     

Segmental and chain orientational behavior of spandex fibers

The internal structure and orientation behavior of two series of spandex fibers, which were made with different spinning methods and different soft and hard segment types, were studied by FTIR (Fourier Transform Infrared Spectroscopy), polarizing light microscopy, and Instron. The orientation behavior of hard and soft segments was studied with FTIR and those of polymeric chains with polarizing miscroscopy while the fibers were being stretched by the mechanical stretcher. The orientation behavior of dry-spun fibers was observed to be very different from that of the melt-spun fibers, which may be explained in terms of the internal structural difference such as the degree of phase separation and mechanical stability of the hard domains between the two types of fibers. In general, the dry-spun fibers showed better elastic recovery property than the melt-spun fibers. Since the polymer for the dry-spun fibers was synthesized with ethylene diamine as a chain extender resulting in the urea groups in the hard segments, it forms more stable hard domain due to the high cohesion energy between the urea groups. The change of the birefringence values during the cyclic deformation was studied with the polarizing light microscopy. The birefringence behaviors of the two dry-spun fibers were similar, whereas there was a noticeable difference between the two melt-spun fibers. The difference was explained in terms of the effect of crosslinking agent in one of the melt-spun fibers, which can stabilize the hard domain structure against the external stress. Mechanical hysteresis values measured gave results consistent with those of FTIR and birefringence measurements. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1821–1832, 1997     

Correlating backbone‐to‐backbone distance to ionic conductivity in amorphous polymerized ionic liquids

The morphology and ionic conductivity of poly(1‐n‐alkyl‐3‐vinylimidazolium)‐based homopolymers polymerized from ionic liquids were investigated as a function of the alkyl chain length and counterion type. In general, X‐ray scattering showed three features: (i) backbone‐to‐backbone, (ii) anion‐to‐anion, and (iii) pendant‐to‐pendant characteristic distances. As the alkyl chain length increases, the backbone‐to‐backbone separation increases. As the size of counterion increases, the anion‐to‐anion scattering peak becomes apparent and its correlation length increases. The X‐ray scattering features shift to lower angles as the temperature increases due to thermal expansion. The ionic conductivity results show that the glass transition temperature (T_g) is a dominant, but not exclusive, parameter in determining ion transport. The T_g‐independent ionic conductivity decreases as the backbone‐to‐backbone spacing increases. Further interpretation of the ionic conductivity using the Vogel–Fulcher–Tammann equation enabled the correlation between polymer morphology and ionic conductivity, which highlights the importance of anion hoping between adjacent polymer backbones. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997     

Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.     

Chain confinement in polymer nanocomposites and its effect on polymer bulk properties

The issue of chain confinement in nanocomposites remains largely unanswered because experimental systems are plagued by additional complicating variables such as particle–polymer interactions and free volume increases brought upon by the addition of the particles. Using computer simulation of high length chain polymers, we show that simple excluded volume interactions between polymer and nanoparticles lead to a wealth of changes in the diffusion coefficient and entanglement density of the chains. This opens up the possibility of using nanoparticles for tuning polymer properties, such as toughness, melt viscosity, and transient rubberlike behavior. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 687–692, 2010     

Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles

Stretching experiments on single molecules of arbitrary length opened the way for studying the statistical mechanics of small systems. In many cases in which the thermodynamic limit is not satisfied, different macroscopic boundary conditions, corresponding to different statistical mechanics ensembles, yield different force-displacement curves. We formulate analytical expressions and develop Monte Carlo simulations to quantitatively evaluate the difference between the Helmholtz and the Gibbs ensembles for a wide range of polymer models of biological relevance. We consider generalizations of the freely jointed chain and of the worm-like chain models with extensible bonds. In all cases we show that the convergence to the thermodynamic limit upon increasing contour length is described by a suitable power law and a specific scaling exponent, characteristic of each model.     

Topological coarse graining of polymer chains using wavelet-accelerated Monte Carlo. I. Freely jointed chains

We introduce a new, topologically-based method for coarse-graining polymer chains. Based on the wavelet transform, a multiresolution data analysis technique, this method assigns a cluster of particles to a coarse-grained bead located at the center of mass of the cluster, thereby reducing the complexity of the problem by dividing the simulation into several stages, each with a fraction of the number of beads as the overall chain. At each stage, we compute the distributions of coarse-grained internal coordinates as well as potential functions required for subsequent simulation stages. In this paper, we present the basic algorithm, and apply it to freely jointed chains; the companion paper describes its applications to self-avoiding chains.     

Spinodal decomposition with varying chain lengths and its application to designing polymer blends

The diffusion equations of spinodal decompositions with unique diffusivities for each species are derived for binary systems and ternary systems. These dynamic equations are linearized to show that the minimum size for growth is independent of diffusivity and is identical to the thermodynamic minimum on phase volume. Increases in chain length will destabilize mixtures and increase quench depth. Numerical simulations were conducted for two-dimensional systems. The considerable influences of chain lengths on morphology represent a competition between smaller diffusivities and larger quench depth when chain length is increased. These influences on several important morphologies in binary and ternary systems are described. The understanding of independent variable chain lengths represents one further step towards the systematical design of polymer blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 897–907, 1997     

Solution properties,unperturbed dimensions,and chain flexibility of poly(1‐adamantyl acrylate)

Poly(1‐adamantyl acrylate) (PAdA) exhibits much higher glass transition and degradation temperatures than other polyacrylates. However, the quantitative evaluation of the stiffness of this polymer chain has not been reported previously. In this study, the dilute solution properties and conformational characteristics of PAdA were evaluated using viscometry and scattering techniques. The unperturbed dimensions of this polymer were evaluated using the Burchard–Stockmayer–Fixman extrapolation and the touched‐bead wormlike chain model. The PAdA chain has a comparable persistence length, diameter per bead and characteristic ratio to poly(methyl methacrylate) and polystyrene. All these results indicate that PAdA is less flexible than common polyacrylates. In addition, the second virial coefficients (A₂) of PAdA in different solvents obtained by static light scattering were compared. Among the solvents investigated, tetrahydrofuran is a moderate solvent. Radius of gyration of a polymer sample in the various solvents ranged from 16.8 to 30.3 nm. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1526–1531     

Design,synthesis, and characterization of main‐chain,aromatic polyesters based on 3,4‐ethylenedioxythiophene

A series of new thermoplastic polyesters based on 3,4‐ethylenedioxythiophene (EDOT) with flexible aliphatic spacers have been synthesized and characterized for the first time. The thermal properties of these polyesters based on EDOT are comparable to those of conventional polyesters based on the 1,4‐phenyl unit, indicating that EDOT is a viable replacement for the phenyl units. The glass‐transition and melting‐transition temperatures decrease monotonically with an increase in the spacer length. Theoretical calculations have revealed that the core angle for EDOT is comparable to that of unsubstituted thiophene and hence should be compatible with the formation of the mesophase. This has been confirmed experimentally by the synthesis of a main‐chain, thermotropic, liquid‐crystalline polyester based on EDOT that exhibits fluid birefringence. In fact, this is the first report in which a main‐chain, liquid‐crystalline polymer based on 3,4‐disubstituted thiophene has been successfully designed and synthesized. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3479–3486, 2006     

Similarities between polyelectrolyte gels and biopolymer solutions

Small angle neutron scattering (SANS) measurements and osmotic swelling pressure measurements are reported for polyelectrolyte gels and solutions under nearly physiological conditions. A synthetic polymer (sodium-polyacrylate) and three biopolymers (DNA, hyaluronic acid, and polyaspartic acid) are studied. The neutron scattering response of these anionic polyelectrolytes is closely similar, indicating that at larger length scales the organization of the polymer molecules is not significantly affected by the fine details of the molecular architecture (e.g., size and chemical structure of the monomer unit, type of polymer backbone). The results suggest that specific interactions between the polyelectrolyte chains and the surrounding monovalent cations are negligible. It is found that the osmotic compression modulus of these biopolymer solutions determined from the analysis of the SANS response decreases with increasing chain persistence length. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3679–3686, 2006     

Multidimensional benzobisoxazole rigid-rod polymers. II. Processing,characterization, and morphology

A high-torque rheometer was used to facilitate the polycondensation of 4-[5-amino-6-hydroxybenzoxazol-2-yl]benzoic acid (ABA) with trimesic acid and 1,3,5,7-tetrakis(4-carboxylatophenyl)adamantane to yield two- and three-dimensional benzobisoxazole polymers, respectively. Although the resultant polymer dopes exhibited improved homogeneity compared to polymer dopes previously prepared in glassware, improved polymer solution viscosities were not achieved. Fibers spun from the two- and three-dimensional polymers did not show a significant increase in compressive strength compared to fibers of the linear or one-dimensional benzobisoxazole polymer derived from the homopolymerization of ABA. Morphological studies of the polymer fibers and films by wide-angle X-ray scattering and scanning electron microscopy strongly indicated more lateral disorder and a more isotropic character for the three-dimensional structures compared to the one-dimensional structures. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 3457–3466, 1997