Monodisperse Polybutadienes Research Articles

Component predictions and the relaxation spectrum of the double reptation mixing rule for polydisperse linear flexible polymers

General, experimentally verifiable predictions of individual component behavior of linear flexible polymers in arbitrary molecular weight distributions are derived from the double reptation mixing rule. The distribution of stress/orientation among the different components of the molecular weight distribution during steady deformation and constrained elastic recovery are developed for the case of a single exponential monodisperse relaxation function. The des Cloizeaux ‘‘double reptation’’ model and the Tsenoglou network model are shown to be equivalent and the precise relationship between the model parameters is determined. Distinct contributions to the relaxation process from the separate mechanisms of reptation and matrix relaxation (constraint release) are identified. Experimental relaxation spectra of bidisperse blends of nearly monodisperse polybutadienes reveal a cascade of discrete peaks in the terminal zone that are in qualitative agreement with theoretical predictions from the double reptation mixing rule with a Doi–Edwards monodisperse relaxation function. The ability to accurately calculate experimental relaxation spectra for complex blends of nearly monodisperse materials is a powerful tool in developing, discriminating, and evaluating new mixing rules.

Relaxation Patterns of Nearly Critical Gels

We measure the complex rheological behavior of nearly critical gels and analyze the data by searching for characteristic patterns and abstracting those patterns into a self-consistent model. The sample is a linear, flexible, nearly monodisperse polybutadiene which gets cross-linked on its vinyl side groups. The dynamic mechanical storage and loss moduli of cross-linking polymers change smoothly during the liquid−solid transition, while equilibrium rheological properties (e.g., zero-shear viscosity and equilibrium compliance) diverge. During gelation, the relaxation occurs in a distinct pattern which can be described in a quantitative way with a minimum number of parameters. The pattern can be understood as a combination of the BSW spectrum (representing the precursor relaxation behavior) and the self-similar Chambon−Winter gel spectrum (modeling the terminal relaxation due to growing clusters). The spectrum is cut off at the material's longest relaxation time, λmax. Our model parameters, λmax and Ge (equilibrium modulus), exhibit characteristic scaling behavior with respect to the distance from the gel point, |p − pc|. The relaxation exponent, n, in the terminal zone is a function of the extent of reaction. Hence, dynamic scaling (requires constant n values) is not valid for our system. The proposed model passes the self-consistency test by predicting the mechanical behavior (at different frequencies) as a function of the extent of reaction and other rheological observations during the sol−gel transition.

A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime

The dynamic mechanical behavior of a series of monodisperse polybutadienes has been investigated from the flow regime to the glassy state. Assuming a linear superposition of the entanglement and glass behavior a mathematical model of the spectrum of relaxation times is developed. It consists in a self-similar spectra for the entanglement contribution and a Fractional Maxwell Fluid (FMF) for the glassy contribution. The model closely represents the master curves of dynamic moduli over 15 logarithmic decades of frequency with three parameters for the flow regime (GN 0 N η0 and a cut-off parameter λmax) and four parameters for the FMF. It is shown that one of the parameter of the FMF is similar to the power-law exponent of a self-similar spectra previously proposed in the literature to model the transition to glass.

Time-temperature superposition and linear viscoelasticity of polybutadienes

A series of monodisperse polybutadienes has been used to perform mechanical relaxation measurements from the flow regime to the glassy state. Results on loss shear moduli have been analyzed within the framework of a coupling model. It has been found to represent well the frequency dependence in the glassy and terminal zones using a segmental motion coupling parameter β α and an entanglement coupling parameter β η . Moreover, our results on apparent shift factors resulting from time-temperature superposition are consistent with the lack of thermorheological simplicity predicted by the coupling theory due to the difference between β α and β η .

A generalized Giesekus constitutive model with retardation time and its association to the spurt effect

This paper presents a simple generalization of the single-mode Giesekus constitutive model with retardation time. It is based on the utilization of the Gordon Schowalter derivatives for the stress and rate-of-deformation tensors, which account for the non-affine motion of polymer strands, and make the model more versatile in terms of its ability to predict the complex flow behaviour. The model is consistent with molecular kinetic theory, and has been tested in several well-characterized shear flows, whereas its ability to describe shear-free flows has been proved as well. Finally, a comparison against steady shear data of nearly monodisperse polybutadienes demonstrates its superiority with respect to other continuum or molecular models exhibiting non-monotonic constitutive behaviour.

Thermodynamic interactions in model polyolefin blends obtained by small-angle neutron scattering

The dependence of Flory-Huggins interaction parameter χ on temperature, composition, and chain length was investigated forbinary blends of amorphous model polyolefins, materials which are structurally analogous to copolymers of ethylene and butene-1. The components were prepared by saturating the double bonds of nearly monodisperse polybutadienes (78%, 88%, and 97% vinyl content) with H 2 and D 2 . Values of χ extracted from SANS data in the single-phase region for two series of blends, H97/D88 and H88/D78 were found to be insensitive to chain length and to the component volume fractions for Φ= 0.25, 0.50 and 0.75

The relaxation time spectrum of nearly monodisperse polybutadiene melts

The relaxation behavior of polymers with long linear flexible chains of uniform length has been investigated by means of dynamic mechanical analysis. The relaxation time spectrum (H(λ)) follows a scaling relationship with two self-similar regions, one for the entanglement and terminal zone, and a second one for the transition to the glass. This can be described in its most general form (termed “BSW spectrum”) as H(λ) = H e λne + H g λ− n g for λ < λmax and H(λ) = 0 for λmax < λ, where H e , H g , n e , n g are material constants and λmax is the molecular weight dependent cut-off of the self-similar behavior. In this study, the dynamic mechanical response has been measured and analyzed for four highly entangled, nearly monodisperse polybutadienes with molecular weights from 20000 to 200000. The data are well represented by the BSW spectrum with scaling exponents of n e = 0.23 and n g = 0.67. The values of the exponents obtained in this work are about the same as those found for polystyrene samples in a previous study. This suggests that the two types of polymers have a similar relaxation pattern. However, at this point further refinement of the experiments is needed before being able to draw definite conclusions about the universality of the exponents.

Oligomers as molecular probes of orientational coupling interactions in polymer melts and networks

Simultaneous measurement of infrared dichroism and birefringence was used to study orientational coupling effects between a series of monodisperse polybutadiene oligomers and the surrounding matrix, which consisted of either polybutadiene polymer melt or polybutadiene network. The oligomers had molecular weights ranging from well below the critical molecular weight for entanglement M e, to several times M e. For the oligomer/network system, the magnitude of the coupling coefficient was found to remain constant at about unity over the range of network crosslink densities, oligomer molecular weights and degrees of swelling examined, thereby confirming the D n.m.r. experiments performed on the same samples. For the oligomer/polymer system, orientational coupling effects were examined as a function of oligomer molecular weight and temperature. It was found that unentangled oligomers experienced almost complete coupling, while fully entangled melts were subject to a much lower coupling. In addition, it was found that the magnitude of the coupling is independent of temperature, indicating that these orientation correlations are entropic in nature, arising from the packing entropy of chain segments. An orientational dependent lattice model, proposed originally by DiMarzio, was found suitable for predicting experimental results.

Infrared polarimetry studies for multicomponent polymer melts

A rheo-optical technique to measure dynamic infrared dichroism was used with deuterium labeling to study component relaxation in a variety of multicomponent polymer melts. For each sample overall relaxation was observed simultaneously using birefringence measurements. Nearly monodisperse poly(ethylene propylene) samples were used to construct three different sets of bidisperse blends. For each sample, results for step-strain relaxation of each component and of the total sample are presented and discussed. Effects of intermolecular orientational coupling were observed and a coupling strength of 0.45 was measured. The results of these experiments were compared to a reptation-based constraint release model, and a qualitative agreement was found. Using nearly monodisperse polybutadiene block copolymers, selected segment relaxations following step strains were examined. It was found that segments located at chain ends relax faster than segments located at chain centers, and that both the Rouse model and the tube model of Doi and Edwards correctly predict the qualitative features of segmental relaxation. The tube model, however, gave exact quantitative agreement with experiment when the effects of orientational coupling interactions of strength 0.4 were incorporated into the model. Additional studies on orientational coupling effects in polymer melts were conducted using a series of monodisperse polybutadiene oligomers dissolved in a polybutadiene polymer matrix. The oligomers had molecular weights ranging from well below the entanglement molecular weight, M e, to several times M e. The results indicate that orientational coupling interactions are significantly reduced for oligomers with molecular weights above M e. This technique can be further applied to study component dynamics in blends of two different polymers where the relaxation of each polymer in the melt can be observed separately.

Catalytic hydrogenation of diene polymers: Part I. Kinetic analysis and mechanistic studies on the hydrogenation of polybutadiene polymers in the presence of RhCl(PPh 3) 3

Chemical modification of diene-based polymers via catalytic hydrogenation offers an efficient synthetic route to elastomers with high stability to oxidative degradation. Detailed kinetic studies involving the hydrogenation of cis-1,4-polybutadiene have been carried out in the presence of RhCl(PPh 3) 3 under mild reaction conditions (65 °C, < 101 kPa H 2). Quantitative hydrogenation of carbon-carbon unsaturation has been achieved without any large scale changes in polymer chain length properties. Polymer structure characterization was accomplished using IR, 1H and 13C NMR spectroscopies. Based on detailed kinetic studies, a mechanism was postulated for the hydrogenation system in order to appreciate the important factors which influenced the nature and extent of the hydrogenation reactions. A rate law was derived from the proposed mechanism. Using this rate law model, statistical analysis of the experimental data has led to the successful estimation of reaction parameters. The selectivity of the catalyst for cis versus trans internal double bonds was also investigated, and the results show that steric effects are important for the catalyst selectivity. It was also found that catalytic hydrogenation of monodisperse polybutadiene could be used to produce monodisperse polyethylene or poly(ethylene-co-butylene) standard for gel permeation chromatography (GPC).

Self-consistent theory of polydisperse entangled polymers: Linear viscoelasticity of binary blends

The effects of polydispersity on the linear viscoelastic properties of concentrated polymer solutions and melts are analyzed. Existing theories for the dynamics of linear polymers, based on the idea of each polymer confined in a fixed tube, are shown to be incapable of describing observed rheological response of polydisperse polymers. A model is proposed which, in a self-consistent manner, solves the many chain problem given the solution to the single chain problem. Two types of polymer relaxation are incorporated in the model. The first type is escape of a polymer from its tube by motion of the polymer itself. It includes all dynamic modes available to the single chain in a tube—those due to its reptation—as well as other modes, such as fluctuations in tube length. The second type is relaxation of a polymer chain by the motions of the surrounding polymers forming its tube (constraint release). The relaxation modulus is then the product of two functions μ(t) and R(t). μ(t) is the fraction of tube occupied at time t=0 that has not been evacuated at time t, thereby representing escape of the polymer from its tube (solution to the single chain problem). R(t) represents relaxation by the constraint release process, which is modeled by a Rouse chain with random bead mobilities. The probability distribution of these mobilities is determined, in a self-consistent way, from the disentanglement rates due to the tube evacuation processes of the surrounding chains. Thus R(t) is calculated from the spectrum of relaxation rates of the μ(t) processes for the surrounding chains. The predictions of the model with some single chain solutions μ(t) from the literature are compared with oscillatory shear data for binary blends of nearly monodisperse polybutadiene, in which both components are well entangled.

Monodisperse polyethylenes: Crystallization kinetics

AbstractCrystallization kinetics of hydrogenated monodisperse polybutadienes have been measured using hot‐stage microscopy, and the data have been analyzed in terms of crystallization half‐time and Avrami exponent. Results obtained from hydrogenated polybutadienes having M̄w's in the range 5,100 to 340,000 were compared with what was obtained from several commercial polyethylenes. A four‐branch star hydrogenated polybutadiene was also included in this study. Crystallization half‐time at constant undercooling was found to go through a minimum when expressed as a function of M̄w; such behavior is consistent with polyethylene data already reported in the literature. It was found that crystallization half‐times for all polyethylene homopolymers studied (hydrogenated polybutadienes as well as commercial polyethylenes with their broad molecular weight distributions) exhibit similar exponential dependences on undercooling.

Viscoelastic properties and unstable flow of monodisperse polybutadiene solutions

The conditions governing the onset of unstable flow when concentrated solutions of monodisperse polybutadiene in α-methylnaphthalene are extruded through a capillary have been investigated. The critical values of the parameters corresponding to these conditions have been found. It is shown that unstable flow of the "elastic turbulence" type is associated with transition of the system to the forced high-elastic state.

Comparative investigation of the diffusion and viscosity behaviour of polybutadiene solutions

A study was made of the concentration dependence of the viscosity and the coefficients of inter- and self-diffusion of solutions of monodisperse polybutadienes in “poor” and “good” solvents over the enitre range of compositions at different temperatures. A relationship between the coefficients of inter- and self-diffusion was found by taking account of the concentration dependence of solvent activity. The micro-viscosity and monomeric coefficients of friction were determined for polybutadienes in solution. The relationship between micro-viscosity and the molecular weight of the polymers was investigated. A correlation was found between the monomeric coefficient of friction and the size of the diffusing molecule.

Influence of Vibrations on the Viscoelastic Behavior of Monodisperse Polybutadienes

Abstract The viscoelastic behavior of monodisperse polybutadienes is studied at different amplitudes of cyclic deformation. The concept of initial relaxation spectrum is introduced, this spectrum corresponding to small amplitudes. Under the action of high amplitudes the relaxation spectrum changed. This changed-effective spectrum can be calculated by means of the linear theory of viscoelasticity. The initial spectra of monodisperse polybutadienes have maxima. Under the action of high amplitudes the long-time parts of the spectra are truncated and the maxima shift into the short-time regions. There is an unambiguous correspondence between the amplitude of the deformation rate on cyclic deformation and the rate of shear on continuous deformation. It is shown that the length of the high-elasticity plateau, estimated on a logarithmic scale of relaxation times, and the maximum relaxation times of polybutadienes, as well as their initial Newtonian viscosities are dependent on molecular weight to a power of 3.6. The apparent viscosity is calculated, making use of the approximate initial relaxation spectrum concept, the law of change of its long-time boundary with the shear rate, and the commonly known relation of the linear theory of viscoelasticity. The results of these calculations were found to agree approximately with the data obtained under conditions of continuous deformation.

Influence of Vibrations on the Viscoelastic Behavior of Monodisperse Polybutadienes

Abstract The viscoelastic behavior of monodisperse polybutadienes is studied at different amplitudes of cyclic deformation. The concept of initial relaxation spectrum is introduced, this spectrum corresponding to small amplitudes. Under the action of high amplitudes the relaxation spectrum changed. This changed-effective spectrum can be calculated by means of the linear theory of viscoelasticity. The initial spectra of monodisperse polybutadienes have maxima. Under the action of high amplitudes the long-time parts of the spectra are truncated and the maxima shift into the short-time regions. There is an unambiguous correspondence between the amplitude of the deformation rate on cyclic deformation and the rate of shear on continuous deformation. It is shown that the length of the high-elasticity plateau, estimated on a logarithmic scale of relaxation times, and the maximum relaxation times of polybutadienes, as well as their initial Newtonian viscosities are dependent on molecular weight to a power of 3.6....

Effects of vibration on the viscoelastic behavior of monodisperse polybutadienes

Abstract The viscoelastic behavior of monodisperse polybutadienes is studied at different amplitudes of cyclic deformation. The concept of initial relaxation spectrum is introduced, this spectrum corresponding to small amplitudes. Under the action of high amplitudes the relaxation spectrum changed. This changed-effective spectrum can be calculated by means of the linear theory of viscoelasticity. The initial spectra of monodisperse polybutadienes have maxima. Under the action of high amplitudes the long-time parts of the spectra are truncated and the maxima shift into the short-time regions. There is an unambiguous correspondence between the amplitude of the deformation rate on cyclic deformation and the rate of shear on continuous deformation. It is shown that the length of the high-elasticity plateau, estimated on a logarithmic scale of relaxation times, and the maximum relaxation times of polybutadienes, as well as their initial Newtonian viscosities are dependent on molecular weight to a power of 3.6....