Method of determination of dielectric relaxation characteristics of plasticized polystyrenes on the basis of calorimetric glass temperature

The dielectric loss measurements of different polystyrenes (fractions and blends) with different molecular weights (M _n 2000–125000 g/mol) were carried out in the frequency range 10^–2–10⁶ Hz and the temperature range of the glass process (60°–135°C, depending on the molecular weight). The measurements of the pure fractions showed that the half-width of the glass relaxation process of the different polystyrenes can be correlated by a straight line, if they are plotted versus the relaxation frequency maxima of the glass process, regardless of the difference in both their molecular weight and glass transition temperature. Moreover, the fine structure of the shape of the glass process of polystyrenes with different molecular weights was found to be the same when the glass process appears at the same relaxation frequency range. The addition of oligostyrenes or low molecular <10% wt additives to the high molecular weight polystyrene did not influence the shape of the glass process. The calorimetric glass transition temperature of polystyrene was found to be only dependent on the number average molecular weight as well as on the number of end groups, but not on the molecular weight distribution. The obtained experimental results were correlated to develop a method for the estimation of the dielectric relaxation characteristics (relaxation frequency as well as the shape parameters) of the glass process of plasticized polystyrenes based on the calorimetric glass transition temperature. A method for the analysis of the dielectric relaxation curves of mixtures of label and polymer is suggested.     

Orientational–deformational nature of flow birefringence in solutions of rigid-chain polymers

The orientational–deformational nature of flow birefringence (FB) in solutions of rigid-chain polymers is confirmed experimentally. The possibility of a direct determination of the internal viscosity parameter by the dependence of the FB relaxation time on the solvent viscosity is demonstrated. Indirect manifestation of internal viscosity in the FB relaxation time is confirmed by the dependence of the form factor on the degree of coiling. © 1993 John Wiley & Sons, Inc.     

Study of the dissolution process of polystyrene in concentrated cyclohexane solution by MNR relaxation

 ¹³C-NMR relaxation times of polystyrene (PS) chains in its theta solvent, cyclohexane, have been measured at different temperatures. It was found that relaxation of carbon nuclei of the side-chain-phenyl groups and those of main chains have remarkably different temperature-dependent relaxation behaviors in the solvent. A two-step model for the dissolution process is proposed. According to the model, swelling of the polymer below θ temperature corresponds mainly to the gradual dispersion of the side-chain phenyl groups; while the complete dissolution above θ temperature corresponds mainly to the gradual dispersion of the main chains at a molecular level. These dispersions reflect the fact that cohesional interaction among side-chain-phenyl rings or main chains are weakened by solvent molecules, which shows the existence of the cohesional entanglements among polymer chains. The results of T ₁(C) are confirmed by the biexponential dependence of ¹H-NMR spin–spin relaxation on temperature. Received: 2 July 1997 Accepted: 21 October 1997     

星形聚苯乙烯本体粘弹性对结构的依赖性

用应力松弛法研完了一组4—12支链星形聚苯乙烯本体的粘弹性。从应力松弛主曲线测定了零切变粘度η_0、稳态柔量J_e~o和其它流变学参数。结果发现,零切变粘度和最大松弛时间τ_m强烈地依赖于聚合物的分子尺寸,并且可以用无扰特性粘度或折合分子量来描述。η_0和τ_m随支化度增大而增大。实验还直接证实了支链长度相同的星形聚合物的J_e~o与支链数目无关,但是星形聚合物的稳态柔量比具有和支链间分子量相同的线形聚合物的稳态柔量大。     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Dielectric studies on some mesogenic,non-mesogenic and organic molecules

Two important molecular parameters, namely, the dielectric relaxation time τ and electric dipole moment are highly useful in having insight into the molecular structure, size, shape, apart from the inter- and intra-molecular forces, etc. With these in view dielectric measurements in benzene at room temperature on the pure samples of o-ethyl phenol, 2-n-butylphenol, 4-n-butylphenol, 2,6-dimethoxyphenol and 3,4-difluorophenol were carried out at a frequency of 9.98 GHz by employing concentration variation method. Similar measurements, on a single weight fraction of each of them at 9.98 GHz and also at 8.74 GHz are carried out. Measurements on a single weight fraction in benzene of each of the liquid crystal samples, namely, EPCP.car (Butyl-p-(p-ethoxy phenoxy corbonyl)-phenyl carbonate), PPPB (p-pentylphenyl-p-propyl benzonate), EPAP.Hp (p-(p-ethoxyphenyl azo) phenyl heptenate) and EPAP. Und (p-(p-ethoxyphenyl azo) phenyl undecylenate were also carried out at the said two frequencies. Using the obtained values of ε′, ε′′ relaxation time and dipole moment were determined using different methods. The obtained results are compared with earlier results wherever available.     

Computer simulation of the mechanical alpha relaxation in isothermally crystallized high-density polyethylene

The influence of thermal history on the dynamic mechanical behavior in the alpha relaxation region of high-density polyethylene (HDPE) is predicted using computer modeling. The model considers the mechanical alpha relaxation as a succession of cooperative single movements occurring within the defect region of the crystal lattice that finally produce a relative displacement between lamellae. A distribution function of the number of such single steps is postulated considering topological properties of the sample: branch content and molecular weight. To carry out the simulation, the model uses the spectrum of the sample subjected to fast cooling as a reference system. In addition, the crystallinity and the segregated material content for the particular thermal history of the object of study are also required. Loss modulus spectra are generated using balance of energy considerations, and a few examples are presented together with several experimental results. © 1993 John Wiley & Sons, Inc.     

Flow birefringence studies of a concentrated polystyrene solution in a two-roll mill. I. Steady flow and start-up of steady flow

We have studied a 4.8 volume percent solution of a narrow distribution polystyrene with molecular weight 3.84 × 10⁶ in flows generated by a co-rotating two-roll mill. These flows have a stagnation point at the midpoint between the roller axes. Further, they are linear, two-dimensional, and the magnitudes of the strain-rates are greater than the vorticity. The overall objective of our studies is to explore the dynamics of concentrated polymer solutions which are in the highly deformed state that is generated in the two-roll mill. Birefringence data are presented for both steady flow and start-up of steady flow in the two-roll mill. The steady and transient data are used to analyze the linear and nonlinear viscoelastic regions of material behavior. In the nonlinear regime, the birefringence upon start-up shows an initial overshoot followed by a strong undershoot that is enhanced as the ratio of elongation to rotation is increased (i.e., the flow becomes increasingly extensional in character.) We attribute this undershoot, which does not seem to appear in simple shear flows, or flows close to simple shear flow, to polymer segment stretching following an initial period of segment reorientation. Model studies are currently underway to test this notion. © 1992 John Wiley & Sons, Inc.     

环氧交联网T_g转变的tanδ-T曲线解析

本文系统地研完了预聚物分子量、固化剂配比和固化条件对环氧交联网T_g松弛内耗峰松弛时间分布的影响。本实验和理论研究结果首次证明了环氧交联网T_g松弛过程具有单一松弛时间描述的线性标准固体的特征,与预聚体分子量、固化剂配比和固化条件无关。此结果可用环氧交联网的两相结构特征加以解释。     

A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes

We report measurements of the nonlinear relaxation moduli after a step-shear strain of polystyrene solutions with nearly monodisperse and with bidisperse distributions of molecular weight. We find, as have others, that for monodisperse solutions with M/M_e > 60, there are anomalies, such as an unusually low nonlinear modulus and a kink in a plot of shear stress versus time after the step strain. Here M is the polymer molecular weight and M_e is the entanglement molecular weight. We find that in the bidisperse solutions the anomalies persist as long as M_w/M_e > 60, where M_w is the weight-averaged molecular weight of the bidisperse solution. The persistence of the anomalies in bidisperse solutions disagrees with a theory of Marrucci and Grizzuti that attributes the anomalies to strain inhomogeneities similar to shear banding. The Marrucci-Grizzuti theory predicts that as little as 10% short chains in the bidisperse mix should eliminate the anomalies, whereas in the experiments reported here at least 30% is required. Nevertheless the way in which the anomalies disappear at high strains when one increases the fraction of low-molecular-weight component is qualitatively similar to the theoretical predictions and supports the notion that strain inhomogeneities occur in these systems. © 1992 John Wiley & Sons, Inc.     

Solid-state 13C-NMR analysis of hypercrosslinked polystyrene

Hypercrosslinked polystyrenes, synthesized by reaction of linear or lightly crosslinked polystyrene with chloromethyl methyl ether (CME) and a Lewis acid in a good solvent, swell even in nonsolvents for polystyrene. Structures and dynamics of hypercrosslinked polystyrenes in both dry solid and solvent-swollen gel states have been determined by ¹³C-NMR spectroscopy. Deconvolution of ¹³C solid-state CP/MAS spectra gave the relative numbers of quaternary carbon atoms in monosubstituted and disubstituted benzenes. A typical sample, crosslinked by reaction of a mixture containing 0.5 mol of CME per mol of repeat units, contains 35% of unreacted and 65% of crosslinked aromatic rings, and no residual chloromethyl groups. Gels swollen in CDCl₃ and in CH₃OH have residual static dipolar interactions enabling crosspolarization and require magic angle spinning (MAS) and high power ¹H decoupling to reduce chemical shift anisotropy from ∼ 10⁴ Hz to ∼ 10³ Hz. A single proton spin-lattice relaxation time in the rotating frame measured from all peaks in the ¹³C spectra of dry samples indicates homogeneity on a nanometer scale. Proton NMR line widths indicate no substantial molecular motions in a dry hypercrosslinked polystyrene up to at least 200°C. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 695–701, 1997     

The in situ reactive compatibilization of nylon-6/polystyrene blends using anhydride functionalized polystyrenes

Nylon-6/polystyrene (PS) blends were reactively compatibilized by addition of various anhydride functionalized polystyrenes. The morphology of the blends was examined using a scanning electron microscopy (SEM) technique. The particle size of the dispersed styrenic phase was about 3.2 μm for the uncompatibilized 8/2 Nylon-6/PS blend while those of the compatibilized blends were decreased by as much as two orders of magnitude depending on the amount and type of the functionalized polystyrene (FPS) added. Several low-molecular weight polystyrenes with terminal anhydride groups, prepared by two different functionalization methods, were examined. The effect of molecular weight on particle size reduction depended on the basis of comparison, mass of additive, or moles of anhydride units. A high-molecular weight random copolymer of styrene and maleic anhydride was most effective when compared on a mass basis. The increase in adhesion between the Nylon-6 and the styrenic phases caused by the in situ reaction was evaluated by a lap shear technique. The free polystyrene, Nylon-6, and Nylon-FPS copolymer formed were separated by solvent extraction technique using formic acid and toluene. The extent of coupling reaction between the functionalized polystyrenes and Nylon-6 ranged from 25 to 43%. © 1992 John Wiley & Sons, Inc.     

Rouse's dynamics of networks with pendant chains

A model to describe the dynamics of networks with linear pendant chains has been formulated based on the properties of ensembles of micronetworks, using the Rouse model. This development indicates that the terminal relaxation time of pendant chains with relatively large molecular weight scales with the square of the molecular weight of those chains. On the other hand, when the molecular weight of pendant and elastically active chains are comparable, a nearly exponential growth of the terminal relaxation time with the molecular weight is predicted. The main predictions of the model are compared with experimental results of model poly(dimethyl siloxane) (PDMS) networks, with controlled amounts of linear pendant chains of known molecular weight. The terminal relaxation time of these networks was estimated from the values of the loss modulus G″(ω) measured experimentally. An exponential dependence on the molecular weight of pendant chains was derived for the terminal relaxation time. This behavior is in good agreement with the predictions of our model for micronetworks, provided that the friction coefficient scales linearly with the number of entanglements. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1121–1130, 1999     

The temperature window of minimum flow resistance in melt flow of polyethylene. Further studies on the effect of strain rate and branching

The existence of a narrow temperature window (150–153°C) of smooth extrudability coupled with a minimum in flow resistance (extrusion pressure) in high-molecular weight polyethylene (>4 × 10⁵ g mol^?1) was the subject of a previous article where it was associated with strain-induced formation of the mobile hexagonal mesophase. The new findings of this note show that this minimum in flow resistance only sets in above a critical strain rate; this is interpreted in terms of the requirement of a critical strain rate in order to stretch molecules to their fully extended configuration. Furthermore, this critical strain rate is shown to be higher for lower molecular weight materials, in agreement with a priori considerations. Additionally, the temperature at which the pressure minimum occurs in a polyethylene containing methyl branches shifts to a significantly lower value than that for the linear material. This is interpreted in terms of the ? CH₃ groups raising the crystal free energy, thereby lowering the temperature at which the transition to the hexagonal phase occurs.     

Molecular motion and interactions in aqueous carbohydrate solutions. II. Nuclear-magnetic-relaxation studies

Nuclear-magnetic-relaxation studies of a range of aqueous mono- and disaccharide solutions are reported. These include¹⁷O relaxation of solvent and¹H,²H,¹³C, and¹⁷O relaxation of various solutes. The limitations of nuclear-magnetic relaxation for providing direct indications of solvent motions or extents of hydration of these sugars are outlined. In contrast to the solvent studies, the motional properties of the solutes themselves have been reasonably well defined, with¹H,²H, and¹³C studies of the sugar ring C–H groups all indicating very similar rotational correlation times. Shorter correlation times estimated for the –CH₂OH and –OH side chains, implying that internal motions make a significant contribution to the relaxation of these groups. Differences in reorientation rates of pentose monosaccharides, hexose monosaccharides, and disaccharides are discussed in terms of molecular size and solvent interactions. In every case examined, the solute NMR rotational correlation time is in serious disagreement with that expected from previous dielectric-relaxation studies. Some of the implications of this discrepancy are considered.     

Relative molecular weight distributions of cis-polybenzoxazole/polyphosphoric acid rodlike liquid crystalline polymer solutions from dilute solution rheometry

The molecular weight for a dilute solution of cis-polybenzoxazole (PBO) in polyphosphoric acid (PPA) was determined by fitting the rheological data with a semiempirical polydisperse hybrid theory. The hybrid theory models a semiflexible rigid rod as an elastic cylinder. The cylinder has both a rotational relaxation spectrum given by an ideal rigid rod and an internal bending relaxation spectrum spaced in accord with the relaxation time spectra of a flexible coil with fully developed hydrodynamic interactions. The model was fitted to rheological data collected for a 0.05 weight percent solution with intrinsic velocity (one-point determination) of 320 ± 10 cc/g. The model predicts a number-average molecular weight near 12800 ± 400 g/mol with a polydispersity index of 2.5 ± 0.1. By using the Yamakawa-Yoshizaki equation the intrinsic viscosity is calculated for the model molecular weight distribution as 310 cc/g.     

Pressure relaxation of polystyrene and its comparison to the shear response

Isothermal pressure relaxation as a function of temperature in two pressure ranges has been measured for polystyrene using a self-built pressurizable dilatometer. A master curve for pressure relaxation in each pressure regime is obtained based on the time–temperature superposition principle, and time–pressure superposition of the two master curves is found to be applicable when the master curves are referenced to their pressure-dependent T_g. The pressure relaxation master curves, the shift factors, and retardation spectra obtained from these curves are compared with those obtained from shear creep compliance measurements for the same material. The shift factors for the bulk and shear responses have the same temperature dependence, and the retardation spectra overlap at short times. Our results suggest that the bulk and shear response have similar molecular origin, but that long-time chain mechanisms available to shear are lost in the bulk response. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3375–3385, 2007     

High-resolution solid-state 13C NMR study of ethylcellulose films

Ethylcellulose films cast from concentrated solutions of chloroform, benzene, and carbon tetrachloride were subjected to the NMR relaxation measurements including ¹H spin-lattice relaxation time (T_1H), rotating-frame ¹H spin-lattice relaxation time (T_1ρH), and ¹³C spin-lattice relaxation time (T_1C). The values of T_1ρH for carbons in the glucose units of ethyl-cellulose were of the same order of magnitude as those reported for the crystalline and noncrystalline regions of ramie cellulose. The values of T_1C for unsubstituted C2, C3 carbons were smaller than those for the corresponding carbons in the noncrystalline region of native celluloses. The T_1C values for unsubstituted C2, C3, and substituted C6 carbons showed a small but definite dependence on the solvent from which the films were cast. © 1993 John Wiley & Sons, Inc.     

Chain scission in polystyrene by impact fracture

The number of chain scissions n_s per unit fracture area by impact in high-molecular weight polystyrene is determined to be approximately 3.3 × 10¹⁴/cm² at room temperature. This is almost 20 times larger than would be expected if chain scissions took place only at, or very close to, fracture surfaces. This result was obtained by measuring the molecular weight decrease and the total fracture area of the impact fragments by using size exclusion chromatography and statistical particle size measurements, respectively. The large n_s strongly indicates that significant chain breakage occurs during crazing before the propagation of cracks. An average craze thickness before breakdown under impact is estimated from n_s to be around 2 μm. In a diluted polymer, n_s is found to be significantly lower than the extrapolated value, assuming a linear dilution of entangled chain crossings at the fracture surface. This low chain scission density, however, can be explained by taking into account the reduction of craze breakdown strain in the diluted polymers. Finally, the broken chain ends of polystyrene appear to be stable under ambient conditions. © 1992 John Wiley & Sons, Inc.     

Local segmental relaxation in bidisperse polystyrenes

Dynamic mechanical results are reported for segmental relaxation of monodisperse polystyrenes (PSs) with molecular weights of 0.7, 3, 18, and 104 kg/mol and bidisperse PSs created from blending pairs of these materials. The data for the monodisperse polymers confirm previous findings; namely, there is an increase in the glass‐transition temperature normalized temperature dependence of the segmental relaxation times (fragility) with increasing molecular weight, along with a breakdown of the correlation between the fragility and the breadth of the relaxation function. For both the monodisperse and bidisperse PSs, the glass‐transition temperature is a single function of the average number of chain ends, independent of the nature of the molecular weight distribution. It is also found that these materials exhibit fragilities that uniquely depend on the number‐average molecular weight, that is, on the concentration of chain ends. In blends with linear PS, cyclic PS with a low molecular weight behaves as a high polymer, similar to its neat behavior, reflecting the overriding importance of chain ends. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2604–2611, 2004