Full‐chain dynamics of entangled linear and star polymers

The full‐chain dynamics and the linear viscoelastic properties of monodisperse, entangled linear and star polymers are simulated consistently via an equilibrium stochastic algorithm, based on a recently proposed full‐chain reptation theory 1 that is able to treat self‐consistently mechanisms of chain reptation, chain‐length fluctuations, and constraint release. In particular, it is the first time that the full‐chain simulation for star polymers is performed without subjecting to the great simplifications usually made. To facilitate the study on linear viscoelasticity, we employ a constraint release mechanism that resembles the idea of tube dilation, in contrast to the one used earlier in simulating flows, where constraint release was performed in a fashion similar to double reptation. Predictions of the simulation are compared qualitatively and quantitatively with experiments, and excellent agreement is found for all investigated properties, which include the scaling laws for the zero‐shear‐rate viscosity and the steady‐state compliance as well as the stress relaxation and dynamic moduli, for both polymer systems. The simulation for linear polymers indicates that the full‐chain reptation theory considered is able to predict very well the rheology of monodisperse linear polymers under both linear viscoelastic and flow conditions. The simulation for star polymers, on the other hand, strongly implies that double reptation alone is insufficient, and other unexplored mechanisms that may further enhance stress relaxation of the tube segments near the star center seem crucial, in explaining the linear viscoelasticity of star polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 248–261, 2000     

Extent of branching from linear viscoelasticity of long‐chain‐branched polymers

We present new results and examine literature data concerning the linear viscoelastic behavior of polyethylene with sparse to intermediate levels of long‐chain branching (LCB). These branched polymers displayed a common rheological signature, namely, a region of frequency‐independent loss tangent along with the corequisite scaling of the storage and loss moduli to the same frequency exponent. This apparent power‐law response occurred within a finite frequency window and bore resemblance to the behavior of physical gels. The appearance of this region, however, was the consequence of the presence of two distinct, yet partially overlapping, terminal relaxation processes. After considering the analogous relaxation behavior of wholly linear polymers with bimodal molecular weight distributions, we considered the polymers with LCB as blends of linear and branched species to develop a simple method of quantifying the extent of LCB. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1671–1684, 2004     

The linear rheological responses of wedge‐type polymers

The linear rheological responses of a series of specially designed wedge‐type polymers synthesized by the polymerization of large molecular weight monomers have been measured. These wedge polymers contained large side groups which contained three flexible branch chains per polymer chain unit. The master curves for these polymers were obtained by time temperature superposition of dynamic data at different temperatures from the terminal flow regime to well below the glass transition temperature, T_g. While these polymers maintained a behavior similar to that of linear polymers, the influence of the large side group structure lead to low entanglement densities and extremely low rubbery plateau modulus values, being near to 13 kPa. The viscosity molecular weight dependence was also somewhat higher than that normally observed for linear polymers, tending toward a power law near to 4.2 rather than the typical 3.4 found in entangled linear chains. The glassy modulus of these branched polymers is also found to be extremely low, being less than 100 MPa at T_g ?60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 899–906     

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     

Mechanical relaxation spectroscopy of three triepoxide-based polymers

Three network structure polymers formed by the chemical reactions of a triepoxide with aniline, 3-chloroaniline,and 4-chloroaniline were prepared and their shear modulus relaxation spectra studied over the 10⁻³- to 1-Hz range and temperatures up to their rubber modulus region. The decrease in the unrelaxed modulus with increase in temperature is found to be a reflection of both an increase in volume, and a decrease in the relaxed modulus of the sub-T_g relaxations process. It is quantitatively shown that the increase in the rubber modulus with increase in temperature above T_g is predominantly due to an increase in the entropy and not to a decrease in the number of cross-links density on thermal expansion. The unrelaxed modulus remained unaffected by the change in the overall size of the phenyl groups of the amines and of the steric hindrance to their rotations caused by the proximity of the chlorine atom to the cross-linking N-atom in the network structure, but the rubber modulus was effected. The shear modulus spectra could be fitted to a stretched exponential decay function with a temperature-independent stretch parameter of 0.25 for two polymers and 0.22 for one. The time–temperature superposition of the spectra did not yield a master curve, and a vertical displacement of the data also failed to produce it. This was more clearly demonstrated by the spectra of the mechanical loss tangent. After considering the various contributions to the shear modulus, it was concluded that deviations from the time–temperature superposition of the spectra are intrinsic to these polymers and arise from the change in the viscoelastic functions for segmental dynamics on change in the temperature such that the overall distribution of relaxation times remains unaffected. The mechanical loss tangent of the three polymers is found to be higher than that of polycarbonate at ambient temperature, implying a higher loss of mechanical energy before these polymers may fracture. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3071–3083, 1999     

A toolbox for parameter-free predictions of solid-state properties of monodisperse glassy polymers with frozen-in molecular orientation

This study presents a toolbox for the prediction of birefringence and craze initiation stress in oriented monodisperse linear amorphous polymers. The toolbox is assembled from a previously proposed melt–solid constitutive model that provides the necessary residual stress components required for predictions of birefringence and craze initiation stress. The Likhtman–McLeish theory for linear rheology of entangled polymers is used to generate the low reduced frequency part of the linear viscoelastic spectrum, the only molar mass-dependent input parameter. All other parameters are obtained by experiment or from literature and can be considered material constants. Toolbox predictions are compared to new experimental data on two grades of linear monodisperse polystyrene (PS) of known molar mass but unknown rheology and to literature data. The toolbox is able to account for the role of molar mass on birefringence and craze initiation stress of PS subjected to supraentanglement orientation processes. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Plastic deformation of glassy polystyrene: A unified model of yield and the role of chain length

A study was made of yield and plastic flow in glassy polystyrene. A range of 12 linear atactic polystyrenes was studied: monodisperse, bimodal blends, and a polydisperse commercial sample. M_n varied between 66,000 and 490,000 g/mol. These were given standardized thermal treatments and then subjected to uniaxial compression tests in the glassy state over the temperature range 40 to 95 °C and nominal strain-rates 10⁻⁴ to 10⁻³ s⁻¹. Their constitutive responses were interpreted in terms of the physically based three-dimensional constitutive model for small or large deformations in amorphous polymers proposed earlier (Polymer 1995, 36, 3301–3312), including plastic strain-induced structural rejuvenation. In multimode form, the model captured closely both linear viscoelastic response and yield and plastic flow. When the reduction of Vogel temperature caused by chain ends was incorporated in the model, it predicted a fall in yield stress with reducing molecular length. This was also observed in experimental data, with the rate of fall approximately in agreement. The results provide further support for the model as a unifying framework for describing the physical properties of polymer glasses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2027–2040, 2004     

Structural effect of linear and star‐shaped poly(L‐lactic acid) on physical properties

The linear and star‐shaped poly(L‐lactic acid) (PLLA) with similar molecular weight were prepared and their physical properties such as thermal properties, rheological properties, and crystallization behavior in quiescent and dynamic states were compared. The differential scanning calorimetry showed that the linear PLLA gave higher glass transition, melting, and crystallization temperatures than the star‐shaped one. In dynamic crystallization, the linear PLLA gave longer induction time and longer overall crystallization time than the star‐shaped one, although the former gave higher rate of crystallization in quiescent crystallization. However, wide‐angle X‐ray diffractometer(WAXD) analysis revealed that the linear and star‐shaped PLLA developed the same crystal structure and application of shear had little effect on crystal structure. As predicted, the linear PLLA gave higher crystallinity than the star‐shaped PLLA. In the dilute solutions, the linear PLLA exhibited higher intrinsic viscosity than the star‐shaped one. In the concentrated solutions, the star‐shaped PLLA gave higher values of dynamic viscosity, storage, and loss moduli than the linear one. Further, the former exhibited more noticeable shear thinning behavior and greater dependence of rheological properties on temperature than the latter. For both PLLA melts, the modified Cole–Cole plot gave slope less than 2. Of two PLLA polymers the star‐shaped PLLA gave smaller slope than the linear one. In addition, the former showed greater change of the slope with temperature than the latter. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 939–946, 2004     

Transitional flow behavior of entangled polyisoprene solutions

A contradiction has recently appeared between the current understanding of entangled polymers in nonlinear shear flow and new experimental observations based on highly entangled monodisperse 1,4‐polybutadiene solutions. Using entangled polydisperse solutions, we have examined the universality of the new revelation that any sufficiently entangled and relatively monodisperse polymeric fluids undergo a flow transition in simple shear when the applied stress is comparable to the plateau modulus. Indeed, a similar flow transition, marking the onset of bulk chain disentanglement, as previously observed for polybutadiene solutions in controlled‐stress experiments, can also be observed in less entangled and more polydisperse polyisoprene solutions, whereas controlled‐rate experiments do not reveal any transitional behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4132–4138, 2004     

Chemorheology of linear polymers

The structural changes brought about by chemical reactions are reflected in the viscoelastic behavior of polymers. Viscoelastic behavior induced by such chemical reactions is called chemorheology. This phenomenon is not readily observed in linear polymers, because molecular flow by diffusion is generally much more rapid than relaxation or flow caused by chemical reaction. It has become possible, however, to treat chemorheology of linear polymers theoretically by taking such physical flow into consideration. The experimental results for linear polystyrene compared with the theoretical ones are described in this paper. Good agreement between theoretical results and experimental ones is obtained for monodisperse polystyrene with low concentration of accelerators.     

Physical aging of an epoxy subsequent to relative humidity jumps through the glass concentration

In our previous work, we showed that the structural recovery responses of an epoxy after relative humidity (RH)-jumps through the glass concentration have similar phenomenology to, but different kinetics from, those obtained by temperature (T)-jumps. In this article, we report results from physical aging experiments of the same epoxy after RH-jumps. The results show that time-RH superposition and time–aging time superposition can be used to describe the viscoelastic responses in RH-jump experiments. The similarities and differences between RH-jump and T-jump conditions are also presented. In addition, the difficulties in modeling the combined effects of temperature and relative humidity changes that result from these differences are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2107–2121, 2004     

Volume recovery of glassy poly-α-methylstyrene

A method for evaluating the relaxation time as a function of both temperature and volume from volume contraction experiments, as proposed by Kovacs, was experimentally examined by using monodisperse poly-α-methylstyrene samples of various molecular weights and blends. It was concluded that his theory can be successfully applied to the present experimental data, though his two different approximations give somewhat different values of the shift factor for the time-temperature superposition of volume contraction data. A difference was observed between the temperature dependence of the shift factor of monodisperse polymers and that of blends.     

PMMA/α-MSAN共混体系长时弛豫区域的时温叠加失效与相分离的关系

通过考察聚甲基丙烯酸甲酯（PMMA）／聚（α－甲基苯乙烯丙烯腈）（α－MSAN）共混体系动态粘弹函数的时温叠加,发现在终端区域时温叠加失效与其相分离有关。相分离使得终端区域的动态储能模量G″（或动态损耗模量G″）与频率的关系[IgG″（IgG″）～Igω]明显偏离经典粘弹模型。随组成的改变,时温叠加的失效呈现温度依赖性,其“失效温度”（Td)可很好地表征LCST类共混物的相分离,而且在用其表征相分离时,IgG″-Igω法比IgG″-IgG″法更优越。     

Confirmation of universality of time–humidity superposition principle for various water‐absorbable polymers through dynamic viscoelastic measurements under controlled conditions of relative humidity and temperature

Dynamic viscoelastic measurements were made for storage (E′) and loss (E″) tensile moduli of water‐absorbable polymers such as nylon‐6, nylon‐66, poly(vinyl alcohol), ethylene–vinyl alcohol copolymers, and regenerated cellulose under the control of stepwise scanned relative humidity at constant temperature by changes in the strain frequency over a wide range. Smooth master curves of log(E′) and log(E″) plotted against log(frequency) were successfully obtained for all samples. The evaluated shift factors changed with the relative humidity and could be interpreted well on the basis of a concept of free volume in the amorphous region. The free volume was affected sensitively, depending on the heat‐treatment condition and the types of polymers used. For nylon‐66 film, the dynamic viscoelastic measurements were made at different humidities and temperatures, from which one smooth master curve was obtained. This experimental result is important in realizing the similar effect of relative humidity and temperature on the expansion of free volume of the amorphous phase: the shift factor change induced by the relative humidity change of about 30% was equivalent to the shift factor change induced by the temperature change of about 30 °C. That is, the time–humidity superposition principle and the time–temperature superposition principle were applicable as equivalent contributors to the mechanical property of water‐absorbable polymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1638–1650, 2001     

Melt rheology of hyperbranched‐polystyrene synthesized with multisite macromonomer

Melt rheological behaviors of hyperbranched‐polystyrene (PS) copolymerized by dendric macromonomer technique are presented. The time–temperature superposition principle was applicable to the hyperbranched‐PS. The branched‐PS showed slightly lower zero‐shear viscosity in comparison with linear PS regardless of a presence of a number of branches expected from the dendric macromonomer technique. Although the influence of use of multimethacryloyl macromonomer in the polymerization process was marginal for linear viscoelastic regime, nonlinear shear and uniaxial elongational flows showed distinct differences between linear and branched‐PS. The strain dependence of the damping function became weak as increase of macromonomer content. The branched‐PS exhibited the growing elongational viscosity function comparing with linear PS. This prominent effect on the elongational flow behavior can be explained by the molecular architecture of the branched‐PS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2226–2237, 2009     

Dynamic mechanical properties of crystalline,linear polyethylene

Two sets of dynamic mechanical property data and some stress relaxation data for semicrystalline, linear polyethylene are treated by data reduction methods previously described. These data can be represented by a master plot of reduced modulus versus reduced frequency and two sets of temperature-dependent shift factors. The first of these factors reflects the change of viscoelastic relaxation times with temperature. The second represents a separable change of modulus with temperature which applies over the entire time or frequency range of the experiments. This change is larger and in the opposite direction to that found applicable in the behavior of noncrystalline plastics and rubbers. The two sets of dynamic data show the same frequency–temperature dependence which can be represented by an activation energy of 22 kcal./mole. Small differences in the modulus–temperature dependence are attributed to differences in molecular weight or annealing conditions. The stress relaxation data superposes to a curve in good agreement with the dynamic data but with a factor of 20 difference in time scale. This difference is attributed to the finite strains used in the stress relaxation measurements. Such strains might be expected to increase free volume in simple extension deformations and so accelerate the relaxation.     

New synthesis of liquid polysulfide polymers in the presence of hydrazine. I. Synthesis of linear polysulfide polymers from 1,1′-[methylenebis (oxy)]-bis-[2-chloroethane] and sodium tetrasulfide

The results of our studies show that liquid linear polysulfide polymers of an average molecular weight 4260–1030 g mol⁻¹ can be obtained by the reaction of sodium tetrasulfide and 1,1′-[methylenebis(oxy)]-bis-[2-chloroethane] in the presence of 2.0–5.0 mol of hydrazine and at least 4.0 mol of sodium hydroxide/mol of hydrazine in a one-step procedure. The disulfide polymers in the form of sodium mercaptide are soluble in the supernatant liquid from which they are separated by acidification of the solution to a pH value of about 4. The average molecular weight and the content of sulfur in the obtained linear polymers were determined and their IR spectra were recorded. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 1363–1367, 1997     

Modeling of the linear viscoelastic behavior of low‐density polyethylene

We predict the linear viscoelastic behavior of low‐density polyethylene from both the molecular‐weight distribution and the individual structure of each species in the sample. The “structure map” of the samples was derived from SEC measurements. This map is a three‐dimensional representation of the seniority distribution, and represents the probability of existence of a segment with seniority i in a molecule of molecular weight M. Moreover, results from the kinetics of the free radical polymerization of polyethylene show that the molecular weight of the segments increases according to their seniority. Finally, tube dilatation was generalized to the case of polydisperse samples. The solvent behavior of the relaxed segments was included through a continuous function of time that describes the instantaneous state of the entanglement network in the sample. The comparison between the theoretical predictions and the experimental data shows a good agreement over the whole experimental frequency range. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43:1973–1985, 2005     

Anomalous aging in two-phase systems: Creep and stress relaxation differences in rubber-toughened epoxies

From time–aging time superposition principles, similar to time–temperature superposition, one would expect similar shifting or superposition behaviors for both creep and stress relaxation responses. In particular, for isotropic homogeneous systems, in the linear viscoelastic regime, consideration of superposition in rheology by Markowitz¹ or the discussion by Ferry² from the Kramers–Kronig relation would seem to demand that creep and stress relaxation shift in the same way. Here we report on results from creep and stress relaxation measurements in two-phase, rubber-toughened epoxies that exhibit Boltzman additivity of creep or relaxation behaviors and follow the time–aging time superposition behavior in creep, but not in stress relaxation. While the lack of superposition in stress relaxation is, perhaps, not surprising, the finding that the creep responses at different aging times superimpose while the stress relaxation responses do not, presents an anomalous behavior that has not been previously reported. In addition, our findings show that the stress relaxation responses show short time “softening” upon aging. Possible reasons for the anomalous behaviors are briefly considered. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1167–1174, 1997