Atomistic Simulation of Bulk Mechanics and Local Dynamics of Amorphous Polymers

Summary: In order to have better insight into the polymer specifics of the dynamic glass transition molecular dynamics (MD) computer simulations of three glass-formers have been carried out: low-molecular-weight isopropylbenzene (iPB), brittle atactic polystyrene (PS) and tough bisphenol A polycarbonate (PC). Simulation of the uniaxial deformation of these mechanically different types of amorphous polymers shows that the mechanical experimental data could be realistically reproduced. Now the objective is to study the local orientational mobility in the non-deformed isotropic state and to find the possible connection of the segmental dynamics with the different bulk mechanical properties. Local orientational mobility has been studied via Legendre polynomials of the second order and CONTIN analysis. Insight into local orientational dynamics on a range of length- and time scales is acquired. The fast transient ballistic process describing the very initial part of the relaxation has been observed for all temperatures. For all three simulated materials the slowing down of cage escape (α-relaxation) follows mode-coupling theory above T_g, with non-universal, material-specific exponents. Below T_g universal activated segmental motion has been found. At high temperature the α process is merged with the β process. The β process which corresponds to the motions within cage continues below T_g and can be described by an activation law.     

Molecular dynamics study of orientational order and rotational melting in clusters of TeF6

Molecular dynamics simulations of the behavior of molecules in crystalline clusters of TeF₆ were carried out on systems of 100, 150, 250, and 350 molecules. Several diagnostic functions were applied to investigate whether rotational melting occurred before translational melting. These functions included the coefficient of rotational diffusionD _θ(T), the “orientational Lindemann index” δ_θ(T), the “orientational angular distribution function”Q(θ,T), and the “orientational pair-correlation function”g _θ(r, T). All indicators implied that rotational melting occurred before translational melting, that it began with the outermost molecules, and that its onset for smaller clusters was at lower temperatures than for larger clusters. Results also showed that the rotational transition coincided with the transition from a lower symmetry phase (monoclinic) to cubic, a phenomenon that had been noted by others to occur with some regularity for systems of globular molecules.     

Dielectric relaxations in the liquid and glassy states of 47% polypropylene oxide in toluene as diluent

Molecular relaxations in 47-wt % polypropylene oxide of molecular weight 4000 in toluene as diluent have been studied by dielectric permittivity and loss measurements from 77 to 320 K, in the frequency range 1 Hz to 2 × 10⁵ Hz. One relaxation process (β process) is observed in the glassy state below T_g (= 148 K), and two processes are observed in the supercooled liquid at T > T_g. Relative to the amplitude of the fast relaxation process (i.e., the local segmental motions of the polymer chain), the amplitude of the slow process is increased and that of the β process decreased on dilution of the pure polymer. The β process has an Arrhenius energy of 17 kJ mol^?1. The rates of the two relaxations at T > T_g follow the Vogel–Fulcher–Tamman equation and seem to merge on cooling the liquid towards T_g. The relative temperatures at which the three relaxation processes occur at the rate of 1 kHz remain largely unaffected on dilution. The increase in static permittivity of the solution on cooling is more than anticipated from the temperature effects alone. It is suggested that the increase is due to the enhanced short-range orientational correlation of the dipoles, which may involve H bonding.     

Rouse–Bueche theory and the calculation of the monomeric friction coefficient in a filled system

Direct experimental access to the monomeric friction coefficient (ζ₀) relies on the availability of a suitable polymer dynamics model. Thus far, no method has been suggested that is applicable to filled systems, such as filled rubbers or microphase‐segregated A–B–A thermoplastic elastomers (TPEs) at T_g,B < T < T_g,A. Building upon the procedure proposed by Ferry for entangled and unfilled polymer melts, the Rouse–Bueche theory is applied to an undiluted triblock copolymer to extract ζ₀ from the linear behavior in the rubber‐glass transition region, and to estimate the size of Gaussian submolecules. When compared at constant T – T_g, the matrix monomeric friction factor is consistent with the corresponding value for the homopolymer melt. In addition, the characteristic Rouse dimensions are in good agreement with independent estimates based on the Kratky–Porod worm‐like chain model. These results seem to validate the proposed approach for estimating ζ₀ in filled systems. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1437–1442     

Enhanced translational diffusion of rubrene and tetracene in polysulfone

Translational diffusion of tetracene and rubrene in bisphenol A polysulfone (T_g = 460 K) was measured using a holographic fluorescence recovery after photobleaching (FRAP) technique. In the temperature range from 493 to 462 K, probe translation was diffusive and the translational diffusion coefficients varied from 10⁻⁸ to 10⁻¹³ cm²/s. Surprisingly, the observed translational diffusion coefficients showed a weaker temperature dependence than the rotational correlation times of the same probes. Rotational correlation times have the same temperature dependence as the viscoelastic relaxation times characteristic of the rubberlike modulus, while translational relaxation times decouple from the viscoelastic relaxation times. On average, probe molecules are translating larger and larger distances per probe rotation time as the temperature is lowered to T_g. These results can be explained qualitatively in terms of spatially heterogeneous segmental dynamics in the polysulfone matrix. © 1996 John Wiley & Sons, Inc.     

A generalized method to calculate diffusion rates in polydisperse systems. Further results on Rouse dynamics in the concentrated regime

Experiments designed to thoroughly test a recently proposedgeneralized method to calculate diffusion rates in polydisperse systems have been carried out. Polydisperse polystyrene (PS) samples were allowed to diffuse in a poly(phenylene oxide) (PPO) matrix. Designed blends were made from anionically polymerized PS with molecular weights which cover most of the ranges where Rouse dynamics control the diffusion processes. The diffusion temperatures range from (T_g – 1 K) to (T_g + 105 K), causing the monomeric friction factor values for PS to change by up to seven orders of magnitude along the diffusion coordinate. Calculations performed with the above mentioned method agree with Raman and DMA experimental data.     

Molecular mobility of poly(methyl methacrylate) glass during uniaxial tensile creep deformation

An optical photobleaching method has been used to measure the segmental dynamics of a poly(methyl methacrylate) (PMMA) glass during uniaxial creep deformation at temperatures between T_g ? 9 K and T_g ? 20 K. Up to 1000‐fold increases in mobility are observed during deformation, supporting the view that enhanced segmental mobility allows flow in polymer glasses. Although the Eyring model describes this mobility enhancement well at low stress, it fails to capture the dramatic mobility enhancement after flow onset, where in addition the shape of the relaxation time distribution narrows significantly. Regions of lower mobility accelerate their dynamics more in response to an external stress than do regions of high mobility. Thus, local environments in the sample become more dynamically homogeneous during flow. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1713–1727, 2009     

Probe rotation near and below the glass transition temperature: Relationship to viscoelasticity and physical aging

Reorientation times ť_c for two probes in several amorphous polymers near the glass transition temperature T_g are reported. T_g for these polymers ranges from 205 to 459 K. Probe reorientation was measured in the time window from 10⁻² to 10⁴ s with a recently developed photobleaching method. ť_c for a given probe at the T_gs of the different polymers varies more than three decades. Viscoelastic relaxation times characteristic of the Rouse modes of the matrix polymers are closely related to probe rotation times and thus also not constant at T_g. The characteristic length scale of motions responsible for the glass transition varies significantly for the three polymers studied. Preliminary physical aging results indicate that probe reorientation in polystyrene ages slightly faster than the volume.     

The temperature dependence of the equilibrium and instantaneous compliances of low molecular weight polystyrene melts

The equilibrium compliance of three low molecular weight polystyrene melts has been determined over the range 15–70°K above T_g from dynamic viscoelastic measurements using alternating shear. Results are favorably compared with the previous results of Plazek and O'Rourke obtained from creep measurements, but agreement with predictions based on the Rouse theory is obtained only in the case of the highest molecular weight sample.     

Solid-state 13C NMR characterization of molecular orientation of hot drawn nylon 6

Two-dimensional cross polarization (CP), magic angle spinning (MAS) rotor synchronization NMR spectroscopy has been used to determine quantitatively the molecular orientational distribution function on hot-drawn Nylon 6. Both films and fibers are studied that had been thermally deformed at temperature above T_g, from 60 to 175°C at draw ratios in the range of 1-5.5. In the two-dimensional NMR spectrum, the sidebands that intrinsically originate from the chemical shift anisotropy reveal the degree of molecular orientational order. No preferential orientational order is detected for the sample without thermal deformation, and the highest degree of order is observed for samples which have been hot drawn above T_g at ratios ca. 5. Based on the aggregate model the maximum achievable order parameters are determined. © 1994 John Wiley & Sons, Inc.     

A relationship between macroradical decay kinetics and α-segmental dynamics in glassy amorphous polymers

For a series of five amorphous polymers with a broad range of T_g values the kinetics of macroradical decay was measured by ESR technique and evaluated by the second-order kinetic model. It was found that the temperature T_tr of the transition between two regions of different reactivity in free radical decay reaction agrees quite well with the temperature parameter T₀ of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation for α-segmental dynamics. This parameter represents the onset of α-segmental mobility in glassy state below T_g. A nontraditional way of the estimation of T₀ values for α-segmental dynamics through study of the macroradical decay in glassy state of amorphous polymers has been suggested. © 1996 John Wiley & Sons, Inc.     

Copolymers of methyl methacrylate with N‐trifluorophenyl maleimides: High glass transition temperature and low birefringence polymers

Copolymers of methyl methacrylate (MMA) with 2,3,4‐ and 2,4,6‐trifluorophenyl maleimides (TFPMIs) were synthesized by a free radical initiator, azobisisobutyronitrile, in 1,4‐dioxane and also in bulk. The refractive indexes of the copolymers were in the range of 1.49–1.52 at 532 nm. The T_gs were 133–195 °C depending on copolymer compositions. In addition, the copolymers were thermally stable, T_d > 350 °C. The orientational and photoelastic birefringence of the copolymers were also investigated. As both of the orientational and photoelastic birefringences of PMMA are negative, whereas those of poly(TFPMI)s are positive, we could obtain nearly zero orientational and photoelastic birefringence polymers when the ratios of 2,3,4‐TFPMI/MMA were 15/85 and 5/95 mol %, respectively. For 2,4,6‐TFPMI, zero orientational and photoelastic birefringences could be obtained when the ratios of 2,4,6‐TFPMI/MMA were 12/88 and 3/97 mol %, respectively. The T_gs of those copolymers with zero birefringences were in the range of 135–140 °C. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Sodium and silver phosphate glasses doped with chlorides of Fe,Mn and Zn

A number of samples of sodium and silver phosphate glasses doped with various compositions of some transition metals viz. iron, manganese and zinc chlorides alongwith undoped samples of sodium and silver phosphate glasses were synthesized and characterized by X-ray diffraction, IR spectral, electrical conductivity and differential scanning calorimetry (DSC). The glass transition temperature (T _g) and crystallization temperature (T _c) values obtained from DSC curves were found to increase with increasing concentration of the dopant Fe/Mn/Zn chlorides in both sodium and silver phosphate glasses and the following sequence is observed: T _g(–FeCl₃)>T _g(–MnCl₂)>T _g(–ZnCl₂) T _c(–FeCl₃)>T _c(–MnCl₂)>T _c(–ZnCl₂) The increase in T _g and T _c values indicate enhanced chemical durability of the doped glasses. The electrical conductivity values and the results of FTIR spectral studies have been correlated with the structural changes in the glass matrix by the addition of different transition metal cations as dopants.     

Effect of chain structure on the glass transition temperature and viscoelastic property of cis‐1,4‐polybutadiene via molecular simulation

In this work, by adopting the united atom model of cis‐1,4‐poly(butadiene) (PB), we systemically investigate the effect of the chain structure on the glass transition temperature (T_g) and the viscoelastic property of PB system. First, we analyze the atom translational mobility, bond reorientation dynamics, torsional dynamics, conformational transition rate, and dynamic heterogeneity of the PB chains with different chain structures in detail by determining the corresponding T_g. In addition, our results clearly indicate that with the decrease of the amount of the free end atoms of PB via the end‐linking method, the mobility of the PB chains quickly decreases. As a result, the T_g of the PB chains gradually increases. Depending on the chain structure and the calculation method, the T_g of the PB chains varies from 154 to 240 K. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below T_g. The calculated activation energy varies from 7.37 to 16.37 KJ/mol for different chain structures above T_g, which can be compared with those for other polymers. In addition, through the end‐linking approach the strong interaction between the PB chains improves the storage modulus G′ and the loss modulus . Meanwhile, the immobility of the free end atoms effectively reduces the friction loss of the chains under the shear field, which is reflected by the low loss factor . In summary, this work can further help to understand the effect of the chain structure on the dynamic properties of the PB chains. Meanwhile, it provides an effective approach to reduce the energy loss during the dynamic periodic deformation, which can cut the fuel consumption via the end‐linking method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1005–1016     

Intra- and inter-chain fluctuations in entangled polymer melts in bulk and confined to pore channels

It is known that topological restraints by “chain entanglements” severely affect chain dynamics in polymer melts. In this field-cycling NMR relaxometry and fringe-field NMR diffusometry study, melts of linear polymers in bulk and confined to pores in a solid matrix are compared. The diameter of the pore channels was 10 nm. It is shown that the dynamics of chains in bulk dramatically deviate from those observed under pore constraints. In the latter case, one of the most indicative signatures of the reptation model is verified 28 years after its prediction by de Gennes: The frequency and molecular mass dependencies of the spin-lattice relaxation time obey the power law T_! ∝ M⁰ v^3/4 on a time scale shorter than the longest Rouse relaxation time τ_R. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r²>∝ M^−1/2t^1/2 predicted for τ_R < t < τ_d, where τ_d is the so-called disengagement time. Contrary to these findings, bulk melts of entangled polymers show frequency and molecular mass dependencies significantly different from what one expects on the basis of the reptation model. The data can however be described with the aid of the renormalized Rouse theory.     

Sub‐glass‐transition temperature interface formation between an immiscible glass rubber pair

We used neutron reflectivity to measure the interfacial width in the immiscible system polystyrene/poly(n‐butyl methacrylate) (PS/PnBMA). Measurements were made on the same samples at temperatures ranging from below the glass‐transition temperature (T_g) of PS to slightly above. We observed significant broadening of the interface at temperatures below the T_g of PS, indicating chain mobility below the bulk T_g value. The interfacial width exhibited a plateau at a value of 20 Å in the temperature range of 365 K < T < 377 K. A control experiment involving hydrogenated and deuterated PS films (hPS/dPS) showed no such broadening over the same temperature region. The results are consistent with a reduction of the T_g of PS in the interfacial region of ～20 K. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2664–2670, 2001     

Solid state a.c. conductivity and FT-IR spectral analyses for the conflicting effects of proton mobility and association in some azophenol derivatives of cyclic phosphazene

Variable strength H-bonding affects the mobility and so electric conduction of protons differently. Also, variable extent mesomerism modifies electric conduction with varying dielectric features. Both these molecular modifiers are properly cited using azophenol derivatives as model compounds for discussion of their consequences in the varying features of electric conduction. The electric permittivity shows low-frequency dispersion characteristic of ionic conduction over mobile charge carries; the mobility shifts at a critical temperature T _c, being structure dependent. The frequency-dependent Z′′-Z′ layout changes with temperature from linear at low temperatures to semicircular above T _c within a frame of temperature-sensitive dipole-ionic mediated conduction. The a.c. conductivity, σ_ac, increases with frequency and temperature and becomes frequency insensitive, like d.c. conductivity, σ_dc, above the T _c because of the escalating contribution from the d.c. conduction. The mesomeric structure seems to prompt a dipole-based electric conduction of high relaxation energy over the strongly associated phenolic protons that may be thermally activated above the T _c into a much lower relaxation energy protonic conduction of up to two orders higher conductivity. The protonic conduction emerges at a T _c that falls with a drop in the relaxation energy following a similar order of increasing proton mobility and mesomerism in the azophenol derivatives: azocatechol>azoquinol>azoresorcinol. On the molecular level, variable temperature infrared spectroscopy reveals higher proton mobility and mesomerism for the azocatechol derivative that demonstrates its higher protonic conductivity at lower T _c and relaxation energy, compared to the azoquinol and azoresorcinol derivatives. This is well verified in the light of conflicting intramolecular H-bonding that assists the proton mobility in azocatechol whereas it associates the protons in azoresorcinol more than in azoquinol. Electronic Publication     

Boson peak and fast relaxation process near the glass transition in polystyrene

Atactic polystyrene, both side group and main chain deuterated, was investigated by inelastic neutron scattering in a wide temperature range around the glass transition from 2 to 450 K. In the glass the Boson peak position is only very weakly influenced by the deuteration of the phenyl group. In the neighborhood of the glass transition temperatureT _g we find a fast relaxation process similar to other glasses. The onset of the fast relaxation in polystyrene, however, is observed already at temperaturesT _g — 200 K. Results from partially deuterated polystyrene suggest a change of the phenyl ring dynamics already far belowT _g.     

An analysis of ionic conductivity in polymer electrolytes

Conductivities for a wide variety of ionically conducting polymer electrolytes with a range of salt compositions have been investigated over the temperature region T_g to 370 K. When the conductivity data are analyzed as a function of temperature using the empirical Vogel-Tammann-Fulcher (VTF) equation a common trend is observed in that deviations in the fits to the data invariably occur in the temperature range 1.2 T_g to 1.4 T_g for all of the samples investigated. This deviation is interpreted as a decoupling of the ions from polymer segmental motion. Recent ²³Na NMR and ²²Na positron annihilation studies of sodium salt-based polymer electrolytes support this interpretation with evidence of a change in dynamics at about 1.2T_g. © 1994 John Wiley & Sons, Inc.