Hindered interdiffusion in asymmetric polymer-polymer junctions

We discuss theoretically the diffuse interface formed when a long (L) polymer is put into contact with shorter chains (S) of the same material (all chains being entangled). At time t shorter than the reptation time T_L of the long chains, the L chains behave like a gel swollen by the S chains. The “penetration factor” ψ (i.e. the volume fraction of S near the gel surface) is controled by a balance between the osmotic pressure of the swollen L chains, and the elastic tension ψ due to swelling. If t is larger than T_S (the reptation time of the short chains), ψ is of order N_e/N_S (where N_e is the number of monomers between entanglement points, and N_S is the degree of polymerisation of the short chains). On the other hand, if t < T_S, N_S must be replaced by the average number s (t) of monomers of an S chain which have entered the L region, and ψ ∼ N_e/ s (t) ∼t^−1/2. The width of the mixed region e(t) increases like s ^1/2(t) at T_S, and like (D_St)^1/2 (where D_S is the reptation diffusion constant of the S chains) at t>T_S.     

Effect of bending and torsion rigidity on self-diffusion in polymer melts: a molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for NNe (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for NNe. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.     

Predictions of a recently proposed non-markovian model for polymer melts and concentrated solutions

Several predictions for a recently proposed mesoscopic model for polymer melts and concentrated solutions is presented. It is a single Kramers chain model in which elementary motions of the Orwoll-Stockmayer type are allowed. However, for this model, the bead jumps are no longer given by a Markovian probability, but rather are described by a fractal “waiting-time” distribution function, with a single adjustable parameter β, which describes the long-time behavior of the distribution: ∼ 1/t^1+β. We find that the model predicts D ∼ 1/N² and η₀ ∼ N^3.4 for β ≈︁ 1.4, where N is the degree of polymerization. The generalized model predicts that the relaxation spectrum has a plateau regime whose height is independent of N, but whose width is strongly N dependent, in agreement with experiment. The model also predicts that rings will diffuse somewhat more slowly than linear chains of the same molecular weight (about 80% as fast), with the same scaling dependence on N as linear chains, also in agreement with preliminary data.     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Synthesis of a novel graft copolymer with hyperbranched poly(glycerol) as core and “Y”‐shaped polystyrene‐b‐poly(ethylene oxide)2 as side chains

The graft copolymers composed of “Y”‐shaped polystyrene‐b‐poly(ethylene oxide)₂ (PS‐b‐PEO₂) as side chains and hyperbranched poly(glycerol) (HPG) as core were synthesized by a combination of “click” chemistry and atom transfer radical polymerization (ATRP) via “graft from” and “graft onto” strategies. Firstly, macroinitiators HPG‐Br were obtained by esterification of hydroxyl groups on HPG with bromoisobutyryl bromide, and then by “graft from” strategy, graft copolymers HPG‐g‐(PS‐Br) were synthesized by ATRP of St and further HPG‐g‐(PS‐N₃) were prepared by azidation with NaN₃. Then, the precursors (Bz‐PEO)₂‐alkyne with a single alkyne group at the junction point and an inert benzyl group at each end was synthesized by sequentially ring‐opening polymerization (ROP) of EO using 3‐[(1‐ethoxyethyl)‐ethoxyethyl]‐1,2‐propanediol (EEPD) and diphenylmethylpotassium (DPMK) as coinitiator, termination of living polymeric species by benzyl bromide, recovery of protected hydroxyl groups by HCl and modification by propargyl bromide. Finally, the “click” chemistry was conducted between HPG‐g‐(PS‐N₃) and (Bz‐PEO)₂‐alkyne in the presence of N,N,N′,N″,N”‐pentamethyl diethylenetriamine (PMDETA)/CuBr system by “graft onto” strategy, and the graft copolymers were characterized by SEC, ¹H NMR and FTIR in details. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

The Long-Periodic Loop-Branched Chain Structure of the Oxonitridophosphate La21P40O46N57, Elucidated by a Combination of TEM and Microfocused Synchrotron Radiation

The lanthanum oxonitridophosphate La₂₁P₄₀O₄₆N₅₇ was synthesized by high-pressure metathesis from partially hydrolysed LiPN₂ and LaCl₃ at 750–950 °C and 7–9 GPa. The combination of transmission electron microscopy (TEM) and diffraction using microfocused synchrotron radiation revealed a monoclinic crystal structure (space group P2₁/n, a=14.042(4), b=7.084(3), c=41.404(10) Å, β=97.73(3)° and Z=2), which is characterized by loop-branched 21 member single chains of P(O,N)₄ tetrahedra that extend along [2 0 1]. These chains are related to the loop-branched dreier single chains with dreier-ring loops in stillwellite (CeBSiO₅). In La₂₁P₄₀O₄₆N₅₇, these chains are characterized by a complex long-periodic conformation and exhibit disorder that involves La/N and P split positions. This is an extraordinarily long periodicity with respect to branched single chains of tetrahedra. La₂₁P₄₀O₄₆N₅₇ constitutes the first rare-earth oxonitridophosphate exhibiting a chain structure. Single-crystal data are consistent with electron and powder X-ray diffraction.     

A Monte Carlo study of a tethered polymer chain in a uniform field

We study the non‐uniform stretching and relaxation of a long flexible end‐anchored polymer chain of N monomers (32 ≤ N ≤ 1 024) in a uniform field B by means of an off‐lattice bead‐spring Monte Carlo model. Our simulational results for the case of a Rouse‐like polymer in the good solvent regime confirm the existence of “trumpet”‐ and “flower”‐type chain conformations, predicted recently by scaling analysis based on the notion of Pincus tensile blobs. The observed elongation of the chain and the critical fields, separating three different regimes of chain deformation, are found to obey the predicted scaling behavior. The segment density distribution matches that of a DNA molecule pulled from one end at constant velocity in a good solvent. As expected, the relaxation of the stretch to coil transition of the polymer of length N is determined by the typical Rouse time τ ∝ N^2ν+1.     

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.     

A Monte Carlo study of the coil-to-globule transition of model polymer chains near an attractive surface

When a polymer chain in solution interacts with an atomically smooth solid substrate, its conformational properties are strongly modified and deviate substantially from those of chains in bulk. In this work, the interplay of two competing transitions that affect the conformations of polymer chains near an energetically attractive surface is studied by means of Monte Carlo simulations on a cubic lattice. The transition from an extended to a compact conformation of a polymer chain near an attractive wall, as solubility deteriorates, exhibits characteristics akin to the “coil-to-globule” transition in bulk. An effective θ-temperature is determined. Its role as the transition point is confirmed in a variety of ways. The nature of the coil-to-compact transition is not qualitatively different from that in the bulk. Adsorbed polymer chains may assume “globular” or “pancake” configurations depending on the competition among adsorption strength, cohesive energy, and entropy. In a very relevant range of conditions, the dependence of the adsorbate thickness on chain-length is intermediate between that of 3-d (“semidroplets”) and 2-d (“pancake”) objects. The focus of this study is on rather long polymer chains. Several crucial features of the transitions of the adsorbed chains are N-dependent and various aspects of the adsorption and “dissolution” process are manifested clearly only at the “long chain” limit. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2462–2476, 2009     

Unconventional consideration of the symmetry properties—New techniques and computer codes: Application for high‐temperature superconductors

The conventional technique for solving the equations of quantum chemistry is extended to the structures possessing certain symmetries. This proposal allows the release of unoccupied electronic states located lower than the ground‐state Fermi level of a specific system. Such states can be treated as “spectral holes.” Application of this technique, in particular, when calculating the electronic structure of the high‐temperature superconductor (HTSC) compound YBa₂Cu₃O_{7? δ} (0 ≤ δ ≤ 1) results in the following. For all versions of the examined charge distributions over a crystal lattice, spectral holes of high spatial localization are found. The “spatial spectral holes” are located mainly at the p_y‐orbitals of the apex oxygens. These orbitals overlap and form linear chains that are parallel to the known Cu(1)? O chains, disappearing when δ is close to 1. One can suppose that the linear chains of the overlapping hole states form a “superconducting channel.” Some other parameters closely related to the critical characteristics of HTSC materials are also calculated. The calculations show that the superconducting channel is broken when the oxygen chain atoms O(1) are removed (δ > 0). © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Synthesis,characterization, electrochromic properties,and electrochromic device application of a novel star polymer consisting of thiophene end‐capped poly(ε‐caprolactone) arms emanating from a hexafunctional cyclotriphosphazene core

Hexa‐armed and thiophene (Thi) end‐capped poly(ε‐caprolactone) star polymer (N₃P₃‐(PCL‐Thi)₆), containing cyclotriphosphazene core, was prepared in a four‐step reaction sequence. Ring‐opening polymerization (ROP) and “click chemistry” techniques were employed in the first and final steps, respectively. Hexa‐armed PCL star polymer (N₃P₃‐(PCL‐OH)₆) was successfully synthesized via ROP of ε‐caprolactone (ε‐CL) by using hekzakis(p‐(hydroxymethyl)phenoxy) cyclotriphosphazene as the multisite initiator and tin(II) 2‐ethylhexanoate (Sn(Oct₂)) as the catalyst in bulk at 115 °C. Further modifications of the N₃P₃‐(PCL‐OH)₆ were accomplished by derivatization of the hydroxyl‐functional chain ends. The obtained N₃P₃‐(PCL‐OH)₆ was then reacted with 2‐bromo‐2‐methylpropanoyl bromide, and this led to a star polymer with bromide end groups, N₃P₃‐(PCL‐Br)₆. In the third step, N₃P₃‐(PCL‐Br)₆ was azidified with sodium azide (NaN₃) in DMF affording N₃P₃‐(PCL‐N₃)₆. Conversion of the azide chain end groups into Thi was quantitatively accomplished via the “click reaction” between N₃P₃‐(PCL‐N₃)₆ and prop‐2‐yn‐1‐yl 3‐thienyl acetate in the final step. Subsequently, the star polymer with six Thi chain ends (N₃P₃‐(PCL‐Thi)₆) was employed in electrochemical copolymerization with both pyrrole and Thi. Electrochromic properties and electrochromic device application of N₃P₃‐(PCL‐Thi)₆/PThi were also investigated. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3668–3682, 2010     

Static and dynamic scaling behavior of a polymer melt model with triple-well bending potential

We perform molecular-dynamics simulations for polymer melts of the coarse-grained poly(vinyl alcohol) model that crystallizes upon slow cooling. To establish the properties of its high temperature, liquid state as a reference point, we characterize in detail the structural features of equilibrated polymer melts with chain lengths 5 ≤ N ≤ 1000 at a temperature slightly above their crystallization temperature. We find that the conformations of sufficiently long polymers with N > 50 obey essentially the Flory's ideality hypothesis. The chain length dependence of the end-to-end distance and the gyration radius follow the scaling predictions of ideal chains and the probability distributions of the end-to-end distance, and form factors are in good agreement with those of ideal chains. The intrachain correlations reveal evidences for incomplete screening of self-interactions. However, the observed deviations are small. Our results rule out any preordering or mesophase structure formation that are proposed as precursors of polymer crystallization in the melt. Moreover, we characterize in detail primitive paths of long entangled polymer melts and we examine scaling predictions of Rouse and the reptation theory for the mean squared displacement of monomers and polymers center of mass. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1376–1392     

Thermotropic liquid crystalline polymers. II. Polymers with amino acid fragments in the side chains

The comblike polymers, poly(N^ε-methacryloyl-N^α-acyl) derivatives of L -lysine, which contain amino acid fragments and long sequences of methylene groups in the side chain, were synthesized. This article, which is based on x-ray data, differential thermal analysis, and optical microscopy, describes the structure of these polymers and their properties. It also shows that the combination of anisodiametric side groups with a “rigid” matrix of main chains leads to a liquid crystalline structure of examined polymers.     

Interdiffusion of polymers across interfaces

Neutron Reflection (NR) and Dynamic Secondary Ion Mass Spectroscopy (DSIMS) experiments were conducted on symmetrically deuterated polystyrene triblock bilayers (HDH/DHD) which directly probed the interdiffusion dynamics of the chains during welding. The HDH chains had their centers deuterated 50%, the DHD chains had their ends deuterated (25% at each end) such that each chain contained approximately 50% D. During welding, anisotropic motion of the chains produces a time-dependent oscillation (ripple) in the H and D concentration at the interface, which bears the characteristic signature of the polymer dynamics. These oscillations were compared with those predicted by Rouse, polymer mode coupling (PMC), and reptation dynamics. The following conclusions can be made from this study. (a) During the interdiffusion of high molecular weight HDH/DHD pairs, higher mobility of the chain ends caused a concentration oscillation which increased to a maximum amplitude, and eventually vanished at times, t > τ_D. The amplitude, or excess enrichment found, was appreciably more than that predicted by Rouse and PMC simulations, and was only slightly less than that predicted from reptation simulations. (b) The oscillations were completely missing in the 30 and 50K HDH/DHD polymers, which are only weakly entangled. The lack of oscillations for the 30 and 50K pairs may be due to a combination of surface roughness and fluctuations of order 30 Å. (c) It was found that the position of the maximum in this ripple stayed at the interface during its growth. This is also consistent with reptation and has not been explained by other theories. (d) All dynamics models for linear polymers produce ripples, many of which are qualitatively similar to that predicted for reptation. However, each ripple bears the fingerprint of the dynamics in terms of its time-dependent shape, position, and magnitude, and the models are clearly distinguishable. Our results, in summary, support reptation as a candidate mechanism of interdiffusion at polymer(SINGLEBOND) polymer interfaces and its uniqueness is being further pursued. © 1996 John Wiley & Sons, Inc.     

4,6‐Dinitro‐N,N′‐di‐n‐octylbenzene‐1,3‐diamine, 4,6‐dinitro‐N,N′‐di‐n‐undecylbenzene‐1,3‐diamine and N,N′‐bis(2,4‐dinitrophenyl)octane‐1,8‐diamine

4,6‐Dinitro‐N,N′‐di‐n‐octylbenzene‐1,3‐diamine, C₂₂H₃₈N₄O₄, (I), 4,6‐dinitro‐N,N′‐di‐n‐undecylbenzene‐1,3‐diamine, C₂₈H₅₀N₄O₄, (II), and N,N′‐bis(2,4‐dinitrophenyl)octane‐1,8‐diamine, C₂₀H₂₄N₆O₈, (III), are the first synthetic meta‐dinitroarenes functionalized with long‐chain aliphatic amine groups to be structurally characterized. The intra‐ and intermolecular interactions in these model compounds provide information that can be used to help understand the physical properties of corresponding polymers with similar functionalities. Compounds (I) and (II) possess near‐mirror symmetry, with the octyl and undecyl chains adopting fully extended anti conformations in the same direction with respect to the ring. Compound (III) rests on a center of inversion that occupies the mid‐point of the central C—C bond of the octyl chain. The middle six C atoms of the chain form an anti arrangement, while the remaining two C atoms take hard turns almost perpendicular to the rest of the chain. All three molecules display intramolecular N—H...O hydrogen bonds between the amine and nitro groups, with the same NH group forming a bifurcated intermolecular hydrogen bond to the nitro O atom of an adjacent molecule. In each case, these interactions link the molecules into one‐dimensional molecular chains. In (I) and (II), these chains pack so that the pendant alkyl groups are interleaved parallel to one another, maximizing nonbonded C—H contacts. In (III), the alkyl groups are more isolated within the molecular chains and the primary nonbonded contacts between the chains appear to involve the nitro groups not involved in the hydrogen bonding.     

Application of thermal blob theory to intrinsic viscosity measurements of poly(4-chlorostyrene) above the theta point

Macromolecular chains obey purely Gaussian statistics close to the theta temperature. An asymptotic regime is also reached far above the theta point. Thermal blob theory permits an approximate calculation of thermal expansion factor. In this theory, an adjustable parameter is used as a prefactor (A*N₁) in order to calculate the reduced blob parameter (N/N_c). In this work, we proposed a different approach to evaluate (A*N₁) by plotting τM_ω^1/2/α_η⁵ against τM_ω^1/2. Chain expansion data of poly(4-chlorostyrene) in various solvents is used to evaluate viscosity expansion factors at various temperatures. It seems that predictions of thermal blob theory provide a better fit to experimental points rather than those evaluations based on Flory-type approaches. © 1996 John Wiley & Sons, Inc.     

NMR Diffusion Measurements as a Simple Method to Examine Solvent–Solvent and Solvent–Solute Interactions in Mixtures of the Ionic Liquid [Bmim][N(SO2CF3)2] and Acetonitrile

The self‐diffusion coefficients of each component in mixtures of 1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide ([Bmim][N(SO₂CF₃)₂]) and acetonitrile were determined. The results suggest that the hydrodynamic boundary conditions change from “stick” to “slip” as the solvent composition transitions from “ionic liquid dissolved in acetonitrile” (χ_IL<0.4) to “acetonitrile dissolved in ionic liquid” (χ_IL>0.4). At higher χ_IL, the acetonitrile species are affected by “cage” and “jump” events, as the acetonitrile molecules reside nearer to the charged centre on the ions than in the “non‐polar” regions. The self‐diffusion coefficients of hexan‐1‐amine, dipropylamine, 1‐hexanol and dipropylether in mixtures of [Bmim][N(SO₂CF₃)₂] and acetonitrile were determined. In general, the nitrogen‐containing solutes were found to diffuse slower than the oxygen‐containing solutes; this indicates that there are greater ionic liquid–N interactions than ionic liquid–O interactions. This work demonstrates that the self‐diffusion coefficients of species can provide valuable information about solvent–solvent and solvent–solute interactions in mixtures containing an ionic liquid.     

One-pot tandem ring-opening polymerization of N-sulfonyl aziridines and “click” chemistry to produce well-defined star-shaped polyaziridines

An effective approach for fast synthesis of well-defined star-shaped poly(2-methyl-N-tosylaziridine)s was developed by one-pot tandem ring-opening polymerization (ROP) of N-sulfonyl aziridines with trimethylsilyl azide (TMSN₃) and “click” reaction with alkynes. Azido terminated polyaziridines (α-N₃-PAzs) could be achieved via ROP of N-sulfonyl aziridines with TMSN₃ in the presence of organic superbases. The catalytic efficiency of organobases, including 1,4-diazabicyclo[2.2.2]octane (DABCO), 1,8-diazabicyclo[5.4.0]-7-undecene (DBU), 7-methyl-1,5,7-triazabicyclo[4.4.0]dec-5-ene (MTBD), 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD), and N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA), was evaluated, and all of them except TBD afforded “living”/controlled ROP of 2-methyl-N-tosylaziridines (TsMAz). Star-shaped polyaziridines were then fastly synthesized by the one-pot tandem strategy. During the reaction process, PMDETA catalyzed ROP first, then was triggered to be a ligand by adding CuBr for “click” reaction. Well-defined 3- and 4-arm star P(TsMAz)s were successfully prepared, and subsequently desulfonylated to give star-shaped polypropylenimines (PPIs). PPI stars exhibited intrinsic photoluminescence properties from the polyamine arms.     

Transition Metal–organic Coordination Polymers Containing 6-(1H-imidazol-1-yl)-2(1H)-Pyridinone: Synthesis,Structure and Fluorescent Sensing for Enoxacin

Three metal–organic coordination polymers, [M(2,6-bip)₂] (M = Zn ( 1 ), Ni ( 2 )) and [Cu (tfbdc)(2,6-bipH)₂]•2H₂O ( 3 ), were obtained with the similar solvothermal reaction systems of bivalent transition metal salt, 6-(1H-imidazol-1-yl)-2(1H)-pyridinone (2,6-bipH) and 2,3,5,6-tetrafluoroterephthalic acid (H₂tfbdc). The three coordination polymers show different framework features, namely 3D ( 1 ), 2D ( 2 ) and 1D ( 3 ) structures, which are resulted from different single-metal ion “node” and “linker” coordination modes. The [ZnO₂N₂] tetrahedron in 1 and [NiO₂N₄] octahedron in 2 as a node, is formed from Zn sp³ and Ni d²sp³ hybrid orbits, respectively, while the linker, 2,6-bip, adopts the μ₂:η¹η¹η⁰ in 1 and μ₂:η¹η¹η¹ in 2 coordination modes. PLATON calculation suggests that 1 possesses the micropore structure with a pore volume of 14.2%. In 3 , the [CuO₂N₂] parallelogram as a node is derived from Cu dsp³ hybrid orbital, while the linkers of 2,6-bipH and tfbdc adopt the μ₁:η¹η⁰η⁰ and μ₁:η¹η⁰/μ₁:η¹η⁰ coordination modes, respectively. Intriguingly, Zn(d¹⁰)-centre coordination polymer 1 shows strong blue emission, which are derived from the π* → π transition of the 2,6-bipH ligand. Moreover, 1 exhibits high stability and strong luminescence in both water and ethanol. At this point, the performance of 1 is studied as a chemical sensor for detecting fluoroquinolones drug. The results show that 1 can detect enoxacin in ethanol solution with a low detection limit of 3.61 × 10⁻⁵ M. The luminescent sensing mechanisms were investigated from experimental methods and theoretical calculation in detail as well.     

A molecular approach to the spurt effect in polymer melt flow

The Doi-Edwards theory of polymer melts, extended to include relaxation processes associated with chain-length equilibration, is used to make quantitative predictions of a discontinuity in the flow curve of a monodisperse melt in a capillary. A fluid interface between regions of high and low deformation rates is found to propagate from the former into the latter. Our results for the “spurt” and its hysteresis compare favorably with experiment using a molecular weight dependence of the ratio of “reptation time” (T_d) to “equilibration time” (T_eq) in agreement with that determined from nonlinear stress relaxation.