Effects of polymer chain disentanglement on NMR properties. II. 13C magnetic relaxation in polystyrene

The transverse magnetic relaxation of ¹³C_α nuclei has been studied in concentrated solutions of polystyrene. The magnetic relaxation rate was measured as a function of molecular weight at several temperatures (313,318, and 323 K) and at several concentrations (0.53, 0.43, and 0.34 g/cm³). The spin-system response of these nuclei in natural abundance exhibits a characteristic evolution from pseudosolid properties to liquidlike one, induced by decreasing the molecular weight of polymer molecules. This evolution is analogous to that already observed in protons attached to polyisobutylene or polydimethylsiloxane chains; it is assumed to be induced by an increase of the disentanglement rate of polymer chains. The spin-system response may be considered as reflecting single-chain magnetic properties, because of the low concentration of ¹³CC_α nuclei, although all chains are in dynamic interaction with one another. The NMR disentanglement transition is interpreted in terms of a two-step motional averaging effect involving submolecules. A numerical analysis of NMR properties is given using a model of polymer chain relaxation based on a multiple-mode relaxation process, characterized by (i)a terminal relaxation time τ^v₁ depending upon M³, the molecular weight, and approximately proportional to the polymer concentration C (like the reptation time); (ii)a relaxation-time spectrum analogous to a Rouse spectrum; (iii)a terminal relaxation time τ^v₁ = 2.5 × 10^?2s for M = 2.5 × 10⁵, C = 0.53 g/cm³ in carbon tetrachloride at 313 K.     

Polyisobutylene: A most unusual polymer

The influence of molecular weight, M, on the fragility and fast dynamics in polyisobutylene (PIB) was studied using dielectric and mechanical relaxation spectroscopies, calorimetry, and Raman spectroscopy. The measurements indicate a decrease in fragility with increasing M for shorter chains, in the range of M where T_g is M‐dependent. Such behavior is not observed for other polymers and is at odds with traditional theoretical models that predict an increase in fragility with chain length. These results confirm the unusual character of PIB, as evident in various properties including extremely low gas permeability, a low fragility, and a segmental relaxation spectrum much broader than expected for a low‐fragility material. The reason for this anomalous behavior remains unclear, but might be related to the symmetric structure of the PIB repeat unit, together with comparable flexibility of both structural components, the backbone and side groups. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1390–1399, 2008     

Preparation and characterization of biodegradable poly(lactic acid)‐ block‐poly(ε‐caprolactone) multiblock copolymer

Biodegradable copolymers of poly(lactic acid)‐block‐poly(ε‐caprolactone) (PLA‐b‐PCL) were successfully prepared by two steps. In the first step, lactic acid monomer is oligomerized to low molecular weight prepolymer and copolymerized with the (ε‐caprolactone) diol to prepolymer, and then the molecular weight is raised by joining prepolymer chains together using 1,6‐hexamethylene diisocyanate (HDI) as the chain extender. The polymer was carefully characterized by using ¹H‐NMR analysis, gel permeation chromatography (GPC), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and Fourier transform infrared spectroscopy (FTIR). The results of ¹H‐NMR and TGA indicate PLA‐b‐PCL prepolymer with number average molecular weights (M_n) of 4000–6000 were obtained. When PCL‐diols are 10 wt%, copolymer is better for chain extension reaction to obtain the polymer with high molecular weight. After chain extension, the weight average molecular weight can reach 250,000 g/mol, as determined by GPC, when the molar ratio of –NCO to –OH was 3:1. DSC curve showed that the degree of crystallization of PLA–PCL copolymer was low, even became amorphous after chain extended reaction. The product exhibits superior mechanical properties with elongation at break above 297% that is much higher than that of PLA chain extended products. Copyright © 2009 John Wiley & Sons, Ltd.     

Polar,functionalized diene‐based materials. V. Free‐radical polymerization of 2‐[(N‐benzyl‐n‐methylamino)methyl]‐1,3‐butadiene and copolymerization with styrene

2‐[(N‐Benzyl‐N‐methylamino)methyl]‐1,3‐butadiene (BMAMBD), the first asymmetric tertiary amino‐containing diene‐based monomer, was synthesized by sulfone chemistry and a nickel‐catalyzed Grignard coupling reaction in high purity and good yield. The bulk and solution free‐radical polymerizations of this monomer were studied. Traditional bulk free‐radical polymerization kinetics were observed, giving polymers with 〈M_n〉 values of 21 × 10³ to 48 × 10³ g/mol (where M_n is the number‐average molecular weight) and polydispersity indices near 1.5. In solution polymerization, polymers with higher molecular weights were obtained in cyclohexane than in tetrahydrofuran (THF) because of the higher chain transfer to the solvent. The chain‐transfer constants calculated for cyclohexane and THF were 1.97 × 10^?3 and 5.77 × 10^?3, respectively. To further tailor polymer properties, we also completed copolymerization studies with styrene. Kinetic studies showed that BMAMBD incorporated into the polymer chain at a faster rate than styrene. With the Mayo–Lewis equation, the monomer reactivity ratios of BMAMBD and styrene at 75 °C were determined to be 2.6 ± 0.3 and 0.28 ± 0.02, respectively. Altering the composition of BMAMBD in the copolymer from 17 to 93% caused the glass‐transition temperature of the resulting copolymer to decrease from 64 to ?7 °C. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3227–3238, 2001     

Molecular motion of ends of isolated poly(isobutylene) chains tethered on the poly(tetrafluoroethylene) surface in vacuo

Poly(isobutylene) (PIB) chains with a radical at the chain end were graft-copolymerized on the poly(tetrafluoroethylene) (PTFE) surface in vacuo at 77 K. The PIB chains tethered on the PTFE surface in vacuo were regarded as isolated chains from neighboring tethered PIB chains. The molecular motion of the ends of the isolated PIB chains was observed by an electron spin resonance (ESR) spectrometer in the temperature range from 3 to 125 K, which was lower than T_g of PIB, 200 K,¹ and two motion modes were found: One is a quantum tunneling of the methyl group located at the chain end at 3 K, and the other is an interconformation transition with freely rotating methyl group at the end at 77 K, where the transition rate was estimated to be 15 MHz at that temperature. The transition rate increased with an increase in temperature. The activation energy of the transition was estimated to be 370 J/mol. The high mobility and low activation energy was attributed to the isolation of PIB chains in vacuo. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2095–2102, 1998     

Optical anisotropy of polyisobutylene: Strain birefringence

Strain birefringence measurements on crosslinked polyisobutylene (butyl rubber) confirm earlier work of Stein and Tobolsky on the linear polymer indicating the optical anisotropy to be much greater than should have been expected from the structural symmetry of the polyisobutylene (PIB) chain. The configuration–optical anisotropy parameter Δa for PIB at 25°C is 4.1(±0.1) × 10^?24 cm³, or about half the value for crosslinked polymethylene, both polymers being undiluted and amorphous. Swelling with cyclohexane, CCl₄, and CBrCl₃ lowers Δa to values of 3.8, 3.4, and 2.8 × 10^?24 cm³, respectively. Contributions from intermolecular correlations in the bulk polymer and from form anisotropy in the diluted systems are small, if not negligible. Temperature coefficients measured isometrically yield d In Δa/dT ≈ 0.2 × 10^?3 deg^?1. Both Δa and its temperature coefficient are much greater than calculated from rotational isomeric state theory assuming additivity of bond polarizabilities. The disparity (more than tenfold for Δa) cannot be relieved by any rational adjustment of the structural parameters. It is suggested that the severe crowding of groups in the PIB chain may affect the anisotropies of group polarizabilities.     

Study of polymer complexes by size exclusion chromatography coupled with light scattering in combination with fluorescence spectroscopy

Poly(methyl methacrylate) stereocomplexes prepared at different concentration in dilute tetrahydrofuran solutions were studied by size exclusion chromatography coupled with refractive and light scattering detectors in combination with fluorescence spectroscopy. A considerable increase in segment density due to complexation compared with free poly(methyl methacrylate) chain was only slightly affected by the polymer concentration in solution where stereocomplexes were formed. At polymer concentrations up to 3×10⁻³ g cm⁻³, an increase in non‐uniformity of polymer complex molecular weight and size and a shift to higher values of both were observed. In semidilute solutions (at c > 3×10⁻³ g cm⁻³) stereocomplexes virtually did not become heavier and larger.     

Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Emulsion polymerization of vinyl acetate using iodine‐transfer and RAFT radical polymerizations

This study deals with control of the molecular weight and molecular weight distribution of poly(vinyl acetate) by iodine‐transfer radical polymerization and reversible addition‐fragmentation transfer (RAFT) emulsion polymerizations as the first example. Emulsion polymerization using ethyl iodoacetate as the chain transfer agent more closely approximated the theoretical molecular weights than did the free radical polymerization. Although ¹H NMR spectra indicated that the peaks of α‐ and ω‐terminal groups were observed, the molecular weight distributions show a relatively broad range (M_w/M_n = 2.2–4.0). On the other hand, RAFT polymerizations revealed that the dithiocarbamate 7 is an excellent candidate to control the polymer molecular weight (M_n = 9.1 × 10³, M_w/M_n = 1.48), more so than xanthate 1 (M_n = 10.0 × 10³, M_w/M_n = 1.89) under same condition, with accompanied stable emulsions produced. In the M_n versus conversion plot, M_n increased linearly as a function of conversion. We also performed seed‐emulsion polymerization using poly(nonamethylene L ‐tartrate) as the chiral polyester seed to fabricate emulsions with core‐shell structures. The control of polymer molecular weight and emulsion stability, as well as stereoregularity, is also discussed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Dielectric Relaxation of Type‐A Polymers in Melts and Solutions

This article describes the dielectric relaxation behavior of flexible polymer chains having the so‐called type‐A dipoles parallel along the chain backbone. This behavior reflects the global chain motion. Viscoelastically well known features of this motion, such as the power‐law relationship between the relaxation time and molecular weight of entangled linear chains (τ₁ ∝ M^3.5), are also observed dielectrically. More importantly, the dielectric behavior of linear chains having once‐inverted type‐A dipoles enables us to find some detailed dynamic features such as changes in the eigenfunctions f_p of a local correlation function with the chain concentration in solutions. These changes are discussed in relation to motional coupling of concentrated chains. The dielectric properties detect the orientational correlation of two submolecules in the chain at two separate times, while the viscoelastic properties reflect the isochronal orientational anisotropy of individual submolecules. Thus the chain motion is differently averaged in the dielectric and viscoelastic properties, and comparison of these properties enables us to find novel dynamic features. Specifically, this comparison reveals the validity of the tube dilation molecular picture for entangled linear chains and weakening of the short‐time coherence of the submolecule motion due to the constraint release mechanism. Moreover, the dielectric method enables us to investigate the chain dynamics under strong flow and/or in a molecularly narrow space. In particular, the retarded dielectric relaxation found for homopolymers and block copolymers in such narrow spaces (in the microdomains for the latter) indicates important effects of the spatial and thermodynamic constraints on the global chain motion. All the above results in turn demonstrate the importance of the dielectric method in investigations of the polymer dynamics.     

Synthesis and characterization of poly[2,5-bis(triethoxy)-1,4-phenylene vinylene]

The synthesis of a highly soluble, 2,5-disubstituted poly(p-phenylene vinylene) with pendant side chains containing ether groups was accomplished by a dehydrochlorination route. Specific interactions of the oxygen-containing side chains with the solvent are presumably responsible for the high solubility of the polymer, especially in protogenic solvents. The polymer microstructure was characterized by ¹H- and ¹³C-NMR. The polymer showed solvatochromic properties when dissolved in a variety of solvents. The relatively high molecular weight (M_n = 17,000) permitted the fabrication of free-standing films. The electrical conductivity of iodine-doped films was approximately 2 × 10^–2 S cm^–1. © 1995 John Wiley & Sons, Inc.     

Nuclear spin relaxation dynamics of 13CO2 sorbed in polyisobutene rubber

Recently we presented the dynamics of ¹³CO₂ molecules sorbed in silicone rubber (PDMS) ascertained from spin relaxation experiments. Results of a similar investigation for ¹³CO₂ sorbed in polyisobutene (PIB) are presented in this report. The spin-lattice and spin-spin relaxation times as well as nuclear Overhauser enhancements (NOE) were determined as a function of temperature and Larmor frequency. The relaxation mechanisms found to be important for ¹³CO₂/PIB system are intermolecular dipole-dipole relaxation and chemical shift anisotropy with a minor contribution from spin rotation relaxation. We have determined the parameters which characterize correlation times for ¹³CO₂ collisional motion, rotational motion, and translational motions in the PIB. The self-diffusion coefficient of 5.15 × 10^?8 cm²/s obtained from the nuclear magnetic resonance (NMR) data is close to the literature value of the mutual diffusion coefficient of CO₂ in PIB at 300 K obtained from permeability measurements. In contrast to the case of CO₂/PDMS in which a broad distribution (characterized by a fractional exponential correlation function of the Williams-Watts type with α = 0.58) is observed, a sharp distribution with a fractional exponent, α, of 0.99 is found for the CO₂/PIB system. Instead of assuming an Arrhenius type temperature dependence, we used a Williams-Landel-Ferry type temperature dependence and found it to be better suited to describe the behavior of this system. PIB is a densely packed “strong” chain polymer which responds gradually to the temperature variation and gas sorption. In contrast PDMS is a relatively loosely packed “fragile” polymer with a propensity to exhibit rapid dynamic responses to the temperature change and gas sorption. © 1993 John Wiley & Sons, Inc.     

Synthesis of nonsymmetric chain end functionalized polyisobutylenes

We present the synthesis of nonsymmetric α‐ω‐functionalized polyisobutylenes (PIBs) bearing different functional moieties on their chain ends. Thus, on one chain end either, a short tri‐ethylene oxide chain (TEO) or a phosphine oxide ligand is attached, whereas the other chain end is substituted by hydrogen bonding moieties (thymine/2,6‐diaminotriazine). The nonsymmetric PIBs were synthesized via living cationic polymerization using methyl‐styrene epoxide as initiator, followed by quenching reaction with 3‐bromopropyl‐benzene. Subsequent bromide/azide exchange and the use of the azide/alkyne click reaction allowed the synthesis of (a) (α)‐TEO‐(ω)‐thymine‐telechelic PIB ( 7a ), (b) (α)‐triethyleneoxide‐(ω)‐triazine telechelic PIB ( 7b ), and (c) (α)‐phosphinoxide‐(ω)‐thymine‐telechelic PIB ( 13 ) with molecular weights M_n ～ 4000 g mol^?1 and low polydispersities (M_w/M_n = 1.3). The chemical identity of the final structures was proven by extensive ¹H NMR investigations and matrix‐assisted laser desorption/ionization‐mass spectroscopy (MALDI). The presented method for the first time offers a simple and highly versatile approach toward supramolecular nonsymmetric α‐ω‐functionalized PIB. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Elongational flow studies on flexible polymer chains in a pseudo-solvent

The dynamics of isolated high molecular weight (M_H) polymer chains dissolved in a nonentangled semidilute solution of a low molecular weight (M_L) polymer were investigated by monitoring the elongational flow birefringence. Because of its nonentangled nature, a low molecular weight matrix polymer solution is regarded as a pure solvent (a binary pseudo-solvent). A ternary solution consisting of a small amount of a high molecular weight probe polymer and the binary pseudo-solvent is effectively a dilute solution of the probe polymer. It was observed that the birefringence from the orientation and/or stretching of the probe polymer chains starts to increase rather abruptly at a certain critical strain rate, , and the spatial birefringence pattern is localized along the elongation axis, characteristics that are reminiscent of the coil-stretch transition of flexible polymer chains in a simple dilute solution. The relaxation time for the chain extension, _el, defined as the reciprocal of the critical strain rate , was determined at various temperatures, matrix polymer concentrations c_L, and test chain molecular weights M_H. It was found that _el varied with molecular weight as _el~M_H^a , with a ranging from 1.3 to 1.8, which is roughly consistent with the molecular weight dependence of the non-free-draining Zimm relaxation time. A scaled relaxation time _elkT/, which can be used to estimate the radius of gyration R_g of the probe polymer, decreased with increasing c_L, indicating contraction of the high molecular weight polymer due to a screening of the excluded volume effect caused by the matrix polymer in the pseudo-solvent.     

Direct functionalization of polyisobutylene by living initiation with α‐methylstyrene epoxide

This article describes the synthesis and characterization of polyisobutylene (PIB) carrying one primary hydroxyl head group and a tertiary chloride end group, [Ph? C(CH₃)(CH₂OH)–PIB–CH₂? C(CH₃)₂Cl] prepared with direct functionalization via initiation. The polymerization of isobutylene was initiated with the α‐methylstyrene epoxide/titanium tetrachloride system. Living conditions were obtained from ?75 to ?50 °C (198–223 K). Low molecular weight samples (number‐average molecular weight ～ 4000 g/mol) were prepared under suitable conditions and characterized by Fourier transform infrared and ¹H NMR spectroscopy. The presence of primary hydroxyl head groups in PIB was verified by both methods. Quantitative Fourier transform infrared with 2‐phenyl‐1‐propanol calibration and ¹H NMR performed on both the hydroxyl‐functionalized PIB and its reaction product with trimethylchlorosilane showed that each polymer chain carried one primary hydroxyl head group. The synthetic methodology presented here is an effective and simple route for the direct functionalization of PIB. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1005–1015, 2002     

Nuclear relaxation in atactic polystyrenes: T1 and T1ρ measurements

Measurements have been made on a series of linear atactic polystyrenes whose molecular weights range from 900 to 1.8 × 10⁶, where M _w/M _n ? 1.2. Spin lattice relaxation times have been measured in the laboratory frame (T₁) and in the rotating frame (T_1ρ) in the temperature range 90–500°K. Two major relaxation minima were observed in both sets of measurements. The high temperature process corresponds to the glass transition (α process), the position of the minimum depending on the chain length. The low temperature process appears to originate from the n-butyl endgroups in the polymer, its position being independent of chain length while its intensity is inversely proportional to molecular weight. No other minima were observed, in contrast to some other observations made by broadline and pulsed NMR techniques. Relaxation was exponential in all cases except in the region of the high temperature T_1ρ minimum and above. This nonexponential behavior is possibly connected with the transition at T > T_g observed by a number of other techniques and which is thought to correspond to a transition between two types of liquid state. A correlation frequency diagram has been drawn for all the processes observed in polystyrene by other techniques, (α, β, αβ, γ, and δ) which shows that the T₁ and T_1ρ minimum positions correlate well with the α process and that there is a possible contribution to the relaxation due to the γ process on the low temperature side of the α process. At these measurement frequencies the α and β processes are merged into an αβ process. There is no evidence for a contribution from the mechanical δ process. The effect of the endgroups is observed to very high molecular weights (4.98 × 10⁵), and it seems that a three-dimensional diffusion model would be more adequate than the one-dimensional model used to interpret similar behavior of paraffins and polyethylenes. Measurements of T₁ in the low-temperature region would constitute a method for a rough measurement of the molecular weight of these polymers.     

Tensile strength of highly oriented polyethylene. II. Effect of molecular weight distribution

The tensile strength of oriented polyethylene filaments is discussed in relation to molecular weight. Short-term tensile properties at room temperature were obtained in our laboratory and from the literature for polymer samples covering the molecular weight (M _w) range from 54 × 10³ to 4 × 10⁶, and polydispersities ranging from 1.1 to 15.6, oriented by solid-state extrusion, melt spinning/drawing, solution spinning/drawing, and “surface growth.” It was found that both the molecular weight and its distribution markedly affected tensile strength. The breaking stress σ of highly oriented fibers varied with molecular weight roughly as σ ∝, M^0.4, at constant M _w/M _n over the entire range studied. Reduction of polydispersity from 8 to 1.1 by an increase of M _n with M _w approximately constant at 10⁵ increased tensile strength of oriented polyethylene filaments by a factor of nearly 2.     

Synthesis and characterization of two novel star blocks: tCum[poly(isobutylene‐b‐norbornadiene)]3 and tCum[poly(norbornadiene‐b‐isobutylene)]3

Two structurally closely related three‐arm star blocks were synthesized and characterized: tCum(PIB‐b‐PNBD)₃ and tCum(PNBD‐b‐PIB)₃ [where tCum (tricumyl) stands for the phenyl‐1,3,5‐tris(‐2‐propyl) fragment and PIB and PNBD are polyisobutylene and polynorbornadiene, respectively]. The syntheses were accomplished in two stages: (1) the preparation of the first (or inner) block fitted with appropriate chlorine termini capable of initiating the polymerization of the second (or outer) block with TiCl₄ and (2) the mediation of the polymerization of the second block. Therefore, the synthesis of tCum(PIB‐b‐PNBD)₃ was effected with tCum(PIB‐Cl^t)₃ [where Cl^t is tert‐chlorine and number‐average molecular weight (M_n) = 102,000 g/mol] by the use of TiCl₄ and 30/70 CH₃Cl/CHCl₃ solvent mixtures at ?35 °C. PNBD homopolymer contamination formed by chain transfer was removed by selective precipitation. According to gel permeation chromatography, the M_n's of the star blocks were 107,300–109,200 g/mol. NMR spectroscopy (750 MHz) was used to determine structures and molecular weights. Differential scanning calorimetry (DSC) indicated two glass‐transition temperatures (T_g's), one each for the PIB (?65 °C) and PNBD (232 °C) phases. Thermogravimetric analysis thermograms showed 5% weight losses at 293 °C in air and at 352 °C in N₂. The synthesis of tCum(PNBD‐b‐PIB)₃ was achieved by the initiation of isobutylene polymerization with tCum(PNBD‐Cl^sec)₃ (where Cl^sec is sec‐chlorine and M_n = 2900 g/mol) by the use of TiCl₄ in CH₃Cl at ?60 °C. DSC for this star block (M_n = 14,200 g/mol) also showed two T_g's, that is, at ?67 and 228 °C for the PIB and PNBD segments, respectively. It is of interest that the Cl^sec terminus of PNBD, , readily initiated isobutylene polymerization. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 740–751, 2003     

Cooperative chain relaxation in miscible polymer blends

Orientation relaxation of dissimilar chains in the molten miscible blends, poly(methyl methacrylate)/poly(vinylidene fluoride) and poly(methyl methacrylate)/poly(vinylidene fluoride-co-trifluoroethylene), were investigated by measuring (1) the change of infrared dichroic ratio with time after the uniaxial stretching of film specimens, (2) the shear stress relaxation spectrum, and (3) birefringence relaxation in shear. The dissimilar polymers showed an identical time variation of the normalized Hermans orientation function. The blend showed a relaxation spectrum with a single characteristic relaxation time τ_c, depending on the blend composition. The birefringence relaxed monotonically, remaining positive. These results suggest that the dissimilar polymers do not relax independently but cooperatively. This behavior may be induced by a constraint due to the specific interactions between the dissimilar polymers, e.g., weak hydrogen bonding. For the cooperative chain relaxation, a third power relationship was found; τ_c/τ_e vprop; (M/M_e),³ where τ_e and M_e are the relaxation time and molecular weight of entanglement strand, respectively, and M is the number average molecular weight in the blend.     

Nonlinear viscoelasticity of polystyrene solutions. III. Stress development at the start of steady shear flow and an experimental check of some constitutive models

The development of the shear stress at the start of shear flow at constant rate of shear κ was measured for polystyrene solutions in diethyl phthalate with a cone-and-plate rheometer. Ranges of molecular weight M and concentration c were 3.10 × 10⁶?7.62 × 10⁶ and 0.112?0.329 g/cm³, respectively. The shear stress as a function of time t exhibited a marked maximum at large κ when either M or c was relatively low. When M and c were high, the maximum was broad and low. In a few extreme cases no maximum was observed in the range of κ studied. The constitutive model of Bernstein, Kearsley, and Zapas could describe approximately the shear stresses at a sudden start and on cessation of steady shear flow with a memory function evaluated from the strain-dependent relaxation modulus. The strain dependence of the memory function for solutions of low M or c was approximately expressed as exp{?α|s|} where α is a constant (ca. 0.37) and |s| is the absolute value of shear strain. When M and c were high, the strain dependence was found to be more diffuse and to require several terms if approximated by exponential functions of |s|. The Lodge model based on a strain-rate dependent relaxation spectrum was not able to describe the strain-dependent relaxation modulus as well as the interrelation between shear stresses at a sudden start and a cessation of steady shear flow.