Nonlinear rheology of highly entangled polymer solutions in start‐up and steady shear flow

Orientation angle and stress‐relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase‐modulated flow birefringence apparatus was developed to facilitate measurements of time‐dependent changes in optical equivalents of shear stress (n₁₂ ≈ Cσ) and first normal stress differences (n₁ = n₁₁ ? n₂₂ ≈ CN₁) in a planar‐Couette shear‐flow geometry. Flow birefringence results were supplemented with cone‐and‐plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow (τ > ) steady shear‐flow experiments using the ultrahigh MW polymer sample (20.6 × 10⁶ MW PS), steady‐state n₁₂ and n₁ results manifest unusual power‐law dependencies on shear rate [n_12,ss ～ ^0.4 and n_1,ss ～ ^0.8]. At shear rates in the range τ < < τ, steady‐state orientation angles χ_SS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle χ_p in the range 20–24° is observed; χ_p values ranging from 14 to 16° are found for the other materials. In the start‐up of fast steady shear flow (γ˙ ≥ τ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2275–2289, 2001     

Intrinsic birefringence of poly(trimethylene terephthalate)

Highly oriented poly(trimethylene terephthalate) (PTT) fiber has a low birefringence that is unexpected for an aromatic polyester with a high refractive index. To explain this observation, the intrinsic birefringence Δn of PTT crystal was calculated from its bond polarizabilities to be 0.029. This Δn is almost an order of magnitude smaller than poly(ethylene terephthalate)'s value at 0.22, although both polymers have nearly identical crystal refractive indices. The small Δn is due to the arrangement of PTT's methylene groups in gauche conformations, causing the chain‐repeating unit to be tilted ～53° away from the c axis toward the basal plane. Because of the small Δn, the crystalline‐phase orientation made only a small contribution to the overall birefringence despite the fiber's high crystallinity and orientation. To understand the effect of the number of methylene groups on polyester optical anisotropy, the Δn's of a series of poly(m‐alkylene terephthalates) with m = 2–5 were compared and correlated with ψ: an angle made by the normal of the benzene ring with the crystal's axis. As ψ′ decreases, Δn of the polyesters diminishes. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1513–1520, 2002     

A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Interaction parameters of crystalline/crystalline polypropylene/poly(butene‐1) blends: Effect of molecular fractionation

Compatibility of crystalline/crystalline polypropylene (PP)/poly(butene‐1) (PB‐1) blends was investigated via the method of equilibrium melting temperature depression followed by determining the polymer–polymer interaction parameter (χ) using the Nishi–Wang equation. The composition variation of the equilibrium melting temperatures of blends (T) was determined with the Hoffman–Weeks plot. The T and its variation with the blend composition depended on the crystallization temperature range. The morphological effect of the blend composition was not a contribution factor for the T depressions of PP and PB‐1 in the blends. The interplay of the dilution effect and molecular fractionation effect of the amorphous component on crystallization of the crystalline component in the blends governed the relation of T with the blend composition. The calculated χ values were negative depending on the blend composition. The negative χ values suggested that PP and PB‐1 in the amorphous region were compatible. The composition variation of the χ values was attributed to the molecular fractionation effect during crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 638–648, 2002; DOI 10.1002/polb.10125     

Entanglement friction and dynamics in blends of starlike and linear polymer molecules

We investigate relaxation dynamics in a series of six‐arm star/linear 1,4‐polybutadiene blends with mechanical rheometry measurements. Blend systems are formulated to systematically probe constraint release and arm relaxation dynamics. Zero shear viscosity and terminal relaxation times of star/linear polymer blends with fixed star arm molecular weights (M_a) and compositions (?_S) are found to follow nonmonotonic dependencies on the linear polymer molecular weight (M_L). At low values of ?_S, at least two scaling regimes are apparent from the data (ξ₀ ～ M and ξ₀ ～ M), where ξ₀ refers to the zero shear viscosity or terminal relaxation time of the blend. The two regimes are separated by a critical linear polymer molecular weight M^* that is more than 20 times larger than the critical molecular weight for entanglements. When the linear polymer contribution to blend properties is removed, a clear transition from dilution dynamics, ξ₀ ～ M, to Rouse‐like constraint‐release dynamics, ξ₀ ～ M, is apparent at low values of ?_S. At higher ?_S values, a new activated constraint‐release dynamic regime is evident in which ξ₀ ～ M and ξ₀ ～ ?, where α changes continuously from approximately 2 to 0.5 as ?_S increases and β varies from 2.0 to 1.0 as M_L increases. The experimental results are compared with theoretical predictions based on a drag coupling model for entangled polymer liquids. All features observed experimentally are captured by this model, including the value of M^* for the transition from dilution to Rouse constraint‐release dynamics. Predictions of the drag coupling model are also compared with published data for the zero shear viscosity and terminal relaxation time in bidisperse linear polymer blends and pure entangled starlike molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2501–2518, 2001     

Molecular orientation in biaxially oriented sheets of poly(ethylene terephthalate). I. Characterization of orientation and comparison with models

A study of molecular orientation in a series of five one-way-drawn sheets of poly(ethylene terephthalate) is reported. Five orientation averages P which characterize the benzene-ring orientation were determined directly by Raman spectroscopy. Two further averages P and P were determined from a combination of Raman spectroscopy and refractive index measurements on the basis of two different conformational models. As in a previous publication, the seven averages P were used to estimate all the P up to fourth order for the benzene rings on the assumption that in each case the actual distribution of orientations is close to the most probable distribution. The seven orientation averages P for each drawn sheet were also compared with those calculated on the basis of two simple models for the development of molecular orientation during drawing, the pseudoaffine deformation scheme and the rubber network model. It was shown that the orientation of the chain axes is closer to that predicted by the rubber network model, the pseudoaffine deformation scheme greatly overestimating the degree of chain biaxiality. The results also show that the benzene ring planes are preferentially oriented toward the planes of the sheets. The chain axis orientation is, however, nearly uniaxial and similar to that observed for uniaxially drawn samples, suggesting that there is no direct connection between the processes of chain axis orientation and preferential orientation of the benzene-ring planes.     

Zone-resolved mass spectroscopic study on RF plasma polymerization of styrene

The radiofrequency (rf) glow discharge plasma of styrene was investigated by direct sampling mass spectroscopy. Measurements were taken in three regions of the discharge: the plasma column and two dark zones before the electrodes. The plasma-polymerized styrene (PPS) thin films were analyzed by infrared spectroscopy (IR). The effects of monomer pressure and rf power on the ratios of mass peak heights C₄H/C₄H, C₆H/C₆H₅()CH in the three discharge regions, the polymer deposition rate, and the polymeric structure of the PPS films were studied. It was found that in the different discharge regions and under various discharge conditions, a variety of reactive species were formed by electron impact on monomer molecules. The polymer deposition rate was mainly dependent on the total number of the reactive species produced in the discharge. The concentration of phenyl groups in PPS films was proportional to the relative concentration of phenyl ring-containing reactive species in the gas phase plasma. © 1996 John Wiley & Sons, Inc.     

Determination of the crystallinity of polyethylene/α‐olefin copolymers by thermal analysis: Relationship of the heat of fusion of 100% polyethylene crystal and the density

The heat of fusion measured with differential scanning calorimetry (DSC) is typically divided by a constant value of the heat of fusion of 100% polyethylene (PE) crystal (ΔH) for the estimation of the fraction crystallinity of PE copolymers, regardless of the density [i.e., the short‐chain branching (SCB) concentration]. In this work, values of ΔH of about 288 J/g were determined with a combined DSC and X‐ray diffraction (XRD) method for a series of PE copolymers containing SCB from 0 to 50 Br/1000 C (density = 0.965–0.865 g/cc). There was no systematic change in ΔH observed across this density range. This result supports the suitability of determining the fraction crystallinity of PE of any density by the simple division of the observed heat of fusion determined by DSC by a constant value of ΔH. This DSC method yielded values of PE crystallinity in good agreement with corresponding values determined by XRD for a series of PE copolymers. The determination of ΔH involved a small precision error for higher density (lower SCB) PEs, but the precision error increased for lower density (i.e., higher SCB) PEs. This was due to the difficulty in measuring the heat of fusion for lower density PEs, which exhibited low values of the heat of fusion and melted only slightly above room temperature, and due to the difficulty of measuring lower values of crystallinity by XRD. The crystal thickness measured by small‐angle X‐ray scattering for this series of PE copolymers decreased exponentially from about 280 to 6 Å. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1637–1643, 2002     

Solid‐state nuclear magnetic resonance relaxation times in crosslinked macroporous polymer particles of divinylbenzene homopolymers

Monodisperse porous particles of poly(divinylbenzene) prepared by the activated swelling method have been investigated by solid‐state ¹³C crosspolarization magic‐angle spinning (CPMAS) nuclear magnetic resonance (NMR) relaxation measurements. Homopolymeric combinations of two porogens (toluene and 2‐ethylhexanoic acid) and two monomers (meta‐ and para‐divinylbenzene) were studied. Residual vinyl groups were systematically reacted with increasing amounts of bromine, producing 20 different polymers samples for which we measured crosspolarization times, T_CH, proton rotating frame spin‐lattice relaxation, T, ¹³C spin‐lattice relaxation, T, and proton spin‐lattice relaxation, T. These parameters were chosen to reflect expected changes in a wide range of frequencies of motion as a function of structure. Relative differences in the molecular mobility of the major functional groups (aromatic, vinyl and aliphatic) is related to initial reactants used, vinyl concentration, relative reactivity of vinyl groups, distribution of vinyl groups, pore structure, and degree of crosslinking. Variable temperature ¹H combined rotation and multiple pulse NMR (CRAMPS) was used to derive activation energies for selected samples via measurement of the proton spin‐lattice relaxation time, T. Irreversible thermal effects were observed in ambient temperature relaxation after heating to temperatures in the range of 393–418 K. Simple univariate statistical analyses failed to reveal consistent correlations among the known variables. However, the application of more sophisticated multivariate and neural network analyses allowed excellent structure–property predictions to be made from the relaxation time data. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1307–1328, 1999     

Structure and viscoelasticity of matched asymmetric diblock and triblock copolymers in the cylinder and sphere microstructures

A polystyrene–polyisoprene (PS–PI) diblock copolymer (10,000–50,000 g/mol) and a matched PS&ndashPI–PS triblock (10,000–100,000–10,000 g/mol) were employed to study the effect of chain architecture on the rheological response of ordered block copolymer melts. Both samples adopt hexagonal microstructures with PS cylinders embedded in a PI matrix; on further heating, an order–order transition (OOT) into a cubic array of spheres takes place prior to the order–disorder transition. Each morphology was verified by SAXS and TEM. Interestingly, at the OOT the low-frequency elastic modulus of the diblock increased abruptly, whereas that of the triblock decreased. In contrast, the modulus of the cubic phase was roughly independent of chain architecture. Chain relaxation parallel and perpendicular to the cylinders was probed by measuring the elastic modulus of a macroscopically aligned sample in directions parallel G and perpendicular (G) to the cylinder orientation. For both materials G < G < G where G is the elastic modulus of a randomly oriented sample. This result is attributed to the ability of the unentangled PS blocks to move along the direction of the cylinder axis, and thus relax the stress in the PI matrix in the parallel alignment. In each of the three cylindrical orientations the triblock had a larger modulus than the diblock, which is attributed to the presence of bridging PI blocks that connect distinct PS domains. About 20° below the OOT G showed a distinct change in its temperature dependence, which, coupled with SAXS measurements, is indicative of the onset of an undulation in the cylinder diameter that presages the pinching off of cylinders into spheres, as recently predicted by theory. The use of oriented samples also permitted SAXS confirmation of an approximate epitaxial relationship between the cylinder and the sphere unit cells, although a distinct change in the location of the structure factor maximum, q^*, is noted at the OOT. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2811–2823, 1997     

Crystallization mechanism of regioregular poly(3‐alkyl thiophene)s

The crystallization properties of three regioregular poly(3‐alkyl thiophene)s (P3ATs) are studied: poly(3‐hexyl thiophene) (P3HT), poly(3‐octyl thiophene) (P3OT), and poly(3‐dodecyl thiophene) (P3DDT). The morphology of the isothermally crystallized samples is a whisker type. The values of the enthalpy of fusion of ideal crystals (ΔH), determined from the melting point depression in the polymer–diluent system, are 99, 73.6, and 52 J/g for P3HT, P3OT, and P3DDT, respectively. The values of the equilibrium melting point (T), determined from the Hoffman–Weeks extrapolation procedure, are 300, 230, and 180 °C for P3HT, P3OT, and P3DDT, respectively. From the linear extrapolation of the P3AT data, the T and ΔH values of unsubstituted polythiophene are predicted to be 400 °C and 139 J/g, respectively. The crystallization kinetics of these polymers are studied with differential scanning calorimetry, and the Avrami exponents vary between 0.6 and 1.4, indicating one‐dimensional heterogeneous nucleation with linear growth. As the P3AT whiskers are produced from the chain‐folding process, the Lauritzen–Hoffman growth rate theory is applied to analyze the temperature coefficient of the crystallization rate data. Graphical plots indicate a transition from regime I to regime II during isothermal crystallization for all the P3ATs studied. The fold surface energy and the work of chain folding calculated from the slopes of the graphical plots decrease with an increase in the number of carbon atoms of the side chain. The primary crystallization process of the side‐chain crystallization is very fast and is attributed to the zipping effect of the main‐chain crystals. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2073–2085, 2002     

Relaxation dynamics of salt‐free polyelectrolyte solutions using flow birefringence and rheometry

Relaxation dynamics of salt‐free, aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) were investigated by mechanical rheometry and flow birefringence measurements. Two semidilute concentration regimes were studied in detail for a range of polymer molecular weights. At solution concentrations c < 10 mg mL, limiting shear viscosity η₀ was found to scale with molecular weight and concentration as η₀ ∼ c^0.5M_w over nearly two decades in concentration. At higher solution concentrations, c > 10 mg mL, a change in viscosity scaling was observed η₀ ∼ c^1.5M, consistent with a change from simple Rouse dynamics for unentangled polyions to near‐perfect reptation dynamics for entangled chains. Characteristic relaxation times τ deduced from shear stress and birefringence relaxation measurements following start‐up of steady shearing at high rates reveal very different physics. For c < 10 mg mL, both methods yield τ ∼ c^−0.42M and τ ∼ c⁰M for c > 10 mg mL. Curiously, the concentration scalings seen in both regimes are consistent with theoretical expectations for salt‐free polyelectrolyte solutions undergoing Rouse and reptation dynamics, respectively, but the molecular weight scalings are not. Based on earlier light scattering studies using salt‐free NaPSS solutions, we contend that the unusual relaxation behavior is likely due to aggregation and/or coupled polyion diffusion. Simultaneous stress and birefringence measurements suggest that in concentrated solution, NaPSS aggregates are likely well permeated by solvent, supporting a loose collective of aggregated chains rather than the dense polymer aggregates previously supposed. Nonetheless, polyion aggregates of either variety cannot account for the inverse dependence of relaxation time on polymer molecular weight for c < 10 mg mL. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 825–835, 1999     

A procedure for predicting sorption equilibrium in ternary polymer systems from Flory–Huggins binary interaction parameters and the inversion point of preferential solvation

A procedure has been developed, based on the Flory–Huggins theory as generalized by Pouchlý, which permits the calculation of preferential (λ) and total (Y) sorption coefficients from previous information on the binary interaction parameters, χ, χ, and g₁₂(?₁₀) and on the mixture composition at which the sign of λ inverts. The expressions obtained were applied to 10 cosolvent polymer systems for which experimental values of λ and Y are known. Practically in all the studied systems, the theoretical predictions are in fair accordance with the experimental data.     

Convergence accelerator approach for the evaluation of some three‐electron integrals containing explicit rij factors

A simplified analysis is presented for the evaluation of the three‐electron one‐center integrals of the form ∫rrrrrred r ₁d r ₂d r ₃, for the cases i, j, k, ≥−2, l=−2, m≥−1, n≥−1. These integrals arise in the calculation of lower bounds for energy levels and certain relativistic corrections to the energy when Hylleraas‐type basis sets are employed. Convergence accelerator techniques are employed to obtain a reasonable number of digits of precision, without excessive CPU requirements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 93–99, 1999     

Quantitative evaluation of stress distribution in bulk polymer samples through the comparison of mechanical behaviors between giant single‐crystal and semicrystalline samples of poly(trans‐1,4‐diethyl muconate)

The Raman shift and crystallite modulus were measured under the application of tensile force for a giant single crystal and a series of uniaxially oriented semicrystalline samples of poly(trans‐1,4‐diethyl muconate) (polyEMU). The apparent Raman shift factor α^app or a vibrational frequency shift per 1 GPa tensile stress was higher for the semicrystalline samples with lower crystallinity or lower bulk modulus. The apparent crystallite modulus E or Young's modulus along the chain axis in the crystalline region was not constant but varied remarkably between the giant single crystal and semicrystalline samples. A systematic change in α^app and E among the polyEMU samples with different preparation history could be interpreted quantitatively on the basis of a mechanical series parallel model consisting of crystalline and amorphous phases. The origin of different E and α^app was speculated to be a stress concentration on the taut‐tie chain contained as a parallel crystalline component in the mechanical model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 444–453, 2003     

Determination of thermodynamic properties of macroporous glycidyl methacrylate‐based copolymers by inverse gas chromatography

Macroporous crosslinked poly(glycidyl methacrylate‐co‐ethylene glycol dimethacrylate) (PGME) was synthesized by suspension copolymerization and modified by ring‐opening reaction of the pendant epoxy groups with ethylene diamine (EDA). Inverse gas chromatography (IGC) at infinite dilution was applied to determine the thermodynamic interactions of PGME and modified copolymer, PGME‐en. The specific surface areas of the initial and modified copolymer samples were determined by the BET method, from low‐temperature nitrogen adsorption isotherms. The specific retention volumes, V, of 10 organic compounds of different chemical nature and polarity (nonpolar, donor, or acceptor) were determined in the temperature range 333–413 K. The weight fraction activity coefficients of test sorbates, , and Flory–Huggins interaction parameters, , were calculated and discussed in terms of interactions of sorbates with PGME and PGME‐en. Also, the partial molar free energy, , partial molar heat of mixing, , sorption molar free energy, ΔG, sorption enthalpy ΔH, and sorption entropy, ΔS, were calculated. Glass transitions in PGME and PGME‐en, determined from IGC data, were observed in the temperature range 373–393 K and 363–373 K, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2524–2533, 2005     

Evaluation of two‐center,three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

An algorithm for evaluation of two‐center, three‐electron integrals with the correlation factors of the type rr and rrr as well as four‐electron integrals with the correlation factors rrr and rrr in the Slater basis is presented. This problem has been solved here in elliptical coordinates, using the generalized and modified form of the Neumann expansion of the interelectronic distance function r for k ≥ ?1. Some numerical results are also included. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Crystallization studies of poly(trimethylene terephthalate) using thermal analysis and far‐infrared spectroscopy

Crystallization of poly(trimethylene terephthalate) (PTT) by annealing was examined using density measurement, differential scanning calorimetry, and far‐infrared spectroscopy (FIR). Crystallinity, measured by density, increased slowly up to the T_a of 185 °C and increases rapidly once T_a exceeds 185 °C. It was found that thermally induced crystallization is mainly temperature‐dependent above T_a = 185 °C and temperature‐ and time‐dependent below T_a = 60 °C. Two melting transitions, T and T, were observed for those samples annealed above 120 °C. No significant change in T was observed as a function of T_a while T showed strong dependency on T_a. Digital subtraction of the amorphous contribution from the semicrystalline FIR spectra provided characteristic spectra of amorphous and crystalline PTT. The bands at 373, 282, and 92 cm^?1 were assigned to the crystalline phase, while the bands at 525, 406, and 351 cm^?1 were attributed to the amorphous phase. It was shown that FIR spectroscopy can be used as a means to estimate the degree of crystallinity of PTT. The band ratio of 373 and 501 cm^?1 was plotted against crystallinity measured by density and reasonably good correlation was obtained. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1675–1682, 2007     

A fourier-transform infrared spectroscopic study of the surface hydrolysis of polythiazyl

The hydrolysis of (SN)_x, in air at room temperature and 90% relative humidity has been studied using the attenuated total reflectance (ATR) method. Decomposition gave rise to strong bands at 3210 and 3150 cm^–1 [v₃ and v₁ (NH)], 1420 cm^–1 (v_b NH), 1220 cm^–1 (S?O), 1089 and 610 cm^–1 [v₁ and v₃ (SO)]. For the first 3 days, the decay of the 808 and 690 cm^–1 bands of (SN)_x was first order, with a half life of about 30 h. The spectroscopic data were consistent with the rapid formation of ? SO₂? NH₂ and ?S?NH chain end groups with subsequent relatively slow hydrolysis to (NH₄)₂SO₄, sulfur, and fresh hydrolysable chain ends.