Scaling and structural properties of a polymer in a simple solvent: A study based on integral equations

We present a statistical mechanical theory for polymer–solvent systems based on integral equations derived from the polymer Kirkwood hierarchy. Integral equations for pair monomer–monomer, monomer–solvent, and solvent–solvent correlation functions yield polymer–solvent distribution, chain conformation in three dimensions, and scaling properties associated with polymer swell and collapse in athermal, good, and poor solvents. Variation of polymer properties with solvent density and solvent quality is evaluated for chains having up to 100 bonds. In good solvents, the scaling exponent v has a constant value of about 0.61 at different solvent densities computed. For the athermal solvent case, the gyration radius and scaling exponent decrease with solvent density. In a poor solvent, the chain size scales as N^v with the value of the exponent being about 0.3, compared with the mean field value of ⅓. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3025–3033, 1998     

Sorption,diffusion, and permeation of ethylbenzene in poly(1‐trimethylsilyl‐1‐propyne)

The solubility, diffusivity, and permeability of ethylbenzene in poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) at 35, 45 and 55 °C were determined using kinetic gravimetric sorption and pure gas permeation methods. Ethylbenzene solubility in PTMSP was well described by the generalized dual‐mode model with χ = 0.39 ± 0.02, b = 15 ± 1, and C^′_H = 45 ± 4 cm³ (STP)/cm³ PTMSP at 35 °C. Ethylbenzene solubility increased with decreasing temperature; the enthalpy of sorption at infinite dilution was −40 ± 7 kJ/mol and was essentially equal to the enthalpy change upon condensation of pure ethylbenzene. The diffusion coefficient of ethylbenzene in PTMSP decreased with increasing concentration and decreasing temperature. Activation energies of diffusion were very low at infinite dilution and increased with increasing concentration to a maximum value of 50 ± 10 kJ/mol at the highest concentration explored. PTMSP permeability to ethylbenzene decreased with increasing concentration. The permeability estimated from solubility and diffusivity data obtained by kinetic gravimetric sorption was in good agreement with permeability determined from direct permeation experiments. Permeability after exposure to a high ethylbenzene partial pressure was significantly higher than that observed before the sample was exposed to a higher partial pressure of ethylbenzene. Nitrogen permeability coefficients were also determined from pure gas experiments. Nitrogen and ethylbenzene permeability coefficients increased with decreasing temperature, and infinite dilution activation energies of permeation for N₂ and ethylbenzene were −5.5 ± 0.5 kJ/mol and −74 ± 11 kJ/mol, respectively. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1078–1089, 2000     

Pulse radiolysis studies of poly(methyl methacrylate) containing pyrene

A pulse radiolysis study of poly(methyl methacrylate) in the presence of pyrene has been carried out in the temperature range 100–295 K. The concentration of pyrene was changed from 10⁻³ to 10⁻¹ mol dm⁻³. The absorption/emission spectra and kinetics of solute excited states and solute radical ions were investigated. It was found that pyrene excited states were formed as a result of their radical ion recombination in a time scale up to seconds. The decay of solute radical ions was influenced by photobleaching and can be described by a time-dependent rate constant. The activation energy of Py ions decay was temperature dependent and was equal to 35.7 and 1.2 kJ/mol for temperatures >T_γ and <T_γ, respectively, where T_γ ∼ 175 K represented the transition temperature responsible for γ-relaxation. The reaction mechanism was proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1209–1215, 1998     

Phase separation in poly(N‐isopropyl acrylamide)/water solutions. II. Salt effects on cloud‐point curves and gelation

The cloud‐point temperatures (T_clo's) of poly(N‐isopropyl acrylamide) (PNIPAM)/water solutions with NaCl, NaBr, or NaI were measured. All these salts reduced the T_clo's of PNIPAM/water solutions to different extents, in the following order: NaCl > NaBr > NaI. The higher the concentration of the added salt was, the more greatly T_clo dropped. A dynamic viscoelasticity investigation of the PNIPAM/water solutions with the salts indicated that during phase separation, the system changed from a homogeneous fluid into a physically crosslinked network, and the addition of salts also reduced the temperature at which this change began. The gelation temperature (T_gel) and the scaling exponent of the PNIPAM/water solutions with NaBr were obtained with dynamic scaling theory, and T_gel was found to be close to T_clo. That the addition of salts to the solution decreased T_clo and T_gel to the same extent further proved that the network structure was formed with the phase separation in the PNIPAM/water solutions. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 901–907, 2001     

Influences of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile solutions around the sol-gel threshold

Viscoelastic experiments were performed to study the influence of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile (PAN) solutions around the sol-gel threshold. The dynamic critical parameters around the sol-gel threshold were determined using dynamic rheometer. The sol-gel transition takes place at a critical gel temperature at which the scaling law of G′(ω) ∼ G″(ω) ∝ ωⁿ holds, allowing an accurate determination of the critical gel temperature by means of the frequency independence of the loss tangent. Although the gel points of PAN solutions increase with increasing H₂O content, the results show that the scaling exponent n at the gel point is found to be universal for all ternary PAN solutions, which is independent of temperature and H₂O content, indicating the similarity of the fractal structure in the critical PAN gels. The gelation of ternary PAN solutions induced by adding a nonsolvent and by decreasing the temperature is demonstrated to be a thermoreversible process, which implies that the PAN gels are physical gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2637–2643, 2008     

Kinetics of dispersion polymerization: Effect of medium composition

The effect of the medium composition (monomer and solvent) on the kinetics of dispersion polymerization of methyl methacrylate (MMA) was studied via reaction calorimetry. It was found that increasing the monomer concentration increased the reaction rate; the exponent of the dependency of the initial reaction rate on the MMA concentration was found to be 0.93. Narrow particle size distributions were achieved at the lower monomer concentrations (0.24–0.81 mol/L) and a minimum size (2.45 μm) was found at an intermediate concentration (0.44 mol/L). The average molecular weight of the PMMA increased and the molecular weight distribution broadened with increasing monomer concentration. During a dispersion polymerization, the MMA concentration was found to decrease linearly with conversion in both phases, whereas the ratio of concentrations in the particles and continuous phase ([M]_p/[M]_c) remained constant (0.47) with partitioning favoring the continuous phase. The average number of free radicals per particle in MMA dispersion polymerization was estimated to be high from the nucleation stage onward (>5000). The increasing rate during the first ～ 40% conversion was primarily caused by the increasing volume of the polymer particle phase. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3638–3647, 2008     

Graft copolymers prepared by ethoxylation of polyamide 12 and poly(ethylene-co-vinyl alcohol)

Graft copolymers consisting of polyamide 12 or poly(ethylene-co-vinyl alcohol) as backbone polymers and side chains of poly(ethylene oxide) have been synthesized. The amide and hydroxyl groups of the backbone polymers were used as initiation sites for the polymerization of ethylene oxide (EO). Potassium tert-butoxide was used for ionization of the active groups, and the polymerization of EO was carried out in dimethyl sulfoxide. The graft copolymers were characterized with respect to molecular weight and composition using elemental analysis, ¹H-NMR, gel permeation chromatography, and FTIR. The size of the side chains varied between 300 and 1000 g/mol. Thermal properties were examined by DSC. The graft copolymers showed increasing crystallinity and increasing melt temperature with increasing molecular weight of the side chains. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 803–811, 1998     

Diffusion of Nanoparticles in Semidilute Polymer Solutions: A Multiparticle Collision Dynamics Study

The diffusion of nanoparticles immersed in semidilute polymer solutions is investigated by a hybrid mesoscopic multiparticle collision dynamics method. Effects of polymer concentration and hydrodynamic interactions among polymer monomers are focused. Extensive simulations show that the dependence of diffusion coefficient D on the polymer concentration c agrees with Phillies equation D-exp (-αc^δ) with a scaling exponent δ≈0.97 which coincides with the experimental one in literature. For increasing nanoparticle size, the scaling prefactor α increases monotonically while the scaling exponent always keeps fixed. Moreover, we also study the diffusion of nanoparticle without hydrodynamic interactions and find that mobility of the nanoparticle slows down, and the scaling exponent is obviously different from the one in experiments, implying that hydrodynamic interactions play a crucial role in the diffusion of a nanoparticle in semidilute polymer solutions.     

Measurement of rotational diffusivity of rodlike molecules in amorphous polymer matrices by the dynamic kerr effect

Electrooptic (Kerr effect) relaxation experiments, designed to measure the rotational diffusivity of collagen (rodlike) molecules in aqueous poly(ethyleneoxide) (amorphous) semidilute solutions under various conditions have been performed. The experimental results have been compared with the predictions of a previously derived model giving the rotational diffusivity of dilute rods in semidilute amorphous polymer solutions as a function of rod length and amorphous polymer concentration. Excellent agreement is found between the predicted scaling D_r ～ ?L^?7 (D_r = rod rotational diffusivity, pi_p = polymer weight fraction, and L = rod length) and the experiments.     

Effects of physical aging on solubility,diffusivity, and permeability of propane and n-butane in poly(4-methyl-2-pentyne)

The effects of physical aging on the solubility, diffusivity, and permeability of propane and n-butane in a hydrocarbon-based disubstituted polyacetylene, poly(4-methyl-2-pentyne) (PMP), were studied. As the relative pressure of propane and n-butane increased, the solubility of both hydrocarbons increased. Like other glassy polymers, the sorption isotherms for propane and n-butane in all PMP films were concave to the relative pressure axis, indicating dual-mode sorption behavior. The diffusion of propane and n-butane in PMP followed typical Fickian diffusion in a plane sheet. The propane diffusivity in both the unaged and aged films increased with increasing concentration of propane sorbed in the film. The n-butane diffusivity in aged films also increased with increasing n-butane concentration. However, unaged films showed the opposite behavior: the diffusivity decreased with increasing n-butane concentration. These diffusion phenomena are a consequence of the interplay between thermodynamic and mobility factors. The permeabilities of propane and n-butane decreased monotonically with increasing penetrant concentration, similar to the behavior observed in other common glassy polymers. The relaxation of the nonequilibrium excess free volume in PMP films induced the decrease in both solubility and diffusivity. As a result, the permeability of propane and n-butane in PMP decreased upon physical aging. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2407–2418, 2004     

Rotational diffusivity of rodlike molecules in amorphous polymeric matrices

In this note, scaling laws for rotational diffusivity of dilute monodisperse rigid-rod molecules (guest rods) in semidilute amorphous polymer solutions (host molecules) are derived. The coillike matrix molecules are modeled as a collection of flexibly connected rigid subunits. This allows an analogy with the Doi-Edwards theory for monodisperse rigid rods in semidilute solutions to be used in the analysis. Very strong dependencies are predicted for the rotational diffusivity of the rods on host polymer volume fraction and rod length. In semidilute polymer solutions the coils dramatically hinder the rotational freedom of the rods for r² ? ψ_p^?1, r being the rod aspect ratio and ψ_p the polymer volume fraction.     

Scaling analysis of cotton cellulose/LiCl·DMAc solution using light scattering and rheological measurements

Semidilute solution of cotton lint (CC1) in 8 wt % LiCl/N,N‐dimethylacetamide was investigated using static light scattering (SLS) and rheological measurements. The reduced osmotic modulus estimated by SLS measurements for CC1 solutions are proportional to c^1.16 in the semidilute region. From the exponent of 1.16, de Gennes' scaling theory derives the relationship between radius of gyration, R_g, and molecular weight, M_w, of CC1 as R_g ∝ M^0.62 This corresponds to the Mark‐Houwink‐Sakurada exponent of 0.86. This exponent is very close to that estimated from scaling analysis of zero shear rate viscosity, that is 0.85. Apparent radius of gyration, R_g,app, estimated by SLS measurements for CC1 solutions are proportional to c^?0.5 in the semidilute region. R_g,app indicates the mesh size of polymer entanglement in the semidilute region. On the assumption of the Gaussian behavior of CC1 molecule in the semidilute region, the exponent of ?0.5 gives the relationship between the molar mass between entanglements, M_e, and c as following relationship: M_e ∝ c^?1. This agrees with the concentration dependence on plateau modulus estimated from the dynamic viscoelastic measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2155–2160, 2006     

Conformation of nonideal hyperbranched polymer in ABn (n = 2, 4) type polymerization

The conformation of hyperbranched polymers from one pot polymerization with AB_n (n = 2, 4) type monomers, applying the reactive 3D bond fluctuation lattice model, are systematically studied using scaling relation R ～ N^λ, where R is the radius of gyration or the hydrodynamic radius of a hyperbranched polymer with the degree of polymerization N. The exponent λ was calculated at various monomer concentrations and group conversions. When the concentration of monomers with the equal reactivity of B groups increases from 0.1 to 0.9, the exponents λ_g and λ_h (corresponding to the radius of gyration and hydrodynamic radius, respectively) are in the ranges of 0.51–0.37 and 0.41–0.34 at the full conversion of A groups. Especially, we find that λ_g decreases linearly with the reaction conversion increasing. The ratio of z‐average radius, R_gz/R_hz, ranges from 1.08 to 1.32 and indicates that hyperbranched polymer is soft macromolecule with penetrable structure. In the case of AB₂ type monomer with unequal reactivities, λ displays complicated dependence on the reaction conversion and the reactivity ratio. The results of our simulation are consistent with those of experiments and theories, and valuable in better understanding the fundamental properties of hyperbranched polymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 610–616, 2010     

(Diisopropylamido) bis (methylcyclopentadienyl) lanthanides as single-component initiators for polymerization of methyl methacrylate

It was first found that (diisopropylamido)bis(methylcyclopentadienyl)lanthanides (MeC₅H₄)₂LnN(i-Pr)₂(THF) (Ln = Yb ( 1 ), Er ( 2 ), Y ( 3 )) exhibit extremely high catalytic activity in the polymerization of methyl methacrylate. The reactions can be carried out over a quite broad range of polymerization temperatures from -78 to 40°C. The catalytic activity of the complexes increases with an increase of ionic radii of the metal elements, i.e. Y > Er > Yb. The results of GPC (gel permeation chromatography) indicate that the number-average molecular weights (M_n) of polymers obtained exceed 100 × 10³ and the molecular weight distribution (M_w/M_n) becomes broad with the increase of temperature. Furthermore highly syndiotactic PMMA (87.7%) can be obtained by lowering the reaction temperature to −78°C. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1593–1597, 1998     

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Polarized Raman scattering of concentrated solutions of poly(dimethyl siloxane) in benzene

Raman depolarization (ρ) measurements have been made over the temperature range 20 > T > 60°C for solutions of poly(dimethyl siloxane) (mol wt 7.7 × 10⁴ and 2.0 × 10⁴) for several concentrations up to 100%. The band studied was the highly polarized methyl stretch at 2907 cm^?1. Computer calculations of the probability p_t of a rotational isomer being trans allow the ρ values to be related to ΔG, the free energy of mixing. ΔG is plotted as a function of concentration and minima are observed at 60 ± 3% (mol wt = 7.7 × 10⁴) and 70 ± 3% (mol wt = 2 × 10⁴).     

Interactions between inorganic salts and polyacrylamide in aqueous solutions and gels

The swelling of poly(acrylamide) (PAAm) gels and the osmotic pressure of linear PAAm in aqueous solutions were predominantly affected by anion type and increased according to the lyotropic series ranking of sodium halide anions: F^? < (H₂O) < Cl^? < Br^? < I^?. The osmotic pressure of PAAm in all examined salt solutions followed the scaling theory, with an exponent of 2.3 ± 0.1. In solutions of a sodium halide series, the value of the pre‐exponential factor seemed to depend on salt concentration, anion radius, and the apparent “anionic‐portion radius” of the water molecule. This radius, extracted from the literature data, marks a transition point of the anion radius effect. Larger anions increase the osmotic pressure of PAAm more significantly as their concentration increases and vice versa. The effects of the anions on the osmotic pressure of PAAm are related to their preferential interactions with the polymer. Iodide, which increased the osmotic pressure of PAAm with respect to its value in pure water, seemed to preferentially adsorb onto the polymer with a binding constant of K_b = 9.7 ± 2.0 M^?1 determined by isothermal titration microcalorimetry. However, fluoride, which decreased the osmotic pressure, was preferentially repulsed. The mechanisms of attraction and repulsion were attributed to ion‐water‐polymer interactions and the solvent quality of the hydrated ions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 508–519, 2003     

Effect of dilution on a block copolymer in the complex phase window

The phase behavior of a styrene–isoprene (SI) diblock copolymer, with block molecular weights of 1.1 × 10⁴ and 2.1 × 10⁴ g/mol, respectively, is examined in the neutral solvent bis(2-ethylhexyl) phthalate (DOP) and the styrene-selective solvent di-n-butyl phthalate (DBP). DBP is a good solvent for PS, but is near a theta solvent for PI at approximately 90°C. Small-angle X-ray scattering (SAXS), rheology, and static birefringence are used to locate and identify order–order (OOT) and order–disorder transitions (ODT); all three techniques gave consistent results. The neat polymer adopts the gyroid (G) phase at low temperatures, with an OOT to hexagonally-packed cylinders (C) at 185°C, and the ODT at 238°C. Upon dilution with the neutral solvent DOP, the C window is diminished, until for a polymer concentration ϕ = 0.65, a direct G to disorder (D) ODT is observed. These results reflect increased stability of the disordered state, based on the different concentration scalings of the interaction parameter, χ, at the OOT and ODT. The OOT follows the dilution approximation, i.e., χ_OOT ∼ ϕ⁻¹, but the ODT is found to follow a stronger concentration dependence, i.e., χ_ODT ∼ ϕ^−1.4, similar to the scaling of ϕ^−1.6 found previously for lamellar SI diblocks in toluene and DOP. Addition of the selective solvent DBP produces dramatic changes in the phase behavior relative to DOP and the melt state; these include transitions to lamellar (L) and perforated layer (PL) structures. The observed phase sequences can be understood in terms of trajectories across the SI melt phase map (temperature vs. composition): addition of a neutral solvent or increasing temperature corresponds to a “vertical” trajectory, whereas adding a selective solvent amounts to a “horizontal” trajectory. When the solvent selectivity depends on temperature, as it does for the SI/DBP system, increasing temperature results in a diagonal trajectory. For both neutral and selective solvents the domain spacing, d*, scales with ϕ and χ as anticipated by self-consistent mean-field theory. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3101–3113, 1998     

Effect of pressure and temperature on chromophore reorientation in a side-chain nonlinear optical polymer

Second harmonic generation (SHG) was used to measure the temperature dependence of the reorientation activation volume of the side-chain copolymer poly(disperse red 1 methacrylate-co-methyl methacrylate) (DR1-MMA). The decay of the SHG signal from poled films of DR1-MMA was recorded at hydrostatic pressures up to 3060 atm and at different temperatures between 25°C below the glass transition temperature (T_g) to 35°C above it. The activation volume, ΔV^*, decreased with increasing temperature. The data suggests that the coupling between chromophore reorientation and the long-range motion of the polymer is stronger for the DR1-MMA side-chain system than in previously measured guest–host systems. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2793–2803, 1998     

High-precision gravimetric technique for determining the solubility and diffusivity of gases in polymers

An in situ gravimetric technique, employing an electrobalance, is described for determining the solubility and diffusivity of gases in polymers over extended ranges of temperature and pressure. Solubilities of CO₂ in polystyrene at 35°C were measured as a test case; the results are in excellent agreement with the literature values determined by the pressure decay method. Solubility and diffusivity results are also reported for PVC-CO₂ at 35°C and for PS-1,1,1,2-tetrafluoroethane at 30, 90, and 120°C. A comparison with other studies shows the in situ method to be more efficient and precise than the ones based on weighing the gas-saturated polymer under ambient conditions. The kinetics of gas sorption were analyzed in terms of two data reduction techniques to derive diffusion coefficients. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2025–2032, 1998