Phase separation in mixtures of poly(ethylene glycol monomethylether) and poly(propylene glycol) oligomers

Time-resolved light scattering was employed to investigate kinetics of phase separation in mixtures of poly (ethylene glycol monomethylether) (PEGE)/poly (propylene glycol) (PPG) oligomers. Phase diagrams for PEGE/PPG of varying molecular weights were established by means of cold point measurements. The oligomer mixtures reveal an upper critical solution temperature (UCST). Several temperature quench experiments were carried out with a 60/40 PEGE/PPG blend by rapidly quenching from a single phase (69°C) to two-phase temperatures (66–61°C) at 1°C intervals. As is typical for oligomer mixtures, the early stage of spinodal decomposition (SD) was not detected. The kinetics of phase decomposition was found to be dominated by the late stage of SD. Time-evolution of scattering intensity was analyzed in accordance with nonlinear and dynamical scaling theories. The time dependence of the peak intensity I_m and the corresponding peak wavenumber q_m was found to follow the power-law {I_m(t)? t^α, q_m(t)? t^-β} with the values of α = 3 ± 0.3 and β = 1 ± 0.2, which are very close to the values predicted by Siggia. This process has been attributed to a coarsening mechanism driven by surface tension. In the temporal scaling analysis, the structure function reveals university with time, suggesting self-similarity. Phase separation dynamics in 60/40 PEGE/PPG resembles the behavior predicted for off-critical mixtures.     

Spinodal decomposition and phase separation kinetics in nanoclay–biopolymer solutions

Intensity of light, I(q,t), scattered from homogeneous aqueous solutions, of nanoclay (Laponite) and protein (gelatin‐A), was studied to monitor the temporal and spatial evolution of the solution into a phase‐separated nanoclay–protein‐rich dense phase, when the sample temperature was quenched below spinodal temperature, T_s (=311 ± 3 K). The zeta potential data revealed that the dense phase comprised charge‐neutralized intermolecular complexes of nanoclay and protein chains of low surface charge. The early stage, t < 500 s, of phase separation could be described adequately through Cahn‐Hilliard theory of spinodal decomposition where the intensity grows exponentially, I(q, t) = I₀ exp.(2R(q)t). The wave vector, q dependence of the growth parameter, R(q) exhibited a maxima independent of time. Corresponding correlation length, 1/q_c = ξ_c was found to be ≈75 ± 5 nm independent of quench depth. In the intermediate regime, anomalous growth described by I(q, t) ～ t^α with α = 0.1 ± 0.02 independent of q was observed. Rheological studies established that there was a propensity of network structures inside the dense phase. Isochronal temperature sweep studies of the dense phase determined the melting temperature, T_m = 312 ± 4 K, which was comparable with the spinodal temperature. The stress‐diffusion coupling prevailing in the dense phase when analyzed in the Doi‐Onuki model yielded a viscoelastic correlation length, ξ_v determined from low‐frequency storage modulus, G ′₀ ≈ k_B T/ξ, which was ξ_v ≈ 35 ± 3 nm indicating 2ξ_v ≈ ξ_c. It is concluded that the early stage of phase separation in this system was sufficiently described by linear Cahn‐Hilliard theory, but the same was not true in the intermediate stage. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 555–565, 2010     

Kinetics of high-intensity electron-beam polymerization of a divinyl urethane

The kinetics of high-intensity electron beam-induced polymerization of di(2′-methacryloxyethyl)-4-m-phenylenediurethane during the network formation has been studied up to complete gelation and up to 56% conversion of unsaturation. From experimentally determined gel fractions, rate of disappearance of unsaturation, kinetic chain length, and intensity dependence, it is proposed that the polymerization takes place in a swollen network where the growing chains undergo unimolecular termination, and where gel-gel reaction is prohibited. The rate expression derived is: In [α(1 ? g)^0.545] = In α0 ? 2.51 k_ik_pt/k_t where α is the total unsaturation and g is the gel fraction. The value of k_p/k_t is found to be 2.1 and that of G_R, the free radical yield per 100 eV absorbed, to be 16; these high values are ascribed to the high viscosity of the polymerizing system.     

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). I. Kinetics of spinodal decomposition

The kinetics of phase separation via the spinodal decomposition of poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) from a delay time period to late stages were investigated with a light scattering technique. The standard procedure for identifying four stages of spinodal decomposition, based on the characteristics of concentration fluctuations, was clearly introduced with the light scattering method. The spinodal limits were divided into four stages: the delay time, the early stage, the intermediate stage, and the late stage. The validity of the linearized theory was reviewed because it was used as an indicator of the limit of the early stage of spinodal decomposition, which divided the delay time period from the early stage and the early stage from the intermediate stage. The linearized theory fit the experimental results very well after the delay time. The scaled structure function of the melt‐mixed blend was analyzed. The universality of the scale structure function, F(x) = S(q,t)q_m³(t) (where S is the structure function, x is equal to q/q_m, q is the scattering wave vector, q_m is the maximum wave vector, and t is the time in seconds), indicated the late stage of phase separation and divided the late stage from the intermediate stage. The simple normalized scaling function profile for the cluster region proposed by Furukawa described the experimental data very well, whereas the profile for deep quenching, which was recently suggested, showed some discrepancies. As a result of the phase separation, the processing of this blend may be able to be developed to provide the most suitable morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 871–885, 2004     

Light scattering and image analysis studies in polymer blends

Various optical techniques have been investigated as potential candidates for characterization of multiphase polymeric materials. The model calculations and corresponding experiments (time‐resolved light scattering and image analysis) have been conducted to investigate the kinetics of phase dissolution of polymer blends. The blends studied were polystyrene/poly (methyl methacrylate) mixtures with diblock copolymer composed of the corresponding homopolymers. The time evolution of the spinodal peak position q_m(t,T) and the scattered intensity maximum I_m(t,T) at q_m have been compared with theoretically predicted values of exponents for distinct time scales of the phase dissolution in various temperature regimes.     

Development and Evaluation of a Nanoporous Iron (Hydr)oxide Electrode for Phosphate Sensing

Nanoporous iron (hydr)oxide electrodes are evaluated as phosphate sensors using cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). The intensity of the reduction peak current (I_cp) of the ferrihydrite working electrode is tied to phosphate concentration at low pH; however, a hematite electrode combined with the use of EIS provided reliable sensing data at multiple pH values. Nanoporous hematite working electrodes produced an impedance phase component (θ) that shifts with increasing phosphate, and, at chosen frequencies, θ values were fitted for the range 1 nM to 0.1 mM phosphate at pH 4 and pH 7 in 5 mM NaClO₄.     

On the statistical independence of various column contributions to band broadening. Part 2: The non-equilibrium contribution predicted by a slow,statistically independent relaxation of concentrations

The mass balance changes of Said's so-called “stage” model, based on the movement of the mobile phase with mean velocity ū (=L/t _m), are synchronized by introduction of the relaxation time of Giddings, t_r=1/(k_m+k_s) where k_m and k_s are the general overall mass rate constants for sample transfer to and from the stationary phase, respectively. This makes the “stage” length equal to the true theoretical plate height, ΔL, related to the classical HETP contribution due to non-equilibrium, H_(α), according to the “discontinuous-ΔL” relation Here k = (t _ms ? t _m)/t _m is the central moment-based capacity ratio, L the column length, and σ²_(α) the second moment contribution from the non-equilibrium only. Correct application of the relaxation-time model to chromatography requires that the real sample concentration in the stationary phase at a given position and time, C_s,l,t, is in a continuous equilibrium with the real sample concentration in the mobile phase, C_m,l+ΔL/2,t at that time displaced down the column by a distance This leads to the classical HETP contribution obtained from various other continuous models, which implies that ΔL is a good estimation of the true theoretical plate height.     

The Impact of Surfactants on FeIII–TAML‐Catalyzed Oxidations by Peroxides: Accelerations,Decelerations, and Loss of Activity

Iron(III) complexes of tetraamidato macrocyclic ligands (TAMLs), [Fe{4‐XC₆H₃‐1,2‐(NCOCMe₂NCO)₂CR₂}(OH₂)]^?, 1 ( 1 a : X=H, R=Me; 1 b : X=COOH, R=Me); 1 c : X=CONH(CH₂)₂COOH, R=Me; 1 d : CONH(CH₂)₂NMe₂, R=Me; 1 e : X=CONH(CH₂)₂NMe₃⁺, R=Me; 1 f : X=H, R=F), have been tested as catalysts for the oxidative decolorization of Orange II and Sudan III dyes by hydrogen peroxide and tert‐butyl hydroperoxide in the presence of micelles that are neutral (Triton X‐100), positively charged (cetyltrimethylammonium bromide, CTAB), and negatively charged (sodium dodecyl sulfate, SDS). The previously reported mechanism of catalysis involves the formation of an oxidized intermediate from 1 and ROOH (k_I) followed by dye bleaching (k_II). The micellar effects on k_I and k_II have been separately studied and analyzed by using the Berezin pseudophase model of micellar catalysis. The largest micellar acceleration in terms of k_I occurs for the 1 a ? tBuOOH? CTAB system. At pH 9.0–10.5 the rate constant k_I increased by approximately five times with increasing CTAB concentration and then gradually decreased. There was no acceleration at higher pH, presumably owing to the deprotonation of the axial water ligand of 1 a in this pH range. The k_I value was only slightly affected by SDS (in the oxidation of Orange II), but was strongly decelerated by Triton X‐100. No oxidation of the water‐insoluble, hydrophobic dye Sudan III was observed in the presence of the SDS micelles. The k_II value was accelerated by cationic CTAB micelles when the hydrophobic primary oxidant tert‐butyl hydroperoxide was used. It is hypothesized that tBuOOH may affect the CTAB micelles and increase the binding of the oxidized catalysts. The tBuOOH? CTAB combination accelerated both of the catalysis steps k_I and k_II.     

Electrochemical formation of a low-dimensional phase on the boundary between the LaF<Subscript>3</Subscript>:Eu<Superscript>2+</Superscript> single crystal and the metal

The kinetics of the formation of a new phase at the interface between the LaF₃:Eu²⁺ single crystal and the (Sn, Bi, or Sb) metallic electrodes was studied using potentiostatic transient measurements and voltammetry with a linear variation of voltage. A comparison of the theoretical and experimental reduced transients that define two-dimensional instantaneous nucleation on a plot of I/I _m vs. t/t _m and three-dimensional growth of the instantaneous and progressive types of nucleation on a plot of I ²/I _m² vs. t/t _m showed that the model was not fully consistent with the experiment. The dependence of the stationary current logI _A(max) of the potentiostatic transients on 1/η during the formation of the intermediate phase on the boundaries of LaF₃:Eu²⁺|Sn and LaF₃:Eu²⁺|Bi was found to be linear, which corresponds to two-dimensional nucleation and growth of the new phase.     

Kinetics of the iodine atom catalyzed gas phase geometrical isomerization of diiodoethylene. Rotation about a single bond

The spectrophotometric determination of the rate of iodine atom catalyzed geometrical isomerization of diiodoethylene in the gas phase from 502.8 to 609.1°K leads to a rate constant for the bimolecular reaction between I and trans-diiodoethylene of log k_t?c(M^?1 sec^?1) = 8.85 ± 0.12 ? (11.01 ± 0.30)/θ. Estimates of the entropy and enthalpy change for the addition of I atoms to trans-diiodoethylene (process a.b) lead to log K_a.b(M^?1) = ?2.99 ? 4.0/θ, and thus to log k_c (sec^?1) = log k_t?c – log K_ab = 11.8 ?7.0/θ for the rate constant for rotation about the single bond in the adduct radical. The theory for calculation of the rotation rate constant is presented and it is shown that while the exact value depends on the barrier height, a value of 6.8 kcal/mole for this quantity leads to log k (sec^?1) = 11.8 ?6.7/θ. The activation energy points to a better value of the group contribution to heat of formation of the group C -(I)₂(H)(C) than one based on bond additivity.     

Investigation on LCST behavior of a new amorphous/crystalline polymer blend: Poly(n‐methyl methacrylimide)/poly(vinylidene fluoride)

The liquid–liquid phase‐separation (LLPS) behavior of poly(n‐methyl methacrylimide)/poly(vinylidene fluoride) (PMMI/PVDF) blend was studied by using small‐angle laser light scattering (SALLS) and phase contrast microscopy (PCM). The cloud point (T_c) of PMMI/PVDF blend was obtained using SALLS at the heating rate of 1 °C min^?1 and it was found that PMMI/PVDF exhibited a low critical solution temperature (LCST) behavior similar to that of PMMA/PVDF. Moreover, T_c of PMMI/PVDF is higher than its melting temperature (T_m) and a large temperature gap between T_c and T_m exists. At the early phase‐separation stage, the apparent diffusion coefficient (D_app) and the product (2Mk) of the molecules mobility coefficient (M) and the energy gradient coefficient (k) arising from contributions of composition gradient to the energy for PMMI/PVDF (50/50 wt) blend were calculated on the basis of linearized Cahn‐Hilliard‐Cook theory. The kinetic results showed that LLPS of PMMI/PVDF blends followed the spinodal decomposition (SD) mechanism. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1923–1931, 2008     

Simulation of phase‐separated structures of liquid‐crystalline polymer/flexible polymer blends

The phase‐separation kinetics of liquid‐crystalline polymer/flexible polymer blends was studied by the coupled time‐dependent Ginzberg–Landau equations for compositional order parameter ? and orientational order parameter S_ij. The computer simulations of phase‐separated structures of the blends were performed by means of the cell dynamical system in two dimensions. The compositional ordering processes of phase separation are demonstrated by the time evolution of ?. The influence of orientational ordering on compositional ordering is discussed. The small‐angle light scattering patterns are numerically reproduced by means of the optical Fourier transformation of spatial variation of the polarizability tensor α_ij, and the azimuthal dependence of the scattering intensity distribution is interpreted. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2915–2921, 2001     

Morphology and Dynamics of Phase‐Separating Fluids with Viscosity Asymmetry

Summary: The effects of viscosity asymmetry of the components on morphology and dynamics of phase‐separating AB fluids are investigated numerically based on a modified Model H. For critical mixtures, in the early stage of phase separation the co‐continuous morphology with droplets of A in B and B in A is observed. In the late stage of phase separation, the viscosity asymmetry leads to morphological change from co‐continuous structure to completely dispersed structure where the less viscous component forms droplet. The pathway of this transformation is accompanied by the breakdown of balance of volume fraction between droplets with different viscosity. Domain growth is characterized by a crossover from a faster growth at intermediate time under the influence of hydrodynamics to Lifshitz–Slyozov behavior at late times. For off‐critical mixture, viscosity asymmetry only plays an important role for domain growth in the intermediate stage of phase separation and the domain growth depends on whether the more viscous phase is dispersed or continuous, and the late stage of domain growth follows Lifshitz–Slyozov power law independent of which phase is dispersed.

Result for the evolution of phase‐separating domains for critical fluid mixtures = 0.5 for t = 1 500 with viscosity asymmetry: η_A = 0.8, η_B = 0.2. A‐rich regions and B‐rich regions are represented by white and black, respectively.     

Laser-induced kinetics: Arrhenius parameters for t-C4H9 + XI → i-C4H9X + I (X = H,D) and the Heat of Formation of the t-butyl radical

The metathesis reaction of DI with t-C₄H₉ generated by 351-nm photolysis of 2,2′-azoisopropane was studied in a low-pressure reactor (VLP? Knudsen cell) in the temperature range of 302–411 K. The data obeyed the following Arrhenius relation when combined with recent data by Rossi and Golden gathered by the same technique (t-C₄H₉ by thermal decomposition of 2,2′-azoisobutane): log k₂^D(M^?1s^?1) = 9.60 – 1.90/θ, where θ = 2.303RT kcal/mol for 302 K < T > 722 K. The metathesis reaction of HI with t-C₄H₉ was studied at 301 K and resulted in k₂^H(M^?1·s^?1) = (3.20 ± 0.62) × 10⁸. An analogous Arrhenius relation was calculated for the protiated system if the small primary isotope effect k₂^H/k₂^D was assumed to be √2 at 700 K. It was of the following form: log k₂^H(M^?1·s^?1) = 9.73 – 1.68/θ. Preliminary data of Bracey and Walsh indicate that earlier Arrhenius parameters determined for the reverse reaction are somewhat in error. Their value of log k₁(M^?1·s^?1) = 11.5 – 23.8/θ yields 7delta;H_f,300⁰(t-butyl) = 9.2 kcal/mol and S₃₀₀⁰(t-butyl) = 74.2 cal/mol7°K when taken in conjuction with this study.     

Viscoelastic phase separation in polyethersulfone modified bismaleimide resin

The polymerization-induced phase separation process of polyethersulfone (PES) modified bismaleimide resin, 4,4′-bismaleimidodiphenylmethane (BDM), was investigated by time resolved light scattering (TRLS) and scanning electronic microscopes (SEM). At the blends with 10 wt% and 12.5 wt% PES, a phase inversion structure was found by SEM. TRLS results displayed clearly the spinodal decomposition (SD) mechanism and the exponential decay procedure of scattering vector q_m, which followed Maxwell-type relaxation equation. The characteristic relaxation time τ for the blends can be described by the Williams-Landel-Ferry equation. It demonstrated experimentally that the phase separation behaviors in these PES modified bismaleimide blends were affected by viscoelastic effect.     

Compatibility and mesophase separation in blends of α-helical polyglutamates

Blends composed of the α-helical polymers, poly-L-glutamates [(? NHC^αHRC′O? )_n, R = ? CH₂CH₂COO? (CH₂)_m(C₆H₅] (Lm) and the corresponding D enantiomers (Dm), have been studied by x-ray diffraction and viscoelastic measurements. Binary blends of L2, D2, L3, and D3 are compatible and form isomorphous mixed crystals at all compositions, whereas other pairs, with the exception of L1/D1, are incompatible. The demixing process is described for a ternary system consisting of L1, D3, and a diluent chloroform at 40°C. The phase diagram comprises four regions, I, IA, A, and AA, with increasing polymer concentration; I: isotropic, A: anisotropic, IA: I–A biphasic, and AA: A–A biphasic. The IA biphasic gap is greater in the ternary system than in the binary ones. The high-molecular-weight component (D3) is partitioned into the A phase in the IA region. The AA separation originates from incompatibility of the polymers. The phase behavior is discussed on the basis of the Abe-Flory theory by incorporating the polymer-polymer interaction parameter.     

Comparative study of the phase behavior of liquid-crystalline components in closely related blends and copolyesters

Phase behavior of blends of a liquid-crystalline (LC) polymer with a non-LC polymer and of a series of copolymers containing mesogenic and nonmesogenic units was studied by thermal, optical, and dynamic mechanical methods. The polymers composing the blends and the copolymers had the same constituent monomers. The blends exhibited phase separation over the whole range of compositions studied as observed by DSC and dynamic mechanical analysis. Two glass transition temperatures (T_g) corresponding to the two components and independence of melting (T_m) and isotropization temperatures (T_i) to changes in composition were observed for the blends. The copolymers did not show phase separation over most of the composition range studied. Only one T_g corresponding to that of the major component could be detected for the copolymers, and the T_g was found to increase with an increase in the amount of nonmesogenic monomer in the copolymers. The difference in phase behavior was explained on the basis of the chemical environment of the constituent units in the blends and in copolymers. Phase inversion in the blends was observed by microscopy when the blends contained 60 mol% or more of the non-LC polymer.     

The carbon–hydrogen bond strength in dimethyl ether and some properties of iodomethyl methyl ether

The kinetics and mechanism of the reaction between iodine and dimethyl ether (DME) have been studied spectrophotometrically from 515–630°K over the pressure ranges, I₂ 3.8–18.9 torr and DME 39.6–592 torr in a static system. The rate-determining step is, where k₁ is given by log (k₁/M^?1 sec^?1) = 11.5 ± 0.3 – 23.2 ± 0.7/θ, with θ = 2.303RT in kcal/mole. The ratio k₂/k_?1, is given by log (k₂/k_?1) = ?0.05 ± 0.19 + (0.9 ± 0.45)/θ, whence the carbon-hydrogen bond dissociation energy, DH° (H? CH₂OCH₃) = 93.3 ± 1 kcal/mole. From this, ΔH°_f(CH₂OCH₃) = ?2.8 kcal and DH°(CH₃? OCH₂) = 9.1 kcal/mole. Some nmr and uv spectral features of iodomethyl ether are reported.     

Mass-spectrometric determination of product branching probabilities for the NH2 + NO2 reaction at temperatures between 300 and 990 K

The product branching ratio, α, for N₂O formation in the reaction of NH₂ with NO₂ has been studied by mass spectrometry at seven temperatures between 300 and 990 K. The value of α was determined by kinetic modeling of the absolute yield of N₂O. α was found to be 0.19 ± 0.02 without significant temperature dependence, assuming the total rate constant for NH₂ + NO₂ to be k_t = 1.8 × 10⁻¹² × T^0.11 exp (+ 597/T) cm³/molecule·s in the temperature range studied. The effect of k_t on α has been discussed. © 1996 John Wiley & Sons, Inc. Inc.     

Polymerization of vinyl chloride in the presence of precipitants. II.

The kinetics of the radiation-induced polymerization of vinyl chloride in the presence of precipitants has been successfully described by a one-parameter equation as follows, where ?₀ is initial monomer volume fraction, X is conversion, t is time, and k is reaction constant. The equation was confirmed for extensive conditions of temperatures and monomer concentrations in the case of polymerization in methanol. The degree of polymerization was related with the reaction constant k, initial monomer volume fraction ?₀, monomer chain transfer constant C_m, conversion X, and the initiation rate I as follows, The factors which determine the value of the reaction constant k were elucidated through measurements of the reaction constant k and the degree of polymerization DP _n.