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     

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 the droplet formation at the early and intermediate stages of the spinodal decomposition in homopolymer blends

The kinetics of the droplet formation during the spinodal decomposition (SD) of the homopolymer blends has been studied by numerical integration of the Cahn‐Hilliard‐Cook equation. We have found that the droplet formation and growth occurs when the minority phase volume fraction, f_m , approaches the percolation threshold value, f_thr = 0.3 ± 0.01. The time for the formation of the disperse droplet morphology (coarsening time) depends only on the equilibrium minority phase volume fraction, f_m . f_m approaches its equilibrium value logarithmically at the late SD stages, and, therefore, the coarsening time decreases exponentially as the average volume fraction or the quench depth decrease. Since the temporal evolution of the total interfacial area does not depend on the quench conditions and blend morphology, the average droplet size and the droplet number density is determined by the coarsening time. Within the time scale studied, the droplet number density decreases with time as t ^{–0.63±0.03}; the average mean curvature decreases as t ^{–0.35±0.05}; the average Gaussian curvature decreases as t ^{–0.42±0.03}, and the average droplet compactness ˜V/S^3/2 where S is the surface area and V is the volume) approaches a spherical limit logarithmically with time. The droplets with larger area have lower compactness and in the low compactness limit their area is a parabolic function of compactness. The size and shape distribution functions have been also investigated.     

Modeling Termination Kinetics of Non‐Stationary Free‐Radical Polymerizations

Pulsed‐laser induced polymerization is modeled via an approach presented in a previous paper.^[1] An equation for the time dependence of free‐radical concentration is derived. It is shown that the termination rate coefficient may vary significantly as a function of time after applying the laser pulse despite of the fact that the change in monomer concentration during one experiment is negligible. For the limiting case of t ≫ c^–1 (k_pM)^–1, where c is a dimensionless chain‐transfer constant, k_p the propagation rate coefficient and M the monomer concentration, an analytical expression for k_t is derived. It is also shown that time‐resolved single pulse‐laser polymerization (SP–PLP) experiments can yield the parameters that allow the modeling of k_t in quasi‐stationary polymerization. The influence of inhibitors is also considered. The conditions are analyzed under which M (t) curves recorded at different extents of laser‐induced photo‐initiator decomposition intersect. It is shown that such type of behavior is associated with a chain‐length dependence of k_t.     

Morphology development and crystallization behavior of poly(ethylene terephthalate)/phenoxy blend

The morphological development and crystallization behavior of a poly(ethylene terephthalate)/poly(hydroxyl ether of bisphenol A) (phenoxy) blend were studied with time‐resolved light scattering, optical microscopy, differential scanning calorimetry, and small‐angle X‐ray scattering (SAXS). During annealing at 280 °C, liquid–liquid phase separation via spinodal decomposition proceeded in the melt‐extruded specimen. After the formation of a domain structure, the blend slowly underwent phase homogenization by the interchange reactions between the two polymers. Specimens annealed for various times (t_s) at 280 °C were subjected to a temperature drop and the effects of liquid‐phase changes on crystallization were then investigated. The shifts in the position of the cold‐crystallization peaks indicated that the crystallization rate is associated with the composition change of the separated phases as well as the change of the sequence distribution in polymer chains during annealing. The morphological parameters at the lamellar level were determined by a correlation function analysis on the SAXS data. The crystal thickness (l_c) increased with t_s, whereas the amorphous layer thickness (l_a) showed little dependence on t_s. Observation of a constant l_a value revealed that a large number of noncrystallizable species formed by the interchange reactions between the two polymers were excluded from the lamellar stacks and resided in the interfibrillar regions, interspherulitic regions, or both. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 223–232, 2008     

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.     

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.     

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

The so‐called “fundamental equation for gradient elution” has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(t_s)), t_s being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t?l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the here called “general equation for gradient elution”, where k is expressed as a function of φ(t,l). However, this approach is more complex. In this work, a method that facilitates the integration of the “general equation” is described, which allows an approximate analytical solution with the quadratic retention model, improving the predictions offered by the “linear solvent strength model.” It also offers direct information about the changes in the instantaneous modifier content and retention factor, and gives a meaning to the gradient retention factor.     

k-resonant toroidal polyhexes

A toroidal polyhex H(p, q, t) is a cubic bipartite graph embedded on the torus such that each face is a hexagon, which can be described by a string (p, q, t) of three integers (p≥ 1, q≥ 1, 0≤ t≤ p−1). A set of mutually disjoint hexagons of H(p, q, t) is called a resonant pattern if H(p, q, t) has a prefect matching M such that all haxgons in are M-alternating. A toroidal polyhex H(p, q, t) is k-resonant if any i (1 ≤ i ≤ k) mutually disjoint hexagons form a resonant pattern. In [16], Shiu, Lam and Zhang characterized 1, 2 and 3-resonant toroidal polyhexes H(p, q, t) for min(p, q)≥ 2. In this paper, we characterize k-resonant toroidal polyhexes H(p, 1, t). Furthermore, we show that a toroidal polyhex H(p, q, t) is k-resonant (k≥ 3) if and only if it is 3-resonant.      

Phase Behavior and Morphology of Poly(Methyl Methacrylate)/Poly(α‐Methyl Styrene‐co‐Acrylonitrile) Blends Under Quiescent and Shear Flow

The kinetics of spinodal decomposition (SD) for the binary blend poly(methyl methacrylate), PMMA, and Poly(α‐methylstyrene‐co‐acrylonitrile), PαMSAN, with 31 wt% AN content (LCST‐type phase diagram) has been thoroughly studied using a time‐resolved light scattering technique. The early stage SD was dominated by a diffusion process and can be well described within the framework of the linearized Cahn‐Hilliard theory. The spinodal temperature could be evaluated from the analysis of the early stage SD based on the Cahn theory. In addition, viscoelastic properties of this system have been systematically investigated at temperatures below and above the LCST phase diagram. The linear viscoelastic properties of the blends were found to be greatly changed by phase separation in the two‐phase regime. This change in the linear viscoelastic properties attributed to an additional contribution of concentration fluctuations to the material functions at the phase separation temperatures. The phase diagram of the blends was also estimated rheologically through the dynamic temperature ramps of G′, G″ and η*. Furthermore, the phase behavior and morphology of this system has been studied under different shear rates using simple shear apparatus and transmission electron microscopy (TEM), respectively.     

A complete characterization for <Emphasis Type="Italic">k</Emphasis>-resonant Klein-bottle polyhexes

A hexagonal tessellation K(p, q, t) on Klein bottle, a non-orientable surface with cross-cap number 2, is a finite-sized elemental benzenoid which can be produced from a p × q-parallelogram of hexagonal lattice with usual identifications of sides and with torsion t. Unlike torus, Klein bottle polyhex K(p, q, t) is not transitive except for some degenerated cases. We shall show, however, that K(p, q, t) does not depend on t. Accordingly, criteria for K(p, q, t) to be k-resonant for every positive integer k will be given. Moreover, we shall show that K(3, q, t) of 3-resonance are fully-benzenoid.      

UNMIXING KINETICS AND ITS MORPHOLOGY OF POLY ( ETHYLENE OXIDE) WITH POLYETHERSULPHONES BLENDS

Unmixing kinetics in a binary polymer mixture of polyethersulphones with poly (ethylene oxide) by spinodal decomposition has been investigated with time-resolved light scattering and microscope methods. The results showed that time evolution of scattered light intensity is of an exponential growth The maximum growth rate R(qm) of phase separation has been obtained. The experimental data did not satisfy the condition that the plot of R(q)/q~2 vs q~2 should be linear For unmixing system annealing at 30℃for three hours, its morphology manifested dish structure The experimental data of the Bragg spacing D_m can be correlated with a straight line which expresses the power-law relation, D_m=bl~α     

The forcing number of toroidal polyhexes

The forcing number, denoted by f(G), of a graph G with a perfect matching is the minimum number of independent edges that completely determine the perfect matching of G. In this paper, we consider the forcing number of a toroidal polyhex H(p,q,t) with a torsion t, a cubic graph embedded on torus with every face being a hexagon. We obtain that f(H(p,q,t)) ≥ min{p,q}, and equality holds for p ≤ q or p > q and t∈{ 0,p−q,p−q + 1,..., p−1}. In general, we show that f(H(p,q,t)) is equal to the side length of a maximum triangle on H(p,q,t). Based on this result, we design a linear algorithm to compute the forcing number of H(p,q,t).     

RUPTURING OF POLYMER FILMS WITH RUBBING-INDUCED SURFACE DEFECTS

It has been a long-standing question whether dewetting of polymer film from non-wettable substrate surfaceswherein the bicontinuous morphology never forms in the dewetting film is due to spinodal instability or heterogeneousnucleation. In this experiment, we use a simple method to make the distinction through introduction of topographical defectsof the films by rubbing the sample surface with a rayon cloth. Spinodal dewetting is identified for those films that dewet by acharateristic wavevector, q, independent of the density of rubbing-induced defects. Heterogeneous nucleation, on the otherhand, is identified for those with q increasing with increasing density of defects. Our result shows that PS films on oxidecoated silicon with thickness less than ≈ 13 nm are dominated by spinodal dewetting, but the thicker films are dominated bynucleation dewetting. We also confirm that spinodal dewetting does not necessarily lead to a bicontinuous morphology in thedewetting film, contrary to the classic theory of Cahn.     

Multiarm star block and multiarm star mixed‐block copolymers via azide‐alkyne click reaction

The synthesis of multiarm star block (and mixed‐block) copolymers are efficiently prepared by using Cu(I) catalyzed azide‐alkyne click reaction and the arm‐first approach. α‐Silyl protected alkyne polystyrene (α‐silyl‐alkyne‐PS) was prepared by ATRP of styrene (St) and used as macroinitiator in a crosslinking reaction with divinyl benzene to successfully give multiarm star homopolymer with alkyne periphery. Linear azide end‐functionalized poly(ethylene glycol) (PEG‐N₃) and poly (tert‐butyl acrylate) (PtBA‐N₃) were simply clicked with the multiarm star polymer described earlier to form star block or mixed‐block copolymers in N,N‐dimethyl formamide at room temperature for 24 h. Obtained multiarm star block and mixed‐block copolymers were identified by using ¹H NMR, GPC, triple detection‐GPC, atomic force microscopy, and dynamic light scattering measurements. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 99–108, 2010     

Conductivity,proton percolation,and gelation during the network growth in a flexible chain diepoxide and diamine mixture

The conductivity of a stoichiometric mixture of diglycidyl ether of 1,4‐butanediol and 1,6‐hexamethylene diamine has been studied during its polymerization at several temperatures where the ultimate product is a crosslinked gel. The decrease in the dc conductivity, σ₀, with the polymerization time, t, fits an equation for bond percolation, σ₀ ∼ [(t_gel‐t)/t_gel]^p, and yields a gelation time, t_gel which agrees with the t_gel determined from the viscosity and shear modulus measurements. It is proposed that as one covalent bond forms on chemical reaction, an indeterminable number of intermolecular H‐bonds in the structure vanish, and protonic conduction is disrupted. Thus, as the original H‐bond network gives way to a covalently bonded network, the mechanical rigidity increases, and protonic conductivity decreases. The gel point is reached when the increase in the number of covalent bonds brings the liquid's state up to its rigidity percolation threshold, and the decrease in the number of H‐bonds brings it down to its electrical percolation threshold. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 122–126, 2000     

Modeling the Effects of Primary Radicals in Free‐Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (k_tz /k_dz) √r_ink_t, where k_tz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, k_dz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, r_in is initiation rate, and k_t is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k_t,s r_in^1/2/k_p,s M r_t,l^1/2, where k_t,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, k_t,l is the termination rate coefficients of two large radicals, k_p,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k_t is deduced from coupled parameters such as k_t /k_p, the dependence of k_p on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.     

Dynamics of end-grafted polystyrene brushes in theta solvents

The dynamics of the concentration fluctuations in end-grafted polystyrene brushes in a theta solvent (cyclohexane) are probed by evanescent wave dynamic light scattering at different wavevectors q and temperatures. When the solvent quality changes from marginal to poor, the relaxation function C(q, t) exhibits strong effects as compared with the smooth variation of the brush density profile. From a single exponential above 50 °C, C(q, t) becomes a two-step decay function. The fast decay is still assigned to the cooperative diffusion albeit slower than in the good solvent regime whereas the slow nonexponential and nondiffusive process might relate to microsegragated and/or chain dynamics in the present polydisperse brush. The relaxation function of the present three brushes with different grafting density reveals similarities and disparities between wet brushes and semidilute polymer solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3590–3597, 2006     

Kinetics of spinodal decomposition in mixtures of low molecular weight liquid crystals and flexible polymers

In this paper, the time-dependent Ginzburg-Landau model for mixtures containing nematogens has been applied to mixtures of low molecular weight liquid crystals and flexible polymers. Dynamic equations for the time evolution of concentration and orientation fluctuations and the structure factors for these fluctuations are given. It is shown that the coupling between concentration and orientation fluctuations is absent in the isotropic spinodal region, thus the evolution of the structure factors for the concentration fluctuations falls into the Cahn-Hilliard classic category and it exhibits no maximum in the structure factors of orientation fluctuations. We should emphasize that, in the anisotropic spinodal region, both concentration and orientation structure factors possess a maximum but not coincide with each other and both are shifting to smaller wave numbers according to the scaling relation, q_max ˜ τ^−α, as time increases. The value of a closely correlates to the interfacial free-energy parameters.