Dissolution of rubbery and glassy polymers

A mathematical model is formulated for solvent dissolution of rubbery and glassy polymers. An exact solution to the problem is derived for the constant diffusivity case, and a weighted residual solution is developed for the case of a concentration-dependent diffusion coefficient. The solution is used to calculate concentration profiles, dissolution curves, dissolution half-times, and pseudointerface positions at various times. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2607–2614, 1998     

Integral sorption in rubbery polymers

Simple equations are derived that describe integral sorption and desorption experiments under conditions where moving boundary effects in polymer films and spheres can be large because of high solvent concentrations. General conclusions are formulated about the nature of sorption and desorption experiments for both rectangular and spherical geometries. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 171–180, 1998     

Molecular model of phenolic polymer dissolution in photolithography

The resolution of photolithographic processes has advanced to the point that difficulties, such as line‐edge roughness, associated with phenomena occurring at molecular length scales are becoming important. In order to control these phenomena, it is necessary to understand them. To that end, a numerical model has been used to simulate the dissolution of phenolic polymers in aqueous base. The simulation applies the Critical Ionization Model to a rectangular‐lattice representation of the polymer matrix. The model has been adapted to describe the dissolution process that is responsible for photoresist function. Both continuum and molecular versions of the model are presented. The Continuum Model yields dissolution profiles that approximate the contours of the calculated spatial variations in chemical blocking (blocking profile). An algorithm has been developed to connect individual cells to form polymer chains, and to fill the lattice in a way that produces a Gaussian chain length distribution. The model employs only a single adjustable parameter, the time‐step correction factor (assuming one can measure the probability of ionization once a site encounters the developer). The Molecular Model predicts a dissolution rate that decreases non‐linearly with respect to degree of chemical blocking, as is observed experimentally. Dissolution profiles can be generated with the Molecular Model based either on this calculated dependence of the dissolution rate on blocking fraction or from direct application of the model to a blocking profile. The probabilistic nature of the model introduces edge roughness of the same degree as that observed experimentally. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2103–2113, 1999     

Molecular mobility in rubbery composites: Effect of filler particle size

We have measured proton NMR T₂ relaxation spectra in Arco R45M OH-terminated poly-butadienes (PBs) cured with isophorone diisocyanate and filled with 65 wt % SiO₂ particles of each of six different average sizes. Identifying the short T₂ component with the gel, we find that the gel fraction is displaced from nominal NCO/OH stoichiometry, probably as a result of water adsorbed on filler particle surfaces. Near effective stoichiometry and in the presence of filler, molecular and segmental mobilities decrease, most strongly in specimens with the smallest filler particles. Comparison with parallel Monte Carlo simulations of the PB matrix geometry indicates that segmental mobility and sol migration decrease uniformly in a wide vicinity of the filler particles. Thus the rigidification of the matrix measured via NMR has a range of approximately 1-3 μm from nearby filler particle surfaces, representing the rms diffusion distance of the light components of the sol during the T₂ relaxation. © 1993 John Wiley & Sons, Inc.     

Transition of polymers from rubbery elastic state to fluid state

On increasing the temperature of a polymer, the transition of the polymer from a rubbery elastic state to a fluid state could occur. The transition temperature is termed the fluid temperature of the polymer, T _f, which has a direct relationship with the polymer molecular weight. As one of polymer parameters, T _f is as important as the glass transition temperature of a polymer, T _g. Moreover, special attention to T _f should be paid for polymer processing. In research on the transition of a polymer from a rubbery elastic state to a fluid state, the concept of T _f would be more reasonable and more effective than the concept of T _l,l because it is neglected in the concept of T _l,l in that the molecular weight of a polymer may affect the transition of the polymer. In this paper the discussion on the fluid temperature involves the characters of polymers, such as the deformation—temperature curve, the temperature range of the rubbery state and the shear viscosity of polymer melt. From the viewpoint of the cohesional state of polymers, the transition of a polymer from a rubbery elastic state to a fluid state responds to destruction and construction of the cohesional entanglement network in the polymer. The relaxing network of polymer melt would be worthy to be considered as an object of study. __________ Translated from Huaxue Tongbao (Chemistry), 2008,71(3) (in Chinese)     

Flocculation by very high molecular weight polymers

Polymer-induced flocculation in which the size of polymer molecules is much greater than that of colloidal particles is investigated. A dynamic analysis is conducted which takes the transient behaviors of the adsorption of particles to a polymer molecule and the particle-particle interactions into account. We show that the number of particles adsorbed to a polymer molecule follows approximately a binomial distribution. An approximate expression for the degree of flocculation of the system under consideration is presented.     

Interdiffusion of polymers across interfaces

Neutron Reflection (NR) and Dynamic Secondary Ion Mass Spectroscopy (DSIMS) experiments were conducted on symmetrically deuterated polystyrene triblock bilayers (HDH/DHD) which directly probed the interdiffusion dynamics of the chains during welding. The HDH chains had their centers deuterated 50%, the DHD chains had their ends deuterated (25% at each end) such that each chain contained approximately 50% D. During welding, anisotropic motion of the chains produces a time-dependent oscillation (ripple) in the H and D concentration at the interface, which bears the characteristic signature of the polymer dynamics. These oscillations were compared with those predicted by Rouse, polymer mode coupling (PMC), and reptation dynamics. The following conclusions can be made from this study. (a) During the interdiffusion of high molecular weight HDH/DHD pairs, higher mobility of the chain ends caused a concentration oscillation which increased to a maximum amplitude, and eventually vanished at times, t > τ_D. The amplitude, or excess enrichment found, was appreciably more than that predicted by Rouse and PMC simulations, and was only slightly less than that predicted from reptation simulations. (b) The oscillations were completely missing in the 30 and 50K HDH/DHD polymers, which are only weakly entangled. The lack of oscillations for the 30 and 50K pairs may be due to a combination of surface roughness and fluctuations of order 30 Å. (c) It was found that the position of the maximum in this ripple stayed at the interface during its growth. This is also consistent with reptation and has not been explained by other theories. (d) All dynamics models for linear polymers produce ripples, many of which are qualitatively similar to that predicted for reptation. However, each ripple bears the fingerprint of the dynamics in terms of its time-dependent shape, position, and magnitude, and the models are clearly distinguishable. Our results, in summary, support reptation as a candidate mechanism of interdiffusion at polymer(SINGLEBOND) polymer interfaces and its uniqueness is being further pursued. © 1996 John Wiley & Sons, Inc.     

Viscoelasticity of low molecular weight polystyrene. Separation of rubbery and glassy components

The complex shear modulus was measured for four low molecular‐weight polystyrenes (M_w = 10,500, 5970, 2630, and 1050) near and above the glass transition temperature. For the lowest molecular weight sample, the method of reduced variables, the time–temperature superposition principle, was applicable, while it was not applicable for the higher M samples. For these higher M samples, it was assumed that the complex modulus is composed of two components (R and G components). The R component was estimated by subtracting the G component, which was assumed to be the same as the modulus of the lowest molecular weight sample. The time–temperature superposition principle was applicable to each of the R and G components, and the shift factors were different from each other. The contribution of the R component to the total complex modulus decreased with decreasing M. Anomalous temperature dependence of the steady‐state compliance for low M polymers as Plazek reported could be attributed to difference in temperature dependence of the two components. The estimated complex modulus for the R component was in accord with that calculated by spring‐bead model theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 389–397, 1999     

Thermodynamic interactions in rubbery polymer/gas systems

The Flory–Huggins interaction parameters χ for 23 gases (He, Ne, Ar, Kr, Xe, H₂, N₂, O₂, N₂O, CO₂, CH₄, C₂H₄, C₂H₆, C₃H₆, C₃H₈, 1,3-C₄H₆, four C₄H₈'s, n-C₄H₁₀, iso-C₄H₁₀, and n-C₅H₁₂) in five rubbery polymers (1,2-polybutadiene (PB), poly(ethylene-co-vinyl acetate)) (EVAc), polyethylene (PE), polypropylene (PP), and poly(dimethyl siloxane) (PDMS) were determined from either literature data on Henry's law coefficient and partial molar volume or those on sorptive dilation for each polymer/gas system. Values of χ for the gases increased in the order of PDMS < PP ≡ PB < EVAc ≡ PE. Among the gases except He and H₂ whose χ values are not reliable, Ne and Xe have respectively the highest and the lowest values of χ for the polyolefins. The χ values of the hydrocarbons were compared together with previously reported χ values of n-alkanes C₃-C₁₀. The dependencies of χ upon concentration and temperature were discussed on the basis of the literature data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1049–1053, 1997     

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Effect of molecular weight in diketopyrrolopyrrole‐based polymers in transistor and photovoltaic applications

Uncovering the precise effect of the conjugated polymer chain length on the semiconducting properties in thin‐film devices is confounded by the step‐growth polymerization techniques typically used. Here, we use preparatory size exclusion chromatography to isolate fractions of two diketopyrrolopyrrole‐thiophene based co‐polymers with low molar‐mass dispersity, ?_M, and number average molecular weights up to 180 kDa. We find that the charge carrier mobility can vary over three orders of magnitude in the range from 9 to 70 kDa, while a factor of 3–4 increase in photovoltaic performance was noted over the same range. The effect of ?_M was found to be most drastic when the largest chains were mixed with the shortest. The study of the thin‐film morphology and crystallinity by GIWAXS give further insights into the origin of these effects. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2245–2253     

Unimodal molecular weight distribution of commercial polymers from viscoelastic data

This article presents a method that provides the molecular weight distribution (MWD) of polymeric material from rheological data. The technique has been developed to deal with linear polymers with a log‐normal molecular weight distribution. The rheological data must include the shear storage modulus, G′(ω), and the shear loss modulus, G″ (ω), ranging from the terminal zone to the rubberlike zone. It was not necessary to achieve the relaxation spectrums via the extremely unstable problem of inverting integral equations. The method has been tested with different polymers (polydimethylsiloxane, polyisoprene, random copolymer of ethylene and propylene, and polystyrene) and the calculated MWDs were in good agreement with experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1539–1546, 2000     

Fractional separation of polymers in nanochannels: Combined influence of wettability and structure

Trapping macromolecules in nanopits finds diverse applications in polymer separation, filtering biomolecules etc. However, tuning the locomotion of polymers in channels of nanoscopic dimensions is greatly restricted by the comparative advective and diffusive components of velocities. Using the polymer affinity toward the solvent and the wall, and the polymer structure, a mechanism is proposed to induce selective trapping of polymers. Similar to fractional distillation of hydrocarbons based on molecular weight, a technique of fractional segregation, depending on the channel wettability of polymeric chains at different depths in a pit that is located perpendicular to the flow is suggested. Depending on the properties of the polymeric chains and the surface chemistry, the segregation of the polymer at a particular level in the pit can be predicted. This behavior stems from the difference in polymer structure leading to a competition between wettability based enthalpic trapping and structure based entropic trapping. The results of this study suggest a novel way of separating biopolymers based on their structure without relying on the channel geometry. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2118–2125     

Full‐chain dynamics of entangled linear and star polymers

The full‐chain dynamics and the linear viscoelastic properties of monodisperse, entangled linear and star polymers are simulated consistently via an equilibrium stochastic algorithm, based on a recently proposed full‐chain reptation theory 1 that is able to treat self‐consistently mechanisms of chain reptation, chain‐length fluctuations, and constraint release. In particular, it is the first time that the full‐chain simulation for star polymers is performed without subjecting to the great simplifications usually made. To facilitate the study on linear viscoelasticity, we employ a constraint release mechanism that resembles the idea of tube dilation, in contrast to the one used earlier in simulating flows, where constraint release was performed in a fashion similar to double reptation. Predictions of the simulation are compared qualitatively and quantitatively with experiments, and excellent agreement is found for all investigated properties, which include the scaling laws for the zero‐shear‐rate viscosity and the steady‐state compliance as well as the stress relaxation and dynamic moduli, for both polymer systems. The simulation for linear polymers indicates that the full‐chain reptation theory considered is able to predict very well the rheology of monodisperse linear polymers under both linear viscoelastic and flow conditions. The simulation for star polymers, on the other hand, strongly implies that double reptation alone is insufficient, and other unexplored mechanisms that may further enhance stress relaxation of the tube segments near the star center seem crucial, in explaining the linear viscoelasticity of star polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 248–261, 2000     

Performance of SuSi: a method for generating atomistic models of amorphous polymers based on a random search of energy minima

The performance of a recently developed method to generate representative atomistic models of amorphous polymers has been investigated. This method, which is denoted SuSi, can be defined as a random generator of energy minima. The effects produced by different parameters used to define the size of the system and the characteristics of the generation algorithm have been examined. Calculations have been performed on poly(L,D-lactic) acid (rho = 1.25 g/cm3) and nylon 6 (rho = 1.084 g/cm(3)), which are important commercial polymers.     

Small molecule diffusion in a rubbery polymer near Tg: Effects of probe size,shape, and flexibility

A novel experimental approach involving fluorescence nonradiative energy transfer (NRET) is employed to study the Fickian diffusion of small molecules in rubbery poly(isobutyl methacrylate) (PiBMA) films near the glass transition, using a formalism that directly relates the small molecule translational diffusion coefficient, D, to changes in the normalized nonradiative energy transfer efficiency, E_N. Values of D for pyrene, 1,3-bis-(1-pyrene) propane (BPP), 1,3-bis-(1-pyrene) decane (BPD), 9,10-bis-phenyl ethynyl anthracene (BPEA), diphenyl Disperse Red 4 (DPDR4), and decacyclene in PiBMA are measured over temperatures ranging from approximately T_g to T_g + 25°C. Among these chromophores, significant differences in both the magnitude and temperature dependence of D are observed which are attributed to differences in molecule shape and flexibility, as well as molar volume. Other factors being equal, chromophore flexibility was shown both to increase the magnitude of D and to decrease its dependence on temperature, as does an increase in aspect ratio. For BPD, these effects are attributed to the ability of the flexible molecule to diffuse in a piecewise manner, requiring the cooperative mobility of fewer polymer chain segments than a rigid molecule of the same molar volume. For BPEA and DPDR4, this deviation from D being dominated by molar volume effects is attributed the to high aspect ratio of these elongated molecules. © 1996 John Wiley & Sons, Inc.     

Arm‐first synthesis of star polymers with polywedge arms using ring‐opening metathesis polymerization and bifunctional crosslinkers

This work presents a two‐step, one‐pot process to make star polymers with polywedge arms. In a one‐pot reaction, after the polywedge arms are synthesized, crosslinker species are added to the reaction, rapidly forming star polymers. Crosslinker species with different degrees of conformational freedom were designed and synthesized and their capacity to generate star polymers was evaluated. Mass conversions up to 92% and stars with up to 17 arms were synthesized with the most rigid crosslinker. The effects of arm molecular weight and molar ratio of crosslinker to arm on mass conversion and arms per star were explored further. Finally, the size‐molecular weight scaling relationship for polywedges with linear and star architectures was compared, corroborating theoretical results regarding star polymers with arms much larger than their core. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 732–740     

Synthesis and properties of carbazole‐layered polymers

New aromatic ring‐layered polymers consisting of carbazole as a layered aromatic group and xanthene as a scaffold were designed and synthesized via the Sonogashira–Hagihara coupling reaction. Their optical and electrochemical behaviors were investigated in detail; the results showed that these polymers could be used as hole‐transporting materials. Polymers with nitrobenzene moieties at the polymer chain ends quenched the emission from the layered carbazoles to the nitrobenzene termini; thus, the polymers acted as the molecular wire that transferred photoexcited energy and/or electrons to the polymer termini. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4279–4288, 2009     

Monte Carlo simulation of size exclusion chromatography for randomly branched and crosslinked polymers

The elution curves of size exclusion chromatography for nonlinear polymers formed through random branching and crosslinking of long polymer chains were simulated with a Monte Carlo method. We considered two types of measured molecular weight distributions (MWDs): (1) the MWD calibrated relative to standard linear polymers and (2) the MWD obtained with a light scattering (LS) photometer in which the weight‐average molecular weight of polymers within the elution volume is determined directly. The calibrated MWDs clearly underestimate the molecular weights for both randomly branched and crosslinked polymers, and this technique can be used to assess the degree of deviation from the true MWD. When the primary chains conform to the most probable distribution, the calibrated MWD can be estimated reasonably well with the Zimm–Stockmayer equation for the g factor with the help of the relationship between the average number of branch points per molecule and the degree of polymerization. However, the LS method gives good estimates of the true MWD for both randomly branched and crosslinked polymers, although the agreement is better for the branched ones. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2009–2018, 2000