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     

Intramolecular screening effects in nondilute polymer solutions: An equation‐of‐state approach

In a previous article, we presented a simple modification of the traditional Flory–Huggins theory that took intramolecular screening effects (or same chain contacts) into account. In this article, we present a natural extension of that work, in which free‐volume effects are also explained with an equation‐of‐state model. The predictions of the interaction parameter, χ, for several polymer–solvent systems are presented, over the entire concentration range, in θ solvents and good solvents. A geometric mean assumption is applied to the calculation of an exchange energy interaction term. The predictions of χ are successful to various degrees when internal pressures are used, whereas the use of solubility parameters in most cases produces fairly good agreement with experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2911–2922, 2003     

Copolymers of (±)2-ethylhexyl acrylate and 3-[3,3,3-trimethyl-1,1-bis (trimethylsiloxy) disiloxanyl] propyl methacrylate

Statistical copolymers of (±)2-ethylhexyl acrylate and 3-[3,3,3-trimethyl- 1,1-bis (trimethylsiloxy) disiloxanyl] propyl methacrylate were synthesized and the reactivity ratios and the Q and e values were calculated. The glass transition temperatures of the copolymers were in good agreement with the predictions of Fox's equation and Wood's formula. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 3571–3574, 1997     

Diffusion constants of polymers in mixed solvents

Dynamics of polymers in mixed solvents are investigated on the basis of linear response theory and mean field arguments. Particular attention is given to the coupling between polymer and fluid fluctuations. This coupling is enhanced by polymer–solvent interaction asymmetry and mixed solvent incompatibility. Cooperative and fluid diffusion constants are analyzed in terms of the interactions in the medium and some predictions for light scattering experiments are made. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3976–3980, 2004     

Macrocyclic oligoimides. I. Preparation of macrocyclic oligoetherimides via Kricheldorf substitution polymerization

Macrocyclic oligoetherimides were synthesized by means of Kricheldorf's nucleophilic aromatic substitution polycondensation. A solution containing equimolar quantities of bis(trimethylsilyl ether) of bisphenol and arylenebis(fluorophthalimide) was continuously added into a high boiling solvent containing CsF catalyst under a pseudo-high dilution condition. The resulting reaction mixture contained a high yield of cyclic oligomers which could be isolated by solvent extraction. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 759–767, 1997     

Photopolymerization of methyl methacrylate with the use of morpholine-chlorine charge transfer complex as the photoinitiator

Polymerization of methyl methacrylate (MMA) was kinetically studied under photo condition using near UV visible light at 40°C and employing morpholine (MOR)–chlorine (Cl₂) charge transfer (C-T) complex as the photoinitiator. The rate of polymerization (R_p) was dependent on morpholine/chlorine mole ratio; the 1 : 2 (MOR–Cl₂) C-T complex acted as the latent initiator complex, C, which underwent further complexation with the monomer molecules to give the actual initiator complex, I. Using 1 : 2 (MOR-Cl₂) C-T complex as the latent initiator, the initiator exponent evaluated for bulk photopolymerization of MMA was 0.071 and monomer exponent determined from studies of photopolymerization in benzene diluted system was 1.10. Benzoquinone behaved as a strong inhibitor and the polymers tested positive for the incorporation of chlorine atom end groups. Polymerization followed a radical mechanism. Kinetic nonideality as revealed by low (≪0.5) initiator exponent and a monomer exponent of greater than unity were explained in terms of primary radical termination effect. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1681–1687, 1997     

The effect of concentration,temperature, and molecular weight on the dynamics of rigid-rod molecules in semi-dilute solutions

The dynamics of rigid-rod-like molecules are studied using rheo-optical techniques. Measurements of flow birefringence as a function of shear rate are utilized to understand the scaling behavior of rotational diffusivity with respect to concentration and temperature. The concentration scaling exponent increases with increasing concentration and the scaling laws are valid in narrow concentration windows. The Doi-Edwards (DE) scaling law D_r ∼ c⁻², holds at very high concentrations (cL³ > 150). The concentration scaling exponent decreases dramatically with increasing temperature at concentrations, cL²d > 1. Scaling of rotational diffusivity, with respect to temperature and solvent viscosity in the semidilute regime, does not follow the predictions of DE theory (and related caging ideas). On the contrary, a model proposed by Fixman was found to explain both the temperature and concentration dependence of the rotational diffusivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 181–190, 1998     

Metastable liquid–liquid and solid–liquid phase boundaries in polymer–solvent–nonsolvent systems

In general liquid–liquid demixing processes are responsible for the porous morphology of membranes obtained by immersion precipitation. For rapidly crystallizing polymers, solid–liquid demixing processes also generate porous morphologies. In this study, the interference of both phase transitions has been analyzed theoretically using the Flory–Huggins theory for ternary polymer solutions. It is demonstrated that four main thermodynamic and kinetic parameters are important for the structure formation in solution: the thermodynamic driving force for crystallization, the ratio of the molar volumes of the solvent and the nonsolvent, the polymer–solvent interaction parameter, and the rate of crystallization of the polymer compared to the rate of solvent-nonsolvent exchange. An analysis of the relevance of each of these parameters for the membrane morphology is presented. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 763–770, 1997     

Scaling law for the radius of gyration of proteins and its dependence on hydrophobicity

The scaling law between the radius of gyration and the length of a polymer chain has long been an interesting topic since the Flory theory. In this article, we seek to derive a unified formula for the scaling exponent of proteins under different solvent conditions. The formula is obtained by considering the balance between the excluded volume effect and elastic interactions among monomers. Our results show that the scaling exponent is closely related to the fractal dimension of a protein's structure at the equilibrium state. Applying this formula to natural proteins yields a 2/5 law with fractal dimension 2 at the native state, which is in good agreement with other studies based on Protein Data Bank analysis. We also study the dependence of the scaling exponent on the hydrophobicity of a protein chain through a simple two‐letters HP model. The results provides a way to estimate the globular structure of a protein, and could be helpful for the investigation of the mechanisms of protein folding. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 207–214, 2009     

Viscoelastic diffusion

A constitutive equation is proposed for the viscoelastic diffusion flux, and this equation is used to calculate sorption curves for differential step‐change sorption experiments. The predictions of the theory are shown to be consistent with eight experimental observations that report a wide range of diffusional behaviors for polymer–solvent systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1529–1547, 2001     

Determining the density profile of confined polymer brushes with neutron reflectivity

Polymer molecules at solid or fluid interfaces have an enormous spectrum of applications in a wide variety of technologies as lubricants, adhesion modifiers, and protective surface coatings. Because polymer brushes have great potential to be used in such applications, there is a need to determine their structure and efficiency in reduced spaces. Using neutron reflectivity, we have directly quantified the density distribution of opposing polymer brushes under confinement in good solvent conditions under confinement. Our measurements show that the density profile in the overlap region between opposing polymer brushes flattens, consistent with predictions from molecular-dynamics simulations. In addition, a significant increase in the density at the anchoring surfaces due to the collapse of the brush layers was observed. This collapse of the brushes in restricted geometries suggests that high-density brushes do not interpenetrate significantly under good solvent conditions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3290–3301, 2004     

Nonuniversal transport behavior in heterogeneous high‐density polyethylene/graphite nanosheet composites

The direct‐current resistivity of high‐density polyethylene/graphite nanosheet composites above the percolation threshold has been measured and fitted to a power law, which gives a conductivity critical exponent (0.10 ± 0.01) and a percolation threshold (2.97 ± 0.03). These fitted parameters are in disagreement with universal theoretical predictions, and plausible explanations of the observed discrepancies are given. The sample‐to‐sample fluctuations in the relative resistivity seem to obey a power law. This fluctuation behavior, if interpreted in terms of correlation‐length fluctuations, yields a correlation‐length critical exponent, 0.52 ± 0.06, that is consistent with the mean‐field value of 1/2. Interpretations of these experimental results imply that nonuniversal transport behavior in disordered composites is caused by composites being in a nonuniversal scaling regime. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1846–1852, 2006     

Swelling equilibrium and sorption kinetics of urethane-modified bismaleimides elastomer

The swelling equilibrium and diffusion kinetics in various solvents of the maleimide-terminated polyurethanes (UBMIs) and of the triol and tetraol-crosslinked polyurethanes (PU) were studied. The polymer volume fraction of the UBMIs at swelling equilibrium is much higher than that of the tetraol-crosslinked PU networks for the same type of polyol used in the PU. It was explained by the high functionality of the UBMIs produced in the network structure. Furthermore, the molecular weight between crosslinks (M_c) has been calculated from the swelling model and the results exhibit good agreement with the proposed network structure. The early time sorption kinetic data were obtained to investigate the diffusion mechanism of the solvent in the networks. The solubility, diffusion coefficients, and permeability of the solvent in UBMI networks were found to be lower than in the multiol-crosslinked PU networks. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1747–1755, 1997     

Finite concentration inverse gas chromatography: Diffusion and partition measurements

Inverse gas chromatography (IGC) is a very fast, accurate, and reliable technique to measure diffusion coefficients. This technique however, has been limited to measurements in the infinite dilution region, i.e., in the region of negligible amount of solvent in the polymer. We have extended the scope of inverse gas chromatography to measure diffusion coefficients at finite concentrations of the solvent. This involves doping the carrier gas with a solvent of interest to achieve finite concentrations of solvent in the carrier gas and hence in the polymer. The carrier gas is passed through a saturator maintained at constant temperature to achieve this purpose. Diffusion coefficients for polyvinyl acetate–toluene, and polystyrene–toluene systems were determined at finite concentrations. The results were compared with the traditional gravimetric sorption and piezoelectric sorption measurements reported in the literature. The data are in excellent agreement with the values reported, correlate well with the Vrentas–Duda free volume theory, and can also be predicted from infinitely dilute data using the free volume theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1279–1290, 1997     

Chemical initiation of graft copolymerization of methyl methacrylate onto styrene–butadiene block copolymer

When a solution containing both styrene–butadiene block copolymer (SBS) and methyl methacrylate is treated with an initiator both homopolymerization of the methyl methacrylate and graft copolymerization of the methyl methacrylate onto the SBS occur. The amount of graft copolymerization depends upon the time and temperature of the reaction, the concentrations of all species, and the identity of the solvent and initiator. The combination of benzoyl peroxide in chloroform gives the highest graft yield and the reaction occurs by removal of an allylic hydrogen from the SBS by the initiator radical and subsequent addition of monomer units to that site; there is a significant solvent effect. Both AIBN and BPO function by the removal of an allylic hydrogen atom from SBS; BPO is able to effect this reaction relatively easily while AIBN can remove the hydrogen atom only with great difficulty and to a limited extent. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 965–974, 1997     

FTIR studies of conformational energies of poly(acrylic acid) in cast films

Fourier transform infrared (FTIR) spectroscopic measurements have been undertaken to estimate the conformational energies of poly(acrylic acid) (PAA) cast films in the temperature range of 40–130°C. The temperature dependence of the IR spectra in the C=O stretching region has been analyzed to yield the side-chain and backbone conformational energies. The estimated energies are close to those previously obtained by polarized Raman spectroscopic measurements for PAA solutions. Combining the FTIR value of conformational energy with the simplified rotational isomeric state (RIS) model proposed in the Raman analysis provides a persistence length in accordance with earlier SAXS experiments. The data also agree with the Gibbs-DiMarzio predictions, further substantiating the validity of the analysis. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 507–515, 1997     

Synthesis and characterization of optically active polyamides derived from carbohydrate-based monomers

The synthesis of three new stereoregular AB-type polyamides based on D -ribono-1,4-lactone, L -arabinose, and D -xylose has been carried out by the active ester polycondensation method. These polyamides were characterized by elemental analysis, IR and NMR spectroscopies, and powder X-ray diffraction. They displayed optical activity and had a pronounced affinity to water, although they were not soluble in this solvent. The polyamide obtained from D -ribono-1,4-lactone was highly crystalline and yielded films with spherulitic texture. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3645–3653, 1997     

Dispersion polymerization of styrene in alcohol media: Effect of initiator concentration,solvent polarity,and temperature on the rate of polymerization

The effects of three different variables (initiator concentration, polarity of the solvent and reaction temperature) on the rate of dispersion polymerization of styrene in alcohols have been investigated. It was found that the rate of polymerization increases with the initiator (AIBN) concentration at the 0% conversion level and becomes independent of it at higher monomer conversions. More significant was the result that the rate was also found to increase with solvent polarity. This is consistent with thermodynamic equilibrium calculations which account for the partitioning behavior of monomer and solvent in both the solution and the particle phases. The results further suggest the existence of two different kinetic regions: one at low conversions, where the reaction takes place primarily in the solution phase, and one at high conversions, where the reaction takes place primarily in the particle phase. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2907–2915, 1997     

Polyepichlorohydrine stabilized core shell microspheres by dispersion polymerization

Polystyrene microspheres ranging in diameter from 2 to 10 μm were prepared by dispersion polymerization in the presence of polyepichlorohydrine as the steric stabilizer precursor in alcoholic media. To clarify the effects of the solvent mixture composition, initiator concentration and steric stabilizer amount on the microsphere characteristics, including the molar mass parameters of the polymeric material, the microsphere size, and the steric stabilizer surface density, a three-factor full factorial design involving two levels of each of the factors and replicate experiments was employed. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 681–688, 1997     

Continuity of solvent quality in polymer solutions. Poor-solvent to Θ-solvent continuity in some polystyrene solutions

Critical temperatures for polystyrene/methyl acetate (PS/MA) and polystyrene/ethyl formate (PS/EF) solutions were measured at positive (PS/MA, PS/EF) and negative (PS/MA) pressure. The results confirm that solvent quality is sensitive to pressure; some solvents, designated Θ, at P_nominal ∼ 0, undergo a Θ-to-poor transition at negative pressure, and others, nominally designated “poor,” show a poor-to-Θ transition at positive pressure. Thus, any dichotomous division into sets of “poor” and “Θ” solvents is inaccurate, unless it accounts for the effects of pressure and other variables on solvent quality. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1251–1259, 1997