Generalized Flory–Huggins model for heat‐of‐mixing and phase‐behavior calculations of polymer–polymer mixtures

An extended and generalized Flory–Huggins model for calculating the heats of mixing and predicting the phase stability and spinodal diagrams of binary polymer–polymer mixtures is presented. In this model, the interaction parameter is considered to be a function of both temperature and composition. It is qualitatively shown that the proposed model can calculate the heats‐of‐mixing curves containing exothermic, endothermic, and S‐shaped or sigmoidal types and predict the spinodals, including the upper and lower critical solution temperatures, and closed‐loop miscibility regions. Using experimental results of analog calorimetry for four polymer mixtures of polystyrene/poly(vinyl chloride) (PS/PVC), polycarbonate (PC)/poly(ethylene adipate) (PEA), polystyrene/poly(vinyl acetate) (PS/PVAc), and ethylene vinyl acetate copolymer (EVA Co)/chlorinated polyethylene (CPE), the capabilities of the proposed functionality for the interaction parameter was studied. It is shown that this function can be used satisfactorily for the heat‐of‐mixing calculations and phase‐behavior predictions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1328–1340, 2000     

Determination of polymer–polymer interaction parameters using inverse gas chromatography

A modified method is discussed that is based on Farooque and Deshpande's method to obtain polymer–polymer interaction parameters using inverse gas chromatography (IGC) data. In the Farooque and Deshpande method, the ratio of the difference of probe–polymer interaction parameters between two polymers and the probe volume [(χ₁₂ ? χ₁₃)/V₁] is used as the abscissa. In the modified method, the ratio [(?₂χ₁₂ + ?₃χ₁₃)/V₁] is used as the abscissa. Experimental data previously reported for a poly(?‐caprolactone)‐polyepichlorohydrin (PCL/PECH) blend and a poly(ethyl acrylate)‐poly(vinyl propionate) (PEA/PVPr) blend are analyzed. It is found that the slopes obtained by the new method had smaller deviations from the theoretical values than the Farooque and Deshpande method. The standard deviations of both slopes and intercepts obtained from the new method are also smaller. Using the new method, the polymer–polymer interaction parameters obtained from the intercept are negative numbers for the PCL/PECH system and very small positive numbers for PEA/PVPr. Explanations are given for the probe and concentration dependency of the polymer–polymer interaction parameters that are generally observed in IGC studies. A new method for selecting the best probe for calculating the interaction parameter is discussed. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 671–680, 2003     

IGC study of filler–filler and filler–rubber interactions in silica‐filled compounds

A modification of the existing methods for evaluating the dispersive and specific components of surface free energy (γ_d and γ_s, respectively) was made to investigate filler–rubber and filler–filler interactions by inverse gas chromatography. Four silicas as fillers and various probes that mimic elastomers were employed in this study. It was shown that the pretreatment of silicas with helium could increase γ_d and decrease γ_s. Modification of the silica surface with silane could enhance the dispersive interaction and weaken the specific interaction. The temperature dependence of the interfacial interaction was also investigated, and it was found that lower temperatures favored filler–rubber interactions and mixing efficiency. Tests on different sizes of agglomerates demonstrated the existence of a filler–rubber and filler–filler network. It was also found that γ_d played a role in agglomeration or filler–filler interaction. Our study showed that the larger the specific surface area was, the stronger the dispersive and specific interactions were. The effectiveness of various fillers and elastomer probes was also compared. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2517–2530, 2001     

Prediction of Flory–Huggins interaction parameters from intrinsic viscosities

Previous articles from this laboratory have described a model for predicting the second virial coefficient of a polymer solution given the polymer molecular weight and its intrinsic viscosity in the particular solvent. The same theory is used in this report to calculate values of the Flory–Huggins interaction parameter χ. The method is different in that χ is obtained through manipulation of simulated exprimental data in exactly the same way as in an actual experiment. Agreement between estimated χ values and those obtained at infinite dilutions from membrane osmometry or light scattering is within 2%, on the average. The model accounts for the molecular weight dependence of χ.     

Probe dependency of polymer‐plasticizer and polymer‐polymer interaction parameters in inverse gas chromatography

Inverse gas chromatography has been widely used to determine the Flory–Huggins parameter, χ, between a plasticizer and a polymer, or between two polymers. Many studies showed that interaction parameters may be probe dependent. In a recent study it was proposed that, when a specific interaction occurred between two polymers, the probes had less interaction with the polymers, leading to a lower solubility parameter for polymer blends than the volume average of the components. An equation was derived to relate the probe dependency to the deviation of solubility parameter of polymer mixtures. Here this approach is applied to plasticized poly(vinyl chloride) (PVC) and a copolymer, and to poly(vinylidene fluoride)–poly(ethyl methacrylate) blends. For a PVC and epoxidized oil system the relative deviation of specific retention volume showed two trends, with saturated hydrocarbons as one group, and polar and aromatic probes as another group. For the poly(vinylidene fluoride)/poly(ethyl methacrylate) system the plot of retention volume deviation versus solubility parameter of probes also showed separate trends for n‐alkanes, esters, and alcohols. But the plot of ?₂?₃RT(χ₂₃/V₂) versus solubility parameter had better linearity for the systems studied. The slope of this plot was used as an indicator for miscibility. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Miscibility enhancement on the poly(vinylchloride)/poly(methylmethacrylate) blend and characterization by inverse gas chromatography: The corrected polymer–polymer interaction parameters from the probes dependency

The miscibility of poly(vinyl chloride)/poly(methylmethacrylate) (PVC/PMMA) system was improved by introducing some pyrrolidone units into the main chains of PMMA. For that purpose, we have synthesized two copolymers of poly(methylmethacrylate‐co‐vinylpyrrolidone) (MMVP) through a radical polymerization and carried out a comparative study of PVC/MMVP blends by inverse gas chromatography (IGC) and differential scanning calorimetry (DSC) methods. The adequacy of seven n‐alkane probes has been tested to determine the thermodynamic parameters. The miscibility of the two systems has been proved by a single T_g for each blend. This observation was also confirmed by DSC analysis. To highlight the presence of interaction and its intensity between PVC and MMVP in the blends, the polymer–polymer interaction parameters have been evaluated by IGC trough which the influence of the solute has been resolved. The Schneider approach confirmed the miscibility of these systems as the K deviates positively from unity. The miscibility has been appeared highlighted from the positive difference in surface energy between the pure polymers and their blends. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Multiparameter solution model and evaluation of polymer–polymer miscibility using inverse gas chromatography data

Inverse gas chromatography (IGC) has been widely used to determine the Flory–Huggins parameters, χ, between solutes (probes) and polymers. This study correlated the Flory–Huggins parameter data using a multiparameter model, which included dispersion, polarity, acidity, and basicity components. The parameters of poly(ε‐caprolactone) (PCL) and polyepichlorohydrin (PECH) were calculated from IGC data using a series of probes. The parameters of the polymers were used to evaluate mutual miscibility between PCL and PECH. The results predicted miscibility in agreement with the conclusion of an IGC study using blends of PCL and PECH. A method to estimate the confidence interval of polymer parameters was proposed. The anomalous solubility parameter of polymer mixtures previously reported was also explained using this model. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Experimental testing of the polymer–filler gel formation theory. II.

In Part I of the present article predictions of the polymer–filler gel formation theory were tested experimentally using fine-particle silica in natural rubber (NR) and in styrene–butadiene rubber (SBR). Part II brings a more detailed experiment–theory comparison using carbon blacks differing in specific surface area and structure, graphitized blacks, fume silica, and surface-modified (hydrophobized) fume silica. In the region of low and medium filler concentration c, the c-dependence of the fraction G of polymer in polymer–filler gel, of the fraction B of total filler-bound polymer, of the fraction w_disp of solvent-dispersed filler particles were found to be correctly predicted by the theory. The effect of filler characteristics and of the method of its incorporation into the polymer on the values of the adjustable parameters of the theory (filler surface adsorptivity, D, and filler particles connectivity, f) was determined and is discussed. In the region of very high c increasing positive deviations of D from the low-c behavior were observed and an explanation for this effect is proposed. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 95–107, 1998     

Biodegradation dynamics of polymer–starch composites

The dynamics of starch biodegradation in polyethylene–starch (PE–S) composites was investigated by aerobic biodegradation methods and computer simulations, with the starch fraction p above and below the percolation threshold p_c. Two models for starch degradation were considered: (i) microbial invasion through the composite and (ii) macromolecular (enzyme) diffusion which results in the back‐diffusion of small molecules to the surface for further assimilation by microorganisms. The microbial‐invasion model was based on scanning electron microscopy (SEM) studies of PE–S composites that contained a 1–15‐micron distribution of starch particles. Following exposure to soil test conditions, micrographs of thin films clearly showed the colonization of microorganisms within channels of the matrix that were initially occupied by starch. The enzymatic diffusion was based on hydrolytic experiments of PE–S composites. Following exposure of a composite to a hydrolytic test condition, small molecules were produced. The starch accessed by microbes and enzymes was computed by simulating degradation of a monodisperse and polydisperse (starch grains of 1–10‐micron diameter) composite. Aerobic degradation studies in a biometer indicate that the starch accessibility. A follows a power‐law dependence with time A ∼ tⁿ, where the exponent n depends on the fractal dimension of the accessed starch clusters and pathways and approaches unity when p > p_c. Microbial invasion simulations indicate that the average power‐law exponent near p_c is approximately 0.5 and approaches 1.0 at p > pc, whereas the enzymatic diffusion simulations indicate that the average power‐law exponent near p_c is about 0.25 and approaches 0.5 at p > pc. The observed exponent for the aerobic degradation study suggests that for composites with a starch fraction less than and greater than p_c the starch is predominantly accessed by microbial invasion. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1643–1657, 2000     

Probe dependency of flory–huggins interaction parameters between solvents: Cases of hydrocarbons and isosteric derivatives

Inverse gas chromatography has been widely used to determine the Flory–Huggins parameter, χ, between two solvents. Many studies showed that interaction parameters were probe dependent. In recent studies, it was proposed that the interaction between two solvents may lead to different contact probability between solutes and solvent mixtures and create an apparent solubility parameter different from volume average rule. An equation was previously derived to relate the probe dependency to the deviation of solubility parameter from the volume average rule. By plotting ?₂?₃RT(χ₂₃/V₂) versus the solubility parameter of solutes, a linear trend could be observed with a negative slope for miscible mixtures. When there was an unfavorable interaction between two solvents, an opposite situation would be observed. In this study, mixtures of 19,24‐dioctadecyldotetracontane (C78) and its derivatives were tested. The solubility parameters of mixtures showed negative deviation from the volume average. The plots of ?₂?₃RT(χ₂₃/V₂) versus solubility parameter of solutes had positive slopes. For two derivatives the best estimated values of RT(χ₂₃/V₂) were negative in certain temperatures. Enthalpy–entropy compensation plot showed that these two derivatives have higher entropy of mixing. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2013     

Phase equilibria in SBR/polybutadiene elastomer blends: Application of Flory–Huggins theory

Blends of anionically-polymerized polybutadiene (BR) and styrene–butadiene copolymer (SBR) must be treated as mixtures of terpolymers and tetrapolymers, due to the presence of three different BR isomers: cis-1,4, trans-1,4, and vinyl-1,2. Moreover, in the absence of specific interactions or chemical reactions that strongly influence miscibility, structural characteristics of the component polymers, such as BR isomer content, SBR styrene content, monomer sequence distribution, molecular weight, and molecular weight distribution, are expected to have an increased role in determining the blend miscibility characteristics. Small angle neutron scattering (SANS) studies of SBR/BR blends have resulted in the computation of the monomer–monomer segmental interaction energetics via a Flory–Huggins treatment. This allows quantitative prediction of miscibility behavior as a function of polymer structure. We have used the Flory–Huggins chi parameters, describing the styrene/cis-1,4, styrene/trans-1,4, and cis-1,4/trans-1,4 segmental interactions, to identify certain blend combinations expected to exhibit phase transitions in an experimentally accessible temperature range. The appropriate polymers were synthesized, solution blended, and the blends analyzed via optical microscopy and thermal analysis. Our results show that the blend behavior, observed experimentally, is consistent with the calculated cloud point curves. © 1994 John Wiley & Sons, Inc.     

Slow release polymer–iodine tablets for disinfection of untreated surface water

Simple water treatment devices are designed to treat small amounts of drinking water for home use. This study was undertaken to develop an iodine‐releasing polymeric formulation and examine its potential as a domestic water purifier for untreated surface water. The antimicrobial tablet formulation was made from gum arabic (GA), poly(vinylalcohol) (PVA), ethyl cellulose (EC), and poly(vinylpyrrolidone)‐iodine (PVP‐I). The formulation consisted of a dispersible core tablet surrounded by a hydrophilic coating of EC and poly(ethylene glycol) mixture. These stable, non‐vaporizing, and water‐insoluble tablets slowly release iodine through diffusion over 48 h when suspended in water. The swelling behavior and release were observed to be the functions of excipient composition, iodine loading, and coating materials. Iodine release was determined by UV–VIS spectroscopy and volumetric titrations. The tablets were also assessed for antimicrobial activity against Escherichia coli, Staphylococcus aureus, Listeria monocytogenes Scott A, and Salmonella typhimurium. The disinfection efficiency of the developed tablets was compared with a commercial formulation (Potable Aqua®) as both contain iodine‐releasing active compounds and work on the antimicrobial property of released iodine. The difference between the two formulations is that water‐dispersible Potable Aqua® has a higher amount of free iodine quickly available in water thereby making it a fast‐action emergency water purifier, whereas the developed water‐insoluble polymer–iodine tablets act slowly and require 24 h to show the same disinfection efficacy with lower content of iodine in water. Overnight release of iodine in water from polymer–iodine tablets was effective in 99.9% reduction of an initial cell count of ～ 10⁷ colony forming units (cfu)/mL. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Thermal behavior,morphology, and the determination of the Flory–Huggins interaction parameter of polycarbonate–polystyrene blends

Blends of bisphenol-A polycarbonate (PC) and polystyrene (PS) prepared by screw extrusion and solution casting have been investigated with weight fractions of PC in the blends varying from 0.95 to 0.05. From the measured glass transition temperatures (T_g) and specific heat increments (ΔC_p) at the T_g, the polystyrene appears to dissolve more in the PC phase than does the PC in the PS phase. The blend appears to be near eqilibrium under extrusion conditions so that the polymer–polymer interaction parameter of PC/PS blends was calculated and found to be 0.038±0.004 for extruded blends at 250°C. Scanning electron microscopy supports the conclusion that the compatibility increases more in the region of PS-rich compositions than in the regions of PC-rich compositions of the PC/PS blends.     

Microwave hall mobility studies on polymer–metal oxide nanocomposites

Films of polymer metal oxide composites with poly(methyl methacrylate) and metallic powders (CuO, Ni, and brushed Fe₃O₄) were prepared with a spin‐casting method. Electric transport studies indicated that the compositions surpassed the percolation threshold limit. Alternating current (AC) conductivity studies confirmed a hopping mechanism with power‐law behavior in frequency. For the first time, the mobility values of the carriers in these films were measured by the contactless microwave Hall effect technique with a bimodal cavity operating at 14 GHz. In this technique, a circular bimodal cavity is used to measure the change in the transmission coefficient (proportional to the carrier mobility) due to the application of a static magnetic field perpendicular to the microwave electric fields. The mobility measurements indicated a decrease in mobility with increasing quantity of CuO and Ni and showed an increase in the carrier–lattice scattering, whereas the mobility increased with increasing Fe₃O₄ due to the negative magneto resistance. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Preparation,characterization, and improvement of hollow epoxy particle‐toughened vinyl ester composites for high‐end applications

Spherical hollow epoxy particles (HEPs) that can serve as advanced reinforcing fillers for vinyl ester thermosets were prepared using the water‐based emulsion method. The HEP fillers were incorporated into the vinyl ester matrices at different loading amounts, ranging from 0 to 9 wt %, to reinforce and toughen the vinyl ester composite. The optimum mechanical properties of the HEP‐toughened epoxy composite can be achieved by the addition of 5 wt % HEP filler into the vinyl ester matrices. The toughening and strengthening of the epoxy composites involved the interlocking of vinyl ester resins into the pore regions on the HEP fillers. The toughening and interlocking mechanisms of HEP‐toughened vinyl ester composites were also proposed and discussed. The addition of HEP fillers into vinyl ester matrices increased the glass transition temperature (T_g) and thermal stability of the composites. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Tribological properties of ethylene–propylene–diene rubber + polypropylene + thermal‐shock‐resistant ceramic composites

This work is part of a program on composites used in thermoelectric devices. Tribological properties of dynamic vulcanizate blends of polypropylene and ethylene‐propylene‐diene rubber filled with 5 wt% of microscale powder have been studied. The microscale thermal‐shock‐resistant ceramic filler contains α‐Al₂O₃, mullite (3Al₂O₃ · 2SiO₂ or 2Al₂O₃SiO₂), β‐spodumene glass‐ceramic and aluminium titanate. We found that our ceramic particles are abrasive; they cause strong abrasion of softer steel ball surfaces during dry sliding friction. To overcome the difficulty of particle dispersion and adhesion, the filler was modified through grafting using three types of organic molecules. Dry sliding friction was measured using four types of counter‐surfaces: tungsten carbide, Si₃N₂, 302 steel and 440 steel. Thermoplastic vulcanizate filled with neat ceramic powder shows the lowest friction compared to composites containing the same but surface‐treated powder. We introduce a ‘bump’ model to explain the tribological responses of our composites. ‘Naked’ or untreated ceramic particles protrude from the polymer surface and cause a decrease of the contact area compared to neat polymer. The ball partner surface has only a small contact area with the bumps. As contact surface area decreases, so does friction and the amount of heat generated during sliding friction testing. Chemical coupling of the ceramic to the matrix smoothens the bumps and increases the contact surface, giving a parallel increase in friction. Copyright © 2012 Society of Chemical Industry     

Effects of a Nd—Fe—B magnetic filler on the crystallization of poly(phenylene sulfide)

The crystallization of poly(phenylene sulfide) (PPS) in a polymer–magnetic Nd—Fe—B powder suspension was studied. Isothermal crystallization behavior was analyzed by way of differential scanning calorimetry, and the kinetics were described via the Avrami equation. The Avrami parameters and the crystallization times were strongly affected by both the particle size and the presence of a coupling agent coated on the filler particles. The small Nd—Fe—B particles exhibited long induction and half‐times, whereas the large particles tended to have short crystallization times. Particles ranging from 38 to 150 μ appeared to have similar crystallization times and to have no significant change in the value of Avrami index with melt crystallization temperature. As a result of these analyses, the dynamic mechanical properties were determined to correlate the fundamental polymer crystallization characteristics and the physical properties of the PPS binder. The enhancement of the wetting of the filler to the binder was promoted through the coupling agent, as confirmed by dynamic mechanical testing performed on the samples. The storage modulus typically decreased because of the presence of the uncoated small particles. Conversely, the loss modulus was enhanced because of the presence of the coated small particles in the PPS binder. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 1091–1102, 2002     

Evaluation of solubility parameters for nonvolatile branched hydrocarbons by inverse gas chromatography

Flory‐Huggins interaction parameters determined by inverse gas chromatographic (IGC) technique have been used for the estimation of solubility parameters of nonvolatile branched hydrocarbon solvents. A family of isosteric branched hydrocarbons consists of one apolar stationary phase, 19,24‐dioctadecyldotetracontane (C78), and four polar stationary solvents formed by replacing one of the ? CH₃ groups of C78 by ? OH (POH), ? CN (PCN), ? SH (PSH), ? CF₃ (MTF), and two other polar solvents formed by replacing four ? CH₃ groups of C78 with four ? CF₃ (TTF) and ? OCH₃ (TMO) are investigated. The three‐dimensional Hansen solubility parameters of the solvents have been estimated following the approaches of Voelkel and the method of Huang at five different temperatures. In the three components estimated by Voelkel method, the dispersion component is decreasing rapidly, whereas the polar, and hydrogen bonding components of the solubility parameters are increasing with temperature. In the components of solubility parameter estimated by Huang method, the dispersion and hydrogen bonding components are slowly decreasing with temperature, however, the polar components are almost constant with temperature. The components of solubility parameters for different solvents have been discussed in terms of solvent polarity. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008