Modified Flory Rehner Equation Research Articles

Exploring the thermomechanical properties of peroxide/co‐agent assisted thermoplastic vulcanizates through temperature scanning stress relaxation measurements

AbstractTemperature scanning stress relaxation (TSSR) measurement of peroxide vulcanized polymer blends of polypropylene (PP) and ultrahigh molecular‐EPDM (UHM‐EPDM) rubber has been performed to study the thermomechanical behavior of thermoplastic vulcanizates (TPVs). Co‐agents play crucial roles in the enhancement of properties of TPVs. Different types of co‐agents (Triallyl cyanurate‐TAC; N, N‐m‐phenylene‐dimaleimide‐HVA2; zinc dimethacrylate‐ZDMA; and in‐situ formed zinc dimethacrylate‐ZMA) have been explored in this work. TSSR study shows that higher T50 and T90 values have been achieved in ZMA co‐agent assisted‐TPV. Higher TSSR‐index (RI) value was also found for the same co‐agent ZMA, indicating higher elastic behavior. TSSR result supports the mechanical and rheological properties, and it is found that the ZMA and ZDMA show higher mechanical strength. Cross‐linked‐density calculated by modified Flory–Rehner equation and the cross‐link‐density as obtained from TSSR method have been compared and the trend was found to be the same. Stress relaxation study shows the slow relaxation‐phenomena of the ZMA‐TPV with slowest relaxation‐time (θr) than the other TPVs, which correlates with superior material strength. Thermogravimetric analysis proves that there is a difference in degradation temperature of the blends at approximately 5–10°C. Ultrahigh molecular weight‐EPDM/PP based TPVs reveal superior thermomechanical and physico‐mechanical properties with ZMA and ZDMA co‐agent over TAC and HVA2. These ultrahigh molecular weight‐EPDM based TPVs can be used in automotive seals/strips, hoses, bellows, and 2 K‐molds for automotive applications.

New Materials Based on Ethylene Propylene DieneTerpolymerand Hemp Fibers Obtained by Green Reactive Processing.

The paper presents the obtaining of new green polymeric composites using a sustainable reactive processing method, namely electron beam irradiation. EPDM rubber mixtures were reinforced with different amounts of short hemp fibers, which were then irradiated at doses between 75 and 600 kGy. The samples were analyzed by determination of physical–mechanical properties, sol–gel analysis, crosslink density (using the well-known modified Flory–Rehner equation for tetra functional networks), determination of rubber–fiber interactions (using the Kraus equation), water uptake test and FTIR analysis. The obtained results indicate an improvement of the hardness, the tensile and tear strength as the quantity of hemp fibers increases. As the irradiation dose increases, there is an increase in the degree of crosslinking and the gel fraction. Analyzing the behavior of the irradiation samples using the Charlesby–Pinner equation, it is observed that all the samples tend to crosslink by irradiation, the share of degradation reactions being low. For these reasons, the new materials can be used in the food, pharmaceutical or medical field, because the obtained products are sterile and can be easily resterilized by irradiation. They have high elasticity values and can be used to make packaging, seals and other consumer goods.

New Elastomeric Materials Based on Natural Rubber Obtained by Electron Beam Irradiation for Food and Pharmaceutical Use.

The efficiency of polyfunctional monomers as cross-linking co-agents on the chemical properties of natural rubber vulcanized by electron beam irradiation was studied. The following polyfunctional monomers were used: trimethylolpropane-trimethacrylate, zinc-diacrylate, ethylene glycol dimethacrylate, triallylcyanurate and triallylisocyanurate. The electron beam treatment was done using irradiation doses in the range of 75 kGy–300 kGy. The gel fraction, crosslink density and effects of different aqueous solutions, by absorption tests, have been investigated as a function of polyfunctional monomers type and absorbed dose. The samples gel fraction and crosslink density were determined on the basis of equilibrium solvent-swelling measurements by applying the modified Flory–Rehner equation for tetra functional networks. The absorption tests were done in accordance with the SR ISI 1817:2015 using distilled water, acetic acid (10%), sodium hydroxide (1%), ethylic alcohol (96%), physiological serum (sodium chloride 0.9%) and glucose (glucose monohydrate 10%). The samples structure and morphology were investigated by Fourier Transform Infrared Spectroscopy and Scanning Electron Microscopy techniques.

Quantitative exploration of the swelling response for carbon black filled hydrogenated nitrile rubber with three-dimensional solubility parameters

Equilibrium swelling data with a range of solvents for non-filled cured rubber samples were used to determine Hansen three-dimensional solubility parameters (HSPs) of seven HNBR grades with nominal acrylonitrile contents from 21 to 49 % using the HSPiP computer program. The results showed that the increase of acrylonitrile contents for HNBR grades led to increase of polar component (δ p) and hydrogen bonding component (δ h), but with little changes of dispersion component (δ d). By using the so far obtained HSPs it is possible to explain and predict the swelling behaviors of the fully formulated HNBR-based vulcanizates in industrial oils (IRM 903 was selected for testing), in a reference bio-fuel (Fuel C was selected for testing) and in bio-diesel (FAME was selected for testing). In these liquids, the volume swellings decreased with increasing of Ra values (calculated by HSPs), and to a certain extent, can be calculated with a modified Flory–Rehner equation by assuming that fillers would not swell in question.

Polymeric composites based on natural rubber and hemp fibers

The purpose of this work is to present the results of preparing a polymeric composite with enhanced properties based on natural rubber and hemp. Amounts of 10 and 20 phr hemp were used to obtain the composites. The samples have been processed by sulfur vulcanization and characterized by several methods. The mechanical characteristics, gel fraction, cross-link density, rubber-fiber interactions and water uptake have been investigated depending on the hemp content. Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM) techniques were also employed for characterization. The values of hardness, tensile strength and tearing strength have increased with the fiber content increasing due to the interaction between the fibers and natural rubber. Also, good adhesion between hemp fibers and rubber matrix was observed in SEM micrographs. The gel fraction value was over 95 % for all composites and increased with the increasing of hemp content. The cross-link density was determined on the basis of equilibrium solvent-swelling measurements applying the modified Flory–Rehner equation. It was observed that cross-linking density of composites increased slightly with the increase of amount of hemp but still was lower than that of the natural rubber without hemp. The extent of interaction between rubber and fiber was determined using the Kraus equation. Results of water absorption tests showed that water uptake increased with the increase of fiber content and temperature. The physical and chemical investigations have shown the reinforcing effect of hemp on sulfur vulcanized natural rubber, as well.

Tailoring thermoresponsive nanostructured poly(N-isopropylacrylamide) hydrogels made with poly(acrylamide) nanoparticles

The thermoresponsive behavior and mechanical properties of nanostructured hydrogels, which consist of poly(acrylamide) nanoparticles embedded in a cross-linked poly(N-isopropylacrylamide) hydrogel matrix, are reported here. Nanostructured hydrogels exhibit a tuned volume phase transition temperature (TVPT), which varies with nanoparticle content in the range from 32 up to 39–40 °C. Moreover, larger equilibrium water uptake, faster swelling and de-swelling rates, and larger equilibrium swelling at 25 °C were obtained with nanostructured hydrogels compared with those of conventional ones. Elastic and Young’s moduli were larger than those of conventional hydrogels at similar swelling ratios. The tuned TVPT and the de-swelling rate were predicted with a modified Flory–Rehner equation coupled with a mixing rule that considers the contribution of both polymers. These behaviors are explained by a combination of hydrophilic/hydrophobic interactions and by the controlled inhomogeneities (nanoparticles) introduced by the method of synthesis.

Thermo‐ and pH‐induced phase transitions and network parameters of poly(N‐isopropylacrylamide‐ co‐2‐acrylamido‐2‐methyl‐propanosulfonic acid) hydrogels

AbstractDual temperature‐ and pH‐sensitive hydrogels composed of N‐isopropylacrylamide (NIPAM) and 2‐acrylamido‐2‐methyl‐propanosulfonic acid (AMPS) were prepared by free‐radical crosslinking copolymerization in aqueous solution at 22 °C. The mole percent of AMPS in the comonomer feed was varied between 0.0 and 7.5, while the crosslinker ratio was fixed at 5.0/100. The effect of AMPS content on thermo‐ and pH‐ induced phase transitions as well as equilibrium swelling/deswelling, interior morphology and network structure was investigated. The volume phase transition temperature (VPT‐T) was determined by both swelling/deswelling measurements and differential scanning calorimetry (DSC) technique. In addition, the volume phase transition pH (VPT‐pH) was detected from the derivative of the curves of the swelling ratio (dQv/dpH) versus pH. The polymer‐solvent interaction parameter (χ) and the average molecular mass between crosslinks ($\overline M_{\rm c}$) of hydrogels were calculated from swelling ratios in buffer solutions at various pHs. The enthalpy (ΔH) and entropy (ΔS) changes appearing in the χ parameter of hydrogels were also determined by using the modified Flory–Rehner equation. The negative values for ΔH and ΔS indicated that the hydrogels had a negative temperature‐sensitive property in water, that is, swelling at a lower temperature and shrinking at a higher temperature. It was observed that the experimental swelling data of hydrogels at different temperature agreed with the modified Flory‐Rehner approach based on the affine network model. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1713–1724, 2008

Swelling and network parameters of pH‐sensitive poly(acrylamide‐co‐acrylic acid) hydrogels

AbstractPoly(acrylamide‐co‐acrylic acid) [P(AAm‐co‐AAc)] hydrogels were synthesized by the free‐radical crosslinking copolymerization of acrylamide (AAm) monomer at fixed amount, but at changing amount of acrylic acid (AAc) as the ionic comonomer in water. The swelling behavior of the hydrogels thus obtained was analyzed in buffer solutions at various pHs. The polymer‐solvent interaction parameter (χ) and the average molecular mass between crosslinks (Mc) of the hydrogels were calculated from swelling studies in buffer solutions at various pHs and were related to the AAc content. The results indicated that the swelling behavior of the hydrogels at different pHs agreed with the modified Flory–Rehner equation based on the affine network model and the ideal Donnan theory. In addition, from differential curves of dOv/dpH versus pH, the volume phase transition pH (VPT‐pH) was found to be 4.33 ± 0.05, independent of the AAc content in the hydrogel. Scanning electron microscope (SEM) was used to identify the morphological changes in the hydrogel as the concentration of AAc increased. In water at 22°C, an increase of the AAc content further increased the response rate of the hydrogels because of simultaneous increase of both the porosity and hydrophilicity of the network. In buffer solution with a pH increase from 9.0 to 2.0 at 22°C, the hydrogels with more AAc also exhibited a more rapid deswelling rate than that of the hydrogels with less AAc. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007

Synthesis and network structure of ionic poly( N, N-dimethylacrylamide-co-acrylamide) hydrogels: Comparison of swelling degree with theory

At four different charge densities, ionic hydrogels based on N, N-dimethylacrylamide (DMAAm), acrylamide (AAm), and itaconic acid (IA) were synthesized by free-radical cross-linking copolymerization in water with N, N-methylenebis(acrylamide) (BAAm) as the cross-linker, ammonium persulfate (APS) as the initiator, and N, N, N′, N′-tetramethylenediamine (TEMED) as the activator. The swelling behaviors of these hydrogels were analyzed in buffer solutions at various pH. It was observed that the swelling behavior of cross-linked ionic poly( N, N-dimethylacrylamide-co-acrylamide) [P(DMAAm-co-AAm)] hydrogels at different pHs agreed with the modified Flory–Rehner equation based both on the phantom network and affine network models and the ideal Donnan theory. In addition, the kinetics of swelling of the hydrogels was studied in pH 2, 5 and 9 buffer solutions. The swelling curves exhibited the characteristic features of transport process, apparently the Fickian diffusion of fast rates.

PH-dependent swelling behavior and network parametes of ionic poly(N-t-butylacrylamide-co-acrylamide) hydrogels

Ionic poly(N-t-butylacrylamide-co-acrylamide) [P(TBA-co-AAm)] hydrogels were synthesized by the free-radical crosslinking copolymerization of N-t-butylacrylamide and acrylamide monomers in fixed amounts and the maleic acid (MA) comonomer in methanol in different amounts with N,N-methylene bis(acrylamide) as the crosslinker, ammonium persulfate as the initiator, and N,N,N′,N′-tetramethylenediamine as the activator. The swelling behavior of these hydrogels was analyzed in buffer solutions at various pHs. The polymer–solvent interaction parameter (χ) and the average molecular weight between crosslinks of the ionic P(TBA-co-AAm) hydrogels were calculated from swelling studies in buffer solutions at various pHs and were related to the MA content. The results indicated that the swelling behavior of the ionic P(TBA-co-AAm) hydrogels at different pHs agreed with the modified Flory–Rehner equation based on the affine network model and the ideal Donnan theory. The enthalpy (ΔH) and entropy (ΔS) changes appearing in the χ parameter for the hydrogels were also determined with the modified Flory–Rehner equation. The negative values for ΔH and ΔS indicated that the hydrogels had a negative temperature-sensitive property in water, that is, swelling at a lower temperature and shrinking at a higher temperature. The experimental swelling data of the hydrogels at different temperatures agreed with the modified Flory–Rehner approach based on the affine network model, which ensured that the sensitive dependence of the χ parameter on both the temperature and polymer concentration was taken into account. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 1624–1630, 2006

PH‐responsive ionic poly(N,N‐diethylaminoethyl methacrylate‐co‐N‐vinyl‐2‐pyrrolidone) hydrogels: Synthesis and swelling properties

AbstractA series of an ionic hydrogels composed of N,N‐diethylaminoethyl methacrylamide (DEAEMA), N‐vinyl‐2‐pyrrolidone (VP), and itaconic acid were synthesized by free‐radical cross‐linking copolymerization in water–ethanol mixture by using N,N‐methylenebis(acrylamide) as the cross‐linker, ammonium persulfate as the initiator, and N,N,N′,N′‐tetramethylenediamine as the activator. The swelling behaviors of these hydrogels were analyzed in buffer solutions at various pH. It was observed that the swelling behavior of cross‐linked ionic poly(N,N‐diethylaminoethyl methacrylamide‐co‐N‐vinyl‐2‐pyrrolidone) [P(DEAEMA/VP)] hydrogels at different pH agreed with the modified Flory–Rehner equation based on the affine network model and the ideal Donnan theory. The swelling process in buffer solutions at various pH was found to be Fickian‐type diffusion. The pH‐reversibility and on–off switching properties of the P(DEAEMA/VP) hydrogels may be considered as good candidate to design novel drug‐delivery system. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2819–2828, 2005

パーオキサイド架橋ＥＰＤＭの構造と動的特性に関する研究 第４報 ハーンエコー法によるイオウ架橋ＥＰＤＭの構造解析

Sulfur-crosslinked EPDMs were examined by 1H pulsed NMR. Spin-spin relaxation time (T2) was measured by Hahn echo method. The decay curve was resolved into two components, T2n and T2nn, which were arising from network molecules and non-network molecules, respectively. For unfilled EPDMs prepared at varying sulfur content, the higher order structures analyzed by Hahn echo method were almost the same as those analyzed for peroxide-crosslinked EPDMs. The reciprocal of Ten measured at 150°C for unfilled EPDMs increased linearly with increase in apparent crosslinking density (νs) values determined by modified Flory-Rehner equation. For EPDMs filled with carbon black (CB), the crosslinking density of rubber phase (νR) was calculated from the relationship between νs and 1/T2n for unfilled EPDMs. The crosslinking density related to CB (νF) was obtained from the difference between the νs and νR. The νF values showed good correlation with the tensile stress at 100% elongation, independent of the kinds of cure agents.

Biodegradation of chemically modified gelatin films in soil

Gelatin films that had been chemically modified (crosslinked with formaldehyde, glyoxal, glutaraldehyde, hexamethylene diisocyanate, butadiene diepoxide, or diepoxyoctane) were tested for their biodegradability by soil burial testing in a laboratory environment under temperature and humidity control. The relationship between weight loss and time of biodegradation showed a linear behavior for all the samples, but the rate of biodegradation showed a dependence on the type of crosslinking agent. The most stable films were those crosslinked with aldehydes, and these biodegraded by the 10th day. The samples crosslinked with hexamethylene diisocyanate and diepoxides completely biodegraded by the fourth and sixth days, respectively. It was shown that the rate of biodegradation depended on the density of crosslinking, which was calculated by a modified Flory–Rehner equation. The biodegraded samples showed considerable changes in the fingerprint region of FTIR spectra, and, thus, these spectra could be used for evaluation of the soil burial biodegradation of chemically modified gelatin samples. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1341–1347, 2000

Characterization of hydrogels formed from acrylate modified poly(vinyl alcohol) macromers

Poly(vinyl alcohol) was modified with pendent acrylate groups to form a macromer that was crosslinked via photopolymerization. Polymerization behavior was studied for several initial macromer concentrations using DSC and Near-IR spectroscopy. Under mild photoinitiating conditions (e.g. 0.05wt% initiator and less than 20mW/cm2 of 365nm light), the hydrogels polymerized to 100% conversion in less than 5min. To characterize the network structure, the hydrogels formed from the acrylated poly(vinyl alcohol) macromer were compared to gels that were chemically crosslinked with glutaraldehyde and gels that were physically crosslinked by semi-crystalline regions introduced through freeze–thaw cycles. The equilibrium swelling ratio and compressive modulus were characterized for all of the resulting PVA hydrogels, and related to the network structure (i.e. Mc) through a modified Flory–Rehner equation and rubber elasticity theory.

Biodegradation of chemically modified gelatin films in soil

Gelatin films that had been chemically modified (crosslinked with formaldehyde, glyoxal, glutaraldehyde, hexamethylene diisocyanate, butadiene diepoxide, or diepoxyoctane) were tested for their biodegradability by soil burial testing in a laboratory environment under temperature and humidity control. The relationship between weight loss and time of biodegradation showed a linear behavior for all the samples, but the rate of biodegradation showed a dependence on the type of crosslinking agent. The most stable films were those crosslinked with aldehydes, and these biodegraded by the 10th day. The samples crosslinked with hexamethylene diisocyanate and diepoxides completely biodegraded by the fourth and sixth days, respectively. It was shown that the rate of biodegradation depended on the density of crosslinking, which was calculated by a modified Flory–Rehner equation. The biodegraded samples showed considerable changes in the fingerprint region of FTIR spectra, and, thus, these spectra could be used for evaluation of the soil burial biodegradation of chemically modified gelatin samples. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1341–1347, 2000

Improved methods for the determination of Hansen's solubility parameters and the estimation of solvent uptake for lightly crosslinked polymers

Two new methods for determining Hansen's three-dimensional solubility parameters (3DSP) for lightly crosslinked polymers are presented and evaluated using commercial glove materials composed of butyl, natural, nitrile, and neoprene rubber. In the first method, the polymer 3DSPs are determined from a weighted average of the 3DSPs of a range of organic solvents, where the weighting factor is the product of the solvent molar volume and the fractional uptake of the solvent measured by immersion testing. The resultant polymer 3DSPs were used to model solvent uptake via the Hildebrand–Scott and modified Flory–Rehner expressions for the Flory interaction parameter. After grouping solvents of similar structure and applying an additional weighting factor, estimates of equilibrium solubility within a factor of two of experimental values were obtained for 176 of the 212 (83%) solvent–polymer combinations examined. In the second method of estimating polymer 3DSPs, the Flory interaction parameters for all solvent–polymer pairs are determined at the outset via the modified Flory–Rehner equation and used to solve for the polymer 3DSP values by multiple nonlinear regression. Solubility estimates are then back-calculated. This method provided different values of the 3DSPs for the polymers, including negative δp values for the butyl and natural rubber. However, the accuracy of solubility estimation was comparable to that obtained using the weighted-average method without the need for any adjustable factors. The advantages of these alternative methods over the graphical method for obtaining reliable estimates of the 3DSPs of lightly crosslinked polymers are discussed. This is the first demonstration of a general 3DSP-based approach to quantitative solubility modeling in polymer–solvent systems. © 1996 John Wiley & Sons, Inc.

Prediction of Equilibrium Swelling in Fuel and Lubricant Ingredients

Abstract In accord with the Porter equation, linear relationship has been found between the apparent and actual network-chain concentrations of DCP-cured NBR reference elastomers containing 18–39% ACN and 0–70 phr N550 black while Porter's k factors and, therefore, the extent of the restriction of swelling by the filler vary somewhat with the diluent. Taking this variation into account, a self-consistent relationship has been obtained between data on swelling in MEK (24 h) and those on equilibrium swelling in some fuel and lubricant ingredients (2 to 4 weeks). By using this relationship and the modified Flory-Rehner equation, the equilibrium swelling in fuel and lubricant ingredients of NBR test vulcanizates can be estimated from determining their nitrile content and from an MEK immersion test if these vulcanizates are filled with only N550 black, and if the only variables in their compositions are nitrile content, state of peroxide cure, and carbon black loading. The development of a similar technique to predict the swelling in mixed solvents of unknown NBR vulcanizates would probably involve serious difficulties which would stem from the presence of plasticizers, antioxidants, and fillers other than N550 black as well as from the assessment of the polymer-solvent interaction factor.

A study of the spatial structure of polyurethanes

A study has been made of the structures of the three dimensional network of a polyurethane based on trimethylolpropane phthalate cured with an aliphatic polyiscoyanate, biuret, at 20 ± 2°C. The degree of network formation has been assessed from the sorption of chloroform measured at 15 25 and 35°C and from the value of the equilibrium modulus of high elasticity. It is shown that the swelling of the polyurethane in chloroform is accompanied by restructuring within the system of physical bonds, which leads to the appearance of a number of regions of linearity on the linear sorption isotherm plotted with the coordinates of a modified Flory-Rehner equation. Sorption, thermomechanical and spectroscopic investigations show that a fairly open network, formed by chemical bonds ( M c=2500), is formed in the polyurethane. Physical nodes, diverse with respect to density ( M c of the order of 200 and 500), considerably raise the effective density of the network. Annealing these films or thermally ageing them in light lead to the physical nodes becoming more dense and to stabilization of the structure.