Three‐dimensional solubility parameters of poly(ε‐caprolactone)

The three‐dimensional solubility parameter model was applied to analyze solution thermodynamic data of 27 solutes in poly(ε‐caprolactone) (PCL) between 70 and 110 °C. A linear regression method was compared with a nonlinear least square regression method, which searches solubility parameter components by minimization of the sum of error squares. The parameters of polymers were the same by both methods. When compared with the error in predicting χRT/V, the data showed a different slope from the simple three‐dimensional model. These deviations were reduced by a different model using a smaller weight on the polar and hydrogen bonding components. In the new model, the solubility parameter components were closer to the value of a structure analogue of PCL. The confidence intervals for the parameters were estimated from a linearized equation based on the sum of error squares. The solubility parameter components obtained were different from the average values of the five solutes with the smallest χ. The inclusion of solutes with high hydrogen bonding components contributed to the increase of the component in the nonlinear regression method. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2002–2009, 2006     

Methods to determine solubility parameters of polymers at high temperature using inverse gas chromatography

Experimental values of Flory–Huggins parameters, χ, between polymers and probes, are frequently used to determine the solubility parameters of the polymers by the method of DiPaola–Baranyi and Guillet. The solubility parameters of probes were usually estimated by using heat of vaporization. When χ is measured at a temperature near the critical temperature of the probes and used to determine the solubility parameter of polymers, the departure of enthalpy of the probe vapor from the ideal gas state should be considered. This study discussed the method to make the correction and its effect on the determination solubility parameter of polymers. Without correction in the vapor phase enthalpy, the solubility parameters of the probes and polymer tend to be underestimated and the error increases when the critical temperature is approaching. Analytical expressions for the effect of correction on the solubility parameter of probes and parameters of polymers were derived. By use of probes with a range of solubility parameters on both sides of the solubility parameter of polymers, the correlation between parameters of polymers was shown to be reduced. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1547–1555, 2004     

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     

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     

Entropy–enthalpy compensation in solution properties of solutes at infinite dilution in nonpolar polymers

The knowledge of the Flory–Huggins interaction parameter, χ, between organic liquids and polymers is very important in the study of their miscibility. From the temperature dependency of χ the enthalpy and residual entropy of solution can be determined. In this study literature data of thirty‐two solutes, ranging from alkanes to alcohols, at infinite dilution in isotatic polypropylene, poly(ethyl ethylene), and poly(dimethylsiloxane), were tested and linear entropy–enthalpy compensation was observed. The plot of residual free energy versus enthalpy of solution was also linear, with a lower correlation coefficient than the entropy–enthalpy plot. The range of enthalpy of solution was wider than those of the size corrected free energy of solution. In nonpolar solvents the enthalpy of solution reflected largely the interaction within the solute liquid state, and showed a linear trend with respect to solute cohesive energy density for n‐alcohols. The wide range of enthalpy of solution suggests the use of a two‐dimensional solubility parameter model to correlate the enthalpy of solution. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1241–1247, 2007     

Simplified theory for linear rheology of monodisperse linear polymers

A new version of the tube theory based on the de Gennes–Doi–Edwards reptation concept (reported in Likhtman and McLeish's work published in 2002) is evaluated, modified to allow for simplified computations, and used to study the relationship between zero‐shear viscosity and molecular weight for monodisperse entangled linear homopolymers. The Likhtman–McLeish model combines self‐consistent theories for contour length fluctuations and constraint release with reptation theory for monodisperse linear polymers. Because of the nature of the Rubinstein and Colby approach used for the treatment of constraint release, the related term is probabilistic and requires stochastic simulations for the calculation of the relaxation modulus G(t). This makes the Likhtman–McLeish model computationally difficult to use. In this work we solve this problem by generating an approximate closed‐form solution for the stochastic term. Then analytical integration of the relaxation modulus function G(t) provides an expression for the zero‐shear viscosity (η₀). Results of the computations of the zero‐shear viscosity and of the slope of η₀ versus molecular weight are compared with available experimental data for monodisperse entangled linear polystyrene and polyethylene (hydrogenated polybutadiene). The model is a major improvement over previous theoretical models, even if there is still some disagreement between the predictions and experimental data of the slope of η₀ versus molecular weight. The possibility of inferring monomer chemistry–dependent parameters from the zero‐shear viscosity remains a difficult task because of the introduction of a constraint‐release parameter. Nevertheless, the model is a useful tool for the prediction of linear viscoelasticity data. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 569–586, 2004     

Determination of Hansen solubility parameters for cellulose acrylate by inverse gas chromatography

The solubility parameters of cellulose acrylate (CEA) were examined by inverse gas chromatography (IGC). The test probes were pentane, hexane, heptane, octane, nonane, ether, acetone, tetrahydrofuran, toluene, chloroform, isopropanol, and hexanol. The minimal test probe was injected into chromatographic column in order to achieve the infinite dilution conditions. The retention times of the test probes were determined and Flory–Huggins interaction parameters (χ) and solubility parameters (δ ₂) were calculated according to DiPaola-Baranyi and Guillet method from experimentally collected retention data for the series of carefully selected test probes. The Hansen’s three-dimensional solubility parameters concept is applied to determine the components (δ _d, δ _p, δ _h) of total solubility parameter (δ _T). The solubility parameter (δ _T) was increased with increasing temperature.     

Dynamic parameter estimation and optimization for batch distillation

This work reviews a well-known methodology for batch distillation modeling, estimation, and optimization but adds a new case study with experimental validation. Use of nonlinear statistics and a sensitivity analysis provides valuable insight for model validation and optimization verification for batch columns. The application is a simple, batch column with a binary methanol–ethanol mixture. Dynamic parameter estimation with an ℓ₁-norm error, nonlinear confidence intervals, ranking of observable parameters, and efficient sensitivity analysis are used to refine the model and find the best parameter estimates for dynamic optimization implementation. The statistical and sensitivity analyses indicated there are only a subset of parameters that are observable. For the batch column, the optimized production rate increases by 14% while maintaining product purity requirements.     

Estimation of solubility parameter components of solutes and polymers using heat of vaporization and heat of sorption of solutes

In a recent study, a two‐dimensional solubility parameter model was used to correlate the heat of solution for solutes ranging from n‐alkanes to alcohols, dissolved in isotatic polypropylene (PP), poly(ethyl ethylene) (PEE), and poly(dimethylsiloxane) (PDMS). When literature data of solubility parameter components of solutes were used, the correlation had some scattering for solutes with low values of cohesive energy density. In this study, the components of solubility parameters of solutes and polymers were estimated from cohesive energy and heat of sorption of solutes. Good correlation was obtained for the specific heat of sorption (ΔU_sorp/V) for solutes ranging from n‐alkanes to alcohols, and PDMS had a polar component as previously estimated. Free volume effect in solution process may be the source of a small systematic deviation from the model. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Evaluation of Two Methods for Measuring Vapor Sorption in Polymers

In this paper, two methods for measuring the equilibrium vapor sorption in polymers are critically compared and data on sorption of toluene, p-xylene, hexane, cyclohexane, and heptane in low density polyethylene are reported. The vapor phase calibration method (VPC) was used to measure vapor sorption at low vapor activities in air (below 0.01), and the gravimetric method was used to measure sorption over wide range of activities of pure vapors (0.1–0.9). The Flory-Huggins interaction parameter (in amorphous phase) varied between 1.00 for cyclohexane and 1.19 for toluene. The resulting confidence intervals are conjunctive, indicating that both methods provide consistent results.     

Predicting solubility and permeation properties of organic solvents in Viton glove material using Hansen's solubility parameters

A model based on a combination of the solubility parameters of Hansen and the polymer solution theory of Flory–Rehner was used to predict the solubility and permeation properties of organic solvents in Viton polymeric glove material. To test the validity of the model, weight gain data were collected for 32 organic solvents versus Viton. Samples were exposed for periods of 2 to 12 weeks until each glove sample had achieved a stable, equilibrium weight. Using a nonlinear least‐squares regression, the three‐dimensional solubility parameter was determined for Viton to be as follows: dispersion = 15.38, polar = 10.49, and hydrogen bonding = 2.47. Breakthrough times, lag times, and steady‐state permeation rates for the solvents verses Viton were also determined and combined with results obtained from the literature. A high level of correlation was observed between the model and the properties evaluated. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2688–2698, 2004     

Controlled Picard Method for Solving Nonlinear Fractional Reaction–Diffusion Models in Porous Catalysts

This paper discusses the diffusion and reaction behaviors of catalyst pellets in the fractional-order domain as well as the case of nth-order reactions. Two generic models are studied to calculate the concentration of reactant in a porous catalyst in the case of a spherical geometric pellet and a flat-plate particle with different examples. A controlled Picard analytical method is introduced to obtain an approximated solution for these systems in both linear and nonlinear cases. This method can cover a wider range of problems due to the extra auxiliary parameter, which enhances the convergence and is suitable for higher-order differential equations. Moreover, the exact solution in the linear fractional-order system is obtained using the Mittag–Leffler function where the conventional solution is a special case. For nonlinear models, the proposed method gives matched responses with the homotopy analysis method (HAM) solutions for different fractional orders. The effect of fractional-order parameter on the dimensionless concentration of the reactant in a porous catalyst is analyzed graphically for different cases of order reactions and Thiele moduli. Moreover, the proposed method has been applied numerically for different cases to predict and calculate the dual solutions of a nonlinear fractional model when the reaction order n?=??1.     

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     

Group contribution lattice fluid equation of state for CO2–ionic liquid systems: An experimental and modeling study

The group contribution lattice fluid equation of state (GCLF EOS) was first extended to predict the thermodynamic properties for carbon dioxide (CO₂)–ionic liquid (IL) systems. The group interaction parameters of CO₂ with IL groups were obtained by means of correlating the exhaustively collected experimental solubility data at high temperatures (above 278.15 K). New group parameters between CO₂ and IL groups were added into the current parameter matrix. It was verified that GCLF EOS with two kinds of mixing rules could be used for predicting the CO₂ solubility in ILs, and volume expansivity of ILs upon the addition of CO₂, as well as identifying the new structure–property relation. Moreover, it is the first work on the measurement of the solubility of CO₂ in ILs at low temperatures (below 278.15 K), manifesting the applicability of predictive GCLF EOS over a wider temperature range. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4399–4412, 2013     

Three-dimensional solubility parameters and chemical protective clothing permeation. II. Modeling diffusion coefficients,breakthrough times,and steady-state permeation rates of organic solvents in Viton® gloves

Three-dimensional (3-D) solubility parameters are used in separate models of the solubility, S, and diffusion coefficient, D, of organic solvents in polymers. Modeled values of these variables are then combined in Fickian diffusion equations to estimate solvent breakthrough times (BT) and steady-state permeation rates (SSPR). Published data on the permeation of 18 solvents through commercial Viton® glove samples are used to test the accuracy of the approach. Estimates of S are determined based on the model described in the preceding article. Of several empirical correlations investigated to model D, best results are achieved using the product of the solvent molar volume, V₁, and either the weighted solvent-Viton 3-D solubility parameter difference, A_w, or the Flory interaction parameter, X, also calculated from 3-D solubility parameters. To account for the change in the value of D over the course of the permeation test, D values are evaluated at breakthrough and steady state. Modeled BT values within a factor of three of experimental values (typically within a factor of two) are obtained for the 15 solvents for which analytical detection limits were reported. Modeled SSPR values within a factor of six of experimental values (typically within a factor of four) are obtained for the 15 solvents with valid SSPR measurements. © 1993 John Wiley & Sons, Inc.     

Synthesis and properties of fluoroalkyl end‐capped sulfobetaine polymers

A variety of fluoroalkyl end‐capped 3‐[N‐(3‐acrylamido)propyl‐N,N‐dimethylammonio]propanesulfonate polymers [R_F–(APDAPS)_n–R_F] were prepared by the reactions of fluoroalkanoyl peroxides with the corresponding monomer under very mild conditions. Similarly, fluoroalkyl end‐capped 2‐vinylpyridinio propane sulfonate polymer was obtained by the use of fluoroalkanoyl peroxide. These fluoroalkyl end‐capped sulfobetaine polymers exhibited a good solubility in water; however, these polymers have a poor solubility in other solvents. In particular, R_F–(APDAPS)_n–R_F polymers caused gelation in methanol, although R_F–(VPPA)_n–R_F polymer showed no gelation in methanol. R_F–(APDAPS)_n–R_F polymers were found to form the self‐assembled molecular aggregates with the aggregations of the end‐capped fluoroalkyl segments and the ionic interactions between sulfobetaine segments in aqueous solutions. On the other hand, it was suggested that R_F–2‐vinylpyridinio propane sulfonate (VPPS)_n–R_F polymer is not likely to form the self‐assemblies in aqueous solutions because of the steric hindrance of pyridiniopropyl betaine units in polymer. We also studied the surfactant properties of R_F–(APDAPS)_n–R_F and R_F–(VPPS)_n–R_F polymers compared with those of other fluoroalkyl end‐capped betaine‐type polymers such as 2‐acrylamido‐2‐methylpropanesulfonic acid polymers and 2‐(3‐acrylamidopropyldimethylammonio) ethanoate polymers. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1144–1153, 2004     

Evaluation of realistic 95% confidence intervals for the activation energy calculated by the iterative linear integral isoconversional method

Cai and Chen have proposed a new iterative linear integral isoconversional method that is capable of providing more accurate values of the activation energy than the traditional linear isoconversional methods (Cai, Junmeng, Chen, Siyu, 2009. Journal of Computational Chemistry 30, 1986–1991). However, an analysis of the estimation of confidence intervals for the activation energy determined by this iterative linear integral isoconversional method is still missing. Therefore, this short communication focuses on estimating realistic confidence intervals for the activation energy calculated by the isoconversional method. For this purpose, a comparison of confidence intervals estimated using the Vyazovkin–Sbirrazzuoli corrected Student's percentiles (Vyazovkin, Sergey, Sbirrazzuoli, Nicolas, 1997. Analytica Chimica Acta 355, 175–180) and a nonparametric method has indicated that the use of the Vyazovkin–Sbirrazzuoli method tends to overestimate confidence intervals for three heating rate estimates. The new corrected Student's percentiles for realistic 95% confidence intervals ?_n–2,0.975 of 2.9, 2.5 and 2.3 for three, four and five heating rate estimates, respectively, can be used to obtain realistic confidence intervals for the activation energy computed by the iterative linear integral isoconversional method.     

Solubility parameters and solvent affinities for polycaprolactone: A comparison of methods

Intrinsic viscosity measurements were used in combination with the functional solubility parameter (FSP) and Hansen solubility parameter (HSP) fitting methods to determine the solubility parameters (SPs) of polycaprolactone (PCL). Despite using only eight solvents, a simple similarity criteria approach showed that the HSPs and FSPs were good predictors of the relative solvent-PCL affinity compared to HSPs available in the literature and SPs calculated using additive group contribution methods. Three complementary computational methodologies—Conductor-like Screening MOdel for Real Solvents (COSMO-RS), partial solvation parameters (PSPs), and a thermodynamic quantitative structure–property relationship (QSPR) approach—were used to substantiate the relative solvent–PCL affinities revealed by the intrinsic viscosity measurements. The solvent affinities predicted by all three techniques were in good agreement with the trend observed in the experimental intrinsic viscosity data, but the COSMO-RS activity coefficients, ln(γ_PCL), were slightly superior to the PSP and thermodynamic QSPR methods, particularly when incorporating the Elbro free-volume combinatorial correction in the COSMO-RS calculations. As part of this study, the FSP fitting algorithm was modified to obtain the PSPs for PCL in terms of the intrinsic viscosity data, thereby, presenting a promising new way to calculate the PSPs of polymers from empirical solubility and solvent affinity data. © 2020 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48908.     

Doped Poly(m-phenylenediamine-co-aniline) (P(mPD-co-ANI)): Synthesis,Characterization, Physical Properties,and Precursor for CuO Nanoparticles

Poly(m-phenylenediamine-co-aniline) P(mPD-co-ANI) and Mn-, Ni-, and Cu-doped poly(m-phenylenediamine-co-aniline) (M-P(mPD-co-ANI)) have been synthesized and characterized. Cu-P(mPD-co-ANI) has been used as a molecular precursor of CuO nanoparticles. The spectral, optical, refractive index, solubility, and thermal properties of the synthesized polymers have been measured and discussed. The optical bandgap (E_g) measurements indicated that Ni(P(mPD-co-ANI)) has wider optical band than the pure (P(mPD-co-ANI)). Calcination of Cu-P(mPD-co-ANI) at 600°C produced (CuO) nanoparticles. The obtained nanoparticles have been characterized by XRD and TEM. The average size of CuO nanoparticles was found to be 42?nm. The refractive index measurements indicate slight change in the refractive index values of the polymer solution than that of pure solvent. The solubility of the synthesized polymers in ethanol, dimethyl formamide (DMF)–aqueous mixed solvents was found to increase as the mole fractions of both ethanol and DMF increase. The UV spectra of the synthesized polymers in ethanol, DMF–aqueous mixed solvents indicate blueshift and hyperchromic effect.