Flory Theory Research Articles

Surface tension — A theoretical study of multicomponent solutions

Surface tension of four quaternary (pentane + hexane + cyclohexane + benzene, pentane + hexane + benzene + toluene and pentane + cyclohexane + heptane + toluene, n-decane + n-hexane + cyclohexane + benzene) and six ternary (toluene + cyclohexane + carbon tetrachloride, benzene + cyclohexane + toluene, pentane + n-hexane + benzene , n-hexane + cyclohexane + benzene, cyclohexane + n-heptane + toluene and benzene + n-hexane + carbon tetrachloride) mixtures containing alkanes at 298.1 5 K have been calculated by applying different approaches including :Altenberg (AL), Mc-Gowan (McG), Sanchez (SZ), Goldsack and Sarvas (GS), Flory Theory (FT) and Group Contribution method (GC). The results have been presented in terms of their average percentage deviation (APD) values and comparative studies have been done. An attempt has also been made to explain the nature of the molecular interactions and forces involved in these mixtures.

Thermodynamic and acoustic properties for binary and ternary mixtures of cyclic ethers with industrially important solvents at 308.15 K

Speeds of sound data, u ijk of 1,3-dioxolane or 1,4-dioxane( i) + benzene or toluene ( j) + formamide or N,N-dimethylformamide ( k) ternary mixtures and their sub-binary mixtures, u ij of 1,3-dioxolane or 1,4-dioxane ( i) + benzene or toluene or formamide or N,N-dimethylformamide ( j); benzene or toluene ( i) + formamide or N,N-dimethylformamide ( j) have been measured using a quartz crystal interferometer as a function of composition at 308.15 K. The experimental data have been utilized to evaluate excess isentropic compressibilities of binary, ( κ S E ) ij and ternary, ( κ S E ) ijk mixtures and the same have been fitted to Redlich–Kister equation to predict binary and ternary adjustable parameters along with standard deviations. ( κ S E ) ij and ( κ S E ) ijk data have also been analyzed in terms of Graph and Flory theories. It has been observed that predicted ( κ S E ) ij and ( κ S E ) ijk values by Graph theory compare well with their corresponding experimental values.

Thermodynamic Properties of Ternary Liquid Mixtures of 2-Pyrrolidinone with Aromatic Hydrocarbons

Molar excess volumes, \({V^{\rm E}_{ijk}}\), and speeds of sound, uijk, of 2-pyrrolidinone (2-Py) (i) + toluene (j) + o-xylene or p-xylene (k) ternary mixtures have been determined by using a dilatometer and interferometer as a function of composition at 308.15 K. The speeds of sound of ternary mixtures have been utilized to predict their excess isentropic compressibilities. The Redlich-Kister equation has been fitted to the molar excess volumes, \({V^{\rm E}_{ijk}}\), and excess isentropic compressibilities, \({\left( {\kappa _S^{\rm E}}\right)_{ijk}}\), to predict ternary adjustable parameters and standard deviations. The observed data have been analyzed in terms of the Flory theory and the Sanchez and Lacombe theory.

Excess thermodynamic parameters of binary mixtures of methanol, ethanol, 1-propanol, and 2-butanol + chloroform at (288.15–323.15 K) and comparison with the Flory theory

In this work we used the experimental result for calculating the thermal expansion coefficients α, and their excess values α E , and isothermal coefficient of pressure excess molar enthalpy and comparison the obtain results with Flory theory of liquid mixtures for the binary mixtures {methanol, ethanol, 1-propanol and 2-butanol-chloroform} at 288.15, 293.15, 298.15, 303.15, 308.15, 313.15, 318.15, and 323.15 K. The excess thermal expansion coefficients α E and the isothermal coefficient of pressure excess molar enthalpy ((∂H m E /∂P) T,x for binary mixtures of {methanol and ethanol + chloroform} are S-shaped and for binary mixtures of {1-propanol and 2-butanol + chloroform} are positive over the mole fraction. The isothermal coefficient of pressure excess molar enthalpy (∂H m E /∂P) T,x , are negative over the mole fraction range for binary mixture of {1-propanol and 2-butanol + chloroform}. The calculated values by using the Flory theory of liquid mixtures show a good agreement between the theory and experimental.

Diffusion of semi-flexible polyelectrolyte through nanochannels

The diffusion of sodium polystyrene sulfonate through polycarbonate nanochanels was studied in salt-free dilute aqueous solution. A stronger molecular weight dependence of diffusion was observed compared to free diffusion in dilute solution. Scaling exponentials relating polymer size to diffusivity were between Flory's theory (Deff ∝ N−0.6) and Rouse's model (Deff ∝ N−1), revealing a crossover regime from 3-D diffusion to 1-D diffusion. Diffusion was less hindered for the polyelectrolyte (Deff/D0), than for a rigid sphere, when the polymer/channel size ratio exceeded 0.2. This is attributed to elongated chains with reduced frictional hindrance. Simulation of the confined diffusion based on an elongated cigar model gave D ∝ N−1 while the experimental results agree with D ∝ N−0.94. For charged polyelectrolytes, the transition to 1-D diffusion therefore begins before the polymer radius of gyration exceeds the channel size contrary to model assumptions. We attribute this to the charged nature of the polyelectrolytes causing extended chain conformations. © 2009 American Institute of Chemical Engineers AIChE J, 2010

A quantitative analysis of alginate swelling

The swelling behavior of physically cross-linked polysaccharides is not fully understood despite its significance in many applications such as drug delivery. In this study the swelling behavior of three types of alginate were characterized experimentally at various calcium concentrations. Additionally, equilibrium swelling data was analyzed in terms of Flory and rubber elasticity theories, which were developed for chemically cross-linked networks. This analysis suggested that these theories are not applicable for alginate. In particular, an increase in the number of monomeric units between cross-links was observed at a higher calcium concentration, whereas the theory predicts the opposite. The kinetics of the swelling process was also analyzed experimentally and theoretically. The experimental data was found to obey second-order kinetics. Moreover, a decrease in the swelling rate constant with elevated calcium concentration was observed. Lastly, it is indicated that the unusual swelling behavior of alginate could be attributed to a lateral chain association.

Tracking gas-liquid coexistence in fluids of charged soft dumbbells

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Recent Monte Carlo work by Camp and co-workers indicates that a fluid of charged hard dumbbells does exhibit gas-liquid (g-l) coexistence. This system has the potential to answer the above fundamental question because the charge-to-charge separation, d , on the dumbbells may be reduced to, at least in principle, yield the dipolar fluid limit. Using the molecular-dynamics technique we present simulation results for the g-l critical point of charged soft dumbbells at fixed dipole moment as function of d . We do find a g-l critical point at finite temperature even at the smallest d value (10;{-4}) . Reversible aggregation appears to play less a role than in related model systems as d becomes small. Consequently attempts to interpret the simulation results using either an extension of Flory's lattice theory for polymer systems, which includes reversible assembly of monomers into chains, or the defect model for reversible networks proposed by Tlusty and Safran are not successful. The overall best qualitative interpretation of the critical parameters is obtained by considering the dumbbells as dipoles immersed in a continuum dielectric.

Spherical brushes within spherical cavities: A self-consistent field and Monte Carlo study

We present an extensive numerical study on the behavior of spherical brushes confined into a spherical cavity. Self-consistent field (SCF) and off-lattice Monte Carlo (MC) techniques are used in order to determine the monomer and end-chain density profiles and the cavity pressure as a function of the brush properties. A comparison of the results obtained via SCF, MC, and the Flory theory for polymer solutions reveals SCF calculations to be a valuable alternative to MC simulations in the case of free and softly compressed brushes, while the Flory's theory accounts remarkably well for the pressure in the strongly compressed regime. In the range of high compressions, we have found the cavity pressure P to follow a scale relationship with the monomer volume fraction v, P approximately v(alpha). SCF calculations give alpha=2.15+/-0.05, whereas MC simulations lead to alpha=2.73+/-0.04. The underestimation of alpha by the SCF method is explained in terms of the inappropriate account of the monomer density correlations when a mean field approach is used.

Excess molar volumes and excess isentropic compressibilities of 2-pyrrolidinone at 308.15 K

Molar excess volumes V ijk E and speeds of sound, u ijk of 2-pyrrolidinone (i) + benzene (j) + toluene or o- or p-xylene (k) ternary mixtures have been measured as a function of composition at 308.15 K. The observed speeds of sound data have been utilized to calculate their excess isentropic compressibilities. The observed data have been fitted to Redlich–Kister equation to calculate ternary adjustable parameters and standard deviations. Molar excess volumes, V ijk E and excess isentropic compressibilities, ( κ S E ) ijk data for the investigated mixtures have been analyzed in terms of Graph theory and Flory theory. It has been observed that V ijk E and ( κ S E ) ijk values calculated by Graph theory compare well with their corresponding experimental values.

The effects of interaction energy on the volume phase transition of N-isopropylacrylamide-co-N-isopropylmethacrylamide nano-sized gel particles: Applicability of molecular simulation technique

Abstract We investigated the volume phase transition temperatures of N -isopropylmethacrylamide (NIPMA)-co- N -isopropylacrylamide (NIPA) gels with various mole ratios. Nanometer-sized NIPA-co-NIPMA gel particles were prepared by precipitation polymerization and their swelling behaviors were measured using photon correlation spectroscopy (PCS). After applying the interaction energies found using the molecular simulation technique, we predicted the swelling equilibria for the hydrogels in a water system. For studying cross-linked hydrogel particles in water, we have combined the modified double-lattice theory with Flory and Erman's theory of elasticity. To correct for the deviation of the volume transition temperature, we considered the additional energy parameter ( ɛ h ) between the cross-linker and solvent molecules. We used the corrected model to describe the swelling behavior of the hydrogel and the volume transition temperature. The corrected model was agreed well with their experimental data with no fitting parameters.

Preparation of porous polyacrylate/poly(ethylene glycol) interpenetrating network hydrogel and simplification of Flory theory

In this article, we successfully designed and fabricated polyacrylate/poly(ethylene glycol) interpenetrating network (PAC/PEG IPN) hydrogel by a two-step technique. The influences of synthesis parameters, such as crosslinker dosage and neutralization degree of PAC, on the equilibrium swelling ratio (SR) of the PAC/PEG IPN hydrogel were investigated. Based on Flory theory, a simplified experiential formula $$ Q_{{{\text{H}}_{2} {\text{O}}}}^{5/3} = 14.72I^{ - 1} + 207.43 $$ was proposed. The results revealed that the theoretical SR of the PAC/PEG IPN hydrogel was consistent with experimental value in the presence of univalent salt solution. In this case, the SR of the hydrogel can be calculated without measurement. While for multivalent salt solutions, the theoretical and experimental results are inconsistent owing to chelations between carboxylic and carboxylate groups of the PAC/PEG hydrogels and the cations in the solution.

Application of the Flory Theory and of the Kirkwod−Buff Formalism to the Study of Orientational Effects in 1-Alkanol + Linear or Cyclic Monoether Mixtures

Orientational effects present in binary mixtures of 1-alkanols with linear or cyclic monoethers have been studied using the Flory model and the Kirkwood−Buff formalism. The alcohols considered are those from methanol to 1-decanol, and the ethers are the following: dimethylether (DME), diethylether (DEE), dipropylether (DPE), dibutylether (DBE), tetrahydrofuran (THF), and tetrahydropyran (THP). In terms of the Flory model, orientational effects have been investigated by analyzing the concentration dependence of the interaction parameter, X12, and comparing the deviations obtained between experimental molar excess enthalpies, HmE, and calculated values with an X12 parameter determined from HmE measurements at equimolar composition. Due to the facts that structural effects are relevant for many of the considered mixtures and their excess molar volumes, VmE, are negative, we have also determined the excess molar internal energies, UV,mE, and X12 parameters from these data. From the X12 variation with the alka...

Thermodynamic and Transport Properties of Binary Liquid Mixtures of 1-Hexanol with Hexadecane and Squalane at 298.15, 303.15 and 308.15 K

Abstract Excess molar volumes, V m E , viscosity deviations, Δη, excess molar isentropic compressibility, K E S,m , deviation of the speeds of sound, u D , from their ideal values u id in an ideal mixture for binary mixtures of 1-hexanol, C6H13OH with hexadecane, C16H34 and squalane (2,6,10,15,19,23-hexamethyltetracosane), C30H62 at T = (298.15, 303.15 and 308.15) K and at atmospheric pressure were derived from experimental density, ρ, viscosity, η and speed of sound data, u. The calculated excess and deviation functions were further fitted to the Redlich-Kister polynomial equation. The Prigogine-Flory-Patterson (PFP) theory has been applied to analyze V m E of these systems and theoretical values of thermal expansivity, α, has also been calculated using Flory theory. Furthermore, the apparent molar volumes, V¯ϕ,i0 and apparent molar compressibility, K¯ϕ,i0 of the components at infinite dilution have been calculated.

Flory Theory of the Folding of Designed RNA Molecules

We construct a Flory theory for the folding of RNA molecules that have a designed, linear ground state.

Effect of monovalent salt on the conformation of polyelectrolyte-surfactant complexes

We study the conformation of polyelectrolyte-surfactant complexes in the presence of monovalent salt. A simple model for the formation of these structures is presented in the framework of the Debye-Hückel-Bjerrum-Manning and Flory theories, with the hydrophobic interactions between the hydrocarbon tails of surfactant molecules treated in the spirit of van der Waals theory as an effective attraction. The extension of the polyelectrolyte-surfactant complexes is analyzed as a function of the salt concentration and a discrete conformational transition between a compact globule and an elongated coil is found, in agreement with experimental results for the unfolding transition of a DNA-cationic surfactant complex.

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

AbstractThe 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

The controlled release behavior and pH‐ and thermo‐sensitivity of alginate/poly(vinyl alcohol) blended hydrogels

AbstractPoly(vinyl alcohol) (PVA) was blended with sodium alginate (Alg) in various ratios and crosslinked with calcium chloride and made into hydrogel membranes. The dependence of the swelling behavior of these Alg‐Ca/PVA hydrogels on pH was investigated. The temperature‐dependent swelling behavior of the semi‐interpenetrating network (semi‐IPN) hydrogels was examined at temperatures from 2 to 45°C and the enthalpy of mixing (ΔHmix) was determined at various temperatures. The molecular structure of the hydrogels was studied by infrared spectroscopy and their water structure in the semi‐IPN hydrogels was measured by differential scanning calorimetry (DSC). The influence of Ca2+ content on the network structure of Alg‐Ca/PVA hydrogels was investigated in terms of the compressive elastic modulus, effective crosslinking density, and the polymer–solvent interaction parameter based on the Flory theory. The loading of alizarin red S (ARS) followed the Langmuir isotherm mechanism and the release kinetics of ARS from the Alg‐Ca/PVA hydrogels followed the Fickian diffusion mechanism. Copyright © 2008 John Wiley & Sons, Ltd.

Estimation of surface tension of ternary liquid systems by corresponding-states group-contributions method and Flory theory

For the first time two-body interaction coefficients between any two molecules are considered to be non-identical. On this basis, various expressions involved in Flory theory have been deduced, and then utilized to compute surface tension of three ternary liquid mixtures. Prior to this, corresponding-states group-contributions method for the first time has been extended to three ternary liquid mixtures, viz. n-pentane + n-hexane + benzene, cyclohexane + n-heptane + toluene, 2,2,4-trimethyl pentane + cyclohexane + decane and some binary mixtures at 298.15 K. On comparing the computed values of surface tension by the present two approaches with experimental data, quite satisfactory results have been observed.

Theoretical estimations of thermodynamic properties of liquid mixtures by Flory's statistical theory

Flory's statistical theory has been employed for the computation of ultrasonic velocity (u), density (ρ), internal pressure (P i), thermal expansion coefficient (α), isothermal compressibility (β T), adiabatic compressibility (β S), heat capacity at constant pressure (C P), heat capacity at constant volume (C V), heat capacities ratio (γ), pseudo-Gruneisen parameter (Γ), excess volume (V E) and excess heat capacity at constant pressure () at varying temperatures for 10 binary and 5 ternary systems. The binary systems under investigation are: acetonitrile + benzene, benzene + DMF, acetonitrile + DMF, cyclohexanol + cyclohexane, piperidine + tetrahydropyran, piperidine + cyclohexane, tetrahydropyran + cyclohexane, benzene + p-xylene, benzene + p-dioxan, acetone + methyliodide, and the ternary systems are: benzene + chloroform + cyclohexane, toluene + chloroform + cyclohexane, chlorobenzene + chloroform + cyclohexane, dioxane + chloroform + cyclohexane and chlorobenzene + cyclohexane + n-heptane. The results of calculations show that for all the systems under consideration, the calculated values of various thermodynamic parameters show the same trend as observed experimentally. Fairly good agreement is found between theoretical and experimental values. The ultrasonic velocity of liquid mixtures is obtained using the most popular Flory theory without the help of any empirical relation.

Thermodynamics of mixtures containing alkoxyethanols: Part XXVII. Predictions on isobaric thermal expansion coefficients, compressibilities and speeds of sound from the Flory theory

The Flory model is applied to predict the isobaric expansion coefficients, α P, isentropic, κ S , and isothermal, κ T , compressibilities and speeds of sound, u, of the highly complex mixtures: hydroxyether + alkane, + dibutylether, + 1-butanol or + 2-methoxyethanol, 1-alkanol + alkane, and 1-alkanol + dibutylether. Predictions were obtained using the energetic parameter, χ 12, determined from values of excess enthalpies, H E, and from values of the excess isochoric internal energies, U V E , at equimolar composition. No meaningful differences exist between such predictions. Deviations between experimental and calculated values are lower than 2% for mixtures containing alkoxyethanols. Poorer results are obtained for 1-alkanol + dibutylether mixtures with deviations up to 5%. It is shown that predictions on α P, κ S , κ T , and u essentially depend on structural effects and not on the orientational effects present in the studied mixtures. Results are improved using χ 12 values fitted to molar excess volumes. In this case, deviations are similar to those obtained from semiempirical models as free length theory, collision factor theory, or Nomoto or Junjie equations.