Flory Theory Research Articles

Applications of statistical mechanical theories for estimating thermodynamic properties of ternary and binary solutions using ultrasonic velocity and density data

Thermodynamic properties of liquids and liquid mixtures play very important role in understanding the nature of molecular interactions occurring in the system. In the present work density (ρ) and ultrasonic velocity (u) of the ternary system benzene+carbon tetrachloride+cyclohexane and its three constituent binaries namely, benzene+cyclohexane, carbon tetrachloride+cyclohexane and benzene+carbon tetrachloride have been measured at 298.15K. Different thermodynamic properties of ternary and binary solutions have also been computed with the help of Flory's statistical theory (FST), hard sphere equation of state (HSE) and hole theory (HT) simultaneously. The calculated values are compared with the experimental findings and quite satisfactory results are obtained.

Understanding the dynamics of rings in the melt in terms of the annealed tree model

The dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in light of the recently developed Flory theory of untangled rings which maps every ring on an annealed branched polymer and establishes that the backbone associated with each ring follows self-avoiding rather than Gaussian random walk statistics. We find the scaling of the ring relaxation time and diffusion coefficient with ring length, as well as the time dependence of stress relaxation modulus, zero shear viscosity and the mean square averaged displacements of both individual monomers and the ring's mass centre. Our results agree within error bars with all available experimental and simulation data of the ring melt, although the quality of the data so far is insufficient to make a definitive judgement for or against the annealed tree theory. At the end we review briefly the relation between our findings and experimental data on chromatin dynamics.

The Thermodynamic Model on Paraffin Wax Deposition Prediction

In process of crude oil production and transportation, wax and other solid deposition issues have a significant impact on oilfield production. Solid precipitation not only reduces the production efficiency and increases the cost of production. Therefore, there is a need to study the rate of paraffin wax deposition and cloud point temperature in order to guide the oil field control the paraffin wax deposition. In this paper, we use the Flory theory of polymer solution to correct the liquid activity coefficients, and regular solution theory to correct for the non ideality of the solid mixture, and we consider the impact of isoparaffin. Finally, thermodynamic model is established. The actual example calculation shows that the forecast results of this model are more accurate.

Equilibrium properties of charged microgels: A Poisson-Boltzmann-Flory approach

The equilibrium properties of ionic microgels are investigated using a combination of the Poisson-Boltzmann and Flory theories. Swelling behavior, density profiles, and effective charges are all calculated in a self-consistent way. Special attention is given to the effects of salinity on these quantities. In accordance with the traditional ideal Donnan equilibrium theory, it is found that the equilibrium microgel size is strongly influenced by the amount of added salt. Increasing the salt concentration leads to a considerable reduction of the microgel volume, which therefore releases its internal material - solvent molecules and dissociated ions - into the solution. Finally, the question of charge renormalization of ionic microgels in the context of the cell model is briefly addressed.

The Prediction of Surface Tension of Ternary Mixtures at Different Temperatures Using Artificial Neural Networks

In this work, artificial neural network (ANN) has b een employed to propose a practical model for predicting the surface tension of multi-component mixtures. In order to develop a reliable model based on the ANN, a comprehensive experimental data set including 15 ternary liquid mixtures at different temperatures was employed. These systems consist of 777 data points generally containing hydrocarbon components. The ANN model has been developed as a function of temperature, critical properties, and acentric factor of the mixture acco rding to conventional corresponding-state models. 80% of the data points were employed for training A NN and the remaining data were utilized for testing the generated model. The average absolute r elative deviations (AARD%) of the model for the training set, the testing set, and the total data p oints were obtained 1.69, 1.86, and 1.72 respective ly. Comparing the results with Flory theory, Brok-Bird equation, and group contribution theory has proved the high prediction capability of the attain ed model.

Liquid crystal solutions at infinite dilution: Enthalpy–entropy compensation of solutes transfer properties between phases

Careful gas chromatographic (GLC) studies provide thermodynamic data for insights into solution processes in non-volatile solvents. In this study, thermodynamic properties of solutes at infinite dilution of several liquid crystals measured by GLC were examined. The enthalpy and entropy of solutions in mesophases were positive and higher than those of isotropic stationary phases. When solute transfer enthalpy (ΔHtr) and transfer entropy (ΔStr) between two phases of a liquid crystal were examined, remarkable enthalpy–entropy compensation relations were observed. This was because the small values of transfer free energy. Both ΔHtr and TΔStr had large values and were almost equal, resulting in small values of transfer free energy. The temperature dependency of the disorder parameter in Flory's theory of liquid crystals was used to explain high values of the enthalpy and entropy of solution.

The kinetics of poly(butylene succinate) synthesis and the influence of molar mass on its thermal properties

ABSTRACTThe synthesis of poly(butylene succinate) (PBS) of Mw ranging from 4000 to 180,000 g mol−1 is realized with molar ratios [COOH]0/[OH]0 of 1 and 0.98, and varying amounts of titanium (IV) tetrabutoxide (TBT) catalyst. Polycondensation kinetics are followed by chemical titration of carboxylic groups, and the kinetic rate constants of self‐catalyzed and external‐catalyzed reactions are calculated. The synthesis of PBS with high molar mass follows the classical Flory theory. The effect of molar mass on PBS thermal properties is also studied. A faster crystallization rate and a higher temperature of crystallization are observed, for very high molar masses. This behavior could be due to a memory effect of the polymer. Complex melting behavior of PBS is induced by a continuous reorganization of the crystalline phase, as observed by MTDSC. DSC measurements also reveal that the crystallinity—and so the amorphous phase—is limited to about 35% when the molar mass Mn is higher than 40,000 g mol−1. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40639.

Thermodynamics of strain-induced crystallization of random copolymers

Industrial semi-crystalline polymers contain various kinds of sequence defects, which behave like non-crystallizable comonomer units on random copolymers. We performed dynamic Monte Carlo simulations of strain-induced crystallization of random copolymers with various contents of comonomers at high temperatures. We observed that the onset strains of crystallization shift up with the increase of comonomer contents and temperatures. The behaviors can be predicted well by a combination of Flory's theories on the melting-point shifting-down of random copolymers and on the melting-point shifting-up of strain-induced crystallization. Our thermodynamic results are fundamentally important for us to understand the rubber strain-hardening, the plastic molding, the film stretching as well as the fiber spinning.

Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: towards the physics of crumpling

A Flory theory is constructed for a long polymer ring in a melt of unknotted and non-concatenated rings. The theory assumes that the ring forms an effective annealed branched object and computes its primitive path. It is shown that the primitive path follows self-avoiding statistics and is characterized by the corresponding Flory exponent of a polymer with excluded volume. Based on that, it is shown that rings in the melt are compact objects with overall size proportional to their length raised to the 1/3 power. Furthermore, the contact probability exponent γcontact is estimated, albeit by a poorly controlled approximation, with the result close to 1.1 consistent with both numerical and experimental data.

Oxidative degradation of polylactide (PLA) and its effects on physical and mechanical properties

The thermo-oxidative degradation of polylactide (PLA) films was studied between 70 and 150°C. It was shown that the oxidative degradation of PLA leads to a random chain scission responsible for a reduction of the molar mass. These molar mass changes affect Tg and the degree of crystallinity, and it was found that Tg decreases according to the Fox–Flory theory whereas the degree of crystallinity increases due to a chemicrystallization process. A correlation between molar mass and strain at break during oxidation has been established: PLA displays a brittle behavior when Mn falls below 40kgmol−1 in agreement with relationships linking the critical value for embrittlement with the molar mass between entanglements.

The Effect of the Molecular Size and Shape on the Volume Behavior of Binary Liquid Mixtures. Branched and Cyclic Alkanes in Heptane at 298.15 K

Excess molar volumes VE for 40 mixtures of heptane with a liquid alkane and apparent molar volumes in heptane for eight solid alkanes have been obtained at 298.15 K. They include five linear, 30 branched-chain, and 13 cyclic alkanes. Almost all systems exhibit negative VE values. For mixtures with open chain alkanes, VE increases from C5 to C7 and then decreases. A similar trend is shown by mixtures with cycloalkanes. VE values are compared with known HE data for mixtures with heptane and tetrachloromethane. Signs and trends of VE and HE are correlated with the free volume and interactional terms of the Flory theory. The partial molar volumes at infinite dilution in heptane, V°, have also been obtained and discussed together with literature data on other hydrocarbons and polar compounds. The calculated contributions to V° by CH3, CH2, CH and C groups are compared with previously determined contributions of polar groups. The lower contributions of the latter groups are explained with the volume contraction caused by dipole-induced dipole interaction. The volume effects associated with branching and cyclization have been evaluated and compared with the corresponding effects on solvation enthalpy. The branching effect, in the order of magnitude of few cm3·mol−1, and the larger negative values of cyclization volumes, down to −24 cm3·mol−1, are discussed in terms of packing and solute–solvent interactions, in analogy to polar organic solutes either in heptane and tetrachloromethane. A negative cyclization effect is also exhibited by the solvation enthalpies.

Long-time crystallization kinetics in zinc-neutralized ethylene–methacrylic acid ionomers

The classic paper by Flory [1] regarding the crystallization of random copolymers presents a theory where fractional crystallization depends only on molar substitution level if the comonomer cannot be incorporated into the crystal structure of the crystallizable comonomer. A rather large number of indirect experiments on ethylene copolymers since that publication nearly 60 years ago are consistent with this hypothesis; for example the crystallinity content in ethylene copolymers depends to a first approximation only on the level of molar substitution and not the identity of the comonomer. Ethylene–methacrylic acid copolymer ionomers offer a unique opportunity to test this hypothesis directly, since it is possible to vary crystallization kinetics simply by varying the neutralization cation or neutralization level, without changing the comonomer content or its distribution along the polymer backbone. After annealing times as long as 6 months, it was found that the constraints caused by the phase-separating ionic groups lead to significantly lower crystallinity levels versus the case where such constraints were not present. Although disproving Flory's theory in this particular case, the result was not surprising since Flory's original paper certainly did not consider the case where the other monomer can phase separate. One surprising result of this study was that the rates of formation of secondary crystals relative to the crystallization amount at infinite time was independent of neutralization level for the phase-separated ionomers; in other words the Avrami constants n and K were independent of neutralization level for the secondary crystals.

Flory theory applied to polycondensation polymers with a finite number of fractions

It was shown that the molecular-weight distribution of polycondensation polymers at any degree of reaction completion could be described by the Flory function with a finite number of high-molecularweight fractions. The practical usefulness of such an approach was illustrated by analyzing published results for computer modeling of the polycondensation kinetics of AH salt and data for the microheterogeneity of PA-6 over average molecular weight.

Molecular-weight distribution of linear polycondensation polymers. Flory theory

The logic of the conclusion of P. Flory regarding the molecular-weight distribution functions of polymers obtained through various types of linear polycondensation was reproduced. It was shown that the reason for the multi-year discussion regarding the correctness of applying this theory to equilibrium polycondensation was an overestimation in several studies of the role of exchange reactions involving the highest polymer molecular fractions in this process. It was emphasized that the independence of the reactivity of end functional groups from the macromolecule size during polycondensation and the independence of the chain-growth reaction rate constant in the polymerization processes, which also produced an exponential macromolecule size-distribution function, were different in principle. Attention was paid to the possibility derived from the theory of P. Flory of preparing linear polymers with $ {{{\bar{M}}^{\prime}}_w}/{{{\bar{M}}^{\prime}}_n} $ during irreversible polycondensation in the presence of monofunctional dibasic chain-length regulators.

Impact of the topology of viral RNAs on their encapsulation by virus coat proteins

Single-stranded RNAs of simple viruses seem to be topologically more compact than other types of single-stranded RNA. It has been suggested that this has an evolutionary purpose: more compact structures are more easily encapsulated in the limited space that the cavity of the virus capsid offers. We employ a simple Flory theory to calculate the optimal amount of polymers confined in a viral shell. We find that the free energy gain or more specifically the efficiency of RNA encapsidation increases substantially with topological compactness. We also find that the optimal length of RNA encapsidated in a capsid increases with the degree of branching of the genome even though this effect is very weak. Further, we show that if the structure of the branching of the polymer is allowed to anneal, the optimal loading increases substantially.

Constitutive equations in finite elasticity of swollen elastomers

Constitutive equations are formulated for the mechanical behavior of rubber-like materials subjected to swelling under an arbitrary deformation with finite strains. Based on the Flory theory of polymer networks with constrained junctions, a novel expression is derived for free energy density of a swollen elastomer. This expression is applied to study the effect of strain rate on the elastic response of hydrogels under tension and compression.

Star polymers confined in a nanoslit: a simulation test of scaling and self-consistent field theories

The free energy cost of confining a star polymer where f flexible polymer chains containing N monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance D apart is considered, for good solvent conditions. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens–Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent field (SCF) theory yield the correct scaling of the parallel linear dimension of the star with N, f and D, but cannot be used for estimating the free energy cost reliably. We demonstrate that the same problem occurs already for the confinement of chains in cylindrical tubes. We also briefly discuss the problem of a free or grafted star polymer interacting with a single wall, and show that the dependence of confining force on the functionality of the star is different for a star confined in a nanoslit and a star interacting with a single wall, which is due to the absence of a symmetry plane in the latter case.

Photochemical funnel in stiff conjugated polymers: interplay between defect mediated polymer conformations, side chain interactions and resonance energy transfer

Observed optical properties of conjugated polymers pose interesting and challenging problems that are yet to be understood quantitatively. The problem is complicated due to the competition between energy migration among chromophores influenced by defects, conformations dictated by attractions among monomers and differing fluorescence rates of the chromophores of different conjugation lengths. In a conjugated polymer in the presence of defects, these chromophores are, to a good approximation, nearly straight planar chain segments with unbroken conjugation. Defects limit the length of a conjugated segment. Single molecules spectroscopic studies have shown that conformation of PPV-derivative polymers is not spherically symmetric as was commonly described using Flory theory; instead they are better represented as defect cylinders. As the defects are randomly distributed along the segments, they render the lengths of the segments random, thus introducing a disorder that does not allow easy formation of ordered structures like rods and toroids. Interactions among side chains of monomers in a conjugated polymer (as in MEH–PPV) can also determine the shape and the arrangement. The said non-spherical shape or conformation can have tremendous implication in optical properties of these polymers. While energy migration among the chromophores may be modelled as a random walk problem, the transfer rates and fluorescence properties of each chromophores need to be obtained quantum mechanically. The rate of hopping between different chromophores can be treated as a resonance energy transfer (RET) process, although Forster's well-known expression might not be reliable because in many cases the chromophores are spatially quite close to each other. Another issue revolves around the coherent or incoherent nature of transport. We discuss a recent theoretical approach that includes some of the features of energy transport discussed above. We discuss how a photochemical funnel can develop in such a system where the longest conjugated segment can form the funnel.

Elasticity of compressed microgel suspensions

We describe the elasticity of compressed microgel suspensions starting from a core--shell model for the single particle. The mechanical properties of the inner core and of the outer corona are described via the mean field Flory theory, and via the Alexander--de Gennes model for polymer brushes, respectively. The model successfully reproduces experimental measures of the elastic shear modulus up to a constant factor that we rationalize in the jamming perspective.

Excess thermodynamic parameters for binary and ternary mixtures of {1-butanol (1) + cyclohexylamine (2) + n-heptane (3)} at different temperatures: A theoretical study

In this work, we used the experimental data of Kijevcanin et al. for determining the excess thermodynamic parameters such as excess thermal expansion coefficients αE, isothermal coefficient of pressure excess molar enthalpy (∂HmE/∂P)T and excess partial molar volumes V¯m,iE for the binary and ternary mixtures formed by {1-butanol+cyclohexylamine+n-heptanes} at (288.15–323.15) K. The αE values, for 1-butanol+cyclohexylamine are S-shaped and for 1-butanol+n-heptane are positive and for cyclohexylamine+n-heptane are negative over the mole fraction range. The (∂HmE/∂P)T values, for 1-butanol+cyclohexylamine are S-shaped and for binary mixture of 1-butanol+n-heptane are negative and for binary mixture of cyclohexylamine+n-heptane are positive over the mole fraction. The values of αE and (∂HmE/∂P)T are calculated by using the Flory theory, the results show a good agreement with experimental data. The values of αE and (∂HmE/∂P)T for ternary mixture {1-butanol+cyclohexylamine+n-heptanes} are determined and the experimental data are correlated as a function of the mole fraction by using the equations of Cibulka, Jasinski and Malanowski, Singe et al., Pintos et al., Calvo et al., Kohler, and Jacob–Fitzner. The results show that the Calvo et al. equation is better than others.