基于链端体积分数的聚合物溶液理论

提出“链端体积分数”的概念以克服Flory-Huggins(FH)理论中的平均场假设.将聚合物多链体系看成一条“间隔连续链”,使一些热力学量写成路径积分的形式.在聚合物/溶剂体系中,保留了FH理论的无热熵假设,把总熵分为两部分,建立了一个新的聚合物溶液理论.计算了聚苯乙烯/环己烷体系的FH相互作用参数和相分离曲线,并与实验数据和FH理论作了比较,结果表明,我们的理论结果比FH的理论结果有了很大的改进.     

改进的聚合物溶液理论

在高分子溶液理论中引入Gibbs分布 ,用统计物理学方法重新推导出了聚合物溶液的热力学公式 .将高分子溶液的自由能和熵分三部分进行了计算 ,无热平动部分 ,无热构象部分和构象有热部分 .无热平动自由能和无热构象自由能分别等于Flory Huggins混合自由能公式的前两项 ,构象有热部分引入了Gibbs分布 ,考虑了链段 溶剂分子相互作用对高分子构象的影响 .在分子间的相互作用足够小时 ,又回到了FH公式     

Pressure Effects on Thermodynamics of Phase Behavior in Polystyrene/Methylcyclohexane Solutions

The calculations presented in this paper are based on the Sanchez-Lacombe(SL)lattice fluid theory.The interaction energy parameter,g12/k,required in this approach was obtained by fitting the cloud points of polystyrene(PS)/methylcyclohexane(MCH)polymer solutions under pressure.The SL lattice fluid theory was used to calculate the spinodals,the binodals,and the Flory-Huggins(FH)interaction parameter of the solutions.The calculated results show that the SL lattice fluid theory can describe the dependences of thermodynamics of PS/MCH solutions on temperature and pressure very well.However,the calculated enthalpy and the excess volume changes indicate that the Clausius-Clapeyron equation cannot be suitable to describe pressure effect on PS/MCH solutions.Further analysis on the thermodynamics of this system under pressure shows that the role of entropy is more important than the excess volume in the present case.     

Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints

We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of "site functions" for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.     

Integral equation theory for two-dimensional polymer melts

The polymer reference interaction site model theory is investigated for two-dimensional polymer melts composed of freely-jointed hard disk chains and tangent-disk rods. Exact results for the intramolecular pair correlation functions are input into the theory, and predictions of the theory for the intermolecular pair correlation functions are tested via comparison with simulation. The theory is not as accurate for this system as it is for three-dimensional polymer melts, and the quantitative predictions are not good except at the highest area fractions. Possible reasons for the deficiency in the theory are discussed.     

Entropy production during reversible polymerization in nonideal systems

A general route is shown to calculate the entropy production sigma as function of time t in a closed system during reversible polymerization. We treat the polymer molecules to behave nonideal and apply exemplarily the classical Flory-Huggins theory to get explicit expressions for the activity coefficient. At the beginning of the polymerization the system is in a nonequilibrium state where chemical reactions take place that irreversibly drive the system towards equilibrium with sigma approaching zero in the limit t-->infinity. The time-dependent course of the entropy production is explicitly calculated for two cases where the reaction starts (i) from monomer molecules polymerizing to a defined number average chain length xn,eq and (ii) from monodisperse polymer molecules reacting with each other under the constrain that xn is the same at the beginning and the end of the reaction. In both cases we find that the nature of the activity coefficient has an important effect on the curvature of sigma which may considerably differ from that of an ideal behavior.     

Lattice cluster theory of associating polymers. II. Enthalpy and entropy of self-assembly and Flory-Huggins interaction parameter χ for solutions of telechelic molecules

The lattice cluster theory for solutions of telechelic polymer chains, developed in paper I, is applied to determine the enthalpy Δh(p) and entropy Δs(p) of self-assembly of linear telechelics and to evaluate the Flory-Huggins (FH) interaction parameter χ governing the phase behavior of these systems. Particular focus is placed on examining how these interaction variables depend on the composition of the solution, temperature, van der Waals and local "sticky" interaction energies, and the length of the individual telechelic chains. The FH interaction parameter χ is found to exhibit an entropy-enthalpy compensation effect between the "entropic" and "enthalpic" portions as either the composition or mass of the telechelic species is varied, providing unique theoretical insights into this commonly reported, yet, enigmatic phenomenon.     

Influence of added particles on the phase behavior of polymer solutions. Analysis by mean-field lattice theory

The influence of added colloidal particles on the phase stability of polymer solutions is investigated theoretically. The polymer has an affinity to the particle surface. A mean-field lattice theory based on the Flory-Huggins theory is used to calculate the phase behavior in solutions containing a single polymer component and particles. The particles are described in two different ways. The first approach considers the surface free energy associated with added solid particles and the mixing entropy of the particles. In the second approach, the particles are simply modeled as large polymers. Both ways of describing the added particles show that the added particles decrease the stability of the polymer solution when the polymer-particle attraction is strong. A higher particle concentration enhances the effect. Experiments where polystyrene latex particles are added at different concentrations to aqueous dispersions of ethyl(hydroxyethyl)cellulose (EHEC) support the theoretical findings.     

The effect of polymer chain length on the thermodynamics of acrylate/cyanobiphenyl mixtures

The effect of polymer molecular mass on the phase behaviour and solubility limits of polymer/liquid crystal mixtures is studied for blends of poly(methyl methacrylate) (PMMA) and the small-molecule liquid crystal, 4'-octyl-4-biphenylcarbonitrile (8CB). The phase diagrams from optical microscopy show a limit to the effect of increasing polymer molecular mass. The Flory-Huggins theory (FH) for polymer solutions is used to extract the interaction parameter, χ, from the phase diagrams. The initial FH fits are performed with the assumption that χ is independent of polymer molecular mass, but result in poor correlation to the microscopy data. When χ is allowed to scale with M _w, however, the FH fits are consistent with the limiting molecular mass behaviour. This result represents, to our knowledge, the first time that this scaling behaviour has been observed in polymer/liquid crystal blends. The solubility limit, β, of 8CB in PMMA for each polymer molecular mass is also determined and, when compared with the results of previous studies, support the concept that β is independent of both polymer composition and molecular masses when the polymer molecular mass exceeds ca. 5×10⁵ g mol^-1.     

Environmental swap energy and role of configurational entropy in transfer of small molecules from water into alkanes

We studied the effect of segmented solvent molecules on the free energy of transfer of small molecules from water into alkanes (hexane, heptane, octane, decane, dodecane, tetradecane, and hexadecane). For these alkanes we measured partition coefficients of benzene, 3-methylindole (3MI), 2,3,4,6-tetrachlorophenol (TeCP), and 2,4,6-tribromophenol (TriBP) at 3, 11, 20, 33 [corrected], and 47 degrees C. For 3MI, TeCP, and TriBP the dependence of free energy of transfer on length of alkane chains was found to be very different from that for benzene. In contrast to benzene, the energy of transfer for 3MI, TeCP, and TriBP was independent of the number of carbons in alkanes. To interpret data, we used the classic Flory-Huggins (FH) theory of concentrated polymer solutions for the alkane phase. For benzene, the measured dependence of energy of transfer on the number of carbons in alkanes agreed well with predictions based on FH model in which the size of alkane segments was obtained from the ratio of molar volumes of alkanes and the solute. We show that for benzene, the energy of transfer can be divided into two components, one called environmental swap energy (ESE), and one representing the contribution of configurational entropy of alkane chains. For 3MI, TeCP, and TriBP the contribution of configurational entropy was not measurable even though the magnitude of the effect predicted from the FH model for short chain alkanes was as much as 20 times greater than experimental uncertainties. From the temperature dependence of ESE we obtained enthalpy and entropy of transfer for benzene, 3MI, TeCP, and TriBP. Experimental results are discussed in terms of a thermodynamic cycle considering creation of cavity, insertion of solute, and activation of solute-medium attractive interactions. Our results suggest that correcting experimental free energy of transfer by Flory-Huggins configurational entropy term is not generally appropriate and cannot be applied indiscriminately.     

Applications of polymer rism theory to blends

Polymer RISM (reference interaction site model) theory is a theory of polymer systems in the liquid phase in which account for chemical realism can be made. Results are reported here of phase diagrams (spinodals) for blend systems calculated by means of this theory, using the mean spherical approximation as a closure. The systems investigated are an isotopic blend, a set of homopolymer/copolymer blends, and a model blend containing specific interactions.     

Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

Microscopic theory of rubber elasticity

A microscopic integral equation theory of elasticity in polymer liquids and networks is developed which addresses the nonclassical problem of the consequences of interchain repulsive interactions and packing correlations on mechanical response. The theory predicts strain induced softening, and a nonclassical intermolecular contribution to the linear modulus. The latter is of the same magnitude as the classical single chain entropy contribution at low polymer concentrations, but becomes much more important in the melt state, and dominant as the isotropic-nematic liquid crystal phase transition is approached. Comparison of the calculated stress-strain curve and induced nematic order parameter with computer simulations show good agreement. A nearly quadratic dependence of the linear elastic modulus on segmental concentration is found, as well as a novel fractional power law dependence on degree of polymerization. Quantitative comparison of the theory with experiments on polydimethylsiloxane networks are presented and good agreement is found. However, a nonzero modulus in the long chain limit is not predicted since quenched chemical crosslinks and trapped entanglements are not explicitly taken into account. The theory is generalizable to treat the structure, thermodynamics and mechanical response of nematic elastomers.     

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.     

A thermodynamic approach to study hydrogen-bonding interactions in solvent/solvent/polymer ternary systems

A thermodynamic approach based on both the classical Flory-Huggins (FH) formalism and the association equilibria (AE) theory has been developed to study the solubility properties of a system formed by a proton-donor solvent (A), a proton-acceptor solvent (B) and a proton-acceptor polymer (C). The miscibility of this ternary system is attained by competitive specific interactions via hydrogen-bonding established between the hydroxyl and carbonyl interacting groups of either solvent-solvent (AB) or solvent-polymer (AC) system components. The binary AB and AC specific interactions and their dependence with the system composition as well as with the extent of the association equilibrium have been quantified by means of two new parameters, Δg_AB and Δg_AC. These excess functions have appeared to be equivalent to the combinatorial or entropic term of the Gibbs free energy of the complex formation process, which accounts for the entropy of mixing plus the intermolecular specific interactions. The theoretical predictions have reasonablely agreed with experimental data on preferential solvation of two systems taken from literature: methanol(A)/1,4-dioxane(B)/poly(alkyl methacrylate)(C) and n-alcohol(A)/heptan-3-one(B)/poly(vinyl pyrrolidone)(C).     

Entropic concepts in electronic structure theory

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations.     

Thermodynamic model of gas permeability in polymer membranes

A new molecular thermodynamic model is developed of the gas permeability in polymer membranes on the basis of configurational entropy and Flory‐Huggins theory to predict permeability dependence on the concentration of penetrant. Three kinds of configurational entropy are taken into account by this model; that is, the disorientation entropy of polymer, the mixing entropy, and specific interaction entropy of polymer/gas. The validity of the mathematical model is examined against experimental gas permeability for polymer membranes. Agreement between experimental and predicted permeability is satisfactory. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 661–665, 2007     

Elastic Behavior of Polymer Chains

The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance, the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution. These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.