聚合物体系散射函数的热力学基础

利用链段浓度和链头浓度的概念，根据热力学涨落理论，给出了聚合物二元共混体系ｄｅＧｅｎｎｅｓ散射函数的一个普遍的热力学证明，指出了这个函数和Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ共混自由能公式一样，也依赖于忽略构象涨落的假设．     

A new class of pressure-sensitive adhesives based on interpolymer and polymer-oligomer complexes

On the basis of previous concepts concerning the molecular nature of pressure-sensitive adhesion, a simple method of preparing new adhesives with the desired mechanical and adhesive behavior and water-absorbability via mixing of nonadhesive polymers has been developed. Pressure-sensitive adhesion is related to the combination of a high energy of cohesion and a large free volume, which leads to a high molecular mobility. This method is based on the formation of interpolymer or polymer-oligomer complexes during mixing of macromolecules capable of hydrogen, electrostatic, or ionic bonding. In interpolymer complexes, a high cohesion results from the formation of bonds between macromolecules carrying complementary groups in main chains, whereas free volume is related to defectiveness of the resulting network and formation of loops. In complexes formed by a high-molecular-mass polymer and an oligomer carrying complementary reactive groups at ends of short chains, a high energy of cohesion is related to their interaction with mainchain functional groups of the polymer, whereas a relatively large free volume is associated with the length and flexibility of intermacromolecular crosslinks via oligomer chains. The adhesive and viscoelastic properties of adhesives and their water absorbability are regulated by changes in the composition of mixtures of a film-forming polymer with a polymer or oligomer crosslinker and a plasticizer. In this case, an increase in cohesive strength is achieved owing to an increase in the crosslinker concentration, while the enhancement of free volume is ensured by the increasing plasticizer content in the blend. Adhesive materials capable of adherence to wet substrates, hydroactivated adhesives, and adhesion moisture sorbents have been prepared for the first time.     

路径积分方法计算聚合物溶液热力学性质

提出了把聚合物溶液的自由能分解为 3部分 ,平动部分、构象部分和热修正项部分 .其中后两部分具有相对于链段的可加性 ,在引入了“有效浓度”的概念后可以用路径积分方法计算 .当采用体积分数代替有效浓度时 ,就回到了李晓毅和赵得禄的溶液理论 .还利用本理论研究了不同分子量聚苯乙烯 环己烷体系的相分离曲线 ,同Flory Huggins(FH)理论相比 ,大大提高了同实验数据的符合程度     

Sedimentation of dissolved macromolecules in the vicinity of the consolute point 1. Strictly binary systems and kinetic considerations

This paper analyzes the effect of gravity on polymer solutions near the consolute point. Calculations are carried out for monodisperse polystyrene in cyclohexane using the Flory-Huggins expression with a concentration-dependent interaction parameter for the free energy of mixing. Depending on molecular weight and distance to the demixing temperature, the influence of gravity leads to non-negligible gradients of the volume fraction in the one-phase region as well as in the two-phase region. In particular, the effect of gravity on the measurement of the coexistence curve in a finite sample is calculated explicitly.In contrast to theory, experiments show that the concentration remains constant throughout the sample over a period of days as long as the system is kept in the homogenous region. Pronounced concentration gradients, however, are established in the twophase region within approximately one day. These findings are discussed with respect to sedimentation kinetics in terms of the droplet model of critical fluids.     

Mesoscale model parameters from molecular cluster calculations

We present an efficient, systematic, and universal method to estimate the interaction parameters used in mesoscale simulation methods such as dissipative particle dynamics and self-consistent field methods from molecular cluster calculations. The method is based on a generalized Flory-Huggins model in which molecules, or fragments thereof, are in contact with their van der Waals surface. We sample the density of states of molecular clusters in the space spanned by the coarse-grained degrees of freedom. From here, we calculate the sum over states and free energy of the cluster at a temperature of interest by histogram reweighting. The method allows to calculate the energy and entropy contributions to the cluster free energy explicitly. For two components, we then obtain the excess free energy of mixing and the Flory-Huggins chi-parameter, and their energetic and entropic contributions. We present two applications of the method: a simple liquid mixture of hexane and nitrobenzene, and a series of polymer blends. In the case of hexane/nitrobenzene, we compare to alternative simulation methods; here we find that the energy of mixing alone is too high to explain the critical point. By including the excess entropy of mixing, however, the predicted phase behavior is in reasonable agreement with experiment. The tendency of calculations based on average energy alone to overestimate the chi-parameter is also apparent in the polymer blend calculations.     

Steric and bridging interactions between two plates induced by grafted polyelectrolytes

If colloidal particles are grafted with a polymer, then the grafted chains can provide steric repulsion between them. If some of the grafted polymer chains are also adsorbed to a second particle, then a bridging force is generated as well. For uncharged plates and polymer, the following contributions to the free energy of the system have been taken into account in the calculation of the interaction force: (i) the Flory-Huggins expression for the mixing free energy of the grafted chains with the liquid; (ii) the entropy loss due to the connectivity of the polymeric segments; (iii) the van der Waals interactions between the segments and the plates; and (iv) the free energy of adsorption of the polymer segments of the grafted chains on the other plate. For charged plates, the electrostatic free energy as well as the free energy of the electrolyte are included in the total free energy of the system. By minimizing the free energy with respect to the segment concentration and, when it is the case, with respect to the electrical potential, equations for the segment number density distribution and for the electrical potential are obtained, on the basis of which the interactions between two plates grafted with polymer chains that can be also adsorbed on the other plate were calculated. The interaction thus obtained includes steric and bridging forces.     

Sorption and diffusion of water in poly(vinylpyrrolidone)

The effect of molecular mass, thermal prehistory, physical state, and three-dimensional chemical crosslinked structure of a polymer on dissolution and diffusion in the PVP-water system has been studied. The kinetic dependences of sorption that correspond to the Fickian or pseudonormal type have been measured. In a certain concentration range, sorption is accompanied by transition of the system to the rubbery state. In the glassy state, the negative concentration dependence of the diffusion coefficient related to the nonequilibrium state of the polymer sorbent is observed. Sorption isotherms are described by S-shaped curves. It has been shown that the thermal prehistory of the polymer sorbent has the most pronounced effect on its sorption behavior. The effect of molecular mass is insignificant, while three-dimensional chemical crosslinks in PVP manifest themselves only in the region of the rubbery state. In accordance with the double sorption model, the experimental isotherms are represented as the superposition of two isotherms described by the Langmuir and Flory-Huggins equations. For the glassy state of the polymer sorbent, the degree of the nonequilibrium state has been estimated. With due regard for the excess free volume, the detailed thermodynamic analysis of isotherms has been performed; namely, the pair interaction parameters and the free energy of mixing have been calculated. The state of water in the polymer has been examined within the framework of hydrate contributions and clusterization theory.     

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.     

Use of numerical methods in the prediction of polymer adsorption

Average polymer segment densities and thermodynamic properties of polymer adsorbed at liquid–solid interfaces were computed by extension of the polymer adsorption theory of Forsman and Hughes. Expressions were derived for the total free energy of adsorbed polymer chains by using the Flory-Huggins theory to represent free energy of mixing. A square-well potential was used to represent segment–surface interaction, and configurational entropy was calculated from the probability density function for the radius of gyration of random-flight chains. For each specified amount of surface coverage the free energy of the adsorbed polymer was minimized by varying the density of segments normal to the adsorbing surface and using a modified gradient search algorithm on a digital computer. Two different segment densities were considered, and they both gave qualitatively the same results. The two densities were (1) the sum of two Gaussian distributions and (2) a two-step density distribution. Isotherms were then calculated by equating the partial molal free energy of polymer at the surface to that of polymer in bulk solution for each specified amount of surface coverage. The results showed that for the initial region of the isotherms the distribution of polymer segments normal to the surface consisted of a high-density layer adjacent to the surface and a low-density “tail” extending far out into the solution. At higher amounts of adsorbed polymer, i.e., in the general concentration range of the pseudo-plateau, the tail of the polymer density distribution was predicted to thicken, and a single Gaussian distribution best described the segment density. Predicted adsorptions were in good agreement with reported experimental values.     

Use of numerical methods in the prediction of polymer adsorption

Average polymer segment densities and thermodynamic properties of polymer adsorbed at liquid–solid interfaces were computed by extension of the polymer adsorption theory of Forsman and Hughes. Expressions were derived for the total free energy of adsorbed polymer chains by using the Flory-Huggins theory to represent free energy of mixing. A square-well potential was used to represent segment–surface interaction, and configurational entropy was calculated from the probability density function for the radius of gyration of random-flight chains. For each specified amount of surface coverage the free energy of the adsorbed polymer was minimized by varying the density of segments normal to the adsorbing surface and using a modified gradient search algorithm on a digital computer. Two different segment densities were considered, and they both gave qualitatively the same results. The two densities were (1) the sum of two Gaussian distributions and (2) a two-step density distribution. Isotherms were then calculated by equating the partial molal free energy of polymer at the surface to that of polymer in bulk solution for each specified amount of surface coverage. The results showed that for the initial region of the isotherms the distribution of polymer segments normal to the surface consisted of a high-density layer adjacent to the surface and a low-density “tail” extending far out into the solution. At higher amounts of adsorbed polymer, i.e., in the general concentration range of the pseudo-plateau, the tail of the polymer density distribution was predicted to thicken, and a single Gaussian distribution best described the segment density. Predicted adsorptions were in good agreement with reported experimental values.     

Phase diagrams of binary crystalline-crystalline polymer blends

A thermodynamically self-consistent theory has been developed to establish binary phase diagrams for two-crystalline polymer blends by taking into consideration all interactions including amorphous-amorphous, crystal-amorphous, amorphous-crystal, and crystal-crystal interactions. The present theory basically involves combination of the Flory-Huggins free energy for amorphous-amorphous isotropic mixing and the Landau free energy of polymer solidification (e.g., crystallization) of the crystalline constituents. The self-consistent solution via minimization of the free energy of the mixture affords determination of eutectic, peritectic, and azeotrope phase diagrams involving various coexistence regions such as liquid-liquid, liquid-solid, and solid-solid coexistence regions bound by liquidus and solidus lines. To validate the present theory, the predicted eutectic phase diagrams have been compared with the reported experimental binary phase diagrams of blends such as polyethylene fractions as well as polycaprolactone/trioxane mixtures.     

Partial miscibility of liquid mixtures of protonated and deuterated high polymers

Certain low-angle neutron scattering experiments on bulk protonated polymers containing a fraction of the deuterated species (or vice versa) suggest that clustering of like isotopes is occurring. In order to see whether this is likely, a form for the Helmholtz free energy of mixing is proposed, using thermodynamics and the ideal solution (Flory-Huggins) entropy of mixing. From this free energy the upper consolute point T_c is found. T_c is calculated for several isotopic molecular solutions. The results suggest that while isotope segregation phenomena are impossible for small hydrocarbons, they may become important for large polymer systems.     

A new formula for the entropy of mixing in polymer systems and free volume

The famous equations of Flory-Huggins for the entropy of mixing with one highmolecular component are of great importance for polymer physics. But Gujrati stated in 1980 [12] that these equations cannot be exact. This is why we derived a new formula for the dependence of the entropy from the fraction of vacant sites in a quasi-lattice. It differs significantly from that of Huggins and still more from that of Flory in the case of low free volume. The equations of Flory-Huggins are correct with reference to low polymer content only.If our formula for entropy is used instead of that of Huggins an important result of the theory of Gibbs-DiMarzio is called in question. The increase of thermal expansion at the glass transition cannot be explained by an increase of vacant sites. A growth of the number of unoccupied sites according to the thermodynamic equilibrium condition would bring about a far too great thermal expansion coefficient. From estimations of the energy of interaction between polymer molecules, which can be found in literature, it follows that the increase of entropy is far too small to enable the formation of vacant sites above the glass transition. It is unambiguously shown that the free volume, commonly regarded to be the decisive quantity with respect to glass transition, cannot consist of holes as considered in the quasi-lattice model and in many theoretical treatments.     

Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Associative phase separation (complex coacervation) in a mixture of oppositely charged polyelectrolytes can lead to different types of (inter-)polyelectrolyte complexes (soluble micelles, macroscopic precipitation). In a previous report [Langmuir 2004, 20, 2785-2791], we presented a model for the electrostatic free energy change when (weakly charged) polyelectrolyte forms a homogeneous complex phase. The influence of ionization of the polymer on the electrostatic free energy of the complex was incorporated but the influence of complex density neglected. In the present effort, cylindrical cells are assumed around each polyelectrolyte chain in the complex, and on the basis of the Poisson-Boltzmann equation, the electrostatic free energy is calculated as a function of the complex density. After combination with Flory-Huggins mixing free energy terms and minimization of the total free energy, the equilibrium complex density is obtained, for a given ratio of polycations to polyanions in the complex. The analysis is used in an example calculation ofpolyelectrolyte film formation by alternatingly applying a polycation and a polyanion solution. The calculation suggests that the often observed exponential growth of a polyelectrolyte film when the polymer is weakly charged has a thermodynamic origin: the polyelectrolyte complex shifts repeatedly between two equilibrium states of different densities and compositions. However, when the polyelectrolytes are strongly charged the difference in the compositions between the two equilibrium states is very small, and exponential growth by an absorption mechanism is no longer possible.     

Polymer fractionation. II. The analytical problem

Complete fractionations into 5, 10, and 20 fractions were calculated by a numerical method based on the Flory-Huggins theory in order to evaluate various procedures for determining the molecular weight distribution from fractionation data. If the initial distributions are wide, the differential distribution cannot be accurately reconstructed, not even if each fraction is characterized by two average molecular weights (instead of one, as is customary). In addition to this inadequacy in the evaluation procedure there are the experimental errors which further detract from the accuracy of the result. The integral distribution can, in some cases, be approximated fairly well by means of the Schulz method, provided that the polymer is separated into many fractions with narrow distributions. However, the integral distribution thus obtained does not reflect details in the differential distribution. Polymer fractionation does not appear to be a suitable procedure for accurate determination of the differential distribution. From the assembled material, a thermodynamic method has been derived which seems to hold out better prospects. It should enable the differential distribution to be directly determined from a detailed analysis of the liquid–liquid phase relationships, provided the free energy of mixing function of the system is known.     

Phase separation of polymer solutions. The calculation of the cloudpoint curve with a concentration and temperature-dependent free energy correction parameter

The free enthalpy correction parameter g in the Flory-Huggins equation for the Gibbs free enthalpy of mixing in polymer solutions is considered generally as a concentration- and temperature-independent parameter. It has been extended here with linear concentration- and temperature-dependent terms. With these parameters, six different types of cloudpoint curves can be predicted. Using the experimental cloudpoint curve for solutions of poly(2,6-dimethyl-1,4-phenylene oxide) in toluene up to about 70 per cent by weight of polymer, a set of g-parameters is obtained, accounting for concentration and temperature dependence. With the parameters thus obtained, the melting point curve has been calculated which agrees very well with the experimental melting points for this system.     

Separation of components in lipid membranes induced by shape transformation

Vesicles composed of a two component membrane with each component characterized by different spontaneous curvature are investigated by minimization of the free energy consisting of Helfrich elastic energy and entropy of mixing. The results show that mixing and demixing of membrane components can be induced by elongating a vesicle or changing its volume, if one of the components forms a complex with macromolecules on the outer monolayer. The influence of elastic coefficients on the separation of components is also examined.     

Termination rate constant in free-radical polymerization

The specific rate constant for the termination reaction between two flexible polymer molecules with active chain ends has been considered in relation to the segmental diffusion of chain ends in solution. The probability of reaction between two chain ends per unit time when the centers of gravity of two polymer molecules are at a distance of separation has been calculated by using the Smoluchowski equation and a Gaussian distribution of chain ends. The time during which two polymer molecules are in contact has also been calculated by using the diffusion equation and the potential energy function for intermolecular interaction. The rate constant may then be completely expressed as a complex function of the intramolecular linear expansion factor, molecular weight, and the frictional properties of the reacting polymers' segment. This expression predicts that the rate constant is inversely proportional to solvent viscosity, decreasing with increasing molecular weight to some extent, and is affected by the excluded volume effect and chain flexibility. The complete expression for the rate constant has been simplified and the result compared with experimental data. Close agreement is found between the calculated rate constants and those experimentally obtained.     

Phase relationships in a ternary solution composed of a solvent and two monodisperse homologous polymers

Exact expressions are derived for the spinodal, critical conditions, and separation factor of a ternary solution consisting of a pure solvent and two monodisperse homologous polymers in which the Flory-Huggins interaction parameter χ depends separately on the concentrations of the polymer components. The results allow one to see the difference from previous expressions obtained with χ depending on the total concentration of the polymer, and are expected to be useful for experimental determination of the Gibbs free energy of ternary solutions.     

Mixing Properties of Two-Dimensional Lattice Solutions of Amphiphiles

Lattice Monte Carlo simulations of two-dimensional amphiphile solutions are used to examine the accuracy of the mixing properties predicted by lattice theories such as the Flory-Huggins theory, random-solution approximation, and quasichemical approximation. The internal energy, Helmholtz free energy, and entropy of mixing have been calculated from the configurational energy data obtained from the simulations, and the effect of nonrandom mixing on these properties has been determined. The quasichemical approximation predicts the entropy and Helmholtz free energy of mixing accurately for the amphiphile solution, but fails to predict the energy of mixing, due to the presence of microphase (self-aggregation) separation, which is beyond the reach of the quasichemical approximation, a mean-field theory. Helmholtz free energy of mixing is predicted accurately, and the shielding of the solvophobic segments in the microphase leads to small energies of mixing compared to the entropy of mixing. Copyright 2000 Academic Press.