An improvement in the flory corresponding-states theory of polymer solutions

The original Flory corresponding-states theory of polymer solutions requires an entropic correction parameter Q₁₂, the sign and value of which seem to be arbitrary, and the physical meaning of which is obscure. Moreover, calculated excess volumes of mixing for many polymer solutions are often in significant disagreement with experimental data. In order to eliminate these problems, we have modified the kinetic part of the partition function, introduced an effective mass for the mixture segment, and adopted the nonlinearity of the number of degrees of freedom with respect to the composition for the mixture segment. In addition, the effect of nonrandom configurations of the segments in the mixture has been included. In the improved equations, derived in this work, the Flory interaction parameter χ can be considered to comprise three parts: (a) a kinetic part due to the contribution of the average number of degrees of freedom and the effective mass of the mixture; (b) a free volume part; and (c) an interaction part including the contributions due to the contact interaction and the nonrandom configuration of the segments in the mixture, caused by the interaction. The improved theory is in good agreement with literature data on polystyrene solutions and poly (dimethyl siloxane) solutions.     

Polymer surfactant kinetics using surface plasmon resonance spectroscopy dodecyltrimethylammonium chloride/polyacrylic acid system

Kinetics of polymer surfactant interactions and the effect of surfactant binding on the conformational dynamics of the polymer were explored in this work using surface plasmon resonance spectroscopy. Polyacrylic acid was modified with thiol to varying degrees so as to force the polymer to form different loop sizes upon adsorption on the gold SPR sensor surface. Dodecyltrimethylammonium chloride in solution was flowed over the polymer-coated sensor surface and the binding was followed in real time. It was found that control of the loop size of the polymer on the solid surface enabled in turn the control of surfactant binding, with the largest loop allowing the maximum amount of surfactant to bind and vice versa. The kinetic plot of the binding showed three distinct segments. The first segment followed convective-diffusive kinetics. The second and third segments followed first-order kinetics with the second rate being significantly faster than the first one. Careful analysis of the second segment showed that it is possible to divide it into two different segments, each following a first-order kinetics, with the second rate being slightly slower than the first one suggesting a gradual slow down of the reaction due to convolution from the polymer conformational changes. Mechanistically, the sudden increase in the rate for the third segment of surfactant binding implies that the polymer matrix is opening up so as to incorporate more surfactant molecules. This was attributed to the formation of charged double surfactant species the repulsive interaction of which prevented the polymer network from imploding. Studies using unmodified polymers suggested the possibility of sudden conformational rearrangement in the polymer network, with progress in surfactant binding. Furthermore, the reflectance of the SPR spectrum was found to increase upon surfactant binding, implying that there is a decreased efficiency of coupling of the incident radiation into the surface plasmon mode of the metal, which suggests that the surfactant actually penetrated the polymer matrix.     

PCL-based Shape Memory Polymers with Variable PDMS Soft Segment Lengths

Thermoresponsive shape memory polymers (SMPs) are stimuli-responsive materials that return to their permanent shape from a temporary shape in response to heating. The design of new SMPs which obtain a broader range of properties including mechanical behavior is critical to realize their potential in biomedical as well as industrial and aerospace applications. To tailor the properties of SMPs, "AB networks" comprised of two distinct polymer components have been investigated but are overwhelmingly limited to those in which both components are organic. In this present work, we prepared inorganic-organic SMPs comprised of inorganic polydimethyl-siloxane (PDMS) segments of varying lengths and organic poly(ε-caprolactone) (PCL) segments. PDMS has a particularly low T(g) (-125 °C) which makes it a particularly effective soft segment to tailor the mechanical properties of PCL-based SMPs. The SMPs were prepared via the rapid photocure of solutions of diacrylated PCL(40)-block-PDMS(m)-block-PCL(40) macromers (m = 20, 37, 66 and 130). The resulting inorganic-organic SMP networks exhibited excellent shape fixity and recovery. By changing the PDMS segment length, the thermal, mechanical, and surface properties were systematically altered.     

Entropically mediated polyolefin blend segregation at buried sapphire and air interfaces investigated by infrared-visible sum frequency generation vibrational spectroscopy

The segregation behavior of binary polymer blends at hydrophilic solid sapphire and air interfaces was investigated by infrared-visible sum frequency generation (SFG) vibrational spectroscopy. SFG spectra were collected from a bulk miscible blend consisting of identical molecular weight (approximately 54,000) and similar surface free energy (29-35 dyn/cm) components of atactic polypropylene (aPP) and aspecific poly(ethylene-co-propylene) rubber (aEPR). Characteristic CH resonances of the blend were contrasted with those of the individual components at both buried (sapphire/polymer) and free (air/polymer) interfaces. Preferential segregation of the aPP component was observed after annealing at both air/polymer and sapphire/polymer interfaces. SFG spectra revealed ordering of the polymer backbone segments with the methylene (CH2) groups perpendicular to the surface at the sapphire interface and the methyl (CH3) groups upright at the air interface. The SFG results indicate that the surface composition can be determined from the peak intensities that are characteristic of each component and that conformational entropy played a likely role in surface segregation. aPP occupied a smaller free volume at the surface because of a statistically smaller segment length (aPP is more flexible and has a shorter length). In addition, the high density of the ordered CH3 side branches enhanced the surface activity by allowing the long-chain backbone segments of aPP to order at the surface.     

共轭/非共轭嵌段聚苯撑乙烯(PPV)类共聚物的合成与性能

用活性中间体直接引发共轭/非共轭单体聚合的新方法合成了3种PPV嵌段共聚物;用核磁共振谱和FTIR光谱确定了共聚物的结构.引入非共轭片段PS缩短了PPV共轭链的长度,改善了聚合物的溶解性和可加工性.荧光光谱结果表明,嵌段聚合物可使发射峰蓝移,发光的量子效率明显提高,进而调节了发光颜色.     

The theta-temperature depression caused by topological effect in ring polymers studied by Monte Carlo simulation

We studied equilibrium conformations of linear and ring polymers in dilute solutions over the wide range of segment number N of up to 2048 with Monte Carlo simulation, and evaluated N dependence of the radii of gyration, R(g), of chains. The polymer molecules treated in this study are assumed to be composed of beads and bonds, and they are put in a three-dimensional face-centered cubic (FCC) lattice. The values of Flory's critical exponent, ν, for linear and ring polymers were estimated from the N dependence of R(g), and the temperatures at which ν reach 1/2 were obtained. Here we define those as Θ-temperatures in this report. The simulation result shows that the Θ-temperature for ring polymers is evidently lower than that of the linear polymers, and the origin of the Θ-temperature depression is discussed. Since R(g) of a ring polymer is smaller than that for a linear polymer at the same N and temperature, the segment density for a ring polymer is increased by the topological effect and the repulsive force between segments of a ring polymer at the Θ-temperature for a linear polymer is stronger. Thus, the origin of the Θ-temperature depression for ring polymers is the repulsive force emphasized by the topological effect of rings.     

Flow rates of polymer solutions through porous disks as a function of solute. II. Thickness and structure of adsorbed polymer films

The thickness of films of poly(methyl methacrylate) (PMMA), poly(vinyl acetate) (PVAc), and polystyrene (PS) adsorbed on Pyrex glass was studied by measuring the flow rates of polymer solutions and the corresponding pure solvents through sintered filter disks. Adsorption isotherms were in agreement with those reported by other workers and showed saturation adsorption equivalent to 2–8 condensed monolayers of monomer units. Film thicknesses were of the order of magnitude of the free coil diameters in solution and were directly proportional to the intrinsic viscosity of the polymer, except for PS in benzene where the thicknesses leveled off as molecular weight increased. It was concluded that polymers adsorb from solution in monolayers of compressed or interpenetrating coils; that below some critical molecular weight which varies with polymer and solvent, a much larger fraction of the segments lies directly in the interface; that adsorbed films may consist of a dense layer immediately adjacent to the surface and a deep layer of loops extending into the solvent; and that it is the segment—solvent interaction rather than the segment—surface interaction which dominates the conformation of the adsorbed chain.     

Control of hard segment size in polyurethane formation

In general, segmented polyurethane elastomers are prepared by reacting an isocyanate-capped polyol prepolymer with a short-chain diol chain extender, yielding an elastomer with hard segments of uniform size. However, the hard segment size will not be uniform if the polyurethane polymer is prepared by forming the hard segment first, followed by soft segment formation. Because the mechanical properties of polyurethane elastomers depend on the relative ratio of the hard to soft segments as well as the effectiveness of the hard segment as a physical crosslinker, the control of the size distribution of the hard segment is a key factor in designing polyurethane elastomers. It was found that reaction conditions can affect the size distribution of hard segments derived from an aliphatic diisocyanate with differential reactivity between the two isocyanate groups. Lower reaction temperatures and simultaneous mixing of all reactants gave the preferred size distribution of hard segments. © 1995 John Wiley & Sons, Inc.     

Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

A combined analytical–numerical study is presented for the slow motion of a spherical particle coated with a layer of adsorbed polymers perpendicular to an infinite plane, which can be either a solid wall or a free surface. The Reynolds number is assumed to be vanishingly small, and the thickness of the surface polymer layer is assumed to be much smaller than the particle radius and the spacing between the particle and the plane boundary. A method of matched asymptotic expansions in a small parameter λ incorporated with a boundary collocation technique is used to solve the creeping flow equations inside and outside the adsorbed polymer layer, where λ is the ratio of the characteristic thickness of the polymer layer to the particle radius. The results for the hydrodynamic force exerted on the particle in a resistance problem and for the particle velocity in a mobility problem are expressed in terms of the effective hydrodynamic thickness (L) of the polymer layer, which is accurate to O(λ²). The O(λ) term forLnormalized by its value in the absence of the plane boundary is found to be independent of the polymer segment distribution and the volume fraction of the segments. The O(λ²) term forL, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant.     

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.     

Thermal diffusion of dilute polymer solutions: the role of solvent viscosity

We have performed measurements of the thermal diffusion coefficient D(T) in the dilute limit on polystyrene in cyclo-octane, cyclohexane, benzene, toluene, tetrahydrofuran, ethyl acetate, and methyl ethyl ketone and of poly(dimethyl-siloxane) in toluene. These data have been combined with literature data to test various theoretical predictions. The viscosity is identified as the dominating and only relevant solvent parameter. On the polymer side, the size or mass of an effective correlated segment determines the strength of the Soret effect. Large and heavy effective segments, as found in stiffer chains, lead to higher D(T).     

Effect of adsorbed polymers on the slow motion of an assemblage of spherical particles relative to a fluid

 The effects of adsorbed polymers on the sedimentation of a homogeneous distribution of colloidal spheres and on the fluid flow through a bed of particles are investigated theoretically. The Reynolds number is assumed to be small, and the surface polymer layers are assumed to be thin with respect to the radius of particles and to the surface-to-surface spacing between neighboring particles. The effects of interaction of the individual particles are taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of spheres within a fluid in the absence of adsorbed polymers. To solve the Stokes flow equations within and outside the polymer layer a method of matched asymptotic expansions in a small parameter λ is used, where λ is the ratio of the length scale of the polymer layer to the particle radius. The results for the sedimentation rate and the pressure drop are expressed in terms of an effective hydrodynamic thickness (L) of the polymer layer, which are accurate to O(λ²). When the concentration of particles in a suspension or a bed is increased, L becomes larger, meaning the settling velocity decreases or the pressure drop increases. The O(λ) term for L normalized by its value in the limit λ→0 is found to be independent of the polymer segment distribution, the hydrodynamic inter-actions among the segments, and the volume fraction of the segments. The O(λ²) term for L, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the particle-interaction effects on the motion of polymer-coated particles relative to a fluid can be quite significant. Received: 28 August 1996 Accepted: 23 January 1997     

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     

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.