Integral equation theory for athermal solutions of linear polymers

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.     

Unified analysis of thermodynamic and rheological properties of high polymer solutions. I. Binary systems

We present a comprehensive experimental study of thermodynamic and rheological properties of semidilute polymer solutions in good solvent. Osmotic pressure and viscosity measurements have been done in several polymer‐solvent systems at different temperatures. A renormalization group technique was applied to analyze the data using de Gennes's blobs model to connect dynamic and conformational quantities. The behavior of polymer systems in the whole range from dilute to semidilute solutions can be satisfactorily described using only a few nonuniversal quantities experimentally determined. An adequate agreement between experiments and theory was found, showing universal behavior with a system‐dependent constant β that does not depend on molecular weight or concentration. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 290–301, 2002     

Unified analysis of thermodynamic and rheological properties of high polymer solutions. II. Ternary systems

We extend to ternary solutions our previous study of conformational, thermodynamic, and rheological properties of semidilute polymer solutions in good solvent. Osmotic pressure and viscosity measurements were performed in several mixtures of two compatible polymers in a common solvent. Renormalization group results were used to analyze the data, using de Gennes's blobs model to connect dynamic and conformational properties. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1071–1079, 2002     

Conductometric properties of linear polyelectrolytes in poor-solvent condition: the necklace model

We present a set of low-frequency electrical conductivity measurements of solutions of differently charged, salt-free polyelectrolytes in poor- and in good-solvent conditions, in the semidilute concentration regime. The data have been analyzed and discussed in light of the necklace model for hydrophobic polyelectrolytes recently proposed by Dobrynin et al. [Macromolecules 29, 2974 (1996)] that predicts the chains to collapse into spheroidal cores connected by narrow strings. By varying the quality of the solvent, we have measured the polyion equivalent conductance lambda(p) in an extended concentration range in the semidilute regime and have demonstrated that this parameter is influenced by the polyion chain conformation, giving further support, when the poor-solvent condition prevails, to the picture of a string of electrostatic blobs. On the contrary, in good-solvent condition, the electrical conductivity data are in reasonable good agreement with the picture of an extended chain consisting of a collection of electrostatic blobs. These electrical conductivity measurements, in light of scaling theory, furnish new experimental support for the necklace model for hydrophobic polyions in poor solvents.     

Dispersions of nanocrystalline cellulose in aqueous polymer solutions: structure formation of colloidal rods

The steady-state shear and linear viscoelastic deformations of semidilute suspensions of rod-shaped nanocrystalline cellulose (NCC) particles in 1.0% hydroxyethyl cellulose and carboxymethyl cellulose solutions were investigated. Addition of NCC at the onset of semidilute suspension concentration significantly altered the rheological and linear viscoelastic properties of semidilute polymer solutions. The low-shear viscosity values of polymers solutions were increased 20-490 times (depending on polymer molecular weight and functional groups) by the presence of NCC. NCC suspensions in polymer solutions exhibited yield stresses up to 7.12 Pa. Viscoelasticity measurements also showed that NCC suspended polymer solutions had higher linear elastic moduli than the loss moduli. All of those results revealed the gel formation of NCC particles and presence of internal structures. The formation of a weak gel structure was due to the nonadsorbing macromolecules which caused the depletion-induced interaction among NCC particles. A simple interaction energy model was used to show successfully the flocculation of NCC particles in the presence of nonadsorbing polymers. The model is based on the incorporation of the depletion interaction term between two parallel plates into the DLVO theory for cubic prismatic rod shaped NCC particles.     

Osmotic pressure and polymer size in semidilute polymer solutions under good-solvent conditions

We consider the lattice Domb-Joyce model at a value of the coupling for which scaling corrections approximately vanish and determine the universal scaling functions associated with the osmotic pressure and the polymer size for semidilute polymer solutions (c/c( *)相似文献   

Self-diffusion of polystyrene in solution 2. Discussion of experimental results on the basis of the reptation mechanism and entanglements

The expressions for polymer self-diffusion in semidilute solutions, theoretically derived from the reptation mechanism, the blob concept and scaling considerations, are discussed and compared against experimental data from the authors' investigations and the literature. In the nonentangled (from viscoelastic data) semidilute solution, the experimentally observed concentration and molar mass exponents are in fair agreement with those derived theoretically. However, a quantitative estimation shows that the experiments cannot be explained by reptation. Experiments with polymer mixtures also give strong evidence against reptation. It is concluded, that in the nonentangled semidilute solution, the polymer self-diffusion is more complicated than simple reptation. This is also supported by recently observed long-range density fluctuations or cluster formation in this concentration region detected by scattering techniques and NMR-PFGT. In the entangled semidilute solution, the self-diffusion data are in accordance with the reptation mechanism; reptation being within a tube having approximately 20 blobs between entanglements.     

Comparison of RNA, single-stranded DNA and double-stranded DNA behavior during capillary electrophoresis in semidilute polymer solutions

We present a study of the separation of RNA, single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) in semidilute linear hydroxyethylcellulose (HEC) solution. Our results strive to provide a better understanding of the mechanisms of nucleic acid migration during electrophoresis in polymer solutions under native and denaturing conditions. From a study of the dependence of mobility on chain length and applied electric field, we found that RNA and ssDNA show better separation and higher resolution over a larger range of sizes compared to dsDNA. In addition, RNA reptation without orientation extends to longer chain lengths in comparison to ssDNA, possibly as a result of different type of short-lived secondary structure formations. Such a comparative study between nucleic acid capillary electrophoresis helps to optimize RNA separation and provides better understanding of RNA migration mechanisms in semidilute polymer solutions under denaturing conditions.     

Capillary electrophoresis of RNA in dilute and semidilute polymer solutions

We report separations of RNA molecules (281-6583 nucleotides) by capillary electrophoresis in dilute and semidilute solutions of aqueous hydroxyethylcellulose (HEC) ether in varying buffers. RNA mobility and peak band widths are examined under both nondenaturing and also denaturing conditions. From studies of sieving polymer concentration and chain length, it is found that good separations can be obtained in semidilute solutions as well as in dilute solutions. The dependence of RNA mobility on its chain length is consistent with separation by a similar to transient entanglement mechanism in dilute solutions. In semidilute entangled solutions the separation proceeds by segmental motion.     

Dynamic light scattering in sols of a poly(N-vinylcaprolactam) and polyacrylamide mixture

The properties of semidilute solutions of a mixture of polyacrylamide and thermoresponsive polyvinylcaprolactam are studied via dynamic light scattering. It is found that the relaxation time (correlation length) distribution contains several modes. The obtained experimental data are interpreted in terms of the theory describing the dynamics of semidilute and concentrated solutions with allowance for viscoelastic interactions. The investigation of mode dispersion (the dependence of relaxation time on the wave vector of scattering) shows that the fastest and slowest modes are of the diffusion type. The fast mode is the mode of collective diffusion; it may be attributed to the fluctuation motion of polymer units inside blobs. The slowest mode corresponds to the diffusion motion of macromolecule clusters. The rate of relaxation of medium modes nonlinearly depends on the squared wave vector, and these modes are apparently viscoelastic.     

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.     

A COMPARATIVE STUDY OF CHAIN DYNAMICS OF DI-AND TRI-BLOCK COPOLYMERS IN SEMIDILUTE SOLUTION IN A NON-SELECTIVE SOLVENT

The chain dynamics of a pair of diblock poly(styrene-b-butadiene) (PS210-b-PB960) and triblock poly(styrene-b-butadiene-b-styrene) (PS200-b-PB1815-b-PS200) copolymers in both dilute and semidilute toluene solutions has been comparatively studied by dynamic laser light scattering. As expected, the mutual diffusion of individual chain changes into a fast cooperative diffusion of the chain segments (“blobs“) between two neighboring entanglement points for both the copolymers as the solution changes from dilute to semidilute. Further increases of the concentration lead to a second slow relaxation mode. For the triblock chains, there exists an additional middle relaxation between the fast and the slow modes.with 0.33 ＜α＜ 0.44, much smaller than 0.75 predicted or 0.72 observed for linear homopolymer chains in good solvent. It implies that the solvent quality of toluene for PB might not be as good as that for PS. Due to such a difference in solubility, it is reasonable to speculate that the PB and PS blocks are transiently segregated in semidilute solution. The relaxation of these transient PB and PS richer domains leads to the observed slow relaxation. Such a speculation is supported by the appearance of an additional slow relaxation mode in the study of polyisoprene-b-polystyrene-b-polyisoprene in semidilute solution in cyclohexane, a non-selective solvent, in which we alternated the solubility difference by a variation of the solution temperature.     

Microrheology of entangled polymer solutions

Microrheology of semidilute polymer solutions is investigated. In this paper we calculate a response function of a probe particle embedded in a semidilute polymer solution by analyzing the two-fluid model. We find that when the size of the probe particle is comparable to the viscoelastic length, the response from the longitudinal compression modes becomes more important than that of the transverse shear modes. As a result, depending on the circumstances, the obtained complex shear modulus cannot be well approximated by that measured in macroscopic rheology experiments. The present results are due to the dynamical asymmetry coupling and the existence of the cooperative dynamics, which are intrinsic to entangled polymer solutions.     

Concentration and saturation effects of tethered polymer chains on adsorbing surfaces

We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling variable related with the saturation concentration of the adsorption layer (saturation scaling). We show that the decrease of the single chain order parameter (the fraction of adsorbed monomers on the surface) with increasing concentration, being constant in the ideal semidilute surface state, is properly described by saturation scaling only. Furthermore, the simulation results for the chains' extension from higher surface concentrations up to the oversaturated state support the new scaling approach. The oversaturated state can be understood using a geometrical model which assumes a brushlike layer on top of a saturated adsorption layer. We provide evidence that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold.     

Coarse grained model of entangled polymer melts

A coarse graining procedure aimed at reproducing both the chain structure and dynamics in melts of linear monodisperse polymers is presented. The reference system is a bead-spring-type representation of the melt. The level of coarse graining is selected equal to the number of beads in the entanglement segment, Ne. The coarse model is still discrete and contains blobs each representing Ne consecutive beads in the fine scale model. The mapping is defined by the following conditions: the probability of given state of the coarse system is equal to that of all fine system states compatible with the respective coarse state, the dissipation per coarse grained object is similar in the two systems, constraints to the motion of a representative chain exist in the fine phase space, and the coarse phase space is adjusted such to represent them. Specifically, the chain inner blobs are constrained to move along the backbone of the coarse grained chain, while the end blobs move in the three-dimensional embedding space. The end blobs continuously redefine the diffusion path for the inner blobs. The input parameters governing the dynamics of the coarse grained system are calibrated based on the fine scale model behavior. Although the coarse model cannot reproduce the whole thermodynamics of the fine system, it ensures that the pair and end-to-end distribution functions, the rate of relaxation of segmental and end-to-end vectors, the Rouse modes, and the diffusion dynamics are properly represented.     

Random copolymers at a selective interface: saturation effects

Combining scaling arguments and Monte Carlo simulations using the bond fluctuation method we have studied concentration effects for the adsorption of symmetric AB-random copolymers at selective, symmetric interfaces. For the scaling analysis we consider a hierarchy of two length scales given by the excess (adsorption) blobs and by two dimensional thermal blobs in the semidilute surface regime. When both length scales match, a densely packed array of adsorption blobs is formed (saturation). We show that for random copolymer adsorption the interface concentration can be further increased (oversaturation) due to reorganization of excess blobs. Crossing over this threshold results in a qualitative change in the behavior of the adsorption layer which involves a change in the average shape of the adsorbed chains towards a hairpinlike form. We have analyzed the distribution of loops and tails of adsorbed chains in the various concentration regimes as well as the chain order parameter, concentration profiles, and the exchange rate of individual chains. We emphasized the role of saturation scaling which dominates the behavior of static and dynamic quantities at higher surface concentration.     

Semiflexible amphiphilic polymers: cylindrical-shaped, collagenlike, and toroidal structures

A coarse-grained model is used to study the conformational properties of semiflexible polymers with amphiphilic monomer units containing both hydrophilic and hydrophobic interaction sites. The hydrophobically driven conformational transitions are studied using molecular dynamics simulations for the chains of varying stiffness, as characterized by intrinsic Kuhn segment lengths that vary over a decade. It is shown that the energy of hydrophobic attraction required for the realization of the coil-to-globule transition increases with increasing chain stiffness. For rather stiff backbone, the coil-to-globule transition corresponds to a first order phase transition. We find that depending on the chain stiffness, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for hydrophobic sites of amphiphilic monomer units. For flexible chains, the amphiphilic polymer forms a cylindrical globule having blob structure with nearly spherical blobs. With increasing stiffness, the number of blobs composing the globule decreases and the shape of blobs transforms into elongated cylinder. Further increase in stiffness leads to compaction of macromolecules into a collagenlike structure when the chain folds itself several times and different strands wind round each other. In this state, the collagenlike structures coexist with toroidal globules, both conformations having approximately equal energies.     

Temperature-induced association and gelation of aqueous solutions of pectin. A dynamic light scattering study

Dynamic light scattering (DLS) measurements were carried out on aqueous solutions of low-methoxyl pectin at different temperatures and polymer concentration. Low temperature and increased polymer concentration promote the formation of multichain aggregates. The time correlation data obtained from the DLS experiments revealed, for all polymer solutions, the existence of two relaxation modes, one single exponential at short times followed by a stretched exponential at longer times. In the semidilute regime, a temperature reduction induced enhanced chain associations in the solutions with high values of the slow relaxation time and a strong wave vector dependence of the slow mode. These features could be rationalized in the framework of the coupling model of Ngai. At low temperatures (10 °C), gelation occurs in the semidilute regime and a transparent gel is formed. In this state, the profile of the correlation function changes and nonergodic signs are observed. The conjecture is that the association complexes and the gel network are stabilized through intermolecular hydrogen bonds, which are broken-up at higher temperatures. The hydrogen-bonded structures are formed in a process where the polymer chains have been “zipped” together in a cooperative manner.     

Impact of solvent quality on nanoparticle dispersion in semidilute and concentrated polymer solutions

We investigated how solvent quality affects the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions, which extends our previous studies on these types of dispersions in good solvents [Langmuir 2008, 24, 5260-5269]. As discussed in the current article, dynamic light scattering (DLS) was used to quantify the diffusion of polydimethylsiloxane-grafted silica nanoparticles, or PDMS-g-silica, in bromocyclohexane as well as in PDMS/bromocyclohexane solutions. We established that bromocyclohexane is a theta solvent for PDMS by varying the temperature of the solutions with PDMS-g-silica nanoparticles and detecting their aggregation at a theta temperature of T(Θ) = 19.6 °C. Using this temperature as a benchmark for the transition between good and bad solvent conditions, further stability tests were carried out in semidilute and concentrated polymer solutions of PDMS in bromocyclohexane at T = 10-60 °C. Irrespective of temperature, i.e., solvent quality, we found that the nanoparticles dispersed uniformly when molecular weight of the graft polymer was greater than that of the free polymer. However, when the free polymer molecular weight was greater than that of the graft polymer, the nanoparticles aggregated. Visual studies were also used to confirm the correspondence between nanoparticle stability and graft and free polymer molecular weights in a wide range of marginally poor solvents with PDMS. Further, the correspondence between nanoparticle stability and instability with graft and free polymer molecular weight and solvent quality was also supported with self-consistent mean-field calculations. Thus, by relating experiment and theory, our results indicate that nanoparticle stability in semidilute and concentrated polymer solutions is governed by interactions between the graft and free polymers under conditions of variable solvency.     

Nanoparticle stability in semidilute and concentrated polymer solutions

The wetting of PDMS-grafted silica spheres (PDMS- g-silica) is connected to their depletion restabilization in semidilute and concentrated PDMS/cyohexane polymer solutions. Specifically, we found that a wetting diagram of chemically identical graft and free homopolymers predicts stability of hard, semisoft, and soft spheres as a function of the bulk free polymer volume fraction, graft density, and the graft and free polymer chain lengths. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. The point of demarcation between the regions occurs when the graft and free polymer chains are equal in length. When graft chains are longer than free chains, the particles are stable; in contrast, the particles are unstable when the opposite is true. The regions of particle stability and instability are corroborated with theoretical self-consistent mean-field calculations, which not only show that the grafted brush is responsible for particle dispersion in the complete wetting region but also aggregation in the incomplete wetting region. Ultimately, our results indicate that depletion restabilization depends on the interfacial properties of the nanoparticles in semidilute and concentrated polymer solutions.