Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Scaling analysis of cotton cellulose/LiCl·DMAc solution using light scattering and rheological measurements

Semidilute solution of cotton lint (CC1) in 8 wt % LiCl/N,N‐dimethylacetamide was investigated using static light scattering (SLS) and rheological measurements. The reduced osmotic modulus estimated by SLS measurements for CC1 solutions are proportional to c^1.16 in the semidilute region. From the exponent of 1.16, de Gennes' scaling theory derives the relationship between radius of gyration, R_g, and molecular weight, M_w, of CC1 as R_g ∝ M^0.62 This corresponds to the Mark‐Houwink‐Sakurada exponent of 0.86. This exponent is very close to that estimated from scaling analysis of zero shear rate viscosity, that is 0.85. Apparent radius of gyration, R_g,app, estimated by SLS measurements for CC1 solutions are proportional to c^?0.5 in the semidilute region. R_g,app indicates the mesh size of polymer entanglement in the semidilute region. On the assumption of the Gaussian behavior of CC1 molecule in the semidilute region, the exponent of ?0.5 gives the relationship between the molar mass between entanglements, M_e, and c as following relationship: M_e ∝ c^?1. This agrees with the concentration dependence on plateau modulus estimated from the dynamic viscoelastic measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2155–2160, 2006     

The effect of concentration,temperature, and molecular weight on the dynamics of rigid-rod molecules in semi-dilute solutions

The dynamics of rigid-rod-like molecules are studied using rheo-optical techniques. Measurements of flow birefringence as a function of shear rate are utilized to understand the scaling behavior of rotational diffusivity with respect to concentration and temperature. The concentration scaling exponent increases with increasing concentration and the scaling laws are valid in narrow concentration windows. The Doi-Edwards (DE) scaling law D_r ∼ c⁻², holds at very high concentrations (cL³ > 150). The concentration scaling exponent decreases dramatically with increasing temperature at concentrations, cL²d > 1. Scaling of rotational diffusivity, with respect to temperature and solvent viscosity in the semidilute regime, does not follow the predictions of DE theory (and related caging ideas). On the contrary, a model proposed by Fixman was found to explain both the temperature and concentration dependence of the rotational diffusivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 181–190, 1998     

Dynamical behavior of xanthan polysaccharide in solution

Dilute-solution hydrodynamic data for xanthan biopolymer in water suggest a rodlike molecule of dimensions 15,000 × 20 Å, and molecular weight 2.2 × 10⁶ g/mol. Upon addition of NaCl to this system, the xanthan molecules self-associate to form stable aggregates. The native xanthan conformation can be thermally denatured to a disordered coil which can be stabilized at room temperature in 4M urea. The transition to semidilute solutions is manifested by discrete changes in the concentration dependence of diffusion coefficient and zero-shear viscosity at c ≈ 2.0 × 10^?4 g/mL. At higher concentrations c ≥ 1.0 × 10^?3 g/mL, the light-scattering and shear-viscosity data are qualitatively but not quantitatively consistent with predictions of the dynamical theory of Doi and Edwards for an isotropic entangled solution of rigid-rod molecules. Measurements of latex sphere diffusion in xanthan-water solution show a sudden retardation at c ≈ 1.0 × 10^?3 g/mL, consistent with the cooperative formation of a motionally restricted network of long, thin, rigid fibers. At high shear rates, flow birefringence experiments indicate enhanced ordering of the xanthan chains in the semidilute regime.     

Kinetics of fluid spreading on viscoelastic substrates

The spontaneous spreading of non‐film‐forming fluids on the surfaces of aqueous solutions of poly(2‐acrylamido‐2‐methyl‐propanesulfonic acid) and its chemically crosslinked gels was studied. The experiments were performed in the same concentration range for the solutions and gels, far above the overlap concentration of the polymer solutions. The leading edge (R) of the spreading liquid showed a power‐law behavior with time t: R = K(t + c)^α, where α is the spreading exponent and K is the spreading prefactor. α and K were significantly different for the polymer solutions and gels. Here c was a constant that depended on the initial conditions of the spreading liquids. Depending on the polymer concentration, α of the polymer solutions varied between the upper (3/4) and lower (1/10) theoretical limits for viscose liquids and solids, respectively. This indicates that no universal scaling law exists for the spreading process on viscoelastic surfaces. On the polymer gels, which were elastic substrates, universal values of α could be observed and could be expressed as R ∝ (t + c)^0.45 and R ∝ (t + c)^0.3 for miscible and nonmiscible spreading liquids, respectively; they showed no dependence on the polymer concentration or network mesh size. This shows that on an elastic gel surface, spreading is more or less similar to that on a solid surface. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 562–572, 2005     

Application of scaling concepts to sedimentation phenomena in semidilute macromolecular solutions

Sedimentation velocity data on polystyrene in a good solvent (toluene) and in a theta solvent (cyclopentane), over a large concentration range are reported. Under good-solvent conditions the exponent β in the apparent scaling law describing the concentration dependence of the sedimentation coefficient (s ∝ c^β) in the semidiiute region is found to be concentration dependent. However, a power law fit to data for the highest molecular weight (M = 20.6 × 10⁶) in the concentration region (c < 2 kg m^?3) yields a value β = ?0.59, somewhat smaller than that (?0.54) predicted theoretically. This discrepancy and the observed curvature in logs vs. logc at higher concentrations are discussed. Under theta-solvent conditions, on the other hand, the concentration dependence of s in the semidilute regime can be represented by a simple power law, with β = ?1.0, in excellent agreement with the theoretical prediction. The crossover concentration c^*, separating the dilute and semidilute concentration regimes, was found to be well defined and located at c = 1/[η]. c^* varies with molecular weight as M^?0.73 and M^?0.50 under good-solvent and theta-solvent conditions, respectively.     

Ordering in Bio-Polyelectrolyte Chitosan Solutions

The scaling of the polyelectrolyte scattering peak in chitosan solutions, as deduced from the relation q_max∼c_p^α was studied by synchrotron SAXS as a function of the charge density of the polymer. We observe a variation in the α exponent corresponding to the limit of the ionic condensation, by varying the degree of acetylation of the polymer. The nature of the solution medium also affects the polyelectrolyte peak, and it is shown that in alcoholic/water mixtures, the lower dissociation of the acid induces a lower charge density, thus influencing the polyelectrolyte ordering.     

Rotational diffusivity of rodlike molecules in amorphous polymeric matrices

In this note, scaling laws for rotational diffusivity of dilute monodisperse rigid-rod molecules (guest rods) in semidilute amorphous polymer solutions (host molecules) are derived. The coillike matrix molecules are modeled as a collection of flexibly connected rigid subunits. This allows an analogy with the Doi-Edwards theory for monodisperse rigid rods in semidilute solutions to be used in the analysis. Very strong dependencies are predicted for the rotational diffusivity of the rods on host polymer volume fraction and rod length. In semidilute polymer solutions the coils dramatically hinder the rotational freedom of the rods for r² ? ψ_p^?1, r being the rod aspect ratio and ψ_p the polymer volume fraction.     

On the universality of sedimentation of flexible polymers in dilute and semidilute solutions

In the present investigation, the sedimentation behavior, over an extended concentration range, in solutions of polystyrenes under good, marginal, and theta solvent conditions, is analyzed in the framework of a recent theoretical model, which takes into account the gradual screening of both hydrodynamic and excluded-volume interactions in the semidilute regime. The model inspires the construction of universal plots of the form S/S₀ versus k_sc, where S is the sedimentation coefficient at polymer concentration c, S₀ is that at infinite dilution, and k_s is the concentration dependence coefficient. The resulting analytical expressions, without adjustable parameters, are consistent with experimental sedimentation data over the whole concentration range studied.     

1H NMR relaxation study of polymer-solvent interactions during thermotropic phase transition in aqueous solutions

The dynamic-structural changes and polymer - solvent interactions during the thermotropic phase transition in poly(vinyl methyl ether) (PVME)/D₂O solutions in a broad range of polymer concentrations (c = 0.1-60 wt.-%) were studied combining the measurements of ¹H NMR spectra, spin-spin (T₂) and spin-lattice (T₁) relaxation times. Phase separation in solutions results in a marked line broadening of a major part of polymer segments, evidently due to the formation of compact globular-like structures. The minority (∼15%) mobile component, which does not participate in the phase separation, consists of low-molecular-weight fractions of PVME, as shown by GPC. Measurements of spin-spin relaxation times T₂ of PVME methylene protons have shown that globular structures are more compact in dilute solutions in comparison with semidilute solutions where globules probably contain a certain amount of water. A certain portion of water molecules bound at elevated temperatures to (in) PVME globular structures in semidilute and concentrated solutions was revealed from measurements of spin-spin and spin-lattice relaxation times of residual HDO molecules.     

Study of polymer complexes by size exclusion chromatography coupled with light scattering in combination with fluorescence spectroscopy

Poly(methyl methacrylate) stereocomplexes prepared at different concentration in dilute tetrahydrofuran solutions were studied by size exclusion chromatography coupled with refractive and light scattering detectors in combination with fluorescence spectroscopy. A considerable increase in segment density due to complexation compared with free poly(methyl methacrylate) chain was only slightly affected by the polymer concentration in solution where stereocomplexes were formed. At polymer concentrations up to 3×10⁻³ g cm⁻³, an increase in non‐uniformity of polymer complex molecular weight and size and a shift to higher values of both were observed. In semidilute solutions (at c > 3×10⁻³ g cm⁻³) stereocomplexes virtually did not become heavier and larger.     

Measurement of rotational diffusivity of rodlike molecules in amorphous polymer matrices by the dynamic kerr effect

Electrooptic (Kerr effect) relaxation experiments, designed to measure the rotational diffusivity of collagen (rodlike) molecules in aqueous poly(ethyleneoxide) (amorphous) semidilute solutions under various conditions have been performed. The experimental results have been compared with the predictions of a previously derived model giving the rotational diffusivity of dilute rods in semidilute amorphous polymer solutions as a function of rod length and amorphous polymer concentration. Excellent agreement is found between the predicted scaling D_r ～ ?L^?7 (D_r = rod rotational diffusivity, pi_p = polymer weight fraction, and L = rod length) and the experiments.     

Linear viscoelasticity of poly(acrylonitrile-co-itaconic acid)/1-butyl-3-methylimidazolium chloride extended from dilute to concentrated solutions

The solution rheology of poly(acrylonitrile-co-itaconic acid) (poly(AN-co-IA)) in 1-butyl-3-methylimidazolium chloride ([BMIM]Cl) spanning dilute, semidilute unentangled and entangled regimes were investigated. The exponents in the specific viscosity η_sp ～ overlap parameter c[η] power law were 1, 2 and 4.7 for dilute, semidilute unentangled and entangled regimes, respectively, which were found to be consistent with the scaling prediction for neutral linear polymers in θ-solvent. For dilute solutions (lower than 0.9 wt.%), the linear viscoelastic responses were observed to be in good agreement with the Zimm model (Flory exponent ν = 0.5). While for semidilute unentangled solutions (between 0.9 and 8 wt.%), results obtained had been found to be consistent with Rouse model. Considering Flory exponent ν = 0.5 and the concentration dependences of the specific viscosity and relaxation time, it had been evaluated that poly(AN-co-IA) in [BMIM]Cl behaves as a neutral polymer in θ-solvent. It had also been suggested that according to the unusual deviation of Cox-Merz rule, poly(AN-co-IA)/[BMIM]Cl solutions are typical neutral polymeric liquids for the concentrated solutions but have shown a more complicated behavior at high deformation rates.     

Dynamics of amphiphilic diblock copolymers at the air-water interface

Two polyisoprene-polyethyleneoxide diblock copolymers with different block length ratios adsorbed to the water surface were investigated by multiple angle of incidence ellipsometry, evanescent wave light scattering, and surface tension experiments. In a semidilute interfacial regime, the transition from a two-dimensional to a "mushroom" regime, in which polymer chains form loops and tails in the subphase, was discussed. A diffusion mechanism parallel to the interface was probed by evanescent wave dynamic light scattering. At intermediate concentrations, the interfacial diffusion coefficient D(∥) scales with the surface concentration Γ, as D(∥) ~ Γ(0.77) in agreement with the scaling observed for polymer solutions in a semidilute regime. At relatively high concentrations a decreasing of D(∥) is discussed in terms of increasing friction due to interactions between polyisoprene chains.     

Associated inter‐ and intrachain conformational transitions in polystyrene solutions

Understanding the conformational changes of polymeric chains in solutions is an essential and integral part of polymer physics. By increasing the concentration of polymer solutions from dilute to semidilute regime, the critical chain overlapping has been reported at the concentration termed as C*. In this study, the associated inter‐ and intrachain conformational transitions in polystyrene (PS) solutions are reported. By comparing the spectroscopic intensity ratio versus concentration for an intrachain PS system, a break point was observed in good solvent which coincided with the theoretically predicted C*. Moreover, the intrachain conformation showed no obvious change below C*, while significant collapse started to occur above C*. This result reveals a new insight in polymer physics, since traditionally the size of polymer chains is considered to decrease weakly regarding the concentration change in the semidilute regime. It is important to find such an abrupt intrachain conformational transition between the dilute and semidilute solutions and provide the first experimental observation that inter‐ and intrachain conformational transitions are correlated to one the other. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1373–1379     

Association under shear flow in aqueous solutions of pectin

Effects of oscillatory and steady shear flows on intermolecular associations in dilute and semidilute aqueous solutions of pectin in the absence and presence of the hydrogen bond breaking agent urea are reported. A weak oscillatory shear perturbation builds up, depending on polymer concentration, multichain aggregates or networks in the course of time and these association structures are mainly stabilized through hydrogen bonds. The association effect is more pronounced at higher concentrations, and the growth of intermolecular interactions is inhibited by the addition of urea. Steady shear measurements on the pectin-water solutions reveal shear thickening at low shear rates for all the concentrations, except the lowest one, and disruption of intermolecular junctions at high shear rates. In the presence of urea, no shear thickening is detected. The polymer concentration dependence of the viscosity at a low shear rate can be described by a power law η ∼ c^x, with x = 1.9 and 1.4 without and with urea, respectively. When a low constant shear rate is applied to pectin solutions and this monitoring shear rate is interrupted periodically by transitory high shear rates perturbations during a short time, prominent association structures evolve upon return to the monitoring shear rate. This effect is more evident at a lower polymer concentration, and in the presence of urea, the growth of the association complexes is damped. The shear-induced alignment and stretching of polymer chains and the formation of hydrogen-bonded structures are analyzed in the framework of a model, where cooperative zipping of stretched chains play an important role. Viscosity enhancement is found for a semidilute pectin-water solution in the presence of moderate levels of salt addition (NaCl), suggesting that partial screening of electrostatic interactions promotes growth of energetic cross-links.     

Phase Separation in Aqueous Polymer Solutions as Studied by NMR Methods

Some possibilities of ¹H NMR spectroscopy in investigations of structural-dynamic changes and polymer-solvent interactions during the temperature-induced phase transitions in aqueous polymer solutions are described. Results obtained recently on D₂O solutions of poly(vinyl methyl ether) (PVME), poly(N-isopropylmethacrylamide) (PIPMAm), negatively charged copolymers of N-isopropylmethacrylamide and sodium methacrylate, and PIPMAm/PVME mixtures are discussed. A markedly different rate of dehydration process in dilute solutions on the one hand, and in semidilute and concentrated solutions on the other hand, was revealed from ¹H spin-spin relaxation measurements.     

Charge density effects in salt‐free polyelectrolyte solution rheology

Solution rheology of 2‐vinyl pyridine and N‐methyl‐2‐vinyl pyridinium chloride random copolymers in ethylene glycol was studied over wide ranges of concentration and effective charge. The fraction of quaternized monomers α and the fraction of monomers bearing an effective charge f of these copolymers were measured using counterion titration and dielectric spectroscopy, respectively. Ethylene glycol is a good solvent for neutral poly(2‐vinyl pyridine), with very few ionic impurities. The viscosity η and relaxation time τ of dilute and semidilute unentangled solutions exhibit the scaling with concentration and effective charge expected by the Dobrynin model. Reduced viscosity data are independent of concentration in dilute solution, giving an intrinsic viscosity that depends on effective charge, and the experimental data obey the Fuoss law in the semidilute unentangled regime. Scaling concentration with the overlap concentration (c/c*) reduces these data to common curves, and c* ～ f ^?12/7 as predicted by the Dobrynin model, where f is the fraction of monomers bearing an effective charge. While the overlap concentration depends strongly on effective charge until counterion condensation occurs, the entanglement concentration c_e is surprisingly insensitive to effective charge, indicating that entanglement effects are not understood using the Dobrynin model. The terminal modulus G = η/τ depends only on the number density of chains G = ckT/N for c* < c < c_e, and G ～ c^3/2 for c > c_e independent of the effective charge. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2001–2013, 2006     

Viscoelasticity and rheology in the regimes from dilute to concentrated in cellulose 1-ethyl-3-methylimidazolium acetate solutions

Dynamic rheological behaviors of α-cellulose 1-ethyl-3-methylimidazolium acetate ([Emim]Ac) solutions were investigated in a large range of concentrations (0.1–10 wt %) at 25 °C. On the basis of data from the dynamic viscoelastic test, the exponents of the specific viscosity η _sp versus concentration c were determined as 1.0, 2.0 and 4.7 for dilute, semidilute unentangled and entangled regimes respectively, which were in accordance with the scaling prediction for neutral polymer in θ solvent. The intrinsic viscosity [η] of the solution was determined to be 253 mL/g at 25 °C. The linear viscoelastic response of the dilute and semidilute unentangled solutions could be described successfully by the Zimm and Rouse model (ν = 0.5 for θ solution) respectively, suggesting that the motion of cellulose chain in [Emim]Ac changed from Zimm to Rouse model with increasing concentration. At low concentrations, failure of the Cox–Merz rule with steady shear viscosity larger than complex viscosity was observed. While as the concentration increased, the deviation from the Cox–Merz rule disappeared due to the formation of homogeneous entanglement structure in cellulose solution.     

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.