Kinetics of chain collapse in dilute polymer solutions: molecular weight and solvent dependences

The molecular weight and solvent dependences of the characteristic time of chain collapse were studied for poly(methyl methacrylate) (PMMA) of the molecular weight Mw=6.4x10(6) and 1.14x10(7) in pure acetonitrile (AcN) and in the mixed solvent of AcN+water (10 vol %). The size of PMMA chains was measured as a function of the time after the quench by static light scattering and the chain collapse processes were expressed by the plot of the expansion factor alpha2 vs ln t. The chain collapse in the mixed solvent AcN+water (10 vol %) was found to occur much faster than that in pure AcN, though the measurement of the former collapse process required several hours. In order to make a comparison between the rates of chain collapses, the fast chain collapse process was superposed on the slow one by scaling the time of the fast process as gammat. The scale factor gamma was determined by comparing the chain collapse processes of nearly the same equilibrium expansion factor with each other. Accordingly, the superposition of the collapse for Mw=6.4x10(6) on that for Mw=1.14x10(7) yielded gammam=4.0+/-0.6 for the process in AcN+water and 5.5+/-0.6 in AcN. The superposition of the chain collapse process in AcN+water on that in AcN yielded gammas=9.5+/-1.4 for Mw=6.4x10(6) and 12.0+/-1.8 for Mw=1.14x10(7). This analysis suggests that gammam and gammas are constant independent of each other. Thus, by assuming the molecular weight dependence of gammam approximately Mz, the characteristic time tauexp of chain collapse was conjectured as tauexp approximately kappaMz, where kappa reflects the nature of solvent species. The ratio of kappa for PMMA in AcN to that in AcN+water is given by gammas. The exponent was estimated to be z=2.4+/-0.7 for AcN+water and 3.0+/-0.7 for AcN. These values are compatible with the theoretical prediction z=3 based on a phenomenological model, though the observed characteristic times are longer by several orders of magnitude than those of the theoretical prediction.     

Apparent relaxation‐time spectrum cutoff in dilute polymer solutions: An effect of solvent dynamics

The apparent short time cutoff of the relaxation‐time spectrum at surprisingly long times for polymers in solution is a well known but not yet understood observation. To elucidate its origins we revisit viscoelastic and oscillatory flow birefringence data for solutions and melts of two linear polymers (polystyrene and polyisoprene) and present new measurements of oscillatory flow birefringence of the latter. Previous measurements have suggested that the “flexibility” of both polymers in solution is smaller than in the melt on the basis of the breadth of the relaxation‐time spectrum of the solution as compared with that of the melt. Our new measurements have explored a higher effective frequency range than was previously possible. This has allowed us to observe the effect of the rotational relaxation time of the solvent on the dynamics of the solution at high frequencies. To obtain the polymer global motion contribution, one now needs to subtract from the solution properties a frequency‐dependent complex solvating environment contribution. We show that the decrease in apparent “flexibility” for solutions arises from the presence of a solvent that exhibits a rotational relaxation time and thus simple viscoelastic behavior somewhat near the frequency window of the experiment. Although recent predictions of a model for a chain in a solvent with a single relaxation time are in qualitative agreement with our results, our data suggest that the solution results may reflect the influence of solvent on the development of the “entropic spring” forces at short times. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2860–2873, 2001     

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 solvent on depolarized light scattering in dilute polymer solutions

An optical model of a system in which both polymer segments and solvent molecules are described as point dipoles has been used to calculate the intensity of light depolarized in scattering. The final expression consists of six terms, the physical meaning of which is briefly discussed. An approximation procedure has been worked out for the calculation of two interaction terms due to deviations of the local field in solution from the Lorentz–Lorenz field; the terms have been calculated for simple models of flexible and rigid molecules. Their dependence on molecular weight appears to be approximately the same as the intrinsic anisotropy of the polymer molecule; their contribution is nonzero even for a solvent isorefractive with the polymer.     

A theoretical analysis of the effect of solvent on the Kerr constant of dilute polymer solutions

A new model in which solvent molecules are regarded as discrete particles is used for investigating the influence of solvent orientation near a polymer chain and of the anisotropy of the internal electric field on the Kerr effect in a polymer solution. The relation derived for the Kerr constant consists of two parts containing nine terms each in the general case (the physical meaning of the terms is briefly discussed). Relations for the above effect in a nonpolar isotropic solvent, and explicit calculations of the Kerr constant for a simple model of a rigid polymer molecule are given.     

Viscoelastic properties of dilute polymer solutions: The effect of varying the concentration

Dynamic viscoelastic behavior was investigated for solutions of polystyrene in tricresyl phosphate, a good solvent, at concentrations, c, less than the coil‐overlapping concentration, c*. At the infinite dilution limit, the behavior was in accord with the theory of Doi and Edwards involving the excluded volume potential and hydrodynamic interaction (HDI). Thus, the viscoelastic functions were completely derived from the intrinsic viscosity–molecular weight relation. At finite c, the complex modulus was represented by the sum of two terms. One was a Rouse–Zimm (RZ) term conveniently represented by the Zimm theory with an arbitrarily chosen value of the HDI parameter. The other was a term with a single relaxation time, longer than the longest RZ relaxation time, and with a high‐frequency modulus proportional to the square of c [the long‐time (LT) term]. The behavior of the RZ term indicated the stronger screening of HDI with increasing c. Using the experimental c dependence of the longest RZ relaxation time to get the relevant parameter, we compared the RZ viscoelastic function with the Muthukumar–Freed theory. The agreement was good at low concentrations, c < c*. The contribution of the LT term, which was not included in the theory, was quite significant at low frequencies; about 60% of the Huggins coefficient was attributable to this term. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 211–217, 2001     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Effects of polymer chain length and stiffness on phase separation dynamics of semidilute polymer solution

Three-dimensional dissipative particle dynamics (DPD) simulations were performed to investigate the phase separation dynamics of semidilute polymer solutions with different polymer chain length and stiffness. For the polymer solution composed of shorter and more flexible chains, a crossover of the domain growth exponent from 1/3 to 2/3 was observed during the course of phase separation, indicating that the growth mechanism altered from diffusion to interfacial-tension driven flow. When the chain flexibility was kept the same but the chain was lengthened to allow for the chain entanglement to occur, the growth exponent changed to 1/4 in the diffusion-dominating coarsening regime while the growth exponent remained 2/3 in the flow-dominating regime. When the chain length was kept short but the stiffness was increased, the growth exponent became 1/6 in the diffusion-dominating regime and little effect was observed in the flow-dominating coarsening regime. The slow down of the phase separation dynamics in the diffusion-dominating coarsening could be explained by that the polymer chains could only perform wormlike movement when chain entanglements occurred or when the chain motion was limited by chain stiffness during phase separation. Moreover, when both the effects of chain length and stiffness were enhanced, polymer networks composed of longer and stiffer chains appeared and imposed an energy barrier for phase separation to occur. As a result, the polymer solution with stiffer and longer chains required a larger quench depth to initiate the phase separation and caused the delay in crossover of the coarsening mechanism from diffusion to flow.     

Chain conformations and phase separation in polymer solutions with varying solvent quality

Molecular dynamics simulations are used to investigate the conformations of a single polymer chain, represented by the Kremer-Grest bead-spring model, in a solution with a Lennard-Jones liquid as the solvent when the interaction strength between the polymer and solvent is varied. Results show that when the polymer-solvent interaction is unfavorable, the chain collapses as one would expect in a poor solvent. For more attractive polymer-solvent interactions, the solvent quality improves and the chain is increasingly solvated and exhibits ideal and then swollen conformations. However, as the polymer-solvent interaction strength is increased further to be more than about twice the strength of the polymer-polymer and solvent-solvent interactions, the chain exhibits an unexpected collapsing behavior. Correspondingly, for strong polymer-solvent attractions, phase separation is observed in the solutions of multiple chains. These results indicate that the solvent becomes effectively poor again at very attractive polymer-solvent interactions. Nonetheless, the mechanism of chain collapsing and phase separation in this limit differs from the case with a poor solvent rendered by unfavorable polymer-solvent interactions. In the latter, the solvent is excluded from the domain of the collapsed chains while in the former, the solvent is still present in the pervaded volume of a collapsed chain or in the polymer-rich domain that phase separates from the pure solvent. In the limit of strong polymer-solvent attractions, the solvent behaves as a glue to stick monomers together, causing a single chain to collapse and multiple chains to aggregate and phase separate.     

Dielectric scaling in polyelectrolyte solutions with different solvent quality in the dilute concentration regime

In this note, we present a set of radiowave dielectric spectroscopy measurements of two dilute, differently-charged polyelectrolyte solutions, under different solvent conditions. We have found that both the dielectric strength, Delta epsilon, and the relaxation time, tau(ion), of the dielectric relaxation process associated with the counterion polarization along a length scale of the order of the correlation length obey the scaling laws with the polyion concentration, according to the Ito model. This is verified with good accuracy independently of the quality of the solvent, which has been varied from poor to good solvent conditions. This finding supports evidence to the fact that, in dilute solutions, the counterion polarization is independent of the polyion concentration, in spite of what occurs at the semi-dilute concentrations.     

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.     

Transient entanglements and clusters in dilute polymer solutions

A convenient method to monitor polymer dissolution is to measure the pressure drop created by passing a polymer solution through a capillary constriction rheometer. In this work, we studied the dissolution of polyethylene oxide (PEO) and cationic starch (C‐starch). We found that for freshly dissolved and entangled PEO, the main contribution to the overall pressure drop is due to the contraction and expansion of PEO entanglements at the entrance and exit of the capillary, and that the friction in the capillary plays a minor role. On the other hand, for well‐dissolved PEO, because of the absence of PEO entanglements, the loss of pressure is mainly due to friction. At high velocities the contraction and expansion coefficient for freshly dissolved PEO was more than 20 times higher than for well‐dissolved PEO, resulting in a three times higher overall pressure drop. C‐starch consists of amylopectin (～ 85%) and amylose and is known to contain clusters when freshly dissolved, likely formed from the globular amylopectin molecules. For C‐starch, the main contribution to the overall pressure drop is due to friction. Entrance and exit effects contribute only 10% to the overall pressure drop, which might be due to the linear amylose molecules in C‐starch. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 253–262, 2008     

The segment-cloud model of the second virial coefficient of polymer solutions: effects of chain length and branching

The segment-cloud model for polymer molecules has been used, and the second virial coefficient A₂ obtained as a function of the interaction parameter z for linear and branched chains having different values of n. It is observed that the chain length effect, though much smaller than in the perturbation theory, increases as the degree of branching increases. Also, the branching parameter g is found to be a better correlating parameter than the segment density distribution for A₂. This is in contrast to earlier results for the perturbation theory of the excluded volume.     

Unforced translocation of a polymer chain through a nanopore: the solvent effect

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.     

Viscosities of dilute polymer solutions in nematic liquids

A nematic fluid is characterized by five friction coefficients. When dilute polymer coils are added to the fluid, all these coefficients are modified. Three Miesowicz viscosities (measured under an aligning magnetic field) and two coupling coefficients between orientation and flow are discussed. In our calculation, elastic dumbbells are used to model the flexible polymer chains. The results are written in terms of two size parameters R_∥ and R_⊥ and two chain friction coefficients λ_∥ and λ_⊥ (the label ∥ refers to a direction parallel to the nematic axis). This could be compared to other experiments (such as translational diffusion) which measure λ_∥ and _⊥ directly. They may give useful estimates of coil conformation in nematic solvents.     

Mechanism of interaction between hydroxypropyl cellulose and water in aqueous solutions: Importance of polymer chain length

The utilization of hydroxypropyl cellulose (HPC) can be regarded as unexpected with regard to certain applications, such as being employed as a solubility enhancer for poorly soluble drugs and as a solubilizing agent for nano-suspensions and amorphous solid dispersions. However, the best results were obtained for low-molecular weight (M_w) HPC grades with a short-chain structure. Therefore, in this study, seven grades of HPC with different polymer chain lengths (M_w) are analyzed in various aqueous solutions by a combination of ¹H quantitative NMR spectroscopy, diffusion NMR spectroscopy, and water ligand observed via gradient spectroscopy; these investigations provide insights into the remarkable solubilizing property of HPC at the molecular and supramolecular levels. Furthermore, the hydration and the water residence time are found to be strongly dependent on the polymer chain length of HPC. The quantitative results obtained herein indicate that HPCs with shorter chain lengths retain smaller amounts of water around their hydrated molecules, as compared to their counterparts with longer chain lengths.     

The Soret effect with chemical reaction in aqueous sulfuric acid solutions

The Soret coefficient of aqueous sulfuric acid has been determined conductimetrically from 0.0005 to 0.2m at 25°C. The derived enthalpies of transport increase sharply as the concentration drops, approaching a limiting value near 35 kJ-mol^–1. The increase, in the enthalpy of transport at low concentrations is due to the large intrinsic enthalpies of transport of the hydrogen and sulfate ions that are produced by the dissociation of bisulfate ions. The enthalpy of dissociation of the bisulfate ions reduces the acid's enthalpy of transport by up to 1.8 kJ-mol^–1.