A mean field theory of polymer solutions

The dynamic behavior of semidilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semidilute solutions are characterized by large fluctuations in polymer concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In nonequilibrium flows, it is generally thought that polymer chains can “self-entangle” in semidilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress in the field, we still lack a complete molecular-level understanding of the dynamics of polymer chains in semidilute solutions. In this work, we use single molecule techniques to investigate the dynamics of dilute and semidilute solutions of λ-phage deoxyribonucleic acid in planar extensional flow, including polymer relaxation from high stretch, transient stretching dynamics in step-strain experiments, and steady-state stretching in flow. Our results are consistent with a power-law scaling of the longest polymer relaxation time τ∼(c/c*)0.48 in semidilute solutions, where c is the polymer concentration and c* is the overlap concentration. Based on these results, an effective excluded volume exponent ν ≈ 0.56 was found, which is in good agreement with recent bulk rheological experiments. We further studied the nonequilibrium stretching dynamics of semidilute polymer solutions, including transient (1 c*) and steady-state (0.2 c* and 1 c*) stretching dynamics in planar extensional flow using an automated microfluidic trap. Our results show that polymer stretching dynamics in semidilute solutions is a strong function of concentration. In particular, a decrease in transient polymer stretch in semidilute solutions at moderate Weissenberg number (Wi) compared to dilute solutions is observed. Moreover, our experiments reveal a milder coil-to-stretch transition for semidilute polymer solutions at 0.2 c* and 1 c* compared to dilute solutions. Interestingly, a unique set of molecular conformations during the transient stretching process for single polymers in semidilute solutions is observed, which suggests transient stretching pathways for polymer chains in semidilute solutions are qualitatively different compared to dilute solutions due to intermolecular interactions. Taken together, this work provides a molecular framework for understanding the nonequilibrium stretching dynamics of semidilute solutions in strong flows.

This paper concerns the viscosity dependence of Xanthan as a function of polymer concentration, shear rate and molecular weight in the ordered conformation. The different samples with various molecular weights are obtained by ultrasonication. A unique curve is obtained for the reduced specific viscosity ( $$\eta _{sp/} \eta _{sp_0 } $$ ) as a function of γ · γ r −1 for the different molecular weight samples and polymer concentrations below an overlap concentration C [η]0⩽ 1.5. The master curve giving the relation $$\eta _{sp_0 } $$ as a function of C [η]0 is drawn and compared with that of polystyrene in good solvent. The largest increase of $$\eta _{sp_0 } $$ in semidilute solution may be due to larger interchain interactions and to larger stiffness of the Xanthan molecule.

We revive an old conjecture that a fixed number of binary contacts between chains collec- tively make up the topological constraint commonly referred to as an entanglement. This leads us to a general scaling theory for semidilute polymer solutions which involves two length scales, the screening length ( and the tube diameter a. In good solvents these two lengths have the same concentration depen- dence and we recover the de Gennes results. In 9 solvents the two length scales depend on concentration differently. Combining the concentration dependences of these two length scales with concepts from the- ories of rubber elasticity and reptation leads to new predictions for the plateau modulus G - kT/(a2{) - c7/3 and viscosity 9 - M2/3(c/c*)14/3 in 9 solvents, where M is the polymer molecular weight and c* is the overlap concentration. These predictions are found to compare favorably with available experimental data.

Birefringent pipes: the steady flow of a dilute polymer solution near a stagnation point

In the present study, we performed molecular dynamics (MD) simulations of the self-assembled monolayer (SAM) interface system in order to investigate heat transfer characteristics over the SAM/alkane solvent interface. 1-dodecanethiol (C12H25S-) SAM chemisorbed on a gold substrate contacting with n-dodecane (C12H26) solvent was examined to compare the microscopic heat transfer mechanisms inside both the SAM and solvent phases. The direct nonequilibrium MD (NEMD) simulation, in which a constant heat flux across the SAM interface was imposed, was performed. The heat flux through the system was decomposed into the microscopic “building blocks”, i.e., the contribution of energy transfer associated with molecular motion and that of energy exchange by intermolecular (nonbonded) and intramolecular (covalent bond) interactions. Interestingly, inside the SAM layer, almost all of the energy is transferred by the intramolecular interaction along the alkyl chain. On the other hand, in the alkane liquid phase, the intramolecular and intermolecular interactions have comparable contributions to the total heat flux in spite of the same molecular structure and alkyl chain length as the SAM molecules. This difference in the heat transfer mechanism implies the relation between the ordering structure of alkyl chains and thermal conductivity in organic materials.

The surface shear rheology of Langmuir monolayers of poly(methyl methacrylate) (PMMA) has been studied as a function of polymer concentration (Gamma) and molecular weight (N). Two different rheology techniques were used, one based on free damped oscillations of a ring with a sharp edge and the other based on a forced oscillation of a biconical disk. Both instruments were used in the oscillatory mode at comparable oscillation frequency and amplitude, which gave access to the viscoelastic shear modulus (S). The two instruments, working in different viscosity ranges, provide complementary and mutually compatible data. The results obtained for four PMMA samples of molecular weight between 8x10(3) and 2.7x10(5) g.mol(-1) show powerlike behavior as S approximately Gamma10 and S approximately N4. These strong dependences suggest a structural scenario based on the 2D percolation of the polymer pancakes.

Polyelectrolyte chains are well known to be strongly correlated even in extremely dilute solutions in the absence of additional strong electrolytes. Such correlations result in severe difficulties in interpreting light scattering measurements in the determination of the molecular weight, radius of gyration, and the second virial coefficient of charged macromolecules at lower ionic strengths from added strong electrolytes. By accounting for charge-regularization of the polyelectrolyte by the counterions, we present a theory of the apparent molecular weight, second virial coefficient, and the intermolecular structure factor in dilute polyelectrolyte solutions in terms of concentrations of the polymer and the added strong electrolyte. The counterion adsorption of the polyelectrolyte chains to differing levels at different concentrations of the strong electrolyte can lead to even an order of magnitude discrepancy in the molecular weight inferred from light scattering measurements. Based on counterion-mediated charge regularization, the second virial coefficient of the polyelectrolyte and the interchain structure factor are derived self-consistently. The effect of the interchain correlations, dominating at lower salt concentrations, on the inference of the radius of gyration and on molecular weight is derived. Conditions for the onset of nonmonotonic scattering wave vector dependence of scattered intensity upon lowering the electrolyte concentration and interpretation of the apparent radius of gyration are derived in terms of the counterion adsorption mechanism.

FTIR methods were used to study intramolecular and intermolecular interactions in solutions and the solid state of the biologically active aminophenols 2-anilino-4,6-di-tert-butylphenol, N-(3,5-di-tert-butyl-2-methoxyphenyl)aniline, and 2,4-di-tert-butyl-10H-1-phenothiazinol. An analysis of the IR spectra has shown that intramolecular interactions between the OH and NH groups occur in solutions of 2-anilino-4,6-di-tertbutylphenol in CCl4 to form O-H⋯N hydrogen bonds. The NH groups in solutions of N-(3,5-di-tert-butyl-2-methoxyphenyl)aniline in CCl4 are present in the non-associated state because of the absence of hydroxyl groups in the molecular structure. The OH and NH groups in solutions of 2,4-di-tert-butyl-10H-1-phenothiazinol in CCl4 do not interact within the molecule due to a decrease in the conformational mobility of the molecular fragments due to the presence of the rigid CAr-S-CAr molecular bond in this compound. Intermolecular interactions involving the NH groups occur in the solid state of these compounds.

We have studied glycosylation patterns in glycoprotein hormones (GPHs) and glycoprotein hormone receptor (GPHR) extracellular domains (ECD) from different species to identify areas not glycosylated that could be involved in intermolecular or intramolecular interactions. Comparative models of the structure of the TSHR ECD in complex with TSH and in complex with TSHR autoantibodies (M22, stimulating and K1-70, blocking) were obtained based on the crystal structures of the FSH-FSHR ECD, M22-TSHR leucine-rich repeat domain (LRD) and K1-70-TSHR LRD complexes. The glycosylation sites of the GPHRs and GPHs from all species studied were mapped on the model of the human TSH TSHR ECD complex. The areas on the surfaces of GPHs that are known to interact with their receptors are not glycosylated and two areas free from glycosylation, not involved in currently known interactions, have been identified. The concave faces of GPHRs leucine-rich repeats 3-7 are free from glycosylation, consistent with known interactions with the hormones. In addition, four other non-glycosylated areas have been identified, two located on the receptors' convex surfaces, one in the long loop of the hinge regions and one at the C-terminus of the extracellular domains. Experimental evidence suggests that the non-glycosylated areas identified on the hormones and receptors are likely to be involved in forming intramolecular or intermolecular interactions.

The Soret coefficient ST and collective (mass) diffusion coefficient Dc of polystyrene dissolved in the good-solvent toluene has been measured over a range of concentrations and molecular masses with an optical beam-deflection method. Our measurements indicate that ST scales inversely with the polymer translational diffusion coefficient in dilute solutions, exhibits a power-law scaling with polymer concentration, and an independence of polymer molecular mass in semidilute solutions. These findings are consistent with the known scaling of 1/Dc in dilute and semidilute polymer solutions, the relative insensitivity of the thermal-diffusion coefficient Dth of polystyrene in toluene to polymer concentration, and the relation ST=Dth/Dc from irreversible thermodynamics. We are able to represent our ST and Dc data by theoretically motivated reduced-concentration master curves, but the concentration-molecular mass scaling variables are found to be different for each transport property, a result contrary to theoretical expectations. However, the asymptotic concentration scaling exponents deduced from these data fits are compatible with de Gennes’ scaling arguments for Dc and with modern estimates of the chain-size exponent ν for swollen polymers in good solvents.

The characterization of hydrophobically modified alkali-soluble emulsions (HASE) using conventional techniques such as gel permeation chromatography or static light scattering is difficult because of the hydrophobic association. Two different approaches were taken to prevent the hydrophobic association of HASE polymers in aqueous solution: (1) hydrolyze the polymer to dislodge the hydrophobic constituents, and (2) use methyl-β-cyclodextrin, which has a hydrophobic cavity and a hydrophilic outer shell, to shield the hydrophobes from associating. Using these two approaches, the molecular weight (Mw), hydrodynamic radius (Rh), and radius of gyration (Rg) of single chains of these polymers were determined using gel permeation chromatography (GPC) and dynamic (DLS) and static (SLS) light scattering techniques. The molecular weight of the control polymer (i.e., polymers with similar composition but with no hydrophobe) is found to be ∼7.0 × 105 g/mol. The molecular weights of these polymers with C8, C16, and C20 hydrophobes were found to be ∼2.0 × 105 g/mol. By comparing GPC and SLS results, we were able to determine that, except for one chemical site, branching or grafting did not occur in the polymer chain during synthesis.

The investigations about the steady shear viscosity of non-Newtonian flow in concentrated polymer solutions have been reported by Porter et al. and Ozaki et al. Log viscosity versus log molecular weight relations obtained by Porter et al. and by Ozaki et al, are those at constant shear stresses and at constant rates of shear, respectively.In the results obtained by Porter et al., the slope of log η"log M relation becomes smaller as the shear stress increases in the region of molecular weight higher than a critical value Mc as is shown in Fig. 1.On the other hand, the slopes of log η"log M relation obtained by Ozaki et al. are 3.4 in the region of molecular weight lower than a second critical value M'c (>Mc) which depends on shear rate γ0 and <3.4 (nearly 2) in the region of molecular weight higher than M'c as is shown in Fig. 2.Since the concentrated polymer solution spreads a network structure crosslinked temporarily by the entanglement of polymer molecules, it is desirable to make clear the viscosity versus molecular weight relations by making use of the theory of network structure.In § 2 the linear theory of viscoelasticity of network structure is reported in a reformed formalism. When we consider a polymer molecule in the network structure, the aggregation of the remaining molecules could be considered to be a sort of viscoelastic medium. When a part of polymer molecule between the adjacent crosslinkages termed chain, a chain in a molecule has the viscoelastic effects on other chains in the same molecule through the viscoelastic medium, so that the system corresponds to a model composed of interacting Rouse model. The viscoelastic interactions between the chains in a, molecule. though they seems intra-molecular interactions, are due to the average inter-molecular interactions induced by the motion of the viscoelastic medium. By using the above model we obtain the slip equation (2.17) and the stress (2.2'), where <γi> and <Di> contained in τi are viscous and elastic effects in the i-th normal coordinate and are given by (2.19). For continuous distribution of relaxation times, the slip equation and the stress are written as (2.21), which are the expressions in the linear theory.In order to investigate the non-Newtonian effect on viscosity, the linear theory is extended by introducing the parameters depending on the shear stress or rate, and we assume the phenomenological relations (3.1), where α and β are parameters characterizing the elastic and the viscous effects and functions depending only on the shear stress. In non-Newtonian flow, the stress and the slip equation are given by (3.2) and (3.3), respectively. τα is the critical relaxation time corresponding to the movement of molecule having molecular weight Mc, τβ being the maximum relaxation time.For steady flow the stress is given by (4, 2), where γo is the shear rate and ν is the number of chains in the unit volume. The log η-log M relation at constant shear stress is given by (4.3'), where Ms (=Mc) is the molecular weight of chain. From (4, 3'), β is determinable as a parameter depending on shear stress from the experimental results obtained by Porter et al. The experimental data show that as the shear stress increases β decreases from 2.5 to 0.On the other hand β is a function of shear rate and molecular weight, since the shear stress is a function of molecular weight M and shear rate γo.

Characterization of polyelectrolyte features in polysaccharide systems and mucin

Proton spin dynamics in polymer melts: New perspectives for experimental investigations of polymer dynamics

Zero shear viscosities η0 were measured for toluene solutions of ten fractionated poly(n‐hexyl isocyanate) (PHIC) samples from dilute regime to concentrated isotropic regime. PHIC is a semiflexible polymer with the persistance length q=37 nm in toluene. For six PHIC samples with the molecular weight less than 14×104, the dependence of η0 on the polymer concentration c did not obey any power law, while for the higher molecular weight samples, n0 was almost proportional to c3.2 in a high c region. At fixed c, η0 was almost proportional to M4v in a high Mv region (Mv: viscosity average molecular weight). These concentration and molecular weight dependences are distinct from not only those for flexible polymer solutions but also those for much stiffer polymer solutions [e.g., schizophyllan (q=200 nm) and xanthan (q=120 nm)]. The results of η0 for PHIC solutions obtained were compared with Teraoka–Hayakawa’s theory for rodlike polymer solutions and with our fuzzy cylinder model theory for semiflexible polymer solutions. The former theory agreed with the experimental results only for the second lowest molecular weight sample with a rodlike conformation. On the other hand, the latter theory succeeded in explaining quantitatively the results for seven samples with intermediate molecular weights. Neither of the theories agree with the data for the lowest molecular weight sample, because they neglected the intermolecular hydrodynamic interaction which becomes important for short chain polymers. For the two highest molecular weight samples, the fuzzy cylinder model theory failed to describe the η0 data, because of some additional flexibility effect which is not cleared yet.