Supermolecular structures in polymer solutions interpretation of static light scattering data

The characterization of supermolecular structures in polymer solutions by static light scattering requires an improved analysis of the scattering curves. A comparison of the experimental curves with model calculations for various basic structure types in a scaled plot offers the possibility to extend the range of a reliable determination of the structural parameters to particle sizes up to 500 nm. The influence of the polydispersity and problems of an unambiguous interpretation are discussed. Especially, a closed analytical expression for the scattering function of polydisperse systems of spheres with a Schulz-Zimm distribution of radii was derived.     

Solvent effects in flow birefringence of polymer solutions. General theory and discussion of form effects

A new, more realistic optical model of a dilute polymer solution is used to calculate the intrinsic birefringence. A general formula is derived valid for an arbitrary equilibrium distribution function of particles in the system. Besides the contributions due to the polymer and solvent, the resulting relation for intrinsic birefringence also contains terms reflecting the effect of orientation of solvent surrounding the polymer chain and the contribution of optical interactions between polymer segments and molecules of solvent. A detailed discussion of the optical interactions in an isotropic solvent reveals that the problem may be transformed in the first approximation into that of interactions between excess dipoles; however, any separation of the macroform and microform effects has no theoretical justification. It is shown that the microform effect depends on a detailed optical model of the statistical segment, and this effect is calculated for two simple models. The expression suggested by Tsvetkov cannot be applied to a segment consisting of anisotropic monomers.     

Flow birefringence of concentrated polymer solutions in two-dimensional flows

The results of flow birefringence measurements are reported for polymer solutions of moderate concentration subjected to a wide range of two-dimensional flows. These flows were generated in a four-roll mill which enables one to systematically vary the ratio of the vorticity to the rate of strain in the flow while holding the velocity gradient constant. It is shown that steady-state birefringence data collected over a wide range of flow types can be correlated against the eigenvalue of the velocity gradient tensor, in agreement with criterion for strong and weak flows from model calculations. Transient birefringence measurements in which purely extensional flows were started from rest are also reported. It was observed that the birefringence went through a pronounced overshoot in time for two different polymer/solvent systems. Flow induced increases in the solution turbidity were also observed and the increased turbidity remained constant over a period of many hours after extensional flows were arrested. The birefringence, on the other hand, decayed to zero almost immediately after the flows were stopped. These changes in the turbidity suggest that crystallization of the polymer was occurring. The qualitative results of experiments are compared to recent network model calculations using the theory of Yamamoto for concentrated polymer systems. It is found that this model can predict qualitatively many of the experimental observations if the function describing the breakage of polymer chain entanglements is allowed to depend on the conformation of the polymer segments bridging the entanglements. In particular, this dependency of the entanglement breakage on the conformation of the network segments leads to a predicted overshoot of birefringence when purely extensional flows are started from rest. It is also demonstrated through this model that birefringence data taken over a wide range of flow types can be used to estimate the degree to which the network deforms affinely with the flow field.     

Phenomenological analysis of elongational flow birefringence in semidilute solutions of hydroxypropylcellulose

The relaxation time of a polymer chain in an elongational flow field was investigated for hydroxypropylcellulose (HPC) semidilute solution systems by two methods: phenomenological analysis of elongational flow-induced birefringence, and dynamic light scattering (DLS) and rheological measurements. To understand the relaxation time of an entangled semiflexible polymer solution in an elongational flow field, scaling analysis of the elongational flow-induced birefringence curve was performed. The results of both temperature and concentration scaling analyses showed that birefringence curves at different temperatures and at several HPC concentrations were described well by a universal birefringence–strain rate curve. This scaling behavior was compared with the "fuzzy cylinder" model. The critical strain rate corresponded to the correlation time of the slow relaxation mode determined by DLS measurement and the relaxation spectrum obtained by dynamic viscoelasticity measurement. The elongational flow-induced birefringence observed in an HPC semidilute solution was concluded to be attributed to the orientation of the HPC segment in the entangled molecular system, because the dominant relaxation mode is found to be the concentration fluctuation of an entangled molecular cluster in a quiescent state.     

Naphthylethyne based liquid crystals with high birefringence and characteristics of selective reflection

A series of high birefringence liquid crystalline molecules with cyano, isothiocyanato and trifluoromethyl terminal compounds based on naphthylethyne core was successfully synthesized and characterized. The molecular structures of the intermediates and resulting compounds were confirmed by Fourier transform infrared (FT-IR), nuclear magnetic resonance (NMR), mass spectrometry (MS), and elemental analysis (EA). Their thermal stability, transition temperatures, and phase sequences were investigated by simultaneous thermal analyzer polarized (STA), optical microscopy (POM) and differential scanning calorimetry (DSC). The birefringence was measured by using an Abbe refractometer. In addition, the selective reflection characteristics with naphthylethyne compounds were also studied.     

Localized flow birefringence of polyethylene oxide solutions in a two roll mill

Experimental observations are reported of the behavior of solutions between two rotating parallel rollers where the form of the flow field between corotating rollers corresponds to that of a col which has nonorthogonal asymptotes. The obliquity of the asymptotes of the flow gives a direct measure of the relative magnitude of the constituent pure shear and rotational components of the flow field. Flow birefringence observations of polyethylene oxide solutions between the corotating rollers show that molecular orientation is limited to a highly localized region near the “outgoing” asymptotic sheet of the flow field in accordance with the predictions of a “persistent extensional flow” analysis presented. Counterrotating rollers show no flow birefringence also as expected. The behavior of polymer solutions and Newtonian fluids are compared. With increasing strain rate using corotating rollers the obliquity of the asymptotes of the flow remains constant for the Newtonian fluid but changes significantly for the polymer solution.     

Localized flow birefringence of polyethylene oxide solutions in a four roll mill

We report flow birefringence observations of polyethylene oxide solutions in a four roll mill where the flow field in the central region of the mill approximates well to that of pure shearing flow. When flow birefringence is observed it is seen to be highly localized within a region close to the “outgoing” asymptotic plane of flow. The phenomenon can be explained in terms of the flow birefringence corresponding to high extension of some polymer chains where the localization is caused by the chains requiring sufficient time in the flow field to become extended. This explanation has important consequences in all “persistently extensional flows” and can explain the origin of previously published results of localized flow birefringence observed for polyethylene solutions in axial compression and axial extensional flows.     

Streaming birefringence. VII. Influence of the intermolecular hydrodynamic interaction on the viscosity and streaming birefringence of polymer solutions

The cavity model used in the theory of dielectrics was applied to hydrodynamics to calculate the force exerted by a system of soft dumbbells on a reference dumbbell in a hydrodynamic field. The influence of this force on the viscosity and flow birefringence and its dependence on both the concentration and velocity gradient were calculated. The system of equations has a real solution only for values of β = M[η]η₀γ/RT which are smaller than a critical value rapidly decreasing with increasing concentration. At zero concentration the results obtained agree with the theory of a single isolated dumbbell model. The calculated Huggins constant is k′ = 0.4. The extinction angle is connected with the relative viscosity very nearly as derived from experiments. However, the theory fails at higher concentrations and gradients yielding an increase in viscosity with the gradient and infinite zero-shear viscosity for the concentration c = 2.5/[η].     

Interface effects in nematic liquid-crystalline structures of polymer solutions

A solution of long semirigid linear macromolecules was considered. The liquid-crystalline nematic ordering in the solution was analyzed theoretically using an Onsager-type approach. The orientation entropy was calculated in the frameworks of Lifshits' approach, successfully developed for this system originally by Khokhlov and Semenov. For homogeneous liquid-crystalline phase using the third virial approximation for intersegmental steric interaction the orientation distribution function, the free energy density, the isotropic-nematic coexistence and the spinodal conditions were computed numerically for two types of polymer flexibility mechanism: persistent chains and chains of freely joint segments. For the asymptotically exact second virial approximation the applicability region was analyzed. We considered the general equations, which describe the concentration and orientational segment distribution for a semirigid persistent polymer chain at a surface (or interface) of any shape and orientation. These equations were numerically solved for the case when the nematic director axis was perpendicular to a planar interface boundary between the real coexisting nematic and isotropic phases. The coordinate-dependencies of the polymer concentration and of the order-parameter take the smooth two-steps form in the interface region.     

Orientational–deformational nature of flow birefringence in solutions of rigid-chain polymers

The orientational–deformational nature of flow birefringence (FB) in solutions of rigid-chain polymers is confirmed experimentally. The possibility of a direct determination of the internal viscosity parameter by the dependence of the FB relaxation time on the solvent viscosity is demonstrated. Indirect manifestation of internal viscosity in the FB relaxation time is confirmed by the dependence of the form factor on the degree of coiling. © 1993 John Wiley & Sons, Inc.     

Relaxation dynamics of salt‐free polyelectrolyte solutions using flow birefringence and rheometry

Relaxation dynamics of salt‐free, aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) were investigated by mechanical rheometry and flow birefringence measurements. Two semidilute concentration regimes were studied in detail for a range of polymer molecular weights. At solution concentrations c < 10 mg mL, limiting shear viscosity η₀ was found to scale with molecular weight and concentration as η₀ ∼ c^0.5M_w over nearly two decades in concentration. At higher solution concentrations, c > 10 mg mL, a change in viscosity scaling was observed η₀ ∼ c^1.5M, consistent with a change from simple Rouse dynamics for unentangled polyions to near‐perfect reptation dynamics for entangled chains. Characteristic relaxation times τ deduced from shear stress and birefringence relaxation measurements following start‐up of steady shearing at high rates reveal very different physics. For c < 10 mg mL, both methods yield τ ∼ c^−0.42M and τ ∼ c⁰M for c > 10 mg mL. Curiously, the concentration scalings seen in both regimes are consistent with theoretical expectations for salt‐free polyelectrolyte solutions undergoing Rouse and reptation dynamics, respectively, but the molecular weight scalings are not. Based on earlier light scattering studies using salt‐free NaPSS solutions, we contend that the unusual relaxation behavior is likely due to aggregation and/or coupled polyion diffusion. Simultaneous stress and birefringence measurements suggest that in concentrated solution, NaPSS aggregates are likely well permeated by solvent, supporting a loose collective of aggregated chains rather than the dense polymer aggregates previously supposed. Nonetheless, polyion aggregates of either variety cannot account for the inverse dependence of relaxation time on polymer molecular weight for c < 10 mg mL. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 825–835, 1999     

Hyperbranched polymer structures via flexible blade flow coating

Evaporative self‐assembly has been shown to be a scalable method for organizing nonvolatile solutes, for example, nanoparticles; however, the influence of substrate surface energy on this technique has not been studied extensively. In this work, we utilized an evaporative self‐assembly process based upon flexible blade flow coating to fabricate organized structures that have been modified to systematically vary surface energy. We focused on patterning of polystyrene. We observed a variety of polystyrene structures including dots, hyperbranched patterns, stripes, and lines that can be deposited on substrates with a range of wetting properties. We explained the mechanism for these structural formations based on the competition between Marangoni flow, friction, and viscosity. The development of this fundamental knowledge is important for controlling hierarchical manufacturing of nanoscale objects with different surface chemistries and compositions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 32–37     

Electric birefringence and conformation of polychlorohexylisocyanate in solutions

Electric birefringence was investigated for solutions of polychlorohexylisocyanate fractions for molecular weights 30·6 × 10⁴–1·2 × 10⁴ in tetrachloromethane.Experimentally found dispersion of the Kerr effect is used for estimating the coefficients of rotatory diffusion D_r of molecules. A comparison of rotatory diffusion D_r values with molecular weights M and intrinsic viscosities [η] of fractions shows that the value of D_rM[η] decreases with M. This illustrates the change in the conformation of molecules from a random coil to a rod.On the basis of experimental dependences of D_r and the Kerr constants K on M, the main structural parameters of the polymer investigated were determined: the number of monomer units in a segment, the projection of the length of the monomer unit on the axis of the molecule, the value of the dipole moment μ₀ of the monomer unit and the angle formed by μ₀ and the chain direction.     

Pressure driven flow of polymer solutions in nanoscale slit pores

Polymer solutions subject to pressure driven flow and in nanoscale slit pores are systematically investigated using the dissipative particle dynamics approach. The authors investigated the effect of molecular weight, polymer concentration, and flow rate on the profiles across the channel of the fluid and polymer velocities, polymer density, and the three components of the polymers radius of gyration. They found that the mean streaming fluid velocity decreases as the polymer molecular weight and/or polymer concentration is increased, and that the deviation of the velocity profile from the parabolic profile is accentuated with increase in polymer molecular weight or concentration. They also found that the distribution of polymers conformation is highly anisotropic and nonuniform across the channel. The polymer density profile is also found to be nonuniform, exhibiting a local minimum in the center plane followed by two symmetric peaks. They found a migration of the polymer chains either from or toward the walls. For relatively long chains, as compared to the thickness of the slit, a migration toward the walls is observed. However, for relatively short chains, a migration away from the walls is observed.     

Determination of molecular parameters from polymer solutions in shear flow

A light scattering photometer with a double cylinder shear cell has been developed which allows detection not only in one plane as usual, but in a half-spherical range around the scattering volume. The anisotropic scattering behavior of oriented and deformed polymer molecules in dilute solution was investigated. All measurements were performed on polystyrene in several viscous solvents. From measurements in the plane of flow the average orientation angle was determined. By variation of detector position and wavelength of the primary beam, the determination of all three axes of the molecular gyration space of polymer coils was possible. Compared to predictions of the well-known dynamic theories by Kuhn, Rouse and Zimm, corresponding orientation data were found while the molecular deformation ratio shows much lower values than expected.     

Flow and electric birefringence in solutions of ladder polychlorophenylsilsesquioxane

Flow birefringence (FBR) and electric birefringence (EBR) have been investigated for dilute solutions of a number of fractions of cyclolinear (ladder) polychlorophenylsilsesquioxane (CLChPhS). FBR and EBR are negative in sign and their characteristic values increase with molecular weight in accordance with properties characteristic of kinetically and equilibrium—rigid chain polymers. In sinusoidal fields, dispersion of EBR characteristic of kinetically rigid chains was found: its dependence on molecular weight quantitatively agrees with the theory of relaxation and rotatory friction of rigid molecules. Analysis of experimental data confirms the validity of the molecular model of CIChPhS as a double-chain ladder cis-structure and permits us to obtain quantitative information concerning important molecular parameters such as the character of rotation of phenyl side groups the values of valence angles in chains and in oxygen bridges and dipole moments of the monomer unit of the chain and of the SiO bond.     

Supermolecular morphology of thermoreversible gels formed from homogeneous and heterogeneous solutions

The supermolecular structures of thermoreversible gels formed from either homogeneous or heterogeneous solutions were examined by scanning electron microscopy. The morphologies of gels of polyethylene and polystyrene of various tacticities were then related to the phase diagram of the polymer–solvent system. We confirmed the morphological findings of Aubert on isotactic polystyrene gels formed either above the binodal or inside the spinodal and extended his study to gels prepared within the metastable region of the phase diagram. For polystyrenes and polyethylene, the morphology of the gels formed inside the coexistence curve differs markedly from that of gels formed outside. Inside the binodal, gels of polyethylene and polystyrenes exhibit remarkable morphological similarities, indicating a common gelation mechanism, namely, liquid-liquid phase separation. Depending on the concentration, these gels exhibit either an open strut-like network structure or smooth spherical globules. The former is attributed to gelation inside the spinodal whereas the latter is believed to result from gelation in the metastable region. For crystalline polymers, gels formed inside the coexistence curve subsequently undergo crystallization within their polymer-rich phase. The morphology of isotactic polystyrene and polyethylene gels formed outside the binodal consists of overlapping lamellar structures, whereas that of atactic and epimerized polystyrene gels is characterized by a sheet-like structure, differentiating the crystallization-based mechanism from others. © 1993 John Wiley & Sons, Inc.     

Effect of aging on flow birefringence of poly(vinyl alcohol) and methyl cellulose solutions

Flow birefringence experiments on aqueous solutions of poly(vinyl alcohol) and of methyl cellulose show that the optical anisotropy changes markedly during aging of the solution. The same effect can be obtained by adding alcohol to fresh aqueous methyl cellulose solutions. The flow birefringence was measured as a function of the velocity gradient on solutions with and without alcohol during the course of aging. The phenomena are attributed to intermolecular and intramolecular interactions between exposed hydroxyl groups of the polymer chains, as these are affected by a change in the degree of hydration during aging or by the addition of a strong hydrophilic agent such as an alcohol. Association or crystallization of the ordered polymer chains may occur and lead to a supermolecular structure in the solutions. By following Sadron's theory and making use of a polar diagram, it was concluded that, after aging or mixing with the additive, the solutions become optically heterogeneous and contain two different components with optical polarizabilities of the same [in poly (vinyl alcohol) solutions] or opposite (in methyl cellulose solutions) sign.     

Orientation relaxation of linear chains enclosed in a network studied by birefringence measurements

 The relaxation of linear poly(styrene sulfonate) chains in a swollen poly(acrylamide) network is investigated by birefringence measurements. After a stepwise deformation of the network relaxation occurs, because the linear chains are initially deformed as well, but diffuse into an isotropic conformation via the reptation mechanism. The course of the birefringence with time agrees essentially with what follows from the reptation model. It could be shown that the relaxation time varies approximately with the third power of the molar mass of the enclosed molecules when networks of sufficiently high network density are used. On the other hand, the dependence of the relaxation time on network density or degree of swelling, respectively, seems to be much stronger than what is expected from theory. Received: 9 September 1996 Accepted: 25 November 1996