Effects of polymer adsorption on the effective viscosity in microchannel flows: phenomenological slip layer model from molecular simulations

Molecular simulations (Dissipative Particle Dynamics - DPD) were used to quantify the effect of polymer adsorption on the effective shear viscosity of a semi-dilute polymer solution in microchannel Poseuille flow. It is well known that polymer depletion layers develop adjacent to solid walls due to hydrodynamic forces, causing an apparent wall slip and reduced effective viscosity (increased total flow rate). We found that depletion layers also developed in the presence of hydrodynamically rough adsorbed layers on the wall. Polymer-polymer (steric) repulsion between flowing and adsorbed polymer expanded the depletion layer compared to no-adsorption cases, and the effective viscosity was reduced further. Desorption occurred for higher shear rates, reducing the repulsion effect and shrinking the depletion layers. A phenomenological algebraic model for the depletion layer thickness, including a shear modified adsorption isotherm, was developed based on the simulation data. The depletion layer model can be used together with the effective viscosity model we developed earlier.     

Studies on the viscosity behavior of polymer solutions at low concentrations

Viscosity measurements had been made on poly(vinyl alcohol) (PVA), poly(N-vinyl-2-pyrrolidone) (PVP) and poly(ethylene oxide) (PEO) solutions down to low concentrations. It was found that defined as the flow time of the pure solvent in ideal conditions and obtained practically by extrapolating the flow time of polymer solution t to zero concentration, was not equal to the flow time of the pure solvent t₀ measured. The reduced viscosity η_sp/C determined by (t/t₀-1)/C exhibited either a drastic increase or a significant decrease with dilution, depending upon the polymer solution investigated. On the other hand, η_sp/C determined by was proportional to C even at low concentrations. The anomalous viscosity behavior of neutral polymer solutions at low concentrations, therefore, was due to the incorrect method by which η_sp/C was determined. The detailed experiments indicated that the effective diameter of the viscometer capillary, the surface property of the capillary wall and the additional pressure corresponding to the measurement of t and t₀ for PVA, PVP and PEO solutions were not the same. Taking into account the contact anger and the surface tension of the liquid, together with the geometric parameter of the viscometer, the influence of the additional pressure upon the flow time measurement could be studied quantitatively. The calculation was in a good agreement with the experimental result. According to the method presented in this paper, the thickness of the adsorbed polymer layers on the capillary walls could be determined. It was noted that the thickness of the adsorbed polymer layers on the capillary walls was closely related to the solvent in which the polymer molecules were dissolved. The polymer molecular weight, however, had little or no effect on the thickness of the adsorbed polymer layers on the walls of the viscometer capillary.     

Analysis of the melt viscosity and glass transition of polystyrene

The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann-Hesse viscosity equation: log η = log A + B/(T ? T₀). Evidence that the glass transition is an isoviscosity state (log η_g ? 13) for lower molecular weight fractions (M < M_c) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ? 19,000; t_g = 89°C.), it is shown that B is independent of the p–v–T state of the polymer liquid and that dT₀/dP = dT_g/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero-pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔV_g* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3?, is reexamined. For polystyrene and polyisobutylene, ?_g/b = 0.03, but ?_g and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ?, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dT_g/dP, one an exact derivation and the other an empirical correlation, are presented.     

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.     

Intrinsic viscosity in branched free-radical polymers

The intrinsic viscosity ratio [η]_B/[η]_L was calculated as a function of average branching density for trifunctionally branched, free-radical polymers. Calculations were made for the g^1/2, g^3/2, and h³ rules, using realistic distributions of molecular weights and branches. Experimental data on branched poly(vinyl acetate) lay between the curves obtained from the g^1/2 and h³ relations.     

Polymers in 2D confinement: A nanoscale mechanism for thermo‐mechanical reinforcement

Acrylate‐clay nanocomposites, a 2D confined system, exhibited unusual increase of thermo‐mechanical properties. The nature of this reinforcement can be ascribed to chain dynamics modification and therefore investigated via dynamic mechanical analysis. Transmission electron microscopy and dynamic light scattering showed a strong nanoconfined regime, 2R_h ≫ d₀₀₁, where R_h is the polymer's hydrodynamic radius and d₀₀₁ is the clay gallery spacing. The geometrical constraints to polymer dynamics led to significant enhancement of the thermo‐mechanical properties. Adding only 1 wt% nanoclay, the glass transition temperature increased significantly, ΔT_g = T_g − T_g,bulk ~ 10°C, and the dynamic modulus E′ increased 10‐fold. Analysis of dynamic mechanical spectra showed an increase of relaxation time τ, ie, polymer dynamics retardation. Furthermore, the mechanical damping tan δ was strongly attenuated evidencing the reduction of viscous dissipation. The activation energy E_a of the α‐transition increased as the confined macromolecules needed to overcome higher energy barriers to achieve configurational rearrangements. The considerable increase of mechanical modulus cannot be explained by polymer composite models, rather it was associated to a “nano‐effect,” scaling with the degree of confinement as E/E_matrix ~ (2R_h/d₀₀₁)ⁿ. This study paves the road for further understanding of polymer dynamics under 2D confinement and the reinforcement mechanism of thermo‐mechanical properties.     

Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Longitudinal volume viscosity of 1,4 cis polybutadiene

Volume flow of 1,4 cis polybutadiene (1,4 cis PB) of ¯M _n =311.900,T _g =156 K, andT _m =266 K, has been measured.Elastic modulus of the elastic wave, longitudinal volume viscosity, initial longitudinal volume viscosity, and retardation times are described at compression rates of ca. 1.0 to 200.0×10^–5 s^–1, and at temperatures of 293 K to 373 K, and pressures up to 150 MPa.Longitudinal volume viscosity decreases with increasing compression rate, and with decreasing volume deformation, the behavior being in all cases a typical non-equilibrium one. Longitudinal volume viscosity decreases with increasing temperature (except at 293 K), the volume flow activation energy being of about 18.2 KJ/mol.     

Dynamics of star branched polymers in a matrix of linear chains — a Monte Carlo study

A simple cubic lattice model of the melt of 3-arm star-branched polymers of various length dissolved in a matrix of long linear chains (n₁ = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star-branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star-branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains.     

Investigating the Dynamic Viscoelasticity of Single Polymer Chains using Atomic Force Microscopy

In single‐molecule force spectroscopy (SMFS), many studies have focused on the elasticity and conformation of polymer chains, but little attention has been devoted to the dynamic properties of single polymer chains. In this study, we measured the energy dissipation and elastic properties of single polystyrene (PS) chains in toluene, methanol, and N,N‐dimethylformamide using a homemade piezo‐control and data acquisition system externally coupled to a commercial atomic force microscope (AFM), which provided more accurate information regarding the dynamic properties of the PS chains. We quantitatively measured the chain length‐dependent changes in the stiffness and viscosity of a single chain using a phenomenological model consistent with the theory of viscoelasticity for polymer chains in dilute solution. The effective viscosity of a polymer chain can be determined using the Kirkwood model, which is independent of the intrinsic viscosity of the solvent and dependent on the interaction between the polymer and solvent. The results indicated that the viscosity of a single PS chain is dominated by the interaction between the polymer and solvent. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1736–1743     

DNA diffusion in aqueous solution in presence of suspended particles

Although nanoparticles, which are comparable in size to polymer chains, are widely used as fillers to polymer matrices for developing functional and high performance materials, the dynamics of polymers constrained between solid particles has not been well elucidated. In this study, dynamics of individual polymer under such condition was investigated with fluorescent microscopy using DNA solutions as model systems. For individual T4 and λ DNA molecules in aqueous suspensions of spherical polystyrene particles with diameter of 1 μm, it was found that (i) the radius of gyration of DNA is independent of the particle volume fraction, ?_p, (ii) DNA diffusion is not sensitive to ?_p up to a certain critical ?_p where the average distance between particle surfaces is close to DNA size, and (iii) the DNA diffusion becomes slower at higher ?_p. The diffusion coefficient of DNA was larger, by a factor of 2, in the suspensions at intermediate ?_p than in the corresponding confined geometry (channel/slit between fixed walls), whereas this difference asymptotically vanished with increasing ?_p. This result suggested that the DNA diffusion in the suspensions with intermediate ?_p is accelerated by the particle motion. In fact, the diffusion coefficient measured for DNA in the suspensions was semiquantitatively described by the Rouse constraint‐release model considering the matrix effect on the probe chain diffusion. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1103–1111, 2009     

Steady-shear viscosity of polydimethylsiloxanes over the range from the lower to the upper Newtonian region

The mechanism of non-Newtonian behavior for flow from the lower to the upper Newtonian region is explained by a modification of Graessley's theory. In the theory proposed here, a viscosity η_fric, which is based on friction between polymer segments and is almost shear-independent, is introduced in addition to Graessley's entanglement viscosity η_ent, which decreases with increasing shear rate. The theory is applied to previously obtained data on steady flow of polydimethylsiloxanes of different molecular weights. The agreement between calculated and experimental results is good. In polymers with the molecular weight above the critical molecular weight for entanglement M_c, the major contribution to viscosity near zero shear rate is η_ent. As the shear rate increases, the flow curve has an inflection where η_fric cannot be disregarded in comparison with η_ent. In the upper Newtonian region, η_fric has more influence on the viscosity than η_ent. The theory can also explain the experimental results on flow of polymers with molecular weight below M_c, which were shown to be slightly non-Newtonian in the previous paper.     

Rheology of heterophase polymer systems

This lecture attempts to elucidate rheological behavior of multiphase polymer systems through a comparison with our studies on much simpler systems such as suspensions of (a) non-aggregating and (b) aggregating monodisperse spheres in viscoelastic media, (c) polymer latex in the same polymer liquids, and (d) emulsions or blends of two polymers with or without an emulsifying block copolymer. For the system (a) not only the viscosity η but also the modulus obey the known simple dependence on volume fraction ϕ of hard-sphere suspensions, while for the system (b) the flow induced-aggregation and dissociation of the particles govern the rheology. In the system (c), relaxations of entanglements of the adsorbed chains as well as the spatial distribution of the latexes are essential. For the emulsion (d) of a biased composition range (e.g., ϕ₁ > ϕ₂) the matrix phase 1 dominates, unless η₁ << η₂. When η₁ ≥ η₂, deformation and/or bursting of the dispersed phase 2 take place. For those of an even composition, the viscosity is additive of those of the components and is enhanced by adding the emulsifying block copolymer component.     

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007     

Longitudinal volume viscosity of poly(methyl methacrylate)

Volume flow of poly(methyl methacrylate) (PMMA) (M?_n = 43,000 and T_g = 384) has been measured in an Instron Capillary Rheometer. Elastic modulus of the longitudinal wave, longitudinal volume viscosity, initial longitudinal volume viscosity, and retardation times are described at temperatures above T_g (418–483K) and compression rates of about 1.00–200.00 × 10⁵ s^?1. An initial increase followed by a decrease in longitudinal volume viscosity has been observed as the compression rate increases and the volume deformation decreases, this last behavior being at the lowest values of the compression rate (6.0 and 30.0 × 10^?5 s^?1) a typical nonequilibrium one. η_L also increases with increasing temperature (T_g decreases 0.18°C/MPa), and volume flow activation energy decreases as the volume deformation increases.     

Lattice treatment of thermodynamic properties of ring and linear polymer mixtures

Expressions for the entropy and free energy of mixing a solvent with a mixture of linear and cyclic polymer molecules are derived. The entropy of mixing is deduced from the number of ways of arranging on a honeycomb lattice a mixture of totally flexible molecules made up of N_R rings and N_C chains. An equation is obtained through the combination of two independent expressions for the number of ways of arranging rings and chains. The free energy of mixing is deduced from the entropy and the enthalpy of mixing, using two distinct interaction parameters for ring and for chain molecules. The chemical potentials for solvent, ring polymer, and linear polymer are derived from the free energy of mixing. These quantities are found to be functions of the mole fraction of rings in the polymer mixture. © 1993 John Wiley & Sons, Inc.     

What is the flow activation volume of entangled polymer melts?

We evaluate the flow activation volume in polymer melts of isotactic polypropylene and atactic polystyrene with step-shear experiments at different melt temperatures. The melt is initially sheared with constant shear rate until the attainment of a melt state with nearly constant viscosity. Perturbations to this experiment, involving shear steps in short-time intervals with decreasing rates, are induced next. Measurements of the shear stress value at each shear rate step allow the evaluation of an experimental (apparent) flow activation volume. The true flow activation volume is evaluated by extrapolating the experimental data to infinite shear stress values. The value obtained is larger than the physical volume of the chain and agrees with the volume of a tube confining chains with a molecular weight between M _n and M _w. Besides supporting the validity of tube model, experiments based on this protocol may be used on model polymer samples, in composites with nanoparticles and in polymer blends to access the validity of mechanisms considered by flow models.     

Solution characterization of poly(isobornyl methacrylate) in tetrahydrofuran

Thermodynamic and hydrodynamic properties of dilute solutions of poly (isobornyl methacrylate) (PIMA) in tetrahydrofuran (THF) were characterized by using viscosity, static, and dynamic light scattering measurements. PIMA samples with different molecular weight were obtained by fractional precipitation of PIMA solution. Chain dimension parameters (R_g and R_H), together with second virial coefficient A₂ and intrinsic viscosity [η], were used to calculate various solution parameters characterizing polymer chains in polymer solutions. The experimental results are compared with calculation, indicating that PIMA behaves as a flexible coil in THF. © 1994 John Wiley & Sons, Inc.     

Hydrodynamic properties of regular star-branched polymer in dilute solution

We calculate quantities such as g = [η]_b/[η]_l and h = (f_t)_b/(f_t)_t for regular star-branched polymer with and without excluded volume. We have applied a numerical method introduced by Barrett for the linear chain and have solved the integral equations which are conducive to calculate the translational coefficient friction and the intrinsic viscosity in the Kirkwood-Riseman theory. We utilize preaveraging but avoid other approximations. In general, we obtain values which have a better accord with experimental data than traditional Kirkwood-Riseman and Zimm-Kilb formulas. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 563–567, 1997