The Rheology of Wetting By Polymer Melts

Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1R_o), where R_o is the initial radius of curvature, (2) cosθ_∞. (l-cosθ/cosθ_∞) where θ_∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ_∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed.     

Estimation of the Surface Energy of Polymer Solids

The methods to estimate the surface tension of polymer solids using contact angles have been reviewed in the first part. They are classified into the following three groups depending on the theories or the equations applied: (1) the methods using the Young's equation alone, (2) the methods using the combined equation of Young and Good-Girifalco, and (3) the methods using the equations of work of adhesion. Some notes and comments are given for each method and results are compared with each other. The two-liquids method for rather high energy surface is also introduced.

Next, some new possibilities to evaluate the surface tension of polymer solids are presented by our new contact angle theory in consideration of the friction between a liquid drop and a solid surface. The advancing and receding angles of contact (θ _a and θ _r ) are explained by the frictional tension γ_F and accordingly two kinds of the critical surface tension γ_C (γ_Ca and γ_Cr ) are given.

This work has shown that one of the recommendable ways to evaluate γ_S is either the maximum γ_LV cos θ_a or the maximum γ_C using the advancing contact angle θ_a alone, and another way is the arithmetic or the harmonic mean of the γ_Ca and γ_Cr . A depiction to determine the γ_C such as ln(1 + cos θ₀ ) vs. γ_LV with cos θ₀ = (cos θ₀ + cos θ_r )/2 has also been proposed.     

Wettability studies of reactive brazing alloys on CVD diamond plates

Wettability of both the diamond and the insert surfaces by the filler metal in CVD diamond brazed-on cutting tools is a key condition for good brazing strength. The brazing process of CVD diamond thick plates still has to be improved, namely on the influence of the brazing alloy composition and of the substrate surface finishing quality in wettability. In this study, contact angle measurements were performed in a dedicated high vacuum furnace coupled with a video recording system. Diamond films with different thickness (75<t<300 μm), and thus having distinct grain sizes and roughness, were grown with fixed conditions by the MPCVD technique on Si substrates and chemically detached for wettability experiments. Roughness parameters were evaluated by profilometry and AFM, which was used to observe the grown diamond surfaces of the self-standing films. The reactive Ag–Cu–Ti brazing system was investigated. Results showed a very good wettability in the temperature range 800–850°C, namely for the diamond surface where a minimal contact angle of 10° was reached. A Ti-rich thin reaction layer (0.5–0.8 μm) was detected at the drop side of the substrate/brazing alloy interface in both substrate materials, proving the affinity of Ti to carbon. The influence of the diamond roughness on the contact angle θ_R is notable, obeying a linear dependence of the type cosθ_R=cosθ₀+k cosθ₀·(R_a/G)², where R_a and G, the grain size, are related to asperity height and width, respectively. This relationship is based on the well-known Wenzel equation that correlates the real contact angle to the surface area increasing with roughness.     

Contribution of interferometry and mechanical parameters in evaluating molecular orientation for drawn polyester

Mechanical and structural parameters related to the optical properties of polyester (PET) (woollen type) fibres drawn at room temperature have been investigated. The changes in the strain were evaluated to obtain the molecular orientation factors 〈P₂(cos θ)〉 and 〈P₄(cos θ)〉. From the optical orientation, the values of f₂(θ), f₄(θ) and f₆(θ) orientation parameters were calculated. The structure and properties of oriented PET have been studied in the light of the rubber elasticity theory. The dielectric constant, magnetic susceptibility, number N′ of chains between crosslinks per unit volume, optical configuration parameter and the segment anisotropy, were among the calculated parameters. The results of the extension were used to calculate the shrinkage factor. Relationships between the calculated parameters and the draw ratios, together with micro-interferograms, are given for illustration. The present study throws light on how the applied stress changes the molecular orientation factors and the structural parameters. © 1999 Society of Chemical Industry     

Penetration of water/ethanol mixtures into silanized silica fibrous assemblies

The penetration rates of water/ethanol mixtures into silica fibrous assemblies were determined from the change in electrical conductivity due to wetting. Silica fibrous assemblies were treated with γ-aminopropyltriethoxysilane (APTES) and methyltriethoxysilane (MTES). The advancing contact angles of the water/ethanol mixtures on silanized silica, _a, were measured by the Wilhelmy method. The electrical conductivity, λ, began to increase at time to after the wetting liquid-fibrous assembly contact and reached a constant value. By comparing the experimental λ - t curve with the curve calculated by the Washburn equation, the capillary distribution of the fibrous assembly was determined. The to value as a measure of the penetration rate increased with increasing volume ratio of ethanol in the water/ethanol mixtures for the untreated and APTES-treated silica fibrous assemblies. This indicates that the addition of ethanol to the wetting liquid decreased the penetration rate. In the case of the MTES-treated silica fibrous assembly, liquid penetration was observed above 30% of ethanol and to decreased with increasing volume ratio of ethanol. On the basis of the Washburn equation, the value of 1/t₀ was plotted against λL cos _a/η, where γL is the surface tension of the liquid and η is the viscosity of the liquid. As expected, the value of 1/t₀ increased linearly with increasing cos _a/η.     

Measurement of polar orientation in poled side-chain NLO polymers using infrared spectroscopy

Infrared spectroscopy has been used to provide an independent estimate of dipole orientation in poled films of a side-chain polymer based on poly(methyl methacrylate) with an oxynitrostilbene side group attached via an aliphatic spacer. In particular, we used the dichroism of the absorption band assigned to the NO₂ symmetric stretching vibration as a measure of the orientation of the nitrostilbene group. This yields 〈P₂(cos θ)〉, where θ is the angle between the transition dipole moment and the symmetry axis of the sample. We then used a Langevin-type model to calculate 〈cos θ〉 from 〈P₂(cos θ)〉 and concluded that values of 〈cos θ〉 as high as 0.5 are being achieved. We find, however, that 〈P₂(cos θ)〉 obtained by comparison of normal incidence measurements on unpoled and poled films does not agree with 〈P₂(cos θ)〉 obtained from tilted-film measurements on poled films. We propose that this discrepancy arises because the local field in a poled sample affects the polarizability of the molecules. To confirm this, we applied high fields to unpoled films in the infrared spectrometer at room temperature. The results clearly show a large reduction in absorbance with the applied field when the infrared electric field vector has a component perpendicular to the plane of the film. A major error therefore occurs as a consequence of the internal field in poled samples if 〈P₂(cos θ)〉 is derived from the tilted film measurements, whereas 〈P₂(cos θ)〉 derived from normal incidence measurements is essentially correct. © 1994 John Wiley & Sons, Inc.     

Critical Surface Tension of Non-crosslinking Linear Low Density Polyethylene-graft-acrylic Acid by the Contact Angle Method

Abstract

The contact angles θ of polar liquid on surface of non-crosslinking linear low density polyethylene-graft-acrylic acid (LLDPE-g-AA) were measured. The critical surface tension (γ_c) of LLDPE-g-AA films were evaluated by three different plots, the Zisman plot, the Young-Dupre-Good-Girifalco plot, and the log(1 + cos θ) versus log θ _L , plot. The θ _c of LLDPE-g-AA obtained by the 1 + cosθ versus θ _L ^?1/2 plot were higher than those obtained by other plots.     

The Strength of Liquid Bridges Between Dissimilar Materials

The strength of the liquid bridge between a sphere and a plate of dissimilar materials was studied. An equation was derived using the surface energy approach. For small amounts of liquid, the force of adhesion f was f=2πRy(cosθ₁ + cosθ₂ where R is the sphere radius, y is the surface tension, and θ₂ , θ₂ the contact angles. In the derivationn, major simplications about the meniscus shape were possible.

The equation was experimentally tested with water, ethyl alcohol, aniline and iodobenzene using factorial combinations with different solids. Force of adhesion measurements were carried out using a tensile testing machine at controlled loading rates. Excellent agreement was obtained in the experimental and predicted adhesion values. The McFarlane-Tabor equation was identified as correct only for small amounts of liquids and similarly wet solids.     

Critical Surface Tension of Acrylamide-Grafted Polypropylene Copolymer by the Contact Angle Method

The contact angles θ of polar liquids on PP-g-AM copolymer (AM content 0.19, 0.26, and 0.37 wt%) were measured. The critical surface tension γ_C of PP-g-AM films were evaluated by the Zisman plot (cos θ versus-γl), the Young-Dupre-Good-Girifalco plot (1 + cos θ) versus 1/γ^0.5 l, and the log(1 + cos θ) versus log-γl plot. The-γl values estimated by the plot log(1 + cos θ) versus log-γl were smaller than those obtained by the other plots.     

Adsorbed states of K on the diamond (100)(2×1) surface

The adsorbed states of K on the C(100)(2×1) surface have been studied by electron energy loss spectroscopy (EELS), work function change (Δφ) measurement and thermal desorption spectroscopy (TDS). In the region where the K coverage is less than one-half of a monolayer (θ_K≤0.5), a loss is observed from ∼1.2 eV (θ_K=0.2) to 1.0 eV (θ_K=0.5); the work function decreases upon K adsorption until reaching a shallow minimum of Δφ=−3.35 eV at θ_K=∼0.5; and a desorption peak (β) is observed from ∼825 K (θ_K=0.05) to 525 K (θ_K=0.5). These results indicate that the K–substrate bond is highly polarized; the 1.2 eV loss is attributed to the electronic transition from the bonding to antibonding states formed at the K–substrate interface. In the region between θ_K=0.5 and 1, two losses are observed at 0.7 and 1.4 eV (θ_K=0.6); there is only a small increase of the work function; and a desorption peak (α) is observed in addition to the β peak. These results indicate that the K regains its electron and becomes, essentially, neutral. The 1.4-eV loss is ascribed to the transition from the 4s to 4p states of K. The origin of the 0.7-eV loss is discussed. The Δφ and TDS results are analyzed by the depolarization model.     

State of adsorption and coverage by overpotential-deposited H in the H2 evolution reaction at Au and Pt

By means of potential decay measurements using a digital data acquisition and computer processing system, accurate values of overpotential decay rates, dη/dt, may be obtained from which the pseudocapacitance and coverage behaviour of overpotential-deposited (OPD) H species in the cathodic H₂ evolution reaction (HER) at Au electrodes may be quantitatively derived as a function of η. The behaviour of the HER at Au is of interest in that an unusual Tafel slope value of 2.3RT/F is exhibited in acid solution while the value of alkaline solutions is the more familiar value of ca 2.32RT/F.Analysis of the overpotential relaxation behaviour on open-circuit, following interruption of cathodic polarization currents, gives an almost constant and small interfacial capacitance corresponding to a double-layer capacitance. Steady-state OPD H coverage (θ) is hence quite small (θ_H<0.3%). The Tafel slope value of 2.3RT/F requires, however, a potential-dependent H coverage determined by an H electrosorption step almost at equilibrium but with θ_H small. The rate-determining step is suggested to be surface diffusion to preferred desorption sites.Comparative results are presented for the HER at activated Pt where, contrary to the behaviour of Au, a large pseudocapacitance for OPD H is derived that may be associated with some surface hydride formation, the possibility of readsorption of H from a boundary layer supersaturated with H₂ having been minimized by electrode rotation at a sufficiently high rate of 3600 rpm.     

Fractal scaling of soot packing density across five size decades

We experimentally map the scaling laws for packing density (θ_f, solid component volume fraction) of soot aggregates across five orders of magnitude of size (R_g/a, normalized radius of gyration by monomer radius). The θ_f ? R_g/a scaling relationship evolves through three successive regimes with distinct power-law exponents of ?1.20 ± 0.01, ?0.58 ± 0.06, and ?1.31 ± 0.14. The first cross-over agrees with the classical aerosol-to-gel transition theory. This agreement, however, breaks down at the second cross-over point, where a late-stage cluster-cluster aggregation of aerosol gels takes over.

© 2017 American Association for Aerosol Research     

Evaporation of Ethanol-Water Mixture Drop on Horizontal Substrate

This study investigates the evaporation of sessile drop comprising ethanol and water mixture on horizontal poly methyl methacrylate surface. The contact angle (θ) and contact radius (R) of ethanol-water mixture drop are recorded with time, considering the impacts of presence of ethanol. With excess ethanol, the drop evaporation is principally controlled by a phase in which both the contact angle and contact radius are falling. A diffusional model assuming linear relation between contact radius and time is proposed as θ = eR ^?3 + cR ^?1, where e and c denote fitting coefficients. This model correlates with the experimental data.     

Scaling laws and internal structure for characterizing electrospun poly[(R)-3-hydroxybutyrate] fibers

Using chloroform/dimethylformamide (CF/DMF) co-solvent, electrospinning of poly[(R)-3-hydroxybutyrate] (PHB) solutions was carried out at ambient temperature. The effects of the applied voltage (V), flow-rate (Q), and solution viscoelastic properties on the Taylor cone, electrified jet, and fiber morphology were investigated. In addition, the electric field developed by the needle-plate electrode configuration was calculated using a finite element analysis to reveal the tip-to-collector (H) effect. Among the processing parameters (V, Q and H), it was found that Q played a key role in determining the jet diameter (d_j) and electrospun fiber diameter (d_f), and scaling laws existed between them, i.e., d_j-Q^0.61 and d_f-Q^0.33. The diameter reduction ratios of D_o/d_j (D_o is the needle diameter) and d_j/d_f were measured as 50-120 and 5-10, respectively; it suggested that major jet stretching took place in the straight electrified jet region, and further chain orientation could be gained by the subsequent process of jet whipping. By changing PHB concentrations from 5 to 15 wt%, the solution viscosity (η_o) was increased from 100 to 4900 cP, whereas the surface tension and solution conductivity remained unchanged; it provided a good model solution to exclusively reveal the η_o effect on the electrospinning process. Our results showed that the η_o-dependence of d_j and d_f also followed simple scaling laws: d_j-η_o^0.06, and d_f-η_o^0.39, with a prefactor depending on the processing variables, mainly the flow-rate. Regardless of the PHB concentrations used, the obtained PHB fibers showed a similar crystallinity fraction of ca. 0.63 and possession of major α-crystals together with a small amount of β-crystals with zigzag chain conformation.     

Zur unverträglichkeit von polymergemischen. 1. Lichtstreuungsmessungen am system polystyrol/polymethylmethacrylat/benzol

A polystyrene (PS) with M?_w = 9,7 · 10⁴ was investigated by means of light scattering in the isorefractive polymer/solvens-mixture polymethylmethacrylate (PMMA)/benzene. It was found, that the second osmotic virial coefficient A₂ of PS was strongly dependent on the average viscosimetric molecular weight M?_v and on the concentration of PMMA, but scarcely on the temperature in the range of 20°C to 60°C. The θ-Point, where A₂ is zero, was independent of the temperature within experimental error. By defining the PMMA concentration at the θ-Point as c_θ, and by reducing the measured PMMA concentration c to c/c_θ, an unequivocal relation was obtained between A₂ and c/c_θ, which is independent of molecular weight and molecular weight distribution of PMMA. PS shows a high second virial coefficient in dimer and trimer MMA as well as in non-hydrogenated and hydrogenated MMA. The investigated PS constitutes a θ-System in PMMA of a degree of polymerisation of P?_w, ～ 17without the use of benzene.     

Surface Modification of Fluorinated Polymers by Microwave Plasmas

We developed a new plasma treating method, incorporating the use of microwaves generated by an electronic cooking range. Using this method, polytetrafluorethylene (PTFE) and a copolymer of tetrafluoroethylene and hexafluoropropylene (FEP) were treated. Dialkylphthalates (DAP) were used as the standard liquids of contact angle measurements for evaluation of the wetting properties of plasma treated polymers. The components of surface tension (γ_L) due to the dispersion force (γ^d _L) and the polar force (γ^P _L) of DAP were calculated by Fowkes' equation from the contact angles (θ) on polypropylene. After plasma treatment cos θ of several standard liquids on PTFE and FEP increased. The linear relationship between γ_L(1 + cos θ)/(γ^d _L)^½ and (γ^P _L/γ^P _L)^½ was verified. γ_s and γ^d _s and γ^d _s of the plasma treated PTFE and FEP also increased. From the results of ESCA analysis, it was found that a significant amount of oxygen was introduced to the polymer surface by the plasma treatment. Peel strengths of a pressure sensitive adhesive bonded to PTFE and FEP increased approximately two-to threefold if the plasma treatment was used prior to bonding.     

Optomechanical variations in cold‐drawn thermally treated polypropylene fibers

A two‐beam polarizing interference microscope with a microstrain device was used for measuring some optical and mechanical parameters for polypropylene (PP) fibers at room temperature (28 ± 1°C). The changes in the molecular orientation were evaluated to obtain orientation factors f₂(θ), f₄(θ), f₆(θ), 〈P₂(cos θ)〉, 〈P₄(cos θ)〉, and crystalline and amorphous orientation functions F_c and F_a, respectively. The shrinkage factor, uniaxial tension, true stress, molar refractivity R, surface reflectivity R′, the crosslink density N_s, the chain entanglement density N_c, the segment anisotropy γ_s, and the number of chains N′ were calculated. In addition, the shrinkage stress was found to increase with the increase of draw ratio. The dielectric constant ε, the dielectric susceptibility η, the average work per chain w′, and the constants of the stress–birefringence equation were obtained. Comparison between Hermans's optical orientation functions and the corrected formulas by de Vries are given. The values of fully oriented refractive indices n₁ and n₂ were found. The generalized Lorentz–Lorenz equation given by de Vries was used to determine the structural parameters of PP fibers. An empirical formula was suggested to correlate the changes in the evaluated parameters with different draw ratios, and its constants were determined. The study demonstrated changes on the molecular orientation factors and evaluated microstructural parameters as a result of an applied cold‐drawing process. Relationships between the calculated parameters and the draw ratios, together with microinterferograms were presented for illustration. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 729–738, 2003     

The influence of processing variables on the wetting properties of a hydrophobic powder

The aqueous wetting properties of samples of a hydrophobic powder (griseofulvin) prepared by crystallisation, controlled precipitation, dry grinding and wet grinding have been assessed by two methods in terms of a contact angle, θ. The first employs drop formation on the surface of compacted powder, previously saturated with solution, while the second employs extrapolation of the quantity, cos θ, obtained for penetration of ethanol—water mixtures into powder beds, to zero mole fraction of ethanol concentration. Both methods establish that a difference exists in the surface properties of the different samples of powder and this appears to be a function of the process rather than the batch of powder. The two methods give significantly different values for the aqueous contact angle, which appears to be related to the actual nature of angle measured. The value derived from liquid penetration appears to provide a better reflection of the properties of the powder samples.     

The CMAS corrosion behavior of high-entropy (Y0.2Dy0.2Er0.2Tm0.2Yb0.2)4Hf3O12 hafnate material prepared by ultrafast high-temperature sintering (UHS)

High-temperature molten calcium-magnesium-alumina-silicate (CMAS) corrosion has become a fatal factor for the failure of aero-engine thermal barrier coatings. In this study, a promising entropy-stabilized (Y_0.2Dy_0.2Er_0.2Tm_0.2Yb_0.2)₄Hf₃O₁₂ (5YH) hafnate was prepared by the emerging ultrafast high-temperature sintering (UHS), and its corrosion and wetting behavior of molten CMAS were investigated. For the corrosion mechanism, the precipitation of the high-entropy apatite phase promotes the formation of the HfO₂ phase, and it can improve the density and stability of the slow-growing reaction layer, hindering the further penetration of molten CMAS. At 1300 ℃, a reaction layer with a three-layered morphology is generated, resulting from the decreased viscosity of the molten CMAS. Moreover, computational analysis shows that molten CMAS on the 5YH surface has a larger contact angle (17°) than traditional YSZ (13°), and the spreading area is about 90 % of traditional YSZ, which benefits for its good CMAS corrosion resistance.     

Practical evaluation of the [η]–M relationship

The Mark-Houwink equation for the relationship between the intrinsic viscosity of a polymer Solution and the molecular weight can be expressed in the more general form: [η] = 32K_θ(M/1000)^a, where the constant K_θ has a theoretical meaning and the constant a is approximately equal to 0.7.