Force-length relation for a short freely jointed chain: mass and volume dependence

We evaluate the force-length relation for short model chains. It is shown that this relation is markedly different when evaluated for static and dynamic model chains with rigid segments. The relation also differs for chains with rigid segments when they are isolated and coupled to a canonical heatbath, respectively. Furthermore, it is derived that the variation of the masses along the chain only has a small influence on the force-length relation. On the other hand, restricting the motion of the chain by walls perpendicular to the chain extension has a pronounced effect. We especially find that in this situation the chain has a finite equilibrium length.Dedicated to Professor W. Pechhold on the occasion of his 60th birthday     

Effect of pH on colloidal properties of native ovalbumin aqueous systems

The effect of pH on the molecular shape and dispersed state of native ovalbumin molecules in 20 mM phosphate and acetic acid buffer solutions has been studied using small-angle x-ray scattering (SAXS) and a rheological method The degree of association of the OA molecule at the 0.5% colloid system increases slightly with decreasing pH, i.e., 2.10 at pH 7.0, and 2.88 at pH 4.0, and the radius of the OA molecule decreases slightly with decreasing pH, i.e., 24.5 Å at pH 7.0, and 22.0 Å at pH 4.0.The OA colloid shows apparent yield stress and rigidity which are due to a certain ordered arrangement of the molecules. The yield stress and the rigidity increase abruptly at a pH value near to an isoelectric point (ca. pH 4.4). In the dilute system this increment is attributed to the change in the ordered arrangement or in the interparticle interaction, and not to the change in the association state of the OA molecules. The values of the yield stress and the rigidity remain almost constant over a wide concentration range and this feature (an auto-controlled mechanism) is kept over a certain range of pH.     

Theoretical investigation of the segment-segment correlation in topological constrained networks

We study the influence of harmonic-like configurational constraints on the segment orientation correlation in polymer networks. The investigation uses the continuous Edwards-chain model. We show that all effects of the special chain model (as well as the constraints) are reflected by an intensive parameter in the distribution function of cos, where is the angle between a segment orientation and the fixed end-to-end distance vector of a network chain. In the case of vanishing constraints the second momentM ₂ yields the classical Kuhn-Gruen-result of the freely rotating chain. Starting with the phantom limit, the functionM ₂ first decreases with increasing constraints and increases by approaching the reference result in the case of strong constraints. Our results are compared with some experimental (²H NMR) findings.     

Thermomechanical degradation of macromolecules

Extensional flow techniques are used to investigate thermomechanical scission of polymer solutions from ambient temperatures up to 150°C. We report precise central scission of chains beyond a critical fracture strain-rate. These results can be well accounted for by a Thermally Activated Barrier to Scission (TABS) model. We speculate upon the origin of degradation in simple shear flows and report novel results on degradation in porous media and ultrasonic sound fields, which contain dominant extensional components. Finally, we show how the nature and degree of degradation is affected by concentration and polydispersity. In semi-dilute entangled solutions, the degradation rates increase, are much higher for polydisperse solutions and the scission becomes progressively more random along the chain.Dedicated to Professor H. H. Kausch on the occasion of his 60th birthday     

Solubilization properties of aqueous solutions of alkyltrimethylammonium halides toward a water-insoluble dye

The solubility of a water-insoluble dye, Sudan Red B, in aqueous sodium halide solutions of tetradecyl-, cetyl-, and stearyltrimethylammonium halides has been measured at different surfactant and salt concentrations, and the dependence of solubilization properties on alkyl chain length has been discussed with reference to the micelle size and shape. At low ionic strengths where only spherical micelles exist, the solubilization power of micellar surfactant slightly increases with increasing the ionic strength, but it sharply increases at high ionic strengths above the threshold value of sphere-rod transition. However, the solubilization power becomes independent of the ionic strength, if their rodlike micelles are sufficiently long. The solubilization capacity increases linearly with increasing the molecular weight, almost independent of counterion species, but the rod-like micelle has a higher solubilization capacity than the spherical micelle. The solubilization capacity is larger for a surfactant with longer alkyl chain, indicating that the dye is solubilized more readily in a larger hydrophobic core. The solubilized dye is situated in a rodlike micelle of alkyltrimethylammonium halides, on average, 4.5–7.5 nm apart from each other.     

Stability of spherical and rod-like micelles of ionic surfactants,in relation to their counterion binding and modes of hydration

Aqueous salt solutions of ionic surfactants in both spherical and rod-like micelles have been treated on the basis of a statistical thermodynamic theory, and the double logarithmic relationship between micelle molecular weight and ionic strength is derived for each micelle. Counterion binding on both micelles are assumed to occur specifically, and their degrees of dissociation are related to the slopes of the linear double logarithmic relations. It is found from the relationship observed for typical surfactants that the effective charge of spherical micelles is 29±4. The degree of dissociation of rod-like micelles of these surfactants is primarily determined by the counterion species, yielding values 0.8 for Na⁺, 0.4–0.6 for Cl^– and 0.2–0.3 for Br^–. Hydrophilic hydration of both micelles can be evaluated from the intercepts of the linear relations. Hydrophilic hydration acts repulsively in spherical micelles, while it is attractive or much less repulsive in rod-like micelles.     

Fluorescence and viscometry study of complexation of poly(acrylic acid) with poly(acrylamide) and hydrolysed poly(acrylamide)

Interpolymer complexation of poly(acrylic acid) with poly(acrylamide) and hydrolysed poly(acrylamide) was studied by fluorescence spectroscopy and viscometry in dilute aqueous solutions. Changes in chain conformation and flexibility due to the interpolymer association are reflected in the intramolecular excimer fluorescence of pyrene groups covalently attached to the polymer chain. Both poly(acrylamide) and hydrolysed poly(acrylamide) form stable complexes with poly(acrylic acid) at low pH. The molecular weight of poly(acrylic acid) and solution properties such as pH and ionic strength were found to influence the stability and the structure of the complexes. In addition, the polymer solutions mixing time showed an effect on the mean stoichiometry of the complex. The intrinsic viscosity of the solutions of mixed polymers at low pH suggested a compact polymer structure for the complex.     

FTIR spectroscopic and NMR studies of hard elastic polypropylene

The variation of amorphous orientation and crystalline regularity of hard elastic polypropylene (HEPP) films during cyclic deformation and stress relaxation processes were studied using a FTIR spectrometer. The result proves entropic elasticity and shows the orientational hysteresis in the amorphous region or within the microfibrils, and also shows that the amorphous orientation increases, but that the crystalline regularity decreases with the increase of extension rate.Three spin-spin relaxation timesT _2f,T _2m, andT _2s and associated mass fractionsF _f,F _m, andF _s of HEPP fibers were measured with a solid echo of NMR method at different elongations and after relaxation or recovery for a long time A new possible interpretation was proposed that, while the microfibrils are formed in HEPP, the medium decay component should be ascribed to inner molecules of the microfibrils, and the slow decay component to the surface molecules of the microfibrils. According to this interpretation, the results implied that subfibrillation is the main process when HEPP is stretched up to 15% strain, and that at above 15% strain thinning and lengthening of the microfibrils become the main process. Thickening of the microfibrils was found in the recovery and relaxation processes.     

Dielectric relaxation in polymeric solids Part 1. A new model for the interpretation of the shape of the dielectric relaxation function

A model is proposed which explains the shape of the dielectric relaxation function at the glass transition of polymers. The model is based on the idea that the molecular mobility at the glass transition is controlled by intra- and intermolecular interaction. In addition, a specific model for the local chain dynamics in amorphous polymer systems is used. According to the scaling hypothesis of molecular dynamics the model relates the high frequency dependence of the dielectric loss curve to the local chain dynamics and the low frequency dependence to the intermolecular correlation.     

The effect of coating on the stiffness and toughness of encapsulated fiber composites

The effect of the coating of the fiber on the stiffness and toughness of composite materials is presented in this paper. The type of composite material considered is of a macroscopically isotropic composite medium containing coated fibers. The models used to simulate such materials consists of: the cylindrical fiber, a cylindrical annulus of the coating, an annulus of the matrix enveloped by an infinite region of an equivalent composite consisting of a transversely isotropic material and representing the real composite with dispersed coated fibers. Solutions for the longitudinal, transverse and shear elastic moduli in the four-phase model were established assuming linear elastic conditions. The results were found to depend on the extent and the mechanical properties of the coating. The stiffness and toughness of the composite were evaluated in models representing plane-stress equatorial sections of the representative volume element of the real material according to the Hashin-Rosen model. The stiffness of the fiber composites was studied by varying the rigidity and the extent of the fiber-coating in the model and evaluating its influence on the overall mechanical behavior of the model. On the other hand, the toughness of the composite was evaluated by the method of caustics in models made of composite PMMA plates with PMMA inclusions coated with a ductile annulus. Interesting results were derived concerning the influence of the soft annulus on the mechanical behavior of the composite.     

Thermodynamics of surfactant-dye complex formation in aqueous solutions. Sodium alkyl sulfates and azo oil dye systems

Thermodynamics of surfactant-dye complex formation have been studied, in terms of equilibrium coefficient, using a spectrophotometer. The systems are 6 sodium alkyl sulfates, which have different alkyl chain lengths, and 4-phenylazo-1-naphthylamine. A pronounced spectral change in the dye solution occurs on addition of the surfactant; the change has a definite isosbestic point and a new absorption band at 535 nm because of surfactant-dye complex formation, which is caused by hydrophilic-hydrophilic interaction. As the alkyl chain length in the surfactant increases, the values of free energy change (negative) increase, while the value of enthalpy change (negative) increases and the value of entropy change (positive) decreases. The longer the alkyl chain length in surfactant increase, the more stable the surfactant-dye complex becomes.Surfactant-dye complex will form due to hydrophilic-hydrophilic interaction and will become more stable due to hydrophobic-hydrophobic interaction.     

Effect of pH on the binding of alkyl sulfates to gelatin

A surfactant-selective eletrode in which the membrane is an o-nitrotoluene phase containing a dissolved complex of cetyltrimethylammonium-dodecyl sulfate has been applied to investigations of the interaction between gelatin and alkyl sulfates as well as gelatin and alkyltrimethylammoniumions in dilute aqueous solutions.The binding isotherms were obtained by comparing emf-values obtained for surfactant in water to the electrode potentials in gelatin solutions plotted in terms of surfactant concentration.The binding of alkyl sulfates was measured as a function of pH at constant free surfactant concentration. At pH values 7 the degree of binding is indpendent of the pH of the solution. The level of binding of alkyl sulfates to gelatin increases strongly with increasing chain length of the alkyl sulfate. At pH values 6 the extent of binding increases steeply with decreasing pH. Octyl sulfate shows a very low level of binding even at low pH. Cationics show much weaker interactions with gelatin than anionic surfactants of comparable alkyl chain length.     

Microhardness and surface free energy in linear polyethylene: The role of entanglements

The microhardness of a series of melt crystallized samples of linear polyehtylene was investigated in a wide range of molecular weights. The x-ray long period was analyzed to study the variation of the hardness-derived constantb as a function of molecular weight (M ). It is pointed out thatb offers a measure of the hardness depression due to the finite thickness of the lamellar crystals. The data obtained show that the increase and final leveling-off (forM 200 000) ofb withM parallels the concurrent increase of the surface free energy, as derived from DSC experiments. Results are discussed using the concept og chain folded lamellae as thermodynamically stable non-homogeneous microphases. Comparison of experimental and calculated data supports the view that the number of molecular entanglements, segregated onto the defective surface boundary of the heterogeneous crystals influence the shearing mechanism within the mesocrystals and thereby control the yield behavior of the material.     

Strength of fibers from wholly aromatic polyesters

A theory of the strength (or the tenacity) of highly oriented Liquid Crystal Polymer (LCP) fibers was developed, and its results were compared with existing tensile strength data of fibers of a copolymer of 1,4-oxybenzoate and 6,2-oxynaphthoate. A basic premise of the theory is that the mechanical load transfer between polymer chains is through intermolecular interaction which acts in a manner similar to that of shear stress, and that the fiber strength is primarily governed by the intermolecular adhesion strength. The theory also incorporates the effects of MW, MW distribution, and the chain orientation distribution. Analysis of the experimental tenacity data demonstrates that the present theory can quantitatively describe the variation of the tenacity of LCP fibers with MW both in the as-spun and in the heat-treated states. The theory further predicts that the predominant factor governing the tenacity of LCP fibers is primarily due to MW increase due to solid-state polymerization. It is also demonstrated that the intermolecular adhesion between LCP chains is relatively weak and does not improve with heat treatment. The absence of factors that limit the MW increase (i.e, imbalanced end-groups and side reactions of end groups) is a prerequisite for fast heat treatment of a LCP fiber to a high tenacity.Symbols A _f the cross-sectional area of a single polymer chain - E _f the theoretical modulus of a polymer chain - G _m the shear modulus of fiber - h(l) the chain length distribution function - l the chain length - l the number average chain length - l _c the length of chain units that are bonded to adjacent polymer chains - n ² 4G _m/CE_f - N _c the number of polymer chains per unit area perpendicular to the fiber axis - P _b the probability that a chain does not have a chain end in the fracture zone - P _e the probability that a chain has, at least, a chain end in the fracture zone - q _e,q _b the probability of finding an ending and a bridging polymer chain, respectively, in the fracture zone - l the length of fracture zone - the elongation of a polymer chain - the chain orientation angle - _f the normal stress that acts on a polymer chain - _fu the fiber tenacity - _e the shear stress that acts on a polymer chain surface Dedicated to Prof. Dr. rer. nat. Wolfgang Hilger, Chairman of Hoechst A.G. in honor of his 60th birthday     

Neutron scattering from a deformed “vander Waals chain”-quasi Gaussian approximation

We calculate the neutron scattering form of an affinely deformed van der Waals chain, i.e., a labeled chain embedded in a network, whose deformation behavior can be described by an effective van der Waals equation in an effective Gaussian approximation. This provides microscopic information about the deformation behavior of van der Waals networks and complements the macroscopic information given by stress-strain relations.dedicated to Prof H.-G. Kilian on occasion of his 66th birthday     

Morphology-shrinkage relationships in semi-crystalline polymers. Epitaxy,a way of eliminating amorphous contribution

A new approach for achieving a highly dimensionally stable film of semi-crystalline polymers via blending is demonstrated. To illustrate this approach, a model system, polyethylene-polypropylene is investigated using TEM, TMA, DSC, and DMA. It is shown that epitaxial growth in polymer blends and laminates can induce a cross-hatch morphology which eliminates or reduces the contribution of an oriented amorphous phase. This ultimately leads to greater dimensional stability and synergism in mechanical properties as well. The presence of an appropriate low-melting component can also be used to reduce shrinkage.     

Dynamics of hydrogen bond complexes in polymer melts

The dynamics of hydrogen bond complex formation between functional groups which are attached to a polymer chain, is studied in the molten state. The concentration of complexes in the thermodynamic equilibrium is distorted by the application of a large oscillatory strain in the nonlinear viscoelastic regime. The relaxation back to the thermodynamic equilibrium is studied as a function of the temperature in the linear viscoelastic regime. From the mechanical response the kinetic analysis can be performed using a modified Doi-Edwards theory. Using the equilibrium constants obtained from IR-spectroscopy, the rate constants for complex formation and decomplexation are obtained. The temperature dependence is equivalent to the temperature dependence of the zero shear viscosity which implies that complex formation is a diffusion-controlled process.     

Small-angle x-ray scattering by crystalline polymer fibers 2. Investigation of the linear paracrystalline model using various materials

The linear position-sensitive detector is well-suited to measure quantitatively the distribution parallel to the fibre axis of the intensity of small-angle x-ray scattering (SAXS) by polymer fibres, except that in the case of four-point patterns their width is greater than that of the detector window. A method is described which overcomes this problem, and which has high angular resolution. Using this method, the variation of scattered intensity with angles from 0.3° to 2.5° has been measured for fibres of poly(ethylene terephthalate), nylon, and low density poly(ethylene) (LDPE), and compared with that predicted by the linear paracrystalline model. In all cases except LDPE, when the distribution of phase lengths was given by the Reinhold function, there was no significant disagreement between the measured and predicted scattering except for a very small range of angles on the low angle side of the peak intensity. With LDPE small but significant discrepancies were found at other angles as well, and these were worse if the symmetrical Gaussian distribution function was used. The method enabled quantitative parameters describing the morphology to be obtained. It is concluded that the morphology of the linear paracrystalline stack is consistent with the SAXS intensity distribution, and that the Reinhold function is a reasonable approximation to the distribution of phase lengths. A small modification so that this decays more rapidly at long lengths might be necessary to explain the scattering for all materials over the entire angular range and other small changes might be needed with LDPE, although the asymmetrical nature of the distribution must be retained.On leave from Department of Physics, University of Technology Malaysia, 81300 Sekudai, Malaysia.