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     

Micelle structure in isotropic aqueous colloids of a poly(oxyethylene) amphiphile C12E8

Micelle structure in aqueous colloids in the isotropic liquid phase (L₁) of a nonionic amphipile (n-dodecyl octa(oxyethylene glycol) monoether (C₁₂E₈) has been investigated as a function of concentration and temperature using light scattering (LS), viscometry, NMR, and small-angle X-ray scattering (SAXS).The spherical micelles, having a radius of 28–31 Å, remain in a wide concentration range from very dilute to ca. 42 wt %. The micelle size increases sligthly with increasing temperature in the range of 25–60 °C. In the concentrated colloids, the spherical micelles are likely to be arranged in a certain ordered structure. Even at such a high concentration as 30 wt %, the isotropic colloid shows Newtonian flow. This suggests that interaction between micelles in the ordered structure is very weak and the structure is very fragile. Moreover, coexistence of the isotropic phase and the ordered structure in L₁ phase is discussed.     

The flexibility of rodlike micelles in aqueous solutions and the crossover concentrations among dilute,semidilute, and concentrated regimes

A flexibility parameter, the persistence length, has been evaluated from the radii of gyration and the contour lengths for rodlike micelles of heptaoxyethylene alkyl ethers (C _n E₇,n=12, 14, 16) and tetradecyldimethylammonium chloride (C₁₄DAC) and bromide (C₁₄DAB) at the observed crossover concentrations between dilute and semidilute regimes. The persistence length range is 43–73 nm, except for C₁₂E₇, for which it is 32 nm. The crossover concentrations between dilute and semidilute regimes for the semiflexible rodlike micelles calculated according to Ying and Chu as a function of the molecular weight, the contour length, and the persistence length are consistent with the observed values. The crossover concentration between semidilute and concentrated regimes was, on the other hand, calculated by using the same micelle parameters, including the value of thickness of cross-section of the rodlike micelles. The obtained values are at variance with the observed values. This means that rodlike micelles in semidilute and concentrated solutions might differ in size and/or flexibility from those in dilute solution.     

The viscoelasticity of spinnable solutions of alkyltrimethylammonium salicylates

The viscoelasticity has been measured for aqueous solutions of tetradecyl-and hexadecyltrimethylammonium salicylates (C₁₄TASal, C₁₆TASal). The aqueous solutions of C₁₄TASal without salt displayed the gel-like behavior at 10.0×10^–2 g cm^–3, but those more dilute than 3.2×10^–2 g cm^–3 presented the viscoelasticity similar to that of a Maxwell liquid. The Maxwell-like behavior was converted to the polymer-like one on the addition of (0.1–0.2) M NaBr or (0.02–0.2) M NaSal. The gel-like viscoelasticity can be connected with the spinnability of cohesive fracture failure, and the Maxwell-like and polymer-like viscoelasticities are concerned with the spinnability of ductile failure. The gel-like and Maxwell-like viscoelasticities originate in the pseudo-network formed by the pseudo-linkages between rodlike micelles, while the polymer-like viscoelasticity is caused by the entanglement of long rodlike micelles in semidilute and concentrated solutions. The aqueous solutions of C₁₆TASal behaved very similar to those of C₁₄TASal.     

Steric repulsion of polyoxyethylene groups for emulsion stability

Rapid coalescence was studied on liquid paraffin emulsion stabilized with a series of poly(oxyethylene) dodecyl ethers [C₁₂H₂₅ (EO),n=1, 2, 3, 4, 5, 6, 7, 8] and of poly(oxyethylene) nonylphenyl ethers [C₉H₁₉(EO) _n ,n=2, 4, 5, 6, 12]. The turbidity of emulsion was measured as a function of the solution pHs at constant ionic strength of 0.1 mol dm^–3.As a result, it was found that the emulsions (which were formed with C₁₂H₂₅(EO) _n surfactants having less than four oxyethylene groups, or with C₉H₁₉ (EO) _n surfactants having less than six oxyethylene groups) brought about rapid coalescence in the bulk pH between 2.03.5, which corresponded to the zero point of charges for the emulsions of the present systems. According to the Tadros treatment for emulsion flocculation, the total flocculation potennual was estimated as a function of the distance relative to the number of oxyethelene groups in the surfactants. The critical coalescence energy was obtained as –343 ×10^–19 J for the C₁₂H₂₅(EO) _n surfactants and –2.14×10^–19) J for the C₉H₁₉ (EO) _n surfactants. Furthermore, the formation of a hole for coalescence was estimated under the simple assumption that the coalescence was caused only by the energy dissipation.     

X-ray diffraction studies on homologous thallium soaps below the temperature range of the neat phase 1. Calculation and comparison of the structure parameters of unit cells

The results of X-ray diffraction patterns of homologous thallium soaps TlC _n (n-8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20 and 22) in dependence on the temperature showed that the structures of the phases below the temperature range of the liquid-crystalline neat phase (so called phase C₁, phase C₂, phase I, phase II) are crystalline-like, not liquid-crystalline.As function of the chain length of the fatty acid group, we found the following phase sequences to be a function of temperature: TlC₈: phase Ineat phase: TlC₉–Tl₁₄: phase C₂phase IIphase Ineat phase; TlC₁₅, TlC₁₆: phase C₁phase IIphase Ineat phase; TlC₁₇–TlC₂₂: phase C₁phase IIneat phase.From the X-ray patterns of the thallium soaps were calculated the lattice parameters and the unit cells of these homologues at various temperatures. The comparison between the lattice parameters of the homologues showed, surprisingly, that these parameters were independent of chain length and temperature. This X-ray data are the basis for the following development of structure models of the phase C₁, phase C₂, phase I, and phase II, including the neat phase (see Part 2).     

Mass,size and shape of micelles formed in aqueous solutions of ethoxylated nonyl-phenols

The study was extended to analysis of mass, size and conformation of micelles formed in aqueous solutions of ethoxylated nonyl phenols. The results obtained by ultracentrifugal technique between 293 and 323 K have proved that the slightly ethoxylated nonyl phenols form micelles with high molecular mass and larger size at constant temperature, while the increasing length of the ethylene oxide chain favours formation of micelles of smaller molecular mass and size. The transformation of conformation from oblate to spherical shapes ensues with increasing temperature at constant ethoxy number or with ethoxylation at constant temperature. The second virial coefficient decreases with increasing temperature and decreasing ethoxy number. In accordance with the earlier conclucions, the change of the second virial coefficient relates to enhanced variation of monomer solubility, stabilization of micelle structure and increased deviation from ideal behaviour of a given micellar system.Symbols a major axis of micelle, Å - a _m attractivity factor, cm³ erg molecule² - b minor axis of micelle, Å - c concentration, g dm^–3 - c _b equilibrium concentration at the bottom of the cell, g dm^–3 - c _m equilibrium concentration at the meniscus of the cell, g dm^–3 - c _o initial concentration in the cell, g dm^–3 - c _M critical micellization concentration, mol dm^–3 - e eccentricity - f _IS Isihara-constant - f/f _o frictional ratio of micelle - amount of water in micelle per ethoxy group, mol H₂O/mol EO - n aggregation number, monomer micelle^–1 - n _EO number of ethoxy groups - r distance of Schlieren peak from the axis, cm - r _b distance of cell bottom from the axis, cm - r _m distance of cell meniscus from the axis, cm - R _h equivalent hydrodynamic radius of micelle, Å - s _t sedimentation coefficient, s - reduced sedimentation coefficient, s - reduced limiting sedimentation coefficient, s - ¯v _t volume of micelle, cm³ micelle^–1 - partial specific volume of solute, cm³g^–1 - partial specific volume of solute reduced to 293 K, cm³ g^–1 - B _a, B_e constants, cm³ mol g^–2 - B ₂ second virial coefficient, cm³ mol g^–2 - M _m ^a mass average apparent molecular mass of micelle, g mol^–1 - M _m mass average molecular mass of micelle corrected withB ₂, g mol^–1 - M _m ^cM mass average molecular mass of micelle belonging toc _M, g mol^–1 - M ¹ mass average molecular mass of monomer, gmol^–1 - N _A the Avogadro's number, molecule mol^–1 - R universal gas constant, erg mol^–1 K^–1 - T temperature, K - _t ^o dynamic viscosity of solvent atT temperature, g cm^–1 s^–1 - dynamic viscosity of solvent at 293 K, g cm^–1 s^–1 - _t density of solution atT temperature, g cm^–3 - _t ^o density of solvent atT temperature, g cm^–3 - density of solvent at 293 K, g cm^–3 - angular velocity, rad s^–1 - time, s     

Changes of mesophase structure of BRIJ 96/water mixtures on addition of liquid paraffin

The influence of the addition of liquid paraffin (LP) on the structure of the lamellar (L ) and hexagonal (H₁) mesophases formed in mixtures of water (W) and BRIJ 96 (B) was studied. Mesophases were identified using polarization microscopy and small angle x-ray diffraction (SAXD). Repeat spacings were also determined with SAXD. Depending on theW/B ratio, addtion ofLP toL gives a large, almost linear one-dimensional swelling or an initial swelling followed by a gradual transition to H₁.L with a highLP-content gives a diffraction pattern showing only the first order diffraction maximum, possibly a result of undulations of the layers. The lamellar structure, however, was confirmed using freeze fracture electron microscopy (FFEM). Addition ofLP to H₁ gives an initial swelling followed by a transition to a transparent, highly viscous, isotropic phase, called the gel-phase (G). The diffraction pattern obtained fromG yields little information on its structure. A large swelling ofG withLP was observed. From the degree of swelling as a function of hydrocarbon content it was inferred that this phase consists of spherical aggregates forming a close-packed structure. Using FFEM, textures were visualized resembling those obtained from the isotropic mesophase (I₁) in water-surfactant mixtures. Finally, geometrical factors are discussed that may play a role in the formation of the gel-phase.     

Structure of casein micelles I. Small angle neutron scattering and light scattering fromβ- andχ-casein

Casein is the main protein component of milk and is of remarkable colloidal stability. Under the influence of milk clotting enzymes casein shows the striking behaviour of coagulation. This clotting process has already been studied by other groups, neglecting the fact that casein is not a homogeneous protein. The purpose of the present study is focused, in this first stage, on the determination of the structure of the various casein components. In cooperation with other laboratories we have been able to obtain the well separated individual proteins. Studies have been performed so far with- and-casein. For detailed structural information we carried out small angle neutron scattering and combined static and dynamic light scattering measurements and determined the molecular weight,M _w, the radius of gyration, S ² the hydrodynamic radius,R _H, the-value and the particle scattering factor, P_z(q). The two caseins show a strikingly different behaviour. For the-casein we found a star-like structure, i. e. an aggregation pattern that is expected for a common micelle. The micelle consists of about 38 monomer chains. The aggregates of-casein appear to be composed of star-like submicelles, where each submicelle contains nine-casein chains and the total degree of aggregation is about 140.     

Interaction of adenosine with alkyltrimethylammonium bromides

The interaction of adenosine with alkyltrimethylammonium bromides, C_mH_2m+1N(CH₃)₃Br(m=16, 14, 12, 10, 8, and 6), has been studied by 1 H NMR spectroscopy. When surfactants exist as monomer units, the adenine ring of adenosine preferentially associates with the middle portion of the alkyl chain of the surfactants. The interaction is less specific with surfactants of shorter alkyl chains. When surfactants form micelles, no specific interaction between the adenine ring and the alkyl chain of the surfactant can be detected. A coordination of the cationic part of the surfactants with the adenine ring is suggested. The degree of association was evaluated from association constants. Similar results were obtained for purine and alkyltrimethylammonium bromide.     

A structural study of the mesophases of two oxyethylene alkyl ether-decane-water systems,a comparison between technical grade C12EO〈7〉 and pure C12EO6

As part of a study polyoxyethylene alkyl ethers (C _m EO _n ), water and decane, the phase diagram and the structures of the mesophases of pure C₁₂EO₆ and technical grade C₁₂EO₇ were compared. The constructed phase diagrams of the two systems show a great resemblance except for one difference: the viscous isotropic phase is only present in the C₁₂EO₆ phase diagram.The swelling behavior of the lamellar and hexagonal phases was studied with smallangle x-ray scattering. Both the lamellar and hexagonal phases showed an ideal swelling behavior and no differences between the lamellar and hexagonal phases of the two systems were detected.With freeze-fracture electron microscopy the hexagonal and lamellar phases were visualized. No differences in the textures of the lamellar phases were found, however, the micrographs of the hexagonal phases of the two systems clearly showed different textures. While in the hexagonal phase of the C₁₂EO₆ system only infinite long rods were visualized, short interrupted rods were found in the hexagonal phase of the C₁₂EO₇ system.     

Thermotropic gelation of ovalbumin 1. Viscoelastic properties of gels as a function of heating conditions and protein concentration at various pH values

A study has been undertaken of stress relaxation in ovalbumin thermotropic gels with a concentration of 8–20%, depending on time and temperature of heating (respectively, 20–60 min, 70°–110°C), at pH 2.5–10.0. In all instances, the dependence of the initial gel elasticity modulus on heating has a single maximum. Gelation conditions corresponding to this maximum are considered optimal. Optimal gelation time is 30 min, regardless of pH. On the other hand, the optimal heating temperature depends on pH. To the right and left of the isoelectric point of protein (2.5pH<4.0 and 5.5G) of gels on heating conditions, pH and protein concentration (X ₁,X ₂,X ₃,X ₄), as well as on time of relaxation (t) may be generally described asG(X ₁,X ₁,X ₁,X ₁,t)=G _e(X ₁,X ₂,X ₃,X ₄)f(t), whereG _e is the equilibrium value of the elasticity modulus, and f(t) the relaxation function. Thus, a change in the parameters only affects the value of the equilibrium elasticity modulus, and exerts no effect on the relaxation time spectrum. For this reason, all the relaxation curves obtained may be transformed into two normalized relaxation functions:f(t)=f(t)/f(1)=G(X ₁,X ₂,X ₃,X ₄,t)/G(X ₁,X ₂,X ₃,X ₄, 1)Each of these normalized functions corresponds to one of the homologous groups. Rheological similarity of gels in each homologous group evidently points to their structural similarity. Invariance of the gel relaxationproperties with regard to protein concentration, leads to a concentration dependence of the equilibrium modulus at various pH values. These dependences are curvilinear on a double logarithmic scale. The slope of the curve exceeds 2 in the entire concentration interval studied. In other words, the dependences obtained cannot be described by the usual law of squares. On the other hand, they adequately match Hermans theoretical relation for a network formed by random association of identical polyfunctional particles without cyclization. This simple model evidently gives a true picture of the major regularities of thermotropic gelation for ovalbumin. An agreement between this theory and experiment was achieved for a protein concentration ofC ^*=6.0±1.0% at the gel point regardless of pH. Invariance of gelpoint position with regards to pH demands further confirmation.List of symbols T _h,t _h heating temperature and time - T _h ^* ,t _h ^* optimal heating temperature and time - C protein concentration - C ^* protein concentration in gel-point - G relaxation modulus - G _e equilibrium modulus - f(t) relaxation function - t time of relaxation - f(t) normalized relaxation function - fT _A (t), f _B (t) normalized relaxation functions of groups A and B - G ₁ T _h,t _h-reduced modulus - G ₂ T _h,t _h, pH-reduced modulus - G ₃ C-reduced modulus - b ₁ T _h, t_h reduction parameter of modulus - b ₂ pH reduction parameter of modulus - b ₃ C reduction parameter of modulus - W_g gel-fraction     

Adsorption of quaternary ammonium chlorides with various hydrocarbon chain lengths to glass

Contact angles, measured with various liquids, have been employed to calculate the surface free energies of glass after adsorption of quaternary ammonium chlorides with a variable hydrocarbon chain length 8n16. The thickness of the adsorbed layers has been determined ellipsometrically. A clear relation is observed between the measured parameters and the hydrocarbon chain lengthn, if only the extremesn=8 andn=16 are considered. Surface free energies decrease from 138 erg.cm^–2 for clean glass to 101 and 64 erg.cm^–2 forn=8 andn=16, respectively, at the highest concentration tested (7.5 mM). The adsorbed layer thickness of C₈ amounts to approximately 50 % of the thickness observed for C₁₆. No clear relation between the measured parameters is observed for the intermediate hydrocarbon chain lengths, which presumably reflects the many configurations possible in these adsorbed layers. It is envisaged that adsorption of C₈ as well as C₁₆ is restricted to a monolayer, which is completed at approximately 2 mM. In the case of C₈ electrostatic repulsion between the polar headgroups will inhibit further adsorption, whereas in the case of C₁₆ the van der Waals attraction from the adsorbed layer and the glass will probably not be sufficient to stimulate further adsorption.     

Scattering from concentration fluctuations in polymer blends: A monte carlo investigation

The collective scattering function S_coll( ), which describes light (neutron-, x-ray) scattering under wavevector , is obtained from Monte Carlo simulations for a symmetrical polymer mixture. The polymers are modelled by self-avoiding walks ofN _A=N_B=N steps on a simple cubic lattice, where a fraction _V of sites is left vacant, and an attractive energy occurs if two neighboring sites are taken by the same kind of monomer. Spinodal curves are estimated from linear extrapolation of S _coll ^–1 (0) vs./k _B T, whereT is the temperature. Also the single chain structure factor is obtained and the de Gennes random phase approximation (RPA) can thus be tested. Unexpectedly, strong deviations are found if one species is very dilute. The estimation of an effective Flory-Huggins-parameter from scattering data is also discussed.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Hamburg, March 14–16, 1987.     

The molecular weight dependence of intrinsic viscosity of rod-like micelles of dodecyldimethylammonium chloride

It is shown that the non-linear logarithmic dependence of the intrinsic viscosity on the molecular weight for rod-like micelles of dodecyldimethylammonium chloride (as reported by Ozeki and Ikeda [1]) can be interpreted in terms of the Yamakawa-Fujii theory of worm-like chains. Characteristic parameters of the micelles are estimated: persistence length (a=14 nm), linear mass density (M _L=4800 nm^–1), diameter (d=3 nm), molecular pitch (b=0.052), and the number of surfactant chains in a layer of rod-like micellen=12. The results are compared with those derived from light-scattering measurements.     

Hemolytic activity of polyoxyethylene cholesteryl ethers

Hemolytic activity of nonionic surfactants, polyoxyethylene cholesteryl ethers, C₂₇H₄₅O(CH₂CH₂O) _n H (Chol-E _n ,n=, 25, 30, 50) and polyoxyethylene dihydrocholeseryl ethers, C₂₇H₄₇O(CH₂CH₂O) _n H (DHChol-E _n ,n=15, 30 50) were measured, changing the concentration of surfactant and erythrocyte at 37 °C. Maximum hemolytic activity was observed in these cholesteryl derivatives with 25–30 oxyethylene units. The time course of hemolysis was also measured as a function of the concentrations of surfactant and erythrocyte. Hemolysis started after a certain induction period,, and then apparently proceeded as a first-order reaction with respect to the erythrocyte concentration. The surfactant inducing 50% hemolysis at low concentration had a small value and large rate constant. The maximum amount of adsorption without inducing hemolysis,a ₀, decreased with increasing polyoxyethylene chain length. Chol-E₂₅ has the maximum activity for the solubilization of egg yolk lecithin at 37 °C. Based on these results, the mechanism of hemolysis by these surfactants was quantitatively discussed.     

CPS GL 799

The effect of illumination on transport of sulfonated bisazo direct dyes, CI Direct Yellow 12, and CI Direct Yellow 4, into a cellulose membrane has been studied at various temperatures. Transport of CI Direct Yellow 12, which exhibits photoinduced reversible trans-cis isomerism in aqueous solution into a cellulose membrane, was influenced by illumination. It is likely that the transport was influenced by transisomerization of the photoisomeric dye and the diffusivity was controlled by surface diffusion rather than by pore diffusion under both light and dark conditions.Notations C Concentration of dye in the pores (mol/dm³) - C _E Concentration of electrolyte in the bulk solution (mol/dm³) - C _o Concentration of dye in the bulk solution (mol/dm³) - D _p Pore diffusivity (m²/s) - D _s Surface diffusivity (m²/s) - [M] Mean concentration of dye in membrane (mol/dm³) - [M] _L Local concentration of dye in membrane (=q+ _p C) (mol/dm³) - [M] Mean concentration of dye in membrane (mol/kg) - [M] _L Local concentration of dye in membrane (=q/V+ _p C) (mol/dm³) - F Fractional attainment of equilibrium - l Thickness of membrane (m) - q Concentration of dye adsorbed on pore wall (mol/dm³) - q _o Adsorbed concentration of dye in equilibrium withC _o (mol/dm³) - q Concentration of dye adsorbed on pore wall (mol/kg) - q _o Adsorbed concentration of dye in equilibrium withC _o (mol/kg) - t Time (s) - V Volume of membrane swollen with water per unit dry cellulose (dm³/kg) - x C/C _o - y q/q _o - z Distance that the dye diffused in the membrane (m) - q _o / _o C _o - D _s /D _p - Coefficient of the Freundlich isotherm - _p Pore void fraction - z/l - _p D _p t/l ² - _s D _s t/l ²     

Theory of ring formation in a reversible system: general solutions

The enumeration theory is extended in this work into a more general theory, taking back-reactions into consideration. The solutions may faithfully reproduce real processes from arbitrary starting points to a steady-state. Therefore, the presented theory includes the equilibrium theory by Jacobson-Stockmayer, the numerical solution by Gordon-Temple, and the irreversible theory by the present authors. The solutions are described first in general forms of transition probabilities {P}, and then explicitly with the aid of rate equations; simple proofs are given. The presented theory was applied to an experimental data: the distribution of cyclic species in poly(ethylene terephthalate). We shall show that agreement between theory and experiment is nearly perfect.AB model N ₀ Total number of units - V System volume - C ₀=N ₀/N _A ·V Initial concentration (N _A : Avogadro's number) - L _x AB type chain x-mer; (AB)_x - N _x Number of AB type x-mers - R _x Ring x-mer - N _Rx Number of ring x-mers - E Small molecule eliminated by bond-formation - N _E Number of small molecules eliminated by bond-formation - h _k Number of reacted functional units (f.u.) in statek - _k Number of reacted functional units (f.u.) in chains in statek - _k Total number of units in chains in statek - D=h _k /N ₀ Extent of reaction in statek - D ^*= _k / _k Extent of reaction in chains in statek - k _L Chain-propagation rate constant - k _Rx Cyclization rate constant of chain x-mers - k _B Bond breakage rate constant of chains - k _B,Rx Bond breakage rate constant of cyclic x-mers - <k _Rx > _k Mean cyclization rate constant in statek - g(x)=k _B,Rx /k _B Ring-opening factor of cyclic x-mers - P _Lx,k Probability that a chain x-mer will be formed in statek - {P} Set of transition probabilities per single jump in forward direction or reverse direction (see the text on individual transition probabilities) AB model M _A Total AA monomer unit number - M _B Total BB monomer unit number - M ₀=M _A +M _B Total particle number - _A,i =2M _A –h _i Unreacted A functional unit (f.u.) number in statei - _B,i =2M _B –h _i Unreacted B f.u. number in statei - _Ax Unreacted A f.u. number on x-mers - h _i Number of reacted A (or B) f.u. in statei - _i Number of reacted A (or B) f.u. in chains in statei - _A,i =2M _A –h _i + _i A f.u. number in chains in statei - _B,i =2M _B –h _i + _i B f.u. number in chains in statei - _i =2(M ₀–h _i + _i ) Total f.u. number in chains in statei - D=h _i /M ₀ Extent of reaction in statei - D _A ^* = _i / _A,i Extent of reaction of A f.u. in chains in statei - D _B ^* = _i / _B,i Extent of reaction of B f.u. in chains in statei - D ^*=2 _i / _i Extent of reaction in chains in statei - L _x (AA-BB)_x-1-AA type chain x-mer;x=1,2,3,... - L _x BB-(AA-BB)_x type chain x-mer;x=0,1,2,... - L _x (AA-BB)_x type chain x-mer;x=1,2,3,... - N _x Number of type x-mers - N _x Number of type x-mers - N _x Number of type x-mers     

Small-angle neutron scattering on shear-induced micellar structures

Small-angle neutron scattering (SANS) experiments on sheared aqueous surfactant solutions of tetradecyltrimethylammoniumsalicylate (TTMA-Sal) are reported. A5-mM-solution without shear shows a weak correlation peak at a momentum transfer of 0.09 nm^–1 which has its origin in the micellar interaction. For shear rates above a threshold value of =40 s^–1 the scattering pattern shows an irregular increase in anisotropy. The analysis of the anisotropic pattern reveals the existence of two types of micelles: Small rodlike micelles which are weakly aligned and very large rodlike aggregates which are strongly aligned and which are present above the threshold value of. The two micelles are in equilibrium with each other and the equilibrium shifts with increasing shear rate to the side of the large oriented micelles.     

X-ray diffraction studies on homologous thallium soaps below the temperature range of the neat phase 2. Structure models of crystalline modifications in the temperature range below the neat phase

In Part 1 were discussed the results of X-ray diffraction measurements on homologous thallium soaps, the lattice parameters and the unit cells of the different phases: phase C₁, phase C₂, phase I, phase II, and the neat phase.The aim of Part 2 is the development of structural models, based on data on lattice parameters, packing densities of hydrocarbon chains and head groups. In order to supplement our experimental data we carried out infrared-spectroscopic measurements at different temperatures within the existence regions of these phases to get additional information on alterations in configurations of head groups and hydrocarbon chains of thallium soaps in these phase regions.By comparing the structural models we can generalize that the phase C₁, phase C₂, phase I, and phase II have some properties in common: they form crystalline structures, their unit cells are monoclinic, and the angles and are orthogonal. The amount of the lattice parametersc is equal to the distances of two molecular bilayers and/or twice the distance between the lamellae.Among the normal lamella, the molecules form a herring-bone-like packing. This indicates that the lamellar structure of the liquid-crystalline neat phase is already preformed in these crystalline modifications of phase C₁, phase C₂, phase I, and phase II. These crystalline phases differ in their lattice parameters and their packing coefficients. The transition from the crystalline phase I or phase II into the neat phase is accompanied by a temperature-dependent contraction of the distances between the lamellae, which originates in the fluidity of the hydrocarbon chains. Simultaneously, the lattice parametersa andb are drastically shortened and attain dimensions considerably lower than the values obtained in crystalline modifications. The X-ray scattering properties of the Tl⁺-ions suggest that the Tl⁺-ions exist in a fluid-like state within the head groups region of the neat phase.We came to the conclusion that the thallium-oxygen-bond is remarkably less polar than the bonds between alkali ions and oxygen resulting from the electro-negativity of the metal-oxygen-bonds of the alkali soaps, in comparison to the thallium soaps. Hence, the absence of polymorphic liquid-crystalline semiphases of thallium soaps is due to the low polarity of the thallium-oxygen-bond. Structure formation of Tl-soaps is mainly influenced by the hydrocarbon chain packing.