Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach

The electrostatic interaction pressure of charged surface layers is considered qualitatively and quantitatively. In the case of mutual penetration of the surface layers in addition to Maxwell stress and osmotic resp. hydrostatic pressure an isotropic stress on the fixed charges carrying molecules of the surface layers has to be taken into account. The derivation of the pressure-distance equations is given starting from both thermodynamic/electrostatic and hydrostatic/electrostatic principles. A possible biological significance of the additional stress is discussed emphasizing its role in modifying the structure of surface layer molecules.List of symbols e ₀ elementary charge - k Boltzmann constant - n _i concentration of theith ionic species in the bulk solution - P hydrostatic pressure - P hydrostatic pressure in the bulk volume (× ) - P ^h integration constant, independent on ×:P ^h =P(h) - T absolute temperature - Z _i electrovalence of theith ionic species - thickness of the surface layer - , ₀ relative and absolute permittivities - II(×) osmotic pressure at position × - II osmotic pressure in the bulk solution (× ) - osmotic pressure in the symmetry plane of interacting identical surface layers (electric field strength equals zero) - integration constant, independent on ×: - _e ^h electrostatic component of the disjoining pressure _e ^h = _e (h) - (×) mobile charge density profile (cations and anions of the electrolyte) - (×) fixed charge density profile - ^t(x) total charge density profile ( ^t = +) - ¹(x) fixed charge density profile of one of the two surface layers ( ¹(×) 0 for 0×) - (×) electric potential profile     

Conformational changes in the human serum albumin-indomethacin binding

The effect of a nonsteroidal anti-inflammatory drug, the indomethacin, on the conformation of human serum albumin is investigated by evaluating-helix,-structure and random coil structure contents from optical rotatory dispersion spectra. The observed structural changes may be attributed to the-helix-to--structure conversion, because the content of random coil is not largely changed. The increase in-structure is due to a loss in the degrees of freedom in albumin.     

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.     

Prediction of the non-Newtonian viscosity and shear stability of polymer solutions

The structure-property relationships derived here permit the prediction of both the zero-shear viscosity ₀, as well as the shear rate dependent viscosity . Using this molecular modeling it is now possible to predict over the whole concentration range, independently of the molecular weight, polymer concentration and imposed shear rate. However, the widely accepted concept: dilute — concentrated, is insufficient. Moreover it is necessary to take five distinct states of solution into account if the viscous behavior of polymeric liquids is to be described satisfactorily. For non-homogeneous, semi-dilute (moderately concentrated) solutions the slope in the linear region of the flow curve (= must be standardized against the overlap parameterc · []. As with the ₀-M-c-relationship, a-M -c- relationship can now be formulated for the complete range of concentration and molecular weight. Furthermore, it is possible to predict the onset of shear induced degradation of polymeric liquids subjected to a laminar velocity field on the basis of molecular modeling. These theoretically obtained results lead to the previously made ad hoc conclusion (Kulicke, Porter [32]) that, experimentally, it is not possible to detect the second Newtonian region.Roman and Italian symbols a exponent of the Mark-Houwink relationship - b exponent of the third term of the ₀-M -c relationship - c concentration /g · cm^–3 - E number of entanglements per molecule - F(r) connector tension - f function - G _i ^A shear modulus; A indicates that it /Pa has been evaluated by a transient shear flow experiment; i is the shear rate to whichG ^A refers to - G storage modulus /Pa - G _p plateau modulus /Pa - H() relaxation spectrum /Pa - h shift factor (₀/_r) - K _H Huggins constant - K _b third constant of the ₀-M -c relationship - K constant of the Mark-Houwink relationship - M molecular weight /g · mol^–1 - M _e molecular weight between two /g · mol^–1 entanglement couplings - N number of segments per molecule - n slope in the power-law region of the flow curve - p p-th mode of the relaxation time spectrum - R gas constant /8.314 J·K^–1·mol^–1 - r direction vector - T temperature /K Greek symbols ß reduced shear rate - shear rate /s^–1 - shear viscosity /Pa·s - _s solvent viscosity /Pa·s - _sp specific viscosity - ₀ zero-shear viscosity /Pa·s - apparent viscosity at shear rate - reduced viscosity - viscosity of polymeric liquid in /Pa·s the second Newtonian region - [] intrinsic viscosity/cm³·g^–1 - screening length/m - /g·cm ^–3 density - relaxation time/s - ₀ experimentally derived relaxation time/s - angular frequency of oscillation Indices conc concentrated - corr slope corrected - cr critical - deg degradation - e entanglement - exp experimental - mod moderately concentrated/semi-dilute - n number average - p polymer - R Rouse - rep reptation - s solvent - sp specific - theo theoretical - weight average - relaxation time - o experimental or steady state - * critical - ** transition moderately conc. — conc. - + transition dilute — moderately cone. Paper presented at the 2nd bilateral U.S.-West German Polymer Symposium, Yountville, the 7th–11th September 1987.     

Complex polarizability as used to analyze dielectric relaxation measurements

The effect of representing dielectric properties in terms of the complex polarizability ^c = – i is examined. Loss curves ( and tan ) are shifted towards higher frequencies, revealing the existence of new relaxations and allowing the clarifications of ones already known. We have calculated the shift ratios (at maximum or tan )/ (at maximum or tan ) from the more conventional empirical equations representing the dielectric behavior. Some examples are given.     

Characterization of water-soluble,cationic polyelectrolytes as exemplified by poly(acrylamide-co-trimethylammoniumethylethacryate chloride) and the establishment of structure-property relationships

The cationic copolymerization products of poly (acrylamide-co-trimethylammoniumethylmethacrylate chloride (PTMAC) having cationic monomer percentages of 8%, 25%, and 50% as well as the cationic homopolymer, were characterized with respect to their molecular dimensions. The light-scattering and viscometric measurements were carried out for molecular weights ranging from 200 000 to 12 800 000 g/mol in 1 M NaCl solution at 25°C. It was possible to establish a relationship between the molecular weight and the two parameters: intrinsic viscosity and radius of gyration, for all four polymers.Rheological investigations of the flow properties in 1 M NaCl solution were also carried out using the polymer with a cationic monomer of 50% (PTMAC 50). Structure-property relationships were formulated which made it possible to describe and predict the shear viscosity, both in the zero-shear region (Newtonian region) and in the shear-dependent region (non-Newtonian region) as a function of the polymer concentration, the molecular weight, and shear rate.Abbreviations a exponent of the []-M relationship - A ₂ 2^nd virial coefficient/mol·cm³·g^–2 - AAm acrylamide - b slope of the flow-curve in the shear-rate dependent region - c concentration/g·cm^–3 - dn/dc refractive index increment/cm³·g^–1 - f function - K constant of the []-M relationship/cm³·g^t-1 - m _c proportion of cationic monomers/mol % - M molecular weight/g·mol^–1 - M _w weight-average molecular weight/g·mol^–1 - M _n number-average molecular weight/g·mol^–1 - NaCL sodium chloride - PAAm polyacrylamide - PS polystyrene - PTMAC poly(acrylamide-co-trimethylammoniumethylme thacrylate chloride) - R_G ^20.5 radius of gyration/nm - TMAC trimethylammoniumethylmethacrylate chloride - shear rate/s^–1 - critical shear rate/s^–1 - viscosity/Pa·s - 0 zero-shear viscosity/Pa·s - _s solvent viscosity/Pa·s - _sp specific viscosity - [] intrinsic viscosity/cm³·g^–1 - relaxation time/s     

Structure of casein micelles II. α s1-casein

Following the earlier study of the- and-casein micelle structure, we will now report results from the _s1-casein. Static and dynamic light scattering measurements were performed in a concentration range from 0.5 to 6.0 mg/ml atT=35 °C. A constant apparent molecular weight of 3.4×10⁶ daltons was found over the whole range. The apparent radii of gyration and the diffusion coefficients also show no detectable concentration dependence. The ratio of the two radiiR _g /R _H =2.78+0.21 is characteristic of extended rigid structures.R _g is the radius of gyration andR _H the hydrodynamic radius defined via the Stokes-Einstein relationship from the translational diffusion coefficient. This is in agreement with the analysis of the pronounced angular dependence of the scattered light, which leads to the conclusion that _s1-casein forms very long worm-like micelles. The contour length of one cylinder was found to beL1600 nm and the chains appear to be composed of about 12 Kuhn segments. At higher concentrations, lateral aggregation proportional to the concentration is observed. Beyond the overlap concentrationc ^* the asymptotic scattering curve changes its shape, which is interpreted as the beginning of a reversible gelation.     

Orientation of the diphenylene propane unit in stretched polycarbonate from two-dimensional magic-angle-spinning NMR

Two-dimensional magic-angle-spinning (2D-MAS) NMR has been used to measure the orientation parameter, P₂, of the diphenylene propane unit in bisphenol-A polycarbonate oriented by stretching to various extension ratios,, atT=295K andT= 403 K.P ₂ is proportional to the birefringencen, with a maximum birefringencen ₀= 0.189. There is some evidence that the order parameterP ₂ of the DPP units with respect to the chain axis deviates from unity.n ₀ is therefore expected to be different from the birefringence,n ₀ , of perfectly aligned chains of polycarbonate. The experimental results obtained forP ₂() are compared to those predicted by the aggregate model.     

Association of poly-(L-lysine) homologues in sodium carbonate solution

The molecular weights of isopoly(L-Iysine), poly(L-ornithine), and poly(L-, -diaminobutylic acid), the homologues of poly (L-lysine), were determined by the sedimentation equilibrium method in aqueous solutions of 1.0 M NaCl or 0.1 M Na₂CO₃. In every sample the molecular weights in the presence of carbonate ions was twice that in NaCl solution. In a previous paper we reported that poly(L-lysine) behaved as a dimer at concentrations higher than 0.4 g/dl in the presence of carbonate ions and as a monomer in dilute solution, and these two forms were related by a monomer-dimer equilibrium. The homologues did not have a monomer-dimer equilibrium relationship under the conditions of the measurements that we carried out. The CD spectrum of isopoly(L-lysine) in water showed a uniform increase with a decrease in the wave length in the presence of carbonate ions. However, in the alkaline region in NaOH solution, the spectrum changed and a small minimum at 212 nm was found. When additional carbonate ions were added a large minimum at 205 nm was observed. This result can be explained by a change in the conformation from a random coil to a regular structure. We could not compare isopoly(L-lysine) with other polypeptides, because it does not have peptide bonds. The CD spectra of poly(L-ornithine) and poly(L-, -diaminobutylic acid) in NaOH or Na₂CO₃ solutions showed only slightly regular structures. It was also confirmed that the dimer-structures of the poly (L-lysine) homologues do not have regular structures.This paper was presented at the VI. Symposium on Analytical Ultracentrifugation, Marburg, FRG, February 16–17,1989.     

Capillary rise of liquids in rectangular tubings

The capillary rise of liquids was investigated in square capillary tubings of different dimensions (e. g. 300 m · 300 m to 1000 m · 1000 m) in the temperature range 25° to 35°C.The data were fitted to an equation:=1/2 · ·g · (S · (C ·H/2 +C ·S)) where is the surface tension of the liquid,S is the side length of the square tubing,H is the capillary rise,C (= 1.089) is a capillary constant.     

Solutions of alkali soaps and water in fatty acids XIII. Circumstances that regulate the extension of theL 2-phase and the role of the acid-soaps rich in fatty acid for the occurrence of the phase

A basic requirement for that type ofL ₂-phase which exists in the system sodium octanoate-octanoic acid-water is the formation of acid-soaps. In order for the phase to be formed at all, the temperature must lie above the melting point of the fatty acid so that a reaction in non-aqueous milieu between neutral soap and fatty acid is possible. In order to obtain the characteristic shape and complete extension of the phase in direction of high water content the temperature must be so high that also the hydrated acid-soaps occur in fluid state. On the other hand the temperature cannot be so high that the acid-soaps become unstable.At temperatures at which the phase has obtained its full extension those circumstances differs which in different regions regulate the location of the phase borders; they depend on the composition of the acid soaps and on their amounts. In that part of the phase where the molar ratio between octanoic acid and sodium octanoate lies between 2 and 3 and where one has a continuous transition from reversed to normal structure only the two acid octanoates 1 NaC₈ 2 HC₈ x H₂O and 1 NaC₈ 3 HC₈ x H₂O occur and both are at 20 °C in fluid state.At water contents from about 22 % to 40 % the hydrate-water molecules belonging to the first mentioned soap are capable of contributing actively to the formation of large aggregates of acid-soap, a process which however is counteracted by the inmixing of the latter acid-soap. This mixture of the two acid-soaps decides in this region where the border of the phase will lie in direction towards an increased content of sodium octanoate; the result is that in spite of the fact that the hydration is increased, the border is only slowly displaced towards a higher content of fatty acid. As soon as the hydration of the acid octanoates has been completed and the additional water occurs as unbound bulkwater, the location of the phase boundary will no longer be influenced by the water content — now it will be the amphiphilic composition of the acid-soaps that determines the location of the border and it remains at the molar ratio 2.5 between octanoic acid and sodium octanoate at water contents from about 40% and up to 82%.In the direction of decreasing content of neutral sodium octanoate and increased content of water theL ₂-phase both at the highest content of fatty acid and the highest contents of water will be in equilibrium with the water-richL ₁-phase; in the first mentioned region with theL ₁-phase below the lac where at the border it is saturated with octanoic acid and in the latter region with theL ₁-phase just above the lac, where the dilute sodium octanoate solution contains dissolved 1 NaC₈ 1HC₈ x H₂O. In the large central part of theL ₂-phase, from about 20 % to about 86 % of water, the location of the border is dominated by the acid octanoate 1 NaC₈ 3 HC₈ x H₂O and that makes an equilibrium with theL ₁-phase impossible; instead one has an equilibrium via a two-phase zone between the amphiphile-rich region of theL ₂-phase and its water-rich region. In the first region the location of the border is regulated by the decreasing capability of the hydrated acid octanoate 1 NaC₈ 3 HC₈ x H₂O to dissolve octanoic acid; in the latter it is regulated by the fact that 1 NaC₈ 3 HC₈ x H₂O is the most fatty acid-rich acid-soap that is formed and that the octanoic acid is very little soluble in water and in the aqueous solution of this acidsoap.The middle part of theL ₂-phase, especially the region between about 55 % and 82 % of water, constitutes a direct continuation of the liquid crystalline lamellarD-phase. The liquid crystalline character of theD-phase is lost at the transition, but the lamellar organization is retained. That the molecules at least up to a water content of about 40 % are of the original reversed type and have an elongated shape with a central part of hydrated polar groups, from which core the hydrocarbon chains extend in two opposite directions, is the reason to that they, at crowding, form transient layer-like agglomerates of tightly packed more or less parallel molecules; this facilitates the transformation to coherent double amphiphilic layers, in which all molecules lie with the hydrated polar groups outwards toward coherent domains of bulk-water, without another liquid phase occurs.     

Change of water structure by solvents and polymers Part 4: Albumin-water solutions with acetylsalicylic,hydrochloric and ascorbic acid,lysine- and ammonium chloride and with dextrane and sorbit

Viscosity measurements were made in the temperature range of 10 °–40 °C. The equation= _o exp(B/(T-T _o )) was used with the parameterT ₀ as structure indicator, which is called the limiting temperature. For instance, hydrocarbons, as liquids with quasifree molecules, haveT ₀=O; water as a highly structured liquid hasT ₀= 140–150 K.The polymer investigated was ovalbumin in aqueous solution in a concentration comparable to that of blood. Acetylsalicylic acid produces a protein conformation which breaks the water structure in solution at a pH of within the in vivo region.The question of whether only the acidity determines the water structure breaking properties of the protein is investigated by acidifying albumin-water solutions with hydrochloric acid, lysine chloride and ascorbic acid. All these acids exhibit similar effects. A stronger influence is observed for ammonium chloride. Its interaction with ovalbumin produces a strong structure-breaking effect. The most powerful water structure breaker in albumin-water solutions is dextrane. In a concentration of 10 % it changes the polymer conformation so that the water structure is broken to such an extent that the solution behaves as an almost quasifree liquid withT ₀=O.     

Equilibrium and non-equilibrium melting of branched polyethylene relating to defect incorporation within crystals

New equilibrium melting point data, for polyethylene containing chain defects, are tested in the light of random copolymer predictions. A simplified expression for the melting point depression of random copolymers containing small amounts of non-crystallizable units is derived. Non-equilibrium melting data for rapidly quenched polyethylene samples are also reported. The fusion enthalpyH(X), and the surface free energy _e for crystals containing defects are evaluated using crystallinity, equilibrium meltingtemperatures and X-ray long period data. It is shown that increasing defect penetration within crystals induces a decrease ofH(X) withX in accordance with theoretical predictions. Finally _e is, similarly, shown to decrease with increasing number of chain defects attached to the crystal surface.     

Amphoteric character of polyelectrolyte complex particles as revealed by isotachophoresis and viscometry

Isotachophoresis and viscometric measurements were performed on aqueous dispersions of non-stoichiometric polyelectrolyte complexes in order to elucidate the surface charge situation of the complex particles in dependence on component charge density, ratio of cationic to anionic groups in the complex, and pH and ionic strengths of the ambient medium. Components for complex formation were acryl-based anionic and cationic polyelectrolytes of the pendent type. From our results, an amphoteric character of the polyelectrolyte complex particles can be concluded, with an isoelectric point characterized by zero mobility and a minimum in reduced viscosity _spec/c of the particle dispersion, and with the sign of net surface charge depending on ambient pH and component charge density. The influence of ionic strength on the _spec/c vs pH plots can be interpreted by assuming a competition between salting-out and electrostatic shielding effects. No correlation could be established between the overall molar ratio of cationic to anionic groups and the isoelectric point of the complex particles, which obviously indicates a different composition of surface and bulk of the polyelectrolyte complex particles.     

Isothermic spherulitic growth and the shape of grain boundaries and growth fronts

We investigate experimentally and theoretically the isothermic growth of two spherulites of different modification into a supercooled isotactic polypropylene film. The faster growing-spherulite grows around the-spherulite, and finally the-spherulite is symmetrically and completely included in. In contrast to literature but in agreement with experimental evidence we find that the grain boundary between the teardropshaped-spherulite and the surrounding-spherulite consists of two parts, where one is always an arc of a logarithmic spiral. This-spherulite ends always in a vertex. Its angle depends on the ratio of the two growth rates only. Behind the vertex an intrinsic--grain boundary exists, degenerating to a channel in bulk material. The growth fron of the-spherulite, which ends on the logarithmic spiral or on the intrinsic grain boundary during growth, consists of an arc of a circle continued by an arc of a logarithmic spirial, too.     

Molecular motions in poly(diethyl siloxane) studied by solid-state29Si NMR

Molecular motions in poly(diethyl siloxane) were studied by solid-state²⁹Si-NMR in the temperature range 180–350 K. In this temperature range two solid phases ₁ and ₂, a mesophase _m, and an amorphous isotropic phase exist. The nature of the chain mobility in the different phases was deduced from the resulting changes in the NMR line-shape governed by anisotropic chemical shift. In the intermediate solid phase ₂ its anisotropy is reduced by 25% compared with the low temperature phase ₁ due to the onset of oscillations around the chain axis and conformational transitions. In the mesophase _m the polymer chain rotates about its long axis yielding an axially symmetric chemical shift tensor opposite in sign to that in the ₁, ₂ phases. The broad transition of the mesophase into the isotropic phase is accompanied by an increase in a narrow Lorentzian line arising from the amorphous phase. The results are compared with previous¹H NMR, Raman-spectroscopy and x-ray measurements.After completion of this work we learnt that PDES has recently also been studied through¹³C-MAS and²⁹Si-NMR by Möller et al. [13].     

Shear-induced deformation of polystyrene coils in dilute solution from small angle neutron scattering 2. Variation of shear gradient,molecular mass and solvent viscosity

The technique of small angle neutron scattering (SANS) has been used to study the conformation of polystyrene chains in dilute solution under a constant shear gradient. The experiments reveal a distinct anisotropy of the molecular dimensions with regard to the directions parallel and perpendicular to the flow direction on the 2D-multidetector. The deformation ratio of the single polymer chain (R ²/R _iso ² )–1 as a function of the reduced shear gradient=([] · · M _w G)/RT shows a transition from the ideal ²-behaviour for dynamic infinitely flexible coils found at small gradients, to a behaviour with smaller increase at larger. These results are qualitatively consistent with the theory of Cerf for a polymer with finite internal viscosity in a shear gradient. At low(<1), a better agreement with the model of a free-draining coil (Rouse behaviour) than with the Zimm model is observed.     

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.     

Electrokinetic study on concentrated suspensions using colloid vibration potential measurements

-potentials of a silica suspension and three types of polystyrene latex suspensions with different surface charge groups were measured, as a function of the particle concentration () in the suspension over a wide range, using the colloid vibration potential (CVP) technique. The concentration dependence of the-potential in silica suspension is explained well by Levine et al.s [1] cell model theory, verifying the applicability of the cell model to the CVP in silica suspension. However, the-potential of latex suspensions ordinarily decreases as the particle concentration increases, even after being corrected by the term of (1-). This tendency is especially noticeable in the systems that have particles with high surface charge densities. Furthermore, the conductivity measurements of these suspensions reveal that the conductivity of these systems, especially in their highly charged state, increases as the particle concentration is increased; opposite in tendency to silica suspensions. These new findings can be explained as follows: on the highly charged surface of a latex particle, a polyelectrolyte-like (hairy) layer is present, which overlaps at some point. This permits interparticle surface conduction and results in the abnormal behavior of CVP in these systems.     

Symmetry and other properties of second-order phenomenological coefficients and thier significance in a chemical system

Using a second-order phenomenological equationJ _i = _j L _ij X_j + _{j, k} L _ijk X_j X_kand assuming that the system is at a state near equilibrium, it has been shown that the symmetry ofL _ijk is retained with respect to the permutations of suffices i j and k Furthermore, using the second-order flux equations, the thermodynamic stability criterion is expressed. The symmetry is shown to be retained in a reaction scheme representing the emplate model. The significance of the stability criterion as expressed by the higher-order phenomenological coefficients is discussed.