The association of urethane-polyethyleneoxide (HEUR) thickeners,as studied by NMR self-diffusion measurements

The concentration and molecular weight dependence of the self-diffusion coefficient (D _self) of associative polymers of HEUR-type in aqueous solution have been investigated using FT-PGSE-NMR technique. The idea of three-dimensional network formation as a result of aggregation of the hydrophobic end-groups of the polymer in junctions is supported through the observed dramatic lowering ofD _self with increased concentration. The network-formation efficiency depends on the polymer molecular weight as well as the hydrophobicity of the end-groups.A double logarithmic dependence of the self-diffusion coefficient versus concentration (c) has been observed:D _selfc ^–a1,a2 . The first exponent,a ₁, is valid at low concentration, <1% polymer per weight solution, and ranges from 0.5 to 1, whereas the second exponent,a ₂, describing systems of higher concentration, ranges from 2 to 2.7.     

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     

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     

Viscosity B coefficients of polyethyleneglycols in water

The viscosity B coefficients of polyethylene glycols (M=62–1000) are determined at 25 °C. The B coefficient increases non-linearly with the number of ethyleneoxide (EO) units. The increase of the B coefficient per EO(0.111 dm³/mole) is less than the B value for two methylene groups (0.160 dm³/mole). This is discussed in terms of changes in the configurations of polyethylene glycols with long EO chains.Molecular size is the major factor that contributes to B at shorter chains, but solvation (hydration) becomes dominant as the number of ethyleneoxide groups increases. The hydration parameter,(gH₂O/g ethyleneglycol), shows a linear dependence on B at low mass followed by a non-linear increase at high molecular mass and the viscosity C coefficient accounts for the solute-solute interactions.Symbols absolute viscosity - _d absolute viscosity of dispersion medium - _r relative viscosity - _sp specific viscosity - ¦ _o ¦ intrinsic viscosity at infinite dilution - ¦ _c ¦ intrinsic viscosity as a function of solute concentration - partial specific volume - volume fraction - hydration (weight of H₂O hydrating 1 g of polyethylene glycol) - _c hydration as a function of solute concentration - K shape function - K _c shape function as a function of solute concentration     

Polymer adsorption on fine particles; the effects of particle size and its stability

The effects of particle size on polyacrylamide (PAAm,M _w =59×10⁴, 500×10⁴) adsorption were investigated using a series of well-characterized hematite (-Fe₂O₃) dispersions. The -Fe₂O₃ particles with highly monodisperse and nearly spherical shape ranged in radius from 23 nm to 300 nm. the maximum amount of PAAm adsorption (M _m ) in each system, showed a steady increase with decreasing particle radius and was influenced strongly by particle concentrations in the medium. Furthermore, it was realized that the diameter of -Fe₂O₃ particles after treatment with PAAm under different particle concentrations decreased with increasing particle concentration. The relation between particle concentration in the medium and particle size after treatment was also influenced by the medium pH, i.e., at the medium pH close to the isoelectric point of -Fe₂O₃ particles (pH^o=9.2), the particle size after treatment increased with increasing particle concentration. All these results suggest that in the system of ultra-fine particles, the mixing process between particle-particle and polymerparticle will play an important role on the conformation of adsorbed polymer layer.     

Gas permeability of block copolymers of styrene and butadiene

The permeability of styrene-butadiene block copolymer foils with different composition prepared by casting and pressing has been investigated for the gases Ar, CO₂, and CH₄ at pressure difference of 400 mbar and at the temperature range 298 T [K] 333.The permeation process can be described by the solution diffusion mechanism. The diffusion coefficients decrease in the sequence of the gases Ar, CO₂, and CH₄ and the solubility coefficients increase in the sequence Ar, CH₄, CO₂.The dependence of the permeability on the composition of the block copolymer can be interpreted by the help of percolation theory and the effective medium theory. It follows the critical volume fraction of the percolation of the transport phase _PB ^c (= 0,23) and the coordination numberz (= 4) giving an information concerning the multiphase structure of the block copolymer.Presented in part at the 33^rd Annual Meeting of the Colloid-Gesellschaft, Graz, Austria, September 14–16, 1987.     

Structure transfer from a polymeric melt to the solid state. Part II: Dependence on molecular weight

Melt spinning experiments of polyethylene, using a high quenching rate have been carried out. Molecular weight has been varied. From measurements of the mechanical properties of the monofilaments produced it is concluded that melt history influences the solid state behavior. This is reflected in the hypothesis of a transference of knots, preexisting in the melt into the solid state. Measurements of the elastic recovery allow to offer an interpretation, in which this network of knots does not percolate, until a critical value of the molecular weightM _{c knot}10⁵ is surpassed. The possible influence of these knots on the mobile entanglements is discussed.On leave from the Institut für Technische und Makromolekulare Chemie, Universität Hamburg, Hamburg, Germany.     

Dynamic shear compliance of polymer melts and networks in dependence on crosslinking density

Mechanical relaxation processes in polymer melts and networks are discussed. This is performed by decomposing master curves of the dynamic shear compliance into i) glass relaxation with its plateau complianceJ _eN ; ii) shearband process with its relaxation strengthJ _B , which is reciprocal to the total crosslink densityp _c ; and iii) flow relaxationJ _F and viscous flow (for uncrosslinked melts only). Plateau complianceJ _eN > is exponentially reduced only by effective crosslinks (p _c ^* p _c /30). This behavior is understood on the level of a meander superstructure, which includes shearbands. The observed saturation inJ _eN at higher dicumylperoxide (DCUP) crosslinking-which doesn't appear with radiation-can be explained by the lack of chemically induced effective crosslinks across the interfaces among meander cubes. This lack may be a consequence of DCUP molecules concentrating at the interfaces and thereby preventing the contact and radical recombination between chains at adjacent meander faces.Crosslink densitiesp _c (per monomer), determined from the reduction of shearband relaxation strength, vary linearly with the crosslinking agent and read: p_c2.4 · 10^–2 Dose/MGy andp _c 0.97 · 10^–2 DCUP/phr for radiation and DCUP crosslinking, respectively. This implies, e.g., that a dose of 0.4 MGy (40 Mrad) is equivalent to 1 part DCUP phr in a crosslinking polyisoprene. From activation-curve analysis it follows that3 r/d stays constant, and _s - _so (free energy of formation of a segment-dislocation) andQ _y -Q _yo (activation energy for segmental jumps) vary with the square ofP _c , as does the glass temperaturT _g -T _go from DSC measurements.     

Dependence of the activity of a rhizopus lipase on microemulsion composition

Enzymatic hydrolysis of a model triglyceride, palm oil, was carried out with lipase fromRhizopus sp. in microemulsions with varying water content. The microemulsions were based on a nonionic surfactant, pentaethylene glycol monododecyl ether (C12 EO5), buffered water solution and an oil component consisting of isooctane and palm oil at a weight ratio of 20:1. The structure of the microemulsions was characterized using Fourier transform pulsed-gradient spin-echo¹H NMR. The rate of reaction decreased as the water content of the reaction medium was increased. The self-diffusion coefficient of water, D_w was found to be constant within the interval 1–20% water. The difference in reactivity is believed to be due to a difference in structure of the palisade layer between water and hydrocarbon microdomains. The nonionic surfactant was demonstrated to be unsuitable for enzymatic reactions since only partial hydrolysis was obtained in all experiments. The surfactant, however, did not cause enzyme deactivation, even at very high concentrations.     

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     

Spreading and compression of n-hexadecyl acrylate at liquid-air interface

Usingn-hexadecyl acrylate, surface pressure-area (F-A) curves and equilibrium spreading pressuresF ^e were measured at various temperatures (5.7°–46°C) by the Langmuir balance (F-A) and the Wilhelmy-plate method (F ^e). At low temperatures (T<13 °C) condensed films and the liquid-condensed/solid condensed transition can be observed. At high temperatures (T>30 °C) liquid-expanded films occur. In the intermediate range the compression curves have two transition points. The transition pressureF ₁ between liquid-expanded and condensed film has a marked temperature dependence. The transition enthalpiesH ₁ decrease with increasing temperature and become zero at 29.2 °C. The second transition is related to a transition between the condensed films (F ₂). The slight temperature dependence of this transition is accompanied by an increasing change of area as well as by increasing transition enthalpiesH ₂.TheF ^e-T curve has two distinct breaks, at the melting pointT _m and atT=30 °C. The break atT _m is due to the melting process and the break atT=30 °C is caused by a phase transition between a liquid-expanded film and a condensed film.The phase diagram was constructed from the transition pressures. It can be demonstrated that the highest pressures of the thermodynamic stable film occurs atT _m. At temperaturesT>T _m equilibrium spreading pressure and equilibrium collapse pressure are identical whereas atT _m supercompression of the monolayer occurs. The film in this state behaves like a supercooled liquid. Obviously, rupture and collapse of such a film lead to a thermodynamically metastable bulk phase.     

Wide angle X-ray diffraction studies of polytetrafluoroethylene and ethylen-tetrafluoroethylen-bipolymers in the range 9.5 K–270 K

PTFE shows in the whole temperature range investigated a triclinic crystal structure with cell parametersa=0.952 nm,b=0.559 nm,c=1.706 nm,=87.9°, = 90.0° and=91.8°. The temperature dependence ofa andb-axis is linear, thec-axis shows a change in thermal expansion at 150 K. The inherent strain is small. The crystallite sizes are measured, paracrystalline distortions are absent.The bipolymers show only an ordered arrangement in lateral direction under maintenance of the helical structure. The lateral arrangement is very distorted and the range of order is aboutD _L 10 nm.     

Determination of unperturbed dimensions of polymers in binary solvent mixtures from viscosity measurements

Intrinsic viscosity measurements were carried out on poly(vinyl pyrrolidone) and poly(vinyl alcohol) in various solvents and solvent mixtures. The values of, [] andk, the latter two being the fundamental terms in the equationC/ _sp =1/kC, were utilized for the determination of the unperturbed dimensions in solution. The values of (¯r _o ² /M _w )^1/2 were calculated.     

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.     

Structure-property relationship of polyurethane ionomer

Polyurethane (PU) ionomers were prepared using various types of polyol (PTAd, PCL, PTMG, and PPG) and isocyanate (MDI, HDI, and IPDI), together with different extender (DMPA) contents, degree of neutralization, and number average molecular weight (M _n) of polyol. Modulus (E), strength (_b), and glass transition temperature (T _g) significantly increased with the increased amount of extender and extender neutralization. Among three of the iocyanate used, PU from MDI gave the highest modulus, strength, andT _g. With regard to theM _n of PTAd (600, 1000, 2000), PU from PTAd 600M _n gave the highest modulus, strength, andT _g, due probably to the highest hard segment content and phase mixing. On the other hand, PU from PTAd 2000M _n gave significantly improved strength over PTAd 1000M _n, and the highest elongation. The results were interpreted in terms of soft-segment crystallization, and soft-hard phase separation, which was concluded from the lowered softT _g.     

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     

Effects of pressure and solvent on the diffusion of aromatic compounds through polymers

The diffusion of six azo and five anthraquinone derivatives through nylon 6, poly(ethylene terephthalate) and secondary cellulose acetate films were studied under high hydrostatic pressures of up to 3000 bar and at temperatures 80–130 °C, by analyzing the diffusion profiles yielded in a stacked multiple film, placed in the solution of the diffusant. It was found that the diffusion coefficient,D, of the diffusant decreased with increasing pressure, giving a linear relationship between InD and the pressure, the slope of which gave the activation volume for the diffusion,V . It was revealedV increased linearly with increasing intrinsic molecular volume of the diffusant,V _w , the slopes being different between the azo and the anthraquinone derivatives. The ratio ofV toV _w (V /V _w ) ranged from 0.13 to 0.93, depending in a sensitive manner on the degree of swelling of the polymer matrix which in turn was varied by the solvent. The overall results could be explained in accordance with the formulation,V _{f, local} +V =V _w , whereV _{f, local} represents the free volume contribution. It was proposed thatV _w is increased by solvation when the solvent is good for the diffusant.     

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.     

Molecular bases of stress relaxation and viscosity of polymers, 1a) New empirical relations

Experiments with several polymers led to new relations which describe stress relaxation at small shears and show the influence of the molecular structure on relaxation. Bubble-free melts of anionically polymerized polystyrenes with the molecular masses (relative molecular mass is referred to as molecular mass throughout this paper)M=6 10² to 1.8 10⁶ g mol^–1 and their blends are studied at several temperatures and at timest>3 ms. As the stress (10² to 10⁶ Pa) deforms the rheometer, a new mathematical method was developed to correct the relaxations. The energy-elastic stress is separated from the entropy-elastic stress. The relaxations of the latter do not confirm the Rouse theory as is proportional to exp (–¦t ^1/2¦) forM<4000. For M>4000 the relaxations deviate from the theoretical functions as well. The initial modulus G(0) then depends onM, and is not proportional to ¦t ^–1/2¦. A new and simple function describes the relaxation of melts with entangled molecules at long times. The influences of concentration and chemical structure on relaxation are formulated for weak intermolecular forces. Published data for the constantD of self-diffusion are used in calculating values ofD for a constant free volume making use of the initial velocity of relaxation and its dependence on temperature. ThenDM ^–1 holds forM<1.3 10⁴ andDM ^–2 for largerM. Correct values of viscosity are calculated from the empirical functions of stress relaxation.Part 2 cf.In memoriam Professor Dr. Drs. h.c. Otto Bayer