Study on laminar viscosity and zero shear viscosity of latex systems

The flowing nature and rheological properties of polymethyl methacrylate latex systems in a coaxial cylinder viscometer were studied on the basis of laminar shear flow model and rheological experimental data. The physical meaning of laminar viscosity (eta(i,j)) and zero shear viscosity (eta(0)) were described. We assumed that laminar shear flows depended on position and shear time, so microrheological parameters were the function of position and shear time. eta(i,j) was the viscosity of any shear sheet i between two neighboring laminar shear flows at time t; j was denoted as j=t/Deltat; and Deltat was the interacting time of two particles or two laminar shear flows. tau(i,j) and gamma(i,j) were shear stress and shear rate of any shear sheet i at j moment. According to Newton regulation tau(i,j)=eta(i,j)gamma(i,j), apparent viscosity eta(a) should be a statistically mean value of j shear sheets laminar viscosity at j moment, i.e., eta(a)= summation operator(i=j)eta(i,j)gamma(i,j)/ summation operator(i=j)gamma(i,j). eta(0) was defined as shear viscosity between a laminar shear flow and a still fluid surface, i.e., eta(0)=(tau(i,j)/gamma(i,j))(j-i-->0). These new ideas described above may be helpful in the study of the micromechanisms of latex particle systems and worthy of more research.     

Critical behavior of 2,6-dimethylpyridine-water: measurements of specific heat, dynamic light scattering, and shear viscosity

The specific heat C(p) at constant pressure, the shear viscosity eta(s), and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature T(c). The amplitude of the fluctuation correlation length xi(0)=(0.198+/-0.004) nm has been derived from a combined evaluation of the eta(s) and D data. This value is in reasonable agreement with the one obtained from the amplitude A(+)=(0.26+/-0.01) J(g K) of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate Gamma of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude Gamma=(25+/-1)x10(9) s(-1). No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity eta(b), resulting from the treatment of eta(s) and D data, with the viscosity eta(s)(nu=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5-130 MHz using a novel shear impedance spectrometer.     

Rheological Behavior of Titanium Dioxide Suspensions

The rheological properties of titanium dioxide dispersed in water are measured over a wide range of powder concentrations, temperatures, and pH values. The value of intrinsic viscosity of titanium dioxide measured with an Ubbelohde capillary viscometer is 3.55, which is useful for determining the shape and aggregation property of the particles. The yield stress and steady shear viscosity of titanium dioxide with broad and narrow particle size distributions were measured over a wide range of solid volume fractions on a Brabender rheometer. It is observed that the rheological properties of the suspensions are quite different due to the difference in particle size distributions. Quemada, Casson, and Zhou's models were used to fit the experimental data and useful parameters were obtained. Calculated data are also in good agreement with the experimental data. As expected, the shear viscosity and yield stress decrease with increasing temperature. But when the temperature is around 50 degrees C, yield stress increases with increasing temperature while shear viscosity exhibits a complex behavior. The phenomena are very interesting and special. The Peclet number was used to analyze the shear thickening behavior. Models were also used to describe the shear viscosity under different temperatures and the master plots of the reduced variables eta/eta(infinity) vs t(c)gamma; at different temperatures are superimposed, which means the agreement is fair and the models are suitable to describe the rheological properties of titanium dioxide suspensions. pH effects were investigated on a Rheometrics RFS-II rheometer and it was found that pH can change the surface charge of the particles, which also affects the rheological behavior. The pH at which maximum shear viscosity and yield stress occur is in concordance with the isoelectric point. Copyright 2001 Academic Press.     

Structural relaxation and rheological response of a driven amorphous system

The interplay between the structural relaxation and the rheological response of a simple amorphous system {a 80:20 binary Lennard-Jones mixture [W. Kob and H. C. Andersen, Phys. Rev. Lett. 73, 1376 (1994)]} is studied via molecular dynamics simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of Tc=0.435 has been identified in the previous studies via the analysis of the system's dynamics in the framework of the mode coupling theory of the glass transition [W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995)]. In the present work, we focus on the question whether a signature of this ideal glass transition can also be found in the case where the system's dynamics is driven by a shear motion. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates gamma, whereas at sufficiently low gamma the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a glass is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity eta decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the gamma is decreased below a (temperature-dependent) threshold value. Below Tc, on the other hand, the shear viscosity grows as eta proportional, etax 1/gamma, suggesting a divergence at gamma=0. Thus, within the accessible observation time window, a transition toward a nonergodic state seems to occur in the driven glass as the driving force approaches zero. As to the flow curves (stress versus shear rate), a plateau forms at low shear rates in the glassy phase. A consequence of this stress plateau for Poiseuille-type flows is demonstrated.     

Crystal growth kinetics exhibit a fragility-dependent decoupling from viscosity

In this paper we establish the temperature dependence of the kinetic coefficient associated with crystal growth into the supercooled liquid for a wide range of organic and inorganic materials. We show that the kinetic coefficient for crystal growth scales with the shear viscosity eta as eta(-xi) and that the exponent depends systematically on the fragility of the liquid. The greater the fragility (i.e., deviation away from an Arrhenius temperature dependence for eta), the larger the difference 1-xi. We argue that this breakdown in scaling between the crystal growth kinetics and the viscosity is a manifestation of heterogeneous dynamics in supercooled liquids. In addition, we show that the absolute growth rate at intermediate viscosities is correlated with the entropy difference between the liquid and the crystal.     

Abnormal viscosity increment observed for an ionic liquid by dissolving lithium chloride

The effect of adding an inorganic salt, lithium chloride, and water on the viscosity of an ionic liquid, 1-n-butyl-3-methylimidazolium chloride (BmimCl), was investigated by shear stress measurements with a rheometer. The shear rate dependence of the viscosity showed shear thinning behavior, which implies that some structure should exist in the liquid and the structure should change at high shear rates. Addition of LiCl enhances the viscosity of BmimCl. The logarithmic value of zero-shear viscosity, eta(0), of BmimCl increases linearly and largely with increasing added salt content. The increasing rate of the viscosity by addition of LiCl was about 10 times larger than that for an aqueous solution of LiCl. When water is added into BmimCl, viscosity decreased. The increasing rate of the viscosity by addition of LiCl for BmimCl with about 5 wt % of water was almost the same as that for BmimCl without addition of water.     

Structural variations of potassium aryloxides

A series of potassium aryloxides (KOAr) were isolated from the reaction of a potassium amide (KN(SiMe(3))(2)) and the desired substituted phenoxide (oMP, 2-methyl; oPP, 2-iso-propyl; oBP, 2-tert-butyl; DMP, 2,6-di-methyl; DIP, 2,6-di-iso-propyl; DBP, 2,6-di-tert-butyl) in tetrahydrofuran (THF) or pyridine (py) as the following: [([K(mu(4)-oMP)(THF)][K(mu(3)-oMP)])(5)]( infinity ) (1), [[K(6)(eta(6),mu(3)-oMP)(4)(eta(6),mu(4)-oMP)(2)(py)(4)].[K(6)(eta(6),mu(3)-oMP)(6)(eta(6)-py)(4)]]( infinity ) (2), [K(mu(3)-oPP)](4)(THF)(3) (3), [K(4)(eta(6),mu(3)-oPP)(2)(mu(3)-oPP)(2)(py)(3)]( infinity ) (4), [K(mu(3)-oBP)(THF)](6) (5), [K(6)(eta(6),mu(3)-oBP)(2)(mu(3)-oBP)(4)(py)(4)]( infinity ) (6), [K(3)(eta(6),mu(3)-DMP)(2)(mu-DMP)(THF)]( infinity ) (7), [[K(eta(6),mu-DMP)(py)](2)]( infinity ) (8), [K(eta(6),mu-DIP)]( infinity ) (9), [K(eta(6),mu-DBP)]( infinity ) (10). Further exploration of the aryl interactions led to the investigation of the diphenylethoxide (DPE) derivative which was isolated as [K(mu(3)-DPE)(THF)](4) (11) or [K(mu(3)-DPE)(py)](4).py(2) (12) depending on the solvent used. In general, the less sterically demanding ligands (oMP, oPP, oBP, and DMP) were solvated polymeric species; however, increasing the steric bulk (DIP and DBP) led to unsolvated polymers and not discrete molecules. For most of this novel family of compounds, the K atoms were pi-bound to the aryl rings of the neighboring phenoxide derivatives to fill their coordination sites. The synthesss and characterization of these compounds are described in detail.     

Lanthanide-transition-metal carbonyl complexes: new [Co4(CO)11]2- clusters and lanthanide(II) isocarbonyl polymeric arrays

Two types of Ln(II)-Co(4) isocarbonyl polymeric arrays, [(Et(2)O)(3)(-)(x)()(THF)(x)()Ln[Co(4)(CO)(11)]]( infinity ) (1-3; x = 0, 1) and [(THF)(5)Eu[Co(4)(CO)(11)]]( infinity ) (4), were prepared and structurally characterized. Transmetalation involving Ln(0) and Hg[Co(CO)(4)](2) in Et(2)O yields [(Et(2)O)(3)Ln[Co(4)(CO)(11)]]( infinity ) (1, Ln = Yb; 2, Ln = Eu). Dissolution of the solvent-separated ion pairs [Ln(THF)(x)()][Co(CO)(4)](2) (Ln = Yb, x = 6; Ln = Eu) in Et(2)O affords [(Et(2)O)(2)(THF)Yb[Co(4)(CO)(11)]]( infinity ) (3) and [(THF)(5)Eu[Co(4)(CO)(11)]]( infinity ) (4). In these reactions, oxidation and condensation of the [Co(CO)(4)](-) anions result in formation of the new tetrahedral cluster [Co(4)(CO)(11)](2)(-). The two types of Ln(II)-Co(4) compounds contain different isomers of [Co(4)(CO)(11)](2)(-), and, consequently, the structures of the infinite isocarbonyl networks are distinct. The cluster in [(Et(2)O)(3)(-)(x)()(THF)(x)()Ln[Co(4)(CO)(11)]]( infinity ) (1-3) possesses pseudo C(3)(v)() symmetry (an apical Co, three basal Co atoms; one face-bridging, three edge-bridging, seven terminal carbonyls) and connects to Ln(II) centers through eta(2),micro(4)- and eta(2),micro(3)-carbonyls to generate a 2-D puckered sheet. In contrast, [(THF)(5)Eu[Co(4)(CO)(11)]]( infinity ) (4) incorporates a C(2)(v)() symmetric cluster (two unique Co environments; two face-bridging, one edge-bridging, eight terminal carbonyls), and isocarbonyl linkages (eta(2),micro(4)-carbonyls) to Eu(II) atoms create a 1-D zigzag chain. Complexes 1-4 contain the first reported eta(2),micro(4)-CO bridges between a Ln and a transition-metal carbonyl cluster. Infrared spectroscopic studies revealed that the isocarbonyl associations to Ln(II) persist in solution. The solution structure and dynamic behavior of the [Co(4)(CO)(11)](2)(-) cluster in 1 was investigated by variable-temperature (59)Co and (13)C NMR spectroscopies.     

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).     

On the breakdown of the Stokes-Einstein law in supercooled liquids

The wavevector-dependent shear viscosity, eta(k), is evaluated for a range of temperatures in a supercooled binary Lennard-Jones liquid. The mode coupling theory of Keyes and Oppenheim (Phys. Rev. A 1973, 8, 937) expresses the self-diffusion constant, D, in terms of eta(k). Replacing eta(k) with the usual viscosity, eta identical with eta(k = 0), yields the Stokes-Einstein law. It is found that the breakdown of the SE law in this system is well described by keeping the simulated k-dependence. Simply put, bath processes on all length scales (wavevectors) contribute to D, the system is much less viscous at finite k, and thus D exceeds the SE estimate based upon eta. The functional form of eta(k) allows for the estimation of a correlation length that grows with decreasing T.     

Structural and shear characteristics of adsorbed sodium caseinate and monoglyceride mixed monolayers at the air-water interface

The structural and shear characteristics of mixed monolayers formed by an adsorbed Na-caseinate film and a spread monoglyceride (monopalmitin or monoolein) on the previously adsorbed protein film have been analyzed. Measurements of the surface pressure (pi)-area (A) isotherm and surface shear viscosity (eta(s)) were obtained at 20 degrees C and at pH 7 in a modified Wilhelmy-type film balance. The structural and shear characteristics of the mixed films depend on the surface pressure and on the composition of the mixed film. At surface pressures lower than the equilibrium surface pressure of Na-caseinate (at pipi(e)(CS) have important repercussions on the shear characteristics of the mixed films.     

Shear thinning and shear dilatancy of liquid n-hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects

Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal (NVT) and isobaric-isothermal (NPT) ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid n-hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates (gamma) affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of gamma<1 x 10(11) s(-1), the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of gamma>1 x 10(11) s(-1), specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flow activation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.     

Ti

Tridentate binding of BH(4)(-) to a zero-valent metal center was found for the first time in [Ti(CO)(4)(eta(3)-BH(4))](-) (shown in the picture), which was obtained from the reaction of the carbonyl metalate anion [Ti(CO)(6)](2-) with BH(3) small middle dotTHF. Displacement of the unusually labile BH(4)(-) anion by a pyrrolyl anion provided the first metal(0) pyrrolyl complex [Ti(CO)(4)(eta(5)-C(4)H(4)N)](-).     

Flow behavior of narrow-distribution polydimethylsiloxane

The flow behavior of α,ω-dihydroxypolydimethylsiloxanes, having a weight-average number-average molecular weight ratio of 1.1–1.2, was studied with a Cannon-Manning viscometer and an Instron rheometer. Comparison of the flow behavior of samples with narrow and broad molecular weight distributions indicated that the onset of non-Newtonian behavior occurred at a much higher shear rate for narrow-distribution polydimethylsiloxanes than for polydisperse polydimethylsiloxanes. A plot of reduced viscosity versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \eta _0 {M \mathord{\left/ {\vphantom {M T}} \right. \kern-\nulldelimiterspace} T} $\end{document} gave two experimental master curves, one for polymer of narrow distribution and the other for polydisperse polymer. The experimental master curve obtained from the narrow-distribution polymer was found to fit the theoretical master curve derived from Graessley's entanglement theory. The viscosity–molecular weight relationship for the higher molecular weight polydimethylsiloxanes was found to be the same for both hydroxydimethylsilyl- and trimethylsilyl-endblocked polymers. However, at low molecular weight, the viscosity–molecular weight curve deviated from linearity because of the association of polydimethylsiloxanols, which apparently is not significant at higher molecular weights. The critical molecular weight of entanglement, M_c, was found to be about 30,000.     

Rheology of binary colloidal structures assembled via specific biological cross-linking

The selectivity and range of energies offered by specific biological interactions serve as valuable tools for engineering the assembly of colloidal particles into novel materials. In this investigation, high affinity biological interactions between biotin-coated "A" particles (RA = 0.475 microm) and streptavidin-coated "B" particles (RB = 2.75 microm) drive the self-assembly of a series of binary colloidal structures, from colloidal micelles (a large B particle coated by smaller A particles) to elongated chain microstructures (alternating A and B particles), as the relative number of small (A) to large (B) particles (2 < or = NA/NB < or = 200) is decreased at a low total volume fraction (10(-4) < or = phiT < or = 10(-3)). At a significantly higher total volume fraction (phiT > or = 10(-1)) and a low number ratio (NA/NB = 2), the rheological behavior of volume-filling particle networks connected by streptavidin-biotin bonds is characterized. The apparent viscosity (eta) as a function of the shear rate gamma, measured for networks at phiT = 0.1 and 0.2, exhibits shear-rate-dependent flow behavior, and both the apparent viscosity and the extent of shear thinning increase upon an increase of a factor of 2 in the total volume fraction. Micrographs taken before and after shearing show a structural breakdown of the flocculated binary particle network into smaller flocs, and ultimately a fluidlike suspension, with increasing shear rate. Rheological measurements provide further proof that suspension microstructure is governed by specific biomolecular interactions, as control experiments in which the streptavidin molecules on particles were blocked displayed Newtonian flow behavior. This investigation represents the first attempt at measuring the rheology of colloidal suspensions where assembly is driven by biomolecular cross-linking.     

Transport Properties of Monatomic Insulating Liquids and Liquid Alkali Metals from a Cage Model

A cage model is used to calculate the shear viscosity m s and the thermal conductivity s for insulating monatomic liquids and for liquid alkali metals. Three empirical laws: (i) $ \eta_s \, \propto \, (1/\sqrt T ) $ for liquid alkalis; (ii) s / m s ～ constant for Rb and Cs respectively; (iii) $ ({\gamma / {\eta _s }})\sim \sqrt {{{k_B T_m } / M}} $ for liquid alkalis at the melting temperature T m , where n is the surface tension and M the ionic mass, are naturally explained.     

Construction of [(eta5-C5Me5)WS3Cu3]-based supramolecular compounds from preformed incomplete cubane-like clusters [PPh4][(eta5-C5Me5)WS3(CuX)3] (X = CN, Br)

Approaches to the assembly of (eta5-C5Me5)WS3Cu3-based supramolecular compounds from two preformed incomplete cubane-like clusters [PPh4][(eta5-C5Me5)WS3(CuX)3] (X = CN, 1a; X = Br, 1b) have been investigated. Treatment of 1a with LiBr/1,4-pyrazine (1,4-pyz), pyridine (py), LiCl/py, or 4,4'-bipyridine (4,4'-bipy) and treatment of 1b with 4,4'-bipy gave rise to a new set of W/Cu/S cluster-based compounds, [Li[((eta5-C5Me5)WS3Cu3(mu3-Br))2(mu-CN)3].C6H6]infinity (2), [(eta5-C5Me5)WS3Cu3(mu-CN)2(py)]infinity (3), [[PPh4][(eta5-C5Me5)WS3Cu3(mu3-Cl)(mu-CN)(CN)].py]infinity (4), [PPh4]2[(eta5-C5Me5)WS3Cu3(CN)2]2(mu-CN)2.(4,4'-bipy) (5), and [[(eta5-C5Me5)WS3Cu3Br(mu-Br)(4,4'-bipy)].Et2O]infinity (6). The structures of 2-6 have been characterized by elemental analysis, IR spectra, and single-crystal X-ray crystallography. Compound 2 displays a 1D ladder-shaped chain structure built of square-like [[(eta5-C5Me5)WS3Cu3(mu3-Br)(mu-CN)]4](mu-CN)2(2-) anions via two pairs of Cu-mu-CN-Cu bridges. Compound 3 consists of a single 3D diamond-like network in which each (eta5-C5Me5)WS3Cu3 unit, serving as a tetrahedral node, interconnects with four other nearby units through Cu-mu-CN-Cu bridges. Compound 4 contains a 1D zigzag chain array made of cubane-like [(eta5-C5Me5)WS3Cu3(mu3-Cl)(mu-CN)(CN)]- anions linked by a couple of Cu-mu-CN-Cu bridges. Compound 5 contains a dimeric structure in which the two incomplete cubane-like [(eta5-C5Me5)WS3(CuCN)2(mu-CN)]- anions are strongly held together via a pair of Cu-mu-CN-Cu bridges. Compound 6 contains a 2D brick-wall layer structure in which dimers of [(eta5-C5Me5)WS3Cu3Br(4,4'-bipy)]2 are interconnected via four Cu-mu-Br-Cu bridges. The successful construction of (eta5-C5Me5)WS3Cu3-based supramolecular compounds 2-6 from the geometry-fixed clusters 1a and 1b may expand the scope of the rational design and construction of cluster-based supramolecular assemblies.     

Wormlike micelles in mixed amino acid-based anionic/nonionic surfactant systems

We present the formation of viscoelastic wormlike micelles in mixed amino acid-based anionic and nonionic surfactants in aqueous systems in the absence of salt. N-Dodecylglutamic acid (designated as LAD) has a higher Krafft temperature; however, on neutralization with alkaline amino acid l-lysine, it forms micelles and the solution behaves like a Newtonian fluid at 25 degrees C. Addition of tri(oxyethylene) monododecyl ether (C(12)EO(3)) and tri(oxyethylene) monotetradecyl ether (C(14)EO(3)) to the dilute aqueous solution of the LAD-lysine induces one-dimensional micellar growth. With increasing C(12)EO(3) or C(14)EO(3) concentration, the solution viscosity increases gradually, but after a certain concentration, the elongated micelles entangle forming a rigid network of wormlike micelles and the solution viscosity increases tremendously. Thus formed wormlike micelles show a viscoelastic character and follow the Maxwell model. Tri(oxyethylene) monohexadecyl ether (C(16)EO(3)), on the other hand, could not form wormlike micelles, although the solution viscosity increases too. The micelles become elongated; however, they do not appear to form a rigid network of wormlike micelles in the case of C(16)EO(3). Rheological measurements have shown that zero shear viscosity (eta(0)) increases with the C(12)EO(3) concentration gradually at first and then sharply, and finally decreases before phase separation. However, no such maximum in the eta(0) plot is observed with the C(14)EO(3). The eta(0) increases monotonously with the C(14)EO(3) concentration till phase separation. In studies of the effect of temperature on the wormlike micellar behavior it has been found that the eta(0) decays exponentially with temperature, following an Arrehenius behavior and at sufficiently higher temperatures the solutions follow a Newtonian behavior. The flow activation energy calculated from the slope of log eta(0) versus 1/T plot is very close to the value reported for typical wormlike micelles. Finally, we also present the effect of neutralization degree of lysine on the rheology and phase behavior. The formation of wormlike micelles is confirmed by the Maxwell model fit to the experimental rheological data and by Cole-Cole plots.     

Effect of finite size on cooperativity and rates of protein folding

We analyze the dependence of cooperativity of the thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N, using lattice models with side chains, off-lattice Go models, and the available experimental data. A dimensionless measure of cooperativity, Omega(c) (0 < Omega(c) < infinity), scales as Omega(c) approximately N(zeta). The results of simulations and the analysis of experimental data further confirm the earlier prediction that zeta is universal with zeta = 1 + gamma, where exponent gamma characterizes the susceptibility of a self-avoiding walk. This finding suggests that the structural characteristics in the denaturated state are manifested in the folding cooperativity at the transition temperature. The folding rates k(F) for the Go models and a dataset of 69 proteins can be fit using k(F) = k(F)0 exp(-cN(beta)). Both beta = 1/2 and 2/3 provide a good fit of the data. We find that k(F) = k(F)0 exp(-cN(1/2)), with the average (over the dataset of proteins) k(F)0 approximately (0.2 micros)(-1) and c approximately 1.1, can be used to estimate folding rates to within an order of magnitude in most cases. The minimal models give identical N dependence with c approximately 1. The prefactor for off-lattice Go models is nearly 4 orders of magnitude larger than the experimental value.     

Rheology of a pyramidal liquid crystal

We have measured the shear elastic modulus and the viscosity values of a pyramidal liquid crystal both normal and parallel to the columnar axis. It was observed that above frequencies of 50Hz, the sample behaves as a Maxwell solid characterized by constant G and eta values. The shear modulus is in the range of 106-107 N m-2, typical for rubbers and polystyrene foams. The viscosity values are in the range of 103-104 Pas, comparable to polymer melts. The observations can be qualitatively explained by temporary entanglements between the side chains of the bowl-shaped molecules, as observed by previous X-ray studies.