Characterization of thermally sensitive interactions in aqueous mixtures of hydrophobically modified hydroxyethylcellulose and cyclodextrins

Effects of beta-cyclodextrin (beta-CD) or hydroxypropyl-beta-cyclodextrin (HP-beta-CD) addition and temperature on thermodynamic, rheological, and structural features of semidilute solutions of hydroxyethylcellulose (HEC) and its hydrophobically modified analogue (HM-HEC) are reported. Differential scanning calorimetric (DSC) measurements revealed a thermally induced crystal melting transition of beta-CD at high concentrations in solutions of HEC and HM-HEC. No transition with HP-beta-CD was observed in aqueous solution. Viscosity results indicated that at a cosolute concentration of 2 mm, the beta-CD units are threaded onto hydrophobic tails of HM-HEC (C16 groups) to form columnar structures. This arrangement is more effective in the encapsulation of the hydrophobic chains than the monomer hydrophobic deactivation accomplished by the HP-beta-CD units. At cosolute concentrations above 8 mm, no further decoupling of the hydrophobic interactions occurs for any of the cosolutes. Small-angle neutron scattering (SANS) experiments on HM-HEC/beta-CD mixtures suggest that the large-scale association structures in HM-HEC/D(2)O solutions are reduced upon addition of beta-CD, and an interesting temperature effect is observed at 2 mm beta-CD addition. At high beta-CD concentrations and low temperatures, the formation of large beta-CD clusters or crystallites generates cross-links in the HEC and HM-HEC networks, resulting in a viscosity enhancement of several orders of magnitude. This strong temperature effect is not reflected in the structural features probed by SANS.     

Frequency dependence of the shear moduli of spectrin studied using a multiple lumped resonator viscoelastometer

The frequency dependence (119-7860 Hz) of the storage and loss shear moduli, G' and G', of human erythrocyte spectrin dimer crude solutions at 22.5 degrees C has been measured using a Birnboim-Schrag multiple lumped resonator viscoelastometer. The measurements were carried out on solutions of ionic strength 1 mM containing 1.1-3.7 mg ml-1 spectrin. This corresponds to the terminal zone for G' and G'. Analysis of the data using the standard theory of hybrid relaxation spectra yields a relaxation time of 22.5 +/- 1 microseconds. The pure spectrin dimer relaxation time is estimated to be 16 +/- 3 microseconds. This result suggests that at an ionic strength of 1 mM, the spectrin dimers are extended and that the main relaxation process is simple end-over-end rotation.     

Use of Cartesian Rotation Vectors in Brownian Dynamics Algorithms: Theory and Simulation Results

Summary: We have shown that the components of Cartesian rotation vectors can be used successfully as generalized coordinates describing angular orientation in Brownian dynamics simulations of non‐spherical nanoparticles. For this particular choice of generalized coordinates, we rigorously derived the conformation‐space diffusion equations from kinetic theory for both free nanoparticles and nanoparticles interconnected by springs or holonomic constraints into polymer chains. The equivalent stochastic differential equations were used as a foundation for the Brownian dynamics algorithms. These new algorithms contain singularities only for points in the conformation‐space where both the probability density and its first coordinate derivative equal zero (weak singularities). In addition, the coordinate values after a single Brownian dynamics time step are throughout the conformation‐space equal to the old coordinate values plus the respective increments. For some parts of the conformation‐space these features represent a major improvement compared to the situation when Eulerian angles describe rotational dynamics. The presented simulation results of the equilibrium probability density for free nanoparticles are in perfect agreement with the results from kinetic theory.

Simulation of p^(eq)(Φ) for free nanoparticles.     

Dynamics of coaxial torsional resonators consisting or segments with different radii,material properties and surrounding media

High-Q torsional resonators constitute the most sensitive transducers for high frequency dynamic viscoelastic measurements of dilute polymer solutions. Most such resonators described in the literature are segmented. Because of the need for torque and torsional displacement transducers the Q-value of the individual segments most often differ, but normally all segments have the same radius.A detailed analysis of the dynamics of such resonators when both the radii, material properties and surrounding media may be different for each segment, is presented. For resonators where all segment lengths equal an integer multiple of a quarter of the torsional wavelength, we find that the Q-value of the resonator as a whole is mainly determined by the Q-value of the segment with the smallest radius. We further find that reduction of the radius of the segment surrounded by polymer solution results in a stronger mechanical coupling between the resonator as a whole and the polymer solution. These findings suggest that the segment radii are important optimization parameters of segmented torsional resonators used to measure the high frequency dynamic viscoelastic properties of e.g. polymer solutions.     

Characteristic mechanical impedance of rheometers with axial symmetry. A theoretical and numerical analysis

The strain wave field generated in a linear viscoelastic medium confined between two infinitely large parallel planar surfaces, one fixed and the other oscillating sinusoidally in its own plane, has been well accounted for (Schrag, 1977). Here, we describe the strain wave field generated between a cylinder and a coaxial surrounding tube, both infinitely long. The tube or the cylinder remains stationary while the complementary component undergoes sinusoidal angular displacements around the common symmetry axis. This geometry is frequently used in dynamic rheometers. Both exact analytic expressions for the characteristic mechanical impedance and series expansions valid close to gap loading or surface loading conditions are provided. The exact analysis is valid for arbitrary gap width, cylinder radius, and linear viscoelastic properties of the medium within the rheometer gap. We also show how standard, modern desktop computers can be used to rapidly obtain accurate numerical values of the characteristic mechanical impedance of rheometers with axial symmetry using the exact analytic expressions.     

An automated high-pressure,high-temperature,low-frequency viscometer

A computerized apparatus for the measurement of low shear rate viscosity on polymer solutions at elevated pressure and temperature is described. The pressure is variable from 1 bar to 400 bar with an accuracy of ±5 bar. The temperature is variable from 0° to 100°C with an accuracy of ±0.3 K. The instrument is operated in a free-relaxation mode in which the decay of oscillation of the torsion pendulum after an initial displacement is recorded and used to compute the viscosity of the sample. The measurements are performed according to the contents of a user-specified control file, and the oscillation data are stored digitally and later analyzed for parameter estimation. The instrument operates in the very-low frequency range (0.03 to 0.25 Hz) and the accuracy of the measured viscosity is ±0.03 x 10^–3 Ns/m2.     

Transient molecular electro-optics Cartesian rotation vector versus Eulerian angles

Comparing the Euler angles, the classical choice of generalized coordinates describing the three rotational degrees of freedom of a rigid body, and the Cartesian rotation vector, we show that they both have their advantages and disadvantages in kinetic theory and Brownian dynamics analysis of molecular electro-optics. The Eulerian angles often yield relatively simple, yet singular, equations of motion, while their counterparts expressed in terms of Cartesian rotation vector are non-singular but more complex. In a special case, we show that the generalized force associated with the Cartesian rotation vector equals the torque. In addition, we introduce a new graphical approach to qualitatively track how changes in the Eulerian angles affect the Cartesian rotation vector.     

Singularity‐Free Brownian Dynamics Analyses of Rotational Dynamics: Non‐Spherical Nanoparticles in Solution

Summary: From kinetic theory we have rigorously derived singularity‐free Brownian dynamics analyses of nanoparticle rotational dynamics. The rigid non‐spherical nanoparticles incorporate all three rotational degrees of freedom. This was achieved by using the components of Cartesian rotation vectors as the generalized coordinates describing angular orientation. The new results constitute an important advance compared to the situation when Eulerian angles specify angular orientation. Our finding eliminates one of the main longstanding obstacles to detailed studies of nanoparticle rotational dynamics in the diffusion time domain. The described formalism is applicable to a wide range of nanoparticle systems including liquid crystals, biopolymers, and colloids.