Matthew E. Briggs

Optical measurement of the Soret coefficient and the diffusion coefficient of liquid mixtures

A temperature gradient in a liquid mixture causes a concentration gradient through the Soret effect. We have developed an instrument to measure the Soret effect by observing the bending of a laser beam propagating horizontally through the liquid mixture subjected to a temperature gradient in the vertical direction. Our design of the liquid cell, with a long path length and controlled temperature uniformity, enables us to measure Soret coefficients with an accuracy of 1–3 %, higher than that obtained by previous investigators. In addition, by measuring the dynamic response of the beam deflection after imposition of the temperature gradient, we can also determine the mutual diffusion coefficient. We have applied the technique to mixtures of toluene and n‐hexane over the temperature range 5–45 °C and to mixtures of ethanol and water at 25 °C. We have verified that the measured value of the Soret coefficient is independent of the magnitude of the temperature gradient imposed up to 14 K/cm. The Soret coefficie...

The susceptibility critical exponent for a nonaqueous ionic binary mixture near a consolute point

We report turbidity measurements of a nonaqueous ionic solution of triethyl n‐hexylammonium triethyl n‐hexylboride in diphenyl ether. A classical susceptibility critical exponent γ=1.01±0.01 is obtained over the reduced temperature range 10−4≤ t≤10−1. The best fits of the sample transmission had a standard deviation of 0.39% over this range. Ising and spherical model critical exponents are firmly excluded. The correlation length amplitude ξ0 from fitting is 1.0±0.2 nm which is much larger than values found in neutral fluids and some aqueous binary mixtures.

Experimental evidence for microscopic chaos

Many macroscopic dynamical phenomena, for example in hydrodynamics and oscillatory chemical reactions, have been observed to display erratic or random time evolution, in spite of the deterministic character of their dynamics—a phenomenon known as macroscopic chaos. On the other hand, it has been long supposed that the existence of chaotic behaviour in the microscopic motions of atoms and molecules in fluids or solids is responsible for their equilibrium and non-equilibrium properties. But this hypothesis of microscopic chaos has never been verified experimentally. Chaotic behaviour of a system is characterized by the existence of positive Lyapunov exponents, which determine the rate of exponential separation of very close trajectories in the phase space of the system. Positive Lyapunov exponents indicate that the microscopic dynamics of the system are very sensitive to its initial state, which, in turn, indicates that the dynamics are chaotic; a small change in initial conditions will lead to a large change in the microscopic motion. Here we report direct experimental evidence for microscopic chaos in fluid systems, obtained by the observation of brownian motion of a colloidal particle suspended in water. We find a positive lower bound on the sum of positive Lyapunov exponents of the system composed of the brownian particle and the surrounding fluid.

THERMAL AND MASS DIFFUSION IN A SEMIDILUTE GOOD SOLVENT-POLYMER SOLUTION

The Soret coefficient ST and collective (mass) diffusion coefficient Dc of polystyrene dissolved in the good-solvent toluene has been measured over a range of concentrations and molecular masses with an optical beam-deflection method. Our measurements indicate that ST scales inversely with the polymer translational diffusion coefficient in dilute solutions, exhibits a power-law scaling with polymer concentration, and an independence of polymer molecular mass in semidilute solutions. These findings are consistent with the known scaling of 1/Dc in dilute and semidilute polymer solutions, the relative insensitivity of the thermal-diffusion coefficient Dth of polystyrene in toluene to polymer concentration, and the relation ST=Dth/Dc from irreversible thermodynamics. We are able to represent our ST and Dc data by theoretically motivated reduced-concentration master curves, but the concentration-molecular mass scaling variables are found to be different for each transport property, a result contrary to theoret...

Discrepancies in turbidity measurements in the ionic binary mixture triethyl n-hexyl ammonium triethyl n-hexyl boride in diphenyl ether

We have repeated and extended turbidity measurements on a new sample of the ionic mixture triethyl n-hexyl ammonium triethyl n-hexyl boride (N2226B2226) in diphenyl ether in a temperature range above its consolute point. Previous measurements on this system by some of us indicated mean-field critical behavior over the range of reduced temperatures 10−4<t<10−1. Our new measurements do not reproduce those reported before. The transmission of the new sample is substantially lower, and the turbidities up to a factor of 3 higher than those of the sample used in the previous work. The correlation-length amplitude is approximately 40% larger than that found for the previous sample. Unlike the earlier results, the new data do not display a substantial range of mean-field critical behavior. In our investigation of this irreproducibility, we have carefully reviewed the earlier experiment, and we report here an effect not previously noted: a time dependence of the turbidity of the earlier sample. It is likely that t...

Tracking a colloidal particle for the measurement of dynamic entropies

The paper describes the apparatus and measurement procedure for tracking long time trajectories of a single colloidal particle undergoing Brownian motion in water. The bulk motion obeys the Einstein–Stokes formulation, while sedimented motion is slowed by an additional drag known as the wall-drag effect. The sedimented particle trajectory is long enough to show diffusive motion spanning four decades in time. We describe the sample preparation, tracking routine, data-acquisition and noise. The experiment shows that Brownian motion exhibits a positive dynamic entropy consistent with microscopic chaos. The theoretical relevance of the experimental results is discussed.

Photothermal deflection in a supercritical fluid

Photothermal deflection is among the most sensitive techniques available for the measurement of small, localized heating, such as that from the absorption of a focused laser beam in the bulk or surface of a material. A thin optical probe beam is deflected by the refractive-index gradients arising from the heating, and the size of the deflection provides the measure of the heating. We describe the use of a critical fluid to enhance the sensitivity of the technique by at least 103. The diverging coefficient of thermal expansion of a pure fluid near the gas-liquid critical point gives this dramatic enhancement when used as a sensing fluid. With sensitivity calculations and measurements in supercritical xenon,Tc≈16.7‡C, we show that the noise floor of our apparatus when used for surface absorption measurements corresponds to a fractional power absorbed ofPabsorbed/Pincident=10−10, while the noise floor for bulk measurements corresponds to an absorption coefficientα=10−13 cm−1. We report the first measurements of the surface absorption of superpolished surfaces of sapphire and fused quartz,Pa/Pi≈2×10−5, and the first measurements of the bulk absorption in xenon,α≈2×10−6 cm−1. We also show how the present work fits into the current status of absorption measurement techniques and describe the effects of the peculiar properties of critical fluids on the execution of photothermal deflection measurements.

Note: Simultaneous measurement of transverse speed and axial velocity from a single optical beam

A method is introduced for simultaneously measuring transverse speed and axial velocity using a single optical beam and a standard photon Doppler velocimetry (PDV) sensing architecture. This result is of particular interest given the recent, widespread use of PDV and the fact that optical velocimetry has thus far been limited to measuring motion in one dimension per probe. Further, this result demonstrates that both axial velocity data and transverse speed data (at least qualitative) may be obtained entirely through signal analysis; not requiring hardware modification. This result is immediately relevant to analyses of existing PDV data and to future efforts in high-speed optical velocimetry.

reply to: Statistical mechanics: Microscopicchaos from brownian motion?

We presented experimental evidence for the existence of microscopic chaos in the mesoscopic motion of a brownian particle in solution. We used standard techniques to analyse long trajectories of a brownian particle and inferred a dynamical entropy from this analysis. We showed that this dynamical entropy can be accessed experimentally by measuring multiple-time correlation functions for the particle. The dynamical entropy was then used to provide a positive lower bound for the sum of the Lyapunov exponents for the underlying deterministic dynamical system composed of the fluid and brownian particles. We concluded that the positive dynamical entropy, obtained experimen-tally, was evidence for the existence of positive Lyapunov exponents in the underlying dynamics, and hence for the existence of microscopic chaos generated by a dynamical instability.

Measurement of the temperature coefficient of ratio transformers

We have measured the temperature coefficient of the output of several ratio transformers at ratios near 0.500 000 using an ac bridge and a dual‐phase, lock‐in amplifier. The two orthogonal output components were each resolved to ±1 ppb of the bridge drive signal. The results for three commercial ratio transformers (an ESI DT72A, a Gertsch RT‐1665u, and an Eaton PRT‐10C) between 20 and 50 °C range from 0.5 to 100 ppb/K for the signal component in phase with the bridge drive, and from 4 to 300 ppb/K for the quadrature component.