Non-critical Mixtures Research Articles

Phase behaviour of mixtures of polyethylene glycol and polypropylene glycol: Influence of hydrogen bond clusters on critical composition fluctuations

The critical behaviour of a binary polymer blend of polyethylene glycol 600 (PEG600) and polypropylene glycol 1000 (PPG1000) was investigated by static and dynamic light scattering. The measurements were carried out in the homogeneous one-phase region (above the critical temperature Tc) and in the two-phase region in both coexisting phases. Additionally to the critical composition (yPPG = 0.46, yPPG: mass fraction of PPG), a mixture of non-critical composition (yPPG = 0.365) was investigated in the one- and two-phase region. From the light scattering measurements, the critical exponents and the amplitudes of the correlation length ξ and the mutual diffusion coefficient D were determined. For the critical mixture the results for the critical exponents and amplitudes of ξ in the one- and two-phase regions are in accordance with the predictions of the 3d-Ising model. The measurements of D in the two-phase region in a wider temperature range gave an indication for a crossover from Ising to mean field behaviour. Since the low molar mass of the PEG and PEG oligomers would lead to Ising behaviour in the composition and temperature range studied, this crossover has to be attributed to an increase of the effective molar mass caused by clusters built by intermolecular hydrogen bonds. The assumption of these clusters is supported by static light scattering and the phase diagram. The data of the non-critical mixture could be described in the frame of the pseudospinodal concept. The results for the non-critical mixture support the interpretation of the data of the critical mixture.

Composition fluctuations in a non-critical binary polymer blend studied by ultrasonic and light scattering experiments

A non-critical mixture of polyethylene glycol (PEG600, M = 600 g mol−1) and polypropylene glycol (PPG1000, M = 1000 g mol−1) was investigated by ultrasonic and light scattering experiments in the one-phase region. The mass fraction of polypropylene glycol in the non-critical mixture was yPPG = 0.365. The explored temperature and frequency range of the ultrasonic experiment was 0.1 ≤ T − TP ≤ 17.3 K and 0.4 MHz ≤ f ≤ 30 MHz (TP: phase separation temperature). The frequency dependence of the ultrasonic attenuation of the non-critical mixture shows a relaxation behaviour typical for composition fluctuations. The data can be analysed by the dynamic scaling theory of Bhattacharjee and Ferrell which was formally extended to the non-critical case using the concept of a pseudospinodal temperature. The characteristic time scale of the concentration fluctuations is described by a frequency ωD = 2D/ξ2 where D is the mutual diffusion coefficient and ξ is the correlation length. In the frame of the pseudospinodal concept the temperature dependence of the characteristic frequency is expressed by ωD = ω0εzν with ε = (T − TPS)/TPS (TPS: pseudospinodal temperature, ε: reduced temperature, ω0: critical amplitude, zν: critical exponent). The temperature dependence of the frequency ωD was determined by the ultrasonic spectra. From this data, using mean field exponents, a value of ω0 = 9.4 MHz was estimated which is comparable to that of the critical mixture. The description of the ultrasonic data with mean field exponents is justified by the results of dynamic light scattering.

Broadening of vibrational Raman spectra by concentration fluctuations : A molecular dynamics survey

Molecular dynamics calculations have been performed on model systems for nitrogen and mixtures of nitrogen with other compounds at high pressure and at ambient temperatures. From these simulations the line shape of the Raman Q-branch was calculated. A short description of the applied methods is given. Our aim is to investigate whether line broadening, experimentally observed in mixtures, may be at least partially caused by critical fluctuations, as appeared to be the case in nitrogen-helium mixtures. For this purpose it is necessary to investigate first the behavior of a noncritical mixture. We analyzed extensively the results of the mixture of nitrogen in neon at 2.4 GPa and 296 K, which is far away from a critical state. In this system a maximum in the linewidth is seen at equal volume fractions, experimentally as well as in simulations. The details revealed by the simulations allow a comparison with existing models, such as that given by Knapp and Fischer. It is seen that assumptions made in that theory are in clear contradiction with the findings of the simulations.

Dynamic scaling of the structure function for spinodal decomposition in critical and non-critical mixtures of poly(vinyl acetate)-poly(methyl methacrylate)

The dynamics of phase separation in a binary polymer blend of poly(vinyl acetate) with poly(methyl methacrylate) was investigated by using a time-resolved light-scattering technique. In the later stages of spinodal decomposition, a simple dynamic scaling law was found for the scattering function S(q, t)(S(q, t) ∼ I(q, t)):S(q, t)q −3 m S ̃ ( q q m ) . The scaling function determine experimentally was in good agreement with that predicted by Furukawa, S ̃ (X) ∼ X 2 (3 + X 8) for critical concentration, and approximately in agreement with that predicted by Furukawa, S ̃ (X) ∼ X 2 (3 + X 6) for non-critical mixtures. The light-scattering invariant shows that the later stages of the spinodal decomposition were undergoing domain ripening.

Kinetics of liquid–liquid phase separation in a binary mixture with miscibility gap: Study of noncritical mixtures of 2,6-dimethyl pyridine/water near the lower critical point

Temperature jump experiments with a characteristic heating time of 0.5 ms are used to study the kinetics of liquid/liquid phase separation in noncritical mixtures of 2,6-dimethyl pyridine and water (‖x-xc‖>0.02; x, mole fraction of 2,6-dimethyl pyridine; xc, critical composition) as functions of composition and supersaturation. The response of the system to a temperature jump is monitored by measuring the intensity of light scattered by the sample at different scattering angles Θ (30°<Θ<90°) as a function of time (up to several seconds). Starting from a level of constant intensity reached with a time constant in the range of milliseconds after a temperature jump the scattered intensity increases with time. For small supersaturations consecutive maxima and minima of scattered intensity develop. They reflect diffusion limited growth of droplets of the emerging second liquid phase (linear relationship between the square of the radius of growing droplets and time). The growth rate increases with increasing supersaturation. Practically no nucleation barrier is found for the onset of growth of droplets for small supersaturations and compositions (‖x−xc‖>0.03). The number density N of growing droplets is obtained from simultaneous measurements of scattered intensity and turbidity. For small supersaturations N is independent of time but changes with supersaturation in a characteristic way (classical nucleation model). There exists an upper limit of overheating δT* above which the number density N increases drastically. The ratio (δT*/ΔTc,p) is independent of the reduced temperature ε̃ of phase separation (ε̃=ΔTc,p/Tc; ΔTc,p=Tc−Tp; Tc, critical temperature, Tp, temperature of phase separation). This is expected for mixtures of noncritical composition. The theory proposed by Langer and Schwartz to treat nucleation and growth of droplets in metastable near critical fluids does not describe the phenomena observed in this study. The composition of the samples used (‖x−xc‖>0.02) appears to be too far away from the critical.

Anomalies of linewidth and intensity in the reorientation spectra of a critical mixture

The critical behavior of the depolarized Rayleigh spectrum in the system nitrobenzene-$n$-hexane has not been previously accurately assessed because in usual Fabry-P\'erot experiments the multiple-scattering contribution completely overwhelms the spectrum within a few degrees of the critical temperature ${T}_{c}$. By using a high-performance double-pass Fabry-P\'erot interferometer, we have been able to obtain accurate measurements of both linewidth and intensity, from 50\ifmmode^\circ\else\textdegree\fi{}C to temperatures as close as 0.026\ifmmode^\circ\else\textdegree\fi{}C to ${T}_{c}$. Two lines due to nitrobenzene molecules in solution are visible. The first line (1) is intense and narrow, while the second line (2) is weak and broad. The spectral intensity of (2) is about ${10}^{\ensuremath{-}2}$ times that of (1). The linewidth of (1) is seen to behave as the inverse shear viscosity, with a critical divergence with exponent $Y\ensuremath{\approx}0.04$. The intensity of (1) exhibits a power-law divergence with exponent $\ensuremath{\Omega}\ensuremath{\approx}0.2$. These results are compared with data obtained in pure nitrobenzene and $n$-hexane, and in noncritical mixtures of nitrobenzene.