Dynamics of critical fluctuations in polymer solutions

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξ_s) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient D_c of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), D_c = k_BT/6πηξ_s, where ξ_s is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient D_c(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

Cononsolvency of the responsive polymer poly(N-isopropylacrylamide) in water/methanol mixtures: a dynamic light scattering study of the effect of pressure on the collective dynamics

The collective dynamics of 25 wt% poly(N-isopropylacrylamide) (PNIPAM) solutions in water or an 80:20 v/v water/methanol mixture are investigated in the one-phase region in dependence on pressure and temperature using dynamic light scattering. Throughout, two dynamic modes are observed, the fast one corresponding to the relaxation of the chain segments within the polymer blobs and the slow one to the relaxation of the blobs. A pressure scan in the one-phase region on an aqueous solution at 34.0 °C, i.e., slightly below the maximum of the coexistence line, reveals that the dynamic correlation length of the fast mode increases when the left and the right branch of the coexistence line are approached. Thus, the chains are rather swollen far away from the coexistence line, but contracted near the phase transition. Temperature scans of solutions in neat H2O or in H2O/CD3OD at 0.1, 130, and 200 MPa reveal that the dynamic correlation length of the fast mode shows critical behavior. However, the critical exponents are significantly larger than the value predicted by mean-field theory for the static correlation length, ν = 0.5, and the exponent is significantly larger for the solution in the H2O/CD3OD mixture than in neat H2O.

Phase transitions affected by natural and forceful molecular interconversion

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g., the equilibrium interconversion of enantiomers) or forcefully (e.g., via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we phenomenologically generalize the Cahn–Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.

Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed Solvents

We present results from an experimental dynamic light-scattering study of poly(ethylene oxide) (PEO) in both a pure solvent (water) and a mixed solvent (tert-butanol + water). The concentration dependence of the diffusive relaxation of the PEO molecules is found to be typical of polymers in a good solvent. However, the mesoscopic diffusive behavior of PEO in the mixed solvent is very different, indicating an initial collapse and subsequent reswelling of PEO caused by co-nonsolvency. Furthermore, in the solutions of PEO with very large molecular weights, we found additional hydrodynamic modes indicating the presence of PEO clusters and aggregates similar to those found by some other investigators.

Direct imaging of long-range concentration fluctuations in a ternary mixture

We used a direct imaging technique to investigate concentration fluctuations enhanced by thermal fluctuations in a ternary mixture of methanol (Me), cyclohexane (C), and partially deuterated cyclohexane (C*) within 1mK above its consolute critical point. The experimental setup used a low-coherence white-light source and a red filter to visualize fluctuation images. The red-filtered images were analyzed off-line using a differential dynamic microscopy algorithm that allowed us to determine the correlation time, τ, of concentration fluctuations. From τ, we determined the mutual mass diffusion coefficient, D, very near and above the critical point of Me-CC* mixtures. We also numerically estimated both the background and critical contributions to D and compared the results against our experimental values determined from τ. We found that the experimental value of D is close to the prediction based on Stokes-Einstein diffusion law with Kawasaki's correction.

Does shear viscosity relaxation control the dynamics of critical fluctuations in polystyrene-cyclohexane?

Between 20 and 90 MHz frequency-dependent shear viscosities of the polystyrene-cyclohexane mixture of critical composition have been measured at polymer molar weight Mw = 30,000. The viscosity data reveal dispersion, in conformity with relaxation characteristics in the non-critical background contributions to the ultrasonic attenuation, i.e., in the longitudinal viscosity of the critical system. The dispersion behavior is discussed with a view to its effect on the critical dynamics of the liquid near its consolute point. Attention is especially given to the relaxation rates of fluctuations of that system. The data as resulting from ultrasonic attenuation spectroscopy on the one hand and from quasi-elastic light scattering and viscosity measurements on the other hand differ near the critical temperature. It is concluded that likely an additional dispersion exists in the shear viscosity at frequencies below the presently available frequency range of measurement.

Broadband ultrasonic spectrometry of polystyrene-cyclohexane critical mixtures

Mutual diffusion coefficients, shear viscosities, and broadband ultrasonic attenuation spectra in the frequency range 100 kHz to 300 MHz have been measured for solutions of polystyrene in cyclohexane at two degrees of polymerization N and various temperatures near the critical. The exponent y(η) in the power law representation of the critical part in the viscosity deviates substantially from the universal value y(η) = 0.0435: y(η) = 0.028 (N = 288) and y(η) = 0.014 (N = 6242). Also, the adiabatic coupling constant g and the amplitudes ξ(0) and Γ(0) in the power laws of the correlation length and the relaxation rate of fluctuations, respectively, depend on N. This is especially obvious with the relaxation rates, for which Γ(0) = 5.8×10(9) at N = 288 and Γ(0) = 6.1×10(7) with the larger polymer results. A noteworthy feature is the difference between the relaxation rates from the diffusion coefficients and shear viscosities on the one hand and from the ultrasonic spectra on the other. Near the critical temperatures the latter Γ values deviate from power law behavior, indicating a coupling between the concentration fluctuations and structural isomerizations of the polymers.

Critical behavior of nanoparticle-containing binary liquid mixtures

Simultaneous measurements of small-angle neutron scattering and dynamic light scattering have been performed on a binary mixture of partially miscible liquids, 2,6-dimethylpyridine and water. At critical composition the temperature dependence of the correlation length of fluctuations in composition is strongly affected by the addition of nanoparticles of a triblock copolymer polyethylene oxide-polypropylene oxide-polyethylene oxide. A crossover between Ising-type critical behavior and mean-field critical behavior is observed when the correlation length is equal to the size of the nanoparticles.

Thermal conductivity of supercooled water

The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.

Pressure assisted stabilization of biocatalysts at elevated temperatures: characterization by dynamic light scattering

The effect of pressure, at elevated temperatures, is reported on the activity and stability of a thermophilic endo-β-glucanase from the filamentous fungus Talaromyces emersonii. The production of reduced sugars after treatment at different temperatures and pressures is used as a measure of the activity and stability of the enzyme. The activity of the enzyme is maintained to higher temperatures with increasing pressure. For example, the relative activity of endo-β-glucanase decreases to 30% after 4 h at 75°C and 1 bar, whereas it is preserved at 100% after 6 h at 75°C and 230 bar. High-pressure dynamic light scattering is used to characterize the hydrodynamic radius of the enzyme as a function of pressure, temperature, and time. At higher temperature the hydrodynamic radius increases with time, whereas increasing pressure suppresses this effect. Changes in the hydrodynamic radius are correlated with the activity measurements obtained at elevated pressures, since the changes in the hydrodynamic radius indicate structural changes of the enzyme, which cause the deactivation.

Critical behavior of polystyrene-cyclohexane: heat capacity and mass density

At temperatures between 7.5 °C and 20 °C as well as 26 °C and 40 °C we have recorded the densities and specific heat at constant pressure for critical mixtures of polystyrene in cyclohexane. The degrees of polymerization were N=288 (critical temperature T(c)=9.77 °C ) and N=6242 (T(c)=27.56 °C), respectively. In the two-phase regime a series of reproducible events exists in the specific-heat traces, indicating the existence of nonequilibrium intermediate states as likely resulting from an oscillatory instability of droplet formation. In the one-phase region the critical contribution to the heat capacity follows power law with critical exponent α=0.11 compatible with Ising-like criticality. At larger N , however, the critical amplitude of the heat capacity is noticeably smaller than at lower degree of polymerization. This finding may be taken as an indication of different effects from competing mesoscale lengths: the radius of gyration of the polymer and the fluctuation correlation length of the mixture. The density traces reveal marginal deviations from simple linear temperature dependencies. If these deviations are analyzed in terms of critical contributions, different signs in the amplitude result, in conformity with the signs in the pressure dependence of the critical temperature. The absolute values of the amplitudes, however, are substantially larger than predicted from the critical amplitudes of the heat capacities.

Characterization of voltage-gated K+ currents contributing to subthreshold membrane potential oscillations in hippocampal CA1 interneurons

CA1 inhibitory interneurons at the stratum lacunosum-moleculare and radiatum junction (LM/RAD-INs) display subthreshold membrane potential oscillations (MPOs) involving voltage-dependent Na(+) and A-type K(+) currents. LM/RAD-INs also express other voltage-gated K(+) currents, although their properties and role in MPOs remain unclear. Here, we characterized these voltage-gated K(+) currents and investigated their role in MPOs. Using outside-out patch recordings from LM/RAD-IN somata, we distinguished four voltage-gated K(+) currents based on their pharmacology and activation/inactivation properties: a fast delayed rectifier current (I(Kfast)), a slow delayed rectifier current (I(Kslow)), a rapidly inactivating A-type current (I(A)), and a slowly inactivating current (I(D)). Their relative contribution to the total K(+) current was I(A) > I(Kfast) > I(Kslow) = I(D). The presence of I(D) and the relative contributions of K(+) currents in LM/RAD-INs are different from those of other CA1 interneurons, suggesting the presence of differential complement of K(+) currents in subgroups of interneurons. We next determined whether these K(+) currents were sufficient for MPO generation using a single-compartment model of LM/RAD-INs. The model captured the subthreshold voltage dependence of MPOs. Moreover, all K(+) currents were active at subthreshold potentials but I(D), I(A), and the persistent sodium current (I(NaP)) were most active near threshold. Using impedance analysis, we found that I(A) and I(NaP) contribute to MPO generation by modulating peak spectral frequency during MPOs and governing the voltage range over which MPOs occur. Our findings uncover a differential expression of a complement of K(+) channels that underlies intrinsic rhythmic activity in inhibitory interneurons.

Multiscale dynamics of pretransitional fluctuations in the isotropic phase of a lyotropic liquid crystal

Using an improved static and dynamic light-scattering technique, we have observed multiscale relaxation of the pretransitional fluctuations in the isotropic phase of a cromolyn aqueous solution, a lyotropic liquid crystal where rods are formed by aggregates of disklike molecules. We have detected the onset of cromolyn aggregation about 12 degrees C above the transition temperature. The onset is manifested by the emergence of strong scattering due to the fluctuations of local anisotropy and by the split of the diffusion dynamics into two distinctly different modes, one associated with the relatively fast diffusion of monomer-size particles and the other one with the much slower diffusion of the cromolyn aggregates. A third observed dynamic mode is associated with the pretransitional slowing down of fluctuations of the local anisotropy. This mode behaves differently in polarized and depolarized light scattering, due to a coupling between fluctuations of the local-anisotropy and velocity fluctuations.

An introduction to critical points for biophysicists; observations of compositional heterogeneity in lipid membranes

Scaling laws associated with critical points have the power to greatly simplify our description of complex biophysical systems. We first review basic concepts and equations associated with critical phenomena for the general reader. We then apply these concepts to the specific biophysical system of lipid membranes. We recently reported that lipid membranes can contain composition fluctuations that behave in a manner consistent with the two-dimensional Ising universality class. Near the membrane's critical point, these fluctuations are micron-sized, clearly observable by fluorescence microscopy. At higher temperatures, above the critical point, we expect to find submicron fluctuations. In separate work, we have reported that plasma membranes isolated directly from cells exhibit the same Ising behavior as model membranes do. We review other models describing submicron lateral inhomogeneity in membranes, including microemulsions, nanodomains, and mean field critical fluctuations, and we describe experimental tests that may distinguish these models.