X-ray Photon Correlation Spectroscopy of Dynamics in Thermosensitive Gels

Summary : Temperature-sensitive hydrogels undergo a volume phase transition (VPT) when heated above a critical temperature T_c. For the poly(N-isopropyl acrylamide) (PNIPA)-water system, T_c. = 34 °C. Below T_c the gels are transparent and highly swollen. On warming above T_c they promptly turn white and start to deswell. The rate of deswelling, however, can be orders of magnitude slower than that of swelling below T_c. The unstable intermediate structure above T_c, can retain the solvent and conserve the sample volume for may days, even with millimetre-sized samples. Light scattering observations of the internal structure of these gels above T_c are precluded by their strong turbidity. Small angle X-ray scattering measurements (SAXS), on the other hand, are less subject to multiple scattering as X-rays penetrate more easily into the bulk material. Conventional (incoherent) SAXS observations reveal intense scattering from smooth internal water-polymer interfaces with an estimated surface area of about 7 m²/g in the swollen gel. The dynamics in the off-equilibrium high temperature state, investigated by X-ray photon correlation spectroscopy (XPCS), displays a relaxation rate that is linearly proportional to the wavevector q, rather than to q² as in diffusion processes. The physical origin of this relaxation is consistent with jamming, a phenomenon that is common in other disordered systems.     

Electrical conductivity investigation of diluted potassium chloride solutions in binary mixture triethylamine-water near its consolute point

The binary liquid mixture of triethylamine + water (TEA-W) has a lower consolute point at a critical composition of 32.27 mass % triethylamine. Starting at a temperature within the one-phase region, the electrical conductivity of a sample of this mixture with addition of (K⁺, Cl⁻) ions was measured and found to be accurately described by the Vogel-Fulcher-Tammann (VFT) law. Before that, for the pure system, in a temperature range ΔT = T_c − T < 2 °C where T_c is the critical temperature, the electrical conductivity (σ) exhibits a monotonous deviation from the VFT behaviour. This anomaly is finite at T_c. The asymptotic behaviour of the electrical conductivity anomaly is described by a power law t^1−α, where t is the reduced temperature |(T−Tc)/Tc| and α is the critical exponent of the specific heat anomaly at constant pressure. For the electrolyte mixtures, by combining the viscosity and the electrical conductivity data, the value of the computed Walden product has been determined and the salt dissociation degrees as well as the Debye screening length have been estimated.     

Droplet coalescence near liquid/liquid critical points

The state of matter within a fluid layer near a critical point differs profoundly in many aspects from states further removed from the critical point. The interfacial tension tends to vanish, the interface thickens, and long-range concentration fluctuations exist. Because of these effects, critical phenomena have been investigated as possible sources of instability in thin films. Shear-field coalescence studies have been performed between phases of a simple ternary system containing no surfactant as a function of distance from a critical point. The coalescence efficiency was measured as a function of temperature through time dependent photomicrographic analysis of emulsion samples within a shear-field coalescence cell. The apparatus, procedure, and analysis are outlined. No evidence was found for the promotion of coalescence by critical phenomena for values of reduced temperature, T_r = (T − T_c)/T_c, down to 4×10⁻⁴.     

Spinodal decomposition and phase separation kinetics in nanoclay–biopolymer solutions

Intensity of light, I(q,t), scattered from homogeneous aqueous solutions, of nanoclay (Laponite) and protein (gelatin‐A), was studied to monitor the temporal and spatial evolution of the solution into a phase‐separated nanoclay–protein‐rich dense phase, when the sample temperature was quenched below spinodal temperature, T_s (=311 ± 3 K). The zeta potential data revealed that the dense phase comprised charge‐neutralized intermolecular complexes of nanoclay and protein chains of low surface charge. The early stage, t < 500 s, of phase separation could be described adequately through Cahn‐Hilliard theory of spinodal decomposition where the intensity grows exponentially, I(q, t) = I₀ exp.(2R(q)t). The wave vector, q dependence of the growth parameter, R(q) exhibited a maxima independent of time. Corresponding correlation length, 1/q_c = ξ_c was found to be ≈75 ± 5 nm independent of quench depth. In the intermediate regime, anomalous growth described by I(q, t) ～ t^α with α = 0.1 ± 0.02 independent of q was observed. Rheological studies established that there was a propensity of network structures inside the dense phase. Isochronal temperature sweep studies of the dense phase determined the melting temperature, T_m = 312 ± 4 K, which was comparable with the spinodal temperature. The stress‐diffusion coupling prevailing in the dense phase when analyzed in the Doi‐Onuki model yielded a viscoelastic correlation length, ξ_v determined from low‐frequency storage modulus, G ′₀ ≈ k_B T/ξ, which was ξ_v ≈ 35 ± 3 nm indicating 2ξ_v ≈ ξ_c. It is concluded that the early stage of phase separation in this system was sufficiently described by linear Cahn‐Hilliard theory, but the same was not true in the intermediate stage. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 555–565, 2010     

Broadening of electronic spectra at the critical point of a binary polar mixture

It is shown that in the vicinity of the critical point of a binary polar mixture the electronic spectral linewidth increases when approaching the critical point. The linewidth obeys the law of A_o[(T-T_c)/T_c]^?γ, where γ is the universal critical index of dispersion of concentration fluctuations.     

Critical Behavior of the Electrical Conductivity of Concentrated Electrolytes: Ethylammonium Nitrate in n-Octanol Binary Mixture

The electrical conductivity of highly concentrated binary ionic mixtures of ethylammonium nitrate in n-octanol at a critical salt mole fraction x = 0.766 and at an off-critical one x = 0.908 was measured over an extended temperature range above the critical consolute point. Far from the critical temperature T _c, the conductivity is accurately described by the Vogel–Fulcher–Tammann (VFT) law. However, in a temperature range T = (T – T _c) 3 K, the conductivity exhibits a monotonous deviation from the VFT behavior. This anomaly is finite at T _c and, for the critical mixture, its amplitude is 0.23% of (T _c). The asymptotic behavior of the conductivity anomaly is described by a power law ^{(1 – )}, with = (T – T _c)/T _c, the reduced temperature, and , the critical exponent of the specific heat anomaly at constant pressure. This critical anomaly is similar to the one observed in other highly concentrated critical electrolytes. The degree of dissociation of the salt for the critical mixture, _diss 0.78 ± 0.04, is estimated from the value of the Walden product computed at T _c, and accounts for the effective free ion concentration in the reduced critical coordinates of the system.     

Kinetics of structural relaxation of poly(ethylene terephthalate)

The results of an experimental study of the kinetics of structural relaxation of amorphous poly(ethylene terephthalate) are reported. Samples were prepared by ultraquenching the melt on rotating stainless-steel discs. Two types of measurements by differential scanning calorimetry were made: (1) the dependence of the “fictive” (or “structural”) temperature T_f(q^?) introduced by Tool, on the cooling rate q^? and (2) the dependence of the glass transition temperature T_g on the heating rate q⁺. In this way the value x = 0.47 was obtained for the dimensionless parameter proposed by Narayanaswamy.     

Novel correlations between the critical constants of the noble gases

For any particular fluid, the set of three critical constants (CC) – pressure P_c, temperature T_c and molar volume V_c – has a central importance in defining the physical behaviour of the fluid in the gas and liquid states. However, little attention seems to have been paid in the past to the relations between the CC of different substances. In the present paper, some simple and apparently novel relations have been found between the three CC for the set of four noble gases: Ne, Ar, Kr, Xe. Defining the critical quotient Q_c ≡ RT_c/P_c (where R is the Gas Constant) the correlations may be summarised by the dual equation: (V_c/cm³ mol⁻¹) = 27 + 0.31 (T_c/K) = 3.3 + 0.280 (Q_c/cm³ mol⁻¹), which describes the CC data for the quartet Ne–Xe with an average uncertainty of 0.5%. Regarding the other two noble gases, the two isotopes of the lightest member, ³He and ⁴He, show the deviations from these relations that are expected from quantal effects and their low molar masses; while for the heaviest member, Rn, the correlations enable a value of 145(5) cm³ mol⁻¹ to be estimated for V_c that is not otherwise well defined in the literature. By contrast, and contrary to the general assumption, the second lightest member, Ne, apparently does not show appreciable quantal effects in the area, so that Ne–Xe may be considered together as a group. These correlations are compared with the behaviour of a selection of polyatomic fluids; in these comparisons, the NG dual correlation equation provides a reference line defining the presumed simplest behaviour. This and related areas show a “Residual Volume Effect”, in that extrapolating the equivalent temperature and energy parameters to zero for the state of zero-mass point particles, referred to here as the hypothetical element zeronium (Ze), the system in each case still has a finite intercept; this intercept amounts to essentially 34% of the average volume for the present quartet Ne–Xe, rather than the zero volume expected for this condition.     

Nonlinear dielectric effect in a critical solution

This paper presents measurements of Δ/E² versus T for the critical solution nitroethane in cyclohexane. The Δ/E² for the temperature near the critical temperature T_c has a positive value and satisfies the following dependence: Δ/E² ∝ 1/(T ? T_c)^λ where λ = 0.34.     

Eight-arm star polystyrene in methylcyclohexane: Cloud-point curves,critical lines,and coexisting densities and viscosities

We measured the cloud-point curves of eight-arm star polystyrene (sPS) in methylcyclohexane (MCH) for polymer samples of three total molecular masses [weight-average molecular weight (M_w) × 10⁻³ = 77, 215, or 268]. We found a downward shift of 5–15 K in the critical temperature (T_c) of the star polymer solutions with respect to linear polystyrene (PS) solutions of the same M_w. The shift in T_c became smaller as M_w increased. The critical volume fraction for eight-arm sPS in MCH was equal within experimental uncertainty (10–40%) to that of linear PS in MCH. For sPS of M_w = 77,000 in MCH, we studied the mass density (ρ) as a function of temperature (T). As for linear polymers in solution, the difference in ρ between coexisting phases (Δρ) could be described over t = (T_c − T)/T_c for 1.1 × 10⁻⁴ < t < 4.7 × 10⁻³ with the Ising value of the exponent β in the expression Δρ = B t^β. Both ρ(T) above T_c and the average value of ρ below T_c were linear functions of temperature; no singular corrections were observed. The measurements of the shear viscosity (η) near T_c for sPS (M_w = 74,000) in MCH indicated a strong critical anomaly in η, but the data were not precise enough for a quantitative analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 129–145, 2004     

A methodology to define the Cubic Equation of State of a simple fluid

A method to define the Cubic Equation of State (CES) of a simple substance is presented in this work. CES is constructed with only three parameters of the fluid, namely, the critical compressibility Z_c≡P_cv_c/RT_c, the acentric factor ω ≡ − log  (P^(sat)/P_c) − 1 (where P^(sat) is the saturated vapor pressure), and the saturated vapor volume v^(sat) at the temperature T^(sat)/T_c = 0.7 (where T_c is the critical temperature, v_c is the critical volume, and P_c is the critical pressure). The resulting CES is unique for each substance and, in general, it is different from other known CES in the literature.     

Application of the modified van der waals equation for unsaturated vapour and liquid states

The Law-Lielmezs (L-L) modification of the Van der Waals equation of state: P = RT/(V-b)-a(T)/V² where: a(T) = a(T_c)·a(T_c·a(T¹) and: a(T¹) = 1 + pT^1q has been extended to include unsaturated states in terms of a correcting function C_f(such that the α(T¹) term becomes: a(T¹) = 1 + _pC_fT^1q The proposed extension has been compared with the results obtained by the use of the original Van der Waals equation of state.     

Algorism for the solution of the exponential integral in non-isothermal kinetics at linear heating

The solution of the exponential integral at linear heating for the general case that the activation energy linearly depends on temperature according toE(T)=E ₀+RBT is

Steric effect of terminal substituents in azomethins and thermal stability of the nematic phase

The paper studies the steric eflect of terminal substituents on the temperature T_c of the phase transition nematic liquid crystal-isotropic liquid in mesogenic azomethins with one or two noninteracting or strongly interacting conformation degrees of freedom. The linear dependence T_c(Q) has been confirmed, where Q=(cos² _N) is the conformation paramefer of the molecular ensemble; _N is the angle between the planes of the bridging group CH=N and the aniline ring in the benzylideneaniline fragment. Direct and indirect steric eflects of lateral substituents are shown to take place, which explain an anomalous variation of T_c in some compounds upon substitutions in them.L. V. Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 4, pp. 89–97, July–August, 1993.Translated by L. Smolina     

1A1⇔5T2 Spin Transition in Heterometallic Solid Phases FexNi1-x(Htrz)3(NO3)2 · H2O (Htrz = 1,2,4‐Triazole)

Solid phases Fe_xNi_1-x(Htrz)₃(NO₃)₂ · H₂O (0.4 x 0.8$) and Ni(Htrz)₃(NO₃)₂ · H₂O were synthesized and studied. The phases were studied by means of magnetochemistry, powder Xray difraction analysis, and electronic and IR spectroscopy. The heterometallic phases are described by the stoichiographic method of differentiating dissolution (DD). The values of x were determined by two methods — atomic absorption and DD. Magnetochemical data showed that the solid phases exhibit a hightemperature ¹A₁ ⁵T₂ 0.5 x 0.8 and disappears at x = 0.4. The spin transition is accompanied by thermochromism (color changed from pink to white at 0.6 x 1 and from pink to light lilac at x = 0.5). A decrease in x leads to a decrease in the temperature of the forward (under heating T_c ) and reverse (under cooling T_c ) transitions, a decrease in hysteresis value ( T_c), and a smearing of the spin transition.     

Length scale hierarchy in sol,gel, and coacervate phases of gelatin

Length scale hierarchy in gelatin sol, gel, and coacervate (induced by ethanol) phases, having same concentration of gelatin in aqueous medium (13% w/v), has been investigated through small angle neutron scattering and rheology measurements. The static structure factor profile, I(q) versus wave vector q, was found to be remarkably similar for all these samples. This data could be split into three distinct q‐regimes: the low‐q regime, I_ex(q) = I_ex(0)/(1+q²ζ²)² valid for q < 3R_g^?1; the intermediate q‐regime, I(q) = I(0)/(1+q²ξ²) for 3R_g^?1 < q < ξ^?1; and the asymptotic regime, I(q) = (c/q) exp(?R_c²q²/2) for q > ξ^?1. Consequently, three distinct length scales could be deduced from structure factor data: (a) inhomogeneity of size, ζ = 20 ± 1 nm for all the three phases; (b) average mesh size, ξ₀ = 2.6 ± 0.2 nm for sol and gel, and smaller mesh size, ξ_os = 1.2 ± 0.2 nm for coacervate; and (c) cross section of gelatin chains, R_c = 0.35 ± 0.04 nm. In addition, the structure factor data obtained from coacervating solution analyzed in the Guinier region, I(q) = exp(?q²R_g²/3), yielded value of typical radius of gyration of clusters, R_g ≈ 69 nm that indicated existence of triple‐helices of length, L ≈ 239 nm; (d) Frequency and temperature sweep measurements conducted on coacervate samples revealed two other length scales: (e) viscoelastic length, ξ_ve = 14 ± 2 nm and (f) correlation length at melting, ξ_T = 500 ± 70 nm. Thus, existence of six distinct length scales, (a–f), ranging from 1.2 to 500 nm has been established in the coacervate phase of gelatin–ethanol–water system. Results are discussed within the framework of Landau‐Ginzburg treatment of dynamically asymmetric systems (Prog Theor Phys 1977, 57, 826; Phys Rev A 1991, 44, R817; J Phys II (France) 1992, 2, 1631). © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1653–1667, 2006     

The vapour pressure,orthobaric volumes,and critical constants of tetramethylsilane

The vapour pressure and orthobaric molar volumes of tetramethylsilane have been messured from 373 K to the critical temperature, and the critical temperature (IPTS-68: T^{o = 448.64 K}), critical pressure (p^{c = 2821 kPa}), and critical molar volume (V_m^c = 361 cm³ mol^?1) have been determined.     

A Boosted Critical Temperature of 166 K in Superconducting D3S Synthesized from Elemental Sulfur and Hydrogen

The discovery of superconductivity in H₃S at 203 K marked an advance towards room-temperature superconductivity and demonstrated the potential of H-dominated compounds to possess a high critical temperature (T_c). There have been numerous reports of the H-S system over the last five years, but important questions remain unanswered. It is crucial to verify whether the T_c was determined correctly for samples prepared from compressed H₂S, since they are inevitably contaminated with H-depleted byproducts. Here, we prepare stoichiometric H₃S by direct in situ synthesis from elemental S and excess H₂. The Im m phase of D₃S samples exhibits a T_c significantly higher than previously reported values (ca. 150 K), reaching a maximum T_c of 166 K at 157 GPa. Furthermore, we confirm that the sharp decrease in T_c below 150 GPa is accompanied by continuous rhombohedral structural distortions and demonstrate that the Cccm phase is non-metallic, with molecular H₂ units in the crystal structure.     

Investigation on LCST behavior of a new amorphous/crystalline polymer blend: Poly(n‐methyl methacrylimide)/poly(vinylidene fluoride)

The liquid–liquid phase‐separation (LLPS) behavior of poly(n‐methyl methacrylimide)/poly(vinylidene fluoride) (PMMI/PVDF) blend was studied by using small‐angle laser light scattering (SALLS) and phase contrast microscopy (PCM). The cloud point (T_c) of PMMI/PVDF blend was obtained using SALLS at the heating rate of 1 °C min^?1 and it was found that PMMI/PVDF exhibited a low critical solution temperature (LCST) behavior similar to that of PMMA/PVDF. Moreover, T_c of PMMI/PVDF is higher than its melting temperature (T_m) and a large temperature gap between T_c and T_m exists. At the early phase‐separation stage, the apparent diffusion coefficient (D_app) and the product (2Mk) of the molecules mobility coefficient (M) and the energy gradient coefficient (k) arising from contributions of composition gradient to the energy for PMMI/PVDF (50/50 wt) blend were calculated on the basis of linearized Cahn‐Hilliard‐Cook theory. The kinetic results showed that LLPS of PMMI/PVDF blends followed the spinodal decomposition (SD) mechanism. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1923–1931, 2008