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PubMed2004

New results for phase transitions from catastrophe theory.

Catastrophe theory predicts that in certain limits universal relations should exist between barrier heights, curvatures and the positions of local maxima and minima on a potential or free energy surface. In the present work we investigate these relations for both first- and second-order phase transitions, revealing that the ideal ratios often hold quite well over a wide range of conditions. This elementary catastrophe theory is illustrated for the melting transition of an atomic cluster, the isotropic-to-nematic transition in a liquid crystal, and the ferromagnetic-to-paramagnetic phase transition in the two-dimensional Ising model.

Journal Article↗
PubMed1999

Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: evidence for a general anesthetic-induced phase transition.

We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable h(e), the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for h(e). The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I ("coma"), corresponding to a strong inhibitory anesthetic effect, h(e) is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic effect, h(e) can take on three values, two of which are stable; we label the stable solutions as "active" (enhanced firing) and "quiescent" (suppressed firing). For region III, corresponding to negative anesthetic (i.e., analeptic) effect, h(e) again becomes single valued, but is now small and negative, resulting in strongly elevated firing rates ("seizure"). If we identify region II as associated with the conscious state of the cortex, then the model predicts that there will be a rapid transit between the active-conscious and comatose unconscious states at a critical value of anesthetic concentration, suggesting the existence of phase transitions in the cortex. The low-frequency spectral power in the h(e) signal should increase strongly during the initial stage of anesthesia induction, before collapsing to much lower values after the transition into comatose-unconsciousness. These qualitative predictions are consistent with clinical measurements by Bührer et al. [Anaesthesiology 77, 226 (1992)], MacIver et al. [ibid. 84, 1411 (1996)], and Kuizenga et al. [Br. J. Anaesthesia 80, 725 (1998)]. This strong increase in EEG spectral power in the vicinity of the critical point is similar to the divergences observed during thermodynamic phase transitions. We show that the divergence in low-frequency power in our model is a natural consequence of the existence of turning points in the trajectory of stationary states for the cortex.

Action Potentials↗
PubMed2006

Low amounts of sucrose are sufficient to depress the phase transition temperature of dry phosphatidylcholine, but not for lyoprotection of liposomes.

Disaccharides such as sucrose and trehalose play an important role in stabilizing cellular structures during dehydration. In fact, most organisms that are able to survive desiccation accumulate high concentrations of sugars in their cells. The mechanisms involved in the stabilization of cellular membranes in the dry state have been investigated using model membranes, such as phosphatidylcholine liposomes. It has been proposed that the lyoprotection of liposomes depends on the depression of the gel to liquid-crystalline phase transition temperature (T(m)) of the dry membranes below ambient and on the prevention of membrane fusion by sugar glass formation, because both lead to leakage of soluble content from the liposomes. Since fusion is prevented at lower sugar/lipid mass ratios than leakage, it has been assumed that more sugar is needed to depress T(m) than to prevent fusion. Here, we show that this is not the case. In air-dried egg phosphatidylcholine liposomes, T(m) is depressed by >60 degrees C at sucrose/lipid mass ratios 10-fold lower than those needed to depress fusion to below 20%. In fact, T(m) is significantly reduced at mass ratios where no bulk sugar glass phase is detectable by Fourier transform infrared spectroscopy or differential scanning calorimetry. A detailed analysis of the interactions of sucrose with the P=O, C=O, and choline groups of the lipid and a comparison to published data on water binding to phospholipids suggests that T(m) is reduced by sucrose through a "water replacement" mechanism. However, the sucrose/lipid mass ratios necessary to prevent leakage exceed those necessary to prevent both phase transitions and membrane fusion. We hypothesize that kinetic phenomena during dehydration and rehydration may be responsible for this discrepancy.

Calorimetry, Differential Scanning↗
PubMed2000

Phonon self-energies and phase transitions in a prototype discotic liquid crystal

Specific Raman active vibrations in the discotic liquid crystal nematogen hexakis(6-hexyloxy)triphenylene are shown to be sensitive to either the isotropic<-->columnar or the columnar<-->solid phase transitions. Changes in frequency and/or intensity of vibrations with specific symmetries demonstrate that the method can be used not only to monitor the phase transitions themselves with a microscopic and noninvasive optical technique, but also to gain physical information on the origin of the molecular interactions that produce them.

Journal Article↗
PubMed2002

Critical behavior of the disorder-induced Raman modes close to the lambda-phase transition in NH4Cl.

This study gives our analysis of the disorder-induced Raman modes of v7 (93 cm(-1)) and v5 (144 cm(-1)) close to the lambda-phase transition (P = 0) in the NH4Cl crystal. We describe the critical behavior of the frequency shifts for those modes by a power-law formula and using our Raman data we obtain the value of 0.1 for the critical exponent which can also describe the critical behavior of the thermal expansivity and the specific heat of NH4Cl close to its lambda-phase transition (Tlambda = 242.9 K).

Ammonium Chloride↗
PubMed2005

Neural correlates of the spontaneous phase transition during bimanual coordination.

Repetitive bimanual finger-tapping movements tend toward mirror symmetry: There is a spontaneous transition from less stable asymmetrical movement patterns to more stable symmetrical ones under frequency stress but not vice versa. During this phase transition, the interaction between the signals controlling each hand (cross talk) is expected to be prominent. To depict the regions of the brain in which cortical cross talk occurs during bimanual coordination, we conducted event-related functional magnetic resonance imaging using a bimanual repetitive-tapping task. Transition-related activity was found in the following areas: the bilateral ventral premotor cortex, inferior frontal gyrus, middle frontal gyrus, inferior parietal lobule, insula, and thalamus; the right rostral portion of the dorsal premotor cortex and midbrain; the left cerebellum; and the presupplementary motor area, rostral cingulate zone, and corpus callosum. These regions were discrete from those activated by bimanual movement execution. The phase-transition-related activation was right lateralized in the prefrontal, premotor, and parietal regions. These findings suggest that the cortical neural cross talk occurs in the distributed networks upstream of the primary motor cortex through asymmetric interhemispheric interaction.

Action Potentials↗
PubMed2004

Generalized Bose-Einstein phase transition in large-m component spin glasses.

It is proposed to understand finite dimensional spin glasses using a 1/m expansion, where m is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-m limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with N(2/5) macroscopically occupied low-lying states.

Journal Article↗
PubMed2002

Phase transitions in a network with a range-dependent connection probability.

We consider a one-dimensional network in which the nodes at Euclidean distance l can have long range connections with a probability P(l) approximately l(-delta) in addition to nearest neighbor connections. This system has been shown to exhibit small-world behavior for delta<2, above which its behavior is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at delta=1. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicates that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behavior of a single quantity, the average bond length. The phase transitions in all dimensions are nontrivial in nature.

Journal Article↗
PubMed2004

In search of temporal power laws in the orientational relaxation near isotropic-nematic phase transition in model nematogens.

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

Journal Article↗
PubMed2002

Phase transition in a two-dimensional Heisenberg model.

We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction V(s,s') = 2K[(1+s x s')/2]p. The analogous nonlinear interaction for the XY model was introduced by Domany, Schick, and Swendsen, who find that for large p the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard (p = 1) Heisenberg model has no phase transition, for large enough p a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.

Journal Article↗
PubMed2006

Soft phonon, dynamical fluctuations, and a reversible phase transition: indium chains on silicon.

The In/Si(111)-(4 x 1) surface is a paradigmatic example of a quasi-one-dimensional system showing a reversible structural and electronic (metal-insulator) phase transition when the temperature is lowered. In this work, we use first-principles simulation techniques to uncover the atomic and electronic origin of this controversial transition. Our calculations show that the ground state consists of insulating (4 x 2) indium chains with a weak interchain coupling that induces opposite shear distortions in alternate chains. First-principles molecular dynamics simulations show that the (4 x 1) <--> (8 x 2) phase transition is due to the "dynamical fluctuations" the system undergoes when, at high temperature, it fluctuates chaotically between degenerate ground states. The metallicity of the In/Si(111)-(4 x 1) surface is related to the low energy cost for the shear distortion.

Journal Article↗
PubMed2001

Ultrasonic frequencies calculated for the q[100] mode in the first-order, tricritical and the second-order phase transitions of NH4Cl.

This study correlates the volume changes to the ultrasonic frequencies of the q[100] mode of NH4Cl for the first-order, tricritical and the second-order phase transitions in this crystal. Using these correlations we were able to calculate the ultrasonic frequencies of this mode at the pressures of 0, 0.6 and 1.1 kbar (first-order), 1.6 kbar (tricritical) and 2.15 kbar (second-order) by means of the volume change data from the literature. Our calculated frequencies are in good agreement with the observed data for the phase region below the critical temperature T(C) for the first-order, tricritical and the second-order phase transitions in NH4Cl. Above T(C) our calculated frequencies do not agree satisfactorily for the q[100] mode and it is incapable of explaining the observed behaviour of NH4Cl. Our method of calculating the ultrasonic frequencies is presented.

Ammonium Chloride↗
PubMed1999

Phase transitions of colloid-polymer systems in two dimensions.

Phase transitions of systems consisting of colloidal particles and non-adsorbing polymer in a solvent are studied theoretically in two dimensions. The colloids are modeled as hard spheres and the polymer as an ideal gas. The imbalance in osmotic pressure induced by the depletion effect gives rise to an effective attraction tail for the colloid-colloid interaction. For a monodisperse polymer, liquid-liquid separation is predicted to occur for appropriate colloid concentrations when the ratio s of the radius of gyration of the polymer to the radius of the colloidal particle is greater than 0.31, while solid-liquid separation is predicted to occur for all colloid concentrations when s is smaller than 0.31. Polydispersity of polymer is found to increase the extent of liquid-liquid coexistence, and when the average s is smaller than 0.31, and for appropriate colloid concentrations, liquid-liquid coexistence occurs provided the polymer size distribution is broad enough. Partitioning and size distribution of polymer in coexisting phases are also predicted.

Journal Article↗
PubMedDate not supplied

[Ion permeability of bilayer membranes formed from synthetic phospholipids in the phase transition region].

Ion permeability of black lipid membranes formed from synthetic phospholipids has been studied. The resistance of BLM formed from phosphatidylcholine, tiophosphatidylcholine, threealkylphosphate and threealkyltiophosphate was 10(7)--10(8) Ohm.cm2. It was shown that the membrane potential of the 10--30 mV arised in KCl gradient indicating the preference cation conductance in synthetic lipid membranes. A sharp decrease of the membrane conductance near to the phase transition temperature was discovered. The change of conductance by phase transition temperature was sensitive to chemical nature of the polar head of phospholipids used.

Electric Conductivity↗
PubMed1979

The influence of dioxan on the bilayer and monolayer phase transition of phospholipids.

The influence of 1.4.-dioxan on the bilayer phase transition of various phospholipids was studied by differential scanning calorimetry and turbidity measurements. The addition of 1.4.-dioxan to lipid bilayers decreases the transition temperature T(m) increases the transition enthalpy of the transition. The cooperativity of the transition is unaffected. The phospholipid monolayer transition from the liquid-condensed to the liquid-expanded phase was measured by recording area versus temperature curves at constant surface pressure (isobars). The monolayer transition temperature at constant surface pressure is increased when 1.4.-dioxan is added to the subphase. The change in molecular area becomes larger. A comparison of monolayer isobars on water and water/dioxan as subphase at constant surface tension rather than surface pressure leads to a decrease of the transition temperature on water/dioxan as subphase. This decrease as well as the larger change in molecular area at the monolayer transition can be correlated to the decrease in Tm and the increase in the transition enthalpy of the corresponding bilayer system. 1.4.-Dioxan seems to accumulate at the lipid head group/water interface, thus lowering the tension of the bilayer membrane. This cyclic ether can be used for altering the characteristics of bilayer membranes without disturbing the lipid chain organization.

Journal Article↗
PubMed1990

Phospholipids showing complex bilayer phase transitions. II. Four sulfur-containing phosphatidylcholines.

The main phase transitions of aqueous dispersions of four synthetic phosphatidylcholines (PCs) containing sulfur atoms in thioester and thioether linkages have been studied by high sensitivity differential scanning calorimetry (DSC). The transition enthalpies ranged from 7.4 to 10.3 kcal mol-1, with values for tm, the temperature of maximal excess heat capacity, in the range 38.0 to 40.8 degrees C. The corresponding values for dipalmitoyl PC (DPPC) are 8.5 kcal mol-1 and 41.7 degrees C. Curve fitting required the sum of from one to four two-state components to give an accurate representation of the observed DSC curves. Comparison of the results given here with those reported by B.Z. Chowdhry, G. Lipka, J. Hajdu and J.M. Sturtevant, (1984) Biochemistry 23, 2044-2049, for PCs containing amide, ether or carbamoyl linkages in place of the usual ester bonds shows that small changes in organic structure can result in large changes in thermotropic behavior. The complexity in the cases showing more than a single two-state component is presumably due to a series of sequential cooperative transitions the character of which is at present unknown.

Calorimetry, Differential Scanning↗
PubMed1986

Phase transitions in monoglyceride bilayers. A light scattering study.

Thermotropic phase transitions in single planar bilayers of glycerol mono-oleate have been investigated using quasi-elastic light scattering from thermally excited membrane fluctuations. In certain cases both spectroscopic and intensity information were derived from the observations. For solvent-free bilayers transitional changes were observed in several membrane parameters: in tension, viscosity and thickness, in a combination of lipid orientational order parameter and dielectric anisotropy, and in the lateral compression modulus. These changes, particularly those in membrane thickness and in the anisotropy/order combination, were clearly indicative of a chain-melting transition in the lipid molecules. The chain-melting transition temperature was identified as 16.6 +/- 0.03 degrees C (delta T 1/2 = 1.5 degrees C). The other changes tended to cluster around 12.5 and 16.6 degrees C, suggesting that a two-stage transition was involved. Analysis of pretransitional fluctuations in membrane viscosity, based on a Landau approach, suggested that at the transition the membrane was close to a critical point (T = 12.7 degrees C). Less information was accessible for membranes containing n-decane within their structure. In this case, the change in membrane tension was much smaller than in the solvent-free case and the transition was considerably broadened. These effects accord with an increase in 'interactive volume' within the bilayer due to solvent inclusion.

Glycerides↗
PubMed2007

In-situ AFM studies of the phase-transition behavior of single thermoresponsive hydrogel particles.

The volume phase transition (VPT) behavior of individual thermally responsive poly(N-isopropylacrylamide-co-acrylic acid) (pNIPAm-co-AAc) hydrogel microparticles was studied by in-situ dynamic mode atomic force microscopy (AFM) and force spectroscopy during heating and cooling cycles. Hydrogel samples were prepared by electrostatic immobilization of microparticles to amine-modified gold surfaces. The AFM studies of particle deswelling were performed by varying the force applied on the particles during imaging as a function of the geometry and material of the AFM probe. Aluminum-coated silicon cantilevers were found to influence substantially the behavior of the particles during the VPT, leading to a significant shape change. Low force impact magnetic excitation of the AFM probe (MAC mode) during dynamic mode measurements resulted in an undisturbed deswelling behavior enabling observation of the expected volume changes of the particles without significant tip-sample interaction. Hence, MAC-mode AFM was determined to be the most suitable technique for in-situ AFM studies on volume and shape changes at single hydrogel particles during VPT. Elasticity measurements performed at single particles at temperatures below and above the VPT revealed a 15-fold increase in the Young's modulus after passing the VPT, indicating the transition from a soft, swollen network to a stiffer, deswollen state.

Acrylamides↗