Order-disorder phase transitions

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

There are two major types of structural phase transitions order-disorder and displacive. An order-disorder phase transition is characterized by disorder of the atoms or molecules in the structure of one of the phases. Sometimes both phases are disordered in different degrees. The disordered (or more disordered) phase is more symmetric, because disorder makes the average distribution of atoms more even. Most of the phase transitions in clathrate crystals are of this type. 

In a displacive phase transition, the positions of atoms are ordered in both phases, but the position changes from a less symmetric site to a more symmetric one as the crystal undergoes the phase transition. Order-disorder transitions are distinguished from displacive transitions by, among other properties, a large entropy of phase transition, dielectric dispersion at low frequencies, and directly, by crystal structure revealing two or more sites fractionally occupied by the same atom. 

Fig. Z4 (a) Temperature ramp at a frequency a> = lOrads (strain amplitude A = 2%) for a nearly symmetric PEP-PEE diblock with Mn = 8.1 X 104gmol l, heating from the lamellar phase into the disordered phase. The order-disorder transition occurs at 291 1 °C, the grey band indicates the experimental uncertainty on the ODT (Rosedale and Bates 1990). (b) Dynamic elastic shear modulus as a function of reduced frequency (here aT is the time-temperature superposition shift factor) for a nearly symmetric PEP-PEE diblock with Mn = 5.0 X 1O g mol A Shift factors were determined by concurrently superimposing G and G"for w > and w > " respectively. The filled and open symbols correspond to the ordered and disordered states respectively. The temperature dependence of G (m < oi c) for 96 < T/°C 135 derives from the effects of composition fluctuations in the disordered state (Rosedale and Bates 1990). (c) G vs. G"for a PS-PI diblock with /PS = 0.83 (forming a BCC phase) (O) 110°C (A) 115°C ( ) 120°C (V) 125°C ( ) 130°C (A) 135°C ( ) 140°C ( ) 145°C. The ODT occurs at about 130°C (Han et at. 1995).

Depending on temperature, transitions between distinct types of LC phases can occur.3 All transitions between various liquid crystal phases with 0D, ID, or 2D periodicity (nematic, smectic, and columnar phases) and between these liquid crystal phases and the isotropic liquid state are reversible with nearly no hysteresis. However, due to the kinetic nature of crystallization, strong hysteresis can occur for the transition to solid crystalline phases (overcooling), which allows liquid crystal phases to be observed below the melting point, and these phases are termed monotropic (monotropic phases are shown in parenthesis). Some overcooling could also be found for mesophases with 3D order, namely cubic phases. The order-disorder transition from the liquid crystalline phases to the isotropic liquid state (assigned as clearing temperature) is used as a measure of the stability of the LC phase considered.4... 

The liberation of blueprinting holographic constituents of amphiphilic transient order-disorder patterns and their meso-phase coherences, order-disorder (rigidity-flexibility) gradients of molecular individuals and their amplification into phase/domain (transition) characteristics. 

The phase transition from disordered states of polymer melt or solutions to ordered crystals is called crystallization-, while the opposite process is called melting. Nowadays, more than two thirds of the global product volumes of synthetic polymer materials are crystallizable, mainly constituted by those large species, such as high density polyethylene (HOPE), isotactic polypropylene (iPP), linear low density polyethylene (LLDPE), PET and Nylon. Natural polymers such as cellulose, starch, silks and chitins are also semi-crystalUne materials. The crystalline state of polymers provides the necessary mechanical strength to the materials, and thus in nature it not only props up the towering trees, but also protects fragile lives. Therefore, polymer crystallization is a physical process of phase transition with important practical relevance. It controls the assembly of ordered crystalline structures from polymer chains, which determines the basic physical properties of crystalline polymer materials. 

In this chapter we describe results of TOF measurements on aliphatic polysilylenes and poly(di-n-butylgermylene) carried out over a broad range of temperature encompassing the glass transition temperature Tg, and the phase I - phase II (order - disorder) transition caused by side chain ordering and melting, which is accompanied by a blue shift in the uv spectra of the polymers. 

A phase transition from disordered microemuision to ordered lamellar structure was observed at about 50 MPa through a coexisting region. The pressure dependence of the repeat... 

Phase transitions (glass transition, order-disorder,...),... 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

The Ag (100) surface is of special scientific interest, since it reveals an order-disorder phase transition which is predicted to be second order, similar to tire two dimensional Ising model in magnetism [37]. In fact, tire steep intensity increase observed for potentials positive to - 0.76 V against Ag/AgCl for tire (1,0) reflection, which is forbidden by symmetry for tire clean Ag(lOO) surface, can be associated witli tire development of an ordered (V2 x V2)R45°-Br lattice, where tire bromine is located in tire fourfold hollow sites of tire underlying fee (100) surface tills stmcture is depicted in tlie lower right inset in figure C2.10.1 [15]. 

Magnussen O M, Hageboeck J, Hotios J and Behm R J 1992 In s/fu scanning tunneiing microscopy observations of a disorder-order phase transition in hydrogensuiphate adiayers on Au(111) Faraday Discuss. 94 329-38... 

Some materials undergo transitions from one crystal structure to another as a function of temperature and pressure. Sets of Raman spectra, collected at various temperatures or pressures through the transition often provide useftil information on the mechanism of the phase change first or second order, order/disorder, soft mode, etc. 

M. Schoen, D. J. Diestler, J. H. Cushman. Stratification-induced order-disorder phase transitions in molecular confined films. J Chem Phys 707 6865-6872, 1994. 

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