Order-disorder transition experimental

Those Warren-Cowley parameters have been determined in situ above the order-disorder transition temperature by diffuse neutron scattering. From these experimentally determined static correlations, the first nine effective pair interactions have been deduced using inverse Monte Carlo simulations. 

Various types of work in addition to pV work are frequently involved in experimental studies. Research on chemical equilibria for example may involve surfaces or phases at different electric or magnetic potentials [11], We will here look briefly at field-induced transitions, a topic of considerable interest in materials science. Examples are stress-induced formation of piezoelectric phases, electric polarization-induced formation of dielectrica and field-induced order-disorder transitions, such as for environmentally friendly magnetic refrigeration. 

Obviously, if we know experimentally the behavior of the macroscopic ordering parameter with T, we may determine the corresponding coefficients of the Landau expansion (eq. 2.52). However, things are not so easy when different transitions are superimposed (such as, for instance, the displacive and order-disorder transitions in feldspars). In these cases the Landau potential is a summation of terms corresponding to the different reactions plus a couphng factor associated with the common elastic strain. 

However, given the uncertainty in the experimental determinations and the necessary assumption that the best LEED pattern corresponds to complete occupation of all available sites, the unambiguous assignment of a coverage to the 2 x 2 structure can only be done with a LEED intensity calculation. Order-disorder transitions at elevated temperatures have been reported for the 2 x 2 structures formed on Ru(001) (148) as well as on Rh(l 11) (146). In the latter case this process is irreversible. 

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).

Not only do the thermodynamic properties follow similar power laws near the critical temperatures, but the exponents measured for a given property, such as heat capacity or the order parameter, are found to be the same within experimental error in a wide variety of substances. This can be seen in Table 13.3. It has been shown that the same set of exponents (a, (3, 7, v, etc.) are obtained for phase transitions that have the same spatial (d) and order parameter (n) dimensionalities. For example, (order + disorder) transitions, magnetic transitions with a single axis about which the magnetization orients, and the (liquid + gas) critical point have d= 3 and n — 1, and all have the same values for the critical exponents. Superconductors and the superfluid transition in 4He have d= 3 and n = 2, and they show different values for the set of exponents. Phase transitions are said to belong to different universality classes when their critical exponents belong to different sets. 

Much experimental work has appeared in the literature concerning the microphase separation of miktoarm star polymers. The issue of interest is the influence of the branched architectures on the microdomain morphology and on the static and dynamic characteristics of the order-disorder transition, the ultimate goal being the understanding of the structure-properties relation for these complex materials in order to design polymers for special applications. 

Floudas and coworkers [88] investigated the static and kinetic aspects of the order-disorder transition in SI2 and SIB miktoarm stars using SAXS and rheology. At temperatures above the order-disorder transition (ODT) the mean field theory describes the experimental results quite well. Near the ODT, SAXS profiles gave evidence for the existence of fluctuations. Both samples separated into cylindrical microdomains below the ODT. The ODT was determined on shear oriented samples and found, by SAXS, to be 379 K in both cases. This was confirmed by rheology. The discontinuities in SAXS peak intensity and in the storage modulus near the ODT were more pronounced for the miktoarm stars than for the diblocks. The %N values, where % is the interaction parameter and N the... 

Order-disorder, or rod-to-coil , transitions in dilute solution have been reported for polydiacetylenes (2, 5-11), polysilylenes (12-15), and alkyl-substituted polythiophenes (16). The interpretation of the experimental observations has been the subject of considerable controversy with respect to whether the observations represent a single-polymer-molecule phenomenon or a many-chain aggregation or precipitation process (3-16). Our own experimental evidence (12, 13) and that of others (5-8, 10, 16) weigh heavily in favor of the single-chain interpretation. In our theoretical interpretation, we will assume that the order-disorder transitions observed in dilute pol-ysilylene solutions represent equilibrium, single-chain phenomena. 

Order-Disorder Transitions. General Features, Experimental data are summarized in Table II, and representative thermochromic behaviors are shown in Figure 2. For the dialkyl-substituted polysilylenes the transition is very sharp, with a barely discernible coexistence region and an approximate isosbestic point. On the other hand, the asymmetrically substituted polymers, except poly(n-dodecylmethylsilylene), display very smooth behavior only in n-hexane solution and a broad but clearly discernible transition in dilute toluene solution. The transition width (ATc) in toluene solution was taken to be the interval between departure from the extrapolated, smooth, high-temperature behavior and the onset of peak absorption wavelength saturation at low temperature. The transition temperature (Tq) is defined arbitrarily as the midpoint of this region. 

The experimental results in Figure 2 and Table II clearly show three qualitatively different behaviors an abrupt order-disorder transition a relatively rapid continuous transition and a gradual, smooth ordering of the polymer backbone. These observations are qualitatively identical to the three possible phase behaviors predicted by the theory. Moreover, a degree of quantitative understanding can be obtained. 

Symmetrical Dialkyl-Substituted Polysilylenes Because of their extremely sharp order-disorder transitions, the nonpolar, symmetrical dialkyl-substituted polysilylenes are almost ideal systems with which to test the predictions discussed earlier. The predicted solvent dependence of Tc was tested by performing a series of experiments with high-molecular-weight poly(di-n-hexylsilylene) in dilute solution. Experimental results for six solvents are listed in Table II, and the theoretically defined solvation coupling constants and solvent parameters are collected in Table III. 

The predicted intrinsic width of the order-disorder transition of a mono-disperse, flnite-molecular-weight polymer solution was also tested. The average molecular weights of dialkyl-substituted polysilylenes are in the order of 6 X 10, which implies that N is 3000-5000 silicon atoms. With equation 9, the theory predicts that ATq/Tc is 0.004-0,006, which for Tc = -30 corresponds to an intrinsic width of roughly 1 or 2 C. This result is in good agreement with the experimental observations summarized in Table II. 

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