Transition discontinuous

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

In a physical system only those variables that leave the energy invariant can exhibit quasi-discontinuous transitions (jumps). 

It is probable that on heating NH HF rotation2) of the NH4 ions is induced, with an accompanying gradual transition to a tetragonal structure with a = b, w = u, v = 0, and z =, or a discontinuous transition to the KHF2 structure (provided that fusion or sublimation does not occur below the transition temperature). 

M molar mass), where I and III are the tricritical or -regions. Here, the chain molecules exhibit an unperturbed random coil confirmation. In contrast, I and II are the critical or good solvent regimes, which are characterized by structural fluctuations in direction of an expanded coil conformation. According to the underlying concept of critical phenomena, the phase boundaries have to be considered as a continuous crossover and not as discontinuous transitions. 

Making the flow rate higher or lower will change from stable to metastable the folded or the stretched state, respectively. The effects of hysteresis associated with this first-order discontinuous transition play an important role in the formation of composite crystalline structures. 

The contact line is considered as a sharp boundary in the classical picture presented above. In this picture, there is a discontinuous transition from the flat... 

Figure 10,20 Major element concentrations in effusive products of Boina series plotted as functions of degree of fractional crystallization, based on equation 10.132. I = first discontinuity (transition from olivine-dominated to plagioclase-dominated fractionation) II = second discontinuity (appearance of Fe-Ti oxides) III = third discontinuity (field of Si02 oversaturated trachytes apatite and Mn-oxides precipitate) IV = beginning of peralkalinity field. From Barberi et al. (1975), Journal of Petrology, 16, 22-56. Reproduced with modifications by permission of Oxford University Press.

Dual discontinuous transitions from constant or nearly constant velocity regimes. This type of transient was observed in cast TNT, fine grained TNT, and in coarse grained TNT (not previously observed)... 

Constant low-order wave propagation suddenly undergoing a sharp or discontinuous transition to normal, high-order deton, as observed in Tetryl and EDNA (definite transition distance) and sometimes in NG and Gelatin Dynamites (irregular transition distance)... 

Work in the millikelvin range revealed, however, a striking difference between InP and InSb. For InSb Mansfield et al (1985) observed a disappearance of a with v = 1 (not claimed by Biskupski et al (1981), though this work was only at liquid-helium temperature). On the other hand, Biskupski et al (1984) and Long and Pepper (1984) have both extended their work on InP to T=50 mK and found an apparently discontinuous transition for a field of about 7 T, at which a=... 

The experiments were repeated but were not reproducible Acrylamide gels were made anew with various recipes and their swelling curves were determined as a function of acetone concentration, but they were all continuous. It took a couple of months to recognize that the gels that showed the discontinuous transition were old ones, that is, gels prepared a month earlier and left within the tubes in which they were polymerized. Subsequent experiments were all carried out on new gels, and, therefore, underwent a continuous transition. At that time all the old gels were used up, and none were left in the laboratory. 

Discontinuous Transition of Gels Within the Flory-Rehner... 

The present article attempts to clarify the nature of the discontinuous transition of gels. First, in Sect. 2 we give an outline of the fundamental aspect of the volume phase transition on the basis of the Flory-Rehner theory of gels, with special attention to how the discontinuous transition comes about within the phenomenological treatment Then, in Sect 3 previous experimental results... 

Discontinuous Transition Within the Flory-Rehner Phenomenological Theory... 

The critical value of x2 for the three roots to appear is shown [11] to be 1/3 for a gel with infinitely long chains. In actual gels, the critical value must be appreciably larger than 1/3. Thus, a discontinuous transition rarely occurs in neutral gels, because it requires an unusually large concentration dependence of %. An NIPA gel with small crosslinking density is one such rare example. 

In ionized gels, unlike neutral ones, the condition for a discontinuous transition can be realized relatively easily. Combining Eqs. (3) and (4), we obtain the effective osmotic pressure due to elasticity of ionized network as... 

Swelling curves of two neutral NIPA gels with different initial polymer concentration crosslinking density Nc/V0 are shown in Fig. 3 [20], One sample (call it gel A) had 0 = 0.075 and Nc/V0 = 1.02 x 1022, which undergoes a slightly discontinuous transition as shown in Fig. 3a, while the other (gel B) had <))0 = 0.114 and Nc/V0 = 2.40 x 1022, which undergoes a continuous transition as shown in Fig. 3b. In the former sample, the coexistence of the swollen and the shrunken phases was observed within 0.05 °C of the transition temperature, which is concrete evidence that the transition is discontinuous. On the other hand, the latter sample was homogeneous, at least by visual inspection,... 

In the present article, we have dealt only with the phase transition of NIPA gels. Hence, it is not clear at present whether the anomalous phenomena observed on NIPA gels are universal features of the discontinuous transitions of gels or not. According to the theory of coherent-phase equilibria, it depends on the values of the elastic constants whether the phase-coexistence structure is... 

This equation indicates that the second term owing to photo-heating effect lowers the transition temperature and finally brings the gel state to an unstable region, resulting in the discontinuous transition. 

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