Ordinary/extraordinary transitions

The materials and methods used in this work have been described in detail in the original publications (1 3). Briefly, the DNA used in the gelation work was prepared by extensive sonication of calf thymus DNA it had a degree of polymerization of 200 30 base pairs (bp). The DNA used in the ordinary-extraordinary transition studies was prepared by nuclease digestion of chromatin from chicken erythrocytes it was an equimolar mixture of two sizes, 140 bp and 160 bp, averaged to 150 bp. 

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

Figure 5. Regions of stability of isotropic and anisotropic solutions of 150 bp DNA, calculated according to Stigter 22L) The light band corresponds to the coexistence region for fully charged DNA, the dark band to DNA with 76% of charge neutralized by counterion condensation. The salt/DNA concentration regions where the gelation and ordinary-extraordinary transitions were studied are indicated by brackets.

The presence of a slow diffusion seems to be characteristic for most polyelectrolyte solutions. The slow mode was first detected by Schurr et al. [218] for poly(L-lysine) upon variation of salt concentration. A sudden drop of the diffusion coefficient was observed as the salt concentration was decreased below some critical value. Since then, this transition is called ordinary-extraordinary transition , the fast diffusion being referred to as ordinary and the slow diffusion as extraordinary . Drifford and Dalbiez [219] later gave an empirical expression which describes the relation between this critical salt concentration... 

The existence of the cluster has also been proposed from dynamic light scattering experiments the time corrdation function obtained for solutions of some ionic polymers at low salt concentrations showed two or three dynamic modes, fast and slow. The very slow mode was first reported by Lin, Lee, and Schurr, who coined the term ordinary-extraordinary transition for its appearance at low salt concentrations [11]. Several authors have also observed essentially the same phenomena by DLS [bb-TO]. The slow mode has been attributed to the translational diffusion of (temporal) cluster by Schmitz [66], or of multi-chain domains (dusto s) by Sedlak [68,70]. We also observed two modes for polystyrenesulfonate solutions we attributed the slow mode to the translational diffusion of the localized ordered structures [71]. 

Fig. 46. Schematic order parameter (magnetization) profiles m(z) near a free surface, according to mean field theory. Various cases arc shown (a) Extrapolation length X positive. The transition of the surface from the disordered state to the ordered state is driven by the transition in the bulk ( ordinary transition ). The shaded area indicates the definition of the surface magnetization ms. (b) Extrapolation length X = oo. The transition of the surface is called "special transition ( surfacc-bulk-multicritical point ), (c), (d) Extrapolation length X < 0, temperature above the bulk critical temperature (c) or below it (d). The transition between states (c) and (d) is called the extraordinary transition , (c) Surface magnetic field Hi competes with bulk order (mi, > 0, 0 < H such that mi < -mb). In this case a domain of oppositely oriented magnetization with macroscopic thickness ( welting layer ) separated by an interface from the bulk would form at the surface, ir the system is at the coexistence curve (T < Tv, H = 0). From Binder (1983).

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

T. W. Burkhardt, H. W. Diehl, Ordinary, extraordinary, and normal surface transitions Extraordinary-normal equivalence and simple explanation of t —singularities, Phys. Rev. B 50 (1994) 3894-3898. 

Fig. 89. Magnetic data for the mixed system (Zni Ax)CMns, where A Al, Ga, Mn. (a) Variation of Bohr magnetons per Mn atom with composition. (Ordinary values obtained b r extrapolation from cubic phase extraordinary value corresponds to low-temperature tetragonal phase.) (b) (facing page) Variation of Curie and phase-transition temperatures with composition. (After Howe and Myers (282).)...

Fig. 4.31. Spectral reflectance data in the visible light range (—400-700 nm) for hematite (left) and ilmenite (right). Data are shown for both the ordinary RJ and extraordinary RJ vibration directions in plane-polarized light. The arrows (labeled to correspond with Fig. 4.30) indicate energies of calculated major electronic transitions (after Vaughan and Tossell, 1978).

Influence of Added Salt on the Slow Mode. As with NaCl and CaCl2, the system NaPSS/LaCl3 presents a pseudo splitting phenomenon between the two modes at a critical salt concentration [32], The amplitude of the slow mode becomes very low and undetectable. Only the fast component of the autocorrelation function is present. These results are analogous to many observations made on a lot of polyelectrolyte solutions and recall the pseudo-transition from extraordinary phase to ordinary phase [31,32,34,37,64]. At last, in the upper one-phase at Cs 0.5 M (D-point on Figure 15), a large scattered intensity is observed with only one relaxation time. The value of the effective coefficient diffusion is about 10 7 cm2/s. 

Orthoscopic examination with crossed polars is carried out first of all to determine the isotropism or the anisotropism of a sample. The polarization colors, the defects and variation in molecular orientation, and the orientation pattern or texture of liquid crystals are observed in this examination. With a heating stage the temperature of phase transition is also determined. In addition, with use of a compensator, the determination of vibration directions of the ordinary and extraordinary rays, the determination of relative retardation and birefringence are possible. In this section, the optical basics for orthoscopic observations are briefly outlined. The description of textures frequently observed for polymeric liquid crystals is given in Section 4.1.4. 

This Datareview outlines the data on optical absorption and refractive index in the various polytypes of SiC. The optical transitions give rise to the characteristic colour of each polytype. Values for both the ordinary and extraordinary refractive indices versus wavelength are given. 

The experimental dependence of the self-diffraction intensity of the extraordinary polarized radiation on the normalized temperature r = (T— 7V)/r is shown in Fig. 1. The same figure shows the temperature dependence of the characteristic hologram-erasure time tff, which is equal to the writing time as well as to half the characteristic relaxation time of the nonlinearity. The value of, which is proportional to (J ), increases as the phase-transition point is approached, even though in this case the hologram-erasure time, which determines the stationary value of (Ref. 2), decreases. The dependence of the refraction intensity of the ordinary polarized radiation is similar in form. 

In accordance with the experimental results [17, 51] the birefringence in the IR region is expected to be nearly independent of the wavelength and mainly determined by the electronic transition moment. The contribution of the molecular vibrational bands to the birefringence is limited to the vicinity of these resonance bands. In the IR region, positive and negative dispersion is observed. When the absorption of the extraordinary ray is more pronounced than that of the ordinary ray the dispersion is positive, and vice versa [17, 51]. 

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