First-and Second-Order Behaviors


The foregoing thermodynamic view of the glass transition assumes that equilibrium criteria are satisfied as a sample is cooled through Tg. In this section we shall set aside the issue of thermodynamic equilibrium and simply consider why the mechanical properties of polymers should undergo a dramatic change over a relatively narrow range of temperatures, an observation which was, in the last chapter, our introduction to Tg. In discussing Fig. 4.14, we saw that volume also shows a change in behavior at Tg —a change more typical of second-order than first-order transitions. Since volume is more readily visualized than the mechanical properties, we shall concentrate on the former in the following discussion. The emphasis is not merely a matter of convenience, however, since most attempts to understand Tg involve some concept of free volume.  [c.248]

For example, a temperature-measuring device, having its sensor placed in a protecting rube, is a system of second order. For such a system no single rime constant exists in the same way as a first-order system. The behavior of such a system is often given by a response time. Another concept is to give the apparent time constant t, which can be constructed by placing a line in the inflection point of the step response curve see Fig. 12.14.  [c.1135]

It has been a persistent characteristic of shock-compression science that the first-order picture of the processes yields readily to solution whereas second-order descriptions fail to confirm material models. For example, the high-pressure, pressure-volume relations and equation-of-state data yield pressure values close to that expected at a given volume compression. Mechanical yielding behavior is observed to follow behaviors that can be modeled on concepts developed to describe solids under less severe loadings. Phase transformations are observed to occur at pressures reasonably close to those obtained in static compression.  [c.51]

In spite of these representative first-order descriptions, experiments, theory, and material models do not typically agree to second order. Compressibility (derivatives of pressure with volume) shows complex behaviors that do not generally agree with data obtained from other loadings. Mechanical yielding and strength behavior at pressure show complexities that are not  [c.51]

In this chapter, the observations on piezoelectric responses of piezoelectrics within the elastic range as described in Chap. 4 are extended into ranges of shock pressures in which multiple stress waves resulting from mechanical yielding propagate within the samples. Furthermore, the behavior of a new class of piezoelectrics, the piezoelectric polymer, is described under conditions that are close to hydrodynamic. Shock compression of ferromagnetic or ferritic solids changes their magnetic states, resulting in electrical signals in external circuits. The behavior of magnetic substances that undergo pressure-induced, second-order and first-order phase transitions under shock compression are considered. Finally, perhaps the most distinctive electrical response of shock-compressed solids, shock-induced electrical polarization, is considered. Shock-induced polarization effects observed in nonpiezoelectric solids, both ionic and polymeric, are described.  [c.98]

Het = heteroaryl residue] follow second-order kinetics, first order with respect to each reactant. Regular kinetics of this kind are also observed in the reaction of sodium arylsulfide in methanol provided that no free thiol is present (see Section II,D, l,c). As to other heterocyclic systems, A -oxides and bromofuran derivatives show similar kinetic behavior.  [c.291]

This fomi is called a Ginzburg-Landau expansion. The first temi f(m) corresponds to the free energy of a homogeneous (bulk-like) system and detemiines the phase behaviour. For t> 0 the fiinction/exliibits two minima at = 37. This value corresponds to the composition difference of the two coexisting phases. The second contribution specifies the cost of an inhomogeneous order parameter profile. / sets the typical length scale.  [c.2370]

In order to use any material for commercial purjDoses, it is important to understand its phase behaviour. Bulk gold, for example, melts at 1065°C and thus would be an unwise choice as an electrical interconnect in a high-temperature environment many ceramics can crack during thennal processing due to solid-solid phase transfonnations that lower the volume of the crystal [178]. The extrapolation of such bulk phase behaviour to the properties of nanocrystals is not a straightforward problem. Nanocrystals are intrinsically metastable materials which, given the right circumstances, would fuse to create bulk crystals. Indeed, metal nanocrystals prepared on surfaces under high-vacuum conditions do spontaneously fuse into larger grains [179, 180]. On the other hand, solutions of nanocrystals stabilized with organic agents can exist for months or even years with unchanging sizes. Evidently, the metastability of nanocrystals is a sensitive function of their surface bonding, but the nanocrystal surface affects the crystallite in two distinct ways. First, surface atoms can make up 5-40% of the mass of a nanocrystal, and thus contribute significantly to the overall thennodynamic properties of the material. Second, the nanocrystal surface chemistry can raise the activation barriers for many thennodynamically favoured processes. Thus, it is important to consider the surface in both the kinetic and thennodynamic treatments of phase behaviour.  [c.2912]

Figure 2-1 is a plot of Eq. (2-10) from n = 0 to = 4. Note that equal time irrcrements result in equal fractional decreases in reactant concentration thus in the first half-life decreases from 1.0 to 0.50 in the second half-life it decreases from 0.50 to 0.25 in the third half-life, from 0.25 to 0.125 and so on. This behavior is implicit in the earlier observation that a first-order half-life is independent of concentration.  [c.19]

As enunciated above, a high-resolving LC-LC system can be implemented by employing columns that operate by using a different separation mechanism (hetero-modal LC-LC). Several combinations of mechanisms with great dissimilarity are conceivable. These include the following size exclusion-ion exchange size exclusion-reversed phase ion exchange-reversed phase reversed phase (alkyl ligand)-reversed phase (ion-pairing eluent) reversed phase (alkyl ligand)-reversed phase (electron-pair acceptor or donator ligand) reversed phase-affinity (biospecific interactions) normal phase (plain silica)-normal phase (electron-pair acceptor or donator ligand (41). In addition, a significant number of applications describing the coupling of immunoaffinity chromatography and reversed-phase HPLC have been reported over the last ten years. A specific antibody is immobilized on a appropriate sorbent to form a so-called immunosorbent (IS) for packing into a HPLC precolumn. The antibodies are selected in order to involve antigen-antibody interactions, thus providing selective extraction methods based on molecular recognition. Samples or extracts from biological matrices are introduced on to this immunoaffinity system with little or no sample pretreatment. The analytes are then eluted from the immunoaffinity column and analysed directly by suitable on-line HPLC methods. Immunoaffinity columns can be packed with chemically activated sepharose beads, and antibodies will then covalently bind to these beads (42). However, Sepharose-based immunosorbents are not pressure resistant and therefore direct connection of the precolumn to the analytical column could not be achieved. When using these immunosorbents, analytes are usually desorbed at low pressure in a second precolumn packed with Cjg, which subsequently can be coupled on-line to the LC system (43-45). Antibodies have also been immobilized on silica-based sorbents. The particular advantage of silica is its pressure resistance, which means that it can be used directly in on-line LC-LC systems (46-48). The on-line set-up using a silica-based immunosorbent precolumn is very simple and does not differ to any great extent from that which uses a single reversed-phase precolumn. Heteromodal LC-LC coupling has also been widely employed as a chiral separation technique, which usually involves sequential chromatography on a chiral and an achiral column. The consecutive order in which the columns are combined can be varied (e.g. first a chiral column, then an achiral column or vice versa), depending on the problem to be solved and the main restrictions involved. Such restrictions may be a low sample amount, a low analyte concentration or a complex sample matrix, as well as a high degree of optical purity to be monitored (49-53). Enantiomeric separations can also be easily achieved by a two-dimensional HPLC system using achiral columns in both dimensions (54). Separation of unmodified amino acids in complex mixtures was achieved by employing two different separation methods. First, the amino acid separation was carried out by means of a cation-exchange column by elution with a lithium chloride-lithium citrate buffer, and then each peak corresponding to an individual amino acid was switched to an achiral reversed-phase column where the chiral discrimination was achieved by using a mobile phase containing a chiral copper (ii) complex.  [c.126]


See pages that mention the term First-and Second-Order Behaviors : [c.51]    [c.170]    [c.573]    [c.1870]    [c.245]   
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Solids under high-pressure shock compression - mechanics, physics, and chemistry  -> First-and Second-Order Behaviors