Inverse temperature dependence

Materials that typify thermoresponsive behavior are polyethylene—poly (ethylene glycol) copolymers that are used to functionalize the surfaces of polyethylene films (smart surfaces) (20). When the copolymer is immersed in water, the poly(ethylene glycol) functionaUties at the surfaces have solvation behavior similar to poly(ethylene glycol) itself. The abiUty to design a smart surface in these cases is based on the observed behavior of inverse temperature-dependent solubiUty of poly(alkene oxide)s in water. The behavior is used to produce surface-modified polymers that reversibly change their hydrophilicity and solvation with changes in temperatures. Similar behaviors have been observed as a function of changes in pH (21—24). 

The result indicates that the activation energy for combination is higher than that for disproportionation by ca 10 kJ mol"1. A similar inverse temperature dependence is seen for other small radicals (Section 2.5). However, markedly different behavior is reported for polymeric radicals (Section 5.2.2.2.1). 

Product analysis by NMR indicated an isotope effect at 118°C of = 2.14, corrected for numbers of H versus D. On lowering the temperature to -12°C, however, it was found that the isotope effect increased to 3.25. Referring to earlier experimental results on the C-H shift in methylchlorocarbene, " the authors cited the normal temperature dependence of the isotope effect as evidence against tunneling in 64. In retrospect, however, as noted above, theoretical support for an atypical inverse temperature dependence in methylchlorocarbene has been refuted. Hence, the involvement of tunneling in 62/64 at ambient temperatures is still an open question. 

For convenience of discussion, a schematic diagram of bacterial photosynthetic RC is shown in Fig. 1 [29]. Conventionally, P is used to represent the special pair, which consists of two bacterial chlorophylls separated by 3 A, and B and H are used to denote the bacteriochlorophyll and bacteriopheophytin, respectively. The RC is embedded in a protein environment that comprise L and M branches. The initial electron transfer (ET) usually occurs from P to Hl along the L branch in 1—4 picoseconds (ps) and exhibits the inverse temperature dependence that is, the lower the temperature, the faster the ET. It should be noted that the distance between P and Hl is about 15 A [53-55]. 

In 1993 Bergbreiter prepared two soluble polymer-supported phosphines that exhibited an inverse temperature-dependent solubility in water [52]. Although PEG-supported phosphine undergoes a phase-separation from water at 95-100 °C, the PEO-poly(propylene oxide)-PEO supported catalyst was superior as it is soluble at low temperatures and phase-separates at a more practical 40-50 °C. Treatment of a diphenylphosphinoethyl-terminated PEO-PPO-PEO triblock copolymer... 

In most cases the catalytically active metal complex moiety is attached to a polymer carrying tertiary phosphine units. Such phosphinated polymers can be prepared from well-known water soluble polymers such as poly(ethyleneimine), poly(acryhc acid) [90,91] or polyethers [92] (see also Chapter 2). The solubility of these catalysts is often pH-dependent [90,91,93] so they can be separated from the reaction mixture by proper manipulation of the pH. Some polymers, such as the poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) block copolymers, have inverse temperature dependent solubihty in water and retain this property after functionahzation with PPh2 and subsequent complexation with rhodium(I). The effect of temperature was demonstrated in the hydrogenation of aqueous allyl alcohol, which proceeded rapidly at 0 °C but stopped completely at 40 °C at which temperature the catalyst precipitated hydrogenation resumed by coohng the solution to 0 °C [92]. Such smart catalysts may have special value in regulating the rate of strongly exothermic catalytic reactions. 

An interesting family of polymeric ligands show inverse temperature dependence of solubihty in water, i.e. they can be precipitated from aqueous solutions by increasing the temperature above the so-called cloud point. Typically these ligands contain poly(oxyalkylene) chains, but the phenomenon can be similarly observed with poly(N-isopropyl acrylamide) derivatives (e.g. 132) and methylated cyclodextrins, too. At or above their cloud points these compounds fall off the solution, due to the break-up and loss of the hydration shell which prevents aggregation and precipitation of their molecules. Conversely, upon cooling below this temperature (also called the lower critical solution temperature, LCST) these substances dissolve again. 

Fortunately C-terms are readily distinguished from A- and B-terms by their inverse temperature dependence. If present, they usually dominate the MCD spectrum at low temperatures, since they can be enhanced up to 70-fold on going from room temperature to liquid helium temperatures. For biological chromo-phores, which generally possess only low symmetry, ground state degeneracy can... 

An alternative approach was reported in 1997. A series of novel water-soluble polyether-substituted triphenylphosphanes was prepared by means of the ethoxylation of mono-, bis-, and tris(p-hydroxyphenyl)phosphanes (47). They manifest inverse temperature-dependent solubility in water that enables them to act as thermoregulated phase-transfer ligands. 

The modified thermal and phase space theories reproduce most three body association data equally well, including the inverse temperature dependence of the rate coefficient (Herbst 1981 Adams and Smith 1981), and are capable of reproducing experimental rate coefficients to within an order of magnitude (Bates 1983 Bass, Chesnavich, and Bowers 1979 Herbst 1985b). They should therefore be this accurate for radiative association rate coefficients if kr is treated correctly. 

Modified thermal (Bates 1983) or phase space (Herbst 1985c) calculations of radiative association rates indicate, as expected, an inverse temperature dependence and a direct dependence on the complexity of the reaction partners. Thus, if theory is to be believed, the importance of radiative association is enhanced by complex molecules reacting in cold clouds. Let us consider two important examples in the synthesis of interstellar methane (Huntress and Mitchell 1979). Although methane can only be observed with difficulty via radioastronomical methods (by centrifugal distortion induced rotational transitions) because it does not possess a permanent dipole moment, its synthesis is an important one because methane is a precursor to more complex hydrocarbons which can be and have been detected. This synthesis can proceed via the following series of normal and radiative association reactions, most of which have been studied in the laboratory ... 

X0 is a positive, inverse temperature-dependent interaction parameter per solvent molecule (Allcock and Lampe, 1981). 

Kawai H, Umehara T, Fujiwara K, Tsuji T, Suzuki T (2006) Dynamic covalently bonded rotaxanes cross-linked by imine bonds between the axle and ring inverse temperature dependence of subunit mobility. Angew Chem Int Ed 45 4281 1286... 

Figure 7. The inverse temperature dependence of initial viscosity and direct dependence of cure chemorheology for poly(urea-urethane) adhesives yield activation energies of 9-12 Kcal/mole for viscous flow and 6-8 Kcal/mole for overall cure, respectively.

Due to the inverse temperature dependence of the Arrhenius relationship, these very low temperature studies cover a wide range on an Arrhenius plot. Combining CRESU results with higher temperature studies enables the competition of reaction channels with opposing temperature dependencies to be observed in some reactions. This produces an Arrhenius plot... 

In general, those resonances which are shifted through interaction with a paramagnetic ion are readily identified in an NMR spectrum their shifts are inversely temperature-dependent. 

However, in view of the rather complex variation of ay with temperature and density, the mean-field approach is. still very useful because it permits an estimate of the inversion temperature from an analytic expression [see Eq. (5.184)] at moderate computational expense. The computed inversion temperatures are plotted in Figs. 5.30 for various situations. In accord with the plots in Fig. 5.29, the inversion temperature depends strongly on the density. For example, plots in Fig. 5.30(a) show that, over a density range of 0.1 < p < 0.5, Tj v changes by about a factor of 3. Over wide ranges of temperature and density the data are again well represented by the mean-field exprassion in Eq. (5.184). 

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