Robertson theory

In another molecular approach Argon (28) has proposed a theory of yielding for glassy polymers based on the concept that deformation at molecular level consists in the formation of a pair of molecular kinks. The resistance to double kink formation is considered to arise from the elastic interactions between chain molecule and its neighbors, ie, from intermolecular forces. This is in contrast to the Robertson theory, where intramolecular forces are of primary consideration. We need to recall that the intramolecular forces are by several orders of magnitude stronger than the intermolecular ones—except for entanglements which operate as if they were primary chemical bonds. 

Piiiing M J and Smith i W M (eds) 1987 Modern Gas Kinetics. Theory, Experiment and Application (Qxford Biackweii) Giibert R G and Smith S C (eds) 1990 Theory of Unimolecular and Recombination Reactions (Qxford Biackweii) Fioibrook K A, Piiiing M J and Robertson S Fi (eds) 1996 Unimolecular Reactions 2nd edn (Chichester Wiiey)... 

Gilbert R G and Smith S C 1990 Theory of Unimolecular andRecombinationReactions (Oxford Blackwell) Holbrook K, Pilling M J and Robertson S H 1996 Unimolecular Reactions (New York Wiley)... 

The theory of Robertson and Yarwood [84] is very similar in its spirit to the initial one of Bratos [83], but it considers, following Kubo [97], the angular... 

Price, D., Jaffe, J. und Robertson, G. E. Shock Sensitivity of Solid Explosives and Propellants, XXXVI. Int. Kongrefi f. Industrielle Chemie, Brussel 1966Lee, J. H., Knystautas, R. und Bach, G. G. Theory of Explosion, McGill University Press, Montreal 1969... 

C. Gatti and A. Famulari Interaction Energies and Densities. A Quantum Theory of Atom in Molecules insight on the Effect of Basis Set Superposition Error Removal , P.G. Mezey and B. Robertson (Eds.), Understanding Chemical Reactivity Electron, Spin and Momentum Densities and Chemical Reactivity, Vol. 2, Kluwerbook series (1999). In press. 

H. Weyl, The Theory of Groups and Quantum Mechanics (tr. H.P. Robertson) (New York, Dover Publications, 1984)... 

Several theories have been advanced to explain the effect. JsTordman and Lipscomb [1] have favoured a thermal explanation. Robertson and Ubbelohde [2], on the other hand, have auvanced a theory in which the effect of the different zero point energies of hydrogen and deuterium is to alter the resonance contribution to the bond. (See also [3].) Evidence will be advanced later to show that the isotope effect is a zero point energy phenomenon. 

Different approaches were used to describe the yielding of polymers quantitatively. Some theories took into account the free volume fraction. Eyring considered thermally activated mechanisms, and Robertson s model was based on changes of chain conformations. Argon s and Bowden s models were based on a metallurgical approach and a dislocation theory. A brief summary of the existing yielding theories is presented. 

Robertson s theory fits experimental data for both thermoplastics and thermosets (Cook et al., 1998) values for the activation volume are comparable with the theoretical ones (va 0.1 nm3), but exhibit some discrepancy at high temperatures. 

S. H. Robertson, N. Snider, and D. M. Wardlaw, J. Phys. Chem., 97, 7556 (1993). Strong Collision Broadening Factors from Theories of Unimolecular Rate Coefficients. 

Bas DC, Rogers DM, Jensen JH (2008) Very fast prediction and rationalization of pKa values for protein-ligand complexes. Proteins 73 765-783. doi 10.1002/prot.22102 Li H, Robertson AD, Jensen JH (2005) Very fast empirical prediction and rationalization of protein pKa values. Proteins 61 704-721. doi 10.1002/prot. 20660 Olsson MH, Sondergaard CR, Rostkowski M, Jensen JH (2011) PROPKA3 consistent treatment of internal and surface residues in empirical pKa predictions. J Chem Theory Comput 7 525-537... 

Here, G(t) is the quantum autocorrelation function (ACF) of the dipole moment operator responsible for the dipolar absorption transition, whereas oo is the angular frequency and t is the time. Equation (1) has been used, for example, by Bratos [45] and Robertson and Yarwood [46] in their semiclassical studies of H-bonded species within the linear response theory. 

The basic quantum theories [47-50], dealing with the IR line shape of the vX-h °f weak H-bonded species working within the linear response theory have been performed with the aid of Eq. (4) in place of (1) used by Bratos [45] and Robertson and Yarwood [46]. 

Equation (153) is the semiclassical limit of the quantum approach of indirect damping. Now, the question may arise as to how Eq. (153) may be viewed from the classical theory of relaxation in order to make a connection with the semiclassical approach of Robertson and Yarwood, which used the classical theory of Brownian motion. 

In Section IE, a theoretical approach of the quantum indirect damping of the H-bond bridge was exposed within the strong anharmonic coupling theory, with the aid of the adiabatic approximation. In Section III, this theory was shown to reduce to the Marechal and Witkowski and Rosch and Ratner quantum approaches. In Section IV, this quantum theory of indirect damping was shown to admit as an approximate semiclassical limit the approach of Robertson and Yarwood. 

Recall that in the slow modulation limit, the Robertson and Yarwood ACF reduces in turn to that used by Bratos, in his pioneering work dealing with the SD of H-bonded species within the linear response theory. Also recall that there are two generalizations of the semiclassical model of Robertson and Yarwood, one by Sakun [78] and the other by Abramczyk [79]. The first is incorporating memory functions and the second rotational structure. 

---