Intramolecular randomization

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

The polymerization of ethyleneimine (16,354—357) is started by a catalyticaHy active reagent (H or a Lewis acid), which converts the ethyleneimine into a highly electrophilic initiator molecule. The initiator then reacts with nitrogen nucleophiles, such as the ethyleneimine monomer and the subsequendy formed oligomers, to produce a branched polymer, which contains primary, secondary, and tertiary nitrogen atoms in random ratios. Termination takes place by intramolecular macrocycle formation. 

Because the tertiary structure of a globular protein is delicately held together by weak intramolecular attractions, a modest change in temperature or pH is often enough to disrupt that structure and cause the protein to become denatured. Denaturation occurs under such mild conditions that the primary structure remains intact but the tertiary structure unfolds from a specific globular shape to a randomly looped chain (Figure 26.7). 

The structure of the chain, i.e., whether it is a helix or a random coil, might influence not only the rate but also the stereospecificity of the growing polymer. For example, it is plausible to expect that in normal vinyl polymerization helix formation might favor specific placement, say isotactic, while either placement would be approximately equally probable in a growing random coil. Formation of a helix requires interaction between polymer segments, and this intramolecular interaction is enhanced by bad solvents particularly those which precipitate the polymer. 

As has been described in Chapter 4, random copolymers of styrene (St) and 2-(acrylamido)-2-methylpropanesulfonic acid (AMPS) form a micelle-like microphase structure in aqueous solution [29]. The intramolecular hydrophobic aggregation of the St residues occurs when the St content in the copolymer is higher than ca. 50 mol%. When a small mole fraction of the phenanthrene (Phen) residues is covalently incorporated into such an amphiphilic polyelectrolyte, the Phen residues are hydrophobically encapsulated in the aggregate of the St residues. This kind of polymer system (poly(A/St/Phen), 29) can be prepared by free radical ter-polymerization of AMPS, St, and a small mole fraction of 9-vinylphenanthrene [119]. 

Reference to the infinite structures as networks would seem inconsistent with our assumption, introduced as an approximation, that no intramolecular reactions occur. A randomly branched structure devoid of intramolecular linkages could hardly be called a network the latter term conveys the notion of circuitous interconnections within the structure. Actually, as will appear later, the assumption referred to need only be applied to the finite molecular species its extension to the infinite structure is superfluous. Certainly it will contain an abundance of intramolecular connections, which, in fact, is an essential feature of the gel structure... 

The local conformational preferences of a PE chain are described by more complicated torsion potential energy functions than those in a random walk. The simulation must not only establish the coordinates on the 2nnd lattice of every second carbon atom in the initial configurations of the PE chains, but must also describe the intramolecular short range interactions of these carbon atoms, as well as the contributions to the short-range interactions from that... 

Many synthetic water-soluble polymers are easily analyzed by GPC. These include polyacrylamide,130 sodium poly(styrenesulfonate),131 and poly (2-vinyl pyridine).132 An important issue in aqueous GPC of synthetic polymers is the effect of solvent conditions on hydrodynamic volume and therefore retention. Ion inclusion and ion exclusion effects may also be important. In one interesting case, samples of polyacrylamide in which the amide side chain was partially hydrolyzed to generate a random copolymer of acrylic acid and acrylamide exhibited pH-dependent GPC fractionation.130 At a pH so low that the side chain would be expected to be protonated, hydrolyzed samples eluted later than untreated samples, perhaps suggesting intramolecular hydrogen bonding. At neutral pH, the hydrolyzed samples eluted earlier than untreated samples, an effect that was ascribed to enlargement... 

In random bond percolation, which is most widely used to describe gelation, monomers, occupy sites of a periodic lattice. The network formation is simulated by the formation of bonds (with a certain probability, p) between nearest neighbors of lattice sites, Fig. 7b. Since these bonds are randomly placed between the lattice nodes, intramolecular reactions are allowed. Other types of percolation are, for example, random site percolation (sites on a regular lattice are randomly occupied with a probability p) or random random percolation (also known as continuum percolation the sites do not form a periodic lattice but are distributed randomly throughout the percolation space). While the... 

The paper first considers the factors affecting intramolecular reaction, the importance of intramolecular reaction in non-linear random polymerisations, and the effects of intramolecular reaction on the gel point. The correlation of gel points through approximate theories of gelation is discussed, and reference is made to the determination of effective functionalities from gel-point data. Results are then presented showing that a close correlation exists between the amount of pre-gel intramolecular reaction that has occurred and the shear modulus of the network formed at complete reaction. Similarly, the Tg of a network is shown to be related to amount of pre-gel intramolecular reaction. In addition, materials formed from bulk reaction systems are compared to illustrate the inherent influences of molar masses, functionalities and chain structures of reactants on network properties. Finally, the non-Gaussian behaviour of networks in compression is discussed. 

The curves in Figure 1 describe intramolecular reaction in irreversible, linear and non-linear random polymerisations. For linear polymerisations, theories have been developed(7,11,12) which account for the decrease in cext as a reaction proceeds and allow Nr to be calculated satisfactorily as a function of p for a given value of Pab. For non-linear polymerisations, the larger numbers of ring structures result in less adequate descriptions of Nr versus p curves using similartheories(12-17). Such theories require more development before Nr as a function of p and the gel... 

The preceding sections have shown that pre-gel intramolecular reaction always occurs in random polymerisations, and that the amount of such reaction dependes on the dilution (ce -- -), molar masses (v), chain structures (b) and functionalities (f) of the reactants. Intramolecular reaction leads to loops of finite size in the network material finally formed by a reaction mixture. Such loops may be elastically ineffective and have marked effects on the properties of the material. The present section investigates the magnitudes of such effects with regard to shear modulus and Tg. 

As is clear from the earlier discussions of pre-gel intramolecular reaction, such reaction in principle always occurs in random polymerisations, although its amount may be reduced by using reactants of higher molar mass, lower functionalities, and stiffer chain structures. Thus, the use of end-linking reactions to produce model networks (for example(35) and references quoted... 

The factors which influence pre-gel intramolecular reaction in random polymerisations are shown to influence strongly the moduli of the networks formed at complete reaction. For the polyurethane and polyester networks studied, the moduli are always lower than those expected for no pre-gel intramolecular reaction, indicating the importance of such reaction in determining the number of elastically ineffective loops in the networks. In the limit of the ideal gel point, perfect networks are predicted to be formed. Perfect networks are not realised with bulk reaction systems. At a given extent of pre-gel intramolecular... 

---