Propagator proton

A protonic acid derived from a suitable or desired anion would seem to be an ideal initiator, especially if the desired end product is a poly(tetramethylene oxide) glycol. There are, however, a number of drawbacks. The protonated THF, ie, the secondary oxonium ion, is less reactive than the propagating tertiary oxonium ion. This results in a slow initiation process. Also, in the case of several of the readily available acids, eg, CF SO H, FSO H, HCIO4, and H2SO4, there is an ion—ester equiUbrium with the counterion, which further reduces the concentration of the much more reactive ionic species. The reaction is illustrated for CF SO counterion as follows ... 

If the initiation reaction is much faster than the propagation reaction, then all chains start to grow at the same time. Because there is no inherent termination step, the statistical distribution of chain lengths is very narrow. The average molecular weight is calculated from the mole ratio of monomer-to-initiator sites. Chain termination is usually accompHshed by adding proton donors, eg, water or alcohols, or electrophiles such as carbon dioxide. 

Oxirane57). If the conditions are chosen such as to avoid propagation (low temperature, Li+ or Na+ are better counterions than K+ in this respect) one single oxirane unit is added, yielding after protonation a polymer fitted at chain end with an alcohol function. 

If the nucleophilicity of the anion is decreased, then an increase of its stability proceeds the excessive olefine can compete with the anion as a donor for the carbenium ion, and therefore the formation of chain molecules can be induced. The increase of stability named above is made possible by specific interactions with the solvent as well as complex formations with a suitable acceptor 112). Especially suitable acceptors are Lewis acids. These acids have a double function during cationic polymerizations in an environment which is not entirely water-free. They react with the remaining water to build a complex acid, which due to its increased acidity can form the important first monomer cation by protonation of the monomer. The Lewis acids stabilize the strong nucleophilic anion OH by forming the complex anion (MtXn(OH))- so that the chain propagation dominates rather than the chain termination. 

Fig. 16. Energy profiles of the protonation and propagation reactions of ethene in the gas phase and in solution (CH2C12) starting with 4 monomer units and a free proton...

Figure 43. Probability density of the wavepacket after 30 fs of field-free propagation of the accelerated wavepacket as a function of (a) proton coordinate, (b) N=C bond length, (c) proton momentum, and (d) N=C bond momentum. Taken from Ref. [41].

Figure 5.1.7 shows the propagator of the motion measured for a clean and a biofilm impacted capillary [14,15] and the residence time distributions calculated for each from these velocity distributions. The clean capillary gives an experimental propagator equal to the theoretical velocity distribution convolved with a Gaussian diffusion curve [14], as shown in Figure 5.1.2. For the flow around the biofilm structure note the appearance of a high velocity tail indicating higher probability of large displacements relative to the clean capillary. The slow flow peak near zero displacement results from the protons trapped within the EPS gel matrix where the...

In an early work by Mertz and Pettitt, an open system was devised, in which an extended variable, representing the extent of protonation, was used to couple the system to a chemical potential reservoir [67], This method was demonstrated in the simulation of the acid-base reaction of acetic acid with water [67], Recently, PHMD methods based on continuous protonation states have been developed, in which a set of continuous titration coordinates, A, bound between 0 and 1, is propagated simultaneously with the conformational degrees of freedom in explicit or continuum solvent MD simulations. In the acidostat method developed by Borjesson and Hiinenberger for explicit solvent simulations [13], A. is relaxed towards the equilibrium value via a first-order coupling scheme in analogy to Berendsen s thermostat [10]. However, the theoretical basis for the equilibrium condition used in the derivation seems unclear [3], A test using the pKa calculation for several small amines did not yield HH titration behavior [13],... 

The titration coordinates evolve along with the dynamics of the conformational degrees of freedom, r, in simulations with GB implicit solvent models [37, 57], An extended Hamiltonian formalism, in analogy to the A dynamics technique developed for free energy calculations [50], is used to propagate the titration coordinates. The deprotonated and protonated states are those, for which the A value is approximately 1 or 0 (end-point states), respectively. Thus, in contrast to the acidostat method, where A represents the extent of deprotonation, is estimated from the relative occupancy of the states with A 1 (see later discussions). The extended Hamiltonian in the CPHMD method is a sum of the following terms [42],... 

Protonic acids are less suitable because the conjugate base is too active a nucleophile. HC1, for example, will not initiate polymerization because chloride ion adds immediately to the carbenium ion before the latter can propagate. Other initiators which have been studied include electroinitiation, photoinitiation and ionizing radiation. 

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