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Not only are the different ring positions on phenol of different reactivity, but one expects that the two functional groups of formaldehyde would also differ. The second functional group of formaldehyde actually corresponds to the methylol group, since the reaction of a methylolphenol with a phenol molecule (or with a second methylolphenol) probably proceeds by a sequence such as

If we take the limit a ---T 0 after doing the integral in (2.159), the various derivatives of a(~) are given by

2-175

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d a d C4 = 0, ... a~O ~ a~O ." a~O ~ a~O ." (2.160) Now if we expand (2.157) into an Euler-Maclaurin series [433], we find that d a a C a 1 ----;u: = - 2c 2 l' dd C2 = -4.", l' d,lC3 1m .", 1m 1m





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Direct kinetic measurements are not available to show the reactivity of the methylol group in this reaction compared to the initial reaction of formaldehyde. However, the general observation that the amounts of di- and polynuclear compounds present in resole prepolymers differ widely depending on the reaction condition (temperature, pH, speci c catalyst used, concentrations of reactants) indicates that the two functional groups of formaldehyde differ in reactivity. A further complication in the phenol-formaldehyde polymerization is that it may involve a decrease in functional group reactivity with molecular size. This can easily happen in systems that undergo extensive crosslinking. Such systems may cease to be homogeneous solutions before the experimentally determined gel point. The gel point may be preceded by the formation of microgel particles (Sec. 2-2d) which are too small to be visible to the naked eye [Katz and Zwei, 1978]. Functional groups in the microgel particles would be relatively unreactive because of their physical unavailability. Similar considerations would apply for the reaction period subsequent to the gel point. A decrease in reactivity with size may not be due to molecular size but a consequence of steric shielding of ortho or para positions of benzene rings within a chain compared to those positions on rings at the chain ends [Kumar et al., 1980].

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2-12b-2

If the relevant physics is independent of the manner in which the reflectivity falls off with frequency, we are allowed to take the limit a ---T 0 in (2.161). Then all derivatives of a vanish at ~ = 0, except the third derivative, and we find that

Phenol formaldehyde prepolymers, referred to as novolacs, are obtained by using a ratio of formaldehyde to phenol of 0.75 0.85 : 1, sometimes lower. Since the reaction system is starved for formaldehyde, only low molecular weight polymers can be formed and there is a much narrower range of products compared to the resoles. The reaction is accomplished by heating for 2 4 h at or near re ux temperature in the presence of an acid catalyst. Oxalic and sulfuric acids are used in amounts of 1 2 and <1 part, respectively, per 100 parts phenol. The polymerization involves electrophilic aromatic substitution, rst by hydroxymethyl carbocation and subsequently by benzyl carbocation each formed by protonation of OH followed by loss of water. There is much less benzyl ether bridging between benzene rings compared to the resole prepolymers.

(2.162) This potential implies an attractive force per unit area, or pressure on the plates, given by 1 dU (2.163) L2 dl This is the Casimir force, or more precisely, pressure. For a plate separation of 1 cm, this pressure is only 1.3 x 10- 18 dyn/cm2. This is so weak that it is even less than half of the electrostatic pressure on the plates if they were charged with a single electron [Le., 47re2/ L 4 ~ 2.9 X 10- 18 dyn/cm 2 (where e is the charge of the electron)). But on the scale of nanomachinery (millimeter to nanometer range) the Casimir force is dominant [83, 309, 352, 353].

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