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probably also responsible for the lower Tc values relative to formaldehyde.) Thus weak bases such as amines cannot be used to polymerize higher aldehydes than formaldehyde. Alkali metal alkyls and alkoxides are required. The presence of adventious water is deterimental, since the initiator reacts to form hydroxide ion, which is too weak to initiate polymerization. Ketones are unreactive toward polymerization because of the steric and inductive effects of two alkyl groups. Exceptions to this generalization are some copolymerizations of ketones with formaldehyde and the polymerization of thiocarbonyl monomers [Colomb et al., 1978]. Aromatic aldehydes are also unreactive. A side reaction occurring with acetaldehyde and higher aldehydes containing a-hydrogens is aldol condensation [Hashimoto et al., 1976, 1978; Yamamoto et al., 1978]. Aldol reaction can be extensive at ambient temperatures and higher but is avoided by polymerization at low temperature. The substitution of halogens on the alkyl group of an aliphatic aldehyde greatly enhances its polymerizability (both from the kinetic and thermodynamic view points [Kubisa and Vogl, 1980]. Trichloroacetaldehyde (chloral) is easily polymerized by such weak bases as pyridine, alkali thiocyanates, and even chloride ion. Further, the polymerization of chloral by butyllithium at 78 C is complete in less than a second [Bus eld and Whalley, 1965]. The electron-withdrawing inductive effect of the halogens acts to stabilize the propagating anion XLIV by decreasing the charge density on the negative oxygen. The effect of halogens on reactivity is also seen for uorothiocarbonyl monomers. Thiocarbonyl uoride is polymerized at 78 C by a trace of mild base such as dimethylformamide. The polymerization of hexa uorothioacetone is an extreme example of the effect of



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d 3 k {II*(k, t) . II(k, t)

ceiling temperature on polymerization. Tc is very low but polymerization proceeds smoothly at 110 C.

+ c2 k 2 A*(k, t) . A(k, t)},

Thioacetone polymerizes adventitiously even at very low temperature, in contrast to the inability of acetone to polymerize. 5-6b Cationic Polymerization

(5.98)

Carbonyl monomers can be polymerized by acidic initiators, although their reactivity is lower than in anionic polymerization. Protonic acids such as hydrochloric and acetic acids and Lewis acids of the metal halide type are effective in initiating the cationic polymerization of carbonyl monomers. The initiation and propagation steps in polymerizations initiated with protonic acids can be pictured as





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Function Elements All functions start with an equals sign (=). Functions are distinct in that each one has a name. For example, the function that sums data is called SUM. You can use functions by typing them directly into your worksheet cells or Formula bar; you can also use the Insert Function dialog box to select and apply functions to your data. Types of Function Excel groups functions into 12 categories, each of which includes a variety of functions:

HO C +(A )

where the first term on the right-hand side of (5.98) is the minimal coupling term describing the interaction with matter. Hamilton equations of motion for the discrete variables {ra, Pa} are obtained from the Hamiltonian H by [108]

5-129

~P .'

(n + 1)

(5.99) (5.100)

O C +(A )

= --!l-'

5-130

where j stands for each of the three independent Cartesian components of these vectors. Hamilton equations of motion for the continuous complex variables {A(k, t), II(r, t)} are obtained from the Hami.ltonian H by [l08]

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The termination reaction probably involves chain transfer with water or some other species present. Competing side reactions in cationic polymerization of carbonyl monomers include cyclotrimerization and acetal interchange. Cyclotrimerization is minimized by low-polarity solvents, low temperatures, and initiators of low acidity. Acetal interchange reactions among different polymer chains do not occur except at higher temperatures. Acetaldehyde and higher aldehydes are reasonably reactive in cationic polymerization compared to formaldehyde. Haloaldehydes are lower in reactivity compared to their nonhalogen counterparts. 5-6c Radical Polymerization

'* A. (k, t)

The carbonyl double bond has not generally been susceptible to polymerization by radical initiators. There are two reasons for this behavior: (1) the carbonyl group is highly polarized and not prone to attack by a radical; and (2) most radicals are produced at temperatures above the ceiling temperatures of carbonyl monomers. There are, however, a few isolated cases of carbonyl polymerizations by radical initiators. Tri uoroacetaldehyde has been polymerized using benzoyl peroxide at 22 C. The polymerization is slow, with 18 h required to obtain 90% conversion [Bus eld and Whalley, 1965]. However uorothiocarbonyl monomers such as thiocarbonyl uoride have been polymerized at high rates by using a trialkylboron oxygen redox system at 78 C [Sharkey, 1975]. Thioacetone is also polymerized by this redox system.

Category Financial Date & Time Math & Trig Statistical Lookup & Reference Database Text Logical Information Engineering Cube Compatibility Description Includes functions for calculating loans, principal, interest, yield and depreciation. Includes functions for calculating dates, times and minutes. Includes a wide variety of functions for calculations of all types. Includes functions for calculating averages, probabilities, rankings, trends and more. Includes functions that enable you to locate references or specific values in your worksheets. Includes functions for counting, adding and filtering database items. Includes text-based functions to search and replace data and other text tasks. Includes functions for logical conjectures, such as if-then statements. Includes functions for testing your data. Offers many functions for engineering calculations. Enables Excel to fetch data from SQL Server Analysis Services, such as members, sets, aggregated values, properties and KPIs. Use these functions to keep your workbook compatible with earlier versions of Excel.

= f/JII.(k, t)'

Radical polymerizations are observed with these monomers because the electronwithdrawing substituents on the carbonyl and thiocarbonyl group decrease its polarity (and polarizability). The greater susceptibility of the thiocarbonyl double bond to radical polymerization is due to the lower electronegativity of sulfur compared to oxygen. The thiocarbonyl group is less polar than the carbonyl group and more prone to attack by a radical. The successful radical polymerization of thiocarbonyl monomers is also due in large part to the low temperature initiation process employed. 5-6d End Capping

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