End-groups

Klein and co-workers have documented the remarkable lubricating attributes of polymer brushes tethered to surfaces by one end only [56], Studying zwitterionic polystyrene-X attached to mica by the zwitterion end group in a surface forces apparatus, they found /i < 0.001 for loads of 100 and speeds of 15-450 nm/sec. They attributed the low friction to strong repulsions existing between such polymer layers. At higher compression, stick-slip motion was observed. In a related study, they compared the friction between polymer brushes in toluene (ji < 0.005) to that of mica in pure toluene /t = 0.7 [57]. 

CFIDF end group, no selective reaction would occur on time scales above 10 s. Figure B2.5.18. In contrast to IVR processes, which can be very fast, the miennolecular energy transfer processes, which may reduce intennolecular selectivity, are generally much slower, since they proceed via bimolecular energy exchange, which is limited by the collision frequency (see chapter A3.13). 

Figure C2.4.1. Schematic diagram of a fatty acid witir a hydrophiiic (COO ) and a hydrophobic end group (CH ) (ieft) and of an amphiphiie in generai (right).

Apart from fatty acids, straight-chain molecules containing other hydrophilic end groups have been employed in numerous studies. In order to stabilize LB films chemical entities such as tlie alcohol group and tlie metliyl ester group have been introduced, botli of which are less hydrophilic tlian carboxylic acids and are largely unaffected by tlie pH of tlie subphase. 

An important step in tire progress of colloid science was tire development of monodisperse polymer latex suspensions in tire 1950s. These are prepared by emulsion polymerization, which is nowadays also carried out industrially on a large scale for many different polymers. Perhaps tire best-studied colloidal model system is tliat of polystyrene (PS) latex [9]. This is prepared with a hydrophilic group (such as sulphate) at tire end of each molecule. In water tliis produces well defined spheres witli a number of end groups at tire surface, which (partly) ionize to... 

The condensation leaves epoxy end groups that are then reacted in a separate step with nucleophilic compounds (alcohols, acids, or amines). Eor use as an adhesive, the epoxy resin and the curing resin (usually an aliphatic polyamine) are packaged separately and mixed together immediately before... 

The effect of different end groups on M can be seen by comparing the true molecular weight with an approximate molecular weight, calculated on the basis of a formula (CH2)n + 2- T se M s and the percentage difference between them are listed here for several values of n ... 

Although the difference is almost 5% for propane, it is closer to 0.1% for the case of n = 100, which is about the threshold for polymers. The precise values of these numbers will be different, depending on the specific repeat units and end groups present. For example, if Mq = 100 and = 80, the difference is... 

The terminal groups of a polymer chain are different in some way from the repeat units that characterize the rest of the molecule. If some technique of analytical chemistry can be applied to determine the number of these end groups in a polymer sample, then the average molecular weight of the polymer is readily evaluated. In essence, the concept is no different than the equivalent procedure applied to low molecular weight compounds. The latter is often included as an experiment in general chemistry laboratory classes. The following steps outline the experimental and computational essence of this procedure ... 

The method of end group analysis for molecular weight determination is not only simple to understand, but can also be done with ordinary laboratory equipment in many instances. 

Aqueous caprolactam is polymerized alone and in the presence of sebacic acid (S) or hexamethylenediamine (H).t After a 24-hr reaction time, the polymer is isolated and the end groups are analyzed by titrating the carboxyl groups with KOH in benzyl alcohol and the amino groups with p-toluenesulfonic acid in trifluoroethanol. The number of milliequivalents of carboxyl group per mole caprolactam converted to polymer, [A ], and the number of milliequivalents of amino groups per mole caprolactam converted to polymer, [B ], are given below for three different runs ... 

Note the units of the end group concentrations [A ] and [B ] milliequivalents per mole polymerized monomer. The reciprocal is therefore moles of monomer per milliequivalent of end groups. Accordingly, the molecular weight is given by... 

Only the last factor is a little tricky it is also different with and without additives. With no additive, polycaprolactam can be represented A BABAB. . . ABAB, where the A and B are acid and base groups, respectively, and those marked with the asterisk are those analyzed. Thus every molecule has one of each. In this case, then, we use the average of 12.0 and 11.6 as the end group concentration, and unity as the number of ends of each kind to obtain... 

The results of end group analyses must be examined on a system-by-system basis for correct interpretation. 

The molecular weights obtained by this method are averages. This is particularly evident from the situations where additives are present. In these cases, two different kinds of chains result, with those terminated by the same end group being stunted in growth compared to the normal polycaprolactam. Yet it is the total weight of polymer and the total number of ends that are... 

Note that the method of end group analysis is inapplicable to copolymers, since the presence of more than one repeat unit adds extra uncertainty as to the nature of chain ends. The above example included the remark that the molecular weights calculated in the example were average values. In the next section we shall examine this point in greater detail. 

How important is the end group correction introduced in Eq. (3.46) for this system ... 

This expression is consistent with the analysis of each of the lines in Table 5.1 as presented above and provides a general answer to one of the questions posed there. It is often a relatively easy matter to monitor the concentration of functional groups in a reaction mixture as we saw in discussing end group analysis as a method for molecular weight determination in Sec. 1.7. Equation (5.4) is... 

One of the most sensitive tests of the dependence of chemical reactivity on the size of the reacting molecules is the comparison of the rates of reaction for compounds which are members of a homologous series with different chain lengths. Studies by Flory and others on the rates of esterification and saponification of esters were the first investigations conducted to clarify the dependence of reactivity on molecular size. The rate constants for these reactions are observed to converge quite rapidly to a constant value which is independent of molecular size, after an initial dependence on molecular size for small molecules. The effect is reminiscent of the discussion on the uniqueness of end groups in connection with Example 1.1. In the esterification of carboxylic acids, for example, the rate constants are different for acetic, propionic, and butyric acids, but constant for carboxyUc acids with 4-18 carbon atoms. This observation on nonpolymeric compounds has been generalized to apply to polymerization reactions as well. The latter are subject to several complications which are not involved in the study of simple model compounds, but when these complications are properly considered, the independence of reactivity on molecular size has been repeatedly verified. 

Calculate the value of p at which the reaction should be stopped to obtain this polymer, assuming perfect stoichiometric balance and neglecting end group effects on. ... 

---