C 0 ca en C 0 � 0 POLYMER COMPOSITE SCIENCE AND HAIR GELS 501 Polyacrylate-2 Crosspolymer Tensile Properties ---.- Elongation 1200.0 ---- Young's Modulus 1000.0 800.0 600.0 400.0 200.0 4.2 4.3 0.0 None NaOH AMP TEA 20.0 18.0 ___ - 16.0 Ica 14.0 ';' ::I - -- 12.0 :i "Cl 10.0 j 8.0 en ·en - 6.0 C ::I , 4.0 � 2.0 0.0 Figure 2. Average tensile data for thin films of polyacrylate-2 crosspolymer, neutralized to pH 7 with NaOH, AMP, or TEA. The unneutralized polymer (none) is also shown for comparison. The error bars represent ± 1 standard deviation for the test. are the same as for chemical crosslinks: the rubbery plateau modulus increases and the glass transition temperature increases at higher crosslink densities (9,10). It has been shown that T g is proportional to cqla, where c is the amount of ionic groups, q is the charge, and a is the distance between ionic centers, which is related to the size of the counterion of the base (11). Because of the different chemical natures of the bases used in this study, it is expected that c) q, and a will vary for each of them. This is true even though the pH was ad justed to be the same for all polymers prior to film formation. A series of simple arguments can be used to establish a reasonable ordering for the cqla parameter. The case for NaOH is relatively clear. It is expected that Na will exist as the + 1 ionic species. Thus q = + 1, and c depends simply on the equivalents of COOH and Na. The relative size of a for Na vs TEA and AMP is easily seen to be: aNa a AMP aTEA· Assigning c and q values for TEA and AMP is more problematic. In the case of these amines, it is clear that c and q will both depend on the value of the equilibrium constant for the following reaction scheme: (2) where R represents H or an alkyl group. Estimation of this quantity is not trivial (12-14). This is mainly due to the possibility of encountering steric effects with non­ primary amines. The situation will be further complicated in the present case since the carboxyl group has additional constraints due to the fact that it is part of a polymer.

502 JOURNAL OF COSMETIC SCIENCE Related work allows us to make reasonable estimates of the relative sizes of the equi­ librium constants for TEA and AMP (15,16). To see how this can be done, first note that AMP is a primary amine whereas TEA is a tertiary amine. Thus, there would be little or no steric effects for AMP but large effects for TEA. Smith and Goulet (15), working with primary amines, make a good case for these molecules having close to 100% neutralization of the acid species. Thus it is to be expected that q - 1 for AMP and c is close to the equivalence ratio of AMP and carboxyl. Likewise, Weiss and Agarwal (16) show that tertiary amines have a significantly lower level of ionic species. Thus q 1 for TEA, and there will be a significant amount of neutral TEA as well as COOH. These data allow reasonable comparisons to be made for the c! q! and a variables for the molecules being investigated here. First consider a. As noted above, it is readily apparent that the size of the ion will be in the order TEA AMP Na. Next consider c. It is apparent that c will be the greatest for Na since its bond with a carboxylate group is purely ionic. However, again as already discussed, TEA and AMP can both exist either as the cation or as the neutral species. Consequently, they will each exhibit a somewhat lower effective charge than the Na species. Even so, the considerations in the previous paragraph indicate that c AMP - 1 and cTEA 1. Thus, the relative order for c is Na - AMP TEA. Finally consider q. This quantity can be estimated in a similar manner to c. Again, Na will be expected to have a value of about 1, but TEA and AMP will be expected to be lower. The expected order will be AMP TEA since AMP has greater access to the H atom of the COOH moiety, which gives it a higher effective charge. Therefore, the relative order for q is Na AMP TEA. The results of these arguments can be summarized as shown in Table I. It can be seen that they are sufficient to order the cqla parameter and hence the T g results for the molecules of interest. In addition to ionomeric crosslinking, AMP and TEA are low-molecular-weight organic molecules, which can plasticize the polymer and lower T g· The same type of arguments used above can be used to establish the relative ordering for plasticization effects. First, note that both size and charge effects are expected to be of importance in determining plasticization. It is expected that a larger size and a smaller charge (i.e., a greater effective amount of neutral species) will produce a greater degree of plasticization. As shown in the table, TEA will have both the greatest amount of neutral species available and also the largest size compared with AMP. Likewise, AMP is larger and less charged than Na. This means that the plasticizing ability is predicted to be in the order TEA AMP Na, as is actually seen in Figures 1 and 2 and discussed above. It will be shown below that these same arguments can also be used to understand relative humidity effects. The overall outcome on polymer cohesion thus depends on the relative levels of ionomer and plasticizer effects caused by the neutralizer. At the two extremes, the sodium Table I Relative Estimates for the Variables of Importance for Determining T g Base q a cqla NaOH High High Low High AMP Medium-high Medium Medium Medium TEA Low Low High Low Definitions for each variable are given in the body of the text.