Determination of the intrinsic proton binding constants for poly(amidoamine) dendrimers via potentiometric pH titration

Macromolecules

Volumn 36, Issue 15, 2003, Pages 5725-5731

  Niu, Yanhui ^a   Sun, Li ^a   Crooks, Richard M ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PROTONATION;

ADSORPTION ISOTHERMS; BINDING ENERGY; HYDROPHILICITY; HYDROPHOBICITY; PH EFFECTS; POLYAMIDES; PROTONS; TITRATION;

DENDRIMERS;

EID: 0042703152     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma034276d     Document Type: Article

References (38)

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14. This is the ionic strength at the end of a titration, where the initial HCl is completely converted to NaCl. At the beginning of the titration, the majority of the proton from HCl binds with dendrimer, and the ionic strength is not well-defined. For example, the ionic strength is lower than the value quoted here if we exclude the contribution from the molecules being studied: i.e., charged dendrimer molecules and their associated counterions. Otherwise, a higher value will be obtained because a highly charged dendrimer molecule contributes more to ionic strength than a simple 1:1 salt.
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17. To quantify this error, two G3-OH models are considered. The first model consists of three proton-binding shells with the following configuration: 3.6 nm (OH-group shell), 2.9 nm (16), 2.2 nm (8), and 1.5 nm (6), where the two core N atoms are included in the innermost shell. The second model consists of four proton-binding shells with configuration: 3.6 nm (OH-group shell), 2.9 nm (16), 2.2 nm (8), 1.5 nm (4), and 0.37 nm (2), where the two N sites (ethylenediamine core) are modeled as a separate shell. Results based on the above models and other typical parameters (temperature, ionic strength, etc.) indicate that, along a typical calculated titration curve, the maximum errors in both pH and in average proton binding number are consistently less than 3%. The corresponding average errors are even smaller (<0.3%).
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19. Equation 4 has exactly the same form as a well-known theory for analyzing protonation of colloids and polymers. In fact, G(h) has already been used to model protonation of a cascade dendrimer. See, for example: Zhang, H.; Dubin, P. L.; Kaplan, J.; Moorefield, C. N.; Newkome, G. R. J. Phys. Chem. B 1997, 101, 3494-3497.
20. The experimental G(h) curve bends upward at low h values and downward at high h values. From these trends we can conclude that there exists systematic errors in experimental h values. One possible cause for these errors is that the ionic strength of the sample solution is different than that of the standard pH solutions used to calibrate the pH meter. However, the magnitude of the error in the experimental G(h) values is probably too large to be explained solely by this factor. Another possible explanation is that dendrimer dimensions are not static, as we have assumed in our model. Rather, dendrimer diameters for all the shells can expand as the degree of protonation increases. To limit the scope of this study, we have chosen to ignore pH-sensitive dendrimer expansion in this paper.
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24. This is the value for a PAMAM dendrimer with an ammonia core (three branches) whereas the dendrimer we used has an ethylenediamine core (four branches). Thus, the value quoted here might be an upper limit because we expect a smaller electrolyte volume for the four-branch core.
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28. This expression gives the electric potential energy around an ion according to the Debye-Hückel theory. The size of the counterions in the Debye-Hückel model is set to zero, as it is in our shell model.
29. AVG is used here: the average dynamic distance between two terminal amines is estimated to be 0.4 nm using established C-N and C-C bond lengths and the root-mean-square formula described in ref 18 (only applicable when the intervening C-N and C-C bonds have complete translational and rotational freedom). As expected, this value is comparable to the average radius difference (0.35-0.45 nm) between two neighboring shells of a PAMAM dendrimer because these shells are separated by roughly the same number of covalent bonds. Other implied assumptions in eq 8 are (a) only mobile ion distribution around one of the amine sites is considered whereas (b) the other site is treated as a nonperturbing test charge.
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34. A will decrease as ionic strength increases. As a result, pK will increase as ionic strength increases.
35. 1 in the following reference, contains a tertiary amine connected to two amide bonds through ethylene linkers: Barbucci, R.; Casolaro, M.; Danzo, N.; Beni, M. C.; Barone, V.; Ferruti, P. Gazz. Chim. Ital. 1982, 112, 105-113.
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37. 2. However, this might not be the case if more scaling factors (e.g., one for each shell) were used.
38. The compound we selected is N-acetylethylenediamine: a primary amine linked to one amide bond through an ethylene linker. Its pK 9.28. See: Hall, H. K., Jr. J. Am. Chem. Soc. 1956, 78, 2570-2572.