Self-Diffusion of Poly(propylene imine) Dendrimers in Methanol Ivo B. Rietveld* and Dick Bedeaux Colloid and Interface Science Group, LIC, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands Received March 21, 2000 ABSTRACT: The self-diffusion coefficients have been determined for five generations of poly(propylene imine) dendrimers in methanol at three different temperaturess5, 25, and 45 °Csover the whole concentration range. Pulsed field gradient spin echo NMR has been used. The Stokes-Einstein hard sphere radii have been calculated in the zero concentration limit. They were equal, within error, to the radii found from the viscosity. The high-generation dendrimers have three concentration regimes: a dilute, a semidilute, and a concentrated regime. For the lower generations, only a dilute and a semidilute regime can be found. In the dilute regime, the self-diffusion coefficient decreases as a function of the concentration. In the semidilute regime, this decrease continues. In part of the semidilute and in the concentrated regime diffusion was very slow, and we were not able to measure the long time self-diffusion coefficient. As the transition from semidilute to concentrated solutions corresponds to a decrease of the radius of the dendrimer, dendrimers in concentrated solutions can be considered as collapsed though still separate molecules. The behavior in the semidilute and the concentrated regimes is very different from polymer diffusion. Introduction Dendrimers are very regularly and precisely defined molecules. Nowadays they seem to become more and more popular for use in many different applications as catalysis, light harvesting, and drug targeting. With this growing interest for the use of dendrimers, knowledge about their physical properties becomes more important. Applying this knowledge can improve the efficiency of the dendrimers in their applications. Furthermore, the regularity and monodispersity of the dendrimers makes them very interesting model systems. They help to understand the behavior of highly branched polymers. Those polymers are often much less well-defined and therefore less suitable for a systematic study of their physical properties. In applications, however, they are cheaper in use since they are much easier synthesized. Moreover, they can form much larger structures than the average dendrimer, which can be an advantage in real applications. The dilute solution properties of the dendrimers are thoroughly investigated. These studies were performed using neutron scattering, 1,2 viscosity, 3 gel permeation chromatography, 4 mass spectrometry, 5 computer simu- lations, 6,7 and methods that are more application based. 8 A picture of the structure and behavior of dendrimers evolves gradually from their results. As understood now, dendrimers have a dense core with back-folding branch- es. 6,9 The density has a maximum in the center. Usually a density plateau is found that, depending on the choice of dendrimer and experiment, falls off fast or slow to a low density tail. 2,6,9-14 Moreover, in dilute solutions these approximately spherical molecules behave like hard spheres. Swelling of dendrimers in simple solvents seems to be present but is much less than for normal polymers. 6,14-16 To our knowledge, the diffusion properties of den- drimers have not yet been studied thoroughly. Only a few studies, to determine the diffusion coefficient in the zero concentration limit and the resulting hard sphere radii 17,18 and the influence of the pH, 19,20 have been published. Furthermore, only a few experimental papers have been published about properties of concentrated solutions using viscometry 3,21 or neutron scattering. 21-23 In an earlier paper 22 we found, from the inverse osmotic compressibility, that dendrimers have three concentra- tion regimes. First, the dilute regime where all den- drimers are separate spheres. The dilute regime can be subdivided into a very dilute regime, where the den- drimers behave like hard spheres and a denser regime, φ > 0.18, where the solvation layers overlap. Second, at about 0.3 volume fraction, the beginning of the semidilute regime, the distance between the centers of the dendrimers becomes equal to twice the radius of gyration, causing them to shrink with increasing con- centration. This is confirmed by a small-angle neutron scattering paper by Topp et al. 23 In semidilute solutions, dendrimers form a close-packed system of soft spheres, with little interpenetration and no network formation. 3 Finally, at very high concentrations the 5th and 4th generations are found to resist any further shrinking. This is then called the concentrated regime. In this paper self-diffusion of dendrimers in dilute, semidilute, and concentrated solutions is studied. The self-diffusion coefficient is measured using field gradient NMR. Self-diffusion measurements make it possible to study the motion of separate dendrimers in solution. The self-diffusion coefficient can be found for a short time limit and a long time limit. 3 In the long time limit, the particle is slowed down due to correlations with other particles. Therefore, the long time diffusion coef- ficient is smaller than the short time diffusion coef- ficient. In a very dilute solution limit, the short and long time self-diffusion coefficients become equal. This limit- ing value is called D 0 . For D 0 , the diffusion is entirely dependent on the size of the particle and the solvent. For a spherical particle we use the Stokes-Einstein equation where k B is Boltzmann’s constant, T the absolute temperature, η the viscosity of the solvent, and r the D 0 ) k B T 6πηr (1) 7912 Macromolecules 2000, 33, 7912-7917 10.1021/ma000509e CCC: $19.00 © 2000 American Chemical Society Published on Web 09/30/2000