J. Phys. Chem. B 2010, 114, 1751–1756
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Intramolecular Structural Change of PAMAM Dendrimers in Aqueous Solutions Revealed by Small-Angle Neutron Scattering Lionel Porcar,† Kunlun Hong,‡ Paul D. Butler,§ Kenneth W. Herwig,| Gregory S. Smith,| Yun Liu,*,§ and Wei-Ren Chen*,| Institut Laue-LangeVin, B.P. 156, F-38042 Grenoble CEDEX 9, France, The Center for Nanophase Materials Sciences, Neutron Scattering Science DiVision, Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, and The NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6100, ReceiVed: July 8, 2009; ReVised Manuscript ReceiVed: NoVember 26, 2009
Small-angle neutron scattering (SANS) experiments were carried out to investigate the structure of aqueous (D2O) G4 PAMAM dendrimer solutions as a function of molecular protonation and dendrimer concentration. Our results indicate unambiguously that, although the radius of gyration RG remains nearly invariant, the dendrimer radial density profile F(r) decreases in the dendrimer core with a continuous increase in protonation. This discovery also suggests that RG, which is commonly adopted by numerous simulation and experimental works in describing the global dendrimer size, is not suitable as the index parameter to characterize the dendrimer conformation change. We also found that RG and F(r), for dendrimers dissolved in both neutral and acidified solutions, remain nearly constant over the studied concentration range. We further demonstrate that the outcome of the widely used Guinier method is questionable for extracting RG in the concentration range studied. Our results reveal the polymer colloid structural duality as benchmarks for future experimental and theoretical studies and provide a critical step toward understanding drug encapsulation by ionic bonds. I. Introduction Dendrimers are a class of regularly branched macromolecules synthesized from a multifunctional core with a succession of iterative processes that double the number of reactive termini for each generation.1 They can be envisioned as polymeric colloidal nanoparticles. Globular in shape like spherical colloids, they exhibit additional internal degrees of freedom that give rise to rich structural and dynamic features.2 In addition to scientific interest, dendrimers possess an array of highly desirable properties that makes them excellent candidates for the templates for specific drug and gene delivery agents.1 An essential step to developing such potential uses is to understand the evolution of their molecular structure as a function of various environmental parameters. Extensive studies have clearly highlighted this necessity; the measurement of intrinsic viscosity has shown the swollen effect of a dendrimer in different solvents.2 Small-angle neutron (SANS) and X-ray (SAXS) scattering experiments have been used to evaluate the molecular characteristics of dendrimers in various aqueous environments of biological relevance.3 Moreover, computer simulations, evolving from a coarse-grain approximation4 to first principles calculations,5 have flourished and provided a complementary means to exploit the conformational dependence of dendrimers on various thermodynamical conditions. Generally, the radius of gyration RG, calculated as the square root of the second moment of the molecular density profile, is * To whom correspondence should be addressed. E-mail: (Y.L.)
[email protected]; (W.-R.C.)
[email protected]. † Institut Laue-Langevin. ‡ The Center for Nanophase Materials Sciences, Oak Ridge National Laboratory. § National Institute of Standards and Technology. | Neutron Scattering Science Division, Spallation Neutron Source, Oak Ridge National Laboratory.
used to quantify the overall molecular size of polymers in solution. The determination of RG has emerged as the parameter of choice to gauge the accuracy of simulations and has been the subject of considerable scattering works. While RG gives a global measure of physical size, the intramolecular structure of dendrimers in solution is poorly understood. In this report, the intramolecular structural response of polyamidoamide (PAMAM) dendrimers in aqueous solution to charging and concentration variation is conclusively unveiled experimentally by SANS for the first time. A mean-field model for the neutron coherent scattering cross section based on standard statistical mechanics is used to analyze the scattering intensity I(Q) and extract the dendrimer radial density distribution F(r).7 Our results show that the significant conformational change due to the protonation of the amines cannot be reflected in the evolution of RG alone. Further, we demonstrate that the common practice used to determine RG with SANS or SAXS is not applicable in the typical PAMAM dendrimer concentration range where counterions association greatly reduced the solvent ionic strength. II. Materials and Experiments8 The biomedical grade G4-NH2 PAMAM dendrimers used in this work were purchased from Dendritech Inc., Midland, MI. Deuterium chloride, deuterium bromide, and deuterium oxide were obtained from Cambridge Isotope Laboratories, Inc., Andover, MA. The preparation of the samples studied in this investigation is detailed in a separate reference.7 The METTLER TOLEDO S20 SevenEasyTM pH meter was used to extract the pD, which is converted by the reading of the pH meter according to a generally accepted relation pD ) pH + 0.41. Furthermore, the deuteron concentration is corrected from the measured deuteron activity.7 In this study, DCl was used to charge the amine groups of fourth generation (G4) PAMAM dendrimers
10.1021/jp9064455 2010 American Chemical Society Published on Web 01/13/2010
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J. Phys. Chem. B, Vol. 114, No. 5, 2010
Porcar et al.
Figure 1. The SANS coherent scattering intensity I(Q) (blue symbols) obtained from G4 PAMAM dendrimers in D2O solutions with concentration of 2.0 wt % in a R range from 0 to 1.6. Red lines are the corresponding fitting curves.
(with ethylenediamine as core) in D2O solutions. The acidity of the samples is represented by R, which is defined as the molar ratio of DCl to that of the terminal amine groups. SANS measurements were performed on the NG-3 SANS instruments at the NIST Center for Neutron Research. The wavelength of the incident neutrons was 6.0 Å with wavelength spreads, (∆λ)/(λ), of 15%. The scattering wave vector Q ranges from 4.5 × 10-3 to 0.45 Å-1. The samples were contained in a 2 mm path length quartz cells obtained from Hellma Optik GmbH Jena, Jena, Germany (category number 120 mat. code QS) and all the experiments were performed at a controlled temperature of 23.0 ( 0.1 °C. The measured intensity was also corrected for detector background and sensitivity, and for scattering contributed from the empty cells and placed in an absolute scale using a direct beam measurement.9 III. Analysis Methods Although the Guinier analysis has been commonly used to estimate the molecular size in terms of RG of various systems, it is not valid in the current situation, as we point out later in the text. Instead of relying on the scattering intensity only at the extreme low angles, the entire scattering curve is modeled in order to obtain a correct value of RG and its dependence on molecular protonation and concentration. We have developed a model for the SANS coherent scattering cross section that extracts the detailed molecular characteristics including the effective charge, ionic strength and RG.7,10 The coherent scattering intensity, I(Q), is factorized into the product of the analytical form factor, P(Q), and the structure factor S(Q). P(Q) approximates the PAMAM molecular density profile by the
convolution of a hard sphere with radius R and a Gaussian function with variance σ2 characterizing the soft corona region. S(Q) is obtained from solving the Ornstein-Zernike (OZ) equation with the hypernetted-chain (HNC) closure, which has been shown by MC simulations, to give an accurate description of the spatial arrangement of the charged colloidal suspensions. The effective inter-PAMAM interaction is approximated by the screened Coulombic interaction potential. Moreover, the physical quantities characterizing the charged PAMAM solutions, such as the effective charge carried by a single PAMAM dendrimer and the ionic strength, are converted from the fitted potential parameters based on the generalized one-component macroion theory (GOCM).11 In this approach, RG is analytically expressed as a function of R and σ.7,12 The radial intramolecular density profile F(r) is calculated using the fitting parameters, R and σ, by convoluting a uniform-density hard sphere with a Gaussian function with variance σ2. Hence, the density distribution of a dendrimer is completely determined by two parameters, R and σ. During the calculation of F(r), the total density inside a dendrimer is normalized to unity. It is important to point out that to properly take into consideration the intrinsic porous structural nature of the dendrimer molecule, which greatly influences the interdendrimer interaction, the counterions present in the solutions are partitioned into two subgroups, one residing passively inside the dendrimer, whose molecular boundary is defined by RG in our study, and the other remaining outside the molecule providing the ionic screening. Detailed description about the data analysis is in ref 7 and a portion of the fitting results are
Intramolecular Structural Change of PAMAM Dendrimers
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Figure 2. (a) RG and its calibrated curve obtained from 2 wt % G4 PAMAM dendrimer in D2O solutions as a function of R. The values of RG at different protonated level calculated by a latest computational work with an improved force field are also presented (red squares). It is important to note that in ref 5 the numerical values of RG at different R are obtained from the equilibrium trajectories weighted by the bound scattering length b, instead of the atomic mass. (b) The dependence of the radial density distribution F(r) on R. The inset gives the total mass fraction, as a function of R, within the molecular central region with radius of 15 Å.
presented in Figure 1, which demonstrates the agreement between our model and experiment. IV. Results and Discussions Figure 2 shows the molecular characteristics of 2 wt % G4 PAMAM solutions, RG and F(r), obtained from the SANS intensity curves, as a function of R. Upon increasing R from 0 to about 2, a G4 PAMAM dendrimer can be progressively charged with the charge number increasing from 0 to about 126. Quantitative measure of both RG and F(r) is obtained from SANS model fitting. Although the overall dendrimer size is not altered as indicated by the invariance of RG (
