The structure and dynamics of poly(amido amide) (PAMAM) dendrimers have been of great interest both scientifically and industrially, but such important features as the distributions of atoms, channels, and strain inside these molecules remain unresolved. This paper reports results from systematic investigations of the atomistic structure of ethylenediamine (EDA) cored PAMAM dendrimer up through the 11th generation (294 852 atoms), at which point the strain energy has risen to a point that limits uniform growth of additional layers. Here we report, as a function of generation, structural properties such as radius of gyration, shape tensor, asphericity, fractal dimension, monomer density distribution, solvent accessible surface area, molecular volume, and end group distribution functions, all evaluated from extensive molecular dynamics (MD) at 300 K. We find that the radius of gyration scales as R g ∼ N 1/3 over the entire range of generations, suggesting rather uniform space filling for all generations. Contrary to common expectation, we find that the outer subgenerations penetrate substantially into the interior of the dendrimer, even for G11. Consequently, the terminal amine groups are distributed throughout the interior, not just on the periphery of the dendrimer. However for G6 through G11 there is a large region of uniform density, supporting the uniform scattering model often used in interpreting the SANS (small-angle neutron scattering) and SAXS (small-angle X-ray scattering) data, which lead to sizes in excellent agreement with the calculations. The calculated single particle form factor approaches that of a sphere as the generation number increases. For the larger generations, we found that the use of continuous configuration biased Monte Carlo (CCBB MC) was essential to construct initial configurations that lead to lower final strain energies.

Presented here is the two-phase thermodynamic (2PT) model for the calculation of energy and entropy of molecular fluids from the trajectory of molecular dynamics (MD) simulations. In this method, the density of state (DoS) functions (including the normal modes of translation, rotation, and intramolecular vibration motions) are determined from the Fourier transform of the corresponding velocity autocorrelation functions. A fluidicity parameter (f), extracted from the thermodynamic state of the system derived from the same MD, is used to partition the translation and rotation modes into a diffusive, gas-like component (with 3Nf degrees of freedom) and a nondiffusive, solid-like component. The thermodynamic properties, including the absolute value of entropy, are then obtained by applying quantum statistics to the solid component and applying hard sphere/rigid rotor thermodynamics to the gas component. The 2PT method produces exact thermodynamic properties of the system in two limiting states: the nondiffusive solid state (where the fluidicity is zero) and the ideal gas state (where the fluidicity becomes unity). We examine the 2PT entropy for various water models (F3C, SPC, SPC/E, TIP3P, and TIP4P-Ew) at ambient conditions and find good agreement with literature results obtained based on other simulation techniques. We also validate the entropy of water in the liquid and vapor phases along the vapor-liquid equilibrium curve from the triple point to the critical point. We show that this method produces converged liquid phase entropy in tens of picoseconds, making it an efficient means for extracting thermodynamic properties from MD simulations.

We report various structural and conformational properties of generations 4, 5, and 6 PAMAM (polyamidoamine) dendrimer [EDA (ethylenediamine) core)] at various protonation levels through extensive molecular dynamics (MD) simulations in explicit solvent. The presence of solvent leads to swelling of the dendrimer (by 33% for G5 compared to the case of no solvent). We find that decreasing the solution from high pH (∼10, no protonation) to neutral (∼7, only primary amines protonated) to low pH (∼4, tertiary amines also protonated) changes the radius of gyration of G5 from 21 to 22 to 25 Å, respectively. We also report such other structural quantities as radial density, distribution of terminal groups, solvent accessible surface area and volume, shape, and structure factors (to compare with SAXS and SANS experiments) at various pH conditions. We find significant back-folding of the outer subgenerations in the interior of the molecules at all levels of pH, contrary to original expectations and some SANS experiments but in agreement with other SANS experiments. We find significant water penetration inside the dendrimer, with ∼3 water/tertiary amine for high pH and ∼6 water/tertiary amine for low pH (all for G5). This indicates that the interior of the dendrimer is quite open with internal cavities available for accommodating guest molecules, suggesting using PAMAM dendrimer for guest−host applications. This estimate of internal waters suggests that sufficient water is available to facilitate metal ion binding.