Shape Effect on Nanoparticle Solvation: A Comparison of Morphometric Thermodynamics and Microscopic Theories

Abstract

Conventional wisdom for controlling the nanoparticle size and shape during synthesis is that particle growth favors the direction of a facet with the highest surface energy. However, the particle solvation free energy, which dictates the particle stability and growth, depends not only on the surface area and surface free energy but also on other geometric measures such as the solvent excluded volume and the surface curvature and their affiliated thermodynamic properties. In this work, we study the geometrical effects on the solvation free energies of nonspherical nanoparticles using morphometric thermodynamics and density functional theories. For idealized systems that account for only molecular excluded-volume interactions, morphometric thermodynamics yields a reliable solvation free energy when the particle size is significantly larger than the solvent correlation length. However, noticeable deviations can be identified in comparison to the microscopic theories for predicting the solvation free energies of small nanoparticles. This conclusion also holds for predicting the potential of mean force underlying the colloidal "key-and-lock" interactions. Complementary to the microscopic theories, morphometric thermodynamics requires negligible computational cost, therefore making it very appealing for a broad range of practical applications.

Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces

“…Because accurate and reliable experimental measurements of γ are rare, much effort has been devoted in recent years to the development of atomistic simulation methods to determine this quantity for interfaces between coexisting solid and fluid phases [1][2][3][4][5] and for systems in which the solid is modeled by a static wall [6][7][8][9][10][11]. These efforts have thus far been primarily restricted to planar interfaces; however, there are many physically relevant systems in which interfacial curvature is relevant, for example, in the formation of critical nuclei in nucleation [12][13][14] or the solvation or wetting of hydrophobic nanoscale particles [15][16][17]. There have been a number of previous simulation studies that examine the effect of curvature in liquid-vapor interfaces [18][19][20][21], but direct simulation studies on solid-liquid interfaces are lacking.…”

“…(4)] at low packing fractions, but exhibit a negative deviation from the SPT curve of a few percent at the higher densities studied. More recently, Jin et al [17] examined the solvation free energy of various ideal nanoscale nonspherical shapes (for example, cones, cylinders, and prisms) using a hybrid Monte Carlo DFT technique. They conclude that the use of "morphological thermodynamics" based on Hadwiger's theorem to determine the solvation free energy (which includes both bulk and interfacial free energy components) for the nonspherical particles compares well with the DFT results.…”

Surface free energy of a hard-sphere fluid at curved walls: Deviations from morphometric thermodynamics

“…The curvature dependence of the solid-liquid interfacial free energy is crucial to understanding the thermodynamics of crystal nucleation from the melt or solution, [1][2][3][4] as well as for the solvation thermodynamics of nanoparticles. [5][6][7] The solvation free energy of a particle with surface S immersed in a fluid can be written in terms of bulk and surface contributions F solv = −PV S + γ S A S , (1) where P is the pressure of the surrounding fluid, V S and A S are the volume and surface area corresponding to the particle, respectively, and γ S is the surface free energy. Often γ is approximated by its value for a planar surface; however, for nanometer scale particles, the contribution of surface curvature to γ can be significant.…”

Equivalence between particles and fields: A general statistical mechanics theory for short and long range many‐body forces

“…In their experiment the lock and key particles were dispersed in a solution, with nano-size polymer particles, used as a depletant agent. These experiments have become a well-established approach for the developing of new self-assembly materials [11,[20][21][22][23][24][25][26][27]. In particular, self-assembly has been previously found for deoxyribonucleic acid (DNA) complexation [28][29][30][31][32][33][34][35][36], DNA nano-technology [37] and viral self assembly [38][39][40][41][42][43][44][45].…”