Abstract
In many cases, the stability of complex structures in colloidal systems is enhanced by a competition between different length scales. Inspired by recent experiments on nanoparticles coated with polymers, we use Monte Carlo simulations to explore the types of crystal structures that can form in a simple hard-core square shoulder model that explicitly incorporates two favored distances between the particles. To this end, we combine Monte Carlo-based crystal structure finding algorithms with free energies obtained using a mean-field cell theory approach, and draw phase diagrams for two different values of the square shoulder width as a function of the density and temperature. Moreover, we map out the zero-temperature phase diagram for a broad range of shoulder widths. Our results show the stability of a rich variety of crystal phases, such as body-centered orthogonal (BCO) lattices not previously considered for the square shoulder model.
Highlights
In the past several decades, the principles of designed colloidal self-assembly [1,2] have been widely used to generate novel structures on the mesoscale by tailored interactions [3,4] and external stimuli [5,6,7]
Our results show the stability of a rich variety of crystal phases, such as body-centered orthogonal (BCO) lattices not previously considered for the square shoulder model
The most stable state in the zero-temperature limit is the phase or coexistence of two phases with the lowest potential energy, the zero-temperature phase diagram can be obtained by connecting the lowest points at each density, as shown in Figure 2 for the interaction range δ/σ = 0.2
Summary
In the past several decades, the principles of designed colloidal self-assembly [1,2] have been widely used to generate novel structures on the mesoscale by tailored interactions [3,4] and external stimuli [5,6,7]. It has been shown that soft repulsive interaction potentials can be tuned to favor e.g., open crystal lattices such as diamond [15,16], lattices with large unit cells such as A15 [17], and even quasicrystals [18,19,20] These predictions are supported by experimental observations on e.g., soft spherical polymers, micelles or dendrons [21,22,23], as well as polymer-coated nanoparticles [24,25,26], which all demonstrate a rich crystal phase behavior [27]. The HCSS model is not designed to quantitatively model a specific system, it can be seen as a phenomenological model for colloidal particles with a hard core and a soft corona, such as polymer-coated nanoparticles [24,25] It serves as a fundamental model for understanding the phase behavior of models incorporating a competition between two length scales, and, as a result, has received significant attention over the past decades.
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