Theory of the nucleation of multicomponent precipitates

Trinkaus, H.

doi:10.1103/physrevb.27.7372

Cited by 136 publications

(111 citation statements)

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“…Instead, we need explicit information about the dynamics undergone by components, together with a predictive theory that works "far" from equilibrium. Despite much progress in this direction [13][14][15][16][17][18][19][20][21][22], such a theory does not exist. Here we present evidence suggesting that concepts of nonequilibrium statistical physics may provide a route to a predictive theory of far-from-equilibrium self-assembly.…”

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Self-Assembly at a Nonequilibrium Critical Point

2014

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We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in two and three dimensions. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between mixed and demixed arrangements of component types. This finding suggests that principles of nonequilibrium statistical mechanics can be used to predict the outcome of multicomponent self-assembly, and suggests an experimental route to the self-assembly of multicomponent structures of a qualitatively defined nature. DOI: 10.1103/PhysRevLett.112.155504 PACS numbers: 81.16.Dn, 05.20.-y, 81.16.Fg Nature builds its materials using multiple component types. The properties of these materials depend on the properties of their components, and on how components are distributed spatially: the exciton transfer properties of a light-harvesting complex, for instance, depend on the way that its constituent proteins cluster [1]. Achieving similar mesoscale spatial control with many synthetic selfassembled materials [2] is made difficult by the fact that the self-assembly of multicomponent systems generally happens "far" from equilibrium, where we possess few predictive theoretical tools. Although self-assembly is a nonequilibrium process, much of our understanding of it is based upon a physical picture that assumes dynamics to play no role except to convey a system along the "easiest" pathways on its free-energy landscape [3]. This "nearequilibrium" or "quasiequilibrium" assumption tends to hold, for instance, for simple one-component systems under mild nonequilibrium conditions [4][5][6][7][8]. It fails when there exist time scales within a given self-assembly process that exceed the time of the experiment or computer simulation. For one-component systems, long time scales can emerge if bonds between particles are strong, and so break infrequently, which can happen when subjected to "harsh" nonequilibrium conditions (e.g., conditions of deep supercooling). Binding errors made as components associate can then fail to anneal as structures grow, and the result is a kinetically trapped structure rather than an object corresponding to a favored position on the free-energy landscape [9][10][11][12].The self-assembly of multicomponent solid structures, however, is also affected by kinetic traps that emerge even under mild nonequilibrium conditions. The long time scale responsible for such trapping is the slow interchange of component types within solid structures [13][14][15][16][17][18][19][20][21][22][23]. Consider Fig. 1(a), which shows in cartoon form a fluid of two types of mutually attractive particles (call them "red" and "blue"), present in equal number, self-assembling into a solid structure. The equilibrium pattern of red and blue within this structure-shown in the figure as demixed red and blue domains-is determined only by the particles' mutual interactions. But achieving this equilibrium pattern via self-assembly requires that particle types interchange their positio...

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“…The long time scale responsible for such trapping is the slow interchange of component types within solid structures [13][14][15][16][17][18][19][20][21][22][23]. Consider Fig.…”

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Self-Assembly at a Nonequilibrium Critical Point

2014

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“…Furthermore, the classical binary nucleation rate depends exponentially on σ 3 , where σ is the composition dependent binary liquid surface tension for the critical cluster. 2,4,[26][27][28][29][30][31][32][33][34][35] A 10% error in σ can affect the nucleation rate by as much as 8 orders of magnitude. In many systems of interest, the critical cluster size is of the order of 10-100 molecules, making the use of bulk surface tension suspect.…”

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Monte Carlo Simulations of Small Sulfuric Acid−Water Clusters

Kathmann

Hale

2001

J. Phys. Chem. B

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Effective atom-atom potentials are developed for binary sulfuric acid-water clusters and applied in a Bennett Metropolis Monte Carlo calculation to determine free energy differences for small neighboring sized clusters of fixed composition at 298 K. The atom-atom pair potentials consist of Lennard-Jones short-range and Coulombic long-range terms and assume rigid SO 4 2δ-with two unconstrained H δ+ and rigid H 2 O molecules interacting via revised central force (RSL2) potentials. The potential parameters are determined from both ab initio studies and tests of the potential using the statistical mechanical formalism for binary cluster size distributions. In the potential tests, fixed composition free energy differences, δf km,m , for [H 2 O] km [H 2 SO 4 ] m clusters are plotted versus (km + m) -1/3 , and the resulting slope and intercept (in the large cluster regime) are used to extract model dependent binary liquid surface tension and partial vapor pressures at 298 K. The potential parameters are adjusted to obtain approximate agreement with experimental surface tension and partial vapor pressures for k ) 1 and 4 (84% and 57% weight percent H 2 SO 4 , respectively). The free energy differences for m e 15 are presented, together with internal cluster energy contributions, snapshots of cluster structure, and evidence for onset of the large cluster regime near m ) 5. The long-range goals have been to test the free energy difference procedure for studying binary cluster properties and to develop model potentials appropriate for the simulation of small binary clusters at low temperatures characteristic of stratospheric sulfuric acid-water aerosols.

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“…However, as suggested already, for example, by Trinkaus,12 in particular, near to the spinodal curve nucleation may proceed not via the saddle but via a ridge of the appropriate thermodynamic potential surface. In Ref.…”

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Comment on “Minimum free-energy pathway of nucleation” [J. Chem. Phys. 135, 134508 (2011)]

Schmelzer

Abyzov

2012

The Journal of Chemical Physics

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In their recent paper [J. Chem. Phys. 135, 134508 (2011)], Philippe and Blavette10.1063/1.3644935 claimed to have found for the first time—based on minimum free energy considerations—that the nucleation pathway in solid solutions involves a universal two-step behavior: nuclei sharply enrich up to near equilibrium values of the concentration and then grow. This claim of priority is not correct. The same scenario was proposed by us long ago [J. W. P. Schmelzer, A. R. Gokhman, and V. M. Fokin, J. Colloid Interface Sci. 272, 109 (2004)]10.1016/j.jcis.2003.08.038 and then applied and further developed. In particular, it was shown by us that only the account of both thermodynamic and kinetic factors allows one to determine correctly the most probable path of evolution in nucleation-growth processes. The two-step scenario is retained, however, also in these generalizations of our original approach.

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Theory of the nucleation of multicomponent precipitates

Cited by 136 publications

References 8 publications

Self-Assembly at a Nonequilibrium Critical Point

Self-Assembly at a Nonequilibrium Critical Point

Monte Carlo Simulations of Small Sulfuric Acid−Water Clusters

Comment on “Minimum free-energy pathway of nucleation” [J. Chem. Phys. 135, 134508 (2011)]

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