The Role of Entropy in Nanoparticle Agglomeration

Kätelhön, Enno; Sokolov, Stanislav V.; Bartlett, Thomas R.; Compton, Richard G.

doi:10.1002/cphc.201601130

Cited by 12 publications

(8 citation statements)

References 8 publications

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“…Earlier, the problem of agglomeration was already discussed in connection with colloids [2][3][4][5][6]. Recently, two studies of the formation of agglomerates of nanoparticles were published [7,8]. In these studies, a distribution of particles exhibiting a maximum of the entropy was sought.…”

Section: Resultsmentioning

confidence: 99%

Agglomerates of nanoparticles

Vollath

2020

Beilstein J. Nanotechnol.

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Nanoparticles tend to agglomerate. The process of agglomeration is ruled by thermodynamics. Depending on the sign of the enthalpy of interaction, ensembles consist of (repelling) poorly agglomerated or (attracting) highly agglomerated particles. For these two cases different distribution functions for the agglomerates were found. The size distribution of the agglomerates is ruled by the maximum of the entropy of the ensemble of agglomerates, which is calculated using Gibbs formula of entropy. The exact determination of the size distribution of the agglomerates also gives the maximum size of the agglomerates. These considerations lead to an improved understanding of ensembles of agglomerated nanoparticles.

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Section: Resultsmentioning

confidence: 99%

Agglomerates of nanoparticles

Vollath

2020

Beilstein J. Nanotechnol.

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“…Using a different mathematical approach to determine the distribution function and the minimum of the Lagrange function, Kätelhön et al [ 18 ] found the results displayed in Figure 5 . In this case, the distribution function was calculated pointwise.…”

Section: Resultsmentioning

confidence: 99%

“… Distribution function of particle sizes according to Kätelhön and co-workers [ 18 ]. Figure 5a displays the results as published by the authors in a double logarithmic plot (base 10), Figure 5b shows the same results, in accordance with Figure 2 , in a linear–logarithmic (base e ) plot.…”

Section: Resultsmentioning

confidence: 99%

Criteria ruling particle agglomeration

Vollath¹

2021

Beilstein J. Nanotechnol.

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Most of the technically important properties of nanomaterials, such as superparamagnetism or luminescence, depend on the particle size. During synthesis and handling of nanoparticles, agglomeration may occur. Agglomeration of nanoparticles may be controlled by different mechanisms. During synthesis one observes agglomeration controlled by the geometry and electrical charges of the particles. Additionally, one may find agglomeration controlled by thermodynamic interaction of the particles in the direction of a minimum of the free enthalpy. In this context, one may observe mechanisms leading to a reduction of the surface energy or controlled by the van der Waals interaction. Additionally, the ensemble may arrange in the direction of a maximum of the entropy. Simulations based on Monte Carlo methods teach that, in case of any energetic interaction of the particles, the influence of the entropy is minor or even negligible. Complementary to the simulations, the extremum of the entropy was determined using the Lagrange method. Both approaches yielded identical result for the particle size distribution of an agglomerated ensemble, that is, an exponential function characterized by two parameters. In this context, it is important to realize that one has to take care of fluctuations of the entropy.

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“…However, if χ PC is small, NPs will aggregate on local scales but form an extended fractal (percolating) cluster on large scales due to entropic reasons. [99][100][101][102] Based on the values of the solubility parameters in Table 1 and 2, we change Δδ from 0 to 3.75 (J cm À3 ) 1/2 , and according to the assumption earlier we may control the morphology of the photoactive layer.…”

Section: Ligand A)mentioning

confidence: 99%

Mesoscale Simulations on Morphology Design in Conjugated Polymers and Inorganic Nanoparticles Composite for Bulk Heterojunction Solar Cells

et al. 2020

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Mixtures of conjugated polymers (CPs) as donors and inorganic semiconducting nanoparticles (NPs) as acceptors are considered to be promising materials for photoactive layers of bulk heterojunction hybrid solar cells (HSCs). To reach the high power conversion efficiency of HSC, the morphology of the photoactive layer for providing optimal charge transport paths is designed. Herein, the coarse‐grained model for predicting the morphology of nanocomposites based on semiconducting CPs and NPs is used. For polymer matrix, well‐known CPs such as poly(3‐hexythiophene) (P3HT), poly [thieno [3,4‐b] thiophene/benzodithiophen] (PTB7), and poly [[2,6′‐4,8‐ di(5‐ethylhexylthienyl)benzo[1,2‐b;3,3‐b] dithiophene][3‐fluoro‐ 2[(2‐ethylhexyl) carbonyl] thieno[3,4‐b]thiophenediyl]] (PTB7‐Th) are selected. For NP fillers, PbS quantum dots modified by ligands (like, e.g., oleic acid) are selected. Via mesoscale computer simulations, it is shown that by choosing appropriate ligands for NPs and varying the weight fraction of NPs, the morphology with bicontinuous charge transport paths for holes and electrons is obtained. Such morphologies are observed in models of homopolymer/NP blends for the first time. This finding is in reasonable agreement with the recent experimental results on these systems.

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The Role of Entropy in Nanoparticle Agglomeration

Cited by 12 publications

References 8 publications

Agglomerates of nanoparticles

Agglomerates of nanoparticles

Criteria ruling particle agglomeration

Mesoscale Simulations on Morphology Design in Conjugated Polymers and Inorganic Nanoparticles Composite for Bulk Heterojunction Solar Cells

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