Origin of porosity in synthetic materials

Schaefer, Dale W.; Wilcoxon, J. P.; Keefer, Keith D.; Bunker, Bruce C.; Pearson, R.K.; Thomas, Ian M.; Miller, Douglas E.

doi:10.1063/1.36386

Cited by 15 publications

(9 citation statements)

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“…In our previous article [25], we showed that the analytical solution of a non-lumped kinetic model is still possible despite the fact that it has an infinite number of concentration variables. The model itself was based on pervious experimental results and theoretical considerations [4,5,[26][27][28][29][30][31]. In the present work, we show that similar analytical solutions can be found in a limited number of other kinetic models as well.…”

Section: Introductionsupporting

confidence: 70%

“…A general nucleation-growth type kinetic model In this paper, a general class of models for nanoparticle formation will be considered, which is based on previous attempts to build such models and a comparison of experimental results [4,5,[26][27][28][29][30][31]. The model contains three different kinds of steps, two of which represent nucleation, whereas the third one includes particle growth.…”

Section: Resultsmentioning

confidence: 99%

“…The function K(i) in Eq. 3 is called a kernel function, it describes how the growth rate constant of a nanoparticle depends on its size [26][27][28][29][30]. Four possible and practically useful kernel functions are shown in Table 1.…”

Section: Resultsmentioning

confidence: 99%

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General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Szabó

Lente

2021

J Math Chem

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In this work, analytical solutions for the time dependences for the concentration of each chemical species are determined in a class of nucleation-growth type kinetic models of nanoparticle formation. These models have an infinitely large number of dependent variables and describe the studied process without approximations. Symbolic solutions are found for the mass kernel (where reactivity is directly proportional to the mass of a nanoparticle) and the diffusion kernel (where reactivity is independent of the size of the nanoparticle). The results show that the average particle size is primarily determined by the type of the kernel function and the ratio of the rate constants of spontaneous nucleation and particle growth. The final distribution of nanoparticle sizes is a continuously decreasing function in each studied case. Furthermore, the time dependences of the concentrations of monomeric units show the induction behavior that has already been observed in many experimental studies.

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Section: Introductionsupporting

confidence: 70%

Section: Resultsmentioning

confidence: 99%

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General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Szabó

Lente

2021

J Math Chem

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“…The proportionality of the rate constant to particle mass can be rationalized if the forming particles are regarded as mass fractals. As such, their reactive surface area is proportional to their mass . Importantly, it is not necessary to assume the formation of spherical particles in the model.…”

Section: Results and Discussionmentioning

confidence: 99%

Kinetic Model for Hydrolytic Nucleation and Growth of TiO₂ Nanoparticles

Forgács¹,

Moldován²,

Herman³

et al. 2018

J. Phys. Chem. C

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A simple kinetic model is derived to describe the formation of TiO 2 particles up to the size of a few hundred nanometers in an aqueous suspension. The model system for the kinetic experiments is the hydrolysis and condensation of titanium(IV)-bis(ammonium-lactato)dihydroxide under basic conditions. The formation of nanoparticles was followed by dynamic light scattering (DLS) and UV−vis spectrometric methods. The turbidity (i.e., the apparent absorbance at 500 nm) of a stable TiO 2 suspension is shown to be proportional to the TiO 2 concentration at a constant particle size and proportional to the size at a constant Ti concentration. The compilation of the DLS and UV−vis data yields characteristic sigmoid-shaped kinetic curves for the evolution of particle size. A kinetic model with three reaction steps is postulated which provides an excellent fit to the experimental data. First, the rapid hydrolysis of the precursor takes place to give primary particles for the subsequent steps. The dimerization of two primary particles is slow and this is followed by the formation of larger particles in the step-by-step addition of subsequent primary units. An integrated rate equation was developed to predict the time-dependent mean particle size as the function of the initial precursor concentration. An important feature of the model is that a simple continuous function describes the temporal evolution of the average particle size up to d = 600 nm. Previously published kinetic data representing various reaction systems were also successfully interpreted by the proposed model.

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“…Among the most outstanding results, Woignier studied the structure change during high-temperature supercritical extraction in alcohol [22]. Vacher in Montpellier [23] and Schaefer et al at the Sandia Laboratories in New Mexico investigated the fractal nature of the silica aerogel network by small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) [24]. A kinetic growth model making easier to control the texture of silica aerogels was also developed at the Sandia National Laboratories [2c] and a two-step acid-base catalysis process permitted to design very low-density silica aerogel monoliths [25].…”

Section: Further Studies On the Synthesis Chemistry Of Aerogelsmentioning

confidence: 99%

History of Aerogels

Pierre¹

2011

Aerogels Handbook

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This chapter presents a historical account of the progressive development of the solid materials known as aerogels. The founding work of Kistler is first summarized. His precursory work attracted the attention of scientists who focused on the physics and chemistry of aerogels, reviewed in the second section. The latter studies allowed for the understanding of how a very high open porosity solid could be maintained when drying a gel and how some specific properties such as transparency or a hydrophobic character could be granted to these materials. In turn, a better knowledge of the scientific basis behind aerogels led to determining their technical characteristics and developing their applications, as addressed in the third section. The most recent developments summarized in the last section aim at a progressive transfer of these applications toward the industry. The Founding Studies by KistlerThe term aerogel was first introduced by Kistler in 1932 to designate gels in which the liquid was replaced with a gas, without collapsing the gel solid network [1]. While wet gels were previously dried by evaporation, Kistler applied a new supercritical drying technique, according to which the liquid that impregnated the gels was evacuated after being transformed to a supercritical fluid. In practice, supercritical drying consisted in heating a gel in an autoclave, until the pressure and temperature exceeded the critical temperature T c and pressure P c of the liquid entrapped in the gel pores.This procedure prevented the formation of liquid-vapor meniscuses at the exit of the gel pores, responsible for a mechanical tension in the liquid and a pressure on the pore walls, which induced gel shrinkage. Besides, a supercritical fluid can be evacuated as gas, which in the end lets the "dry solid skeleton" of the initial wet material. The dry samples that were obtained had a very open porous texture, similar to the one they had in their wet stage.Overall, aerogels designate dry gels with a very high relative or specific pore volume, although the value of these characteristics depends on the nature of the solid and no official convention really exists (Chap. 21). Typically, the relative pore volume is of the order of 90% in the most frequently studied silica aerogels [2]

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Origin of porosity in synthetic materials

Cited by 15 publications

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General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Kinetic Model for Hydrolytic Nucleation and Growth of TiO₂ Nanoparticles

History of Aerogels

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Origin of porosity in synthetic materials

Cited by 15 publications

References 0 publications

General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

General nucleation-growth type kinetic models of nanoparticle formation: possibilities of finding analytical solutions

Kinetic Model for Hydrolytic Nucleation and Growth of TiO2 Nanoparticles

History of Aerogels

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Kinetic Model for Hydrolytic Nucleation and Growth of TiO₂ Nanoparticles