Steady-state nucleation rate and flux of composite nucleus at saddle point

The steady-state nucleation rate and flux of composite nucleus at the saddle point is studied by extending the theory of binary nucleation. The Fokker-Planck equation that describes the nucleation flux is derived using the Master equation for the growth of the composite nucleus, which consists of the core of the final stable phase surrounded by a wetting layer of the intermediate metastable phase nucleated from a metastable parent phase recently evaluated by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)]. The Fokker-Planck equation is similar to that used in the theory of binary nucleation, but the non-diagonal elements exist in the reaction rate matrix. First, the general solution for the steady-state nucleation rate and the direction of nucleation flux is derived. Next, this information is then used to study the nucleation of composite nucleus at the saddle point. The dependence of steady-state nucleation rate as well as the direction of nucleation flux on the reaction rate in addition to the free-energy surface is studied using a model free-energy surface. The direction of nucleation current deviates from the steepest-descent direction of the free-energy surface. The results show the importance of two reaction rate constants: one from the metastable environment to the intermediate metastable phase and the other from the metastable intermediate phase to the stable new phase. On the other hand, the gradient of the potential Φ or the Kramers crossover function (the commitment or splitting probability) is relatively insensitive to reaction rates or free-energy surface.     

Molecular dynamics simulations of cluster nucleation during inert gas condensation

Molecular dynamics simulations of vapor-phase nucleation of germanium in an argon atmosphere were performed and a unexpected channel of nucleation was observed. This channel, vapor-induced cluster splitting, is important for more refractory materials since the critical nucleus size can fall below the size of a dimer. As opposed to conventional direct vapor nucleation of the dimer, which occurs by three-body collisions, cluster-splitting nucleation is a second-order reaction. The most important cluster-splitting reaction is the collision of a vapor atom and a trimer that leads to the formation of two dimers. The importance of the cluster-splitting nucleation channel relative to the direct vapor nucleation channel is observed to increase with decreasing vapor density and increasing ratio of vapor to carrier gas atoms.     

Styrene miniemulsion polymerization initiated by 2,2′-azobisisobutyronitrile

The effects of various parameters on the dodecyl methacrylate (DMA) or stearyl methacrylate (SMA) containing styrene miniemulsion polymerizations were investigated. These parameters include the type of initiators [2,2′-azobisisobutyronitrile (AIBN) vs. sodium persulfate (SPS)], the size of the homogenized monomer droplets, the AIBN concentration, and the SDS concentration. A small quantity of a water-insoluble dye was also incorporated into the polymerization system to study the related particle nucleation mechanisms. The oil-soluble AIBN promotes nucleation in the monomer droplets, whereas homogeneous nucleation predominates in the reaction system with the water-soluble SPS. Homogeneous nucleation, however, cannot be ruled out in the DMA or SMA containing polymerizations with AIBN as the sole initiator. Increasing the level of AIBN or SDS enhances formation of particle nuclei via homogeneous nucleation. The reaction kinetics is primarily controlled by the competitive events of monomer droplet nucleation and homogeneous nucleation. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2537–2550, 1999     

Polymer Lamellae as Reaction Intermediates in the Formation of Copper Nanospheres as Evidenced by In Situ X‐ray Studies

The classical nucleation theory (CNT) is the most common theoretical framework used to explain particle formation. However, nucleation is a complex process with reaction pathways which are often not covered by the CNT. Herein, we study the formation mechanism of copper nanospheres using in situ X‐ray absorption and scattering measurements. We reveal that their nucleation involves coordination polymer lamellae as pre‐nucleation structures occupying a local minimum in the reaction energy landscape. Having learned this, we achieved a superior monodispersity for Cu nanospheres of different sizes. This report exemplifies the importance of developing a more realistic picture of the mechanism involved in the formation of inorganic nanoparticles to develop a rational approach to their synthesis.     

Gas-bubble effects on the formation of colloidal iron oxide nanocrystals

This paper reports that gas bubbles can be used to tailor the kinetics of the nucleation and growth of inorganic-nanocrystals in a colloidal synthesis. We conducted a mechanistic study of the synthesis of colloidal iron oxide nanocrystals using gas bubbles generated by boiling solvents or artificial Ar bubbling. We identified that bubbling effects take place through absorbing local latent heat released from the exothermic reactions involved in the nucleation and growth of iron oxide nanocrystals. Our results show that gas bubbles display a stronger effect on the nucleation of iron oxide nanocrystals than on their growth. These results indicate that the nucleation and growth of iron oxide nanocrystals may rely on different types of chemical reactions between the iron-oleate decomposition products: the nucleation relies on the strongly exothermic, multiple-bond formation reactions, whereas the growth of iron oxide nanocrystals may primarily depend upon single-bond formation reactions. The identification of exothermic reactions is further consistent with our results in the synthesis of iron oxide nanocrystals with boiling solvents at reaction temperatures ranging from 290 to 365 °C, by which we determined the reaction enthalpy in the nucleation of iron oxide nanocrystals to be -142 ± 12 kJ/mol. Moreover, our results suggest that a prerequisite for effectively suppressing secondary nucleation in a colloidal synthesis is that the primary nucleation must produce a critical amount of nuclei, and this finding is important for a priori design of colloidal synthesis of monodispersed nanocrystals in general.     

Obtaining reaction coordinates by likelihood maximization

We present a new approach for calculating reaction coordinates in complex systems. The new method is based on transition path sampling and likelihood maximization. It requires fewer trajectories than a single iteration of existing procedures, and it applies to both low and high friction dynamics. The new method screens a set of candidate collective variables for a good reaction coordinate that depends on a few relevant variables. The Bayesian information criterion determines whether additional variables significantly improve the reaction coordinate. Additionally, we present an advantageous transition path sampling algorithm and an algorithm to generate the most likely transition path in the space of collective variables. The method is demonstrated on two systems: a bistable model potential energy surface and nucleation in the Ising model. For the Ising model of nucleation, we quantify for the first time the role of nuclei surface area in the nucleation reaction coordinate. Surprisingly, increased surface area increases the stability of nuclei in two dimensions but decreases nuclei stability in three dimensions.     

Shape and aggregation control of nanoparticles: not shaken, not stirred

The aggregation of nanoparticles during synthesis, particularly the effect of mechanical agitation, is investigated from a viewpoint of nucleation using a conjugated polymer, polyaniline, as an example. Homogeneous nucleation of polyaniline results in nanofibers, while heterogeneous nucleation leads to granular particulates. Mechanical agitation, which is a common method for disrupting aggregates, instead dramatically triggers aggregation during the synthetic process and favors the formation of granular particulates. Correlating the shape and aggregation of polyaniline nanoparticles with the mode of nucleation, a new aggregation mechanism is proposed in which aggregation is triggered by heterogeneous nucleation. The mechanism may be quite general as indicated by experiments with other materials such as silica nanoparticles. Highly dispersible polyaniline nanofibers can now be reproducibly prepared from a conventional reaction simply by not mechanically agitating the reaction and carrying it out at an elevated temperature. This work may prove to be of great value in reproducibly synthesizing nanoparticles with well-controlled sizes and shapes and in effectively preventing aggregation in chemical, pharmaceutical, and materials production processes.     

Using the histogram test to quantify reaction coordinate error

Many schemes for calculating reaction rates and free energy barriers require an accurate reaction coordinate, but it is difficult to quantify reaction coordinate accuracy for complex processes like protein folding and nucleation. The histogram test, based on estimated committor probabilities, is often used as a qualitative indicator for good reaction coordinates. This paper derives the mean and variance of the intrinsic committor distribution in terms of the mean and variance of the histogram of committor estimates. These convenient formulas enable the first quantitative calculations of reaction coordinate error for complex systems. An example shows that the approximate transition state surface from Peters' and Trout's reaction coordinate for nucleation in the Ising model gives a mean committor probability of 0.495 and a standard deviation of 0.042.     

Polymer Lamellae as Reaction Intermediates in the Formation of Copper Nanospheres as Evidenced by In Situ X-ray Studies

The classical nucleation theory (CNT) is the most common theoretical framework used to explain particle formation. However, nucleation is a complex process with reaction pathways which are often not covered by the CNT. Herein, we study the formation mechanism of copper nanospheres using in situ X-ray absorption and scattering measurements. We reveal that their nucleation involves coordination polymer lamellae as pre-nucleation structures occupying a local minimum in the reaction energy landscape. Having learned this, we achieved a superior monodispersity for Cu nanospheres of different sizes. This report exemplifies the importance of developing a more realistic picture of the mechanism involved in the formation of inorganic nanoparticles to develop a rational approach to their synthesis.     

Bubble nucleation algorithm for the simulation of gas evolving electrodes

We propose a bubble nucleation algorithm to link a Lagrangian bubble tracker to the multi-ion transport and reaction model. This algorithm computes the bubble growth rate and the surface blocking effect at nucleation sites.     

Microwave Synthesis of SAPO‐11 and AlPO‐11: Aspects of Reactor Engineering

AlPO‐11 and SAPO‐11 are synthesized using microwave heating. The effects of precursor volume, reaction temperature, reactor geometry, stirring, applicator type and frequency on the microwave synthesis of SAPO‐11 and AlPO‐11 are studied. The nucleation time and crystallization rate are determined from crystallization curves for SAPO‐11 (and/or AlPO‐11), for the various parameters investigated. Increasing volume of the reacting material decreases the reaction rate of SAPO‐11 at 160°C. In particular, the nucleation time increases with increase in the reaction volume. Increasing the reaction temperature increases the crystallization rate and decreases the nucleation time, however it decreases the particle size. Nucleation of SAPO‐11 and AlPO‐11 under microwave heating is strongly dependant on the reaction temperature. Using wider geometry vessel (33 mm compared to 11 mm diameter) enhances the reaction rate, producing larger crystals in the same reaction time, even though the crystallization rate is decreased. The crystallization rate is enhanced by applicator type in the following order CEM MARS‐5 oven>CEM Discover “focused” system>monomode waveguide. Stirring the reacting solution during heating affects primarily the nucleation time. The effect of microwave frequency on the nucleation and growth of SAPO‐11 shows a dependence on the applicator type more than the specific frequency, for the frequency range 2.45–10.5 GHz. The difference between the crystallization rate observed at higher frequencies and that at 2.45 GHz maybe due to the multimode nature of the waveguide at frequencies above 2.45 GHz. Sweeping the microwave frequency linearly between 8.7 and 10.5 GHz at rates of 10 min^?1 and 100 min^?1 shows an intermediate crystallization curve to that for fixed frequencies of 2.45 GHz and that for 5.8, 8.7 and 10.5 GHz.     

Solid-state photodimerization kinetics of alpha-trans-cinnamic acid to alpha-truxillic acid studied via solid-state NMR

The present work focuses on the topochemical photoconversion process in which alpha-trans-cinnamic acid becomes alpha-truxillic acid. This solid-state [2 + 2] cycloaddition reaction has previously been studied with X-ray diffraction, atomic force microscopy, and vibrational spectroscopy. However structural and kinetic details about the reaction are still debated. We present results from (13)C cross-polarization magic angle spinning solid-state NMR experiments that suggest that the Johnson, Mehl, Avrami, and Kolmogorov model of phase transformation kinetics can be applied to this system. The model elucidates parameters of the reaction, such as the nucleation rate, diffusion rate, and dimensionality of the reaction. From our data, it is concluded that this reaction follows one-dimensional growth with a decreasing nucleation rate.     

Na_5P_3O_(10)-Ca(OH)_2-CO_2-H_2O体系纳米CaCO_3的成核与生长

通过化学分析、SEM显微分析技术结合RosinRamiler概率统计理论从介观层次研究Na5P3O10CaOH2CO2H2O体系纳米CaCO3的合成反应及其成核和生长过程。结果表明Na5P3O10对CaOH2的碳化反应具有抑制作用。随着Na5P3O10的增加体系中CaCO3的成核速率B0逐渐增大。在Na5P3O10=0ppm时CaCO3结晶的生长由长程扩散和凝聚生长控制Na5P3O10=380.4760.9ppm时前期受短程扩散和界面反应控制、后期受长程扩散控制。Na5P3O10的存在抑制了纳米CaCO3的晶体生长。     

Surface-mediated nucleation in the solid-state polymorph transformation of terephthalic acid

A molecular mechanism for nucleation for the solid-state polymorph transformation of terephthalic acid is presented. New methods recently developed in our group, aimless shooting and likelihood maximization, are employed to construct a model for the reaction coordinate for the two system sizes studied. The reaction coordinate approximation is validated using the committor probability analysis. The transformation proceeds via a localized, elongated nucleus along the crystal edge formed by fluctuations in the supramolecular synthons, suggesting a nucleation and growth mechanism in the macroscopic system.     

Miniemulsion polymerization of styrene with liquid polybutadiene as the sole co-stabilizer

A low-molecular-weight liquid polybutadiene (LPB) is employed as the sole co-stabilizer in miniemulsion polymerization of styrene in present work. Results indicate that the LPB can be used as an effective co-stabilizer to retard the diffusional degradation of monomer droplets in miniemulsion system and get stable miniemulsions. When the miniemulsions were initiated, particle formation occurred predominantly by monomer droplet nucleation. Moreover, the effects of various reaction parameters on the polymerization kinetics and the nucleation mechanisms were also investigated. These parameters include the level of LPB ([LPB]) and the concentrations of SDS ([SDS]) and potassium persulfate ([KPS]). It is shown that the polymerization rate indicates little dependence on [LPB], while increases with increasing [SDS] and [KPS]. Competition between droplet nucleation and homogeneous nucleation occur in the course of polymerization, but droplet nucleation becomes more important by increasing [LPB] or decreasing [SDS]. Furthermore, the result that the particle size is rather insensitive to changes in [KPS] provides the most compelling evidence for the dominant droplet nucleation.     

Initial nucleation of platinum clusters after reduction of K(2)PtCl(4) in aqueous solution: a first principles study

The initial nucleation of platinum clusters after the reduction of K(2)PtCl(4) in aqueous solution is studied by means of first principles molecular dynamics simulations. A reaction mechanism leading to a Pt dimer is revealed both by gas-phase simulations and by simulations which model the solution environment. The key step of the observed reaction process is the formation of a Pt-Pt bond between a Pt(I) complex and an unreduced Pt(II) complex. In light of this result, we discuss the reduction process leading to the formation of platinum nanoparticles. In the generally accepted model, the nucleation of Pt particles starts only when a critical concentration of Pt(0) atoms is reached. Here, we discuss a complementary mechanism where metal-metal bonds form between Pt complexes in higher oxidation states. This is consistent with a number of experimental results which show that a high concentration of zerovalent atoms is not necessary to start the nucleation.     

Effects of 2‐hydroxyalkyl methacrylates on the styrene miniemulsion polymerizations stabilized by SDS and alkyl methacrylates

The effects of 2‐hydroxyalkyl methacrylates (HEMA and HPMA) on the styrene miniemulsion polymerizations stabilized by SDS/lauryl methacrylate (LMA) or SDS/stearyl methacrylate (SMA) were investigated. A mixed mode of particle nucleation (monomer droplet nucleation and homogeneous nucleation) is operative during polymerization. Homogeneous nucleation plays a crucial role in the polymerizations stabilized by SDS/LMA, whereas monomer droplet nucleation becomes more important in the polymerizations stabilized by SDS/SMA. The polymerization kinetics is insensitive to the type of 2‐hydroxyalkyl methacrylates, but the difference in the relative importance of monomer droplet nucleation and homogeneous nucleation is detected. Incorporation of 1‐pentanol (C₅OH) into the reaction mixture also shows a significant influence on the polymerizations stabilized by SDS/LMA or SDS/SMA. This is attributed to the formation of a close‐packed structure of SDS and C₅OH on the droplet surface, which acts as a barrier to the incoming oligomeric radicals. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3188–3199, 2000     

三元无皂乳液共聚合动力学及其模型的研究

以苯乙烯（ Ｓｔ） 和甲基丙烯酸甲酯（ Ｍ Ｍ Ａ） 为主单体,以丙烯酸（ Ａ Ａ） 为功能单体进行了无皂乳液批量共聚合．考察了功能单体浓度、引发剂过硫酸铵（ Ａ Ｐ Ｓ） 浓度及聚合温度对其动力学行为的影响．建立了转化率 时间关系曲线的模型函数——— Ｇａｍ ｍａ 积分函数,用它拟合了转化率 时间关系曲线,获得了聚合过程的重要特征参数,如平均成核速率（ Ｎ Ｖ） ,聚合最大速率（ Ｍ Ｖ） 和平稳期平均聚合速率（ Ａ Ｖ） 及成核结束和聚合进入完成期对应的转化率．同时对聚合速率与以上各聚合参数的关系数据进行了非线性拟合,得到了它们之间的关系式．研究发现拟合误差很小,成核结束时转化率在１５ ％ 以内,成核及聚合速率均随以上参数增大而增大,引发剂过硫酸铵在聚合过程中起决定作用．     

Facile Synthesis of Platinum Right Bipyramids by Separating and Controlling the Nucleation Step in a Continuous Flow System

Colloidal synthesis of metal nanocrystals with controlled shapes and internal structures calls for a tight control over both the nucleation and growth processes. Here we report a method for the facile synthesis of Pt right bipyramids (RBPs) by separating nucleation from growth and controlling the nucleation step in a continuous flow reactor. Specifically, homogeneous nucleation was thermally triggered by introducing the reaction solution into a tubular flow reactor held at an elevated temperature to generate singly-twinned seeds. At a lower temperature, the singly-twinned seeds were protected from oxidative etching to allow their slow growth and evolution into RBPs while additional nucleation of undesired seeds could be largely suppressed to ensure RBPs as the main product. Further investigation indicated that the internal structure and growth pattern of the seeds were determined by the temperatures used for the nucleation and growth steps, respectively. The Br⁻ ions involved in the synthesis also played a critical role in the generation of RBPs by serving as a capping agent for the Pt{100} facets while regulating the reduction kinetics through coordination with the Pt(IV) ions.