Kinetics of Ag300 nanoclusters formation: The catalytically effective nucleus via a steady-state approach

The kinetics of formation of silver nanoparticles consisting of nearly 300 metal atoms is investigated, which were prepared by reduction of silver nitrate with hydrazine in ethylene glycol at 25°C without any stabilizer other than the glycol solvent. The resulting sigmoidal kinetic curves are analyzed by using the 1997 Finke–Watzky two-step mechanism of slow continuous nucleation with subsequent fast autocatalytic surface growth. The kinetics of homogeneous nucleation of metal nanoparticles was analyzed using the assumption about the stepwise adjunction of precursor and the quasi steady-state approximation. The equations were proposed to calculate the concentration of the formed metal nanoparticles and their mean size from the experimentally determined values of the Finke–Watzky rate constants. It is shown that a stepwise nucleation process can be described in the terms of the catalytically effective nucleus concept and that the number of atoms in the catalytically effective nucleus can be estimated.     

Experimental probes of silver metal nanoparticle formation kinetics: Comparing indirect versus more direct methods

The kinetics of noble metal nanoparticle formation in bottom-up syntheses are important for controlling and optimizing these methods. Hence, experimental probes that are easily accessible to most laboratories are also of interest. We collected kinetic curves for the formation of silver nanoparticles in a modified Turkevich method with citrate acting as the reducing and stabilizing agent by (i) measuring the change in silver nanoparticle surface plasmon resonance by UV-visible spectroscopy, a somewhat indirect method, and then also by (ii) measuring the change in silver ion concentration by ion-selective electrode potentiometry and/or atomic absorption spectroscopy, two more direct methods. The resulting sigmoidal kinetic curves were curvefitted with the Finke-Watzky two-step kinetic model of slow, continuous nucleation and fast autocatalytic growth to extract average rate constants. We found that the kinetic curves obtained by following the change in silver ion concentration were apparent mirror images of those constructed by following the change in nanoparticle surface plasmon resonance, and that their respective curvefits displayed the same sigmoidal characteristics. The resultant values of the rate constants for nucleation and growth overlapped within experimental error between the methods and showed similar trends over the range of citrate concentrations studied. The use of multiple probes in this work to follow the kinetics of nanoparticle formation helps fill a need for the comparison and evaluation of different methods available to scientists, particularly those considered easily accessible.     

Estimation of the nucleation and crystal growth contributions to the overall crystallization energy barrier

Classical kinetic theories of polymer crystallization were applied to isothermal crystallization kinetics data obtained by polarized optical microscopy (PLOM) and differential scanning calorimetry (DSC). The fitted parameters that were proportional to the energy barriers obtained allow us to quantitatively estimate the nucleation and crystal growth contributions to the overall energy barrier associated to the crystallization process. It was shown that the spherulitic growth rate energy barrier found by fitting PLOM data is almost identical to that obtained by fitting the isothermal DSC crystallization data of previously self‐nucleated samples. Therefore, we demonstrated that by self‐nucleating the material at the ideal self‐nucleation (SN) temperature, the primary nucleation step can be entirely completed and the data obtained after subsequent isothermal crystallization by DSC contains only contributions from crystal growth or secondary nucleation. In this way, by employing SN followed by isothermal crystallization, we propose a simple method to obtain separate contributions of energy barriers for primary nucleation and for crystal growth, even in the case of polymers where PLOM data are very difficult to obtain (because they exhibit very small spherulites). Comparing the results obtained with poly(p‐dioxanone), poly(ε‐caprolactone), and a high 1,4 model hydrogenated polybutadiene, we have interpreted the differences in primary nucleation energy barriers as arising from differences in nuclei density. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1478–1487, 2008     

Homogeneous nucleation and growth of melt in copper

Molecular dynamics simulations are conducted to investigate homogeneous nucleation and growth of melt in copper described by an embedded-atom method (EAM) potential. The accuracy of this EAM potential for melting is validated by the equilibrium melting point obtained with the solid-liquid coexistence method and the superheating-supercooling hysteresis method. We characterize the atomistic melting process by following the temperature and time evolution of liquid atoms. The nucleation behavior at the extreme superheating is analyzed with the mean-first-passage-time (MFPT) method, which yields the critical size, steady-state nucleation rate, and the Zeldovich factor. The value of the steady-state nucleation rate obtained from the MFPT method is consistent with the result from direct simulations. The size distribution of subcritical nuclei appears to follow a power law similar to three-dimensional percolation. The diffuse solid-liquid interface has a sigmoidal profile with a 10%-90% width of about 12 A near the critical nucleation. The critical size obtained from our simulations is in reasonable agreement with the prediction of classical nucleation theory if the finite interface width is considered. The growth of melt is coupled with nucleation and can be described qualitatively with the Johnson-Meh-Avrami law. System sizes of 10(3)-10(6) atoms are explored, and negligible size dependence is found for bulk properties and for the critical nucleation.     

INFLUENCE OF SAMPLE THICKNESS ON ISOTHERMAL CRYSTALLIZATION KINETICS OF POLYMERS IN A CONFINED VOLUME

Isothermal crystallization process of polymers in a confined volume was simulated in the case of instantaneous nucleation by use of the Monte Carlo method. The influence of sample thickness on some kinetic parameters of crystallization was quantitatively evaluated. It was found that there was a critical thickness value. Influence of thickness on the crystallization behavior was only found for samples of thickness near and less than the critical value. For thick samples the Avrami plot showed straight lines with a turning point at the late stage of crystallization due to the secondary crystallization. When the thickness was near or less than the critical value a primary turning point appeared in the Avrami plot at the very beginning of the crystallization process. A model was proposed to explain the mechanism of this phenomenon. According to this model the critical thickness value is related to the nucleation density or the average distance between adjacent nuclei, and the primary turning point is an indication of a transformation of crystal growth geometry from a three-dimensional mode to a two-dimensional one. Analysis of experimental results of PEO isothermally crystallized at 53.5℃ was consistent with the proposed model.     

聚丁二酸丁二醇酯的自成核结晶行为

利用差示扫描量热仪(DSC)研究了自成核对聚丁二酸丁二醇酯(PBS)的结晶行为的影响. 研究结果表明, PBS的有效自成核温度处理区间为118～120 ℃. PBS经自成核处理后结晶温度提高, 可以在100~118 ℃温度区间内迅速结晶. 同时, 研究了自成核处理后样品在100～104 ℃范围内的等温结晶行为、动力学过程及熔融行为. 结果表明, 随着等温结晶温度的升高, 结晶速率变慢, 熔融曲线出现多重熔融峰. Hoffman-Weeks方程分析结果表明, 自成核处理对PBS的平衡熔点没有影响. Avrami等温结晶动力学方程适合分析自成核处理样品的等温结晶动力学过程, 获得其动力学参数K与n, 其中n值偏大的原因在于自成核的样品结晶生长点增多. 根据Arrhenius方程, 计算获得PBS自成核处理后等温结晶活化能为-286 kJ/mol.     

Nucleation of Organic Crystals—A Molecular Perspective

The outcome of synthetic procedures for crystalline organic materials strongly depends on the first steps along the molecular self‐assembly pathway, a process we know as crystal nucleation. New experimental techniques and computational methodologies have spurred significant interest in understanding the detailed molecular mechanisms by which nuclei form and develop into macroscopic crystals. Although classical nucleation theory (CNT) has served well in describing the kinetics of the processes involved, new proposed nucleation mechanisms are additionally concerned with the evolution of structure and the competing nature of crystallization in polymorphic systems. In this Review, we explore the extent to which CNT and nucleation rate measurements can yield molecular‐scale information on this process and summarize current knowledge relating to molecular self‐assembly in nucleating systems.     

Does conventional nucleation occur during phase separation in polymer blends?

The kinetics of liquid–liquid phase separation in off-critical polymer blends was studied with time-resolved small-angle neutron scattering. Our objective was to study the nature of the nuclei that formed during the initial stages of the phase transition. The blends were composed of model polyolefins—deuterium-labeled poly(methyl butylene) (PMB) and poly(ethyl butylene) (PEB)—with molecular weights of about 200 kg/mol. A direct examination of the initial clustering of molecules before macroscopic phase separation was possible because of the large size of the polymer chains and concomitant entanglement effects. We discovered that the scattering profiles obtained during nucleation merged at a well-defined critical scattering vector. We propose that this is the signature of the critical nucleus and that the size of the critical nucleus is inversely proportional to the magnitude of the critical scattering vector. The kinetic studies were preceded by a thorough characterization of the equilibrium thermodynamic properties of our PMB/PEB blends. The locations of the binodal and spinodal curves of our system are consistent with predictions based on the Flory–Huggins theory. This combination of thermodynamic and kinetic experiments enabled the quantification of the dependence of the size and structure of the critical nuclei on the quench depth. Our results do not agree with any of the previous theories on nucleation. Some aspects of our results are addressed in recent theoretical work by Wang in which the effects of fluctuations on the classical binodal and spinodal curves in polymer blends are incorporated. Both theory and experiment support the notion that the traditional stability limit (spinodal) should be replaced by a metastability limit. Although Wang's theory provides an explanation for some of our observations, many fundamental issues regarding nucleation in polymer blends remain unresolved. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1793–1809, 2004     

Formation of crystal nuclei near critical supersaturation in small volumes

This work deals with the nucleation of crystals in confined systems in response to the recent high interest in research on crystallization in emulsion and microemulsion droplets. In these confined systems, crystallization often occurs at high supercooling; thus, nucleation determines the overall crystallization process. A decrease in the volume of the confined mother phase leads to the higher supercooling needed for the phase transition. We have numerically solved kinetic equations in order to determine the conditions under which the first crystal nuclei are formed by homogeneous and heterogeneous nucleation from supercooled melt and supersaturated solution, depending on the volume of the mother phase. Supersaturation (or supercooling) increases with decreasing volume of the mother phase. The nucleation barrier depends linearly on the logarithm of volume of the mother phase in all cases under consideration, as follows from the numerical solution of kinetic equations.     

Some novel efforts to describe the nucleation and growth at electrodeposition

Some alternative ways are developed of looking at the model concepts on electrochemical nucleation. The article consists in several parts concerning several stages of the overall process of nucleation and growth: the statistical approach to nucleation kinetics, the kinetics of the initial stage of the nuclei growth, the growth of an individual cluster under combined charge transfer and diffusion control, nucleation rate and the overall number of clusters, the growth of an increasing number of clusters at overlapping of diffusionally depleted zones, and galvanostatic nucleation.     

A competitive particle nucleation mechanism in the polymerization of homogenized styrene emulsions

The effects of concentrations of surfactant (sodium lauryl sulfate [SLS]) and initiator (sodium persulfate [SPS]) on the polymerization of homogenized styrene emulsions, stabilized by SLS/lauryl methacrylate (LMA) or SLS/stearyl methacrylate (SMA), were studied. The rate of polymerization increases with increasing [SLS] or [SPS]. In addition to monomer droplet nucleation, the formation of particle nuclei in the aqueous phase (homogeneous nucleation) plays a crucial role in the polymerization kinetics. In comparison with the LMA containing polymerization system, monomer droplet nucleation becomes more important when the more hydrophobic SMA was used as the costabilizer. Furthermore, the degree of homogeneous nucleation increases with increasing [SPS].     

Kinetics of the Establishment of Quasi-Steady-State Regime of Overcoming Activation Barrier of Nucleation on the Macroscopic Wettable Nuclei

The solution of the kinetic equation of nucleation on macroscopic wettable condensation nuclei was constructed for the initial (incubation) stage. The solution thus constructed determines the times of relaxation to quasi-steady-state distribution of droplets generating on droplet nuclei in the vicinity of maximum of the work of droplet heterogeneous formation as well as the relaxation to quasi-equilibrium droplet distribution throughout the entire region located to the left of this vicinity at the droplet size axis. The dependence of relaxation times on the height of activation barrier of nucleation, size of nuclei, their nature, and characteristics of matter comprising condensate was elucidated. It was shown when the non-steady-state rate of nucleation becomes actually equal to the quasi-steady-state rate of nucleation.     

Diketopyrrolopyrrole‐based polymer nanowires: Control of chain conformation and nucleation

Understanding the nucleation process is very important in growing polymer nanowires as it plays a decisive role in determining the crystal structure and size distribution. Polymer chain conformation determines whether the polymer chains could assemble to nuclei or not. Here, chain conformation and the nucleation process were controlled to grow 3,6‐bis‐(thiophen‐2‐yl)‐N,N′‐bis(2‐decyl‐1‐tetradecyl)‐1,4‐dioxo‐pyrrolo[3,4‐c]pyrrole and thieno[3,2‐b]thiophene (DT‐PDBT‐TT) nanowires. We changed the conformation of DT‐PDBT‐TT in solution and controlled the nucleation process by using a main solvent:cosolvent system. The main solvent was a low boiling point good solvent, and the cosolvent was consisted of two high boiling point solvents with different solubility. In fact, the chain conformation in the pristine solution was changed by choosing different main solvents (with H‐bond, π–π or none interaction with the main chain) and temperatures. The absorption spectrum and TEM images showed that trichloro ethylene (TCE) was the best main solvent because it has H‐bond interaction with the polymer main chain and DT‐PDBT‐TT conformation in it approaching unimer coil conformation, which is beneficial to grow nanowires. Mixed o‐dichlorobenzene (ODCB) and anisole (AS) with different ratios were used to changing the solubility step by step to control nucleation process. Only when marginal cosolvent (ODCB:AS = 1:1) was added, could it decrease the nuclei number and avoided the aggregates simultaneously. As the main solvent evaporated slowly, the nucleation and growth happened, leading to the nanowires formation. The resulting nanowires were about 63 nm in width and one to two microns in length. The width of the DT‐PDBT‐TT structures suggests that the polymer chains are oriented along the fibril axis. Our results indicated that there are two requirements for the nanowire formation, (1) the polymer chain conformation should approach unimer coil; (2) the nucleation density should be optimized, not too much and no aggregation happened. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 833–841     

Experimental study of shear-induced crystallization of an impact polypropylene copolymer

The crystallization kinetics of polypropylene was observed during shear and after shear experiments under isothermal condition. The crystallizations were performed in a plate-plate and a fiber pull-out device. The nucleation density, the crystalline growth and the overall kinetics were measured and compared with data obtained in a similar way but during static experiments. The morphologies are spherulitic and formed from nuclei which seem to be randomly distributed. -phase spherulites are always observed but with a nucleation density and a growth rate which depend on shearrate. The nucleation density is strongly enhanced by shear and acts as the main factor on the overall kinetics. The overall kinetics can be analyzed with a two-step Avrami model, where an Avrami exponentn ₁ with a very high value is always observed first after shear and a more usual parametern ₂ for the subsequent crystallization period. This high value ofn ₁ seems to be related to the strong enhancement of nucleation density. The growth rate increases with the shear-rate, but the basic growth mechanisms do not seem to be modified. For crystallizations after shear the growth rate decreases with a long-time delay after shear but not down to the static value. The effect is characteristic of a partial relaxation of chain orientation after shear but with a very unusual time constant.     

Mechanism of silver particle formation during photoreduction using in situ time-resolved SAXS analysis

Formation mechanisms of silver (Ag) particles in an aqueous ethanol solution of poly(N-vinyl-2-pyrrolidone) (PVP) by the photoreduction of AgClO(4) were investigated by means of in situ small-angle X-ray scattering (SAXS) measurements. The kinetics of association process (nucleation, growth, and coalescence) of Ag(0) atoms to produce Ag particles was successfully revealed by the quantitative SAXS analysis for the number-average of radius (R(0)), number of particles (n(Ag)), reduced standard deviation (σ(R)/R(0)), and volume fraction (?(Ag)) of Ag particles produced by the photoreduction. The rate of nucleation and growth process during Ag particle formation strongly depend on the initial metal concentration. The time evolution of radius and number of Ag particles indicates that a mechanism of Ag particle formation is composed of different three processes, that is, reduction-nucleation, Ostwald ripening, and particle coalescence. In a rapid reduction-nucleation process, small nuclei or particles (average radius ～2.5 nm) are produced by an autocatalytic reduction. After the formation of small nuclei or particles proceeds, Ostwald ripening and particle coalescence, predicted by the Lifshitz-Slyozov-Wagner theory (LSW theory), subsequently occur, resulting in the particle growth (average radius ～11.5 nm).     

A comparative study on the single-scan and multiple-scan techniques in differential scanning calorimetry: Application to the crystallization of the semiconducting Ge0.13Sb0.23Se0.64 alloy

A method has been developed for analysing the evolution with time of the volume fraction transformed and for calculating the kinetic parameters at non-isothermal reactions in materials involving formation and growth of nuclei. By considering the assumptions of extended volume and random nucleation, a general expression of the fraction transformed as a function of time has been obtained in isothermal crystallization processes. Considering the mutual interference of regions growing from separate nuclei the Johnson–Mehl–Avrami equation has been deduced as a particular case. The application of the transformation rate equation to the non-isothermal processes has been carried out under the restriction of a nucleation which takes place early in the transformation and the nucleation frequency is zero thereafter. Under these conditions, the kinetic parameters have been deduced by using the techniques of data analysis of single-scan and multiple-scan. The theoretical method developed has been applied to the glass-crystal transformation kinetics of the semiconducting Ge_0.13Sb_0.23Se_0.64 alloy. The kinetic parameters obtained according to both techniques differ by only about 2.5%, which confirms the reliability and accuracy of the single-scan technique when calculating the above-mentioned parameters in non-isothermal transformation processes. The phases at which the above-mentioned semiconducting glass crystallizes after the thermal process have been identified by X-ray diffraction. The diffractogram of the transformed material shows that microcrystallites of Sb₂Se₃ and GeSe are associated with the crystallization process, remaining a residual amorphous matrix.     

Spinodal for the solution-to-crystal phase transformation

The formation of crystalline nuclei from solution has been shown for many systems to occur in two steps: the formation of quasidroplets of a disordered intermediate, followed by the nucleation of ordered crystalline embryos within these droplets. The rate of each step depends on a respective free-energy barrier and on the growth rate of its near-critical clusters. We address experimentally the relative significance of the free-energy barriers and the kinetic factors for the nucleation of crystals from solution using a model protein system. We show that crystal nucleation is 8-10 orders of magnitude slower than the nucleation of dense liquid droplets, i.e., the second step is rate determining. We show that at supersaturations of three or four k(B)T units, crystal nuclei of five, four, or three molecules transform into single-molecule nuclei, i.e., the significant nucleation barrier vanishes below the thermal energy of the molecules. We show that the main factor, which determines the rate of crystal nucleation, is the slow growth of the near-critical ordered clusters within the quasidroplets of the disordered intermediate. Analogous to the spinodal in supersaturated fluids, we define a solution-to-crystal spinodal from the transition to single-molecule crystalline nuclei. We show that heterogeneous nucleation centers accelerate nucleation not only because of the wettinglike effects that lower the nucleation barrier, as envisioned by classical theory, but by helping the kinetics of growth of the ordered crystalline embryos.     

Fluctuation‐assisted crystallization of an iPP/PEOc polymer alloy prepared on a single multicatalyst reactor granule

The new fluctuation‐assisted mechanism for nucleation and crystallization in the isotactic polypropylene/poly(ethylene‐co‐octene) alloy has been studied. We found that the liquid–liquid phase separation (LLPS) had a dominant influence on the crystallization kinetics through the nucleation process. After LLPS, the nucleation of crystallization mainly occurred at the interface of the phase‐separated domains. It is because that the concentration fluctuations of the LLPS induced the motion of polymer chains and possibly some segmental alignment and/or orientation in the concentration gradient regions through interdiffusion, which could assist the formation of nuclei for crystallization. In other words, the usual nucleation energy barrier could be overcome (or at least partially) by the concentration fluctuation growth of LLPS in the unstable regions. This could be viewed as a new kind of heterogeneous nucleation and could be an addition to the regular nucleation and growth mechanism for crystallization. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 166–172, 2009     

Kinetics of island growth in the framework of “planar diffusion zones” and “3D nucleation and growth” models for electrodeposition

In the electrochemical deposition of thin films, the measurement of the current-time curve does not allow for a direct determination of the nucleus growth law, electrode surface coverage, and mean film thickness. In this work, we present a theoretical approach suitable to gain insight into these quantities from the knowledge of nucleation density, solution parameters, and current-time behavior. The model applies to both isotropic and anisotropic growth rates of nuclei and a study on the effect of nucleus shape and aspect ratio on the kinetics is presented. Computer simulations and experimental results from literature are also discussed in the framework of the present approach.