Nano-nucleation

Direct Observation of Nano-Nucleation by Synchrotron Radiation, 128... 

Relationship between Nano-Nucleation and Macro-CrystaUization, 133... 

Solving the nucleation mechanism is important to understand structures and physical properties of any materials. To our best knowledge, no one has succeeded in observing directly the nucleation from the melt, because the number density of small nuclei on the order of nanometers (which we will henceforth call a nano-nucleus ) is too small to detect [4, 5]. Hence, only alternative experimental studies have been performed on macroscopic crystals (macro-crystals) by means of optical microscopy (OM) or bubble chamber [2]. Recent simulation studies performed on colloid systems [6, 7] also fail to provide a direct observation of nano-nucleation because the thermal fluctuation of nano-nuclei should be much more significant than that of macro-crystals or macro-colloids. This chapter introduces CNT, describes experimental approaches, and discusses the results of direct observation of nano-nucleation. 

The scientific goal of nucleation study is to obtain an experimental real image of nano-nucleation and to propose a correct nucleation theory that can explain and predict the nucleation. We have to approach the scientific goal from two different angles, one experimental and the other theoretical. 

The theoretical approach constructs a basic equation to explain the observed f(N, t). CNT proposes a fundamental kinetic equation as a basic equation of nucleation by using/(N, t) [3]. However, the kinetic equation of CNT (as presented below) does not satisfy the fundamental mass conservation law, which means that the kinetic equation cannot be regarded as a basic equation. Any basic equation includes parameters (the so-called kinetic parameters determined experimentally) that give actual information about nucleus, nucleation, and so on. It remains an important problem to obtain correct kinetic parameters of nano-nucleation. 

DIRECT OBSERVATION OF NANO-NUCLEATION BY SYNCHROTRON RADIATION... 

This section describes two case studies by synchrotron radiation [16,17], The first is the small-angle X-ray scattering (SAXS) observation of nano-nucleation of polyethylene (PE). The second is the t revolution off(N,t). 

We observe nano-nucleation directly by adding nucleating agent (NA) to a sample by which the SAXS intensity Ix(q, t) from the nano-nuclei increases as much as lO" times, where q is the scattering vector [18,19]. At the same time, we determine the correct y(A/, r) and the 2D shape of the nano-nucleus. In addition, obtaining the AT dependence of f N, t) directly by SAXS shows that nucleation controls the induction period of crystallization, while spinodal decomposition does not [20]. 

Figure 4.2 AT dependence of Ix(q, 0 against as a parameter of t. (a) re=129.0°C and AT = 10.5 K. (b) T, = 126.5°C and AT = 13.0 K. Ixiq, t) increases with the increase of f, which is the evidence of nano-nucleation. Since Ixiq, 0 increases slowly with the decrease of AT, it indicates that nano-nucleation becomes difficult with the decrease of AT.

Rgure 4.5a shows the t evolution of/(JV, t) as a function of N.J N, t) of smaller N increases significantly and quickly and becomes saturated with the increase of t, whereas J N, t) of the larger N increases more slowly and becomes saturated with the increase of t. Rgure 4.5a shows after the definition of Andres and Boudart [27]. Rgure 4.5b, which illustrates the nano-nucleation, shows... 

Figure 4.5 Time evolution of/(A, t). (a) Time evolution of f(N, t) as a function of N. Right axis indicates f N, t) of = 20 rep. unit, and left axis indicates that of the other Nj.f(N, t) of smaller N increased signilicantlyfaster and saturated with the increase of t. t s are also shown, (b) Illustration of nano-nucleation. Smaller nano-nuclei generated for f = 7 min. Many nanonuclei are generated and a fraction of them grow up to larger ones for f = 35 min. Much more nano-nuclei and larger ones were generated and grew up for t = 100 min.

If nano-nucleation is a thermal equilibrium phenomenon for all N, we expect that fst(N) should satisfy the Boltzmann distribution. Hence fst(N) should give a minimum at and increase significantly for N>N. However, the observed/st(A ) decreases with the increase of N. Therefore Pfifnano) does not lit for A > A. This means that the nucleation in A > A should be a kind of... 

The use of SAXS to clarify a real and exact image of nano-nucleation is not easy, unlike the use of OM, which is both easier and practical. Classical nucleation (CN) studies generally assume that OM can detect the most essential process in nucleation as the zero-th approximation. Suggesting instead that the most essential process in nucleation should be the critical nano-nucleation... 

Figure 4.8 AT dependence of nano-nucleation and macro-crystallization, (a) Plots of AT dependence of f(N, t) against f for = 2.2 X lO rep. unit > At. ff AT = 10.5 K) = 450 rep. unit, which is the maximum N" in this study. f N, t) of AT = 13.9 and 11.5 K are shown in the left and top axes. f N, t) of AT = 10.5 K is shown in the right and bottom axes. It was impossible to observe the saturation of f N, t) for larger AT due to onset of lamellar stacking, r of AT = 10.5 K and rs for each AT are also shown, (b) Plots of 7, and theoretical j against and comparison of these slopes. The paraUel lines confirm the same AT dependence.

Figure 4.9 illustrates the sequential process of nucle-ation, which shows AG(N) against N. AG (A ) corresponds to critical nano-nucleation. In the nucleation theory, the so-called net flow of nucleation (j) plays an important role in the nucleation process as illustrated in Figure 4.9 (also see Section 4.4). As the zero-th approximation, critical nano-nucleation should become the main controlling process with an activation barrier in nucleation following Eyring s kinetic theory of absolute reaction rate (theory of absolute reaction rate) [30]. Hence,y can be given by... 

AG (AT) is given by AG (A ) 4aaJAg for Ag Act, the 2D nucleus [12]. We define them here per one particle or repeating unit. If critical nano-nucleation mainly controls both nano-nucleation and macro-crystallization, j can be rewritten as... 

Figure 4.9 Illustration of AG against N. A is the surface area of the nucleus. The nano-nucleus shows significant fluctuation with respect to its size and shape. AG (nano) corresponds to critical nano-nucleation, as shown in Reference [16]. According to Eyring s theory of absolute reaction rate, critical nano-nucleation should become the activation barrier of nucleation. The macro-crystal has smooth and flat surfaces and does not disappear. (See color insert.)...

It is impossible to observe j directly, but some observable quantities should correspond to it. The inverse of in nano-nucleation should be directly related to j, as well as I in macro-crystallization [2], Equation (4.17) defines I by the rate of macro-crystaUization per unit volume and time. If critical nano-nucleation mainly controls nano-nucleation and macro-crystalUzation, both and I should be proportional to j, respectively, that is, Tf j. We verify the direct correspondence between nano-nucleation and macro-crystaUization by obtaining this proportionality experimentally. 

The next section, which introduces a mass distribution function Q N, i), also describes a new basic equation of the mass conservation law based on the introduction of the net flow j N, t). We directly observe Q N, i) and obtain the overall crystalUnify during nano-nucleation in the bulk melt, which confirms our proposed nucleation theory. 

Sections 4.1 and 4.2 introduced nucleation by reviewing CNT. Section 4.3 discussed observation of nano-nucleation by means of SAXS.The correct size distribution f(N, t) and 2D shape (kinetic parameters) of a nano-nucleus are obtained simultaneously by analyzing SAXS intensity Ix(q, t) using the extended Guinier plot method. f N, t) is shown to decrease with the increase of N for each t. f(N, i) increases with the increase of t and saturates for each N. With the increase of t,f(N, t)... 

The relationship between nano-nucleation and macro-crystallization has been studied. We obtain the AT dependence of nucleation rate (I) of a macro-crystal whose size is more than 1 pm by optical microscopy. We describe the empirical formula by /(AT) exp[-C7AT], where C is a constant. We obtain t and I by using the AT dependence of fiN, t) proportional to the net flow of nucleation (/), that is, t °c / as the zero-th approximation. This shows that the critical nano-... 

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