Nucleation measurements

Laaksonen, A., V. Talanquer and D. W. Oxtoby, Nucleation Measurements, theory, and atmospheric... 

For mineralization, the normal, metastable state is adjusted by nucleation, measured by the seed and solubility tests. The seed test measures amount of solid apatite required to precipitate Ca2+ and HP042- ion concentrations exceeding their solubility product. The solubility test measures the minimal concentrations of Ca2+ and HP042- necessary to induce precipitation. Type I collagen fibers nucleate bone formation as the concentrations of Ca2+... 

Another method of nucleation measurement that differs from both diffusion and expansion chambers involves the rapid turbulent mixing of two gas streams (Wyslouzil et al. 1991a,b). This method is particularly suited to studies of binary nucleation. Two carrier gas-vapor streams are led to a device where rapid turbulent mixing takes place. The two-component vapor mixture is supersaturated and begins to nucleate immediately. The stream passes to a tube where nucleation may continue and the nucleated particles grow. Residence time in the flow tube is the order of seconds. When the nucleated particle concentration is sufficiently low, droplet growth does not deplete the vapor appreciably, and constant nucleation conditions can be assumed. 

C of Na nucleate, measurements on floccules, except for Li, Na and K, where the measurements were made on suspended SiOg particles. 

The time elapsed from the creation of the initial supersaturation to the detection of the first crystals formed in the system is known as the induction period. The level of supersaturation attained is then akin to the metastable hmit . Neither quantity (viz. the induction time and metastable limit) is therefore a fundamental quantity. Both are useful measures, however, of the propensity of a solution to nucleate. Measurement of the induction time as a function of supersaturation can be used to help determine crystallization kinetics and mechanism. Thus, the induction time may be expressed by (Walton, 1967)... 

FIG. 13 The rate of CO2 bubble nucleation measured as a function of (cr/ ) for two conditions. The upper curve (triangles) is for silanized P5rex, with a contact angle of close to 80°. The lower curve (squares) is for clean P5rex, with a contact angle close to 0°. 

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

Because of the large surface tension of liquid mercury, extremely large supersaturation ratios are needed for nucleation to occur at a measurable rate. Calculate rc and ric at 400 K assuming that the critical supersaturation is x = 40,000. Take the surface tension of mercury to be 486.5 ergs/cm. ... 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Additives, whether hydrophobic solutes, other surfactants or polymers, tend to nucleate micelles at concentrations lower than in the absence of additive. Due to this nucleating effect of polymers on micellization there is often a measurable erne, usually called a critical aggregation concentration or cac, below the regular erne observed in the absence of added polymer. This cac is usually independent of polymer concentration. The size of these aggregates is usually smaller than that of free micelles, and this size tends to be small even in the presence of added salt (conditions where free micelles tend to grow in size). 

In spite of these obstacles, crystallization does occur and the rate at which it develops can be measured. The following derivation will illustrate how the rates of nucleation and growth combine to give the net rate of crystallization. The theory we shall develop assumes a specific picture of the crystallization process. The assumptions of the model and some comments on their applicability follow ... 

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

The relative effectiveness of nucleating agents in a polymer can be determined by measuring recrystallization exotherms of samples molded at different temperatures (105). The effect of catalyst concentration and filler content has been determined on unsaturated polyesters by using dynamic thermal techniques (124). Effects of formulation change on the heat of mbber vulcanization can be determined by dsc pressurized cells may be needed to reduce volatilization during the cure process (125). 

Although magma density is a function of the kinetic parameters fP and G, it often can be measured iadependentiy. In such cases, it should be used as a constraint ia evaluating nucleation and growth rates from measured crystal size distributions (62), especially if the system of iaterest exhibits the characteristics of anomalous crystal growth. 

The crystalliza tion resistance of vulcaniza tes can be measured by following hardness or compression set at low temperature over a period of time. The stress in a compression set test accelerates crystallization. Often the curve of compression set with time has an S shape, exhibiting a period of nucleation followed by rapid crystallization (Fig. 3). The mercaptan modified homopolymer, Du Pont Type W, is the fastest crystallizing, a sulfur modified homopolymer, GN, somewhat slower, and a sulfur modified low 2,3-dichlorobutadiene copolymer, GRT, and a mercaptan modified high dichlorobutadiene copolymer, WRT, are the slowest. The test is often mn near the temperature of maximum crystallization rate of —12° C (99). Crystallization is accelerated by polyester plasticizers and delayed with hydrocarbon oil plasticizers. Blending with hydrocarbon diene mbbers may retard crystallization and improve low temperature britdeness (100). 

Solutions vaiy greatly in their ability to sustain measurable amounts of supersaturation. With some materials, such as sucrose, it is possible to develop a supersaturation coefficient of 1.4 to 2.0 with little danger of nucleation. With some common inorganic solutions such as sodium chloride in water, the amount of supersaturation which can be generated stably is so small that it is difficult or impossible to measure. 

Modtilus Measurements Another SCC test technique is the use of changes of modulus as a measure of the damping capacity of a metal. It is known that a sample of a given test material containing cracks will have a lower effec tive modulus than does a sample of identical material free of cracks. The technique provides a rapid and reliable evaluation of the susceptibility of a sample material to SCC in a specific environment. The so-called internal friction test concept can also be used to detect and probe nucleation and progress of cracking and the mechanisms controlling it. 

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