Particle size distribution interpretation

A procedure for proplnts is presented by J.W. French (Ref 27), who used both OM and EM (electron microscope) to study plastisol NC curing. He found that the cure time of plastisol NC is a logarithmic function of temp, and direct functions of chemical compn and total available surface area, as well as of particle size distribution. It should be noted that extensive use of statistics is required as a time-saving means of interpreting particle size distribution data. The current state-of-the-art utilizes computer techniques to perform this function, and in addition, to obtain crystal morphology data (Ref 62)... 

A very powerful method for the evaluation of solubility differences between polymorphs or solvates is that of intrinsic dissolution, which entails measurements of the rates of solution. One method for this work is to simply pour loose powder into a dissolution vessel, and to monitor the concentration of dissolved solute as a function of time. However, data obtained by this method are not readily interpretable unless they are corrected by factors relating to the surface area or particle size distribution of the powder. In the other approach, the material to be studied is filled into the cavity of a circular dissolution die, compressed until it exhibits the effective planar surface area of the circular disc, and then the dissolution rate is monitored off the surface of the rotating disc in the die [130],... 

Measurement of particle size and of particle size distribution is a highly specialised topic, and considerable skill is needed in the making of accurate measurements and in their interpretation. For details of the experimental techniques, reference should be made to a specialised text, and that of Allen(1) is highly recommended. 

Raman spectroscopy s sensitivity to the local molecular enviromnent means that it can be correlated to other material properties besides concentration, such as polymorph form, particle size, or polymer crystallinity. This is a powerful advantage, but it can complicate the development and interpretation of calibration models. For example, if a model is built to predict composition, it can appear to fail if the sample particle size distribution does not match what was used in the calibration set. Some models that appear to fail in the field may actually reflect a change in some aspect of the sample that was not sufficiently varied or represented in the calibration set. It is important to identify any differences between laboratory and plant conditions and perform a series of experiments to test the impact of those factors on the spectra and thus the field robustness of any models. This applies not only to physical parameters like flow rate, turbulence, particulates, temperature, crystal size and shape, and pressure, but also to the presence and concentration of minor constituents and expected contaminants. The significance of some of these parameters may be related to the volume of material probed, so factors that are significant in a microspectroscopy mode may not be when using a WAl probe or transmission mode. Regardless, the large calibration data sets required to address these variables can be burdensome. 

The methods just discussed are only two of a wide variety of techniques that provide essentially the same kinds of information. In general, any measurement that gives (a) the amount of suspended material a fixed distance below the surface at various times or (b) the amount of material at various depths at any one time can be interpreted in terms of particle size distribution. Pressure, density, and absorbance are additional measurements that have been analyzed this way. 

Robust formulations are today an absolute prerequisite. Concerning the production of granules, the granule size distribution should not vary from batch to batch. The key factors are the correct amount and the type of granulating liquid. The interpretation of the power consumption method can be very important for an optimal selection of the type of granulating liquid. The possible variation of the initial particle size distribution of the active substance and/or excipients can be compen-... 

The chain model corresponding to the closed circuit milling system with localised models of all its elements is presented in Fig. 2. It can be constructed in different ways, but first let us examine the model shown in Fig. 2a. Every column of the set of cells corresponds to an element of the circuit a mill a classifier or an absorber. The cells within columns correspond to fraction numbers with the total number of fractions equal to r. The fraction size decreases with increasing fraction number. The state of the system is characterised by the set of probabilities f, to occupy the cells, every of which can be interpreted as the relative mass content of particles in the cell ij. In particular, the set fj, I = 1,2,.. .r, corresponds to the particle size distribution in the hold-up of the /111 element of the circuit. 

The overall conclusion from the analysis of equation 18 over the complete domain of a is that, in principle, information about the shape of the particle size distribution can be obtained directly from turbidity, or in general, from scattering measurements. However, the discriminating power of the measurements in terms of the particle size distribution depends upon the wavelength range selected for the analysis. The major difficulty in the interpretation of the data arises from the behavior of the extinction itself as function of the size parameter which causes the measurements "see" a different average at every wavelength. 

In the small particle size regime, two equivalent formulations lead to the interpretation of the data in terms of ratios of moments of the particle size distribution or in terms of powers of the D32 average (equations 15 and 20). It is clear that in either case a sufficient number of terms in the series has to be included in order to account for the behavior of the extinction as function of a. The number of terms required cannot be decided a priori, rather the data itself has to dictate how many terms in the power series approximation the measurements can detect. 

It is not always easy to determine what procedure to follow in making a particle-size distribution. Obviously, if the particles are soluble in water or any other fluid, sedimentation procedures must be applied with caution. It is likewise clear that any sedimentation technique is markedly affected by the shape of the particles used, and that results are subject to interpretation. In other words, determinations depending upon sedimentation (and elutriation) are merely equivalent measures of spheres having the same rate of settling. Greatest reliance naturally applies to that size range whose motion is known to be specified by Stokes law. 

This paper,11 which is a model of its kind, reported a study of the reaction on two Au/SiC>2 catalysts, having respectively 0.15 and 5% gold unfortunately both had somewhat broad particle size distributions, namely 3 9 nm (0.15% Au) or 3-7 nm (5% Au), with a significant number of very large (>10nm) particles. This complicated the interpretation of the results, as no clear particle size effect could be seen. However, silicalite-1 (Si-MFI) and TS-1 (a titanium-containing silicalite, Ti-MFI) were also used, and the size of the channels constrained the particle size to be less than 3nm in both cases. These size differences accounted for the marked variations in activity observed at 433 K ... 

There are, however, also some drawbacks to these techniques The inversion of elution from the normal to the steric mode complicates measurements in the particle size range around 1 pm and, although this transition region can be shifted by experimental conditions, serious interpretation errors can occur if the particle size distribution spans this transition region. 

An important feature of processing plastic waste is the grinding down to an appropriate particle size to suit the next processing stage. The particle size distribution of a hammer mill ground PVC has been interpreted and a model developed to describe the distribution, relevant to separation (428). Selective grinding has been proposed to induce differences in size and shape... 

Product particle size distributions of impact ground thermoplastics (specifically PETP and PVC) are interpreted and models describing these distributions developed. Results from multiple and single particle breakage in a hammer mill are used. The values of the model coefficients are related to the brittle-ductile transition grinding conditions and breakage mechanisms. Results are relevant to the separation of thermoplastics, as for example, is required when recycling consumer products such as bottles. 3 refs. 

The kinetics of cement hydration are dominated by the effects associated with the particle size distribution of the starting material, and attempts to explain them in which this is ignored can lead to very misleading results (T41,B98,B105,K37,J27,K38,K39). Even laboratory-prepared samples with close distributions (e.g. 2-5 pm) (K20) are far from monodisperse from the kinetic standpoint. Two approaches to the resulting problems of interpretation will be considered. 

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