Roller’s equation

Roller obtained good agreement with an extensive amount of experimental data. However, the application of his equation is dependent on straight-line plots between log w/ /d.and 1/d in order that a and b may be determined. Roller s equations appear to have no distinct advantage over the Hatch-Choate equations. 

Roller s Equation. A relationship between the percentage weight and the size of powders w = aVd. exp(-b/d), where w is the weight percent of all material having diameters less than d, and a and b are constants. Other equations were deduced relating to specific surface and to the number of particles per gram or powder. (P. S. Roller, J. Franklin Inst., 223,609,1937.) Roller s Plasticity Test. A method for the assessment of plasticity on the basis of the stress/deformation relationship when clay cylinders are loaded. (P. S. Roller, Chem Industries, 43, No. 4,398, 1938.)... 

Rosin-Rammler Equation—Rosin and Rammler (1933) proposed an equation which in some respects is similar to Roller s basic equation, Eq (3-32). Their equation fits size-frequency data of friable material such as coal, but otherwise does not have the wide application of the Hatch-Choate and Roller equations. The Rosin-Rammler equation is... 

Remember that you didn t learn to roller-skate, or to ride a bicycle, until you could balance yourself on your feet. You cannot devise new chemical reactions until you can balance chemical equations. It s fun to mix things in a laboratory and to guess or predict the results. You may not always be correct in your predictions, nor will you always be correct in your mixing, but it will always be fun to account for every single atom involved in a chemical reaction. You will learn how to do this gradually, as you do the experiments in this book. 

Equation (12-112), as it stands, would give an overestimate of the maximum drying rate for the case of contact drying over heated rolls, when there are significant heat losses from the ends of the drum and only part of the drum s surface can be used for drying. In the roller drying arrangements shown in Eig. 12-80, only a fraction a of the drum s periphery is available from the point of pickup to the point where the solids are peeled off... 

Roller and his coworkers have reported that the sultam 121 rapidly hydrolyses in dilute acid (equation 213)242. Helferich and Kleb have reported268 that whereas N-4-acetamidophenylpropane sultam is cleaved by boiling sulphuric acid (16%), the corresponding butane sultam does not react suggesting that the order of reactivity of sultams towards acid hydrolysis is P>y>S. 

A mechanistically different type of nitrosation was discovered by Keefer and Roller (1973), namely a nitrosation of secondary aliphatic amines with nitrite anions in alkaline solution, catalyzed by aldehydes. Although it is unlikely to be applicable to diazotization, i. e., to primary amines, it will be mentioned here because it is a good example of the fact that, in chemistry, particularly in organic chemistry, for a certain type of reaction, e. g., nitroso-de-protonation (which includes substitution of protons bonded to C, N, O, S, etc., atoms), practically all methods follow the same basic pattern (in the case of nitrosation substitution by an electrophilic nitrosating reagent). The Keefer-Roller nitrosation is apparently different if one looks at the stoichiometric equation (4-8). A careful kinetic investigation (Casado et al., 1981b, 1984 a) on the concentration and pH dependence of this reaction revealed that the nitrite anion and free amine base enter the substitution process and that formaldehyde is a true catalyst, as it is not required in equimolar amounts. 

Microscope transmission samples suffer from the same opacity problem as macroscopic samples. The solution to this problem is to prepare samples that are 1 to 20 microns thick. Fortunately, many microscopic samples can be turned into thin films by applying pressure and flattening them. This works because it does not take a lot of force to put a lot of pressure on a sample of small area, as shown in Equation 4.3. There are many ways to apply pressure to a microscopic sample to flatten it. In the author s opinion the best tool for this purpose is a roller knife, as shown in Figure 6.6, so called because it has a roller at one end and a scalpel at the other. 

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