Growth rate constant, definition

For crystal growth at constant rate, if the crystal composition can respond to interface melt composition through surface equilibrium, steady state may be reached (Smith et ah, 1956). At steady state, (dCldt) = 0 by definition. Hence,... 

Polymer alloys and blends constitute over 30 wt% of polymer consumption, and with an annual growth rate of about 9.3% that has remained constant for the last ten years (i.e., four times the growth rate of the plastics industry as a whole), their role can only increase. In the text, the following standard definitions will be used [Utracki, 1989 1991 see also Nomenclature in Chapter 1 of this Handbook],... 

If the necessary conditions for a parabolic growth rate are not fulfilled, then other rate laws will be obeyed. One may find, for example, that the reaction rate is constant (i.e. independent of the instantaneous thickness of the product layer). However, this observation alone does not permit one to decide upon a definite rate-controlling elementary reaction mechanism, since several mechanisms can give rise to an overall linear rate law. 

Discussion. The turbidity of a dilute barium sulphate suspension is difficult to reproduce it is therefore essential to adhere rigidly to the experimental procedure detailed below. The velocity of the precipitation, as well as the concentration of the reactants, must be controlled by adding (after all the other components are present) pure solid barium chloride of definite grain size. The rate of solution of the barium chloride controls the velocity of the reaction. Sodium chloride and hydrochloric acid are added before the precipitation in order to inhibit the growth of microcrystals of barium sulphate the optimum pH is maintained and minimises the effect of variable amounts of other electrolytes present in the sample upon the size of the suspended barium sulphate particles. A glycerol-ethanol solution helps to stabilise the turbidity. The reaction vessel is shaken gently in order to obtain a uniform particle size each vessel should be shaken at the same rate and the same number of times. The unknown must be treated exactly like the standard solution. The interval between the time of precipitation and measurement must be kept constant. 

Figures 3.80(a) and (b) show the behaviour of n, k and the thickness L of a polypyrrole film during its growth on a Pt electrode in aqueous perchlorate solution obtained via in situ ellipsometry. A definite lag can be seen between the change in L and the changes in n and k. Up to c. 1.3 s the thickness of the film increases linearly with time while n and k remain constant. Between 1.3 and 2 s the growth almost tails off before increasing slowly up to 4 s and then more quickly until attaining a steady rate of increase at t > 4 s. Similarly at 1.3 s < t < 4 s both n and k increase, with n attaining a maximum value at 4 s before decreasing, while k increases at a lower rate at t > 4 s than at t < 4 s.

The concept of balanced growth was introduced by Campbell (1957) to describe a metabolic state of a culture in terms of the distributed concentration (xj) or total mass (X- ) of a metabolic variable. According to Campbell s definition, growth is balanced when the specific rate of change of all such variables is constant. That is. 

Whilst programmed cooling (i.e. operation at constant nucleation rate within the metastable zone) increases the mean product crystal size cf. natural cooling, is it the optimum in producing the largest possible crystals The problem is to find the maximum of the integral of crystal growth over the batch time. Thus because batch operation is by definition transient, a functional has to be maximized over time rather than just a function at some point in time. Jones (1972, 1974) addressed this problem by application of a particular result in... 

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