T rade studies

The early understanding of the geometry and dynamics of dislocations, as well as a detailed discussion of the role of vacancies in diffusion, is to be found in one of the early classics on crystal defects, a hard-to-find book entitled Imperfections in Nearly Perfect Crystals, based on a symposium held in the USA in 1950 (Shockley et al. 1952). Since in 1950, experimental evidence of dislocations was as yet very sparse, more emphasis was placed on a close study of slip lines (W.T. Read, Jr.,  [c.114]

Subsequent rate studies have shown that there is significant rate retardation for reactions in which the norbomyl radical is generated in a rate-determining step." Typically, such reactions proceed 500-1000 times slower than the corresponding reaction generating the t-butyl radical. This is a much smaller rate retardation than that of 10 " found in SnI solvolysis. Rate retardations are still smaller for less strained bicyclic systems. The EPR spectra of the bridgehead radicals A and B are consistent with pyramidal geometiy at the bridgehead carbon atoms."  [c.678]

Prepare the solutions, thermostat them at the temperatures to be used in the rate study, and then adjust them all to the same pH value by the addition of small volumes of concentrated strong acid or base. The pH meter must be correctly calibrated at each temperature. Now carry out the kinetic study and calculate Eobs. Because this procedure has set d In (H )/d(l/T) = 0 experimentally, use Eq. (6-36) in the form = Eqh +  [c.259]

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195).  [c.483]

A classic shock-tube study concerned the high-temperature recombination rate and equilibrium for methyl radical recombination [M, Ml- Methyl radicals were first produced in a fast decomposition of diazomethane at high temperatures (T > 1000 K)  [c.2124]

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides  [c.2947]

Graham himself clearly recognized the shortcomings of his experiments on effusion through mechanically formed orifices, and in later work i.87] he studied effusion into a vacuum through a thin plate of pencil lead graphite. In this case he claims that Che pores are sufficiently small Chat effusion cakes place by a "molecular mechanism" -- what we should now call Knudsen streaming-- in contrast to his earlier work with stucco plugs and punched orifices. Of course, the length of the pores in the graphite plate Is such that collisions between molecules and the pore walls generate the main resistance to flow, so conditions are still such Chat no test of the kinetic theory formula (A.2.1) is possible. A direct test of this equation had to await the development of vacuum techniques, which permit the upstream pressure to be reduced to a point where the mean free path is long compared with the orifice dimensions. The critical experiments were finally performed by M. Knudsen [3]. Recognizing that equations (A.2.2) and (A.2.3) predict an identical dependence of the effusion rate on upstream temperature and pressure, Knudsen made careful microscopic measurements of the area of his orifice, in order to determine from his experiments the factor multi-plying A(T/M) in Che expression for the effusion rate. As the upstream pressure decreased, this was found to converge accurately to the value of  [c.188]

HyperChem automatically calculates a default number of cycles as 15 times the number of atoms. Use the cycle number as a termination condition when mixing optimization algorithms. Suppose you are preparing a protein for a molecular dynamics simulation. The initial structure of the protein comes from X-ray crystallography studies. A molecular mechanics force field or a quantum mechanics method would undoubtedly find some large forces associated with the protein. An efficient minimization scheme would first subject the protein to 500-1000 cycles of steepest descent minimization. Then it would minimize the structure using a conjugate gradien t or Newton -Raph son optim izer, with th e root-mean-square gradient as a termination condition.  [c.61]

Electron Spin Resonance. Electron spin resonance (esr) also known as electron paramagnetic resonance (epr) is a second magnetic resonance technique which finds particular appHcations in the study of free radicals, paramagnetic species, and other molecules containing an unpaired electron. The electron has a spin of 1/2 and, because of its low mass, a gyromagnetic ratio of 1760 rad/ (T-s). Eield strengths required for esr are much lower, typically 0.34 T (3.4 kG) and the frequencies higher (9—35 GHz) than for nmr. Data are usually reported in terms of intensity, signal strength, versus energy where the energy for a transition is usually expressed as  [c.400]

Nylon-4,6 has a high melting temperature (T, = 295° C), high crystallinity, and a much faster crystallization rate, ie, four to eight times faster than that for nylon-6,6. As an unfilled plastic, nylon-4,6 has a high tensile strength, 80 MPa (12,000 psi), compared to 55—65 MPa (8250—9750 psi) for other polyamides when filled with 30% glass, it has a heat deflection temperature of 285°C, vs 190—240°C for most other polyamides (160). Its dielectric properties have been well documented (161). AH these properties make nylon-4,6 a good candidate for high temperature appHcations and end uses that require good resistance to impact and abrasion. Nylon-4,6 has been studied for fiber appHcations (162) and as tire cord it is claimed to be 30% better than nylon-6,6 in flat-spot index measurements, which is even better than polyester in this test (155). Besides its limited stabHity in the melt phase, its other  [c.235]

Eundamental studies of blends of polycarbonate with ABS indicate that the presence of ABS greatly decreases the melt viscosity in the blend, enhancing processibiUty. Even as Htfle as 20% ABS provides a decrease in melt viscosity of a factor of 4—5 (55). A synergistic improvement of the notched impact strength at low temperature is also seen for polycarbonate—ABS blends (Fig. 3). About 35,000 t of these blends are produced annually, and significant growth in the market has been seen, with a yearly growth rate of 12—13%. More than half of the blends produced are used in the automotive market, mostly on instmment panels. The other large use for polycarbonate blends is in office and business machines such as computer housings.  [c.289]

At temperatures between T and T, PPS crystallizes readily. However, because the rate of crystallization is slow, rapid cooling from the melt can result in a molded part that is not fully crystallized. If the cooling is sufficiendy rapid, a nearly amorphous part is obtained. Amorphous PPS crystallizes readily when heated to temperatures above T, as indicated by the exothermic crystallization peak located at approximately 120—130°C (Fig. 5). PPS also crystallizes readily when cooled from the melt. PPS displays a melt crystallization exotherm located between 160 and 250°C, depending on variables such as polymer stmcture (98—100), end-group chemistry (99), level of cure (36,111), molecular weight (103,105), the presence or absence of materials that function as nucleating agents (109), blends with other polymers (104), and plasticizing agents such as sorbed gases (110). The implication of these studies is that processing conditions can determine the level of crystallinity in molded PPS parts. Proper choice of mol ding and/or annealing conditions allows the molder to obtain crystalline parts having both dimensional stability and good mechanical properties.  [c.446]

The glass-transition temperatures, T, of vinylidene chloride copolymers have been studied extensively (70,71). The effect of various comonomers on the glass-transition temperature is shown in Figure 3. In every case, T increases with the comonomer content at low comonomer levels, even in cases where the T of the other homopolymer is lower. The phenomenon has been observed in several other copolymer systems as well (73). In these cases, a maximum T is observed at intermediate compositions. In others, where the T of the other homopolymer is much higher than the T of PVDC, the glass-transition temperatures of the copolymers increase over the entire composition range. The glass-transition temperature increases most rapidly at low acrylonitrile levels but changes the slowest at low vinyl chloride levels. This suggests that polar interactions affect the former, but the increase in T in the VDC—VC copolymers may simply result from loss of chain symmetry. Because of these effects, the temperature range in which copolymers can crystallize is drastically narrowed. Crystallization induction times ate prolonged, and subsequent crystallization takes place at a low rate over a long period of time. Plasticization, which lowers T, decreases crystallization induction times significantly. Copolymers having lower glass-transition temperatures also tend to crystallize mote rapidly (74).  [c.431]

The advantages of the PLS method are many. First of ah, the goal of many studies is to understand the interrelationships between several parts of a large, complex system. Examples that have been studied using PLS include the modeling of a watershed system in which the influence of various sources of water is characterized (37,38) and the way the quaUty of a chemical product is related to physical process conditions such as temperature, pressure, flow rate, stirring rate, and feedstock (39). In such problems, blocks of data are connected together by some predetermined scheme or causal pathway. The PLS method ahows the influence of each block to be evaluated with respect to the path model. Secondly, when the number of variables exceeds the number of samples in a regression problem, stepwise regression can be used, but the variables eliminated may contain useful information, whereas selected variables may have only a spurious correlation. The PLS method allows all of the variables to be retained in the problem by extracting latent variables by an iterative procedure. Latent variables are mutually orthogonal, linear combinations of all the original variables. The power of PLS results from the fact that the latent variables simultaneously describe the maximum predictive variance of a block, and provide maximal fit to the path model. A fundamental assumption made in multiple regression is that the independent variables are truly independent. To the degree that this assumption is invaUd, the resulting model parameters are more affected by noise. Attempts to eliminate this colinearity problem have lead to the development of methods such as principal components regression and ridge regression. PLS regression provides a solution because the latent variables derived from the independent variable block are constrained to be orthogonal. Another advantage of the PLS method is the signal-to-noise enhancement gained by using all the measurements. By using only the significant number of latent variables in the procedure, a noise filtering effect is obtained. The simplest type of apphcation is PLS regression where a relationship is sought between a single response or dependent variable. Latent variables T are extracted both to model X and to correlate with Yin contrast to principal component analysis, where the latent variables, eigenvectors, only model X.  [c.426]

In designing coatings that must withstand large deformations without cracking, such as in container and coil coating apphcations, the T, as deterrnined at a rate of apphcation of stress comparable to that which is experienced in the forming operation, should be lower than the temperature at which forming takes place. If the deformation is large, the cross-link density must be low or the elongation-to-break even above T is too small to withstand the deformation. In general, thin films resist deformation better than thicker films. In apphcations such as can coatings and coil coatings, the film thicknesses apphed are kept to the minimum necessary to achieve the requited protection and hiding. Formabihty is also affected by adhesion. If the adhesion between the substrate and the coating is exceUent, the stresses can be dissipated and failure is less likely. Impact resistance, such as is encountered when gravel hits the coating on a speeding automobile, is related to formabihty of coatings. The rates of apphcation of stresses encountered can vary widely. In coatings, as in plastics, impact resistance is enhanced in coatings that exhibit broad tan delta peaks in comparison with coatings having relatively narrow tan delta peaks (40,131). Complex phenomena are involved in the deformation of multiple coats of paint when stmck by gravel. In addition to impact resistance, effects of fracture mechanical properties are being studied (136).  [c.350]

In the other common paradigm, desorption from a system or a material is studied. At t = 0, the system is loaded with a known concentration or activity of dmg and is immersed in an infinite, weU-stirred receiver solution maintained at concentration C = 0. The amount released per unit area is then measured over time. For a uniform slab of thickness / where the release of dmg is from both sides, the fraction released / Q is linear with the square root of time and is given by  [c.225]

A study of how a sohd dries may be based on the internal mechanism of liquid flow or on the effec t of the external conditions of temperature, humidity, air flow, state of subdivision, etc., on the diying rate of the sohds. The former procedure generally requires a fundamental study of the internal condition. The latter procedure, although less fundamental, is more generally used because the results have greater immediate application in equipment design and evaluation.  [c.1179]

It turns out that in low-viscosity blending the acdual result does depend upon the measuring technique used to measure blend time. Two common techniques, wliich do not exhaust the possibilities in reported studies, are to use an acid-base indicator and inject an acid or base into the system that will result in a color change. One can also put a dye into the tank and measure the time for color to arrive at uniformity. Another system is to put in a conductivity probe and injecl a salt or other electrolyte into the system. With any given impeller type at constant power, the circulation time will increase with the D/T ratio of the impeller. Figure 18-18 shows that both circulation time and blend time decrease as D/T increases. The same is true for impeller speed. As impeller speed is increased with any impeller, blend time and circulation time are decreased (Fig. 18-19).  [c.1632]

Hyland, L., Toma.szek, T, and Meek, T, 1991. Human immunodeficiency viru.s-1 protease 2 Use of pH rate. studies and solvent isotope effects to elucidate details of chemical mechanism. Biochemistry 30 8454-8463.  [c.532]

The expression for N(t, E) in equation (A3.12.67) has been used to study [103.104] how the Porter-Thomas P (Ic) affects the collision-averaged monoenergetic imimolecular rate constant /r(oi, E) [105] and the Lindemaim-Hinshelwood unimolecular rate constant /fu (ra, T) [47]. The Porter-Thomas P(lc) makes /r(oi, E) pressure dependent [103]. It equals m the high-pressure co—>co limit and [(v-2)/v] in the or —> 0 low-pressure limit.  [c.1034]

Absorption spectroscopy is a coimnon and well developed teclmique for studying electronic transitions between the ground state and excited states of atoms or molecules. A beam of light passes tlirough a sample, and the amount of light that is absorbed during the passage is measured as a fiinction of the wavelength or frequency of the light. The absorption is measured by comparing the intensity, /, of light leaving the sample with the intensity, Iq, entering the sample. The transmittance, T, is defined as die ratio  [c.1121]

The equation describes the manner in which the nuclear magnetization, M, at position r and time t processes about the magnetic flux density, B, in which it is found. The constant y is the magnetogyric ratio of the nuclides under study. The precessional frequency, co, is given by the Lannor equation.  [c.1520]

Roth H D, Weng H and Herbertz T 1997 CIDNP study and ab initio calculations of rigid vinylcyclopropane systems evidence for delocalized ring-closed radical cations Tetrahedron 53 10 051-70  [c.1618]

A flow calorimeter developed by Picker suitable for the measurement of heat capacity of a liquid is shown in figure B1.27.8. The metliod measures the difference in heat capacity between the fluid under study and some reference fluid. The apparatus contains two themiistors T and T2 used to measure the temperature change that occurs when the flowing fluid is heated by two identical heaters and Z2. The standard procedure is to flow the reference material from A through both cells. With the same fluid, same power and same flow rate the temperature change AT should be the same. The temperature difference observed on flowing the sample material from B tln-ough cell C while the reference is still flowing tln-ough C2 is a measure of the heat capacity difference between the two liquids. The flow method has been extensively developed for measurement on biological systems and on liquid mixtures at high temperatures and pressures. The apparatus constructed by Christensen and Izatt, shown in figure B 1.27.9 can be used to measure positive and negative enthalpy changes at pressures up to 40.5 MPa and temperatures up to 673 K. Two high pressure pumps were used for the fluid flow. Mixmg occurs in the top half of the isothemial cylinder where the fluid from the two pumps meet. A control heater encircles the cylinder, which is attached by tliree heat-leak rods to a base plate maintained 1 K below the cylinder temperature. A pulsed electrical current is passed tlirough the control heater to maintain the temperature of the cylinder the same as that of the walls of the oven. During mixing the frequency of the pulses are either increased or decreased depending on the size of the enthalpy of mixing. Coimnercial calorimeters are available based on both the Picker and Cln-istensen et al designs.  [c.1914]

In contrast to transient teclmiques, which involve the perturbation of a system and studying its relaxation with time, when the perturbation is sinusoidal, the analysis is perfonued in the frequency domain, which is obtained by applying Laplace transfonus to the time-domain infonuation. Altemating-current impedance teclmiques employ the ratio of an imposed sinusoidal voltage and the resulting sinusoidal current to define the impedance, which is a fiinction of the frequency of the signal. When a steady-state system is perturbed by an applied AC voltage, it relaxes to a new steady state and the time taken for this relaxation is known as t. r = RC, where R is the resistance and C the capacitance of the system. Analysis of this relaxation process provides infonuation about the system. In the frequency domain, fast processes, low x, occur at high frequencies, while slow processes, with high t, occur at low frequencies. Thus, dipolar properties may be stirdied at high frequencies, bulk properties at intenuediate frequencies and surface properties at low frequencies.  [c.1943]

Tyliszczak T, Hitchcock A, Wu S, Chen A, Szymanski G and Lipkowski J 1998 X-ray absorption studies of mixed overlayers formed by copper adatom co-adsorbed with anions at the Au(111) electrode surface Synchrotron Radiat. News 11 31-8  [c.2759]

Nonclassical ions, a term first used by John Roberts (an outstanding Caltech chemist and pioneer in the field), were defined by Paul Bartlett of Harvard as containing too few electrons to allow a pair for each bond i.e., they must contain delocalized (T-electrons. This is where the question stood in the early 1960s. The structure of the intermediate 2-norbornyl ion could only be suggested indirectly from rate (kinetic) data and observation of stereochemistry no direct observation or structural study was possible at the time.  [c.140]

Resistance to Jiirbome Chemical Contamination. Several methods for attenuating a CA resist s sensitivity to the presence of trace volatile bases were described earlier. Resist process stability in the presence of airborne bases also can be improved by consideration of how this stability is influenced by properties of the resist polymer. Using radiotracer methods to tag the basic contaminant, the kinetics and extent of contaminant uptake can be quantified (106). In one study, a wide range of polymer stmctures were cast as thin films on silicon wafers, and then stored in air containing a known, very low concentration of C-labeled NMP (107). The rate of NMP uptake was found to vary by almost a factor of fifty depending on the polymer stmcture. The contaminant uptake of each polymer could be related to its physical properties, specifically its solubility parameter and T. The correlation between NMP uptake and polymer T (Fig. 33) was attributed to a reduction in free volume (a consequence of the nonequilibrium nature of the spin-coating process) due to polymer film annealing during post-apply baking, thereby reducing diffusant mobility.  [c.131]

The good glass formabiHty of Al-based glasses must ultimately be related to the atomic iateractions and the stmcture of the amorphous state. Neutron and x-ray scatteting have been appHed to study the atomic stmcture of amorphous Al2QFe Ce2 (25,26). In these amorphous alloys, the distance of an Fe—Al pair is 0.02 nm shorter than the sum of the atomic radii of Al and Fe atoms. Further stmctural analysis of these data reveals that Fe atoms are surrounded by approximately 10 Al atoms (0.3 nm), and of these, six are ia close contact with Fe. Also, the rare-earth atoms ia Al—Fe—Ce metallic glasses form a dilute dense random packing substmcture, and repel each other, whereas the substmcture of Fe atoms and the surrounding Al atoms are substantially different from the random packiag. The strong Al—Fe iateraction suggested from stmctural studies is consistent with the large negative volume additivity of the Al—Fe alloys ia the Hquid or soHd state (27). Furthermore, an Al melt actually contracts with a small addition of Fe, and more remarkably the shear viscosity of molten Al is sharply iacreased by dissolution of small amounts of Fe (28). Based on these analyses, the unusual glass formabiHty ia Al—TM—RE may be explained by an iacrease ia the shear viscosity of the molten alloy through Al—TM iateractions (29) resulting ia a high resistance to nucleation and crystallization. The amorphous arrangement of Al—TM clusters is further stabilized by the randomly distributed rare-earth atoms. This behavior occurs through the entire supercooling process to temperatures lower than glass temperature T assuting the glass formation.  [c.335]

The auxins include the first natural PGR recognized, indoleacetic acid (lAA). In plants, lAA is the chemical signal responsible for the first identified auxin-response, phototropism (199). Auxin mediation is observed in stem and root elongation, as well as in control of lateral bud development and fmit set. Auxin also stimulates inttaceUular ethylene production. Similar synthetic compounds that induce the physiological responses associated with lAA include naphthalene acetic acid, indolebutyric acid, 2,4-D, 2,4,5-T, and MCPA (see Table 1). The last three compounds belong to the chlorophenoxy acid class of herbicides (2,199). Development of 2,4-D and its phenoxyalkanoic acid analogues occurred during World War II, and use of these herbicides in food production was readily accepted as a consequence of increased labor costs in the industrialized countries after that war (3,199). The stmcture-activity studies of the phenoxyacetic acids were the basis of the initial QSAR papers (5,6). Trace levels of 2,4-D stimulate elongation growth, as does lAA. Higher concentrations ate needed to produce the inhibitory effects associated with these herbicides (72,200).  [c.46]

The ratio k lhas been estimated by measuriag the steady-state ozone concentration, formed by means of electric discharge (20), photochemicaHy (21,22), and low temperature reaction of molecular oxygen and glow-discharge generated oxygen atoms (23). The reaction of ozone with glow discharge-generated oxygen atoms has been studied ia rapid flow systems (24). The preferred temperature-dependent equation for determined by laser photolysis of ozone and monitoring the oxygen atom concentration by time-resolved resonance fluoresence is 4.8 x 10 exp(—2060/T)L/(mol-s) (11). For / 2 (M = O2), the preferred equation is 2.2 X 10 (T/300) L /(moF-s) (11), which is based on the generation of oxygen atoms by flash photolysis and measurement of ozone by uv spectrometry.  [c.491]

Therniomechanical analysis (tma) measures the dimensional changes of a fabricated polymer part at a constant heating rate. First-order (T and second-order (Ip transitions may be measured from graphing length of specimen (J ) versus temperature (T). This technique may also be used to determine the coefficient of linear thermal expansion (CLTE) for a material. Thermomechanical analysis can be more sensitive to small changes ia enthalpy typical of highly crystalline polymers than differential scanning calorimetry (133). This technique has also been used for evaluating dimensional changes of polymers ia fluid environments. Studies have been completed on water—nylon 6 at different temperatures (134), nylon 6 at different levels of water absorption (135), chloroben2ene—polyethylene (136), and elastomers ia various fluids and oils.  [c.151]

The problems of cross-linking reaction rates are not just a question of kinetics of the reaction of pairs of functional groups. Before two functional groups can react, they must be in close proximity. If there is no free volume, the functional groups cannot reach each other to react. If the free volume is sufficiendy large, the functional groups have easy access to each other and the rate of reaction is governed by the kinetic parameters of the reaction. At intermediate levels of free volume, the reaction rate is controlled by the rate of diffusion of the reactants through the reaction matrix and the principal factor controlling availability of free volume is (T — T ). As low molecular-weight resins and cross-linking agents react, T increases and free volume decreases. If the cure temperature is at least somewhat higher than the T of the fully reacted system, the reaction can go to completion at rates governed by kinetic parameters. If, however, the cure temperature is significantly below the T of the fully reacted system, the reaction can go to completion at rates governed by kinetic parameters. If, however, the cure temperature is significant below the T of the fully reacted system, the reaction slows to a rate controlled by diffusion and stops before completion. As the reaction proceeds, T increases and in some cases it has been suggested that reactions stop when T has increased to the reaction temperature (12,13). Other work indicates that when the T equals T, the reaction rate diminishes by two to three orders of magnitude but continues slowly until the T has increased to a temperature 50°C above the reaction temperature (14). Examination of the WLF equation indicates that the universal constant in the denominator is 51.6, indicating that at 51.6°C below T, viscosity becomes infinite, that is, free volume approaches 2ero. Further studies are required, but coatings formulators can make practical use of the principles involved.  [c.335]

Isotope Effects. Any difference in the chemical or physical properties of two substances that differ only in isotopic composition constitutes an isotope effect. Isotope effects are usually largest when the isotope is directly involved in the rate-determining step of a reaction. The greater the mass of an atom, the lower its 2ero-point bond energy, and the greater the activation energy required to cleave a chemical bond. In general, therefore, reactions involving mpture of a —C—T bond may proceed at a markedly slower rate than those involving cleavage of a corresponding —C—H bond. Kinetic isotope effects arising from bond cleavage are termed primary isotope effects. Secondary isotope effects occur as a result of the presence of the isotope in nearby molecular sites. Bonds involving the isotope are neither broken nor formed in the reaction. Secondary isotope effects are generally smaller than primary effects. The latter may easily be 10 to 100 times greater. Solvent isotope effects include many important primary effects, eg, solvolyses and acid-base reactions, as well as secondary effects such as solvation. Although primary and secondary kinetic isotope effects are the most extensively studied, numerous other isotope effects have been observed with tritium. Thus, an H/T separation factor of about 14 occurs in the electrolysis of HOT (25,26).  [c.13]

Wf is usually not known for continuous mills, but it can be determined from Wf = t Q, where L is determined by a tracer measurement. Eq. (20-37) will be vahd if the holdup Wf is geometrically similar in the two mills or if operating conditions are in the range in which total production is independent of holdup. From studies of the kinetics of milling [Patat and Mempel, Chem. Ina. Tech., 37(9), 933 (11), 1146 (12), 1259 (1965)] there is a range oT holdup in which this is true. More generally, Ausrin, Luclde, and Klimpel (loc. cit.) developed empirical relations to predict S as holdup varies. In particular, they observe a slowing of grinding rate when mill filhng exceeds ball void volume due to cushioning.  [c.1839]

See pages that mention the term T rade studies : [c.339]    [c.1605]    [c.2114]    [c.61]    [c.424]    [c.607]    [c.164]    [c.27]    [c.104]    [c.489]    [c.34]    [c.123]    [c.144]    [c.669]   
Machanics of composite materials (1998) -- [ c.388 ]