Homogeneous initiator

The method has severe limitations for systems where gradients on near-atomic scale are important (as in the protein folding process or in bilayer membranes that contain only two molecules in a separated phase), but is extremely powerful for (co)polymer mixtures and solutions [147, 148, 149]. As an example Fig. 6 gives a snapshot in the process of self-organisation of a polypropylene oxide-ethylene oxide copolymer PL64 in aqueous solution on its way from a completely homogeneous initial distribution to a hexagonal structure. 

If dye molecules are embedded into an amorphous matrix, preferably transparent polymers, greatly and inbornogenously broadened spectral lines are observed. This broadening is caused by the energetic interaction of the dye molecules with the locally different environment in the polymer matrix. The ratio of the homogenous initial line width of the dye molecule T to the inhomogenous line width of the dye in the polymer T ranges from 1 10 to 1 10 . ... 

Let us now calculate some solutions for short values of the time. For a sphere with homogeneous initial concentration and zero surface concentration, we replace On/a2 by z. From equation (8.6.11), the fraction Fsph left at z is... 

For a slab with homogeneous initial concentration and zero surface concentration, the dimensionless variable t/X2 is replaced by t. The fraction left at t, given by equation (8.5.16), is transformed as in the case of the sphere., 92 now appears in place of and is replaced by 94 through the first of the equations (8B.2). 

The brash layer thickness (dry collapsed state) obtained after seven days of polymerization time and successive soxhlet extraction was found to be approx. 10 nm and very uniform ( 0.3 nm). The uniform thickness values are provided by the homogeneous initiation, polymerization and termination reaction. Meanwhile poly(2-oxazoline) homopolymers brushes with layer thicknesses of 20 to 30 nm can be obtained [275]. 

Some chiral initiators have structures such that alternate monomer placements occur with opposite faces of the monomer to yield the syndiotactic polymer. This is syndioselective polymerization proceeding with catalyst site control and is usually observed only with some homogeneous initiators, both traditional Ziegler-Natta and metallocene. 

The classical paper on the homogeneous initiation of LE is that of Campbell et al (Ref 1 la). Their views have since received considerable international support (Refs 17,... 

Some semi-quantitative confirmation of these A factors comes from the consideration that the pyrolysis of C2H8 at 900°K. is a chain reaction in which the data on maximal inhibition indicate a chain length X of the order of 10. Since the only likely homogeneous, initiation process is the fission of C2H8 into 2CH3, the hypothetical first-order rate constant for the pyrolysis can be set equal to this initiation rate constant multiplied by X ... 

If prior information is not available, solvent selection should be based on some small-scale trials. A few millimetres of suspension or solution to be extracted are placed in a small test tube and shaken with an equal volume of diethyl ether, when dissolution of suspended material clearly indicates that the solvent would be satisfactory. If the solution to be extracted is homogeneous initially, then the ether solution is removed with a dropper pipette on to a watch glass, and the ether is allowed to evaporate to determine whether material has been extracted. A little experience soon enables the student to differentiate between organic liquids so extracted and traces of water simultaneously removed during the extraction process. If extraction with diethyl ether proves unsatisfactory the experiment is repeated with a fresh sample of reaction mixture... 

Here I = denotes the identity matrix. The interface potential (( -potential) ( may by assumed to be constant. We consider a more general case where ( = ((x,T(e 1x)u>). Since we are interested in the macroscopic equations, we do not consider boundary conditions on dQe(uj). For the sake of simplicity we assume homogeneous initial conditions for ue, ve, (I> and r/ ) . 

We have presented here a non-trivial case study of a chemical reactor where fluid mechanics, diffusion, and chemical reaction are treated at the same level of complexity. The results indicate that conversions and product distributions can be significantly modified by mixing effects, for operating conditions of interest considerable error can be introduced by assuming homogeneous initial conditions. 

Overberger and Schiller (52) attempted polymerization of methyl vinyl sulfone with alkali metals. Using a homogeneous initiator, potassium dissolved in diglyme (dimethyl ether of diethylene glycol) at — 78°, no polymer was obtained. However, a high yield of the dimer... 

The deviations from Eq. (5.46) probably result from the delayed process of liquid outflow from either films to borders or upper to lower layers. This applies to foams with higher expansion ratio and homogenous initial liquid distribution along the foam column. 

Coordination heterogeneous initiating system. h Coordination homogeneous initiating system. 

Trie classical paper on trie homogeneous initiation of LE is that of Campbell et al... 

We saw in the previous section that Model I is insensitive to initiation. In particular, we reviewed results showing that, when the detonation is caused by flyer plate impact, the plate velocity required for initiation decreases to a limiting value of about 3.9 km/s as the mass of the flyer plate is increased. This behavior is consistent with the known insensitivity of crystalline explosives to high velocity impacts. In this section the initiation characteristics of Model I are examined more closely in the vicinity of the threshold for initiation. We find that the detonation begins behind a compaction front that is subsequently overrun by the detonation front. ° Hence the behavior of the model is qualitatively similar to that observed in experimental studies of homogeneous initiation and delayed detonation associated with low velocity impacts. 

Number of Monomer Droplets, Free Emulsifier Concentrations, and Probabilities for Droplet and Homogeneous Initiation ... 

Shock-tube experiments will yield the rate of the homogeneous initiation reactions because nuclei do not form in time to influence the rate appreciably the activation energy of 103 kcal.mole obtained from the shock-tube experiments is consistent with this suggestion. The carbon-deposition measurements of Palmer and Hirt will also yield the initiation rate since the principal fate of CH3 in ordinary vessels is to produce carbon at the wall the activation energy given by these experiments was, in fact, consistent with those of the later shock-tube work. Studies in flow systems, however, are complicated by subsequent reactions, a fact that may explain the somewhat different results obtained. 

Although activation energies and pre-exponential factors can be deduced for a homogeneous initiation, the intervention of surface activity makes the interpretation of the chain initiation rates and even the mechanism of... 

Figure 2. Hyper-surface of the thermodynamic potential difference between the heterogeneous state consisting of a cluster in the otherwise homogeneous ambient phase and the homogeneous initial state (here demonstrated for the case of a binary system). The curve via the saddle corresponds to the generalized Gibbs approach while the classical Gibbs method corresponds to ridge crossing, nj and n2 are here the number of particles in the cluster.

As in the previous transient problems that we have discussed, this problem for the difference between the actual velocity and its large-time form, uzXj, is reduced to a homogeneous initial-value problem that can be solved by standard methods such as separation of variables. Our interest, in the present problem, is primarily with the large-time behavior of the solution. Hence the details of solving (3 372) and (3-273) are left as an exercise (nontrivial) for the reader, and we concentrate our attention in the remainder of this section on the solution of (3-269) and (3-270). 

Slurry Homogeneous Initiator Phosphine Low Reaction Rate Low Bulk Density Low Maximum Slurry Concentration... 

A similar problem for an annular channel with a homogeneous initial velocity field was solved in [296], For t > 0 and b < U < a, we consider the equation of motion in cylindrical coordinates... 

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