Chain lifetime

For example, at 60°C, = 2300 and = 2.9 x 10. An estimate of kinetic chain lifetime, ie, the time from initiation to termination by reaction with... 

Chain lifetimes are small and the concentration of free radicals is low. To a reasonable approximation, the system consists of unreacted monomer, unreacted initiator, and dead polymer. The quasi-steady hypothesis gives... 

Molecular Weight Distributions. The CSTRs produce the narrowest possible molecular weight distributions for fast chain growth, short chain lifetime... 

This reaction has been shown to be very rapid77. Sulphuric and acetic acids sup press the polymerisation. Evidently their anions are ineffective as initiators, and the enhanced proton concentration provided by them must reduce the chain lifetime. The slight retarding effect of oxygen could be due to electron scavenging. However, the authors suggest that there may be a small free radical component of the chain reaction, which is inhibited in the presence of oxygen. 

Abstract Since the uncertainty of each link in the traceability chain (measuring analytical instrument, reference material or other measurement standard) changes over the course of time, the chain lifetime is limited. The lifetime in chemical analysis is dependent on the calibration intervals of the measuring equipment and the shelf-life of the certified reference materials (CRMs) used for the calibration of the equipment. It is shown that the ordinary least squares technique, used for treatment of the calibration data, is correct only when uncertainties in the certified values of the measurement standards or CRMs are negligible. If these uncertainties increase (for example, close to the end of the calibration interval or shelf-life), they are able to influence significant-... 

An analysis of the traceability chain lifetime in the field of chemical measurement is discussed in the present paper. 

For example, at 60°C, kp = 2300 and kt = 2.9 x 107. An estimate of kinetic chain lifetime, ie, the time from initiation to termination by reaction with another radical, is 1—2 s at 50°C and 4% per hour rate of polymerization. If there are five chain-transfer steps in the course of the kinetic chain, then a PVAc molecule forms in 0.2—0.4 s. Faster rates of conversion give shorter kinetic chain lifetimes in inverse proportion, but an increased percentage of conversion leads to longer chain lifetimes. At 75% conversion and at 60°C, the radical lifetime is ca 10 s. 

Elastomeric polypropylenes with thermoplastic behavior can be prepared from conformationally dynamic metallocenes such as bis(2-arylindenyl)zirconium dichlorides. These can exist in two conformations in the course of the chain lifetime a chiral rac isomer which is stereodirecting and an achiral meso isomer which is aspeciflc. The resulting polymer consists of blocks of isotactic polypropylene alternating with runs of atactic material (equation 12). 

The only way to control the polymer structure properly during its synthesis is by a living process. In conventional FRP, in fact, bimolecular combination limits the chain lifetime to a small fraction of the entire process time and, therefore, changes in the operating conditions (monomer concentration and... 

Therefore, one is dealing with a heterophasic reaction which could be controlled by typical kinetic factors such as a) formation and decay of active centers with time, b) presence of a multiplicity of active centers energetically, structurally and chemically different form one another and therefore having different kinetic constants. Moreover a role could also be played by true physical phenomena such as a) variety of growing chain lifetime depending on the different degree of active centers encapsulation in the polymeric matrix, and b) limitations to heat transfer and, above all, to mass transfer from the gas phase to the liquid phase, from liquid to polymer surface and from the polymer to the surface or to the interior of the catalyst. 

The precise experimental conditions for the measurements of chain lifetimes of polyethylene with the TiCl4/Al(i-Bu2 )H catalyst are not explicitly stated, but there is clear evidence for a steady increase in lifetime with polymerization time. For an average lifetime of 4 min after 40 min polymerization time, the instantaneous values were 4 min after 18 min polymerization and 10 min after 40 min polymerization. As the concentration of active centres remains almost steady after a sharp initial fall, the increase cannot be accounted for wholly by changes in the monomer/active sites ratio. The explanation may lie in a reduced rate of chain transfer with increase in conversion, as has been found for propene with a-TiClj/AlEt2 Cl [121]. In accord with this view average chain lifetimes of polypropene have been calculated to increase with conversion [123]. 

Similarly, a variety of two, three, and multiblock olefin polymers [(P-E)jj, P-EP-P, P-E-P, E-EP] have been reported. However, in most cases the nature of Ziegler-Natta catalysis (low chain lifetimes, chain transfer from Ti to A1 or Zn, thermal dieout, different reactive sites, etc.) is such that the polymer produced is often a mixture of homopolymer, unattached copolymers, and two or three segment block polymers. It is clear that the larger the number of blocks desired, the more difficult it is to obtain a... 

CSTRs produce the narrowest possible MWDs for fast-chain-growth, short-chain lifetime polymerizations like free-radical and coordination metal catalysis. The mean residence time in the CSTR will be minutes to hours, and the chain lifetimes are fractions of a second. Any chain that initiates in the CSTR will finish its growth there. All the polymer molecules are under identical, well-mixed conditions and will have as narrow an MWD (typically PD 2) as is possible for the given kinetic scheme. 

Author Monomer Catalyst system Temp. (°C) Mean chain lifetime Refer- ences... 

This heterogeneity may, however, also be expressed in terms of polymer lifetimes instead of propagation rates. By assuming a Gaussian distribution of chain lifetimes Mussa (35) has been able to derive molecular weight distributions of the type observed experimentally. This treatment appears to imply a chain termination which has the form of an error function round a mean value. On the whole it seems that a variable propagation rate is the more likely. 

One challenge in producing these materials has been the production of true block copolymers, rather than a mixture of two homopolymers. " Therefore, living polymerization systems are more attractive for the synthesis of well-defined block copolymers because the long chain lifetimes allow the sequential addition of monomers. Block length can be controlled by the reaction time or monomer concentration. General depictions of the synthesis of sPP-EPR and iPP-EPR block copolymers with living catalysts are shown in Scheme 22.6. 

The fluxional catalyst, a phenyl-substituted unbridged bis-Cp structme, periodically changes its conformation from one that makes iPP to one that produces aPP. The conformation cycle is short with respect to chain lifetimes. Thus true stereoblock copolymers are possible. A new generation of flexible propylene polymers is expected to result from applications of this catalyst. 

Because chain lifetimes are much shorter than chain residence times, the instantaneous MWD w(r) of group I polymerization is determined only by the birth condition but not influenced by the residence time. In a steady-state homogeneous CSTR, there is only one single condition for chains to be generated, that is, imder constant r and fi. The MWD of the total polymer WeA(r) represents a single instantaneous distribution and is therefore narrower than those of batch reactor and PFTR, which are cumulative of many instantaneous distributions at various r and p values. 

The lifetime of free-radical chains is, in fact, so short that changes in concentrations are entirely negligible during a chain lifetime. Hence, it is perfectly proper to characterize chains formed at any instant when [M], [/], T, and [R H] have a particular set of values. All the quantities defined to this point (x , x , q) and, therefore, the distributions are just such instantaneous quantities. For this reason, it was necessary to specify conditions at the start of the reaction in earlier examples to permit their calculations. 

Calculate and compare the average chain lifetime at the start of the reaction with the monomer half-life for the system in Example 9.10. Is the concept of an instantaneous quantity valid for this system kf = 14.5 — lO L/mol/s. 

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