Polymer number

Therefore by combining equations (9) and (10) and assuming some appropriate value for e, the number average number of LCB points per molecule can be calculated as a function of elution volume. The corresponding whole polymer number average number of LCB points per molecule is given by... 

In order to determine the branching structure factor e, Foster ( ) studied a large qroup of high pressure low density polyethylene resins (HP-LDPE). Using the MWBD method, he calculated the whole polymer number average number of branch points per JOOO carbon atoms from SEC data as a function of e. Then the Xfj values were compared with those obtained by nMR. 

The IR-spectrum of the polymer was measured with a Nippon Bunko Model DS-403G infrared spectrometer. The concentration of the unsaturated groups in the polymer (number of unsaturated group per 1000 carbons) was determined from the absorbances at 966 cm l (trans-vinylene), 910 (vinyl) and 890 (vinylidene) in the IR-spectrum by the method reported by Cernia et al. (7). 

Rate Constants and Polymer Number Concentration Depertdence for Dilution-, Cold-, and Calcium Ion-Induced Microtubule Disassembfy ... 

Other experiments such as treadmilling measurements (see Section VII) is not feasible because the polymer number concentration is far less than that required in radiometric measurements. 

ELONGATION (With No Change in Polymer Number Concentration)... 

Although the self-assembly of polymeric structures can involve nucleation and elongation steps (See Actin Assembly Kinetics Microtubule Assembly Kinetics), one can simplify the assembly process through what is known as seeded assembly. At an initial monomer concentration [M], seeded assembly is induced by the addition of pre-assembled polymeric structures consequently the polymer number concentration must remain constant. The rate of monomer incorporation into indefinite length polymers can be written as follows ... 

Consider the case where the protein consists of o /3 dimers exclusively at the very beginning of an assembly experiment. Suppose further that spontaneous nucleation is sufficiently infrequent as the polymerization reaction reaches 5-10% of its maximal amplitude achieved over the remaining course of elongation. In this case, a reduction of the protomer concentration from about 20 to 18 JU.M would reduce the apparent extent of nucleation by a factor of about 10-20, such that the polymer number concentration remains fixed throughout the ensuing elongation phase. If nucleation were viewed as a one-step cooperative event, then the rate of nucleation would be proportional to the ith power of the protomer concentration if /protomers cooperatively form the polymerization nucleus ... 

While there are several statistically described averages, we will concentrate on the two that are most germane to polymers—number average and weight average. These are averages based on statistical approaches that can be described mathematically and that correspond to measurements of specific values. 

Polymer Number of Weight fraction Tm(°C) Water absorption... 

Type of Polymer Number of Samples Styrene monomer level (mg/kg) range and average Potential off-flavor substance frequency measured, range and levels in material (mg/kg)... 

Fig. 3. Typical TLC chromatograms of cellulose triacetate (CTA) fractions and whole polymer (Ac w = 61.0wt%) having various Mw 12) solid lines fractions broken line whole polymer numbers on curves represent 10 4 Mw. (Rf = rate of flow.)...

On the other hand the kinetic methods suffer from experimental error connected with the evaluation of the polymer number average molecular weight. Moreover, if the kinetics are not steady from the initial moments of polymerization, the latter... 

Polymer Number Molar ratio average of residues molecular weight Solvent [ 1d I Id, oorreoted ... 

The most outstanding feature of this work is that it describes the synthesis of MIPs which possess not only the attributes of typical imprinted polymers (number and strength of binding sites, pore size distribution) but that they are also transparent It is rather surprising that this has not been further exploited. Such MIPs could conceivably be used for the determination of any analyte possessing a suitable chromophore. Alternatively, they could be used, in conjunction with a chromogenic reporter, in competitive assays. 

Modifled from Oahima (25) activity values are moles/day per milligram polymer. Numbers refer to the proportions by weight of aspartic acid, glutamic acid, equimolar mixture of 16 neutral amino acids, and (where present) histidine - HCl present in the reactants. 

In this conversion we made use of the fact that p = pc = 1 /(/ 1) near the gel point, so (1 -p) was replaced with (/-2)/(/- 1). The polymer number density near the gel point on the Bethe lattice decays as a power of the number of monomers in a polymer ... 

Polymer Number-Average Molecular Weight, M (x KF3) Styrene-to-Rubber Ratio (wt/wt) Yield Stress, Vy (MPa) Engineering Fracture Stress, Vf,e,mrg (MPa) Fracture Stress, (Tf(MPa) Fracture Strain, f(%)... 

Low Acid Number Polyester Glycol Effects Figure 3 shows the polymerization viscosity-time-temperature relations for two additional (2.0) ratio polymers, Numbers 4 and 5. Both were made from reactant lots III, IV and X... 

One final area for discussion is the use of NMR for the determination of polymer number average molecular weights. End group resonances were clearly visible in the 13c NMR spectrum of the ethylene-l-hexene copolymer in Figure 3. An opportunity to determine polymer degrees of polymerization or number average molecular weights should not be overlooked. 

The growth of microtubules, like that of other self-assembling biopolymers, is traditionally described by the endwise addition of subunits to the polymer at a roughly constant polymer number concentration [12,13]. Thus, the elongation can be described by the reaction MTn + S <. .. > MTn + 1. This scheme predicts an exponential approach to a steady state where microtubules are in equilibrium with a critical concentration of free subunits. In standard assembly conditions this is indeed observed (see Figs. 3,4). However, microtubules are capable of more complex reaction mechanisms that are not compatible with the above scheme. 

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