Dependence on the Molecular Weight

In polymer solutions and blends, it becomes of interest to understand how the surface tension depends on the molecular weight (or number of repeat units, IV) of the macromolecule and on the polymer-solvent interactions through the interaction parameter, x- In terms of a Hory lattice model, x is given by the polymer and solvent interactions through... 

L exposure would produce 1 ML of adsorbates if the sticking coefficient were unity. Note that a quantitative calculation of the exposure per surface atom depends on the molecular weight of the gas molecules and on the actual density of surface atoms, but the approximations inlierent in the definition of tire Langmuir are often inconsequential. 

Above Tjj, the material is liquid and its viscosity depends on the molecular weight of the polymer and the time scale of the observation, but it would be considered high by all standards. 

We shall discuss three types of phenomena for polymer solutions thermodynamic properties in Chap. 8, frictional properties in Chap. 9, and lightscattering properties in Chap. 10. A common feature of virtually all phenomena in these areas is that they all depend on the molecular weight of the solute. Thus observations of these properties can be interpreted to yield values for M we shall use this capability as a unifying theme throughout these chapters. 

Structure. The physical properties of LDPE depend on the molecular weight, the molecular weight distribution, as well as the frequency and distribution of long- and short-chain branching (2). 

In plasma chromatography, molecular ions of the heavy organic material to be analy2ed are produced in an ionizer and pass by means of a shutter electrode into a drift region. The velocity of drift through an inert gas at approximately 101 kPa (1 atm) under the influence of an appHed electric field depends on the molecular weight of the sample. The various sonic species are separated and collected every few milliseconds on an electrode. The technique has been employed for studying upper atmosphere ion molecule reactions and for chemical analysis (100). 

Using both condensation-cured and addition-cured model systems, it has been shown that the modulus depends on the molecular weight of the polymer and that the modulus at mpture increases with increased junction functionahty (259). However, if a bimodal distribution of chain lengths is employed, an anomalously high modulus at high extensions is observed. Finite extensibihty of the short chains has been proposed as the origin of this upturn in the stress—strain curve. 

Vatty Acids andFattyAcidLsters. Sulfolane exhibits selective solvency for fatty acids and fatty acid esters which depends on the molecular weight and degree of fatty acid unsaturation (40—42). AppHcations for this process are enriching the unsaturation level in animal and vegetable fatty oHs to provide products with better properties for use in paint, synthetic resins, food products, plastics, and soaps. 

For permeation of flavor, aroma, and solvent molecules another metric combination of units is more useful, namely, (kg-m)/(m -sPa). In this unit the permeant quantity has mass units. This is consistent with the common practice of describing these materials. Permeabihty values in these units often carry a cumbersome exponent hence, a modified unit, an MZU (10 ° kgm)/(m -s-Pa), is used herein. The conversion from this permeabihty unit to the preferred unit for small molecules depends on the molecular weight of the permeant. Equation 4 expresses the relationship where MW is the molecular weight of the permeant in daltons (g/mol). 

The properties of PVC may also he expected to depend on the molecular weight distribu n. Most commercial polymers, however, appear to have similar values for MJM and in any case there is little published information on effects of altering the parameter. It is perhaps rather surprising that there appears to be little work reported on the effect of blends of polymers of differing molecular weight on mechanical and rheological properties. 

Optical properties of the blends are somewhat dependent on the molecular weight of the polystyrene, presence of additives such as lubricant in the polystyrene, ratio of polystyrene to SBS, processing conditions and mixing effectiveness of the extruder. It is stated that the optical properties of the sheets are similar whether linear or radial type stereoblock polymers are used. 

Resin viscosity is an important property to consider in handling the resins. It depends on the molecular weight, molecular weight distribution, chemical constitution of the resin and presence of any modifiers or diluents. Since even the diglycidyl ethers are highly viscous materials with viscosities of about 40-100 poise at room temperature it will be appreciated that the handling of such viscous resins can present serious problems. 

The properties of the solvent-bome CR adhesives depend on the molecular weight, degree of branching and rate of crystallization of the polymer. The ability of polychloroprene adhesives to crystallize is unique as compared to other elastomers. The higher the crystallization rate, the faster the adhesive strength development. 

The primary air flow rate per jet necessary for smokeless combustion depends on the molecular weight and degree of unsaturation of the flare gas. Experience indicates that it varies linearly with percent unsaturates, from a minimum of 20 % excess air for a flare gas containing 0 % unsaturates to 35 % excess air for a gas containing 67 mol % unsaturates. Based on this relationship and a gas flow rate of 72.2 mVh per jet, the required primary air flow rate can be computed directly from the gas composition, or approximated conservatively from the following equation ... 

Concentration The amount of a substance present in a given volume of a gas or liquid, in parts per million (ppm) or jLg m . In the case of gases, the ppm is proportional to the molecular concentration, hence the relationship between ppm and pg m " depends on the molecular weight of the gas concerned. 

FIGURE 6.8 Guidelines for Shodex column selection depending on the molecular weight of polymer. Column Shodex GPC KF-800 series, 8 mm i.d. x 300 mm. Eluent THE. Flow rate 1.0 mUmin. Detector Shodex Rl. Column temp. 40°C. Sample EPIKOTE 828... 

Traditionally, column efficiency or plate counts in column chromatography were used to quantify how well a column was performing. This does not tell the entire story for GPC, however, because the ability of a column set to separate peaks is dependent on the molecular weight of the molecules one is trying to separate. We, therefore, chose both column efficiency and a parameter that we simply refer to as D a, where Di is the slope of the relationship between the log of the molecular weight of the narrow molecular weight polystyrene standards and the elution volume, and tris simply the band-broadening parameter (4), i.e., the square root of the peak variance. 

The shape of the pore size distribution curve strongly depends on the molecular weight distribution of the linear polymer. The narrowest pore size distributions were obtained with the linear polymers having the lowest polydisper-sity indices. 

In general, physico-mechanical properties of polymers depend on the molecular weight. However, the physico-mechanical properties of PSs decreased in the presence of cationic catalysis, but increased in the case of the binding of functional groups to the aromatic ring in spite of the destruction of PS. Therefore, new properties such as adhesion and photosensitive capability increase... 

Kaneko et al. [80, 81] prepared copolymers of AA (93.9-95.9 mol%) and vinylbipyridine (1.6-3.7 mol%) with pendant Ru(bpy)2+ (2.4-2.5 mol%) (25). The quenching of the excited state of the pendant Ru(II) complex by MV2+ was accelerated in alkaline aqueous solution owing to the electrostatic attraction of the cationic quencher. Interestingly, the quenching efficiency was dependent on the molecular weight of 25. The quenching of the polymer with MW 2100 occurred... 

The relative importance of these mechanisms, and the value of the overall kt, depends on the molecular weight and dispersity of the propagating species, the medium and the degree of conversion. The value of k, is not a constant ... 

The reactivity of macromonomers in copolymerizalion is strongly dependent on the particular comonomer-macromonomer pair. Solvent effects and the viscosity of the polymerization medium can also be important. Propagation may become diffusion controlled such that the propagation rate constant and reactivity ratios depend on the molecular weight of the macromonomer and the viscosity or, more accurately, the free volume of the medium. 

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

K.—Ordinarily the intrinsic viscosity should depend on the molecular weight not only owing to the factor occurring in Eq. (26), but also as a result of the dependence of the factor on M. The influence of this expansion resulting from intramolecular interactions may be eliminated by suitable choice of the solvent and temperature. Specifically, in an ideal solvent, or -solvent, a = l and Eq. (26) reduces to... 

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