Polymer chains relaxation rate

Relaxation of dilute spedes (star or linear) in monodisperse matrices (star or linear) can also be worked out with Eq. 98, using F(t) appropriate to the dilute spedes and R(t) for the matrix. Preluninary results indicate that long-arm molecule relaxations can be controUed over wide ranges by the choice of chain length for a linear polymer matrix. On the other hand, relaxations of linear chains in a star matrix should be less affected by matrix chain structure. Their behavior should move from the homologous linear melt behavior when in the matrix is of the order of ra for the linear chains to behavior as unattached linear chains in a network when r , > ra. The latter prediction seems inconsistent with recent experimental lesults where linear chain relaxation rates were found to be the same in the homologous melt and in a star matrix with > Ta. This may indicate some fundamental problem with the equation suggeted to estimate (Eq. 85). 

Above the the rate of polymer chain relaxation is faster than the diffusion of CO2, and hence Fickian diffusion is to be expected. The diffusion of CO2 is believed to occur within the amorphous domains of the polymer matrix, and for this reason the diffusion in semi-crystalline polymers may be more complex than it in the case for glassy polymers. In the case of semi-crystalline polymers, CO2 is not soluble in the crystalline domains, and therefore the degree of crys-taUinity and hence the amorphous fraction available for CO2 molecules may influence the diffusion characteristics. Furthermore, C02-induced crystallization is likely to lead to an increase in the tortuosity factor, and thus the diffusion path length may increase as a function of time. Syndiotactic polystyrene and poly(4-methyl-l-pentene) [45] are semi-crystalline polymers which have crystalline phases (helical in the case of sPS) with lower densities than that of the amorphous phase and are exceptions, as CO2 access is not restricted to the amorphous domains, in fact CO2 diffuses faster in the helical sPS than in the amorphous polymer [46]. 

SW6lling Kinetics. A first-order relaxation process in which the polymer chains relax and diffuse into the aqueous solution controls the swelling rate, which is given by equation 3 ... 

Viscoelastic properties of covalent polymers can be understood with a model that supposes snakelike reptation of polymer chains through a tube formed by entanglements with other polymer chains. Relaxation of stress imposed on a sample is represented by reptation of a polymer chain out of its tube to a stress-free environment. In this model, the rate of stress relaxation is determined by... 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

When a penetrant diffuses into a polymer, the perturbation will cause the polymer molecules to rearrange to a new conformational state. The rate at which this conformational adaptation occurs depends on the mobility of the polymer chains. At temperatures well above the glass transition, this occurs quite rapidly and the diffusive process resembles that in the liquid state. At temperatures near or below the glass transition, the conformational change does not take place instantaneously. Instead, there is a finite rate of polymer relaxation induced by the... 

Although many different processes can control the observed swelling kinetics, in most cases the rate at which the network expands in response to the penetration of the solvent is rate-controlling. This response can be dominated by either diffu-sional or relaxational processes. The random Brownian motion of solvent molecules and polymer chains down their chemical potential gradients causes diffusion of the solvent into the polymer and simultaneous migration of the polymer chains into the solvent. This is a mutual diffusion process, involving motion of both the polymer chains and solvent. Thus the observed mutual diffusion coefficient for this process is a property of both the polymer and the solvent. The relaxational processes are related to the response of the polymer to the stresses imposed upon it by the invading solvent molecules. This relaxation rate can be related to the viscoelastic properties of the dry polymer and the plasticization efficiency of the solvent [128,129],... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

Star-shaped polymer molecules with long branches not only increase the viscosity in the molten state and the steady-state compliance, but the star polymers also decrease the rate of stress relaxation (and creep) compared to a linear polymer (169). The decrease in creep and relaxation rate of star-shaped molecules can be due to extra entanglements because of the many long branches, or the effect can be due to the suppression of reptation of the branches. Linear polymers can reptate, but the bulky center of the star and the different directions of the branch chains from the center make reptation difficult. 

An increase in the amount of hydrophobic modification restricts segmental mobility by an increase of viscosity within the monolayer for the same molecular weight (300,000) and hydrophobe chain length (C g), the polymer monolayer with the higher amount of hydrophobe has a smaller relaxation rate constant (Experiments Numbers 3 and 7). 

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