Friction, molecular

In Chap. 9 we shall discuss in considerable detail a parameter called the molecular friction factor f. For velocities that are not too great, the friction factor expresses the proportionality between the frictional force a particle experiences and its velocity ... 

MolekuLar-grSsse,/. molecular magnitude mo> lecular weight, -kraft, /. molecular force, -reibung, /, molecular friction, -stoning, /. molecular disturbance, -strahl, m. moleculat ray. -verbindung, /, molecular compoimd. -warme, /, molecular heat, -wirkung, /. molecular action (or effect), -zustand, m. molecular state or condition, molecularity. 

Of major importance is the fact that the specific character of polymer chains of a given type enters the relationship (17) only through the effective size of one of its beads as indicated by the ratio f/970. Even the effect of this factor vanishes when the total internal resistance to flow is sufficiently large. Hence, in this limit, which will include nearly all actual cases of interest (see Sec. 4), the molecular frictional coefficient should depend only on the size /s and not otherwise on the nature of the polymer. Accordingly, we choose to let... 

The photoisomerization reaction gives a valuable tool to investigate the molecular friction at the interface. Depending on the exact location of the reaction path, whether predominantly in one or the other phase, the time scale of the rate of the reaction is severely modified. The photoisomerization reaction of the dyes malachite green and 3,3 -dieth-yloxadicarbocyanine iodide (DODCI) has been reported at several interfaces, the air-... 

Diffusion coefficient, cm /sec Molecular frictional factor Molar frictional factor... 

The Rouse-Bueche model (97,98) replaces the real molecule of n main chain atoms by a mechanical chain of N +1 beads joined in sequence by N linear springs. The frictional interactions with the medium, which are distributed uniformly along the length of the real molecule to give a molecular frictional coefficient n(0, ate concentrated at regular intervals in the beads. The frictional... 

The number of beads in the model macromolecule is n, and is the Stokes law friction coefficient of each bead. The are to be evaluated for each macromolecule in its own internal coordinate system, with origin at the molecular center of gravity and axes (k = 1,2,3) lying along the principal axes of the macromolecule. The coordinates of the ith bead in this frame of reference are (x ]),-, (x2)i, and (x3)f. The averaging indicated by < > is performed over all macromolecules in the system. Thus, < i + 2 + 3) is simply S2 for the macromolecules. The viscosity is therefore identical, for all free-draining models with the same molecular frictional coefficient n and the same radius of gyration, to the expression from the Rouse theory ... 

It should be pointed out that this agreement cannot be used to support the Rouse model per se, since any model with the same total molecular friction and value of S2 would... 

The combination of enhancement terms for the molecular friction coefficient from Eqs.(6.22) and (6.26) with the Rouse equation for viscosity yields... 

Further examination of the Williams approach seems called for, both to improve the method for estimating parameters such as the relaxation time, and to clarify the relationship between the intramolecular potential form and non-thermodynamic frictional forces. The method might provide a fairly unified description of non-linear flow porperties if a suitable potential function for large scale molecular friction were found. Aside from the Williams work, there have been no theoretical studies dealing with t] vs. y at low to moderate concentrations. The systematic changes in the master curve /(/ ) with coil overlap c[ij] are thus without explanation at the present time. 

Eq. (2.14) is identical in form to that derived by Debye (21) in his "pearl-necklace in shear model, where a Stokes law molecular friction factor was also assumed. 

As the temperature of water increases, its internal molecular friction (viscosity) decreases and both chemical and physical reactions, such as the formation of chemical inhibitor films, flocculation, and degassing, occur more rapidly. 

Molecules subjected to microwave radiation may undergo excitation by specific frequencies of that radiation. Such dielectric coupling causes reorientation of molecules, molecular frictions, changes in hydration, and so on. All of these factors lead to absorption of microwave energy, which is transformed into heat. The dielectric constant and moisture content of the sample are important factors for targeted heating by microwaves. 

In practice, dielectric heating is a technique in which, when placed in a high-frequency or RF field, non-conducting materials can be brought to a required temperature. There is a tendency for the molecules of the materials to vibrate in sympathy with the applied field, resulting in molecular friction that appears as heat. The extent of vibration of the molecules is related to the loss factor (F) of the material (see below), and the higher the loss factor the greater the rise in temperature. 

Because the radius of a nonspherical molecule cannot be defined precisely, molecular friction coefficients and diffusion coefficients are often related to the Stokes radius (or Stokes diameter). This is defined as the radius (or diameter) of a sphere having / and D values identical to those of the molecule under consideration. 

The mobility, or rate of migration, of a molecule increases with increased applied voltage and increased net charge on the molecule. Conversely, the mobility of a molecule decreases with increased molecular friction, or resistance to flow through the viscous medium, caused by molecular size and shape. Total actual movement of the molecules increases with increased time, since mobility is defined as the rate of migration. 

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