Self chain-length dependence

Xiao, X. D., Hu, J., Chayuch, D. H., and Salmeron, M., Chain Length Dependence of the Frictional Properties of Alkylsilane Molecules Self-Assembled on Mica Studied by Atomic Force Microscopy," Z,angmmr,Vol. 12,1996, pp. 235-240. 

Malinsky MD, Kelly KL, Schatz GC et al (2001) Chain length dependence and sensing capabilities of the localized surface plasmon resonance of silver nanoparticles chemically modified with alkanethiol self-assembled monolayers. J Am Chem Soc 123 1471-1482... 

Fenter P, Eisenberger P and Liang K S 1993 Chain-length dependence of the structures and phases of CH3 (CH2) . 1SH self-assembled on Au(111) Phys. Rev. Lett. 70 2447-50... 

Fig. 9 Chain-length dependence of the self-diffusion coefficients of n-alkanes in silicalite-1 (cf. [65]) at 303 K derived from the FR technique (- -) compared with the results measured by PPG NMR [50] at 298 K (-o-), QENS [51] (-A-) at 300 K and molecular dynamic calculations [52] (-0-) at 300 K...

The diffusion coefficient for the reptation chain shows weaker chain-length dependence than that for the Rouse chain Dr rT ). Both (5.48) and (5.49) imply that the tube makes an additional confinement to the self-diffusion of the polymer chains. Therefore, the long chains diffuse slower, and the diffusion coefficient becomes more sensitive to the chain length. 

Xiao, X., Hu, J., Chatych, D.H., Salmeron, M. Chain length dependence of the frictional properties of alkylsilane molecules self-assembled on mica studied by atomic force microscopy. Langmuir 12, 235-237 (19%)... 

The self-diffusion coefficient, (Equation 5.48), depends on the molecular weight through the chain-length dependence of the hydrodynamic radius R. A common empirical expression for this quantity is... 

The first two quantities allow determination of relaxation times of corresponding objects in the model (bonds and chains) and the last two allow determination of diffusion constants. Chain length dependencies of the self-diffusion constant and of the relaxation times of bonds and chains are presented in Fig. 3. These results show that the dynamic behavior of... 

FIG. 3 Chain length dependencies of (a) self-diffusion constants of chains and (b) relaxation times of bonds and end-to-end vectors in model systems of linear chain melts. 

We present a quantitative study of frictional properties of pure self-assembled monolayers (SAMs) of alkanethiols as a function of chain length and mixed SAMs of dodecanethiol and 11-mercapto-l-undecanol as a function of surface composition on Au (111) using atomic force/friction force microscopy (AFM/FFM). The lateral and normal forces were calibrated in situ using a combined two-slope and added-mass method. Molecular dynamics simulations were also carried out to interpret the chain length dependence of frictional properties of alkanethiols. We then extended the in situ force calibration method to the mixed SAMs and investigated the effects of chemical nature and relative humidity on the frictional properties. Friction coefficients were plotted as a function of surface composition with different relative humidity. Such a plot could serve as a reference in determining surface composition in a nanoscale domain by measuring its friction coefficient. 

G. Fleischer, "The Chain Length Dependence of Self-diffusion in Melts of Polyethylene," Colloid Polvm. Sci.. 265. 89-95 (1987). 

The RRM predictions for the chain length dependences of the self-diffusion coefficient, and of the terminal relaxation time, are... 

At very high molecular weights, when the diffusion coefficient due to flip-flop spin diffusion of the order 10 m /s is getting comparable to the ordinary Brownian self-diffusion coefficient, a flatter chain length dependence of the effective diffusion coefficient is expected [10]. 

Before any chemistry can take place the radical centers of the propagating species must conic into appropriate proximity and it is now generally accepted that the self-reaction of propagating radicals- is a diffusion-controlled process. For this reason there is no single rate constant for termination in radical polymerization. The average rate constant usually quoted is a composite term that depends on the nature of the medium and the chain lengths of the two propagating species. Diffusion mechanisms and other factors that affect the absolute rate constants for termination are discussed in Section 5.2.1.4. 

Figures 8 and 9 show the dependence of the self-diffusion constant and the viscosity of polyethylene melts on molecular weight [47,48]. For small molecular weights the diffusion constant is inversely proportional to the chain length - the number of frictional monomers grows linearly with the molecular weight. This behavior changes into a 1/M2 law with increasing M. The diffusion...

Sikorsky and Romiszowski [172,173] have recently presented a dynamic MC study of a three-arm star chain on a simple cubic lattice. The quadratic displacement of single beads was analyzed in this investigation. It essentially agrees with the predictions of the Rouse theory [21], with an initial t scale, followed by a broad crossover and a subsequent t dependence. The center of masses displacement yields the self-diffusion coefficient, compatible with the Rouse behavior, Eqs. (27) and (36). The time-correlation function of the end-to-end vector follows the expected dependence with chain length in the EV regime without HI consistent with the simulation model, i.e., the relaxation time is proportional to l i+2v The same scaling law is obtained for the correlation of the angle formed by two arms. Therefore, the model seems to reproduce adequately the main features for the dynamics of star chains, as expected from the Rouse theory. A sim-... 

Further information on the dependence of structure of microemulsions formed on the alcohol chain length was obtained from measurement of self diffusion coefficient of all the constitutents using NMR techniques (29-34). For microemulsions consisting of water, hydrocarbon, an anionic surfactant and a short chain alcohol and C ) the self diffusion... 

Thus, in summary, self diffusion measurements by Lindman et a (29-34) have clearly indicated that the structure of microemulsions depends to a large extent on the chain length of the oosurfactant (alcohol), the surfactant and the type of system. With short chain alcohols (hydrophilic domains and the structure is best described by a bicontinuous solution with easily deformable and flexible interfaces. This picture is consistent with the percolative behaviour observed when the conductivity is measured as a function of water volume fraction (see above). With long chain alcohols (> Cg) on the other hand, well defined "cores" may be distinguished with a more pronounced separation into hydrophobic and hydrophilic regions. 

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