Benoit expression

The calculation of the form factor for an ideal uniform star chain was performed by Benoit [60]. The result can be expressed as... 

Calculation of Results from Differential Viscometry and SEC. The familiar relationship first expressed by Mark (25) and Houwink (26) in the 1940 s is central to the concept of universal calibration first suggested by Benoit et al. (27). In this relationship,... 

Accordingto Benoit and Doty [72], the unperturbed 0 of a monodisperse wormlike chain is expressed by... 

These results are now in terms of correlation functions of P2Ct) and, in the field on cases, of P (t), as in linear dielectric and other response theories. The asymmetry given by the last term of the field on expression reveals the interesting possibility of obtaining both P correlations (from the field off response) and P correlations (from the asymmetry). One easily verifies that Benoit s result is obtained for diffusional reorientations, as then = (l/5)exp(-6D t), -(2/15)exp(-6Dt), and PoP2PlPl(t)> = (2/15)exp(-2D t)7 but this form of dynamics is not assumed in the development End effects of joint correlations Eire included in eqs.13 and 14. 

Using the Benoit-Doty expression for 0 of a monodisperse wormlike chain 121), the relationship between q and Z of polymers having a Schulz-Zimm type molecular weight distribution is derived as follows 67 ... 

Experimental Assessment, The most direct experimental assessment of the persistence length may be obtained from the root-mean-square radius of gyration measured by light scattering. The analytical expression for the unperturbed Rq of a. wormlike chain has been given by Benoit and Doty (5) ... 

The molecular weight estimated from equation 23 is a function of the copolymer composition through the refractive index increments. (dn/dc)c=0. By assuming a linear dependence of (dn/dc) with respect to composition, Bushuk and Benoit (74) derived an expression for the weight average molecular weight of copolymers as functions of the refractive index increments... 

Apparent mean square radius of Brownian block copolymers The linear block copolymers are made of different successive subchains a — 1,2,. . . and so on. For the Brownian case, Benoit and Wippler16 obtained an expression of °ka2pp(x) in terms of rather simple contrast parameters. Their result can be recovered as follows. First, let us write (7.3.46) in the form... 

An approximate expression of h(x) for a chain with a critical exponent v can be obtained in a very simple way as was done by Peterlin (1955)31, and also Ptitsyn (1957)32 and Benoit (1957).33 The basic assumptions are that... 

By different techniques, especially by viscosimetry, it can be shown that the higher styrene content of the grafts results from the preferential solvation of PB by styrene. According to Dondos and Benoit (8), the preferential solvation can be expressed by A, which is the excess volume of styrene near or in the polymer coil per gram of PB. Therefore, in the close vicinity of the PB, the concentration of styrene is higher than its concentration far from any macromolecule. 

Benoit, G.G., C.F. Naud, M.A. Simard, and A.L. Astier (1997). Noninterference of cytochrome P4501A2 in the cytotoxicity of tacrine using genetically engineered V79 Chinese hamster cells for stable expression of the human or rat isoform and two human hepatocyte cell lines. Biochem. Pharmacol. 53, 423-427. 

Benoit and Benmouna [18] applied the Omstein-Zemike relation [19], first proposed for simple liquids, to polymer solutions. According to it, Qj(i)jt(2) can be expressed as follows ... 

According to Dondos and Benoit," Read, and Hertz and Strazielle," the dependence of preferential adsorption coefficient X, with molecular weight or with segment density can be expressed empirically as ... 

Benoit and coworkers (15) showed that size exclusion chromatography separates polymer molecules by hydrodynamic volume. The hydrodynamic volume can be expressed as the product of intrinsic viscosity and molecular weight ... 

Following the treatment of Benoit et al (1967) on the properties of rigid rods, it is possible to derive a molecular weight for the xanthan from the expression ... 

Houzelstein, D., Auda-Boucher, G., Cheraud, Y., Rouaaud, T., Blanc, I., Tajbakhsh, S., Buckingham, M.E., Fontaine-Perus, J. and Benoit, R. (1999) The homeobox gene Msxl is expressed in a subset of somites, and in muscle progenitor cells migrating into the forelimb . Development, 126, 2689-701. 

Use of Average Comonomer Composition Parameters Benoit provided a useful alteruative representation of in terms of mass weighted moments of the copolymer composition distribution. Generalizing his method to N comonomers, F. is expressed as ... 

Strazielle and Benoit showed that influenced by whether the PS and or the cyclohexane was deuterated. They estimated a difference in the cohesive energy densities between the deuterated nd undeuterated polystyrenes to be 6h-PS-5d-PS = A8 = 0.038 The X parameter may be approximately expressed as... 

In 1966, Benoit et aL [48] introduced the universal calibration method utilizing the hydrodynamic volume of macromolecul This volume Vj, can be expressed by the theory [49] as the product of the molecular weight M by the intrii ic viscosity [t]] ... 

Benoit. The above equation returns to the usual Debye expression for linear chains if

self-interactions for all arms of the star, scaling theory provides new results which are confirmed by numerical simulations. For recent neutron scattering experiments on stars see ref. 280. 

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