Chain average

For relatively long chains, average value of interaction energies of solvent molecules surrounding the chain is independent of the chain length. One more additional component of free energy of chain formation occurs because the distance between solvent molecules is defined... 

The glucose tetra-acetate was used as an initiator and results in each araban chain (average degree of polymerisation 23.6) terminating in a glucosyl reducing unit. 

Square root of the mean-square end-to-end distance of a linear macromolecular chain averaged over all conformations of the chain. For a freely jointed chain consisting of N segments each of length L, r Y =. ... 

Here D, D , and Dr are, respectively, the longitudinal, transverse, and rotational diffusion coefficients of the chain averaged over the internal degree of freedom, h an external field, and v and angular velocity of the chain induced by a flow field in the solution. Furthermore, I is the unit tensor and 91 is the rotational operator defined by... 

Methods are presented for calculating mean-square dipole moments, , of polypeptide chains, averaged over all configurations of the chain skeleton. They are applicable to chains of any number (x+ U of residues, the residues being In any specified sequence. Dipole moments of glycine peptides are calculated and compared with experimental determinations. The effects of stereosequence on the dipole moment are well reproduced by the calculations. Ip is taken to be 380 pm. 

The alcohol sulfate of choice today ranges between a carbon chain average of to Cj. This alcohol sulfate can be found in some laundry produces at 3 to 5 percent of the total formulation. 

A more detailed analysis of the NMR signal from elastomer samples, addresses finer details such as the chemical structure of chain segments. In general a hierarchy of dipolar interaction between protons exists instead of a single chain-averaged dipolar interaction [34, 35]. For example, in cis-l,4-poly(isoprene) these different dipolar interactions can... 

Alkylates made specifically as feedstocks for synthetic petroleum sulphonates are typically long chain (average C chain > 16) and may use propylene oligomers which result in branched chains. Naphthalene products use the same propylene technology but tend to shorter chains (di-isopropylnaphthalene, di-nonylnaphthalene). 

The numbers are averages over all atoms for a particular class, except that proline residues were excluded for the side-chain averages. Numbers in parentheses are standard deviations. 

A polymeric HOBt (132), which is soluble in dichloromethane, DMF or water and bears a poly (ethylene glycol) (PEG) chain (average molecular wt 4000), has been prepared from PEG-NH2 and l-hydroxybenzotriazole-5-carboxylic acid using DCC as coupling agent [135]. The corresponding active esters were prepared by reaction with an excess of carboxylic acid anhydrides and used for the synthesis of the model tetrapeptide Cbz-Leu-Ala-Gly-Val-OtBu [136]. 

For a network generated from stoichiometric quantities of a difunctional polymer and a tetrafunctional cross-linker where cross-linking occurs only at the chain ends the network chain average molecular weight should approximate the prepolymer 1. ... 

Crosslinked polymer showing 5 linked polymer chains (polymer chains average over 100 units between crosslinkers in real EAP)... 

FIGURE 36 The dependences of polymer chain average end-to-end distance ( h j on... 

The current opinion, widely held, is that all biological membranes, including mammalian plasma membranes, have as a structural framework a phospholipid bilayer of which the characteristic feature is a parallel array of hydrocarbon chains, averaging 16 carbon atoms in length. This bilayer has some of the properties of a two-dimensional fluid in which individual lipid molecules can diffuse rapidly in the plane of their own monolayer, but cannot easily pass into the other monolayer. This lipid matrix provides the basic structure of the membrane. Whereas some protein molecules cover part of the membrane, particularly its outer surface, other protein strands penetrate the lipid layer, every here and there, and some of these strands are bunched together to form water-filled tubes or pores (Wallach and Zahler, 1966). These proteins are responsible for most of the membrane s functions, e.g. receiving and transduc-... 

It was determined, that electromagnetic susceptibility s equilibrium elastic coefficient does not depend on temperature (Table 1). It is values and values of weighting coefficient decrease slope oppositional to hardeners molar amounts ratio that can be ejqrlained by growth of intermolecular interaction s level during the increase of crosssite chains average numerical degree of polymerization. 

Here, Mo is the mean molecular weight of the repeat unit of the chain (averaged over the skeletal bonds in the repeat unit) and / is the average bond length per skeletal bonds of the repeat unit. Ks in Eq. (15.9) is expressed in dl.g (g mol wt) /. ... 

The length of the polymer has been reported to vary from three to several hundred units of ADP-ribose 84) and may depend on experimental conditions. Number of chains and chain length can be estimated by isolation and quantification of the products (5 -AMP and iso-ADP-ribose) of the snake venom phosphodiesterase digestion. The number of 5 -AMP molecules represents the number of polymer chains. Average chain length can be estimated utilizing the relationship ... 

Instead of enforcing the incompressibility constraint on each of the microscopic conformations, we thus only require that the single chain averages in the external field obey the constraint. We recall that the 4>a functionals of Wa = (iU + W)/2 and Wb = iU - W)/2 (cf. Eq. 28), thus Eq. 40 implicitly defines a functional U [W. Substituting the saddle point value into the free energy functional (Eq. 11), we obtain an approximate partition function... 

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