Molecular expansion

Equation (10) directs attention to a number of important characteristics of the molecular expansion factor a. In the first place, it is predicted to increase slowly with molecular weight (assuming t/ i(1 — 0/T) >0) and without limit even when the molecular weight becomes very large. Thus, the root-mean-square end-to-end distance of the molecule should increase more rapidly than in proportion to the square root of the molecular weight. This follows from the theory of random chain configuration according to which the unperturbed root-mean-square end- o-end distance is proportional to (Chap. X), whereas /r = ay/rl. 

The reference state dimensions unperturbed dimensions, because of the unknown influence of the presence of crosslinks, possibly specific diluent effects, and perhaps at high swelling even an excluded volume effect. We have pointed out that (r2)0 may depend on the concentration of the diluent. Therefore the reference state is in general not a constant. We have also pointed out that, if (r2)0 contains a molecular expansion term due to an excluded volume effect, the use of the Flory-Huggins free enthalpy of dilution is no longer adequate. A difference between the % parameter in a network and the X parameter of the same polymer material but then in solution, may occur because the presence of crosslinks may modify %. 

In spite of this, Rijke assumes that the Flory-Huggins expression for AGdil is sufficiently adequate and then finds a molecular expansion factor, a from ... 

In GPC, the product [77] M, (or the hydrodynamic radius Re) has been widely accepted as a universal calibration parameter. In the Ptitsyn-Eizner modification of the Flory-Fox equation the quantity 4>, which relates the dimensional parameters to the above product, is taken as a variable. The value of < depends upon molecular expansion in solution as represented by a function f(e). Because of this dependence polymeric species having the same [77] M value cannot have the same statistical dimensions (radius of gyration or end-to-end distance) unless they have the same e value. Thus, if [77] M is a universal calibration parameter, the statistical parameters cannot be used as such. A method is presented for obtaining the Mw/Mn ratio from GPC data even though universal calibration is used. 

The parameter (e) is the exponential dependence of a2 on M where a is the molecular-expansion coefficient. From the value of 2.86 X 1023 found by Ptitsyn and Eizner for 0, it follows that 0 = 0.875. 

B4++ He reaction. This collisional system has been investigated theoretically within the framework of the semiclassical close-coupling formalism using different model potential approaches [2,3] which lead to a discrepancy of about a factor 5 for the double capture cross section values. We have thus performed an alternative study of this system by means of a full molecular expansion method, focusing our attention on the double electron capture process. 

Molecular expansion variational method Korobov [7] developed a variational method using the molecular-type basis functions involving excited... 

The molecular expansion travels parallel to the microwave cavity axis and, as a result, the observed transitions are split into Doppler doublets at sufficient resolution. Typical linewidths are 10 kHz and depend on the observation time, that is, the time required for the beam to travel from the nozzle to the opposite mirror. This in turn depends on the mirror separation and the backing gas (typically He, Ne, or Ar) used. 

Figure 2 Spectrum of the J = 8-7 rotational transition of I32xe65cu35ci xiig complicated hyperfine structure arises from nuclear quadrupole interactions of Cu (7cu = 3/2) and Cl (Id = 3/2). All transitions are split into Doppler doublets as a result of the molecular expansion traveling parallel to the microwave cavity axis. For clarity of the picture, the quantum number assignments of only a few hyperfine components are given as F -F". The...

The acid transformation of serum albumin has been studied further with the solvent-perturbation technique (Section VI,G ) by Leonard and Foster (1961), and by Herskovits and Laskowski (1962). The results of these studies support the idea that the tyrosyl groups of serum albumin do become progressively more exposed to solvent, both in the N-F transformation and in the molecular expansion at slightly lower pH. However, it is not yet possible to make unique assignments for the causes of the spectral perturbations observed by Williams and Foster (1959). 

Problem 3.12 Deduce from Eq. (3.132) that the molecular expansion factor a should increase with increase in temperature in a poor solvent, decrease with... 

Thus there will be neither a molecular expansion nor a molecular contraction. Accordingly, AUj = AHj. 

As an example of the first technique, let us consider the case of a polyamide containing photoresponsive azobenzene groups on its main chain (14). The distance between the two para-positions is 9.0 A in trans-azobenzene, and only 5.5 A in the cis-isomer. The cis-trans photoisomerization of these groups is reflected directly by a molecular expansion of the... 

Figure 2 Spectrum of the 7 = 8-7 rotational transition of Xe Cu Cl. The compUcated hyperfine structure arises from nuclear quadrupole interactions of Cu (7cu = 3/2) and C1 (7qi = 3/2). All transitions are spUt into Doppler doublets as a result of the molecular expansion traveling parallel to the microwave cavity axis. For clarity of the picture, the quantum number assignments of only a few hyperfine components are given as Fj -F/, F -F". The angular momentum coupling scheme Fi = Icu + J F = Fi + Iq was used. The compound was produced using laser ablation of a copper rod in a molecular expansion of a mixture of 0.1% CI2, 15% Xe, and 85% Ar. The particular isotopomer was measured in its natural abundance of 6.3%. This spectmm was recorded using 15 000 averaging cycles with a total accumulation time of about 3.5 h...

The term constitoselectivity has been proposed to denote selectivity controlled by molecular size and molecular expanse cf. Weber, E. Csoregh, I. Stensland, B. Czugler, M., /. Am. Chem. Soc., 1984,106, 3297. 

From Equation 12.71, the intrinsic viscosity depends on the molecular weight as a result of the factor and also through the dependence of the expansion factor on molecular weight. By choosing a theta-solvent or 0 temperature, the influence of the molecular expansion due to intramolecular interactions can be eliminated. Under these conditions, a = 1, and the intrinsic viscosity depends only on the molecular weight. Thus Equation 12.71 is reduced to ... 

Serum albumin exists in a compact form between pH 4.3 and 10.5 but undergoes conformational expansions below pH 4.3 and above pH 10.5 (Tanford et al., 955a,b Yang and Foster, 1954 Bro et al., 1955 Weber, 1952). Conformational transitions not accompanied by molecular expansion also occur, nhmely the N-F transition between pH 4.8 and 3.9 and the neutral transition, N-B, observed between pH 7 and 9 (Leonard etal., 1963). 

The mechanism described above is consistent with essentially all of the existing experimental evidence which we have evaluated. Evidence for the molecular expansion on which this theory is based is summarized in [4]. Furthermore, the existence of high strain rates in shear flows was shown by water jet experiments [10]. Fluid particle elongations of sufficient magnitude are indeed apparent in near-wall flow visualization [11]. The assumption that polymers affect the small... 

Since molecular expansion, a, depends (10) on the number of charged sites on the molecule, CS, and the number of backbone atoms, B... 

Addition of a nonbound salt (such as NaCl) to the anionic surfactant system reduces the molecular expansion of the polymer because the added counterions (i.e., Na+) screen the repulsions between the bound surfactant anions. 

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