Chemical correlators

Along with the traditional manner of the description of the chemical structure of linear copolymers by means of the hierarchy of probabilities P Uk of sequences of units Uk(k = 1,2.), there is one more mode of the description of this structure. It is based on the consideration of the hierarchy of chemical correlation functions (so-called chemical correlators) (Kuchanov, 1978, 2000). The simplest among them, Yaj3(fc), has the meaning of probability to find two randomly chosen monomer units of types a and j3 divided along a macromolecule by any sequence Uk consisting of k units. This two-point correlator is of the utmost importance because its generating function enters into the expression for spinodal (Kuchanov, 

where the spatially homogeneous state of a polymer liquid becomes absolutely unstable. An arbitrary representer of the hierarchy is the n-point chemical correlator YQ ...o2(/ci,. which equals the probabil- 

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The structures of 129 and 131 are determined by X-ray single crystallographic analyses (2001H1237). Structures of both 128 and 130 are confirmed by chemical correlations to 129 by the reaction with AcaO and pyridine. 

The power of the new spectrometer to reveal configurations of difficult cyclitols or sugars was first tested with mt/o-inositol (2), using deuterium oxide as solvent. At 60 or 100 MHz. the one equatorial and five axial protons appear to have different chemical shifts as shown by Lemieux in 1956 with a 40 MHz. instrument (14,15). However, since the five-proton axial signal could not be resolved, one could probably not have assigned the configuration 2 (which was already known from laborious chemical correlations extending over many years.)... 

The absolute (25,1 i ) configuration of these products was established by chemical correlation and X-ray crystal structure analysis of a prehydrolysis adduct30. 

The addition of (Z)-3-(alkylamino)-2-butenoic acid esters to nitroalkenes derived from open-chain sugars gave a 50 50 mixture of diastereomeric products 32. The reaction of chiral 2-sub-stituted l-(2-nitroethenyl)pyrrolidines with zinc enolates of 3-substituted tetrahydro-2//-pyran-2-oncs in 1,2-dimethoxyethane at — 78 °C afforded the corresponding 3,3-disubstituted products in 82-96% ee via an addition-elimination process33. The stereochemical course of the reaction was determined by chemical correlation of (S)-( )-3-ethyltetrahydro-3-(2-ni-troethenyl)-2//-pyran-2-one with ( + )-quebrachamine. 

Qualitatively, at least, there is a unifying theme and chemical correlation to be found in these series. Namely, values decrease with increasing reducing power of the ligands and/or increasing oxidizing power of the metal ions. These two statements can be joined to yield the simple result ... 

During the course of the development of our group s alkylation/reductive decyanation strategy, a very reliable method for distinguishing between syn-and anfz-l,3-diols was discovered [17,18]. The acetonide methyl groups reliably display diagnostic C-NMR chemical shifts, allowing for stereochemistry to be determined simply by inspection (Fig. 1). Evans later extended the C-NMR chemical correlation to polypropionate chains [19,20]. 

One more quantitative way to characterize the chemical structure of copolymers is based on the consideration of chemical correlation functions (correlators) [2]. The simplest of these, Ya k), describes the joint probability of finding two randomly chosen monomeric units divided along the macromolecule by an arbitrary sequence Uk ... 

The correlator (6) is of the utmost importance because its generating function enters into an expression which describes the angular dependence of intensity of scattering of light or neutrons [3]. It is natural to extend expression (6) for the two-point chemical correlation function by introducing the w-point correlator ya1... (kl...,kn l) which equals the joint probability of finding in a macromolecule n monomeric units Maj.Ma> divided by (n-1) arbitrary sequences... 

As active substances are separated and purified they are characterized by a combination of spectroscopic analyses and chemical correlations. Particularly useful spectroscopic analysis techniques are nuclear magnetic resonance (proton and carbon), mass spectrometry and Infra-red and ultraviolet spectrophotometry. 

Basic hydrolysis of 6 afforded alcohol 19 and methyl veratrate. The H-NMR spectrum of 19 (Table II) revealed the presence of one methylenedioxy, one N-methyl, and two methoxyl groups. The mass spectrum (Table IV) exhibited the most abundant and significant ion peak at m/z 229 indicative of metaphanine-type cleavage. Treatment of an aqueous THF solution of stephavanine (18) with excess sodium hydride and methyl iodide gave N.O-dimethylstephine, a compound identical to alcohol 19. Thus, the structure of the new alkaloid 6 was established by chemical correlation with stephavanine (79). 

Finally, the structure of oxostephasunoline (4) was confirmed by the following chemical correlation with several known hasubanan alkaloids. Heating the new alkaloid 4 in an ethanolic hydroxide solution gave 16-oxoprometaphanine (33), which on treatment with dilute hydrochloric acid yielded 16-oxometaphanine (33). Thus structure 4 was proposed for oxostephasunoline (4). As stated in Section I, the hasubanan alkaloids carrying a... 

Chemical correlation configuration of chiral molecules were related to each other through reactions of known stereochemistry. 

Glyceraldehyde the standard compound for chemical correlation of configuration. 

The structures and relative stereochemistry of epi-eudesmanes 25-27 from Axinella cannabina were formulated from 2D NMR and chemical correlation experiments [36]. The 500 MHz HNMR spectrum of 1 l-formamido-7/ H-eudesm-5-ene (27) measured in CDC13 showed a 2 3 cis.trans ratio of the -NHCHO group (cis 3 8.06 d, J = 2 Hz trans 5 8.20 d, J — 12 Hz). Isothiocyanate 26 was one of several sesquiterpenes reported from Acanthella pulcherrima [20]. 

Murthy MS Induction of gene conversion in diploid yeast by chemicals Correlation with mutagenic action and its relevance in geno-toxicity screening. Mutat Res 1979 64 1-17. 

The expression for the two-point chemical correlator (Eq. 5) for a Markovian copolymer looks as follows... 

Chemical correlations in chains of a random copolymer are entirely absent, as can be seen from formula (Eq. 11) at s = 1, while the distribution (Eq. 4) of blocks for lengths looks like... 

The partition function (Eq. 26) may be regarded as a functional of external field H = H(r]),..., H(rl), which can be determined from the self-consistence condition [30]. Of utmost importance in finding the chemical correlators... 

Eigenvalues of the operator Qr are real while the largest of them, Af, equals unity by definition. As a result, in the limit n-> oo all items in the sum (Eq. 38), excluding the first one, Q Q f = Xr/Xfh will vanish. In this case, chemical correlators will decay exponentially along the chain on the scale n 1/ In AAt values n < n the law of the decay of these correlators differs, however, from the exponential one even for binary copolymers. This obviously testifies to non-Markovian statistics of the sequence distribution in molecules (see expression Eq. 11). The closer is to unity, the greater are the values of n. The situation when n 1 corresponds to proteinlike copolymers. 

As to quantities 0 (Eq. 39), they are equal to Xa8Vfl, where 8Vfl is the Kro-necker symbol. In view of this, only the first item in the sum (Eq. 38), XaXp, is distinct from zero. This corresponds to the absence of chemical correlations along the macromolecule on all scales. In other words, the distribution of units for such copolymers is Bernoullian [2]. 

It is easy to derive expressions for other chemical correlators as well. For instance, the three-point correlator (Eq. 7) can be determined by the formula... 

Essentially, expressions (Eq. 34) have a physical sense only for values of quantities ev which are appreciably less than unity when the eigenvalues of operators Qdiff and Q coincide. The number of such values of sv will be the larger, the longer is the macromolecule. Hence, in the asymptotic limit l oo, expression (Eq. 38) for the two-point chemical correlator is reduced to the following form... 

Calculating other chemical correlators along with 6>°° = Xa and 0°v (Eq. 46), one should additionally know quantities at nonzero values of both super-... 

The substitution of expressions (Eqs. 46 and 47) and into formulas (Eqs. 42 and 43) permits finding the generating function of two- and three-point chemical correlators. Extension of these results to an arbitrary m-point correlator is obvious. 

In order to analyze the rate of the decay of chemical correlations in macromolecules of proteinlike copolymers, it is necessary to calculate the dependence on n of the irreducible correlator o>ap(n) = Yap(n) - XaXp where the reducible correlator Yap(n) is obtained by formula (Eq. 45). Correlator coap(n) is calculated as the sum of series (Eq. 45), each item of which is the product of two cofactors. The first of them is controlled just by the number of monomeric units l in a globule, as well as by their volume fraction [Pg.160]

Among all correlation lengths entering in expression (Eq. 45) centrally important is the largest one, n = e l = because just on scale n n the chemical correlations in macromolecules of the proteinlike heteropolymers decay. On this scale, the chemical structure of such heteropolymers resembles that exhibited by the Markovian copolymers (see Fig. 3). The only distinction is that for the former the quantity n rises with the length l of a macro-... 

The potentiality of this algorithm is easy to exemplify by the derivation of the expression (Eq. 38) for the two-point chemical correlator (Eq. 5) of proteinlike copolymers. For the macromolecules with labeled units such a correlator can be obtained proceeding from apparent formula... 

Exploiting the Markovian property of random process. Rib, it is possible to derive in a standard way the expression for an arbitrary chemical correlator. In particular, for the three-point correlator the expression... 

The simplification, which enables reducing expression (Eq. 42) into (Eq. 58) remains in force in considering the generating function of the arbitrary chemical correlator. This means that in order to use expression (Eq. 54) for the calculation of the dependence of the vertices of the Landau free energy expansion on wave vectors at region Qs <[Pg.164]

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