The Empty Polymer

The polymer consists of two subunits, each of which can attain one of the two states, denoted L and //, having energies and Eh, respectively. In addition, we have intersubunits interactions, which we denote by Ell, Elh = Ehl, and Ehh, depending on the state of the two subunits. Note that in general Elh could be different from Ehl, Fig. 3.8. But for simplicity we assume that Elh = Ehl - Denote 

FIGURE 3.8. Two subunits with symmetrical (lower) and unsymmetrical (upper) Elh Ehl Ehh interactions. 

We first examine the equilibrium properties of this system in the absence of ligands— i.e., the empty polymer. The PF of a single polymer is 

Note that this is actually the canonical partition function for a single polymer. We denote it by ( (0) to stress that this is the limit of the grand PF of a single polymer obtained for A - 0 (see subsection 3.3.3). 

Formally this model can be viewed as an extension of the model treated in section 3.2, but instead of two states, we have four states, with the three energy levels 2El + 

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The fluorescence of the DVMB-Eu complex within the MIP is significantly altered in the presence of PMP. The sharp 610 nm peak, present in the spectrum of the original polymer-bound DVMB-Eu -PMP complex and absent in the spectrum of the empty polymer, is restored upon exposure of the polymer to 1 M NaOH solutions containing PMP. While a benchtop model of the sensor was more... 

S-G photo-biodegradable polyethylene is now being used in a different way to reduce the pollution of water courses by fertilisers. By encapsulating the fertiliser in porous photo-biodegradable capsules fertiliser release times can be achieved from 40 days to one year. Nitrogenous fertiliser based on this principle are manufactured by Chisso-Asahi Fertilizer Company of Japan and scientific studies by Kawai of Okayama University have shown (personal communication) that the empty polymer capsules biodegrade rapidly in soil. 

Two limiting cases can be obtained immediately from (3.2.10) and (3.2.11). For A->0, the polymers will be empty and x and Xh reduce to the distribution of the empty polymers (3.2.2). The other extreme case is A oo here, the polymers are fully occupied and the corresponding mole fractions are... 

Note that the averages in (3.2.26) are taken with respect to the distribution (3.2.13) of the empty polymer. These probabilities depend on A. We examine two limiting cases For A 0, we find... 

From now on we restrict ourselves to the limit A = 0 hence (3.2.26) still applies with the reinterpretation of the averages as in the empty polymer (see Appendix I). 

The average in (3.2.34) is taken with the distribution of the two states L and H of the empty polymer, given in Eq. (3.2.2). Here we introduce the subscript (0, 0) to stress the condition that both sites are empty to distinguish this average from the conditional average defined below. 

In the first form of the rhs of (3.4.24), the two average quantities are taken with respect to the probability distribution in the empty polymer. More specifically,... 

Figure 3.17 shows representations of all the possible states of the hemoglobin molecule. There are sixteen states of the empty polymer. A circle represents a subunit in the L conformation and a square, a subunit in the H conformation. There are four states for which one subunit is H and three are Ls. There are six states for which two subunits are Ls and two are Hs, and so on. Only one of each of these is presented in the first row. 

This is the canonical PF of an empty polymer with a specific set of subunit conformations. For instance, the upper subunit is in state a =L,H) the left-hand subunit in state P =L,H), the right-hand subunit in the state /(=L,/Z), and the front subunit (in the tetrahedron of Fig. 3.17) in the state = L, H). Altogether, there are sixteen terms for the empty polymer. Thus... 

Note that S without a subscript is the direct correlation as defined in Chapter 3 on the other hand, S denotes a polymer with n ligands. Thus So is the empty polymer which is also denoted by P, Si the singly occupied polymer, etc.) In this particular model, the corresponding work is simply the direct ligand-ligand interaction energy U12. 

Fibers of the conducting polymer polypvrrole are woven into radar camouflage cloth. Because it absorbs microwaves, rather than reflecting them back to their source, the cloth appears to be a patch of empty space on radar. 

The empty state is the LL state on the top left comer of Fig. 4.18. The binding of a ligand on any of the subunits will shift its conformation completely from L to H without affecting the conformation of the second subunit. Binding of the two ligands will shift the entire polymer to the state HH. Thus, in each binding process there is a total change of conformation of one subunit hence the term sequential model. 

Experimental error entered the data, of course, through the manual measurement of the viscosities of the four very dilute fractions. Another error in the viscosities was introduced by contamination of each fraction by some of the fraction preceding it. Not all of the liquid in the measuring syphon could be removed as the syphon emptied thus a small portion of the fraction was retained and added to the incoming fraction. Furthermore, the previous procedure required exact weights in each fraction, whereas now only relative weights are necessary. The relationship developed here can be extended to polymers other than cellulose. To do this, the values of K and a have to be determined for the particular polymer, dissolved in the desired GPC solvent which was used to establish the calibration curve. 

P-atom due to an inductive effect, hence destabilizing the HOMO. The LUMO of the chromophore Pd(CNR)2(P) is stabilized, going from a saturated chain P(CI I2) P to P—C=C—P, via coupling of the empty d orbitals located onto P and the empty ir-orbital located onto ethynyl fragment. The emission lifetimes in these polymers were surprisingly short (a few ns). Nevertheless, the quantum yields obtained are larger than expected for such short lifetimes (Table 5). This phenomenon remains unexplained. 

If dendrimers are introduced on stiff backbone polymers cylindrical molecules are created and an empty inner volume becomes available between the stiff backbone and the outer dendrimer shield. Furthermore the peripheral groups of the dendrimer can be manipulated to control the solubility characteristics of the resulting polymers. 

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